ISOTHERMAL RESPONSE OF GEOSYNTHETICS TO DIFFERENT LOADING REGIMES
BlRENDRA MAHASETH
A thesis suhmitted in partial fulfillment for the degree of Master of Engineering
Department of Civil Engineering Bangladesh University of Engineering and Technology Dhaka, Bangladesh
1111111111111111111111111111111111 #96965# ISOTHERMAL RESPONSE OF GEOSYNTHETICS TO DIFFERENT LOADING R£GIMES
by
BIRENDRA MAHASETH
Approved as to style and content by:
-----ft.~"-- Dr. Abdul Jabbar Khan Chairman Assistant Professor (Supervisor) Department ofCE, BOOT, Dhaka
----~--- Dr. Saiful Alam Siddiquee Member Associate Professor Department ofCE, BUET, Dhaka rp1g1_~jLjA~ Dr. Mehedi Ahmed Ansary Member Associate Professor Department ofCE, BUET, Dhaka
June 2002
o DECLARATION
I hereby declare that the research work reported in this thesis has been performed by me and this work has not been submitted elsewhere for any other purposes except for publication.
June 2002 ---~---
Birendra Mahaseth ACKNOWLEDGEMENTS
I wish to express the deepest of my gratitude to Dr. Abdul Jabbar Khan for being fully contributive throughout this work. Without his supportive and friendly nature this thesis would not have come to an end in time. It was his encouragement that kept me working on computer.
In this regard, I would also take the opportunity to express my appreciation to Professor Dr. M. H. Kabir for arousing my interest in the topic of study.
Besides my parents, I am indebted to my wife and son who supported me morally to stay out of home for the study. I would also like to pay my appreciation to my colleagues and seniors for their encouragement and moral support to pursue the study.
I am thankful to all my Nepalese friends in Rashid Hall and Intemation Hostel for their company and help. My due thanks goes to the inmates of Shahid Smrity Hall, especially to Ashish, Tapan and the floor mates who comforted me with the hospitality and their company. Finally I must thank the members of the dining in The Shahid Smrity Hall for providing their services. ABSTRACT
This study is undertaken to show the conservatism inherent in the existing design methods after observing the satisfactory performance of geosynthetic reinforced soil structures (GRSSs) during the 1995 Kobe and 1994 Northridge, California earthquakes, since these structures were designed according to these methods for lesser seismic shocks than what they experienced.
In fact, neither any test data pertaining to, nor any general approach to the understanding of the behaviour of geosynthetics under MSA (multi stage action) was existent. The geosynthetics being elasto-visco-plastic (EVP) in nature, the same geosynthetic is likely to show different load-strain-time responses under various loading regimes at isothermal conditions. The Isochronous Strain Energy (ISE) approach, although capable of pronouncing the behaviour of geosynthetics under different loading regimes, seems quite complex for the practicing engineers. For this reason, a simpler approach to the understanding of the behaviour of geosynthetics under sustained-short-term loading regime has been attempted to show the conservatism of the present design methods.
It is identified that the total strain in an EVP material consists of two components namely 'Recoverable' strain and 'Locked-in' strain and these two strain components may combine in many different ways resulting in a strain envelope for a particular total strain, geosynthetic and loading regime. Identification of the strain components shows the likely behaviour of a geosynthetic under any single-stage and multi-stage loading regimes. To this end, a range of single-stage and multi-stage (sustained-short term) data are analyzed and presented to show the conservatism inherent in the current design codes/methods and the validity of the strain envelope approach in understanding the behaviour of geosynthetics subjected to combined sustained plus short-term seismic loading regime. Eventually, a approach to design GRSSs under this regime is suggested.
11 Contents Acknowledgements
Abstract II Contents iii Notations viii List of Tables xii List of Figures xiii
Chapter 1 INTRODUCTION
1.1 General 1 1.2 Development of Geosynthetic Reinforced Soil Structures 1 1.3 Design Approaches and Computer Programs 2 1.4 Actions and Design input parameters 4 1.4.1 Soil Properties for Single-Stage Actions 4 1.4.2 Soil Properties for Multi.Stage Actions 5 1.4.3 Geosynthetic Properties for Single-Stage Actions 5 1.4.4 Geosynthetic Properties for Multi-Stage Actions 6 1.5 Background of the present study 8 1.6 Objectives of the Present Study 9 1.7 Layout of the Thesis 9
Chapter 2 LITERATURE REVIEW
2.1 General 12
iii 2.2 Components ofGRSSs 12
2.2.1 Reinforced Fill 13
2.2.2 Retained Fill 13
2.2.3 Foundation Soil 14
2.2.4 Facing Units 14
2.2.5 Connections 15
2.2.6 Reinforcements 15
2.2.6.1 Inextensible Reinforcements 16
2.2.6.2 Extensible Reinforcements 17
2.3 Geosynthetics 18
2.3.1 Elasto-Visco-Plastic Nature ofGeosynthetics 18
2.3.2 Rheological and Mathematical Modelling of Geosynthetics Behaviour 21
2.3.2.1 Maxwell Model 22
2.3.2.2 Kelvin or Voigt Model 22
2.3.2.3 Maxwell and Kelvin Model 22
2.3.2.4 Zener (Standard Linear Solid) Model 23
2.3.2.5 Esteve's Method 23
2.3.2.6 Boltzmann Superposition Principle 24
2.4 Strength tests for geosynthetics 24
2.4.1 Constant rate of strain test 25
2.4.2 Sustained load creep test 25
2.4.2.1 Isochronous load-strain curves 26
2.5 Design strength of geosynthetics in GRSSs 27
2.5.1 Reference Strength 27
IV 2.5.I.1 Reference Strength for Single-Stage Actions 27
2.5.1.2 Reference Strength for Multi-Stage Actions 28
2.5.2 Partial Factors and Design Strength 30
2.6 Design approaches for GRSSs 31
2.6.1 Limit Equilibrium Approach 32
2.6.1.1 AASHTO Standard Specifications for Highway Bridges (1997) 33
2.6.1.2 The Deutsches Institut fllr Bautechnik (Dmt) Method (1998) 34
2.6.1.3 HA 68/94 Method (1997) 36
2.6.2 Hybrid Approach 37
2.6.2.1 BS8006 (1995) Method 37
2.6.2.2 Tensar Tie-back Wedge (TBW) Design Method (1998) 42
2.6.3 Limit State Approach 44
2.6.3.1 A Model for Internal Ultimate Limit State Mechanism. 45
2.6.3.2 A Model for Internal Serviceability Limit State Mechanism 46
2.7 Research outputsl Case studies related to Multi-stage actions 47
2.7.1 Sustained plus Cyclic loading 47
2,7.2 Combined Sustained plus Earthquake loading 48
2.7.2.1 Duration of Earthquake 48
2.7.2.2 Available test results 49
2.7.2.3 Case studies 49
Chapter 3 BEHAVIOUR OF MATERIALS UNDER DIFFERENT
LOADING REGIMES 3.1 General 80 3.2 Types of Actions 80
v 3.2.1 Single-stage actions 82
3.2.2 Multi-stage actions 83
3.3 Strain response of materials under Single-stage Action (SSA) 83 3.3.1 Perfectly Elastic material 84 3.3.2 Perfectly plastic material 85 3.3.3 Elasto-plastic material 85 3.3.4 Elasto-visco-plastic material 86
3.4 Development of &R - EL plot and strain envelope for elasto-visco-plastic
(EVP) material 88
3.5 ER - EL plots for EVP material under different single-stage action (SSA) 89
3.6 Strain response of materials under multi-stage actions (MSA) 90
3.6.1 Perfectly elastic material 91
3.6.2 Perfectly plastic material 91
3.6.3 Elasto-plastic material 92
3.6.4 Elasto-visco-plastic (EVP) material 93
3.7 ER - EL plots for EVP materials subjected to different Multi-stage actions (MSA) 94
Chapter 4 ISOTHERMAL REBA VIOUR OF SOME GEOSYNTHETICS
SUBJECTED TO SINGLE STAGE LOADING 4.1 General Il2 4.2 Test set up and Procedure 112 4.2.1 Single-stage action (SSA) tests 113 4.2.1.1 Constant rate of strain (CRS) test
",/ 113 4.2.1.2 Long-term sustained CREEP test 113
VI 4.3 Extrapolation of CREEP test Data 1I4
4.4 Isochronous load-strain curves and strain envelopes lIS
4.5 Discussion on test results 1I6
4.6 Summary 1I7
Chapter 5 ISOTHERMAL BEHAVIOUR OF SOME GEOSYNTHETICS
SUBJECTED TO MULTI STAGE LOADING
5.1 General 133
5.2 Test set up and Procedure 133
5.2.1 Multi-stage action (MSA) tests 134
5.2.2.1 Combined sustained-short-term loading test 135
5.3 Discussion on test results 137
5.4 Interpretation ofMSA (sustained-short term) test results on ER - EL plot 139
5.5 Summary 141
5.6 Suggested approach of designing GRSS for MSA 142
Chapter 6 DISCUSSION AND CONCLUSIONS
6.1 Discussion 164 6.2 Conclusions 168
RECOMMENDATIONS FOR FUTURE RESEARCH 170 REFERENCES 171
VII NOTATIONS
Y Calculated Factor of Safety ).! Coefficient of Friction between Soil and the Reinforcements cr'vi Total Vertical Stress in the ith Layer of Reinforcement Yl Density of the Reinforced Fill I3r Slope Angle ofthe Face of the Structure Ym Partial Factor Vertical Stress on Reinforcing Element [4>~] True Angle of Friction [4>'cv] Constant Volume Angle of Friction [4>'m] Mobilised Angle of Friction [4>'p] Peak Angle of Friction [Ed Limiting Strain [Ed 'Locked-in' Strain
[ Edes,eq] Factored Limiting Strain [Ep] Performance Limit Strain
[ &pel Actual Post-Construction Strain [M's] Additional Short Term Load [ER] Recoverable Strain
[Esoo] Strain in the Soil, Sufficient to Mobilise the Large Strain Constant Volume Angle of Friction [4>'ev] [Et] Lateral Tensile Strain [Pal Earth Pressure on the Wall [PRed Reference Strength
[Ps] Sustained Load [P,] Additional Transient (traffic) Loading [t] Time [T] Temperature [to] Equivalent Instantaneous Loading Time [T Ipcs] Force Required in Order to Mobilise 1% Post-Construction Strain
V11l [Tall Long-tenn Strength of the Reinforcing Element [tep1 Construction Period [Tdl Design Strength of the Reinforcing Elements for Single-Stage Actions [1&1 Design Lifetime [tEDd Time at the End of Design Life [T81 Glass Transition Temperature [tRLl Reinforcement Loading Period [tsoo] Time of Switch-on of Gravity c' Effective Cohesion of Soil CAD Computer Aided Design CRS Constant Rate of Strain EDL End of Design Life EOC End of Construction
fm Partial Factor
fml Partial Factor Related to the Intrinsic Properties of the Material
fml Partial Factor to Allow for Material Manufacturing Variations and Confidence in the Extrapolated Strength fmll Partial Factor Related to the Consistency of the Manufacturer fmlll Partial Factor Related to whether or not a Standard for Specification, Manufacture and Control Testing of the Reinforcement Exist fml12 Partial Factor for whether or not Standards for the Dimensions and Tolerances Exist fml2 Partial Factor Related to the Extrapolation of Test Data Dealing with Base Strength fml21 Partial Factor for the Assessment of Available Data fm122 Partial Factor for Extrapolation of the Statistical Envelope over the Expected Service Life of the Reinforcement fm2 Partial Factor Concerned with the Effects of Construction and Environmental Effects fm21 Partial Factor for the Effects of Construction Activities fm21 Partial Factor which Deals with the installation Damage of the Reinforcements fm211 Partial Factor Related to Short Tenn Effects of Damage Prior to and During Installation fm212 Partial Factor for the Long Tenn Effects of the Short Tenn Damage
ix fm22 Partial Factor for the Effects of Environmental Degradation
fm22 Partial Factor which Deals with the Environmental Effects of the Reinforcements Overall Factor of Safety
fm, Partial Factor for c'r
fm, Partial Factor for Material
fn Partial Factor for Economic Ramifications of Failure
fp Partial Factor against Pullout f, Factor of Safety against Base Sliding GRSSs Geosynthetic Reinforced Soil Structures H Height of the Structure above Ground Level
hj Depth of Reinforcement of jib Layer ISE Isochronous Strain Energy Ko Coefficient of Earth Pressure at Rest
Ka Coefficient of Active Pressure L Effective Base Width for Sliding Anchorage Length beyond Failure Plane OBF Out of Balance Forces
PMu1ti stage Design Strength for sustained plus seismic loading Ultimate Bearing Capacity of the Foundation RF Reduction Factor RFCR Reduction Factor for Long Term Rupture Strength RFD Reduction Factor to Prevent Rupture of the Reinforcement Due to Chemical and Biological Degradation RFID Reduction Factor for Damage from Placing and Compaction SLS Serviceability Limit States Vertical Spacing of Reinforcing Element T Total Tensile Force to be Resisted By Reinforcing Elements Unfactored Reinforcement Base Strength Extrapolated Creep Strength (at 10% Limiting Strain) of the Reinforcement at Specified Design Life Time and Operational Temperature Ti Maximum Tensile Force in the ilb Layer Tmax Maximum Disturbing Force
x Tult Short Term CRS Rupture Strength of the Reinforcing Element per metre Width ULS Ultimate Limit States
Ws Surcharge Load Reference Strength Ex-works strength of geosynthetics Partial Factors Factors those take account of any changes of geosynthetics due to construction damage, environmental degradation and/or any uncertainties involved in the manufacturing and extrapolation of test data Design
Strength Reference Strength divided by the Partial Factors
XI
•
• •• LIST OF TABLES
Table 2.1 Damaged retaining walls for railways and roads, after Tatsuoka et al(1995)
Table 2. 2 Damaged embankments for railways and roads, after Tatsuoka et a1(1995)
Table 2.3 Factors of Safety in different design methods, after Khan( 1999)
XII LIST OF FIGURES
Figure 2.1 Some examples of reinforced soil walls, (after Bonaparte et aI, 1985) Figure 2.2 Reinforced slopes, (after Bonaparte et aI, 1985) Figure 2.3 Different sections of reinforced soil structures, (after Pradhan, 1996) Figure 2.4 Factors relevant to the nature of the facings, (after McGown et aI, 1993) Figure 2.5 Forms of geotextiles and related products Figure 2.6 Load transfer between soil and grid reinforcements Figure 2.7 Classification of reinforcing elements after, McGown et al (1978) Figure 2.8 Idealised constant load creep curve imder isothermal conditions, after Khan (1999) Figure 2.9 Elasto-visco-plastic behaviour of geosynthetics Figure 2.10 Rheological model Figure 2, II Various Mathematical Models Figure 2.12 Various Mathematical models Figure 2.13( a) Scheme used in constant rate of strain test Figure 2. 13(b) Load vs strain plot from constant rate of strain test Figure 2.14(a) Scheme of test apparatus used in sustained load creep tests Figure 2.14(b) Strain verses time plots from sustained load creep tests Figure 2.15 Series of loading verses time for deriving Isochronous curves Figure 2.16 Deriving Isochronous load-strain curves for elasto-visco-plastic geosynthetics
Figure 2.17 Definitions of reference strength for geosynthetic reinforcements, after Khan (1999).
Figure 2.18 Assessment of SLS base strength TCS, (after BS8006, 1995) Figure 2.19 The Ka x Sv check
Figure 2.20 The distribution of force in the wedge check Figure 2.21 The strain distribution in the wedge check Figure 2.22 Model ULS mechanism, (after McGown et aI, 1998) Figure 2.23 Model SLS mechanism (after McGown et aI, 1998)
XlII Figure 3.1 Examples of single stage actions Figure 3.2 Examples of multi stage actions Figure 3.3 Strain response of perfectly elastic material under SSA Figure 3.4 Strain response of perfectly plastic material under SSA Figure 3.5 Strain response of elasto-plastic materials to SSA Figure 3.6 Strain response of elasto-visco-plastic material to SSA Figure 3.7 Series of sustained loadings verses time for deriving strain envelope for EVP material
Figure 3.8 Combinations of strain components for different sustained loadings to EVP material
Figure 3.9 Total strain eT and its components for EVP material
Figure 3.10 Plot ofER - ELand strain envelope for EVP material Figure 3.11 ER- ELplot for EVP material under different single stage actions
Figure 3.12 Strain response ofEVP materials using Boltzmann's superposition principle Figure 3.13 Strain response of perfectly elastic material under multi stage actions (MSA) Figure 3.14 Strain response of perfectly plastic material under multi stage actions (MSA) Figure 3.15 Strain response of elasto-plastic material under MSA Figure 3.16 Strain response ofEVP material under MSA Figure 3.17 ER- ELplot for EVP materials under different MSA FIGURE 4.1 Total strain vs Time plot from creep test for SS2 at 20°C FIGURE 4.2 Total strain vs time plot from creep test for SR80 at 20°C Figure 4.3 Curve fitting into total strain-time plots Figure 4.4 Deriving the coefficient A for extrapolation Figure 4.5 Deriving the coefficient B for extrapolation FIGURE 4.6 Load vs Total strain plot from creep test for SS2 at 20°C FIGURE 4.7 Load vs Total strain plot from creep test for SR80 at 20°C FIGURE 4.8 Load vs Recoverable strain plot from unloading test for SS2 at 20°C Figure 4.9 Load-Recoverable strain plots for SR80 at 20°C FIGURE 4.10 Load - Locked in strain plot from creep test for SS2 at 20°C
FIGURE 4.II-Load - Locked in strain plot from creep test for SR80 at 20°C J
XIV Figure 4.12 Total strain and it's components vs Time plot at 20ce Figure 4.13 Total strain and it's components vs Time plot at 20ce Figure 4.14 Total strain and it's components vs Time plot at 20ce Figure 4.15 Strain envelopes at different strain levels for SS2 and SR80 geogrids at 20ce Figure 5.1 Loading schemes used for combined sustained-short-term loading tests, after Khan (1999)
Figure 5.2 Effective durations for soil (A) and rock (0) sites as a function of distance, after Kupec (2000)
Figure 5.3 Effective durations verses Moment Magnitude at distances ofless than lOkm from epicenter, after Kupec (2000) Figure 5.4 Dimensions of the uniaxial geogrid B specimen, after Khan (1999) Figure 5.5 Scheme of test apparatus used in combined sustained-short term loading tests, after Khan (1999) Figure 5.6 Various stages in combined sustained-short term loading tests, Khan (1999) Figure 5.7 Guide mechanism for unloading, after Khan (1999) Figure 5.8(a) Results of combined sustained-short term loading tests (Time in hours scale), after Khan (1999) Figure 5.8(b) Results of combined sustained-short term loading tests (Time in seconds scale), after Khan (1999) Figure 5.9 Results of combined sustained-short term loading tests for Stage2 loading of 10 kN/m, after Khan (1999)
Figure 5.10 Results of combined sustained-short term loading tests for Stage2 loading of 20 kN/m, after Khan( 1999)
Figure 5.11 Results of combined sustained-short term loading tests for Stage2 loading of 30 kN/m, after Khan (1999) . Figure 5.12 Results of combined sustained-short term loading tests for Stage2 loading of 40 kN/m, after Khan (1999)
Figure 5.13 eR - eL plot from combined sustained plus short-term loading test for SR80, (stage 1+2)
Figure 5.14 eR - eL plot from combined sustained plus short-term loading test
xv for SR80, stage (1+2+3» Figure 5.15 Superposition ofMSA test results on the strain envelope at 10% limiting strain, time of event after 100 hrs of construction Figure 5.16(a) Superposition ofMSA test results on the strain envelope at 10% limiting strain, time of event after 1000 hrs of construction Figure 5.16(b) Superposition ofMSA test results on the strain envelope at 10% limiting strain, time of event after 10000 hrs of construction FIGURE 5.17 Additional short-term load Vs time of occurrence ofthe event
FIGURE 5.18 cR - 6L plot for combined sustained-earthquake load FIGURE 5.19 Load- Recoverable Strain curve FIGURE 5.20 Determination of design strength for a combination of sustained- short term acti ons
..•. •
XVI CHAPTER ONE
INTRODUCTION
1.1 General
In civil engineering application, there has always been a need for retention systems to retain soil in walls, embankments, dams, slopes etc. With the advancement in knowledge and better understanding of behaviour of materials, there has been advent of many kinds of soil retaining systems from time to time. Soil retention methods, these days, may be chiefly grouped into two categories: Externally and Internally stabilized systems.
Conventional Gravity walls, RC cantilever and RC counterfort retaining walls may be regarded as externally stabilised systems. Internally stabilised systems are characterised by reinforced soils with predominantly horizontally layered reinforcing elements, such as metallic strips or polymeric geotextiles or geogrids. Effectively, the soil mass in the internally stabilised systems is partitioned into horizontal layers so that the lateral pressure arising from each section is arrested by local reinforcing elements.
The economy accrued from the reinforced soil structures may vary in the range of 20 - 80%, depending on. the heights of these applications compared to conventional solutions, Jones (1996). Features like reduction in cost and ease of construction have led the application of reinforced soil systems widely and rapidly acceptable since its inception.
1.2 Development of Geosynthetic Reinforced Soil Structures
The concept of earth reinforcement and soil structures was proposed by Casagrande who idealised the problems in the form of a weak soil reinforced by high-strength membranes laid horizontally in layers, Westergaard (1938). Later, the concept of modem form of earth reinforcement was introduced by Vidal (1969) that was of a Chapter One Introduction
composite material fonned from flat (metal) reinforcing strips laid horizontally in a frictional soil, where the interaction between the soil and the reinforcements is solely generated by gravity. This introduction of Vidal-type structures led into the development of better understanding of t~e fundamental concepts involved therein resulting in advent of different forms of reinforcement like polymeric strips and grids.
The developments of soil reinforcing materials and reinforced soil structure are closely interrelated. Historically, reinforced soil structures were constructed using organic materials as reinforcements, like timber, straw or reeds. Later, as early as the th 19 century, Pasley (1822) recognised the potential of more advanced forms of reinforcement. His use of canvas as a reinforcing membrane. may arguably be considered as the first application of geotextile reinforcement, Jones et al (1996). But because of its limited life before deterioration, Pasley's structures were expected not to be very durable in the long term.
Whatsoever, the use of non-metallic materials (geosynthetics) as permanent reinforcement could be seriously contemplated only after the development of synthetic polymer based materials. Synthetic fabrics were known prior to 194'0,but it was not until late 1960s and early 1970s that the advances in synthetic fabrics and geosynthetics produced materials meant that their longevity could be assured, Jones et al (1996). A salient feature of these polymer-based geosynthetics is that they exhibit a rather complex time and temperature dependent elasto-visco-plastic strain behaviour upon loading. For this reason, the design of Geosynthetic Reinforced Soil Structures [GRSSs] requires due attention with respect to controlling structural deformations within tolerable limits at the end of design life time.
1.3 Design Approaches and Computer Programs
The earliest applications Ofgeosyntheic reinforcements were in road pavements and embankment slopes, although there were some notable steep slopes and walls constructed, McGown and Ozelton (1973), Holtz and Massarsch (1976), and Jarrett et al (1977). Mostly, Limit Equilibrium Approach (LEA) was used in the designs,
.2 Chapter One Introduction
where the soil was uniquely represented by their peak strengths and the geosynthetics by either their factored short term or long term rupture strengths.
Within the LEA, little or no account was given to the deformation characteristics of soil and geosynthetics. Large global Factors of Safety were applied which were intended to ensure explicitly that collapse did not occur and to ensure implicitly that deformations of soil reinforcement system under working conditions were not excessive. As implemented, many of these design methods were semi-empirical and proved to be commonly acceptable and economical compared to other engineering solutions prevailing at that time.
Parellely, as GRSSs were being designed and constructed based on LEA, a fundamental change in the design of civil engineering structures was underway that brought the introduction of deformations and strains as design criteria to be assessed and controlled in an explicit manner. This concept was incorporated into what is now known as the Limit State Approach [LSA], where both collapse conditions, Ultimate Limit States [ULS], and operational conditions, Serviceability Limit States [SLS], are analysed. Additional feature of this approach is the introduction of risk factors, Partial Factors, to replace the use of global Factors of Safety.
The LSA has been adopted in structural engineering ever since 1980's and recently it has been gaining greater acceptance in geotechnical engineering. Some design codes/methods take account of Limit State principles, e.g. Eurocode (1996), BS 8006 (1995) and TBW (1998), but mostly, they include factors, mis-termed Partial Factors, that "Manipulate" outcome designs to ensure them to be in the proximity of the designs based on pre-existing semi-empirical, LEAs, These methods have been termed as Hybrid Approaches to the design of GRSSs, Pradhan (1996) and Khan (1999).
For limit state design, Pradhan (1996), McGown et aI (1998) and Khan (1999) have suggested the valid mechanisms involving the ULS and SLS analyses. To date, their suggested approach may be considered to represent the only "True" Limit State Approach [LSA] applicable to the design of GRSSs, which is based on internal strain
3 Chapter One Introduction
compatibility and force equilibrium between the soils and geosynthetic reinforcements. Their approach to the design of GRSSs does not exhibit any "manipulations", but involves rigorous analyses and iterations to be performed
Almost all of the methods above are too complex and impractical to perform manually. Therefore, Computer Aided Design [CAD] programs are required for the purpose. Amongst those available are; Winwall, Winslope and Tensoil programs. Winwall and Winslope programs have been developed by Netlon (1998) and are Hybrid designs based on both Limit Equilibrium Approach and Limit State principles. The Tensoil program, developed by Khan (1999), is based on the "True" Limit State Approach.
1.4 Actions and Design input parameters
An important aspect to be accounted for in the design of GRSSs is the different types of Actions. GRSSs may be subjected to Single-Stage Actions, e.g. self-weight. However in most operational conditions, Actions imposed on GRSSs are likely to be a combination of long term sustained (self-weight) and transient load or deformation (from traffic or earthquake etc.), which are termed as Multi-Stage Actions.
Despite the current design codes/methods, e.g. BS8006 (1995), AASHTO (1997) and DlBt (1998), recognise the Multi-Stage Actions, the input parameters for soils and geosynthetics are determined invariably from Single-Stage Loading tests alone. It should be appreciated that these tests fail to simulate the actual Actions and hence the data thus obtained may not be appropriate for use in the design of GRSSs, Khan (1999), Kupec (2000).
1.4.1 Soil Properties for Single-Stage Actions
For granular soils, the important input parameter for "True" LSA is the relationship between Mobilised Angle of Friction Wm] and Lateral Tensile Strain [g,l It is recommended that the large strain Constant Volume Angle of Friction Wev] of granular soils should be used for ULS analyses, where the rupture strain of GRSS
4 Chapter One Introduction
exceeds 10%, Bolton (1996), Jewell (1996), Pradhan (1996) and McGown et al (1998). For SLS analyses, relationship between Mobilised Angle of Friction W m] and Lateral Tensile Strain [Btl under plane strain condition should be used with soil
strengths in the range of $'a'-rest to $'peak.
Relationships between Mobilised Angle of Friction Wm] and Lateral Tensile Strain [Btl under plane strain condition have been systematically investigated for the reinforced fills, Khan (1999). Although some design methods suggest Constant Volume Angle of Friction [$'ov] for ULS analyses, the values chosen for this
parameter by practitioners are often very low, sometimes lower than the actual $'ov of the soil, Khan (1999).
1.4.2 Soil Properties for Multi-Stage Actions
The strength properties of clean granular fills, having no fines at all, do not vary with the types of loading, Shimming and Saxe (1964). Therefore, the same input parameters for granular fills are applicable to both Single-Stage Actions and Multi- Stage Actions. However, the fills other than this often exhibit different properties under Single-Stage Actions and Multi-Stage Actions, Khan (1999).
1.4.3 Geosynthetic Properties for Single-Stage Actions
In the design of GRSSs, the main input parameters related to geosynthetics are there Reference Strength, Partial Factors and Design Strength. Reference Strength may be considered as the nominal base strength of a geosynthetic. Partial Factors, intended to take account of construction damage, environmental degradation and biological attack, are applied to the Reference Strength to obtain the Design Strength.
The available design codes/methods define the Reference Strength of geosynthetics for Single-Stage Actions as a factored short-term strength, or as a long-term creep rupture strength for a particular limiting strain. It should be appreciated that the properties of a geosynthetic are likely to be strain level and time dependent which
5 Chapter One Introduction
necessitates the Reference Strength to be determined for particular limiting strain and time, Khan (1999).
Partial Factors are generally determined by companng the 'strength' of a geosynthetic 'before' and 'after' construction damage or environmental degradation. Different design codes/methods and researchers suggest different methods of determining these Partial Factors on the basis of the strength at rupture, or' a pre- defined limiting strain obtained from Constant Rate of Strain [CRS] test or long term sustained load [creep] test. As a result of elasto-visco-plastic nature of polymeric geosynthetics, the values of Partial Factors obtained from different testing methodologies are likely to be different from each other even for a particular type of geosynthetic, Esteves (1996), Khan (1999 and 200 I).
In most design codes and methods, a single value of Partial Factor obtained from CRS tests are applied to the 'Ex-works' long term strength to obtain the long term Design Strength of geosynthetics. The inherent assumption, that the effects of construction damage and environmental degradation on the properties of geosynthetics are the same for both the short term and long .term, is not always true, Khan (1999 and 2001). Further as the Partial Factors are also likely to be strain level and time dependent, it may not be appropriate to assign a single value of them both for ULS and SLS analyses in the "True" LSA to designing GRSSs, Khan (1999 and 2001).
1.4.4 Geosyntbetic Properties for Multi-Stage Actions
Mostly in the design codes, traffic loads in spite of their transient nature, are specified/calculated as the wheel load divided by the contact area, viz. BS5400 (1978), and considered as a uniform static surcharge over the whole design life time, BS8006 (1995) and AASHTO (1997). No consideration is given to the transient nature of this Action. The external and internal stability analyses are then carried out for GRSSs for the critical loading combination as outlined in BS8006 (1995) or AASHTO (1997). For internal stability analyses, Reference Strengths are considered as the creep rupture strength or factored short-term strength in these codes.
6 Chapter One Introduction
In contrast, it has been shown by Miiller-Rochholz (1994) and Khan (1999) that the same strain response due to cyclic loading can be obtained by applying a sustained load equal to half or less of the amplitude of the cyclic load. This indicates that the present approaches are conservative.
For designs against short term transient loads like earthquake shocks, it has been suggested by Fukuda et al (1994), AASHTO (1994) and Jones (1996) that the Reference Strength of a geosynthetic for Single-Stage Actions should be increased by 1.5 times. Some recent design codes/methods suggest that a CRS strength of the geosynthetics should be used as the Reference Strength for design against earthquake loading, for example AASHTO (1997), NCMA (1997) and DIBt (1998). Nevertheless, the technical justification for the consideration of using these strengths is inadequate.
It is essential that, while designing GRSSs against earthquake shocks, the time of occurrence of an earthquake be predicted so as to determine whether a geosynthetic is capable of withstanding any additional short term loads or not. Current. codes/methods suggest a single value of Design Strength for a geosynthetic for the design of a GRSS against earthquake loading, irrespective of when a GRSS is hit by an earthquake. The geosynthetic is attributed with a constant strength, which is used to determine if a particular amount of additional short-term transient load can be supported.
This is not likely to be true. If a structure is designed to refrain from surpassing a particular limiting strain at its ULS, the time of occurrence of an earthquake is extremely significant. For example, if an earthquake hits a structure immediately after construction, the geosynthetic reinforcements are likely to be able to carry higher additional short-term loads compared to that, if the same earthquake hits the structure at the end of its design life.
In addition, no design codes/methods have to date, dealt with the determination of Partial Factors for geosynthetics under Multi-Stage Actions and the Partial Factors
7 Chapter One Introduction
are usually obtained from short term Single-Stage CRS tests which are likely to be inappropriate, Khan (1999).
1.5 Background ofthe present study
In civil engineering applications, geosynthetics as the reinforcing elements in GRSSs are usually subjected to different loading regimes i.e., single-stage (e.g. self-weight) or multi-stage (e.g. self-weight plus cyclic loading or self-weight plus earthquake loading). However, in actual operational conditions they mostly encounter Multi- stage loadings. Geosynthetics are essentially elasto-visco-plastic in nature and at a constant temperature, the same geosynthetic is likely to show different time- dependent strain response when subjected to different loading regimes. Although, there may be many different MSAs, the current focus is on sustained plus short-term earthquake loading.
It may be noted that the (GRSSs) designed according to the current codes/methods suffered either no damage or insignificant damage compared to other structures in the proximity which either collapsed or were badly damaged during the 1995 Kobe and 1994 Northridge, California earthquakes, Tatsuoka et al (1996) and White and Holtz (1996). The survival list includes the GRSS at Tanata as well that has been reported to have experienced the strongest shock amongst the modern GRSSs. Due to construction constraints, the reinforcement lengths for this structure were curtailed to be shorter than that recommended by railway guidelines. Further, the structures were designed for a low seismic coefficient (kh = 0.20) allowing them to suffer little damage but not a total collapse.
Since in the original design, the structures in these two areas were designed to withstand earthquake shocks ofless than what they experienced, a plausible question was posed regarding the conservatism of the design methods and lack of adequate understanding of the load-strain behaviour of geosynthetic under such combined actions.
8 Chapter One Introduction
In fact, neither any test data pertaining to the behaviour of geosynthetics under combined sustained plus short-term earthquake loading was available nor any general approach to the understanding of the behaviour of elasto-visco-plastic geosynthetics was existent until the work of Khan (1999) and Kupec (2000).
Khan (1999) developed the Isochronous Strain Energy [ISE] approach to facilitate the understandings of geosynthetics under different loading regimes. This approach, although capable of explaining the behaviour of the materials for the afore mentioned loading regimes, seems very complex for the practising engineers. A simpler approach towards understanding the behaviour of geosynthetics under different loading regimes, therefore, requires to be developed.
1.6 Objectives of the Present Study
On the basis of the problems identified in above section, the present study is destined to fulfil the following objectives:
• To identity strain components and develop strain envelope of a range of geosynthetics from the available single stage loading data.
• To present the effects of MSA (sustained plus short-term earthquake loading) within the strain envelope plot.
• To characterise the geosynthetics in terms of "Available Strain" with respect to the time of occurrence of an earthquake:
• To identity the conservatism/drawbacks in the present design methods/codes .
• To suggest a design approach for MSA (sustained plus short-term earthquake loading) on the basis of strain envelope and available strain concept.
1.7 Layout ofthe Thesis
Chapter Two contains a general description of GRSSs and their components with an emphasis on the reinforcement types, especially geosynthetics. Various Rheological
9 Chapter One Introduction
and Mathematical models for understanding the complex behaviour of geosynthetics are incorporated. Further, the Boltzmann's superposition principle and the extrapolation techniques suggested by Esteve are presented in brief. Salient features of design codes/methods based on Limit Equilibrium Approach and Hybrid Approach are outlined briefly and valid mechanisms for "True" Limit State Approach are. presented in this Chapter. Also, problems associated with input parameters related to soils and geosynthetics for Single-Stage Actions and Multi- Stage Actions, considered by the existing design codes/methods, are identified. Additionally, the research outputs and case studies related to MSAs are presented.
Chapter Three presents a conceptual understanding of different types of materials with a particular reference to geosynthetics. The likely isothermal strain responses of these materials to different loading regimes (SSA and MSA) are presented. Different strain components are identified and strain envelopes at various limiting strains are described showing that geosynthetics can be characterized with these strain
components, namely "Recoverable Strain" CR and "Locked-in Strain" CL.
Chapter Four deals with the data analyses and validation of the understandings for
geosynthetics' undertaken in Chapter Three for SSA. Various CR-CL plots at different limiting strains are developed. In addition, the procedures for SSA tests are presented.
Similarly, Chapter Five deals with the data analyses and validation of the understandings for geosynthetics undertaken in Chapter Three for MSA. The procedure for MSA (sustained plus short-term loading) test is also outlined briefly.
The test results from the MSA (sustained-short term) are superposed on CR-CL plot and interpreted using the strain envelope concept. Further, the significance of the time of occurrence of the event is identified therein. Thereafter, based on the outcomes of the present study, i.e. the variability of the strength of geosynthetics to take additional short term earthquake load, a suggested design approach for designing GRSSs for Multi-stage (combined sustained plus short-term) loadings are incorporated in.
10 Chapter One Introduction
To the end, Chapter Six includes the discussion and conclusions made on the basis of the present study and eventually recommendations for the future work are presented.
11 CHAPTER TWO
LITERATURE REVIEW
2.1 General
In order to have an understanding of the behaviour of (geosynthetic-reinforced soil structures) GRSSs and the problems associated with the current design methods, it is necessary to appreciate the range of components used in GRSSs, their response and properties towards the operational conditions imposed on them. Therefore, the salient features of the different components of GRSSs are presented in this chapter. Various models that have been developed for the understanding of elasto-visco-plastic materials are also presented. The recent design approaches available for GRSSs are incorporated in this chapter with particular emphasis on the numerous ways they deal with multi-stage loadings. In addition, available research outputs and case studies related to Multi-stage actions have also been compiled herein.
2.2 Components of GRSSs
Horizontal layers of compacted soil and reinforcement are typical ingredients employed in the construction of Geosynthetics Reinforced Soil Structures (GRSSs). Although not necessary, some kinds of facings are essential in order to prevent localized surface erosion along the exposed side of the reinforced soil mass and a progressive overall failure in this type of structures. In GRSSs, the strength of the structure is mainly attributed to the strength of reinforcements by adding tensile strength to the soil mass and by increasing soil strength as a result of increased soil confinement, Jewell (1980). This eventually enables the construction of stable soil structures even at angles steeper than the Angle a/Repose of the soil viz.
• Almost vertical soil walls with various types of facings such as full height panels, sectional panels and segmental concrete facings, "wrap around" facings and other facings such as timber, brick, or gabions, Fig 2.1.
12 Chapter Two Literature Review
• Reinforced slopes used for embankment construction, natural slope stabilization and excavations, Fig 2.2.
In brief, Geosynthetics Reinforced soil structures are composed of a number of components, including reinforced fill; retained fill; sub-soil; in-situ soil behind the reinforced fill or retained fill; reinforcements; facing units and connections, Fig 2.3. The nature and salient features of these components are presented and discussed in the subsequent sections.
2.2.1 Reinforced Fill
The technical requirements of the structure, availability of the fill and the financial constraints dictate the type of reinforced fill to be used in GRSSs. The load transfer mechanism in GRSSs is mainly due to the development of shear forces at the soil- reinforcement interface. This major requirement of frictional forces has resulted in the use of cohesionless or slightly cohesive soil backfills with high friction angles, Yogarajah (1993). Most codes of practice and most design methods suggest granular soils with little or no cohesion to be used, for example, BE3178 (1987), Geospec 2 (1989), BS8006 (1995), AASHTO (1997), DIEt (1998) and the TBW Method (1998). Generally, it has been suggested that the granular materials should not contain more than 15% finer than O.08mm,Lee (1978). In addition, the reinforced fill is usually required to conform to certain electro-chemical and other conditions to reduce the corrosion/degradation of reinforcements.
Nevertheless, these days cohesive reinforced soil structures are .also being constructed in some countries on an increasing scale especially in Japan, Kasahara et al (1992). Number of experiments and full-scale trials on the use of cohesive fills have revealed that cohesive soils may require a large amount of reinforcement with good adhesion and possibly good drainage qualities.
2.2.2 Retained Fill
Most of the time, Retained fill (fill behind the reinforced soil section) may be present in GRSSs, Figure2.3(a). However, at times when structures are built to reinstate
13 - Chapler Two Lileralure Review
existing slopes or to widen an existing road, they may not contain the retained fill, Figure2.3 (b) and (c), but the in-situ soil behind the reinforced fill. Otherwise, the retained fill will be the same soil as that of the reinforced fill. Good quality retained fills should be used and their properties appropriately determined, since the properties of the retained fill may govern the external stability of the reinforced soil structures.
2.2.3 Foundation Soil
The important design parameters in GRSSs are the shear strength, (consolidated undrained, and drained parameters), and compressibility properties of the subsoil and the in-situ soils behind reinforced or retained fills. Most of the design methods presume a competent foundation in the design of GRSSs. In the case of embankments over a soft soil foundation, the properties of embankment materials themselves may not be critical rather the properties of the sub-soils at the end of construction and their subsequent changes with time may be the dominant influences.
2.2.4 Facing Units
Geosynthetics Reinforced Soil Structures (GRSSs) like walls and steep slopes are generally provided with some kinds of facing to. prevent localized surface erosion and progressive failure, although structurally being insignificant. Various kinds of facings have been developed over the years to suit the structures and the site condition. Of these, the most common are concrete panels, (incremental, full height and segmental) and "wrap around" facings where the facing is provided by wrapping the reinforcement around the outside of the compacted soil layer, Fig. 2.1.
Facings may be selected to be relatively rigid or flexible and lightweight. The latter is employed to resist low pressures only, Jones (1993), Tatsuoka (1993). Commonly, they share a relatively low cost per unit area of exposed surface, Jones et al (1987).
GRSSs without facings as in the case of unfaced slopes and embankments represent the condition of no restraint on the lateral soil boundary whereas the same with facings represent various levels of lateral restraint conditions. The actual lateral soil
14 Chapter Two Literature Review
boundary conditions depend upon four factors imposed by the nature of the facing employed, McGown et al (1993), Fig 2.4:
• Axial compressibility
• Lateral compressibility
• Flexural rigidity, and
• Frictional characteristics of the rear surface of the facing
2.2.5 Connections
For GRSSs with facings, Connections between the reinforcement and the facings are vital in that they should be able to transmit the stress from the ends of reinforcement to the facing. In addition, the tensile load-deformation behaviour and flexural properties of the connections are equally important. The different possible connections are, for example, vertically sliding connections, loose fitting connections, rigid connections and connections tightened up during or after placement of the fill, McGown et al (1993).
Andrawes and Yogarajah (1994) have reported from large scale model tests carried out on 2m high reinforced soil walls with different connection types that when the reinforcing elements were Locked-on to facing units (with no horizontal or vertical movement allowed), the maximum tensile strain occurred close to the facing and thereafter was essentially linear away from the facing. On the contrary, the maximum tensile strain occurred away from the facing for loose fitting connections. For the latter case, larger shear resistance was mobilised in the soil and this resulted in reduced lateral earth pressures on the facing units.
2.2.6 Reinforcements
The range of reinforcing elements used in reinforced soil structures covers steel, fiberglass and polymer synthetics in the forms of sheets, strips or grids, Fig 2.5. The choice of material and the form in which it is used generally dictates the load transfer
15 Chapter Two Literature Review
mechanism from the soil to the reinforcement. In the case of strips, sheets and grids with melded junctions, the load transfer mechanism at the soil/reinforcement interface is principally surface friction, while for grid with integral junctions, stress transfer is a combination of surface friction and bearing stresses developed at the junctions or protrusions, Fig 2.6.
When stressed, reinforcements have to be capable of sustaining the loads without rupture or unacceptable strains during their lifetime. The wide variety of reinforcements and the variation in their behaviour has led to the classification of reinforcements into various categories.
Relatively lnextensible and Relatively Extensible, the two groups of reinforcements have been identified by McGown et al (1978), which are as in Fig 2.7 and discussed in brief below.
2.2.6.1 InextensibIe Reinforcements
According to McGown et al (1978) and BS 8006 (1995) reinforcing elements, subject to design loads of a sustained nature, may be classified as lnextensible when the total axial tensile strains are less than I%, viz. Steel, fiber glass.
Relatively lnextensible reinforcements are thus defined as those which have rupture strains less than the maximum tensile strain in the soil without reinforcement, under the same operational conditions. The properties of this type of reinforcement are often independent of time and temperature, in which case their stress-strain behaviour can be determined from short- term Constant Rate of Strain (CRS] tensile tests.
The embedding of Relatively Inextensible reinforcements in soil, in the direction of the principal tensile strain, results in a net increase in the load carrying capacity of the soil and a reduction of soil boundary movements when compared to the soil alone under the same operational conditions. However, when rupture of the reinforcement occurs, the composite behaviour reverts back to the behaviour of the soil alone.
?
16 \ Chapter Twd Literature Review
These reinforcements have two main inadequacies: they are susceptible to corrosion, King (1978) and hinder the development of active soil pressures due to their inextensibility, McGown et al (1968) and Yogarajah (1993). The lack of predictability of the extent of corrosion and the need to allow adequate soil movement for active pressure development has led these materials being in part replaced with materials made from synthetics polymers.
2.2.6.2 Extensible Reinforcements
According to BS 8006 (1995) reinforcing elements, subject to design loads of a sustained nature, may be classified as Extensible when the total axial tensile strains exceed I%, viz. Synthetic polymeric reinforcements, natural fibers. .
Relatively Extensible reinforcements, that include almost all geosynthetic strips, sheets or grids, are thus defined as those which have rupture strains larger than the maximum tensile strain in the soil without reinforcement, under the same operational conditions. The properties of this type of reinforcement are time and temperature dependent. This is why, it has been suggested that long term sustained load [creep] tests at the appropriate temperature are required to determine their load-strain-time- temperature behaviour, Kabir (1984), McGown et al (1984a), Murray and McGown (1987), Andrawes et al (1986) and many others.
Generally, extensible reinforcements allow larger strains to occur without reinforcements rupturing. In these circumstances, the benefit ofthe mobilized tensile strength of the reinforcement is available even after the peak strength of the soil is reached, McGown et al (1978).
The variety and availability of extensible materials have greatly increased in recent years. Most are manufactured from polymeric synthetic materials. These reinforcements have their own disadvantages such as being susceptible to long term creep and stress relaxation. Further, they exhibit degradation due to ultraviolet light when exposed to sunrays together with the decay caused by thermal cycling and physical, chemical or biological attack. Despite these disadvantages, they are gaining
17 Chapter Two Literature Review
wider acceptance due to economical benefits accrued from their use. The thesis covers extensible synthetic polymeric (geosynthetics) reinforcements only. The following section deals with the various materials under this category.
2.3 Geosynthetics
Geosynthetics are produced in various forms of plastics like sheets, strands, fibers, etc., whiCh are linked and arranged in a variety of orientations. They are the produce of polymeric materials whose long chain molecules are obtained by the process of polymerization of monomers. In order to suit the purpose of use, their properties are modified by mixing additives like plasticizers, reinforcements and stabilizers, etc.
Two most important plastics are:
I. Thermoplastic materials: The features of these plastics are the relatively weak Intermolecular Van-der -Waals forces. When these materials are heated, they become soft and flexible and eventually, at high temperatures, exhibit a viscous melt. When they are allowed to cool, they solidify again. This process of softening by heating and solidifying on cooling may be repeated more or less indefinitely.
2. Thermosetting materials: Crosselinking of the long chain-like molecules dominates their behaviour. This takes place during moulding under heat and pressure. The resulting material is rigid when cooled and does not soften on heating.
2.3.1 Elasto- Visco-Plastic Nature of Geosynthetics
The majority of geosynthetics are manufactured using thermoplastic materials (existing in the form of sheets, strands, fibers, etc.). These materials may exhibit a wide range of mechanical behaviours; from brittle-elastic at low temperatures through plastic, to visco-elastic or leathery, to rubbery and finally to viscous at high temperature. Their behaviours are dictated by the nature of the constituent materials, processing during manufacturing and their operative temperature.
18 Chapter Two Literature Review
The behaviours of polymers are characterized by the Glass Transition Temperature [T8]' below which the material behaves like glass, i.e. it is hard and brittle. At a
temperature greater than Tg• the Van der Waals bonds between the long polymer chains weaken due to the increase in the free volume in the polymers. This free volume makes it easier for the molecules to move past each other when a load is
applied at a temperature higher than Tg. Consequently, the polymers strain more
easily under a load at higher temperatures than Tg, compared to the temperatures
lower than Tg. Alternatively, Tg may be regarded as the threshold ten:tperatureabove which lesser energy is required to develop a particular strain over a certain period of time in the material, and below which more energy is required.
The more important is the fact that at normal operational temperatures, the load- strain-time-temperature behaviour of geosynthetics is dependent upon their micro and macro-structures. The principal micro-structural features that characterize all polymers are the molecular size, basic polymer network structure, chain stiffness and rigidity.
Mostly there are no network structures or cross-linking within engineering thermoplastics; nevertheless, polymer-processing operations may result in small amounts. The molecular state of the material is manipulated from the amorphous to semi-crystalline and finally to crystalline state in this operation. Degree of crystallinity within the thermoplastic components of geosynthetics is of great significance. Most of the thermoplastic materials and processes, used to produce various geosynthetics, lead to microstructures that are partly amorphous and partly crystalline. Consequently, the mechanical behaviour of the components is often elastic initially followed by visco-plastic which is the result of the long molecular chains unfolding, (if chain-folded), or drawing out of the amorphous tangle, (if glassy), together with straightening and aligning.
If a constant load is applied, viz. sustained load (creep) test, the geosynthetics exhibit an instantaneous elastic strain followed by primary creep, secondary creep and tertiary creep, Figure 2.8. Primary creep is dominated by its quick rate and occurs in
19 Chapter Two Literature Review
a very short time; whereas secondary creep occurs at a very slow rate and requires load to be applied over a longer time. Tertiary creep occurs at higher load levels where non-linear visco-elasticity becomes predominant. The material rupture under tertiary creep conditions is influenced by various factors and therefore it is difficult to predict.
The degree of crystallinity is an important indicator in that it represents the thermoplastic component in the materia!. Under isothermal conditions, a 2% strained specimen is less crystalline than a 10% strained specimen, because the straightening and aligning of the long polymer molecules within it increase the degree of crystallinity.
Another important aspect of the effect of microstructure is the basic structure of the constituent polymer itself This structure defines the ability of molecular chains to slip past one another. In the case of polyesters, due to the relative inability of the molecular chains to slip past one another arising from the effective knots, they show little time dependent creep at low load levels. On the contrary, the smoother and straighter molecules in polypropylenes can slip past one another more easily, which is why they can exhibit a significant creep even at low load levels.
In the final stage of manufacturing process of geosynthetics the various thermoplastic components are linked and arranged geometrically to form the macro-structure, which result in different generic types of geosynthetics including wovens, needle- punched and melt bonded non-wovens, nets, grids and linear composites. These various macro-structures further have a highly significant influence on the time dependent load-strain behaviour of geosynthetics. Nevertheless, their temperature dependent behaviour may not be highly influenced by the macro-structures, as this is a microstructure issue.
Thus, it may be appreciated that geosynthetics exhibit elasto-visco-plastic behaviour. This means that their mechanical behaviour is in part similar to that of elastic solid, in part similar to that of a viscous liquid and in part similar to that of a plastic, with all these parts being temperature dependent. Therefore, when subjected to an
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o Chaoter Two Literature Review
externally applied load as shown in Figure 2.9(a), they respond by exhibiting a combination of elastic displacement, viscous flow and irrecoverable plastic deformation, Figure 2.9(b).
The rupture of geosynthetics may occur in either a brittle or ductile mode, depending on the micro and macro structures, operational temperature, etc. For most of the geosynthetics this rupture domain is difficult to identifYin a consistent manner, Kabir (1984) and Yeo (1985). A rupture criterion should be used only if a geosynthetic exhibits a clearly defined rupture domain. For the majority of geosynthetics a limiting strain is the more appropriate criterion. This is the reason why the limiting strain criteria for different applications are set within some of the latest design methods, for example HA 68/94 (1997) and the TBW (1998).
These complex properties make it difficult to characterize the mechanical behaviour of geosynthetics in a simpler mathematical form and call for complex modellings, of which some are given below.
2.3.2 Rheological and Mathematical Modelling of Geosynthetics Behaviour
Several attempts have been made in the past to simulate the behaviour of geosynthetics with an aim to
(i) facilitate analysis of the behaviour of geosynthetics products,
(ii) assist with extrapolation and interpolation of experimental data, and
(iii) reduce the need for extensive, time consuming creep tests.
In this regard, various Rheological and Mathematical models, varying from simple to complex, have been developed and been successful in characterizing the problems associated with the mechanical behaviour of geosynthetics. The most successful of the Rheological and Mathematical Models are based on spring and dashpot elements to represent the elastic and viscous responses of geosynthetics, respectively. Although, none of the elements of the models behave like the discrete molecular
21 Chapter Two Literature Review
structures, they do however aid in the understanding and analysis of the behaviour of geosynthetics. Of many Rheological Models, the most simple is illustrated in the Figure 2.10, with four elements of spring and dashpot.
2.3.2.1 Maxwell Model
Like the Rheological Models, there are numerous Mathematical Models that have been developed for the understanding of the mechanical behaviour of geosyntheics. The simplest form is modelled of two elements with a spring and a dashpot in a series and attributed to Maxwell, Figure 2.l1(a). This model predicts the response under three common time dependent modes of deformation, such as creep, relaxation and recovery.
This model fails In predicting adequately the behaviour In creep and recovery, although the relaxation behaviour is acceptable as a first approximation to the actual materials response.
2.3.2.2 Kelvin or Voigt Model
Unlike the Maxwell model, this is modelled with the spring and the dashpot in parallel, Figure2.l1 (b). The response is predicted in three modes of deformation (creep, relaxation and recovery) in this model like the Maxwell. This model predicts an acceptable first approximation to creep and recovery behaviour but does not account for relaxation.
2.3.2.3 Maxwell and Kelvin Model
It may be observed that none of the two models indicated above could give an acceptable firSt approximation to all the three deformation behaviours, i.e. creep, relaxation and recovery. The Maxwell can account for relaxation but lacks in the rest, whereas the Kelvin can account for creep and recovery but lacks in relaxation. Thus, in order to make a compromise, these two models have been married together, Figure 2.12(a), and is named as Maxwell and Kelvin Model, wherein the effects are the sum of that from the individual Model.
22 Chapter Two Literature Review
2.3.2.4 Zener (Standard Linear Solid) Model
In this model the springs and the dashpot are in series and parallel, Figure 2. I2(b). This model predicts the deformation behaviours for creep, relaxation and recovery, as well. The other forms of the models presented above may be considered as the special cases of this.
In this way, additional elements may be added to simulate the nature of the geosynthetics better but the mathematical solution of the governing equation becomes complex.
2.3.2.5 Esteve's Method
A mathematical model of creep data should describe the structural properties of geosynthetics. Hence a suitable function should be chosen to represent its strain behaviour. The method suggested by Esteve can be briefly outlined step by step as:
• Strain-Time plots are developed from the data obtained from creep tests for a particular type of geosynthetics at different load levels.
• A suitable function is selected to fit in the curve. For the present case, a
logarithmic function viz. Y= A Ln (x) +B and power function Viz. Y= A (x) B are chosen.
• The coefficients A and B are plotted against different load levels and the plots are adjusted by selecting proper functions. For the current case, linear series is found to fit well within the range.
• From these plots, the coefficients A and B are determined for the required load levels.
• These coefficients are substituted in the selected logarithmic and power functions to yield the strain-time plot at the required load levels.
23 Chapter Two Literature Review
2.3.2.6 Boltzmann Superposition Principle
The creep behaviour of geosynthetics to date has assumed that the level of the applied stress is constant, while in service the material may be subjected to a complex pattern of loading and unloading cycles. It may not be feasible to obtain experimental data to cover all possible loading situations for determining the input parameters for design.
For tackling the problem of the sort above, the simplest theoretical model has been presented by Boltzmann to predict the strain response to a complex stress history. This is referred to as the Boltzmann superposition principle, which proposes that for a linear viscoelastic material, the strain response to a complex loading history is merely the algebraic sum of the strains due to each step in loading. The implication of the idea in this principle is that the behaviour of a geosynthetic is a function of its entire loading history.
This principle of Boltzmann is explained in detail in the section 3.6 with the aid of figures for the loading history and it's strain response against time. Therefore, it is not felt necessary to elaborate the principle in detail here.
2.4 Strength tests for geosynthetics
There are varieties of test methodologies developed so far to determine the strength of geosynthetics. Depending upon the time and the purpose, an appropriate test may be selected. To be named, they are CRS (constant rate of strain) test, CREEP (Iong- term sustained loading) test, Stress relaxation test and Cyclic tests. These tests utilize different specimen shapes and sizes, loading methodologies, rates ofload application and test temperature for. measuring mechanical behaviour of geosynthetics, Kabir (1984).
Test specimens must be of sufficient size and shape to be representative of the macro-structure of the product, Kabir (1984) and Yeo (1985). However, even when this condition is satisfied, each test may investigate the response of different features of the micro and macro-structures of geosynthetics. Indeed, changing a single test
24 Chapter Two Literature Review
condition may result in a change in the load-strain response. For example, for wide width specimens tested at a given test temperature, a change in the rate of strain in monotonic tests has a significant effect on the measured properties of geosynthetics as has changing the test temperature whilst using the same rate of strain has a significant effect, Kabir (1984) and Yeo (1985).
2.4.1 Constant rate of strain test
This test is very famous and widely performed since it involves very little time. A constant rate of strain is maintained while' applying the load increasingly until the specimen ruptures. Load verses strain is recorded and the ultimate load at the rupture is found out.
Different standards specify their own rate of strain at which the test is to be performed. For example, BS 6906, Part 5 specifies a rate of strain at 7-13% per minute and the temperature to be (20 :t 1)0 C.
The test scheme is shown in Figure 2.13(a) and the qualitative load -strain plot is shown in Figure 2.13(b).
2.4.2 Sustained load creep test
The scheme of test apparatus used in sustained load creep test is shown in Figure 2. 14(a). This test involves very longer period of time compared to CRS test. The specimens are loaded with different weights that are sustained for a long period. The strain verses time at these loads is recorded up to generally 1OOOOhrs.The qualitative plots are shown in Figure 2.14(b). From these plots load-strain curves are developed.
For this test also the test temperature in BS is specified as (20 :t 1)0 C. The test procedure is explained in detail in Chapter Four.
25 Chapter Two Literature Review
2.4.2.1 Isochronous load-strain curves
Isochronous curves are the plots of load verses strain at the same temperature from different loading tests such as CREEP (long term sustained load) or CRS (constant rate of strain) tests. In order to obtain isochronous (load-strain) curves the materials
(specimens) are subjected to a series ofJoads PI, P2, and p] at time to and sustained as shown in the Figure 2.15, which is a plot ofJoad verses time.
The plots of total strain ET against time for the above loadings are constructed as shown in the Figure 2.16 for elasto-visco-plastic materials following the procedure described below.
For any time tl, total strain values corresponding to the loads PI, P2, and p] are scaled off from the figures (a) of total strain -time plots. In the same manner for any times t2 and h, corresponding strain values to the loads are obtained from the same figures and marked on the plots of load vs strain. These points corresponding to different times tl, t2 and t], respectively, are joined to produce curves for tl, t2 and t3 respectively. Thus a family of curves is obtained. The typical isochronous curves for elasto-visco_plastic materials are shown in the Figure 2.16(b).
Each of the test methodologies involves different form of data presentation and for a particular test several forms of data presentation can be used. The most widely applicable form of presenting these data is in the form of Isochronous Load-Strain curves at a constant temperature. Commonly, these are produced from sustained load [creep] test data. However, they can also be produced from most test procedures, for example CRS test. Recently it has been shown by Miiller-Rochholz et al (1994) that the data obtained from cyclic load test can be represented by an equivalent sustained loading. This allows Isochronous Load-Strain curves to be obtained from cyclic load test data as well.
It should be noted that the areas under the Isochronous Load-Strain curves represent the absorbed Strain Energy at the specific time and limiting strain and may be termed as the Isochronous Strain Energy.
26 Chaoter Two Literature Review
2.5 Design strength of geosynthetics in GRSSs
In the design of GRSSs, two types of strength have been considered so far, viz.
Reference strength" [PRed and Design Strength [Td]. Various testing techniques have been developed to obtain Reference Strength [PRed. Customarily, Design Strengths [Td] for geosynthetics are determined by applying Partial Factors to the Reference Strengths. However, the Partial Factors need to be modified for their appropriate application, khan (1999).
2.5.1 Reference Strength
The Reference Strength [PRed is obtained from different testing techniques, most often by CRS and CREEP tests. Various design codes and methods define Reference Strength [PRedin different ways for Single-Stage and Multi-Stage Actions.
2.5.1.1 Reference Strength for Single-Stage Actions
The maximum load at rupture of the 'Ex-works' materials under Constant Rate of Strain [CRS] tensile testing is chosen to be the basis of defining the Reference Strength of geosynthetics by DlBt (1998) and AASHTO (1997). To avoid long-term creep rupture, the Reference Strength [PRed, is then obtained by dividing the CRS rupture strength by a Reduction Factor, Figure 2. 17(a). The DlBt and the AASHTO design methods specify 33% per minute and 10% per minute strain rates respectively, for the CRS tests. Kabir (1984) and Yeo (1985) have shown that the CRS test can give different strengths at different test strain rates and temperatures. Therefore, even for a particular type of geosynthetic the same Reduction Factor may not be applicable to all CRS data in order to obtain the long term creep rupture strength, i.e. the Reduction Factor is dependent on the strain rate used in the CRS test.
Troost and Ploeg (1990), BS8006 (1995) and Jewell (1996) have defined the Reference Strength [PRedas the load to cause creep rupture of 'Ex-works' specimens at the end of design life [t.n], Figure 2.17 (b). However, many geosynthetics exhibit a wide range of scatter of creep rupture strains for different sustained [creep] load levels, Fig 2.17 (c). Hence, the Reference Strength [PRed,defined on the basis ofload
27 Chapter Two Literature Review
at creep rupture for a specific design life time [!ctJ], can be very difficult to select with any certainty related to the strain level developed at creep rupture, McGown et al (1998).
Some design methods define the Reference Strength [PRedas the load obtained from the Isochronous Load-Strain curves, corresponding to a Performance Limit Strain [Ep], for example the TBW Method (1998) and the HA 68/94 Design Method (1997). This value is always less than the strength at creep rupture, Figure 2.l7( d). Adoption of the Performance Limit Strain [!>p] to define the Reference Strength [PRed for Ultimate Limit State design can be seen to be the quite conservative choice of strength value, Khan (1999).
This way, the Reference Strengths for Single-Stage Actions are defined in two different ways, i.e. on the basis of long term creep rupture strength, and on the basis oflong term creep at a limiting strain.
2.5.1.2 Reference Strength for Multi-Stage Actions
Of Multi-Stage Actions, one illustration is sustained loading plus traffic loading that may be applied to the reinforced roads. Although the traffic loads are transient in nature, in most of the design codes, they are calculated as the wheel load divided by the contact area; viz. BS5400 Part2 (1978), and considered as an uniform surcharge load over the whole design life time, GeoguideI (1989), BS8006 (1995) and AASHTO (1997). This implies that these codes permit the Reference Strengths for Single-Stage Actions to be used in designs for sustained loading plus traffic loading. The external and internal stability analyses for the sustained loading plus traffic loading are carried out for the critical loading combination as outlined in the respective codes.
The consideration of wheel contact pressure as a sustained load over the whole design lifetime of the structure does not consider the transient nature of the load which may be economical considering the elasto-visco-plastic behavior of geosynthetics.
28 Chapter Two Literature Review
Further illustration of Multi-Stage Actions is sustained loading plus short-term seismic loading. The development of designs for GRSSs involving earthquake forces is presently empirical. Fukuda et al (1994) reported that until 1993, the GRSSs were designed for earthquake on the basis of the procedure for design under ordinary static conditions, as given by Jewell et al (1984). In this procedure the long term creep rupture strength of geosynthetics was used as Reference Strength. The structures, so designed, were found to maintain stability during the Lorna Prieta Earthquake in 1989 having a magnitude of 7.1, Collin et al (1992), and Kushiro Offshore Earthquake in 1993 having a magnitude of7.8, Fukuda et al (1994).
During the Kobe (Hyogo-ken Nanbu), 1995 earthquake with magnitude of 7.2, a great number of RC columns and piers collapsed by shear failure in a brittle manner, in contrast to a number of geogrid soil retaining walls that performed very well. In particular, the geogrid reinforced soil retaining walls with full height rigid facings at Tanata did not collapse despite the site were located in one of the most severely shaken area, Tatsuoka et aI, (1995).
Similarly, the performance of seven geosynthetic-reinforced slopes and walls shaken in the Northridge, California earthquake of January 17, 1994, was adequate, particularly compared to the performance of other immediate neighbouring structures, White and Holtz, (1995).
These data indicate that the geosynthetics were actually capable of taking higher loads applied rapidly, than the long-term creep strength used that time. After the adequate performance of GRSSs in Lorna Prieta Earthquake (1989) and Kushiro Offshore Earthquake (1993), it was suggested by Fukuda et al (1994), AASHTO (1994) and Jones (1996) that the Design Strength of geosynthetic for sustained loading condition should be increased by 1.5 times when designing for sustained loading plus short term earthquake loading. In the recent codes/methods, as more confidence is gained from the performances of GRSSs during recent earthquakes, factored short term CRS strengths of geosynthetics are suggested for use in designs against sustained loading plus short term earthquake loading, AASHTO (1997),
29 Chapter Two . Literature Review
NCMA (1997) and DIBt (1998). However, it should be noted that the considerations of higher strengths of geosynthetics, from 1994 to 1998, were all empirical, Khan (1999).
The test results from the Multi stage combined sustained-short term loadings revealed that after the subsidence of the short term load, the strain level in the geosynthetics is likely to be similar to that due to the sustained load alone in course of time, as if there were no occurrence of any earthquake ever, Khan (1999). This further indicates that the geosyntheics are in fact capable of taking larger short-term load.
In this regard, it has been also reported by Kupec (2000) about the ability of the geosynthetics to take larger short-term load. The Combined Sustained-Short term loading test results from the series used by him showed that even a load of 80% (1.8 times) the sustained load altered the material only temporarily and that with time this alteration decreases.
In the design codes/methods higher strengths of geosynthetics have been suggested, presumably, .on the basis that the earthquake loading would be very transitory, but they do not pronounce any valid technical justification. It is unlikely that the same amount of high strength of geosynthetics may be available over the whole design lifetime of the structure, irrespective of the time of occurrence of an earthquake. If so, current practice of designing GRSSs against earthquake might be unsafe.
2.5.2 Partial Factors and Design Strength
The strengths of the geosynthetics for ULS and SLS analyses require to be modified by applying Partial Factors. Four Partial Factors of major concern have been identified for geosynthetics, Voskamp and Risseeuw (1987), Jewell and Greenwood (1988), Greenwood and Jewell (1989) and Troost and Ploeg (1990) as the followings: a) The Damage Factor; to allow for mechanical damage during construction.
30 Chapter Two Literature Review
b) The Environmental Factor; to allow for the chemical environment and microbiological exposure in the ground.
c) The Material Factor; to allow for the uncertainty inherent in the e~trapolation of test data, and
d) The Overall Factor; to allow for the properties of materials not meeting the manufacturer's specification.
Conventionally, the Design Strengths for the geosynthetics are determined by applying Partial Factors to the Reference Strengths.
T =PR,r (2.1) D fm
BS 8006 (1995), AASHTO (1997), DlBt (1998) and TBW (1998) suggest that the Partial Factors should be determined by comparing the material strengths of geosynthetics "before" and "after' an event, as obtained from CRS tests.
However, it should be noted that no Partial Factors are given for the combined effec!s of Multi-Stage Actions.
2.6 Design approaches for GRSSs
Traffic, earthquakes, explosions and variety of intermittent loads result in cyclic or short-term loading to GRSSs in combination with sustained load. Very little is known about the behaviour of these structures under such Multi-stage Actions. Nevertheless, it is appreciated that the duration of the cyclic or the short-term loading during these events has an important influence on the response of the foundation materials and the structures themselves.
The current design approaches to external stability have been founded on classical methods for gravity retaining walls with the appendices of internal stability calculations to take the effect of reinforcements into account. Majority of the design methods for GRSSs is based on Limit Equilibrium Approach. Though Limit State
31 Chapter Two Literature Review
principles are included in some desi/,'tl codes and methods, these may be termed as Hybrid Approach as they are based partly on Limit Equilibrium Approach and partly on Limit State Approach. Three, main existing design methods involving these three design approaches are reviewed in the subsequent sections with a special emphasis on Multi-stage actions.
2.6.1 Limit Equilibrium Approacb
The method of analysis is based on the assumption that all the constituting elements simultaneously reach their limiting stress conditions. This assumption is not valid for GRSSs, since the limiting stress conditions for soils and geosynthetics may occur at quite different strain levels. This method calls for the following stability analyses to be carried out to ensure the safety of the structures:
• External Stability
• Internal Stability
The reinforced soil zone is assumed to act as a monolithic structure. The analysis of external stability for the GRSSs is similar to that of the conventional retaining walls and involves the analysis of:
• Sliding of the structure at the base
• Overturning of the structure
• Bearing failure of the subsoil, and
• Overall stability of the structure
The internal stability analysis, which is different from that of a customary retaining wall, consists of the following:
• Tension failure of the reinforcing elements
• Wedge/Pull-out failure of the reinforcing elements
32 Chapter Two Literature Review
No direct or explicit analysis for deformation of the soil boundary is considered in this approach. It is assumed that once the external and internal stability criteria are satisfied, the deformation criteria will also be satisfied. Although this assumption may be overlooked for inextensible reinforcements, this may be seen to be a very critical issue for extensible reinforcements.
Many design methods have evolved on the basis of the Limit Equilibrium Approach. Examples of these are the AASHTO (1997), the DJBt (1998) and the HA 68/94 (1997) methods. The salient features of these design methods are outlined below.
2.6.1.1 AASHTO Standard Specifications for Highway Bridges (1997)
This method suggests the procedure for designing walls and steep slopes.
The soil property used in the analysis is the Peak Angle of Friction [~'p] and the Long Term Strength [Tal] of the reinforcing element for Single-Stage Actions and Multi- Stage Actions such as sustained loading plus traffic loading is calculated by:
T _ Tult af - RF (2.2)
wherein,
RF = Reduction Factor
= RFCR X RFll) X RFD
TwI = short term CRS rupture strength of the reinforcing element per meter width.
RFCR = Reduction Factor for long term rupture strength.
RFID = Reduction Factor for damage from placing and compaction.
33 Chapter Two Literature Review
RFD = Reduction Factor to prevent rupture of the reinforcement due to chemical and biological degradation
The Reduction Factor RFCR is determined by comparing the CRS rupture strength (at 10% per minute strain rate) to the long-term rupture strength of a geosynthetic at a
specific time and temperature. The Reduction Factor RFCR thus depends on the type, design lifetime and operational temperature of the reinforcement.
The Reduction Factors RFm and RFD are determined by comparing the CRS rupture strengths of a geosynthetic 'before' and 'after' construction damage and environmental degradation respectively.
For design against sustained loading plus traffic loading, the live load surcharges are treated as uniform distributed surcharge loads that are effective over the whole design life.
For design against sustained loading plus short term earthquake loading, [Tal] is increased by reducing RF to eliminate creep as a consideration, i.e. by considering
RFCR = I.
Global Factors of Safety are applied at the end of both external and internal stability analyses, Table 2.3. This design method requires checking the rupture and pullout failures of the reinforcements. The single wedge method is employed in the analysis of calculating the disturbing force. A critical wedge is found by trial and error that gives maximum disturbing farce. This disturbing force should not exceed the minimum of (i) the long-term strengths, or (ii) the pullout resisting forces provided by reinforcements within a failure wedge.
2.6.1.2 The Deutsches Institut fiir Bautechnik (DIRt) Method (1998)
This design method is based on the Deutsches Institut fur Bautechnik Certificate No. Z20. 1-102 and is meant for designing walls and steep slopes. Stability analyses have to conform to different DIN Codes, e.g. the sliding check has to conform to DIN 1054 and the bearing check to DIN 4017.
34 Chapter Two Literature Review
The soil property used in the analysis is the Constant Volume Angle of Friction [$'ev] and the Permissible Working Load [Fperm]ofthe reinforcing element for Single-Stage
Actions and Multi-Stage Actions such as sustained loading plus traffic loading is calculated by:
F =~ (2.3) pm" A A f>j 2Y
Wherein,
FB short tenn CRS rupture strength of the reinforcing element per metre width.
AI Reduction Factor for long term strength, (= 2.40 to 2.75).
A2 Reduction Factor for damage from placing and compaction, (= 1.05 to 1.5).
y = calculated Factor of Safety, (= 1.75).
The Reduction Factor Al is determined by comparing the CRS rupture strength (at 33% per minute strain rate) to the long-term rupture strength of a geosynthetic at a specific time and temperature. The Reduction Factor AI thus depends on the type, design lifetime and operational temperature of the reinforcement.
The Reduction Factor A2 is determined by comparing the CRS rupture strengths of a
geosynthetic 'before' and 'after' construction damage. The values of A2 thus depend on the type of the soil and the type of geosynthetic.
For design against sustained loading plus traffic loading, the live load surcharges are treated as uniformly distributed surcharge loads that are effective over the whole design life. Two loading cases are considered: Permanent traffic loads (load case I), where the overall Factor of Safety [FOS] is given as YI = 2.0, and for temporary traffic loads (load case 2), where overall [FOS] is given by Y2= 1.5.
35 Chapter Two Literature Review
For design against sustained loading plus short-term earthquake loading, Permissible
Working Load [Fperm]is increased by considering AI = I and y = 1.31.
Global Factors of Safety are applied at the end of both external and internal stability analyses, Table 2.3. The method does not require checking the individual reinforcing element against its permissible working load. The structure is checked against the pullout failure. The single wedge method is employed in the analysis of calculating the disturbing force. A critical wedge is found by trial and error that gives maximum disturbing force. This disturbing force should not exceed the minimum of (i) the permissible working load, or (ii) the pullout resisting force. The pullout check is carried out at the places only where the reinforcement spacing or type changes.
2.6.1.3 HA 68/94 Method (1997)
The British HA design method is based on the Department of Transport Advice Note HA 68/94. It provides a single unified Limit Equilibrium design approach for all
types of reinforced highway earthworks with slope angle ranging from 100 to 700 to the horizontal. The design presumes that the foundation is competent.
The philosophy of the design method lies in using the soil strength parameters that represent the minimum conceivable values so that no further overall Factor of Safety needs to be applied to the design. The design suggests the use of the Constant Volume Angle of Friction [ . Wherein, :.-fk Td- (2.4) Ym fk = characteristic long term strength (at 10% limiting strain) of the reinforcing element per meter width, Ym Partial Factor obtained from CRS tests. 36 Chapter Two Literature Review No specific Design Strength [Td] is suggested for sustained loading plus traffic loading or sustained loading plus earthquake loading within this method. A two- part wedge method is the basis for analysis. The reinforcement length at the base of the structure is determined using a trial and error method to obtain the wedge that gives the disturbing force equal to zero. This is termed as the Tob mechanism. The length at the top of the structure is based on the so-called Tmax mechanism. This process involves a trial and error method used to find the wedge that gives the maximum disturbing force, which is known as the Tmax mechanism. Different wedges are analyzed at different depths, to ensure that the disturbing force does not exceed the resisting force from the reinforcing elements. In this method, individual reinforcing elements are not checked against rupture failure, neither any Factor of Safety is applied. 2.6.2 Hybrid Approach Few design codes and methods like BS8006 (1995) and the TBW Method (1998) have used Hybrid Approach for the design of GRSSs. The main features of these methods are dealt in the following sections. 2.6.2.1 BS8006 (1995) Method BS8006 has adopted a limit state design approach whereby individual Partial Factors applied to the various forces acting on .the structure and the soil/reinforcement properties. Their purpose is to apply appropriate Partial Factors where they are required, i.e. the greatest Partial Factors to the greatest uncertainty. The peak effective shear strength parameters are recommended for the soils for both Ultimate Limit State [ULS] and Serviceability Limit State [SLS] analyses, i.e. ~'p, c' p. For walls, steep slopes and embankments the Design Strength [Td] of the reinforcement for Single-Stage Actions and Multi-Stage Actions (sustained loading plus traffic loading) is taken as _ Tb Td- (2.5) Im 37 Chapter Two Literature Review Wherein, Tb unfactored Reinforcement Base Strength fm Partial Factor Reinforcement Base Strength [Tb] should be as: a) For the Ultimate Limit State [VLS] the base strength is the tensile creep rupture strength [Tcr] at the appropriate times and design temperature. b) For the Serviceability Limit State [SLS] the base strength is the tensile load in the reinforcement [Tc,] which induces the prescribed post construction limit state strain (0.5% for abutments and 1.0% for retaining walls). For design against sustained plus traffic loading, the traffic loads are calculated as the wheel load divided by the contact area and considered as a uniform surcharge load over the whole design lifetime. For design against sustained plus earthquake loading, no Design Strength [Td] is suggested within this code. The Partial Factor [fm] has two components: (2.6) Where, fml Partial Factor related to the intrinsic properties of the material fm2 = Partial Factor concerned with the effects of construction and environmental effects Partial Factor fmI is further divided into several components as: fml = fmll x fml2 (2.7) fmI = (fmlII x fmII2) x (fmI21 x fmI22) (2.8) 38 Chapter Two Literature Review fmll = Partial Factor related to the consistency of the manufacturer fml2 = Partial Factor related to the extrapolation of test data dealing with Base Strength fmlll = Partial Factor related to whether or not a standard for specification, manufacture and control testing of the reinforcement exist fml12 = Partial Factor for whether or not standards for the dimensions and tolerances exist fml21 = Partial Factor for the assessment of available data fml22 = Partial Factor for extrapolation of the statistical envelope over the expected service life of the reinforcement Partial Factor fm2 is also divided into several components as: (2.9) (2.10) where, fm21 Partial Factor which deals with the installation damage of the reinforcements fm22 Partial Factor which deals with the environmental effects of the reinforcements fm2l1 Partial Factor related to short term effects of damage prior to and during installation fm212 = Partial Factor for the long term effects of the short term damage All the Partial Factors are certified and specified by the British Board of Agreement (BBA) for applications within UK. Ultimate Limit State Analyses a) Sliding Analysis The Factor of Safety against sliding failure (fs] is given by the equation: (2.11 ) 39 Chapter Two Literature Review where, fs Factor of Safety against base sliding (=1.20) Rv = vertical factored resultant force Rh horizontal factored disturbing force $' p peak angle offriction c' p effective cohesion of soil L effective base width for sliding fms Partial Factor for material (I for tan$' p and 1.6 for c'p) b) Bearing Failure The imposed bearing pressure [qrl must be compared to the factored ultimate bearing capacity as follows: (2.12) Where, fb Factor of Safety for bearing capacity (=1.35) qull = ultimate bearing capacity of the foundation Dm = embedment depth c) Reinforcement Rupture Each layer of reinforcement requires checking against rupture. The maximum tensile force in the itb layer T; is then calculated by: (2.13) Where, Ka coefficient of active earth pressure within the reinforced zone crv vertical stress on reinforcing element Sv vertical spacing of reinforcing element 40 Chapler Two Literature Review In order to ensure stability with regard to rupture failure, the following relationship must be satisfied: (2.14 ) where, Td = Design Strength of the reinforcement fn Partial Factor for economic ramifications offailure d) Pullout Failure The resistance provided by each individual reinforcing element must be taken to be the lesser of (i) pullout resistance, or (ii) the design strength. The total resistance from all reinforcing elements is checked by: (2. I 5) where, Lei anchorage length beyond failure plane fp Partial Factor against pullout [=1.30] J.! = coefficient of friction between soil and the reinforcements f[ Partial Factor for surcharge load YI density of the reinforced fill h; = depth of reinforcement of ith layer w, surcharge load c', adhesion between the fill and reinforcement fms = Partial Factor for c', T total tensile force to be resisted by reinforcing elements 41 Chapter Two Literature Review Serviceability Limit State Analyses For a polymeric reinforcement where short term axial tensile stiffness decreases with time through the agency of creep, the strain occurring between the end of construction and the end of selected design life can be estimated from isochronous load strain curves for these two times. Figure 2.18 demonstrates this procedure, where Tc, is the capacity of the reinforcement at a prescribed limiting value of post construction strain. 2.6.2.2 Tensar Tie-back Wedge (TBW) Design Method (1998) Due to the relatively large strains occurring within GRSSs, critical state or constant volume shear strength properties are used for the soils i.e. ~'cv, c' cv, in this method. The Design Strength [Td] of the reinforcement for Single-Stage Actions is given by: _ 7~ Td- Im! xlm21 Xlm22xlm3 (2.16) Where, Tc extrapolated creep strength (at 10% limiting strain) of the reinforcement at specified design life time and operational temperature fm! Partial Factor to allow for material manufacturing variations and confidence in the extrapolated strength fm2l Partial Factor for the effects of construction activities fm22 Partial Factor for the effects of environmental degradation fm3 = overall Factor of Safety (=1.35) For the design against Multi-Stage Actions, no Design Strength [Td] is suggested thereby. The Partial Factor fml and the overall Factor of Safety fm3 are specified by the manufacturers. Partial Factors fm2! and fm22 are obtained by comparing the short term CRS rupture strengths 'before' and 'after' an event in the case of construction damage or environmental degradation. 42 , Chapter Two Literature Review Ultimate Limit State Analyses The procedure for ULS analyses adopted in this method conforms to BS8006 (1995) except that no Partial Factor is applied to the soil properties. Further this method differs in that a Factor of Safety of 2.0 is applied to sliding, bearing and pullout failure but no Factor of Safety is applied against rupture failure. Serviceability Limit State Analyses Two types of checks are performed within the analysis in order to satisfY SLS conditions that follow as: 1. The K.x O"~ check This check is to scrutinise the post-construction strain occurrIng in the reinforcements due to overburden pressure. The assumption is that wedges emanating from the toe at angles greater than (45°_ ~p'/2) mobilise full active pressure given by Ka, while wedges at angles less than ~p' mobilise zero active pressure i.e. K is zero. The active pressures acting on wedges at angles between ~p' and (45°- 4>p'/2) are obtained by linear interpolation, Fig 2.19. th The force mobilised in the i reinforcement T; is given by K. x cr'vi, at any point. For normal walls, the force required to mobilise 1% post-construction strain [Tlpcs] (usually around two-third of the creep limited strength) is determined for each reinforcement type from isochronous curves. The actual post-construction strain [Epc] in an individual reinforcement is then approximated by the equation: & =l pc T (2.17) lp~ Likewise approach is adopted for bridge abutments, but here the serviceability limit is reduced to 0.5% post-construction strain. 43 Chapter Two Literature Review 2. The WedgeCheck To perfonn the check, Out of Balance Force [OBF] for a series of wedges is first determined and then the OBF for each wedge is distributed amongst. the reinforcements cut by the wedge in proportion to their strength Figure 2.20. Groups of wedges at 2° intervals are analysed at the base of the wall and at levels of one tenth of the height of the face. The strain in each wedge for the individual reinforcement is then determined in accordance with Equation 2.17 and a strain distribution curve is obtained, Figure 2.21. The area under the curve divided by the reinforcement length is defined the average post-construction strain for each grid. 2.6.3 Limit State Approach The soil as well as the geosynthetics, both influence the behaviour of GRSSs, and the equilibrium is too complex to be reflected by a single 'lumped' factor or global Factor of Safety. Rather the procedure should be to select representative design values for the parameters influencing stability and then to perform calculations to show that possible undesirable design situations do not occur. This is considered in the Limit State Approach, Jewell (1996). The Limit State Approach differs from others in that no global Factors of Safety are used in this approach, rather Partial Factors are applied to the calculations where uncertainties lie. The aim of using Partial Factors is to distribute margins of safety to the places in the calculation where there are uncertainties. Further, Partial Factors have the advantage that "margins of safety" can be shared appropriately amongst the main parameters employed in the design. For example, a structure may be subjected to two Actions, one adverse and another favourable, so that the nominal value of each cancels the other. Thus the resistance required for the structure would be very small or zero, on the basis of the nominal Action. But in reality if one of the Actions is different from the expected value, the required resistance might be tremendously high. This possible situation can be arrested using Partial Factors, while could be missed in the global Factor of Safety approach, McGown et al (1998). 44 Chgpter Two Literature Review Essentially, there are two main areas of concern for design in Limit State Approach. Firstly, the risk of collapse must be shown to be acceptably small by means of Ultimate Limit State [ULS] calculations. Secondly, the risk of excessive deformations interfering with the functioning of the structure must also be shown to be acceptably small by means of Serviceability Limit State [SLS] calculations. The Limit State Approach of design is set out in International and European Standards (ISO 2394 and CEB Bulletin III) and is becoming widely accepted in geotechnical engineering. The draft Eurocode 7 (1995) for geotechnical engineering is based on the Limit State Approach. The Limit State Approach to the design of GRSSs should be based on internal force equilibrium and internal strain compatibility as set out by Jewell (1985) and (1988). Valid mechanisms for ULS and SLS analyses need to be identified first and then the appropriate parameters of the materials can be identified on the basis of these mechanisms. The mechanisms regarding the external stability and operational performance of GRSSs are considered to be the same as that for conventional soil structures. Only the differences between conventional soil structures and GRSSs are the mechanisms regarding the internal stability and operational performance. 2.6.3.1 A Model for Internal Ultimate Limit State Mechanism Long term sustained load [creep] test data for geosynthetics are most appropriate to the design of GRSSs under Single-Stage Actions. To simulate the creep test conditions and to facilitate the direct application of the test data to the design of a prototype structure, a constant Out of Balance Force [OBF] must be applied to the reinforcements from the End of Construction (EOC] to the End of Design Life [EDL]. A situation ofthis sort can be achieved only when the tensile strain in the soil is large enough to mobilise the large strain Constant Volume Angle of Friction [~'cv] at the End of Construction. Thereafter, until the End of Design Life, the soil may strain further whereas the mobilised shear strength of the soil will remain constant, i.e. the Constant Volume Angle of Friction [~'cv]will continue to be mobilised. 45 ChapterTwo LiteratureReview For the above condition, a Model Limit State Mechanism for GRSSs can be identified. In this model it is assumed that a constant load is applied to the reinforcements from the time of Switch-on of Gravity [tsOG]to the End of Design Life, [tEDd, Figure 2.22. Practically, all the loads are not applied instantaneously, although it is generally assumed that they are applied simultaneously at some point during the Construction Period, [iep]. Sometimes, the overall Construction Period may be much longer than the Reinforcement Loading Period, [tRL],depending on the construction procedures adopted. For example, a wall may be fully propped until the fill is placed to full height, during which time the reinforcements will not be loaded, but will be loaded only when the props are removed. This necessitates for the great care to be taken while selecting the Reinforcement Loading Period, [tRL]. When the loads are "switched-on", say at two-thirds the Reinforcement Loading Period, (2/3 tRL),they will develop a strain in the soil, [EsOGlsufficient to mobilise the large strain Constant Volume Angle of Friction [4>'cv] of the soil. If such a situation is achieved, there would be no change in the Out of Balance Force from the time of Switch-on of Gravity to the End of the Design Life and the geosynthetic reinforcements will always carry the same load. Long tenn sustained load [creep] test data thus directly apply and the Model Limit State Mechanism applies. 2.6.3.2 A Model for Internal Serviceability Limit State Mechanism As stated above, in practice all loads are not applied instantaneously. Similar to the Ultimate Limit State condition, it can be assumed that all the Serviceability Limit loads are applied at say two-thirds of Reinforcement Loading Period (2/3 tRL), although this depends on the construction procedures. Nonnally, these loads mobilise an Angle of Friction WmRL]in the soil less than the Peak Angle of Friction [lj>'p] , Fig 2.23. With time, the soil and the reinforcement strain and at the End of Desib'tl Life, the Mobilised Angle of Friction WmEDd is likely to remain less than the Peak Angle of Friction but higher than the Mobilised 46 Chapter Two Literature Review Angle of Friction at the End of Construction Loading. As the mobilised shear strength of the soil increases with time, the force required to be carried by the reinforcements will gradually become less, which means that the applied force on the reinforcements will change with time. If the change is significant, then an iterative approach to the determination of the deformations in the soil and the reinforcements must be undertaken. 2.7 Research outputs! Case studies related to Multi-stage actions Many tests have been carried out to identify the understanding of the behaviour of geosynthetics towards Multi-stage loadings in the past. Despite the fact that it is extremely difficult to create the situation that represents the actual multi-stage loading, utmost efforts have been made to simulate the practical multi-stage loading. Two cases of loadings namely: combined sustained plus cyclic and combined sustained plus short-term have been studied and researched in the past. Since the sustained plus cyclic loading case is out of scope of the present study, it is outlined in brief and the main emphasis is given on the sustained plus short-term loading case. 2.7.1 Sustained plus Cyclic loading A seismic event can be described as a sequence of repeated cycles, which are additionally applied over a sustained load. This situation consists of a dynamic and static loading part. Muller-Rochholz (1994) studied the effects of dynamic loading. The tests showed that a dynamic loading has no significant influence on the creep performance. In fact, if peak load is constant, the dynamically loaded specimen shows less creep deformation. This kind of load history is close to the deformation of mean level of load. The Combined Sustained-Cyclic Loading test on a range of uniaxial geogrids, carried out by Khan (1999), have confirmed these results. Traffic flow may be either frequent (without rest period between the vehicles passing) or rather less frequent (with rest period). He selected the case with no rest period, as it happened to be the 47 Chapter Two Literature Review more critical than that with a rest period, because there would be more 'locked in' strain in the material without rest period than the material with a rest period. Further, it was shown that the strains at the end of Loading and Unloading Phases were close to the strain envelopes obtained from the creep tests at a load level of[ps+ O.SP,]. This means under a total combined sustained-cyclic loading of [Ps+P,J, the uniaxial geogrid behaved as ifit was subjected to a sustained load of[ps+ O.5P,]. Therefore, it may be suggested that dynamic loading can be conservatively simulated by and appropriate sustained loading regime. Further, the practice of considering the traffic load as a sustained load equivalent to the contact tyre pressure by different codes/methods seems to be conservative in contrast to the test results. 2.7.2 Combined Sustained plus Earthquake loading Bommer et al (1999) showed that a seismic event is of a cyclic in nature; hence CRS testing is not essentially an appropriate test methodology. The duration of seismic events is important to obtain the realistic test results. During an earthquake, if a structure is deformed beyond its elastic limit, then the amount of permanent deformation would depend on how long the shaking is then sustained, Kupec (2000). 2.7.2.1 Duration of Earthquake This shaking is defined as the Earthquke Strong Motion by Bommer et al (1999). Therefore, it is important to ensure that the duration of the strong motion be consistent within the design scenario. The effective duration includes 91% of the total recorded energy released by the strong motion and also considers the rest period between sub-events in multiple events of this type. Khan (1999) showed that the creep deformation depends on these rest periods. A specimen is likely to show higher deformation when subjected to Cyclic Loading without rest periods. The variation of strong motion duration with distance is complex, i.e. depends on the geology. On one hand, as the energy wave separates due to different propagation 48 Chapter Two Literature Review velocities and scattering, the duration will increase with increasing distance. On the other hand, energy will decrease with distance due to attenuation of the motion. The review, of the recent major earthquakes at a distance of less than lOkm from epicenter for soil and rock sites including the Kushiro Offshore Earthquake (I 993) and the Northridge Earthquake (I 994), shows that, although there exist earthquakes with the Effective Durations of the Earthquake Strong Motion larger than 60 seconds, in most cases, they are below 20 seconds, Kupec (2000). This is the reason why the duration of the short-term loading was chosen to be 20 seconds. 2.7.2.2 Available test results Khan (1999) performed the combined sustained-short term loading test on a uniaxial geogrid. Generally, the seismic shakings are cyclic in nature with irregular frequency. To avoid the complexities of simulating the actual earthquake loading, it is represented by a uniform load applied over a short period of time. From these test results it was observed that after the removal of the Additional Short Term Load [&,], the geosynthetic is likely to show the same strain behaviour as that of a creep test under a load of25 kN/m, i.e. the sustained load alone. For lower levels of Additional Short Term Load [~P,], e.g. 10 kN/m and 20 kN/m, this was observed within 200 hours of the test. For higher levels of Additional Short Term Load [&,], e.g. 30 kN/m and 40 kN/m, although this was not observed within 200 hours of the test but it was likely to be observed after a longer period of time. 2.7.2.3 Case studies White and Holtz (I 997), reported on the performance of seven geosynthetic- reinforced structures (three walls and four slopes) with varying types and methods of reinforcements located in the areas that experienced the shaking of Modified Mercalli Intensity (MMI) from V to VIII during the Northridge California Earthquake of January 17, 1994. In no case was a failure (neither any significant displacement nor 49 Chapter Two Literature Review cracks) of the reinforced slope or wall observed, even in the areas where other nearby structures failed. Similarly, Tatsuoka (1997) reported on the performance of reinforced soil structures during the January 17,1995 Hyogo-ken Nanbu (Kobe) Earthquake with a magnitude of 7.2 on Richter scale, Tables 2.1 and 2.2. It should be appreciated that in general, older RWs (retaining walls) were damaged more seriously while masonry, leaning type and gravity type unreinforced concrete RWs showed a very low stability against the strong seismic shaking. Further, many cantilever type or inverted T-shaped (reinforced concrete retaining walls) RC RWs, mostly without piles performed badly. Further, a great number of RC (reinforced concrete) columns and piers collapsed by shear failure in a brittle manner. On the other hand, a number of geogrid or metal-reinforced soil RWs performed satisfactorily. In particular, the geogrid-reinforced soil RWs with full height rigid (FHR) facings that were constructed in 1992 at Tanata did not collapse despite the fact that the site was located in one of the most severely shaken and damaged areas. Based on these experiences, many damaged embankment slopes and conventional RWs were replaced with GRS-RWS with (full height rigid) FHR facings, Tatsuoka et al (1997). One of the two (geotextile reinforced soil retaining walls) GRS-RWs without FHR facings that experienced the earthquake showed no problematic deformation despite the cracks with a maximum opening of 20cm appeared on the ground surface in front of the wall and unequal settlement of 20cm was observed. While in the case of another wall, the ground settled unevenly and large crack reached to the subsoil below the facing blocks due to liquefaction in the subsoil in front of the wall. Yet, the deformation of the facing was smaller than that in the subsoil. Similarly, of the four GRS-RWs that experienced the quake, the three were located in the area where (Japanese Meteorological Agency seismic intensity) JMA scale was V or VI. In two cases, no deformation of the wall was observed, while in the third case the wall moved outward about 2cm maximum at the top ofthe facing. The GRS-RW 50 Chapter Two Literature Review located at Tanatata experienced the highest seismic load among the modern GRS- RWs and hence the scale of damage to this wall needs to be appreciated. The bottom of the wall moved outward on average about Scm relative to the supporting foundation subsoil, pushing the subsoil in front of the wall laterally. At the highest part of the wall, the largest outward displacement occurred, which was 26cm at the top of the wall and 10cm at the ground surface level. Despite the noticeable movement of the wall, the performance of the GRS-RWs were considered quite satisfactory, since in the areas adjacent to these GRS-RWs with FHR facings a number of wooden houses, railway and highway embankments and conventional types ofRWs were seriously damaged. These GRSSs, thus survived, were designed as per limit equilibrium-based pseudo- static static analyses using relatively a low seismic coefficient kh = 0.20. Probably, this situation results from a consideration that in case soil structures in secondary applications are damaged, the influence of damage would not be vast and serious and they could be easily repaired. On the other hand, use of higher kh values could lead to uneconomical structure. The seismic stability of the GRS-RWs was evaluated by the two-wedge method, Horii et ai, where the seismic loads are resisted mainly by the tensile force in the reinforcements and partly by the reaction force at the bottom of the facing. The design standard for railway earth structures (Ministry of Transport, 1992) specified the minimum allowable length of grid reinforcement for GRS-RW system to be the larger value of either 35% of the wall height or 1.5m. For most of the GRS- RWs constructed so far, to be conservative, several reinforcement layers were made larger than the others at lower levels. However, for Tanatata GRS-RW, all the reinforcement layers were truncated to nearly the same length due to construction constraints that is similar to that adopted in the design of modern GRSSs. This truncation might have reduced the seismic stability of the wall, particularly in terms of overturning. 51 ., Chapler Two Literature Review Further, several GRSSs were found to maintain stability during the Lorna Prieta Earthquake in 1989 having a magnitude of 7.1, Collin et al (1992), and Kushiro Offshore Earthquake in 1993 having a magnitude of7.8, Fukuda et al (1994). The GRSSs that survived the quakes, particularly the Kobe, were designed with a low seismic coefficient kh = 0.20 and the reinforcements were curtailed to the same lengths (Tanatata) due to construction difficulties, i.e. the lengths were not as per the railways guidelines. Yet, they did not fail except with a noticeable displacement, although other structures in the vicinity were badly damaged. This indicates the conservatism inherent in the design of the GRS-RW. The above data lead to the conclusion that the GRSSs were in deed capable of taking greater loads, had it been applied rapidly. The development of designs for GRSSs involving earthquake forces is presently empirical. Fukuda et al (1994) reported that until 1993, the GRSSs were designed for seismic forces on the basis of the procedure for design under ordinary static conditions, as given by Jewell et al (1984). In this procedure the long term creep rupture strength of geosynthetics was used as Reference Strength. Later, it was suggested by Fukuda et al (1994), AASHTO (1994) and Jones (1996) that the Design Strength of geosynthetic for sustained loading condition should be increased by 1.5 times when designing for sustained loading plus short term earthquake loading. In the recent codes/methods, as more confidence is gained from the performances of GRSSs during recent earthquakes, factored short term CRS strengths of geosynthetics are suggested for use in designs against sustained loading plus short term earthquake loading, AASHTO (1997), NCMA (1997) and DIBt (1998). Nevertheless, the considerations of higher strengths of geosynthetics, from 1994 to 1998, were all empirical without any concrete justification. An important aspect that may be noted that all these GRSSs were constructed very recently prior to the event, i.e. the time interval between the construction and the occurrence of the earthquake was not more than five years. This may be the possible reason for their survival of the shocks, since there would be more 'available' strain 52 Chapter Two Literature Review and less 'locked in' strain during the initial phase of the operational life in the geosynthetics and the reverse during the later phase. In other words, the GRSSs could take more loads in the initial part of its design life due to greater available strain but less load in the later stages of its design life due to lesser available strain. Therefore, it is unlikely that the GRSSs would be able to take the same amount of load throughout their design life regardless of the time of occurrence of the earthquake. Those GRSSs might not have survived the earthquake, had they been hit during the later part of their design life. If it were so, considering the same design strength of geosynthetics over the entire operational life of the GRSSs is likely to be unsafe. 53 Table 2.1 Damaged retaining walls for railways and roads, after Tatsuoka et al (1995) Facility SUe Location 'f)'pe of wall HeightlLength Subsoil Brief description of of wall Condition damageIPennanent restoration metbod Railway MSI Between Setsu.Motoyamll & Mnsonry 4 m/50m - Total Collapse! GRS-RW Sumiyoshi Slutions of m Kohc I,inc Railway MS2 Adjacent to Nlshi-Nada Station Masonry 3.4 !o3.8m! - Tilting of upper of Hanshin Main Line wall, SOxlm sctt1ement of cmbankmentJ GRS-RW Road MS3 City Road Nishi-Nada-Harada & Masonry Max. about 5m1 - Vertical & Horizontal crocking Rokko-.Sannomiya Lines o. 70m of wall, lateral deformation & Iwayakila ] & 4-chome, Nada- settlement of embankment Ku, Kobe city Railway LTI Between Setsu-Motoyama & Leaning -type 2.6m1500m Pleistocene Complete overturning, portia! Sumiyoshi Stations of JR Kobe gravel breakage at the level of subsoil Line fN m surfaoet GRS-RW, RW with =15-50up) embankment reinforced by large diameter nailinli!. Railway LT2 Between Okamoto & Mikagc Leaning -type S.Om/500xlm Tilting on both sides., cracking Stations ofHankyu Kobe Line - near the bottom, settlement of embankmentJ V-shaped RW --. ---. filled with cement treated soil Road LT3 City mad Higashi-Nada-Sato No Leaning -type Max. about 5m1 Vertical opening & horizontal 143 Line at Higashi-Nada. Ku, 160m sliding Kobe city at construction joint/ partial reconstruction to increase wall heiAAt Railway GTI Adjacent to Jshiyagawa Station of C'Ifavlty.type 5.0m/1OOx2m Holocene Tilting on both Hanshin main line sides, partial sand (N SI'T breakage at construction joint =1 ()-.]O) & overtumin21 viaduct Road GTl City road Ookubo No 18 line at GrllVity -type Mnx. 3.0/160m - Tilting, Longitudinal cracking Ookubo-eho, Akashi city of ernba:n.lanenV reconstruction of original RW Railway CLl Between Byogo & Shin-Nagata Cantilever-type 4.0m/400x2m Tilting on both stations of JR Sanyo Line - sides, settlement of embankment, defonnation of foot path! reinforcement by anchoring & tie rods Railway CL2 At Shin-Nagata Station of JR Cantilever-type 4.1m ( +5.3m Holocene Tilting & sliding,. Cracking at Sanyo line for overlying clay fN"" the middle height, settlement of emhankment,Y =5) embankmentJ GRS-RW, 200m Cantilever type R W with pile foundation Railway CLJ At Tanatata Between Ashiya & Cantilever.type 5.4m150m Holocene Tilting & sliding, settlement of Setsu-Motoyama stations of JR w;th pile sand & clay embankment/reinforcement by Kobe Line foundation fN horizontal tie rods connected to =25-50 ""& upper RW adjacent to RC box 10-25) Railway CL4 Adjacent to Ishiyagawa Station of Cantilever-type 5.0m/30m Holocene Hanshin main line Tilting, crocking at the middle sand (N SPT height of a section without Railway CL5 =I()-.30) counterfortsl viaduct Between Higashi- Nada & Kobe. Cantilever-type 4.5m ( +1.6m - Tilting, Crocking near the Kou stations of JR Kobe Line for overlying bottom, (freight branch) settlement of embankment)! embankmentJ cut off sheet 50m piles with tie rods & upper Road bock fiJI reinforeed by geogrid CL6 Prefactural highway Shiozc- Cantilever-type About 4m/80m (adjoining Subsidence, tilting & sliding of Mondosou Line ot Koma-No- waterway) wall, longitudinal fisswing of Machi, Takarazuka city embankment reconstruction of originalRW 54 Facility Site Location Type of wall HcightlLcn~th Subsoil Brief description of of wall Condition damagelPennanent restoration method Rom! CL7 City road Yamatc Main Line at Cantilevcr.type About 3m160m - Tilting of wa1~ longitudinal Yuminoki.I-Chome, Nada-Ku, fissuring of embankment! Terre Kobe city Annee Rom! CL8 City Road Nishi-Nada-Harada Cantilever - Max. about 5m/ - Tilting and vertical cracking of Rokko-Sannomiya ""d Lines at type? 250m wall, opening of vertical joint, lwaya-Kita 3 & 4 55 Facility Site Location Type of wall HeightlLength Subsoil Brier detcriptlon of orWlu Condition damageIPermanent restoration method Pari< TA2 In Hoshi-ga-oka Park al Tarumi- Terre Arnlee Max. 5.1ml - Tilting and sliding of facing, ku, Kobe City 43m partial cracking of facing at the corner/? Others TA3 In Midori-ga-oka Pool at Hami TcrrcAnncc Max. 33m! - Tilting of facing, partial Cily 36m cracking of facing at the oomer, settlement of embankment/? Road TM Approach Road to Akashi Kaikyo Tl.'1Te Annee Max. 6-7ml 1m - Noticeably compressing at the Bridge (under construction) at bottom of facingf7 Maiko, Tanuni-ku, Kobe Citv RW; retaining wa1I, GRS: geogrid.reinforccd soil, Terre Amlce: metal-strip reinforced soil with discrete RC facing 56 Table 2. 2 Damaged embankments for railways and roads, after Tatsuoka et al (1995) Fadlity Site Location Slope angle! Height! length Sublloil Brief description of damagel facing condition of condition pennanent restoration embankment method Railway EM! Between Hyogo & Shin-Nagata 1:1.51 cas1-io- 4.4m! 450m - Settlement and lllteml Stations of JR Sanyo Line place concrete (full deformation, sliding of lattice and embankment) concrete facing/embankment precast concrete partially reinforeed by pancl gcogrid and covered with , =embmne (artificial lawn Railway EM2 Between Higashi-Nada & Kobe- l :1.5/ vegetation 6.0m! 320m - Settlement and IlIleral kou Stations of JR Kobe Line (full deformation, longitudinal (freight branch) embankment) crack! embankment reinforced by large diameter nailinlZ Road EM3 Ookum-dani Interchange of the - 15m! 30m (full Soft clay Collapse of embenkm.ent/? Second Shinmei Expressway embankment) and partial sand (N,,.,. 57 Table 2.3 Factors of Safety in different design methods, after Khan(1999) AASHTO (1997) DIBt (1998) Sliding 1.5 1.5 Overturning 2.0 - Bearing 2.5 2.0 Rupture 1.2-1.5 - Pullout 1.5 2.0 ,I" 58 .. --", '. ...•.• --' . " _- ..:=.:""; >c.~Z~'r~:~J!:~" (a) Concrete faced (b) "Wrap-aronnd" faced (c) Bridge abutment (d) Dam Figure 2.1 Some examples of reinforced soil walls (after Bonaparte et aI, 1985) (a) Embankment (b) Landslide repair Figure 2.2 Reinforced slopes (after Bonaparte et al, 1985) 59 Reinforced fill Retained fill In-situ soil Sub-soil (8) With retained fill Reinforced fill In-situ soil Sub-soil (b) Without retained fill Widened Existing Widened In-situ soil Reinforced slope (c) Without retained fill Figure 2.3 Different sections of reinforced soil structures (after Pradhan, 1996) 60 Axial COIIIp. Low Low Hlab Low HiBb LIt. ceq. Low Low Low Low Low Flex. riJ. HiBb Low Low Low Low (a) Without compressible layer Axial camp. HiBb Hip HIgb High HiBll LaI. COlIIp. High HiBll HiBll High HiBll Flex. riB' HiBb Low Low Low Low (b) With compressible layer Figure 2.4 .Factors relevant to the nature of the facings (after McGown et ai, 1993) 61 (a) Wovens (b) Non-wovens (d) Strap. (c) Nets and grids (e) Uniaxial geogrids (I) Biaxial geogrids Figure 2.5 Forms of geotextiles and related products 62 a...lo....lo....lo.e_...lo....lo.e...lo....lo. • =444 4'44 4;' (a) Surface friction . ~ ..-.-_.•-- (b) Bearing stress Figure 2.6 Load transfer between soil and grid reinforcements 63 Reinforcing Elements I Relatively Inextensible Relatively Extensible Rupture Strain Rupture Strain < > Maximum Tensile Strain Maximum Tensile Strain', In soil without reinforcement In soil without reinforcement' , " ~- , ...- - Time and Temperature Time and Temperature Independent Dependent ,', Behaviour from Behaviour from Short Time Tests LongTime Tests ...' Geosyntbetics Steel, Fiberglass (Grids, Sheets, Streeps) , ' Figure 2.7 Classification of reinforcing elements after McGown et al (1978) 64 STRAIN Tertiary creep Creep rupture Secondary Primary creep 0- creep lA .-• Initial plastic strain Initial elastic strain TIME Figure 2,.g Idealised constant load creep curve under isothermal conditions 'v I' Loadl m 2 3 Ir Time (a) Loading applied Strain Total Elastic +Viscous ,/ +Plastic strains Elasti c recovery .• /Niscous+Plastic strains ./ Viscous recovery Elastic Ii- Permanent strain plastic strain 4', Time (b) Strain response Figure 2.9 Elasto-visco-plastic behaviour of geosynthetics 66 I ,I '.'. 67 (a) Maxwell model PI PI (b) Kelvin or Voigt model Figure 2.11 Various Mathematical Models 68 PI (a) Maxwell and Kelvin model PI (b) Standard linear model Figure 2.12 Various Mathematical models 69 FIGUREE 2.13(a) Scheme used in constanf'rate of strain tests Loadl Pptak PRupture Rupture Strain FIGURE 2.13(b) Load vs strain plot from constant rate of strain test 70 Test rig Load cell Sustained load FIGUREE 2.14(a) Scheme of test apparatus used in sustained loading creep tests 71 Strain (%) Time FIGURE 2.14(b) Strain verses time plots from sustained load creep tests 72 p I SPECIMEN 1 I I SPECIMEN 2 I I SPECIMEN 3 I P3 ;:;l Pz PI PI Pz P3 to t Figure 2.15 Series ofIoading verses time for deriving Isochronous curves (a) Total strain-time plot (b) Isochronous load-strain curves &r I ET=EE+Ey+Ep I p P3 P •...... t, Pz 3 Pz •...... _ . PI P, , _ _ _ ' ~ ! •• i i En En ! En to t, t En En En &r Figure 2.16 Deriving Isochronous load-strain curves for elasto-visco-plastic geosynthetics Loadl Isothermal Rupture loadim Isothermal Rupture I Reductioo _,_ =-- J~~~r~)."9'!".I'~ / Ref I Strain tdl Time (a) Based 00 CRS test data (b)Based 00 creep rupture data Strain , ,, ,, PI P • " 44-Raoge of •••Q> ,':,-1 rupture straios E P, t "',,,,. ';= •• lli!> Rupture straio, sa 00••• ~ /J - PI> P2> P, ;- Ij' j" Iostability limit straio, s. I ,', , Performaoce limit straio, sp .', ,,. (c) Typical Sberby-Dom plot Load/m Isochronous PRupture PRe! Strain (d) Based 00 performaoce limit strain Figure 2,17 Definitions of reference strength for geosynthetic reinforcements, after Khan (1999), 75 Load/m Isochrone for end of construction Isochrone for end of design life Prescribed post-construction strain limit Strain Figure 2.18 Assessment ofSLS base strength Tcs (after B88006, 1995) Assumed strain distribution K=K,. K=O Reinforcement being considered 45 -q>'!2 Reinforced section boundary Figure 2.19 The K,. x cr. check 76 Magnitude of force resulting from this particular wedge Wedge being considered Reinforced section boundary Figure 2.20 The distribution of force in the wedge check Strain Reinforcement length Figure 2.21 The strain distribution in the wedge check 77 WLcedi:wIS~ ••dqn lU •.•••••••••• Time if Reinforcement '!! Loading Period c.~~ 1 UUl Load ,9 ~- -r r;.•• ill* -=-..T ' J'5 I _08F_ I ~j I Time u I I I Time !soo (b) tEDL tsoo (c) fwL Figure 2.22 Model ULS mechanism (after McGown et ai, 1998) f SI.S~ J Time .U•• ] 0IlF_ ~ IDCRIR duD 10 cn:cp o@ .S innmaOfQftlc:k:mc:nc ~ .9 ••• aiirao ~m -. 1I&:miiduc'1O - ""- to IOiI f ~demaatlold~cun-. Time 1J Time (b) tEDL t_ tEDL o ",00 (c) STRAIN _0 - r l:,. EDL ,------COMPATlBll..lTy9 I p".".... -.,...... •• •••• crcep ~ -,- ~ ~ -- !l •••••••••• ~ '" = ~i SLS Condition AduoI -'!-fiJi l:,.EDL °B~ .;;;.. \..'~ •..... ~.9 ,!oil ••••••••• ITERATrON Time REQUIRED (d) tEDL !soo !soo Time J, 0 -..:. !L:J 1 Incr.a'lOg 10 Design lir. ~ •.. jf (0 Tensile Slrain in Soil Figure 2.23 Model SLS mechanism (after McGown et ai, 1998) CHAPTER THREE BEHAVIOUR OF MATERIALS UNDER DIFFERENT LOADING REGIMES 3.1 General Geosynthetics, being renowned for their complex behaviour towards loading have set forth a vital task for the designers to arrive at the appropriate values of the design inputs while designing geosynthetic reinforced soil structures (GRSSs). In order to choose the appropriate input design parameters concerned with geosynthetics such as Reference strength and Design strength, Partial Factors etc, it is utmost important that the mechanical behaviour of geosynthetics under different loading regimes and their load carrying capacity be clearly understood, i.e. in the manner they react upon subjection of loading. In this respect, Isochronous Strain Energy Approach, developed by Khan (1999), although articulates the isothermal properties of geosynthetics under different loading regimes, is much too complex for practical purposes. For this reason, to ease this complexity for the practising engineers, a simpler approach called Strain Envelope Concept is deemed necessary to be identified, which happens to be one of the objectives of the present study. In this chapter, different types of actions are discussed with examples and understanding of isothermal strain response of various materials ranging from perfectly elastic to elasto-visco-plastic (EVP), under these actions are made. Different strain components for these materials are identified and their various combinations depending on time to attain different limiting strains to produce strain envelope are also discussed. Further, the understandings of &R-&L plots for EVP materials under single-stage and multi-stage actions are also developed on the basis of Boltzmann's superposition principle. 3.2 Types of Actions 80 • Chapter Three Isothermal Behaviour Of Materials An Action may be defined as a load/force applied to the structure or an imposed or constrained deformation caused by temperature changes, moisture variation or uneven settlement, Eurocode I (1996) and DIN 1055 (1976). Actions for GRSSs should include all loads, forces and displacements related to any specific Limit State condition. In addition, the Duration of Actions needs to be considered, including changes in Actions resulting from changes in the properties of materials with time. There are various kinds of actions, that may be likely to be imposed on the structures during their operational tenure, identified and classified in many ways by various codes. Eurocode Classification Various types of Actions are identified in Eurocode I (1996) for structural engineering. Actions have also been suggested in Eurocode 7 (1995) for geotechnical engineering such as: Direct Actions can be classified in the following manner: • Actions varying with time: Permanent Actions e.g. self-weight of structures, fittings, fixed equipment, road surfacing etc. Variable Actions e.g. imposed loads, wind loads or snow loads. Accidental Actions e.g. explosions or impacts from vehicles. • Actions which vary spatially: Fixed Actions e.g. self-weight Free Actions e.g. movable imposed loads, wind loads, snow loads • Actions related to a structural response: 81 Chapter Three Isothermal Behaviour Of Materials Static Actions, which do not cause significant acceleration of the structure or structural member. Dynamic Actions, which cause significant acceleration of the structure or structural member. Dynamic effects may be taken into account either by increasing the magnitude of the static Actions or by the introduction of an equivalent static Action. Indirect Actions can be classified as: Permanent Actions e.g. settlement of support Variable Actions e.g. temperature effect. In simple term, the actions occurring in practice may be broadly grouped into two categories; • Single- stage actions (e.g. sustained, cyclic, impact etc.) • Multi-stage actions (e.g. stepped, sustained plus cyclic, sustained plus short-term etc.) These actions are il1ustrated with suitable diagrams in the fol1owing sections. 3.2.1 Single-stage actions The Actions when applied alone are termed as Single-stage Actions. Single-stage actions may be sustained, cyclic or short-term loading in nature. The sustained loading may represent the dead weight of the structure or surcharge on it. The cyclic loading may represent the traffic loads that are transient in nature. Similarly, the short-term loading may represent an impact due to an explosion or an earthquake force. Figure 3.1 il1ustrates the nature of different Single-stage Actions, i.e. sustained, cyclic and impact, respectively. Fig 3.1(a) is an example of sustained loading where a load PI is applied at to, sustained until II and removed there after. Fig 3.2(b) is an example of cyclic loading where the load PI is applied gradual1y from to to tl and 82 Chapter Three Isothermal Behaviour OfMa/erials released in the same fashion from tl to t2forming the loading and unloading phases in each cycle. The Action may repeat for a number of cycles. Similarly, Fig 3.I(c) is an example of an impact loading where a load PI is applied from tl to t2 for a short duration and released completely on one or more occasions during the life time of the structure. 3.2.2 Multi-stage actions It may be noted that the Actions imposed on theGRSSs are not wholly static, intermittent or dynamic. In most of the applications there will be a combination of any of the Single-Stage Actions, which are termed as Multi-stage Actions. Examples of Multi-stage Actions are stepped loading representing dead weight plus surcharge, sustained plus cyclic loading representing dead weight plus. traffic load, and sustained plus short-term loading representing dead weight plus impact load due to explosion or earthquake. Figure 3.2 (a), (b) and (c) demonstrate these Multi-stage Actions respectively. Fig 3.2 (a) is an example of stepped loading where a load PI is applied at to and sustained until tl, to which an additional load P2 is added and sustained until h. In the same manner, another load P3 is added to them at t2and sustained. Fig 3.2 (b) is an example of sustained plus cyclic loading representing dead load plus traffic load. A sustained load Ps is applied at to,to which a gradually increasing transient load P, is added from time t, to t2and released in the similar fashion from tl to t2, thus forming a complete cycle. Similarly another cycle is completed followed by the consecutive cycle, thus forming a chain of loading and unloading cycles. Fig 3.2 (c) is another example of sustained plus short-term loading. A sustained load Ps is applied at to and a sort-term load Pshort-tenn is imposed from t, to t2 and released. 3.3 Strain response of materials under Single-stage Action (SSA) The materials in engineering application may be chiefly categorised into elastic, plastic and viscous on the basis of their responsive behaviour to different loading regimes, i.e. the manner in which they react to the act of loading. However many 83 Chapter Three Isothermal Behaviour Of Materia is materials, owing to their complex intrinsic structure, may exhibit more than one. of the above properties, and hence may be typified accordingly. The behaviour of these materials upon subjection to loading may be best illustrated with the aid of figures as in the following sections. 3.3.1 Perfectly Elastic material Figure 3.3 (a), (b) and (c) illustrate the strain response of a perfectly elastic material under single-stage action (SSA), viz. sustained, cyclic and short-term loading, respectively. These are the qualitative plots of total strain verses time. In Fig 3.3 (a), at time to, the material has no strain at point A, but attains an instantaneous elastic strain EE, with the application of the sustained load PI corresponding to point B, Fig 3.I(a), which is sustained as long as the load is continued till time tl, point C. Immediately after withdrawal of the load PI at t], the elastic strain EE retards back to zero, point D. That is the whole of the EE strain is recovered leaving no residual flocked in strain, since the material is perfectly elastic. Fig 3.3(b) is a ET -t plot of a perfectly elastic material under the cyclic loading shown in Fig 3.1(b). The elastic strain increases gradually from zero at to, point A to EE t], point B as the load PI increases from zero to peak during the loading phase. This elastic strain EE reduces to zero following the reduction in the load PI at t2, point C. The whole of the elastic strain EE is recovered leaving no locked in strain EL. In the same manner, in the Fig 3.3(c), the elastic strain increases from zero, point A to EE, point B at t] with the application of the short-term load Pshort-tcnn as in the Fig 3.1 (c). This strain is sustained from B to C corresponding to the load Pshort-tcnn and retards back to zero at t2, point D leaving no locked in strain EL, i.e. the whole of the elastic strain EE is recovered. Thus in the case of a perfectly elastic materials it follows that 84 Chapter Three Isothermal Behaviour Of Materials 3.3.2 Perfectly plastic material Figure 3.4 (a), (b) and (c) are the qualitative plots of strain verses time showing the responsive behaviour of a plastic material corresponding to the loading sequences as in Figure 3.1(a), (b) and (c). In the case of sustained load in Fig 3.4 (a), at time to. there is no strain with zero load at point AlB. With application of the load PI, the plastic strain Ep increases gradually (linearly) until point C/D as long as the load is sustained giving ET ~ Ep (t ~ tl). Even after the load is withdrawn at time tI, the strain is not recovered at all and the material inherits a residual/locked in strain EL, which continues to be left over at any time t2, point E. Similarly, in the case of cyclic loading as in Fig 3.4 (b), the strain increases from zero to Ep following the increasing load Pt from zero to peak, from to to tl, point A to B, gradually during the loading phase. After reaching the peak. the strain Ep continues to persist even after the load Pt is released to zero gradually from tl to t2, point B to C, during the unloading phase. That is, no strain is recovered and all of the Ep is left as locked in EL. Hence, in the beginning of the next cycle the material has already acquired the lpcked in strain CL, point C. Fig 3.4 (c) is the case of short-term loading where the strain increases from zero to EP. time to to tI, point AlB to C/D, as the short-term load. Pshort-tenn is sustained. At time tl. although, the load Pshort-term is released to zero, the strain Ep does not recover at all and the whole of the cp is left as the locked in strain c. At any time t2, the locked in strain is equal to cp. Thus, for the perfectly plastic materials, it follows that 3.3.3 Elasto - plastic material The strain responses of an elasto-plastic material under SSA following the loading sequences as in Fig 3.1 (a), (b) and (c) are illustrated in the Fig 3.4 (a), (b) and (c), respectively. It may be seen from the figure that an elasto-plastic material behaves partly like an elastic and partly like a plastic material upon subjection to loading. 85 Chapter Three Isothermal Behaviour Of Materials For sustained loading, Fig 3.I(a), at time to(point A), with no strain with zero load, it acquires an instantaneous elastic strain gE (point B) upon application of the load PI, followed by a linear increase in plastic strain gp (' = 'Il until the load is removed (point C) at time tl, Fig 3.5(a). After removal of the load PI, there is an elastic recovery (gR = gE), leaving the plastic strain gp (t = 'Il as a locked in strain gL, that continues to persist corresponding to any time t2 (point E). In the case of cyclic loading, Fig 3.I(b), as the load PI increases from zero to peak, to to tI, the strain also increases from zero to gT (t = 'Il, to to t], Fig 3.5 (b), point A to B during the loading phase. During the unloading phase, as the load PI is released gradually, t] to t2,point B to C, the elastic strain gE is recovered gradually and fully at t2, point C, leaving whole of the plastic strain gp as the locked in strain gL. That is, in the beginning of the next cycle, the material will already have a locked in strain gL =gp (' = (2)'that will be followed by the similar pattern of strain as in the first cycle. Similarly, under the short-term loading as in Fig 3.I(c), at time to (point A), from no strain with zero load, the material acquires an instantaneous elastic strain gE, point B, as the load PI is imposed. This elastic strain gE is followed by the gradual acquisition of plastic strain cp, t] to t2, until sustenance of the load PI, point C, which is reduced entirely to the plastic strain gp, t2 , point D. To say, the entire elastic strain gE is recovered back, while the plastic strain cp is left as the locked in strain CL, so that at any time t3, the locked in strain gL =gp (t = (2) Hence it follows for the elasto- plastic materials that 3.3.4 Elasto-visco-plastic material 86 Chapter Three Isothermal Behaviour Of Materials An elasto-visco-plastic material exhibits the characteristics of an elastic in part, a viscous in part and of a plastic material in part, as can be appreciated from the Figures 3.6 (a), (b) and (c), which are the strain responses of this material to the different single-stage loading as in the Fig 3. I(a), (b) and (c) for sustained, cyclic and short-term, respectively. Fig 3.6 (a) is the strain response for the sustained loading as in Fig 3.1(a), where, at time to (point A), the material has no strain with zero load. With application of the sustained load PI, at time to, it acquires an elastic strain EE,point B, followed by an attainment of plastic as well as viscous strain (Ep+ Ev) gradually, with continuation of the load PI until time t/, point C. Following the removal of the load PI, the elastic strain EEis recovered completely leaving (Ep+ Ev) as locked in strain EL(191)'point D. With lapse of time, also the viscous part Ev of the EL('= 'I) is recovered gradually at t2. Eventually, at any time t3, the whole of Ev is recovered leaving Eponly as the locked in strain EL('= '2),point E. In the Fig 3.6 (b), which is the strain response of the cyclic loading as in Fig 3.1 (b), at time to (point A), the material has no strain with zero load. The strain increases gradually to Er (t= 'Il. from to to t" point A to B, as the load PI reaches to the peak gradually, during the loading phase. During the unloading phase, as the load PI is phased out gradually, there is elastic plus viscous recovery (EE+ Ev), from t1 to t2, point B to C, leaving the plastic strain Ep('= t I), as the locked in strain EL('= '2). This locked in strain will be accumulated at the commencement of the next cycle of loading. Similarly, Fig 3.6 (c) illustrates the strain response of the short-term loading as in Fig 3.1 (c). At to, there is no strain with no load, point A, but attains an elastic strain EE immediately with the application of the short-term load. This elastic strain is followed by the development of viscous and plastic strains as long as the load is maintained, tl to t2, B to C. When this load is released at t2, the elastic strain EEis fully recovered instantaneously and the viscous part Ev in due time. Ultimately at any 87 t ..' Chapter Three Isothermal Behaviour Of Materials time t], the plastic strain is left over as the locked in strain Ep. Consequently, it follows for the elasto-visco-plastic materials that 3.4 Development of ER- ELplot and strain envelope for elasto-visco-plastic (EVP) material Before proceeding to the development of the ER- ELplot and the strain envelope for EVP materials, it is necessary to appreciate the ways in which different strain components of EVP materials combine to yield a particular strain depending upon time and loading. For this reason, to have an understanding of different strain components and their combinations to yield total strain at any time for geosynthetics, Figure 3.7 may be considered where a series ofloads PI, P2 and p] are applied to the specimens I, 2 and 3, respectively. Their strain - time plots are portrayed in Figure 3.8. It may be appreciated from the figure that total strain may be attained with various combinations of strain components, viz. locked in and recoverable, for different loads and times. For example, if the material is to reach a total strain Etoat to, there can be only elastic strain EE]with load p]; whereas it may attain the same total strain Elj with load P2 at time t I, but with a combination of recoverable strain, ER2= EE2and a small amount of locked in strain, EL2.However, it may also attain the same amount of strain E'l with load PI at time t2 combining the recoverable strain EEl = ERIand a greater locked in strain ELI.Thus, it may be observed that the strain components uniquely combine for a particular total strain for different load levels depending on time. Figure 3.9 shows the curves for total strain EII and its components (recoverable strain ERand locked in strain EL)plotted against time. It can be identified from this figure that the total strain EI may be arrived at in various ways combining ER and EL 88 , Chapter Three Isothermal Behaviour Of Materials depending on time. The features of the curves indicate that recoverable strain ER decreases with time while the locked in strain ELincreases. Recoverable strain ERand locked in strain Et.,when plotted against each other as in the Figure 3.10, give rise to a strain envelop at the particular limiting strain ETI' It may be noticed that the same limiting strain may be arrived at with a higher value of recoverable strain ER and lower value of EL, point A; or a lower value of ERand higher value of EL,point B. It may also be appreciated from these figures that at initial stages of the loading, the recoverable strain ERis greater than the locked in strain EL,but later on, it becomes vice versa. In other words, if it were required to reach the limiting strain quickly, point A, large recoverable strain ERand small locked in strain ELwould be developed; . whereas the reverse would be employed if the same limiting strain were to be attained slowly, point B. 3.5 ER - EL plots for EVP material under different single-stage action (SSA) Figure 3. I I (a), (b) and (c) are the recoverable strain ER-locked in strain ELplots of EVP material for sustained, cyclic and short-term loading under single-stage actions (SSA), respectively. In Fig 3. II (a), the recoverable strain ERincreases from zero to ER(' ~to)as the sustained load PI is applied at to, Fig 3.I(a), with the locked in strain ELas zero. This EL increases from zero to EL(I ~ II)' to to tl, as long as the load is sustained. At time t], the ERdrops down to zero as the load is removed leaving the locked in strain EL(I ~ liJ in the material. Similarly, in the Fig 3.1 I(b), the recoverable strain ERas well as the locked in strain ELincreases gradually, from time to to tl, as the cyclic load increases from zero to the peak during the loading phase, Fig 3. I(b). During the unloading phase, tl to t2, as the load reduces gradually to zero, the recoverable strain ERretards back to zero leaving the locked in strain ELin the material. Thus, before the commencement of the next cycle, the material would have the locked in strain from the previous cycle. 89 ( Chapter Three Isothermal Behavimtr Of Materials In the case of short-term loading, Fig 3.11(c), the plot is similar to that in the case of the sustained loading, Fig 3.11(a). The l;R first increases instantaneously upon imposition of the load and maintained until the load is imposed, to to t], which retards back to zero as the load is released. In the contrast, the locked in strain l;L increases from the time of imposition of the load and remains there in the material even after the load is released. 3.6 Strain response of materials under multi-stage actions (MSA) In order to have a clear understanding of the strain response of various materials under multi-stage actions (MSA), it is required to elaborate the Boltzmann's superposition principle. This superposition principle, basically proposes that for a linear visco-elastic material, the strain response to a complex loading history is simply the algebraic sum of the strains due to each step in load. The principle is illustrated in the following paragraphs with the aid of the diagrams. Figure 3.12 (a) and (b) are the loading history and it's strain response against time, respectively. In Fig (a), a load p] is applied at to and sustained till t], whereupon an additional load P2is imposed. The total load (P]+P2) is then sustained until hwhere it is reduced to zero. The material thus inherits no load from t2 to t3, At tJ, it is again imposed upon with another load P3that is sustained. Figure 3.12 (b) illustrates the strain response ofEVP material, corresponding to the loading history in Fig 3.12 (a). At to,the strain response curve A corresponds to the load P]and at t] the curve B corresponds to the load P2. According to the principle of superposition, the total strain response at tlcan be represented by adding the curve B to A, as shown in the figure. At t2, as the load (P,+P2) are released the material experiences the elastic recovery followed by the viscous (A+B). The material assumes an additional strain as curve C at t3,due to application of the load P3. Which again is superposed onto the out-coming locked in strain curve. In this way, the strain response of EVP materials can be simply represented by the algebraic sum of the individual loading history. 90 Chapter Three Isothermal Behaviour OfMqterials 3.6.1 Perfectly elastic material Figures 3.13 (a), (b) and (c) are the illustrations of strain response of perfectly elastic material for stepped loading, sustained plus cyclic and sustained plus short-term loading under MSA, respectively. In Fig 3.13 (a), the material assumes an elastic strain at to, point A to B, due to the load Plas in Fig 3.2 (a). This strain sustains until point C, at tl, corresponding to the sustained load PI. where the material acquires additional elastic strain, point C to D due to another additional load P2. Thus total strain due to the sustained loads PI and P2 remains to be there until again, another load is imposed upon at t2and so on. Tn Fig 3.13 (b), the material acquires an elastic strain at to, point A to B that sustains corresponding to the sustained load P, as in Fig 3.2 (b). From tl to t2, the strain increases gradually as the cyclic load (traffic load) P, is applied gradually, point C to D and reaches the peak during the loading phase. This strain is recovered in the same fashion as the load P, is released gradually from t2 to t3, point D to E during the unloading phase, as the strain being purely elastic. Similarly, in .Fig 3.13 (c), the material with an elastic strain at to, point A to B, sustains it along with the sustained load P" point B to C. At tl, it acquires additional elastic strain due to application of the short-term load P,hort.""'"point C to D, sustains as long as the load is imposed, point D to E and reduces to the pre-event strain level, at t2. point E to F. That is, whole of the strain is recovered upon withdrawal of the short-term load, since the material being purely elastic. 3.6.2 Perfectly plastic material Figures 3.14 (a), (b) and (c) are, respectively, the illustrations of the strain responses of stepped, sustained plus cyclic loading and sustained plus short-term loading under MSA. In Fig 3.14(a), the material assumes the strain gradually, to to tl, point A to B, as long as the load PI is sustained. At tI, when an additional load P2 is applied, the strain is added up from tl to t2, point B to C, and so on for further additional loads. 91 Chapter Three Isothermal Behaviour OrMaterials In Fig 3.14 (b), the material acquires the plastic strain gradually from to to tl, point A to B as the load is sustained. From tl to t2, the strain due to the increasing traffic load Pt is added upon to that due to the sustained load P, gradually, point B to C, during the loading phase. During the unloading phase, point C to D, the rate of increment in strain is reduced due to the diminishing traffic load PI, t2 to t]. Nevertheless, the increment is there during the unloading phase as well, due to the sustained load. Similar accumulation of plastic strain is illustrated for further cycles in the same figure. The similar pattern as in (a) is shown in the Fig 3.14 (c). The plastic strain increases gradually from to to tI, point A to B due to the sustained load P,. From t] to h, the strain due to application of the short-term load P'hort-tenn is added gradually to that due to the sustained load P" point B to C. No strain is recovered even after recession of the short-term load P'hort-tcrm, at t2, since the material is perfectly plastic. There is a further increase in the plastic strain beyond C due to the sustained load and there is no recovery of the strain at all. 3.6.3 Elasto-plastic material Figures 3.15 (a), (b) and (c) are the diagrams portraying the strain response of elasto- plastic material for stepped, sustained plus cyclic and sustained plus short-term loading under MSA, respectively. In the case of stepped loading, Fig 3.15 (a), there is an acquirement of elastic strain at to, point A to B, with the application of the sustained load PI, followed by the plastic strain from to to t], point B to C as long as the load is sustained. At t], there is again an assumption of additional elastic strain, point C to D, followed by the plastic strain from t] to t2, point D to E, due to another additional sustained load P2. Similar pattern of strain follows for other additional loads as portrayed in the same figure. In Fig 3.15 (b), at to, there is an assumption of elastic strain followed by the plastic strain from to to t], point B to C, due to the sustained load P,. At tI, the cyclic load P, is applied which induces a gradual increase in strain from t] to t2, point C to D during the loading phase. The elastic but the plastic part of this strain is recovered upon 92 Chapter Three Isothermal Behaviour Of Materials release of the traffic load Pt gradually, from t2to tJ, point D to E, during the unloading phase. Similarly it follows for the other cycles. In the case of sustained plus short-term loading as in Fig 3.15 (c), at to and from toto tl, the strain pattern due to the sustained load Ps can be observed to be similar as in the case of sustained plus cyclic loading. At tl, an additional elastic strain is induced, point C to D as the short-term load Pshort.termis applied, followed by the plastic increase from tl to t2, point D to E, as long as the load Pshort-termacts. At t2, when the load Pshort-termis released the elastic part of the strain is recovered leaving the plastic strain as locked in, point E to F. Thus the material acquires an additional locked in strain after the subsidence of the short- term loading. 3.6.4 Elasto-visco-plastic (EVP) material In Fig 3.16 (a), which is an illustration of the strain response ofEVP material due to stepped loading under MSA, the material assumes an elastic strain at to, point A to B, as the sustained load PI is applied. This is followed by the gradual induction of viscous and plastic strain from to to tI, point B to C, until the load is sustained. An additional load P2is imposed onto the material at tl, that induces the additional elastic strain, point C to D, followed by the increase in plastic plus viscous strain due to sustenance of the load P2, from tl to t2, point D to E. Similar strain pattern is illustrated for another additional sustained load PJ in the figure. Figure 3.16 (b) is an illustration of the strain response of EVP material due to sustained plus cyclic load under MSA. At to, the material acquires an instantaneous strain due to application of a sustained load Ps, point A to B, followed by the gradual increase in viscous plus plastic strain, from toto tj, point B to C. A traffic load Pt, is applied at tj, that induces an additional strain increasing gradually and reaching the peak at t2, corresponding to the load PI, from tl to t2, point C to D during the loading phase. During unloading phase, from t2 to tJ, Point D to E, the strain is reduced gradually as the traffic load P, subsides. Thus there is an increasing locked in strain in the material after every cycle. 93 Chapter Three Isothermal Behaviour Of Materials Similarly, in Fig 3.16 (c), which is the illustration of the strain response of the EVP material due to sustained plus short-tenn load under MSA, the strain pattern due to the sustained load Pt is identical to that in the above case. At tj, a short-tenn load Pshort-termis applied which induces an additional elastic strain, point C to D, followed by the viscous plus plastic strain increase, from tlto tz, Point D to E. The elastic strain is recovered as the load Pshort-tennis released at tz, point E to F. Thus the material is left with a certain amount oflocked in strain after occurrence of the event (short-tenn load). 3.7 ER - EL plots for EVP materials subjected to different Multi-stage actions (MSA) Figures 3.17 (a), (b) and (c) are the plots ofERand ELfor EVP materials subjected to different multi -stage loading viz. stepped, sustained plus cyclic loading and sustained plus short-tenn loading, respectively. In the case of stepped loading, Fig 3.17 (a), the material achieves a recoverable strain ER upon application of the sustained load PI at to, point A to B. This recoverable strain ERremains constant but the locked in strain ELincreases from zero as long as the load PI is sustained, from to to tj, point B to D. Similar pattern of additional recoverable strain ERand locked in strain ELare illustrated in the figure due to another additional sustained load P2, from tl to tz. And so on and so forth for further stepped loads. Fig 3.17 (b) is an illustration of ER- ELplot for sustained plus cyclic case where the material acquires an instantaneous recoverable strain ERat to that remains constant whereas the locked in strain CLis induced from zero onward, from toto tj, point B to C, due to the sustained load P,. From tl to tz, as the traffic load Pt increases during loading phase, both the recoverable CRand locked in CLstrains increase gradually. During the unloading phase, from tz to tJ, the whole of the recoverable strain ERis recovered while the locked in strain ELin part with the release of the traffic load Pt. That is, after every cycle the locked in strain CLgets accumulated. Similarly in the 94 Chapter Three Isothermal Behaviour OfMateria!s further cycles, the recoverable strain ER and locked in strain EL increase during loading phase and reduce during unloading phase of the traffic load P(, gradually. In the same manner, Fig 3.17 (c), which is the illustration for the case of sustained plus short-term load, the recoverable strain ER is induced at !D, point A to B, which remains constant followed by the increase in the locked in strain EL from toto t], point B to C, due to the sustained load Ps. At tl, the recoverable strain ER increases instantaneously upon the application of the short-term load Pshort-term, point C to D, from where onward, the locked in strain EL is induced that increases until the sustenance of the short-term load Pshort-term, from t1 to t2, point D to E. This. recoverable strain ER retards back to the previous value at t2, point E to F, while the locked in strain EL does not, and continues to grow. . 95 p B c A to (a) Sustained p B t p c A D t1 t2 t (c) Impact/short term Figure 3.1 Examples of single stage actions 96 p P,+ P2 +PJ, J p]+ P2~ PJ P, P2 P, ~ tj t2 t~ (a) Stepped loading p P P, • t (b) Sustained plus cyclic loading p" • P, P, ~; 1 ~ t] ~ t~ (c) Sustained plus short term loading Figure 3.2 Examples of multi stage actions 97 &r= Total Strain BE = Elastic Strain ,B c BR =Recoverable Strain , C = E &R E A ..E ~ t (a) Sustained loading t (b) Cyclic loading B ~ C A , ,E t~ ~ (b) Short-term loading Figure 3.3 Strain response of perfectly elastic material under SSA 98 ., &T = Total Strain &p = Plastic Strain CID &L=Locked-in Strain t (a) Sustained loading t (b) Cyclic loading &p t (c) Short-term loading Figure 3.4 Strain response of perfectly plastic material under SSA 99 Er = Total Strain Er=EE+Ep EE = Elastic Strain =ER + EL Ep = Plastic Strain c ER =Recoverable Strain ...... } EL = Locked-in Strain ER =EE •. Ep (' ~ 'Il p D ...... j " . ! ! 1 A to t (a) Sustained loading Er=EE+Ep = ER + EL ER = EE ~ Ep(''"l2)= Ep (I~ 'I) tl ~ t (b) Cyclic loading Er=EE+Ep =ER + EL C B....::::IEp ('~(2) ER =EE D ,.. Ep(t=t ) = Ep(,~,) t1 ~ 3 t (c) Short-term loading Figure 3.5 Strain response of elasto-plastic materials to SSA 100 &T = Total Strain & T = & E+ & y+ & P &E = Elastic Strain &p = Plastic Strain ...... & T{t~t~ . =& R+&L &R =Recoverable Strain &L = Locked-in Strain &p+ & y =& y+&p &y E A to t (a) Sustained loading &or & T = & E+ & y+ & p =&R+ &L C ! & L(l~t) = & P(t=t) t1 lz t (b) Cyclic loading & T = & E+ & y+ & P = & R+ & L & p+ & y t (c) Short-term loading Figure 3.6 Strain response of elasto-visco-plastic material to SSA 101 p I SPECIMEN 1 I . I SPECIMEN 2 I I SPECIMEN 3 I PJ o IV Pz PI PI Pz PJ 1:0 t Figure 3.7 Series of sustained loadings verses time for deriving strain envelope for EVP material E,. P3 P2 PI &n = &RI + ⋘ for PI = &R2+&L2; forP2 o 1 &Ll o = &RJ+J{3; for P3 w- &E39&RJ &orl •...... ):.: . &E2=1&R2 Where, &RI < &R2< &RJ &LI > &Ll &El ! to t( ~ t Figure 3.8 Combinations of strain components for different sustained loadings to EVP material A ...... <;'------.1: TJ Bi I:L t Figure 3.9 Total strain I:T and its components for EVP material A ..- Strain envelop at limiting strain I:T1 B Figure 3.10 Plot of I: R - I: L and strain envelope for EVP material 104 c A D at to at t) (a) Sustained loading at to at t2 (b) Cyclic loading at to at t} &L (c) Short-term loading Figure 3.11 ER - EL plot for EVP material under different single stage actions 105 ~ LoadP (kN/m) PI +P2 \ P" P" ,~ ~ t,. (a) Loading history ...... A+B ; ...... • A B .,' Ii' C i t (b) Predicted strain response Figure 3.12 Strain response ofEVP materials using Boltzmann's superposition principle 106 ET t (a) Stepped loading B t (b) Sustained plus cyclic loading D E , B C F ~ G T ! U\ ! ~ t~ to tl ~ t3 (c) Sustained plus short-term loading Figure 3.13 Strain response of perfectly elastic material under multi stage actions (MSA) 107 t (a) Stepped loading t (b) Sustained plus cyclic loading t (c) Sustained plus short-term loading Figure 3.14 Strain response of perfectly plastic material under multi stage actions (MSA) 108 o A to tl t (a) Stepped loading A to tl ~ t3 t (b) Sustained plus SVclicloading D to t] t2 t3 t (c) Sustained plus short-term loading Figure 3.15 Strain response of elasto-plastic material under MSA 109 t (a) Stepped loading t (b) Sustained plus cyclic loading D G c B A to t (c) Sustained plus short-term loading Figure 3.16 Strain response of EVP material under MSA 110 F (a) Stepped loading ~~ ~~~~~~ , (b) Sustained plus cyclic loading at ~ at t1 at t2 at t) EL (c) Sustained plus short-term loading Figure 3.17 ER - EL plot for EVP materials under different MSA 111 CHAPTER FOUR ISOTHERMAL BEHAVIOUR OF SOME GEOSYNTHETICS SUBJECTED TO SINGLE STAGE LOADING 4.1 General A range of data required for the purpose of the present study was procured from various researches undertaken at the Department of Civil Engineering, University of Strathclyde, Glasgow, UK. These data have been obtained from CREEP tests, Unloading tests and Multi stage (combined sustained- short term) loading tests for a range of geogrids. The data thus procured, were analyzed using available techniques in order to correlate and compare the results with the understandings made for the geosynthetics under different loading regimes at isothermal conditions in Chapter Three. The outcomes of the analyses are eventually presented in self-explanatory graphical format for further interpretation. The main aim to analyze the data was to develop Isochronous curves so that total strain and its components; "Recoverable Strain" ER and "Locked-in Strain" EL could be obtained at different times for various limiting strains (2%, 5% and 10%). Eventually, ER - EL plots as well as strain envelopes at different limiting strains are developed in this chapter. Additionally, the test procedures for SSA are also briefly presented. 4.2 Test set up and Procedure Either factored short-term strengths from CRS tests or long term Creep test rupture strengths are used as Reference Strengths in the design of GRSSs by different codes and methods. Generally, two types of Single stage loading tests; namely CRS 112 Chapter Four Isothermal Behaviour OfGeosynthetics ToSSA (constant rate of strain) and CREEP (long-term sustained) tests are performed in order to determine the strength of geosynthetics. 4.2.1 Single-stage action (SSA) tests There are two types of single-stage loading tests, which are commonly employed and widely accepted to determine the strength of geosynthetcs; namely CRS (constant rate of strain) test and long term sustained CREEP test. The procedures for these tests are briefly outlined below. 4.2.1.1 Constant rate of strain (CRS) test The test specimen of geogrid or geotextile is cut to the specified shape and size by different standards. One end at top and one at bottom are clamped which are fitted to the CRS testing machine, Figure 2. 13(a). The load is applied hydraulically maintaining the rate of strain at which the test is performed. The lower clamp is fitted with the LTDV. transducers to a programmable data logger. Finally the data are recorded in the computer at specified intervals from which the plots of load and strain are developed, Figure 2.13(b). The test temperature by BS is specified as (20:t I) 0 C and the rate of strain as 7-13%. 4.2.1.2 Long-term sustained CREEP test The scheme of test apparatus used in sustained load creep test is shown in Figure 2.14(a). The specimens are cut to shape and size as specified in different standards. The upper end is fixed to a clamp that is fixed to the machine. The lower end is fixed to a clamp where it is loaded. Different specimens are loaded with different eights, e.g. 5, 10, 15kN/m and so on. The lower clamp is fitted with the LTDV transducers that transmit the readings to computers. For the first minute the readings are taken at I, 2, 4, 8, 16, 30 and 60 seconds. From Imin to Ihr they are taken at 2, 4, 8, ... minutes and after Ihr they are taken at every 24hrs up to 10000hrs.These data are used to plot strain-time plots from which load strain curves are developed for further usage. The test temperature for this test is similar to that of the CRS test in BS. 113 Chapter Four !solherma! Behaviour Of Geosynlhelics To SSA 4.3 Extrapolation of CREEP test Data Mostly GRSSs are designed for an operation period that is greater than the duration of long term CREEP tests. Therefore, it becomes necessary to extrapolate CREEP test data to the required design life of the structure. In the same manner, it also becomes essential to extrapolate CREEP test data at higher load levels other than those employed during the tests. Khan (1999) showed it that the data for much larger duration than the CREEP test could be obtained by extrapolation using best curve fitting technique. The data from Creep tests perfonned on SS2 and SR80 geogrids are collected for analyses. The Creep tests were undertaken at 20°C on SS2 geogrid at a series ofload levels like 6.9,8.5, lOA and 13.8 kN/m; and similarly that on SR80 geogrid at 5, 10, 15, 20, 25 and 30 kN/m load levels. Figures 4.1 and 4.2 are the total strain-time plots developed from these data. The test data thus obtained from different research works have been modelled using mathematical modelling suggested by Esteves as outlined in chapter two. Two types of equations were found to fit the curves derived as total strain-time plots from the CREEP tests at different load levels, i.e. power series for SS2 and logarithmic series for SR80, Figures 4.3(a) and (b) respectively. The typical forms of the equations are gIVen as: (for power series) Eq4.1 y = A Ln (x) + B (for logarithmic series)' Eq 4.2 Thus the parameters A and B were separated and plotted at different load levels where a linear fit was found to represent them, Figures (a) and (b) of 4A and 4.5. The equations of both parameters for the geogrids are in the fonn of (y = a x + c). From these linear fits, the parameters A and B have been extrapolated at higher load levels required for the study which upon substitution into the above equations generate the required total strain-time curves at higher load levels. In this way, the CREEP test data were extrapolated at higher load levels viz. 18.8, 23.8, 28.8 and 33.8 kN/m for 114 Chapter Four Isothermal Behaviour Of Geosynthetics To SSA SS2; and 37.5, 45.0, 52.5, 60.0, 67.5 and 75.0 kN/m for SR80 geogrids respectively so as to obtain the required loads at different times corresponding to the total strain of 10% 4.4 Isochronous load-strain curves and strain envelopes There are numerous forms in which the data from the strength tests on geosynthetics may be presented. However, the most convenient and broadly accepted form is to present them as Isochronous Curves. These are the load-strain curves for different times at a constant temperature. Figures 4.6 and 4.7 are the load-total strain plots derived from the total strain-time plots (Figures 4.1 and 4.2) at 20°C and different load levels for SS2 and SR80 geogrids, respectively, following the procedure described in Chapter 3. Once the Isochronous curves have been derived, the strain at any load level for any time may be found. Alternatively, the load corresponding to a particular strain for any time could be found from these curves. Thus the curves for 0.0 I, 0.1, I, 10, 100 and 1000 hrs may be used to obtain the strengths (strain) at various loads up to 1000 hrs. In the same fashion, the curves for larger duration may also be derived. In order to derive the load- locked in strain curves, a set of data from the Unloading tests that were performed at 20°C for the same geogrids at different load levels have been compiled and extrapolated at higher load levels, Figures 4.8 and 4.9, from which the recoverable strain at any load level may be found. Recoverable strain ER is attributed to solely elastic recovery and therefore the value would be constant at a particular load level irrespective of time. The Figures 4.10 and 4.11 are the load-locked in strain curves, which have resulted from the fact that (EL= ET - ER), i.e. after subtraction of Figures 4.8 and 4.9 from the corresponding Figures 4.6 and 4.7. For various limiting strains viz. 2%, 5% and 10% the loads are obtained from the Isochronous curves which are then used to find the corresponding recoverable strains and thus the locked in strains. Figures 4.12, 4.13 and 4.14 show the total strains and 115 Chao/er Four Isothermal Behaviour OfGeosvllthetics To SSA their components vs. time for the limiting strains of 2%, 5% and 10%, respectively for SS2 and SR80 geogrids. Once the strain components, I. e. ER and EL are obtained, they have been plotted against each other giving rise to the envelopes. Figures 4.15(a) and (b) show the ER- EL plots at 2%, 5% and 10% limiting strains for SS2 and SR80 geogrids respectively. It should be appreciated that these envelopes have identical linear patterns. 4.5 Discussion on test results In order to reach the strain of 10%, the total strain-time data have been extrapolated at higher loads. These curves exhibit linear extension behaviour. The Isochrones derived from these strain-time plots comply with their general shape. However, more linearity is conspicuous at higher load levels due to extrapolation. It was identified in Chapter Three that geosynthetics would develop strain upon loading and that this total strain ET at any time comprises of strain components called "Recoverable Strain" ER and "Locked-in Strain" EL. From the fact that, ET = ER + EL for any time, the plots of load- locked in strain are developed which are resulted by subtracting Figures 4.8 and 4.9 from the corresponding Figures 4.6 and 4.7. These curves also have similar pattern to the Isochronous curves. Also the strain components ER and EL at 2, 5 and 10 % limiting strains for SS80 and SS2 are obtained using the same relation, i.e. EL = ET - ER and plotted along with ET against log (time) scale, Figures 4.12 through 4.14. These figures show an agreement with the Figure 3.9. From these figures, it may be appreciated that the strain components may combine at any time uniquely to yield the total strain. The locked in strain EL is seen to be very small at initial stages but increases with time, in contrast with the recoverable strain ER that is reverse. At one point, they are even equal. In other words, if the geosynthetic were to assume a particular strain in a very short period, it would acquire greater ER and a smaller EL. On the other hand, if it 116 Chqpter Four Isothel?!fQfBehaviour OfGe05';nthetics To SSA were to assume the same strains in a longer dUmtice a sm:aii Ett but larg,w-fiL. would be acquired. This will become clearer in. the folkw;iDg pmgrapn. It may be noticed that for each limiting strain, the &R vs. &L plots for SS80 and SS2 show an agreement with Figure 3.14. Again, ifit were to reach the limiting strain in 1 hr, it would acquire a very large &R but small &L; whereas if it were to acquire the same strain in say 1000 hrs, a small &R but very large &L would be required. Thus the geosynthetic may acquire a particular strain with various combinations of &R and &L depending upon time. 4.6 Summary • Isochronous curves Of many forms, Isochronous curves, which are the load-strain curves for different times at a constant temperature, are the mostly accepted and convenient forms to represent test data. Strain at any load level for different times can be found from these curves, or vice versa. • Strain components and strain envelope The total strain in geosynthetics upon loading consists of two components, namely recoverable &R and locked in &L strains. These components combine uniquely for different times to yield a particular strain at isothermal conditions and when the plotted against each other they result in a strain envelope for a particular strain. 117 15 -.- 6_9kN/m -.- 8.5kN/m -.-IOAkN/m -y y- -Y-13.8kN/m ~ 12 ~~ // /Y 9 • ~ 1 ~~ ;;. ~.s- o: / -03 tl • • 6 / .--. 'IS ~ .---- ~ ".---- / .' - -. • • /• ---.-. 3 o o 250 500 750 1000 Time (hrs) FIGURE 4.1 Total strain vs time plot from creep test for SS2 at 200C 118 15 -.-5kN/m -e-10kN/m -~-15kN/m -9'-20kN/m 12 -,-25kNlm -+-30kN/m 500 1000 1500 2000 2500 3000 3500 Time (hrs) FIGURE 4.2 Total strain vs time plot from creep test for SR80 at 20.C 119 y ~ 1.9666xO.1455 -+-6.9kN/m Power series (a) For SS2 y ~ 2.5398xO.1494 -e-S.5 kN/m trend lines y ~ 2.9628xO.1584 -.!>- 104 kN/m y~4.512xOI595 ~13.8kN/m 16. ---- 14 - 12 ;? 10 "---'~ ~ 8 S 6 0 f- 4 2 o ----,------(-- - --~----'---' o ZOO 4()0 600 800 \000 1200 Time (hrs) y ~ 0.0461Ln(x) + 0.5946 .5 kN/m (b) For SR80 Logrithmic series trend lines y ~ 0.1 093Ln(x) + 1.3223 1lII10kN/m y ~ 0.IS95Ln(x) + 2.2216 lJ. 15kN/m y ~ 0.2621 Ln(x) + 3.0376 X20kN/m y ~ 0.3367Ln(x) + 3.5049 J:25 kN/m y ~ 0.35Ln(x) + 4.7414 .30 kN/m 3000 4000 Figure 4.3 Curve fitting into total strain-time plots 120 y = 0.3642x - 0.6105 (a) For SS2 5 4 «: E 3 - .<3" !Ei 2 0 u" o ------~-~~---.----. o 5 10 15 Load kN/m y = 0.0124x - 0.0073 (b) For SR80 0.4 0.35 0.3 - «: E 0.25 - .0" 0.2 !Ei 0 0.15 U" 0.1 . 0.05 - 0 0 5 10 15 20 25 30 35 40 45 Load kN/m Figure 4.4 Deriving the coefficient A for extrapolation 121 .... _. - -- -_._-- -_.~--_._---_._-- (a) For SS2 y = O.002x + 0.1322 I.Linear fit I 0.162 --~----~-- 0.16 0.158 .. 0.156. 0.154 - 0.152 0.15 - 0.148. 0.146 0.144 ------, ------, . o 5 10 15 Load kN/m (b) For SR80 y = 0.1671:\ - 0.2904 10 9 - 8 ~ 7 E 6. '<3" IE 5. 0 4 U" 3 2 - I. O. 0 5 10 15 20 25 30 35 40 45 50 Load kN/m Figure 4.5 Deriving the coefficient B for extrapolation 122 50 --+-lOOOhr ----+- IOOhr ~lOhr ~Ihr 40 _.Ihr -.Olhr 30 10 o o 3 6 9 12 15 18 Total strain e,.(%) FIGURE 4.6 Load vs Total strain plot from creep test for SS2 at 20"C 123 50 -+-1000hr ---+-100hr -T-10hr ----6-1hr 40 -.1hr -.01hr 30 ~ E -z ~..>< a. ""C Ol 0 20 ...J 10 o o 2 4 6 8 10 Total strain e,- (%) FIGURE 4.7 Load vs Total strain plot from creep test for SR80 at 20.C 124 •• 50 I--I~lo-t. I 40 30 ~ S Z C 0.. -g 20 0 -l 10 o o 3 6 9 12 Recoverable strain e (%) R FIGURE 4.8 Load vs Recoverable strain eR plot from unloading test for 552 at 20.C 125 50 1- t= to-t~ I 40 10 o o 369 12 Recoverable strain &R (%) Figure 4.9 Load-Recoverable strain &R plot for SR80 at 20°C 126 50 -+-lOOOhr ----+- 100hr -"f'-]Ohr -.a.-lhr 40 -e-.lhr -.-.Olhr 30 20 10 o o 3 6 9 12 Locked in strain (%) FIGURE 4.10 Load - Locked in strain plot from creep test for SS2 at 200C 127 50 -.-.Olhr --.Ihr -A-Ihr -,,-IOhr 40 -+-lOOhr -+-lOOOhr 30 ,'",-".~,. '.1:",' ~ j IJI.f' -€ ~ ~ "g 20 1/11/1 -'0 jl/III 10 jJ/~ fir o o 3 6 9 12 Locked in strain (%) FIGURE 4.11 Load - Locked in strain plot from creep test for SR80 at 200C 128 •• 5 -- Total strain aT 2% -- Recoverable strain SR ---6--- Locked ill straill S 4 3 ~ ~ ::: •••l: 2 • • • • • • '" o IE-3 0.01 0.1 10 100 1000 10000 (a) For SS2 Log.Time (hrs) 5 -- Total strain aT 2% -- Recoverable strain OR ---6--- Locked ill strain 0L 4 ~ ~ 3 •~ .S •• (I)- 2 • • • • • • >< : : : o IE-3 0.01 0.1 10 100 1000 10000 (b) For SR80 Log.Time (brs) Figure 4.12 Total strain and it's components vs Time plot at 20°C 129 10 • -- Total strain "T5% -- Recoverable strain "R ~ Locked in strain ", 8 6 ~ 0~ ~•.. • • • • • • c'" 4 ~ 2 o IE-3 0.01 0.1 I 10 100 1000 10000 (a) For SS2 Log.Time(brs) 10 -- Total strain "T5% -- Recoverable strain "R 8 ~ Locked in strain ", ~ ~ 0 6 ~•.. c"' 0i! • • • • • • ;;; 4 2 >< : : : o lE-3 0.01 0.1 10 100 1000 10000 (b) For SR80 Log.Time (hrs) Figure 4.13 Total strain and it's components vs Time plot at 20"C 130 12 10 • • • • • • 8 IO -- "T % ~ 6 e~ -", '-' ~" w•• .~= 4 ~ '" 2 o IE-3 om 0.1 10 100 1000 10000 (a) For SS2 Log.Time (hrs) 12 10 • • • • • • 8 ~ e~ '-' w•• 6 1O .9•• -- "T % b -"p '" 4 ~" 2 o IE-3 0.01 0.1 10 100 1000 10000 (b) For SR80 Log.Time (hrs) Figure 4.14 Total strain and it's components vs Time plot at Wee 131 10 -.-10% -.-5% -*-2% Fiigure 4.15 Strain envelopes at different strain levels for SS2 and SR80 geogrids at 20"C 132 CHAPTER FIVE ISOTHERMAL BEHA VIOUR OF SOME GEOSYNTHETICS SUBJECTED TO MULTI STAGE LOADING 5.1 General The objective of the study was to present and interpret the outcomes of the Multi- stage loading test from the strain envelope concept developed in the way described in the Chapter Four. Therefore the results from the Multi-stage (combined sustained- short term) loading test performed by Khan (1999) are presented here. Further, the results are superimposed on the ER - EL plots and interpreted with the highlights on the second stage loading effects, time of occurrence of an earthquake and available strain in the geogrids. In other words, the variation of the capacity of GRSSs to take additional shock due to seismic events is interpreted from the strain envelope concept in terms of available strain which itself is likely to depend on the time of occurrence of an earthquake. 5.2 Test set up and Procedure The Single stage loading tests; namely CRS (constant rate of strain) and CREEP (long-term sustained) tests are performed in order to determine the strength of geosynthetics. These tests alone are inadequate to represent the actual loading conditions arising after construction and operation of GRSSs, because in practice it is seldom that the structures would encounter SSA only. Rather they would experience Multi-stage loading in most situations. In MSA situations again, two types loading are commonly imposed on GRSSs; one, combined sustained plus cyclic and another, combined sustained plus short-term. The first case represents the self-weight plus traffic loads, while the second one the self-weight plus earthquake loads. The present study is focused on the latter only. 133 Chapter Five Isothermal Behaviour OfGeosvntheticsTo MSA During the Multi-stage loading test (combined sustained plus short-term), the loading on the structure has been considered in three stages as shown in the loading scheme, Fig 5.1. Stage I represents the state where the GRSS is being acted upon by the self- weight alone. Stage2 represents that where the short-term load is being applied in addition to the self-weight of the structure. The application of the Short-term load is arbitrarily chosen to be 100 hrs from the assumption of the sustained load in order to allow for the time gap between the construction and occurrence of an earthquake. Stage3 represents again the loading state similar to the Stage 1, but after withdrawal of the short-term load, i.e. after the subsidence of the earthquake. The duration of the Stage2 loading was selected to be 20 sec, because the effective periods of most earthquakes were found to be less than 20 sec, Figures 5.2 and 5.3, Kupec (2000). Thus the consideration of the loading period of the short-term load (Stage2) for 20sec is likely to be on pessimistic side. Further, the pattern of seismic forces is cyclic in nature with irregular frequencies and it is tremendously difficult to model the seismic loading from an actual event in the laboratory testing conditions. Therefore, to avoid the complexities in simulating the earthquake load in the test, a uniform load equivalent to the maximum load from a seismic event over 20sec period is imposed in Stage2. The material upon loading with (Ps + P,) during Multi-stage loading (combined sustained plus cyclic) test behaved as if it were loaded with (Ps+ 0.5 P,), Khan. Hence, representing the actual earthquake load with a sustained load equivalent to the maximum load from a seismic event over the period of 20 sec in Stage2 is likely to be pessimistic. 5.2.1 Multi-stage action (MSA) tests For Multi-stage actions, there are two types of tests being developed; combined sustained plus cyclic loading. to represent the self weight plus traffic load, and combined sustained plus short-term loading representing the self weight plus earthquake load onto GRSSs. The scope of the current study being the latter, the test set-ups for this test are presented in the sections below. 134 Chapter Five Isothermal Behaviour OfGeosVIltheticsToMSA 5.2.2.1 Combined sustained-short-term loading test Loading Scheme Figure 5.1 shows the loading scheme adopted in the combined sustained-earthquake loading. The scheme consisted of three stages. In Stagel, a sustained load [Ps] was applied and maintained over the entire tenure of the test. In Stage2, i.e. at the end of 100 hours of Stagel, an additional sustained load [~Ps] was applied for a maximum period of 20 seconds. In Stage3, i.e. at the end of total duration of 100 hours plus 20 seconds, the additional load [~Ps] was removed and the material was left with only Stage I sustained loading [Ps] for another 100 hours. Tests were carried out for different combinations of Stage I and Stage2 loadings. In all cases, Stagel loading was 25.0 kN/m and Stage2 loading was varied from 10 kN/m to 50 kN/m at an increment of 10 kN/m. Test Material, Sampling and Conditioning The material used for the test was Uniaxial geogrid B. The samples were extracted from a roll as per recommended in BS6906: Partl (1987). First two turns as well as 100mm from either edge were discarded. None of the samples was taken from the same row and column. The geogrid test specimen contained five ribs within the width and one cross- member along the length, excluding cross-members by which the sample was held in the clamps. Of the five ribs, two outer ribs were cut at least lOmm away from any node, which resulted in three numbers of effective ribs subjected to tensile force. The dimensions of the geogrid test specimen are shown in Figure 5.4. Samples were conditioned for 24 hours at (20 '" 2)OC temperature and 65 '" 2 % relative humidity before commencing the tests. 135 Chapter Five Isothermal Behaviour Of GeasyntheticsTo MSA Test Apparatus and Methodology A special testing rig was developed at the University of Strathclyde for this test, Figure 5.5. Different states of the test apparatus at various stages of testings are shown in Figure 5.6. A calibrated load cell was placed in the central position of this bar. The top clamp for holding the specimen was attached to the load cell via a mild steel saddle. A specimen of uniaxial geogrid B was then slide from one side through the jaw-shaped gap in the top clamp. The bottom clamp was also slide through the bottom part of the hanging specimen of the geogrid. Two calibrated LVDTs were attached to either side of the top clamp for measuring deformations. The load cells and the LVDTs were then connected to a programmable data logger. This data logger was further connected to a 486DX computer to facilitate transfer of data from the data logger to the hard disk. The data logger was programmed to record data in accordance with the creep test methodology described in BS6906: PartS (1991) for Stage 1 and Stage3 loading. For Stage2 loading, the data logger was programmed to record data at an interval of 0.2 second . • The Stagel loading was then placed on a fork-lift in the form of lead bars. The arrangement of lead bars consisted of a vertical screw road having a stainless steel saddle on top and a small and nearly square hollow box at the bottom of it. The data logger was then started and the dead loads were applied to the specimen within 5 seconds. After 100 hours, i.e. at the end of Stagel, the dead loads were connected to another loading platform through a screwed rod for the application of Stage2 additional sustained loading for a maximum period of 20 seconds. During this period of 20 seconds in Stage2, loads and deformations were measured by the load cell and transducers. In Stage3, it was essential to ensure instantaneous recovery of the material and free fall of the additional load in Stage2 without disturbing the specimen and the sustained load in Stagel. For this purpose a release mechanism was developed which consisted of a connection thread which was cut to remove the Stage2 loading 136 Chapter Five Isothermal Behaviour Of GeosvntheticsTo MSA instantaneously. Further, to prevent the clamped specimen from shooting back, thus disturbing the test and damaging the LVDT's, a guide mechanism was developed, Fig. 5.7. The loads and deformations in this stage were recorded in the data logger. 5.3 Discussion on test resuIts The Sustained-short term loading test was designed to simulate the sustained- earthquake loading in the laboratory. The earthquake accelerations are cyclic in nature having irregular frequencies. Due to the complications involved in simulation, they are represented by a uniform load applied over a short duration. This consideration of a uniform load is likely to be conservative, Khan. The test was carried out on uniaxial geogrid B and comprised of three stages. Stagel consists of a single level of Sustained Load [P,] to simulate the sustained loads acting on a GRSS, Stage2 consists of the original Sustained Load [P,] plus various levels of Additional Short Term Loads [AP,] to simulate an earthquake loading and Stage3 consists of the original Sustained Load [P,] to simulate the sustained loads acting on a GRSS after the earthquake. The loading scheme chosen for the tests is as shown in Figure 5.I.The Stage I Sustained Load [P,] was 25 kN/m which is the long term Design Strength of uniaxial geogrid B at 20°C according to BS8006 (1995). The Stage2 Additional Short Term Loads [AP,] were varied from 10 kN/m to 50 kN/m in increments of 10 kN/m, applied over a period of20 seconds. The maximum Total Load of75 kN/m in Stage2 was chosen as this was the strength obtained in CRS tests carried out at the University of Strathclyde at a strain rate of 25% per minute. The duration of Additional Short Term Load [AP,] was chosen on the basis of the durations of the main strokes of Kushiro Offshore Earthquake in 1993 and Northridge Earthquake in 1994, reported by Fujii et al (1996) and Frankenberger et al (1996) respectively. The time for application of the Stage2 loading was arbitrarily chosen to be 100 hours after the start of Stagel loading, in order to allow for the time gap between the end of construction of a structure and the occurrence of any earthquake. After removal of 137 Chapter Five Isothermal Behaviour OfGeosvntheticsTo MSA the Stage2 Additional Short Tenn Load [liPs] after 20 seconds, the Stage3 loading was again equal to 25 kN/m. To observe the material behaviour in the Stage3, this sustained load was maintained for a further 100 hours. Figures 5.8(a) and (b) portray the test results over the entire period of 200 hours in 'hours' and 'seconds' Time scale showing the strains in Stage2 and Stage3. It should be noted that only under Additional Short Tenn Load [liP,] of 50 kN/m in Stage2 the material strained more than 10% and rupture in 18 seconds. Therefore, no Stage3 was available for this combination of load. For other Additional Short Tenn Loads [liP,], i.e. for 10 kN/m to 40 kN/m, the Total Strain of the material was less than 10%. It should be noticed that at all Additional Short Tenn Loads [liP,] of upto 40 kN/m the material showed more or less linear extension behaviour, except 50kN/m at which it showed non-linear. The results for each level of Stage2 Additional Short Tenn Load [liP,] are presented in Figures 5.9 to 5.12, in nonnal and in semi-log plots. The Total Strain in Stage3 may be observed to have remained almost constant at least up to 200 hours. At the lower levels of Stage2 Additional Short Tenn Loads [LiP,], i.e. 10 kN/m and 20 kN/m, the strain behaviour in Stage3 was similar to that of Creep test under a load of 25 kN/m. However, at higher levels of Stage2 Additional Short Tenn Load [liP,], e.g. 30 kN/m and 40 kN/m, the Total Strain in Stage3 was higher than that of creep test at a load level of 25 kN/m. The explanation follows that after withdrawal of the additional Stage2 Short Tenn Load [liPs], the Recoverable Strain recovered immediately in Stage3, while the 'Locked-in' Strain was recovering with time. On the other hand, a constant Recoverable Strain and increasing 'Locked-in' Strain with time were contributed from the Stage I Sustained Load [P,], which effected in the net Total Strain in Stage3 to be constant. For this reason, the geosynthetic is likely to show the same strain behaviour as that of a creep test under a load of 25 kN/m. This behaviour was visible within 200 hours for lower levels of additional Short Tenn Load [liPs], e.g. 10 kN/m and 20 kN/m. However, this behaviour was not visible within 200hrs for higher 138 ." Chapter Five Isothermal Behaviour OfGeosvntheticsToMSA levels of additional Short Term Loads [t.P,], e.g. 30 kN/m and 40 kN/m, but it was likely to be observed in a course of time. 5.4 Interpretation of MSA (sustained-short term) test results on I:R - I:L plot Figure 5.1 shows the loading scheme used in combined sustained-short term loading tests. The Second stage load is applied after 100 hrs from the application of the sustained load to cater for someti me after construction. The strain- time plots for the tests are shown in the Figures 5.8(a) and (b) in hour and second scales, respectively. The material was reported to rupture in 18 seconds at (25+50) kN/m load. The pair of strain components, i.e. recoverable strain I:R and locked in strain I:L for the peak strains as well as at the end of Stage I and Stage 2 are obtained and superposed on the strain envelope plot for lO % limiting strain, since this is considered to be the failure criteria for GRSSs by most of the codes/methods. The strains at the end of Stage2 loading is taken to be that at (lOOhrs + 30sec), because practically it takes at least 5sec to unload the Stage2 load. Figure 5.13 shows the €R -I:L plot for the Stage I and 2 loadings. Similarly, Figure 5.14 shows that for the Stagel, 2 and 3 loadings. It may be noticed that at the end of Stage I, or at the start of Stage2, i.e. 100 hrs, the geosynthetic would have assumed I:R (100 Iu,) = I:R (0 hrs) and I:L (l00 hi,) due to the sustained load of 25 kN/m. Following the application of Stage2 loading, there has been an introduction of an additional pair of €R and I:L components into the material for each of the second stage loads. These I:WI:L plots for each Second stage load are denoted by different colours, Figure 5.13 and 5.14. Figure 5.15 shows the superposition of €WI:L plots from the results of the test onto the strain envelope at 10%. It may be observed that the strain components at 50 kN/m only cross the 10% strain envelope. Naturally, since it was reported to be the rupture load for the specimen. Other strain components from all upto 40 kN/m of Stage2 additional short-term loads are well within the envelope. That means the specimen did not fail at the lower levels of Stage2 additional short-term loads upto 40kN/m but at 50 kN/m. 139 Chapter Five Isothermal Behaviour Of GeosvntheticsTo MSA On the other hand, let the Stage2 load be assumed to apply after 1000 hrs from the commencement of the sustained load to the same specimen. Due to the application of the sustained load, the specimen would have assumed the same amount of ER (lOOhrs) but greater EL (1000) and the strain components from Stage2 loads would shift to point2 instead of pointl, Figure 5. 16(a). In this case, the strain components in the specimen are derived from the Isochronous curves at 1000hr. It may be noticed here that although the Stage2 load of 40 kN/m does not cross the failure envelope, it is very close to it, meaning it is approaching the failure strain. To elaborate this point let the event occur at IOOOOhrfrom the completion of the construction of the structure. In this case the strain components at 10000hr are not computed but assumed, since the Isochronous curve at that time was not available. The plots are superposed in Figure 5.16(b). It may be appreciated from the figure that Stage2 loadings of 40kN/m in addition with 50kN/m surpass the envelope and even 30kN/m is very close to the failure strain. Likewise, it may be extended that even the Stage2 lower loads like 30, 20, or even IO KN/m would cross the failure envelope, had they been applied after long period since the commencement of the sustained load. In the above test, the sustained load simulates the self-weight of the structure and Stage2 loads the forces due to earthquake events. Thus, if a GRSS were stricken with an earthquake after 100hrs of construction, it would fail (cross 10% strain) at additional short-term load of 50KN/m but remain safe at the additional short-term loads upto 40 KN/m due to the event. On the contrary, if the same GRSS were stricken after 10000 hrs, even the 40KN/m-quake force would cause a failure. Similarly, towards the end of operational tenure of the structure, even small additional forces like 10 or 5 KN/m due to seismic events might cause a failure to the structure. This behaviour of GRSSs may be attributed to the available strain that enables the GRSSs to withstand the quake forces. The available strain may be defined as the difference between the limiting strain and the strain just before an event. The available strain thus may be likely to reduce with the operational tenure of GRSSs due to gradual development of EL, i.e. greater in the beginning and smaller towards 140 Chapter Five Isothermal Behaviour Of GeosvntheticsTo MSA the end of their age. In other words, the GRSSs may withstand higher quake forces during the initial period of their operational life, but smaller forces during the latter period of their operational life. The additional short-term load that a GRSS may withstand thus may be said to decrease with its age. This is portrayed qualitatively in the Figure 5.17, which is a plot of ~Pm", (additional maximum short-term load) against time of occurrence t. For example, at the end of the service life of a GRSS if the strain in the structure is already lO%, it can take no further load since there is no available strain left in it. On the other hand, if the strain in it is less than 10%, say 8%, there is an available strain of 2% and the structure can take further loads until the strain reaches 10% (the failure criteria). Further, the material ruptured after 18 sees at (25+50) kN/m load during the sustained-short term loading test. If the rupture is considered to be the failure criteria, the structure could have been designed as safe even for the Stage2 loading of 50kN/m upto the duration less than l8secs. The above interpretation is based on the assumption that the same amount of strain components, due to the same earthquake event, would be introduced into the geosynthetic irrespective of the time of occurrence of the event. That is a GRSS may acquire the same amount of strain due to the same earthquake, had it been hit at different stages of its service life. If the earthquake induces an equal strain at any time of the service life of the GRSS, the above extension that the capacity to withstand an additional short-term load decreases with time might be true. However, it should be verified with tests as how far it conforms to the assumption. 5.5 Summary • Multi stage action interpreted in strain envelope concept The occurrence of an event like earthquake has a great influence on the load carrying capacity of a GRSS. This capacity of a GRSS to withstand an additional earthquake load depends on the available strain in it, which reduces with the service life of the GRSS. The available strain is considered to be the difference in the limiting strain and that just before an earthquake event. 141 Chapter Five Isothermal Behaviour OfGeosvnthelicsToMSA 5.6 Suggested approach of designing GRSS for' MSA On the bases of understandings of the geosynthetics made so far, it may be noted that the ability of a GRSS to withstand additional short-term load due to an earthquake decreases with its service life, Fig 5.17. This may be attributed to the reduction in ,Available Strain' in the geosynthetics, which is defined as the difference between the limiting strain and the strain just before an event. Naturally, the available strain decreases with the age of the structure, because there is a continuous development of 'Locked- in Strain' in the geosynthetics due to the sustained load. For this reason, a GRSS is likely to withstand greater shocks in the initial stage of its service life and smaller shocks at the latter stages. Therefore, while designing GRSSs for combined sustained plus short-term loading, the approach should be such that there is still some amount of 'Available Strain' at the end of design life (EDL) of the GRSS. This is to ensure that the GRSS is able to withstand the shocks due to probable earthquakes even at EDL. In order to design a GRSS for sustained plus short-term loading, the forces induced from an earthquake event may be estimated in advance, say L\P. In Fig 5. I 8, it may be noticed that there is a pair of strain components namely ERand EL,contributed from the short-term load I1P. The major contribution is in 'Recoverable Strain' ER part since the material does not get much time to develop significant amount of 'Locked-in Strain' EL.For design purposes, this ELpart may be ignored and the total strain due to the earthquake load I1P may be considered to be wholly Recoverable, viz.ER. The additional 'Recoverable Strain' I1ERdue to this additional load I1P may be obtained from the Load-Recoverable Strain curves from Unloading test, Fig 5.19, knowing the slope K ofthe curve which is more or less a straight line. Let the value of I1ERbe equal to 4%, Thus the Available Strain which should be equal to t'.ERor 4%, should be left in the geosynthetic in order to take the additional short-term load of L\P. In Fig 5.20, after 142 Chapler Five Isothermal BehaviourOfGeosvntheticsToMSA deducting this strain from the limiting strain of 10%, the strain level of 6% may be considered to be the failure criteria and the sustained load PMult! stage corresponding to that to be the Design Strength for the combined sustained plus seismic load. In other words, PMult! stage may be taken as the sustained load for which the GRSS is designed and is capable of taking an additional short-term load of L'>Pat the EDL. Further, a small Partial Factor (PF) like 1.1 may be applied to this Design Strength PMult! stage to cater for neglecting the 'Locked-in Strain' !:L component. However, the exact value of this PF should be established on the basis of further MSL testing. 143 Load (kN/m) Stage2 loads .75.'.kNi;ii~: ", ,.. '•. '";i 65.kNim 55 k:'\/m 45 k.'l/m J5 k\flll Stagel Stage3 25 k\'fm 25 I,]'\/m 100 hrs.' 20 sec. I 100hrs. I ••I • -.------. TIme FIGURE 5.1 Loading schemes used for combined sustained- short term loading tests, after Khan (1999). 144 I Imperial Valley, 15 October 1979 Whittier, 7 October 1987 u ~"". c .~0 ~10))- C 0 .' .::• ". t> ~, ~ "' .0 . . . . Ul • • J no+-~---r'~-'"",~~-"_"""""",,,,,,,,,,,,, '"'"!--:c..--.:':-"":':"""'"-.-..,...,...,c-"'"":r"--,- .•...•~ :1; o ~ ~ ~ ~ ro ~ M ~ ~ ~ o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I)iSlllll(,C Ikml Distance (km) ii, i:iii'Ii' Lorna Prieta, 18 October 1989 Northridge, 17 January 1994 'I: i I o I • . I . '. .~ • u I 1~" " t: • 0 .. "' ~. • • • ,. • • ll-f-~~"I-_~_~' •••";uo._...,.~.~, • • i u ~ ]0 m ~o ~ ~ ,~ ~ ~ ~ l?'-...... -f". " .•(I' " I ,I 1-", I Figure 5..2.Effective Durations for soil (A) and rock (0) sites as a function of distance 145 OJ.O 60.0 "':;; a t :.lJt,... ..,. ~~ . .~ 6.0 ~e09/7~ ..~ 0 o 0 8/0 ~ 3.0 0° /. WOo 0 ..0' 0 o R;'/a 8 to 8Q/'" a Y/' .. (a8 0,6- 0 /. 0 0 a O.J a a O.,.j-,-.rr,-,-,-rrTT,,-,rr, ,..,T' .,.""-'''' T' ""'~'''' ,.., ""'~'ClI U ~ U ~ U W ~ Magnitude Mw (a) Soil sites 1OO.0~ 00.0 Ul' -".I'lo- o C ~ . ..,,,.' .2 •• 1.0. ~.;'i'••. , ...••••.••••••••••••••••••• ,.•.•••../" '3 o ,/ 0 "o no .0'(l o 0,/" .~ 6.0 0..../ 00 0,../ a ~-~_ J.O ./,/.. °0 0 W q,.... o ,.- to / .•..// 0.6 o O.J 0.1 l'-~",-'r--r'T"T"T--r-r-l'~' T,~",~,~, T,T'''',~,-~,T1T'~-,~, .•..5 5.0 5.5 G.O 6.S 7.0 73 Magnitude Mw (b) Rock sites Fiqure 5"3 Effectlvo Durations versus Moment Magnitude at distances of less than 10km from Epicentre 146 A-A ------ "'00"'0 N~ •••• 00 -~ -.J a 3 A'J>:. 3 3 I'" 160 mm ., I'" 320 mm .1 ,... 300 mm clamped width .1 Ell A= 1.3mm Ell B=3.5mm @C=3.8mm FIGURE 5.4 Dimensions of the uniaxial geogrid B specimen :~: Test rig, Sustained load i Short term load FIGUREE 5.5 Scheme of test apparatus used in combined sustained-short term loading tests 148 Test rig Tesli-ig. Test rig Specimen Specimen Sustained Sustained \0••• load load ~ Short term Short term Iload load ~ ~ ~ .'----; (a) Stage I (b) Stage2 (c) Stage3 FIGURE 5.6 Various stages in combined sustained-short term loading tests /"' / ..,.:lOll .Si•• = ------oS•• .~a c( c( ••= .%_-- -_. _'!. ~a :E•• I.:)= ,HL'>:1 150 \ 20 Slagle Stage SustaiDed Load 18 '" -25kNlm Slage 1& 3 load: 25kN/m 16 ~ aod Stage210ads -- 25kNim + 50kN/m 14 - 25kN/m + 40kNim - 25kN/m + 30kN/m -- 25kN/m + 20kN/m "'"' 12 Q:l!: Rupture x - 25kN/m + IOkN/m '-' .~10 v.l 8 -V> 6, ,- 4 2 •• o • • o -- • • 25 50 75 100 125 150 175 200 Time (hours) Figure 5.8(a) Results of combined sustained-short term loading tests (Time in hours scale), after Khan (1999) 20 Single Stage Sustained Load 18 ~ - 25kNim Stagel & 3 load: 2SkNIm 16 and Stage2 loads: - 25kNim + 50kNIm 14 - 25kNim +40kNim -- 25kNfm + 30kNfm - 25kNim + 20kNim 12 _~xRupture -- 25kNim + IOkNlm ~-- .! 10 I'l 8 N'"- .~~ 6 ~ r l 4 ~ Stage2 Stage3 •• ••• •• ------2 •• 0 • • . • o 10 20 30 40 50 Time (seconds) Figure S.8(b) Results of combined sustained-short term loading tests (Time in seconds scale), after Khan (1999) , :zo Creepiest 18 - •• 25kNim 16 •• Combined - -- Slagel: 25kNim 14 - Stage2: 25kNim + 10kN1m - Stage3: 25kNim - 6 •• , 4 ~ 2 l- o . . . . . o 25 50 75 100 125 150 175 200 (ft) Strain-time plot TIme (boul'$) 20 CreepWll 18 ..-- 25kNim 16 Combined - -- Stagel: 25kNim 14 Slage2: 25kNim + lOkNlm '0' ~ 12 Slagc3: 25kNim '-' .~10 J:: '11 8 6 , 4 . 2 . o . .. . 0.1 1 10 100 1000 (b) Slrain-Iog.time plot Time (bours) Figure 5.9 Results of combined sustained-short term loading testsfor Stage2 loading of 10 kN/m, after Khan (1999) 153 20 18 Creep test 2SkN/m 16 Combined StBgel: 2SkN/01 14 Slage2: 2SkN/m + 20kN/m ~ ~ 12 •.• Stage 25kN/m '-' .~ 10 •.• :: en 8 ~ 6 ~ L 41' 2 ~ 0 . . • 0 25 50 75 100 125 150 175 200 (a) Strain-time plot Time (hours) 20 18 Creep te,t 2SkN/m 16 Combined 14 Stagel: 2SkN/m '0' StBge2: 2SkN/m + 20kN/m ~ '-' 12 Stage 2SkN/m .~10 en:: 8 6 4 2 0 0.1 10 100 1000 (b) Strain-Iog.time plot Time (hours) Figure 5.10 Results of combined sustained-short term loading tests for Stage2 loading of 20 kN/m, after Khan (1999) 154 • 20 Creep test 18 - 25kN/m 16 Combined - -- Stage I : 25kNim 14 Stage2: 25kN/m + 30kN/m '0' 12 StageJ: 25kN/m ~ .~10 J3 8 l- LI ______6 • 4 2 o . . . . . • o 25 50 75 100 125 150 175 200 (a) StraIn-time plot Time (hours) 20 Creepiest 18 I- -- 25kN/m 16 I- CombIned - -- Stagel: 25kNim 14 I- Stagel: 25kN/m + 30kN/m '0' 12 ~ Stage3: 25kNim ~ ] 10 - 00 8 - I ~ 6 ~ _. 4 ~ 2 ~ _. _. o 0.1 I 10 100 1000 Time (hours) (b) Strain-Iog.time plot Figure 5.11 Results of combined sustained.short term loading tests for Stage2 loading of30 kN/m, after Khan (1999) 155 20 18 Creep test 25kN/m 16 • Combined Stagel: 25kNim 14 I- Stage2: 25kN/m + 40kN/m ~ 121- Stage3: 25kNim '-' "'.~10 I- I ~ 8 I- IL _ 6 . ••.. 4 2 o . . • o 25 50 75 100 125 150 175 200 Time (hours) (a) Strain-time plot 20 ~ 18 I- Creep test 25kN/m 16 I- Combined Stage I: 25kNim 14 I- Stage2: 25kN/m +40kN/m ";' 12 I- Stage3: 25kN/m "''-' .) 10 l- v.> I 8 I L_- 6 • 4 2 . _. 0 0.1 I 10 100 1000 Time (hours) (b) Strain.log.time plot Figure 5.12 Results of combined sustained-short term loading tests for Stage2 loading of 40 kN/m, after Khan (1999) 156 Ot 8 --+- (25+50) kN/m -+- (25+40) kN/m 7 ~-(25+30)kN/rn --'0- (25+20) kN/m -+- (25+I0) kN/m 6 Rupture at (100 hrs + 18 sec) •••••••• 5 -+"'++1"III lllill (lOObrs+20sec) (100 hrs + 20 sec) (100 hrs + 20 sec) (100 hrs + 20 sec) 2 stage 1 end-_._------_._.-.-._._.ofstage 1 o o 2 3 100hrs 4 5 6 7 8 Locked In strain SI, (%) Figure 5.13 BR-S" plot from combined sustained plus short-term loading test for SR80 stage 1+2 157 8 -+- (25+50)kN/m --(25+40)kN/m -+-(25+30)kN/m 7 ----(25+20)kN/m -- (25+10)kN/m 6 Rupture at (100 hrs + 18 sec) 5 '0' ~ '-' ~-+"'JIIJlllIll'l •••• 4 ] •• JI 1 3 J 2 stage 1 stage 3 -_.._ .•.-.•-.._.-._ .. (100 hrs + 30 sec) I o o 1 2 3 100hrs 4 5 6 7 8 Locked in strain "L (%) Figure 5.14 "R-"L plot from combined sustained plus short-term loading test for SR80, stage (1+2+3) 158 -.-Strain envelop 10% --+--(25+50)kN/m --+--(25+40)kN/m Rupture at --+--(25+30) kN/m (100 hrs + 18 sec) -- (25+20) kN/m --+-(25+10)kN/m (l00 hrs + 20 sec) (100 hrs + 20 sec) (l00 hrs + 20 sec) (.. (100 hrs + 20 sec) End of Stage 1 1.~._._._._._._._._._._._._._.-2 100hrs Locked in strain &L(%) FigureS.lS Superposition ofMSA test results on the strain envelope at 10% limiting strain (time of event after 100 hrs of construction) 159 8 7 -.-Strain envelop 10% --+--(25+50)kN/rn 6 -+- (25+40) kN/rn ...... •...... (25+30)kN/m -- (25+20) kN/m Rupture -+-(25+10)kN/m 5 (1000 hrs + 20 sec) 4 (1000 hrs + 20 sec) 3 (1000 hrs + 20 sec) (1000 hrs + 20 sec) 2 I 1 _ End of Stage I I I I I I I I I o I o I 2 3 4 5 6 7 8 1000 hrs Locked in strain EL(%) Figure 5.16(a) Superposition ofMSA test results on the strain envelope at 10% limiting strain (time of event after 1000 hrs of construction) 160 ..~ 8 7 -a-Strain envelop 10% 6 ---+- (25+50) kN/m --(25+40) kN/m ---+- (25+30) kN/m Rupture -- (25+20) kN/m -+-(25+10) kN/m ~ May rupture ~ ..•.+ -- to;: 4 (10000 brs + 20 sec) 3 (10000 brs + 20 sec) (10000 brs + 20 sec) 2 1 2._------_.-._------End of Stage I I I I I I I I I o o 2 3 4 5 6 7 10000 hrs Locked in strain 8L(%) Figure 5.16(b) Superposition ofMSA test results on the strain envelope at 10% limiting strain (time of event after 10000 hrs of construction) 161 BDL (beginning of design life) EDL (end of design life) Time of occurrence 't' FIGURE 5.17 Additional short-term load Vs time of occurrence of the event A Strain envelop at limiting strain = 10% .:lIlR(Eq) ilL (!=tl) IlR(~l i B to tl FIGURE 5.18 "R • ilL plot for combined sustained-earthquake load 162 p FIGURE 5.19 Load- Recoverable strain curve Load/m Design curve for sustained loading PSustained PMulti stage Available strain t.tR = 4% ELimJting=lOo/Cl Strain FIGURE 5.20 Determination of design strength for a combination of sustained short term actions 163 • CHAPTER SIX DISCUSSION AND CONCLUSION 6.1 Discussion In Chapter One, it was highlighted that despite considerable research and evidence from case histories, the design methods and codes for GRSSs have remained essentially the same or conservative over the last two decades. The choice of vel)' conservative and inappropriate input parameters concerning soils and the geosynthetics as well as the calculation models used in the analyses may be the reasons for this insignificant improvisation. Additionally, it has been indicated that the input parameters for soils and geosynthetics should be separately identified for Single-Stage Actions and for Multi-Stage Actions. Further, the significance of the time of a seismic event on the service lifetime of a GRSS was highlighted. At last, a need of developing a simpler approach compared to ISE approach for understanding the complex behaviour of geosynthetics under different loading regimes was identified. In Chapter Two, the basic mechanism of behaviour of GRSSs was introduced and different types of a GRSS and its components were presented. Thereafter a range of reinforcements was presented and compared. Further it was shown that the presently used extensible geosynthetic reinforcing elements exhibit a rather complex time and temperature dependent elasto-visco-plastic behaviour. Different models that have been developed for understanding the complex behaviour of (EVP) elasto-visco- plastic materials viz. Rheological and Mathematical models were briefed. Similarly the Boltzmann's principle of superposition and the Esteve's extrapolation techniques were also presented. Additionally, in the same chapter, vanous design codes/methods for designing GRSSs were presented which were based on the Limit Equilibrium Approach and the Hybrid Approach. These design methods were the AASTHO Standard Specifications 164 Chapter Six Discussion and Conclusions for Highway Bridges (1997), the Deutsches Institut fur Bautechnik (DIEt) Method (1998), the HA 68/94 Method (1997) and the BS 8006 (1996). Furthermore, the model mechanisms for "True" Limit State Approach, developed by McGown et al (1998), were presented. Different input parameters for the same soils and geosynthetics were shown to have been used for both Single-Stage-Actions and Multi-Stage-Actions by various codes. These main input parameters for geosynthetics were identified as their Reference Strengths, Partial Factors and Design Strengths which are dealt with in a variety of ways by different existing codes/methods and by researchers. For Single-Stage Actions, the Reference Strengths are determined either by factoring the short term CRS strengths so that the end results are equal to the long term creep rupture strength, or by taking the load corresponding to a particular limiting strain from sustained load (creep) tests. For Multi-Stage Actions (sustained loading plus short term earthquake loading), most design codes consider the Reference Strengths to be equal to the short term strength obtained from CRS tests or factor up the Reference Strength used for Single-Stage Actions, (e.g. multiply the Reference Strength by 1.5). Partial Factors are determined by comparing the strength of geosynthetics 'before' and' after' the construction damage or environmental degradation. The Design Strengths for both Single-Stage Actions and Multi-Stage Actions are obtained by dividing the appropriate Reference Strengths by the Partial Factors. To the end, the research outputs and case studies related to MSA were outlined where it was indicated that the GRSSs were able to take large additional short-term load and this ability is likely to be profoundly influenced by the time of occurrence of the seismic event. In Chapter Three, different types of actions were illustrated and Eurocode Classification presented. Further, the isothermal behaviour of various materials 165 ,. ChaplerSir Discussion and Conclusions ranging from elastic to elasto-visco-plastic was characterised for Single-Stage Actions and Multi-Stage Actions. It was shown that the geosynthetic reinforcing elements exhibit a rather complex time and temperature dependent elasto-visco- plastic behaviour. Later, it was shown that for EVP materials the likely strain components; namely 'Recoverable' and 'Locked-in', may combine in various many ways at different load levels and times to yield a particular limiting strain. Thereafter, the understandings of the isothermal behaviour of EVP materials such as the strain components Vs time and &R-&L plots were made therein. In Chapter Four, on the basis of the understandings made in Chapter three, various plots like Isochronous curves, total strain and its components Vs time and &R-&L plots were developed after extrapolating the Creep and Unloading tests data. It was shown that the strain components when plotted against time generate identical shapes. It was pointed out that if the material were required to reach a particular strain in a short duration it would assume greater recoverable strain and a smaller amount of locked in strain. On the other hand, if it were to acquire the same amount of strain in relatively larger duration it would assume a smaller recoverable strain and comparatively larger locked in strain. Further that &W&L plot at each limiting strain give rise to a particular strain envelope and the envelopes thus generated are of similar pattern (almost linear). In Chapter Five, the procedure for MSA (Combined-Sustained plus Short term loading) test was outlined briefly and pointed out that the current test protocols may not truly represent the field conditions and the data obtained from these tests may not be appropriate for use in design. Finally, the strain components from the Multi,Stage- Action (combined sustained plus short term loading) test results were superimposed on the &W&L plot at 10% limiting strain, which was developed from the Creep test data. Further, these results were interpreted with the help of strain envelope concept. On the basis of the above, it was suggested that geosynthetics are likely to be able to carry a much larger short-term load than the long term sustained load. Tests showed that a particular geosynthetic could carry an additional Short Term Load [M's] of 166 Chapter Six Discussion and Conclusions about 50 kN/m in addition with a Sustained Load [Ps] of 25 kN/m for a period of 18 seconds, whereas its long term Reference Strength was just 30.5 kN/m at 10% limiting strain. This ability of geosynthetics to carry large short-term loads greater than the long term Reference Strength may be the reason why GRSSs designed according to the current codes/methods performed satisfactorily compared to other structures in the ,tproximity... ' during the Northridge Earthquake in 1994 and the Kobe Earthquake in 1996. One thing particular about those structures was that they were built very recently (not more than 5 years) prior to the events. It may be noticed from the interpretation of the test results that the material was likely to surpass the limiting strain of 10% even at the additional short-term loading of 40 kN/m, had the event occurred after 1000hr. Therefore, whether these structures would survive further earthquakes in the years to come, still remains a question. Thus, the amount of additional Short Term Load [t.ps] taken by a geosynthetic may not be constant but would considerably reduce with the time of occurrence of a seismic event over its service life. The ability that a geosynthetic would be able to take additional Short Term Load [t.Ps] may be explained from the view of 'Available Strain', which is defined as the difference between the strain before the earthquake and the limiting strain. This ability is likely to depend greatly on the available strain. For example, if the strain in a geosynthetic is equal to the limiting strain of 10% for a sustained load [Ps] at the end of service life, there is no Available Strain left and hence no further load can be . applied. At the same time, if the strain at the end of design life (EDL) is 6%, Available Strain is 4% and the geosynthetic will be able to take a further amount of additional short-term load at EDL until the strain reaches 10%. Nevertheless, further research needs to be taken up to confirm the relationships between time of occurrence and the amount of additional Short Term Load [t.Ps], the Available Strain and the Stiffness Properties for the geosynthetics. Thus, the above indicates that the current practice of using a single value of Design Strength over the entire design lifetime of GRSSs is inappropriate and could be unsafe. 167 ChapterSi~ Discussion and Conclusions Eventually, an approach for designing GRSSs for combined sustained plus seismic load was suggested wherein a certain amount Available Strain within the limiting strain itself is reserved in order to withstand probable earthquake shocks at the EDL. 6.2 Conclusions The conclusions drawn from the present study are the followings: 1. Although in practice, the actions encountered by GRSSs are Multi-stage actions, they are treated as Single-stage actions by existing design codes/methods 2. In the current codes/methods the Reference Strengths for geosynthetics are defined either as a load for creep rupture or for a performance limit strain. 3. For sustained loading plus earthquake loading situations, the Reference Strengths are defined either as the short-term CRS strengths or a multiple of the Reference Strengths used for Single-Stage Actions by various current codes. 4. The cyclic nature of seismic load is ignored and the load is taken to be a sustained load equivalent to the peak load of the event over its duration by current codes/methods. 5. The existing design codes/methods for designing GRSSs for sustained plus seismic load are empirical. There is no valid justification for increasing the Design Strength for SSA by 1.5, while designing for sustained plus seismic load. 6. Total strain in geosynthetics at isothermal conditions is likely to have a pair of strains 'Recoverable' ER and the 'Locked-in' EL and these components may be used to characterize the load-strain-time-temperature behaviour of geosynthetics. 7. These strain components may combine in many ways to yield a particular strain at different loads and times at isothermal conditions. 168 ..•... Chapter Six Discussion and Conclusions 8. The 'Recoverable' ER and the 'Locked-in' EL strains when plotted against each other yield a strain envelope that may be used to interpret the isothermal behaviour of geosynthetics under SSA and MSA. 9. The results from combined sustained-short term loading tests, simulating the sustained loading plus earthquake loading condition, interpreted using the strain envelope concept, reveals that the geosynthetics are capable of carrying a larger amount of additional Short Term Loading than their long term Reference Strengths. 10. The amount of additional Short Term Load that a geosynthetic can carry depends on the Available Strain and is unlikely to be the same over the entire service life. 11. The time of occurrence of a seismic event has great influence on the ability of GRSS to withstand the seismic shocks. 12. The same value of Design Strength of geosynthetics over the entire design life in the current practice, while designing for earthquake loading, might be unsafe. 13. The design approach of GRSSs, while designing for sustained plus seismic load should such that there is still some Available Strain left so that the GRSS can withstand the earthquake shocks at the EDL. 169 Chapler Six Discussion and Conc/usions RECOMMENDATIONS FOR FUTURE RESEARCH I. Similar strain envelopes (ER-ErJ plots as in the present study from Creep tests may be generated from CRS tests for geosynthetics at isothermal conditions. 2. The (ER-EL plots) strain envelopes from the CREEP test in the present study may also be used to interpret the. MSA (sustained plus cyclic loading) tests at isothermal conditions. 3. 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