Alternative Approach for Predicting Modulus of Deformation Using Fem

ALTERNATIVE APPROACH FOR PREDICTING MODULUS OF DEFORMATION USING FEM

A DISSERTATION Submitted in partial fulfillment of the requirements for the award of the degree of MASTER OF TECHNOLOGY in CIVIL ENGINEERING (With Specialization in Geotechnical Engineering)

By KALE LAKSHMI GAINESH

DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROORKEE ROORKEE - 247 667 (INDIA) JUN E,, 2007

INDIAN INSTITUTE OF TECHNOLOGY ROORKEE ROORKEE CANDIDATE'S DECLARATION

I hereby certify that the work which is being presented in the dissertation entitled, "ALTERNATIVE APPROACH FOR PREDICTING MODULUS OF DEFORMATION USING FEM" in partial fulfillment of the requirements for the award of the degree of Master of Technology with specialization in Geotechnical Engineering, submitted in the Department of Civil Engineering, Indian Institute of Technology, Roorkee, is an authentic record of my own work carried out during the period from August 2006 to June 2007 under the guidance of Prof. M. N. Viladkar, Department of Civil Engineering, IIT Roorkee. The matter presented in this report has not been submitted by me for the award of any other degree of this or other Institute/ University.

Date: VS-06-04 K. L .6Cx1A-Q11/4 (KALE LAKSHMI GANESH)

This is to certify that the above statement made by the candidate is correct to the best of my knowledge.

Date: 2_c51 0 6 I 67 (M. N. VILADKAR) Professor Department of Civil Engg, IIT Roorkee Roorkee-247 667(India) ABSTRACT

Modulus of deformation is an important parameter which defines the engineering behaviour of rock mass. It is generally determined by in-situ methods like Plate Loading Test, Plate Jacking Test etc. Due to difficulties encountered while conducting in-situ tests, modulus of deformation is often estimated by design engineers on basis of empirical correlations developed for the purpose on the basis of available field test data. For the interpretation of in-situ test data, the rock mass behaviour is assumed to be elastic which does not represent the actual behaviour of rock mass in nature.

In the present work, simulation of plate jacking test conditions has been carried out for five different dam sites for which field data was readily available in the literature (Mehrotra, 1992). The analysis considers the elasto-plastic response of the rock mass through Drucker-Prager yield criterion and the theory of cyclic plasticity. The analysis has been performed using the finite element method with the help of ANSYS 10.0. The modulus of deformation of rock mass has been determined from load intensity versus strain response of rock mass corresponding to different loading and unloading cycles for various stress ranges. It has been observed that modulus of deformation is greatly affected by geological conditions and the geotechnical properties of rock mass and its degree of saturation. The analySis also provides an alternate means for predicting the modulus of deformation, which would be useful in situations where it is difficult to conduct such tests. ACKNOWLEDGEMENT

I would like to express my deep sense of gratitude and sincere thanks to Dr. M. N. VILADKAR, Professor, Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, for his expert guidance, invaluable suggestions and keen interest throughout the period of this dissertation work. In fact, words would fail to describe the invaluable help and the unending encouragement which I am highly privileged to receive from him on many occasions. I am extremely grateful to Dr. Priti Maheshwari, Lecturer, Department of Civil Engineering, IIT Roorkee, for her valuable suggestions and invaluable help during this work without which, it would not have been possible to compile this report in the present form. I am also thankful to all my teachers and staff of Geotechnical Engineering, Deptt. of Civil Engineering for their help and cooperation. I specially thank Mr. Rajib Sarkar, Research scholar, Deptt. of Earthquake Engineering, IIT Roorkee, for his help during my work. My sincere thanks to my parents and my brother who have been a constant source of inspiration to me and I am also grateful to my friends who have provided suggestions at different stages of my work.

(KALE LAKSHMI GANESH)

CONTENTS

Title Page No.

ABSTRACT ACKNOWLEDGEMENTS ii LIST OF FIGURES vi LIST OF TABLES ix NOTATIONS CHAPTER-I INTRODUCTION 1.1 UNDERGROUND SCENARIO 1 1.2 NEED AND IMPORTANCE OF MODULUS 2 1.3 BRIEF REVIEW OF EARLIER WORKS 2 1.4 DEFINITION OF PROBLEM 3 1.5 ORGANISATION OF DISSERTATION 3

CHAPTER-II LITERATURE REVIEW 5 2.1 GENERAL 5 2.2 EXISTING FIELD METHODS 5 2.3 REVIEW OF EARLIER WORK 7 2.4 CRITICAL COMMENTS 9 2.5 JUSTIFICATION OF PROBLEM 11 2.6 OBJECTIVES AND SCOPE OF WORK II

CHAPTER-III FIELD GEOLOGICAL DATA 13 3.1 IMPORTANCE OF GEOLOGY 13 3.2 GEOLOGY OF JAMRANI DAM SITE 14 3.3 GEOLOGY OF KOTLIBHEL DAM SITE 14 3.4 GEOLOGY OF LAKHWAR DAM SITE 15 3.5 GEOLOGY OF SRINAGAR HYDEL DAM SITE 15 3.6 GEOLOGY OF TEHRI DAM SITE 16

CHAPTER-IV FIELD GEOTECHNICAL DATA 22 4.1 IMPORTANCE OF GEOLOGICAL DATA 22

iii

4.2 ROCK MASS PROPERTIES 23 4.3 MODULUS OF DEFORMATION 23 4.3.1 Details of Field Tests 23 4.3.2 Test Data 25 4.3.3 Interpretation of Test Data 25 4.4 CONCLUDING REMARKS 26

CHAPTER-V NUMERICAL SIMULATION OF PLATE JACKING TESTS 33 5.1 GENERAL 33 5.2 GEOMETRICAL IDEALIZATION 33 5.2.1 PLANE82 Element Description (ANSYS 10.0) 34 5.2.2 Description of Model 34 5.3 BOUNDARY CONDITIONS 34 5.4 LOADINGS 34 5.5 MATERIAL PROPERTIES 35 5.6 YIELD CRITERION 35 5.7 PLASTIC STRESS - STRAIN RELATIONS - FLOW RULE 37 5.8 SOLUTION ALGORITHM 38 5.8.1 Overview 38 5.8.2 Convergence 41 5.8.3 Line Search Algorithm 41 5.8.4 Program Developed in ANSYS 10.0 for Present Study 42

CHAPTER-VI DISCUSSION OF RESULTS 51

6.1 GENESIS OF THE PROBLEM 51

6.2 VERIFICATION OF THE SOLUTION ALGORITHM 52 6.3 LOAD INTENSITY VERSUS STRAIN RESPONSE OF JAMRANI DAM SITE 53

6.4 LOAD INTENSITY VERSUS STRAIN RESPONSE OF KOTLIBHEL DAM SITE 54

6.5 LOAD INTENSITY VERSUS STRAIN RESPONSE OF LAICHWAR DAM SITE 55

6.6 LOAD INTENSITY VERSUS STRAIN RESPONSE OF SRINAGAR HYDEL DAM SITE 55

6.7 LOAD INTENSITY VERSUS STRAIN RESPONSE OF TEHRI DAM SITE ZONE 55

6.8 ESTIMATION OF LOADING AND UNLOADING MODULII FOR DIFFERENT CYCLES OF LOADING 56

6.9 COMPARISON OF MODULII WITH THE FIELD TEST DATA 56

6.10 CONCLUDING REMARKS 57

CHAPTER-WI CONCLUSION 81 7.1 SUMMARY OF WORK DONE 81 7.2 CONCLUSIONS 81 7.3 SCOPE FOR FUTURE WORK 82 REFERENCES 83 APPENDIX-1 85 LIST OF FIGURES

Figure No. Title Page No.

Fig. 2.1 Principles of Three Main Methods for In Situ Deformation 12 Measurement

Fig. 3.1 Geological Section Along the Axis of Jamrani Dam Project 17

Fig. 3.2 Geological Section Along the Axis of Kotlibhel Dam Project 18

Fig. 3.3 Geology Below Spillway Section of Lakhwar Dam 19

Fig. 3.4 Cross Section of the Deepest Block Showing Foundation Geology of Srinagar Dam 20

Fig. 3.5 Geological Section Along Tehri Dam Project 21

Fig. 4.1 Set-up of Equipment for Uni-axial Jacking Test in Vertical Direction in a Drift 27

Fig. 4.2 Typical Pressure-Settlement Curve for Poor Quality Rock Mass (RMR=25) Obtained from Uni-axial Jacking Test 28

Fig. 4.3 Typical Pressure-Settlement Curve for Poor Quality Rock Mass (RMR=31) Obtained from Uni-axial Jacking Test 29

Fig. 4.4 Typical Pressure - Settlement Curve for Fair Quality Rock Mass (RMR=43) Obtained from Uni-axial Jacking Test 30

Fig, 4.5 Typical Pressure - Settlement Curve for Fair Quality Rock Mass (RMR=54) Obtained from Uni-axial Jacking Test 31

Fig. 4.6 Correlation Between Rock Mass Rating (RMR) and Modulus of Deformation (Ea) 32

Fig. 5.1(a) Finite Element Model Developed in ANSYS with Full Meshing 44

Fig. 5.1(b) Zoomed View of Finite Element Mesh near the Loaded Area 45

Fig. 5.2 Boundary Conditions Applied Along Three Sides of Finite Element Mesh 46

Fig. 5.3 Geometrical Representation of Mohr-Coulomb and Drucker-Prager Yield Surfaces in Principal Stress Space 47

vi Two-Dimensional 7r - Plane Representation of Mohr-Coulomb Fig.5.4 and Drucker-Prager Yield Criteria 47

Fig.5.5 Drucker-Prager Yield Criterion in Terms of Stress Variants 48

Fig.5.6 Drucker-Prager and Von-Mises Yield Surfaces in

Principal Stress Space 48

Fig.5.7 Newton-Raphson Solution-One Iteration 49

Fig.5 .8 Newton-Raphson Solution-Next Iteration 49

Fig.5.9 Incremental Newton-Raphson Procedure 50

Fig.5.10 Initial - Stiffness Newton — Raphson Solution 50

Load intensity vs Deformation Response for Verification of Fig 6.1 Solution Algorithm 62

Fig. 6.2(a) Variation of Vertical Stress Along the Plate Width for Jamrani Dam Site 63

Fig.6.2(b) Variation of Vertical Deformation Along Plate Width for Jamrani Dam Site 63

Fig. 6.3(a) Variation of Vertical Stress Along Line of Symmetry for Jamrani Dam Site 64

Fig. 6.3(b) Variation of Vertical Deformation Along Line of Symmetry for Jamrani Dam Site 64

Fig.6.4 Spread of Plastic Zone for Different Load Increments at Jamrani Darn Site(Eioading = 2000 MPa, Eunloading = 2500 MPa, = 0.33, c = 0.33 MPa and 0 = 45°) 65

Fig.6.5. Deformations in Rock Mass at Different Load Increments for Jamrani Darn Site(Eloacting = 2000 MPa, Eunloading = 2500 MPa, = 0.33, c = 0.33 MPa and = 45°) 66

Fig.6.6(a) Load Intensity vs Strain Response at Jamrani Dam Site for 2-Cycles of Loading (Natural Moisture Condition) 68

Fig. 6.6(b) Load Intensity vs Strain Response at Jamrani Dam Site for 5-cycles of Loading (Natural Moisture Condition) 69

vii Fig. 6.7(a) Load Intensity vs Strain Response at Jamrani Dam Site for 2-Cycles of Loading (Saturated Condition) 70

Fig. 6.7(b) Load intensity vs Strain Response at Jamrani Dam Site for 5-Cycles of Loading (Saturated Condition) 71

Fig. 6.8(a) Load Intensity vs Strain Response at Kotlibhel Dam Site for 2-Cycles of Loading (Natural Moisture Condition) 72

Fig. 6.8(b) Load intensity vs Strain Response at Kotlibhel Dam Site for 2-Cycles of Loading (Saturated Condition) 73

Fig. 6.9(a) Load Intensity vs Strain Response at Lakhwar Darn Site for 2-Cycles of Loading (Natural Moisture Condition) 74

Fig. 6.9(b) Load Intensity vs Strain Response at Lakhwar Dam Site for 2-Cycles of Loading (Saturated Condition) 75

Fig. 6.10(a) Load Intensity vs Strain Response at Srinagar Dam Site for 2-Cycles of Loading (Natural Moisture Condition) 76

Fig. 6.10(b) Load Intensity vs Strain Response at Srinagar Dam Site for 2-Cycles of Loading (Saturated Condition) 77

Fig. 6.11(a) Load intensity vs Strain response at Tehri dam Site for 2-cycles of Loading (Natural Moisture Condition) 78

Fig. 6.11(b) Load Intensity vs Strain Response at Tehri Darn Site for 2-Cycles of Loading (Saturated Condition) 79

Fig. 6.12 Method for Calculating Modulus of Deformation from Test Data (Mehrotra, 1992) 80

viii LIST OF TABLES

Table No. Title Page No.

Table 2.1 Empirical Expressions for Estimating Modulus of Deformation 8

Table 3.1 Details of Hydro-Electric Projects in Lesser Himalaya 16

Table 4.1 Summary of Results of In-Situ and Laboratory Investigations 24

Table.5.1 Rock Mass Properties of all Project Sites 43

Table 6.1 Modulus of Deformation Values from Present Study and Field Test Data for Natural Moisture Condition 58

Table 6.2 Modulus of Deformation Values from Present Study and Field Test Data for Saturated. Condition 60

•

ix 6 11)isplacerrient P- Poisson's ratio cal Major principal stress 02 Intermediate principal stress cr3 Minor principal stress Cie Tjnia,cia.1 compressive strength

xi CHAPTER-I

INTRODUCTION

1.1 UNDERGROUND SCENARIO Miners have been excavating below the ground surface for many years in their ceaseless search for minerals. These operations are simply a downward extension for smaller depths. Sophistication in exploration methods have resulted in the discovery of openings into larger depths. Most mining excavations are temporary, however, tunnels, underground power house caverns etc. need to remain stable for long periods. Underground openings like tunnels and caverns play an important role in relation to road and rail transport, mining, water supply and hydropower. The construction of underground openings has increasingly become the only feasible means of providing such infrastructure while minimizing short term as well as the long term impact on the environment. Advancements in design concepts result in faster progress, reduced costs and better management risks. Underground opening is an extremely complex structure and due to involvement of various parameters, its design also becomes quite involved. The basic aim of any underground excavation design should be to utilize the surrounding rock mass as the principle structural material. Hence, the accurate interpretation of geology and the geophysical data are essential for a rational design. From the geotechnical engineer's point of view, the classification of underground excavations is related to its degree of stability. Depending on the degree of stability, underground excavations can be divided into following categories: a. Temporary mine openings. b. Vertical shafts. c. Permanent mine openings, water tunnels for hydro electric projects. d. Storage rooms, water treatment plants, road and railway tunnels, surge chambers. e. Underground power caverns, major road and railway tunnels, civil defence chambers. f. Underground nuclear power stations, railway stations, underground factories. 1.2 NEED AND IMPORTANCE OF MODULUS OF DEFORMATION Rock is a discontinuous mass containing cracks, fissures, joints, faults and bedding planes. The engineering properties of rock mass depend far more on the nature of these discontinuities. For foundations on rock mass, it is generally deformation rather than the strength of rock mass which determines the design criteria. The deformability of rock mass governs the strains that develop around an excavation during its initial deformation. For the design of structures in rock mass, it is important to know the deformability characteristics of rock mass for following reasons: • To assess expected displacements during excavation and for checking the stability • To assess the correct and appropriate design of supports that must be able to accommodate the expected deformation without failure. Correct prediction and determination of modulus of deformation, therefore, becomes very important for the analysis and design of underground excavations. The International Society for Rock Mechanics (ISRM) has defined the modulus of deformation of rock mass as the ratio of stress to corresponding strain during loading of rock mass, including elastic and inelastic behaviour (Palmstrom & Singh, 2001).

1.3 BRIEF REVIEW OF EARLIER WORK Modulus of deformation can be determined by various in-situ and indirect methods. The in-situ methods for determination of deformation modulus are, plate jacking test, radial jacking test, borehole jack test, plate load test (George et al. 1999), Goodman jack test, flat jack tests, cable jacking tests and dilatometer tests. The in-situ tests are time consuming, costly and difficult to conduct. The interpretation of data is also another difficult aspect, which requires experience and engineering judgment. The analysis of field-test results is usually carried out by assuming that the rock mass displays linear elastic behavior upon the application of loads (CSMRS, CBIP, 1998). Due to various problems encountered while conducting in-situ tests, the value of modulus of deformation is often estimated from relevant rock mass parameters which can be obtained easily from different rock mass classification systems such as RMR, Q, GSI, RMi etc. Many research workers have developed various empirical relationships between these rock mass parameters and the deformation modulus. Bieniawski (1978), Serafim

2 and Pereira (1983), Mehrotra (1992) and Read et al. (1999) developed correlation between RMR and the modulus of deformation. Hoek et al. (1998, 2005) have proposed empirical relations based on GSI system and IJCS. Further, empirical relations based on Q system and RMi were suggested by Grimstad et al. (1993) and Palmstrong et al. (1995).

1.4 DEFINITION OF PROBLEM Interpretation of in-situ tests results involve the assumption that rock mass behaves elastically; however, considering the loading intensity to which rock mass is subjected during testing, it is well known that this behaviour is elasto-plastic. An attempt has therefore been made to evaluate modulus of deformation considering elasto-plastic behaviour of rock mass. Modeling of rock mass and simulation of plate jacking test has been done using finite element method and the ANSYS software package. The analysis has been carried out by treating the plate jacking test situation as an axi-symmetric problem and therefore a particular plane has been analysed. The area of rock mass loaded by the plate during jacking was so chosen so that mesh distance between the tunnel perimeter and the external boundary was fifteen times the loaded area which is sufficiently large to avoid the undesirable boundary effects. In order to determine the modulus of deformation, an appropriate material model and yield criterion has been used. Axi-symmetric condition has been assumed and quadratic 8-noded solid element (PLANE 82) has been used for the analysis by FEM package ANSYS. The loading has been applied in cyclic manner using 2-5 cycles till the convergence is achieved.

1.5 ORGANISATION OF DISSERTATION The thesis has been divided in seven chapters. Chapter-II consists of the available literature related to the problem considered. Chapter-III deals with the importance of geology and describes geology of five different dam site locations considered for analysis. Rock mass properties, details of in-situ tests and their interpretation at these sites are presented in Chapter-IV. Chapter-V explains the numerical simulation of plate jacking tests. Idealization of geometry, loading, boundary conditions, material properties,

3 yield criterion and solution algorithm have been presented in this Chapter. Chapter-VI presents the results and the related discussion. The conclusions drawn from the present study and scope for future work have been presented in Chapter-VII.

4 CHAPTER-II LITERATURE REVIEW

2.1 GENERAL As a result of an increase in the number of large diameter tunnel constructions and underground excavations, determination of rock mass properties has become one of the most important steps in the design and construction in rock engineering When rocks and rock masses are classified for geotechnical purposes, this needs to be on the basis of strength or static modulus of deformation to give an indication of their stability or deformational response. In addition, strength and modulus of deformation are the necessary input parameters of rock masses to be used as an essential data in various numerical methods. The modulus of elasticity of the rock material is a geomechanical parameter that best represents the mechanical behaviour of rock material. However, the deformational characteristics of rock masses are best represented by the modulus of deformation. All the in-situ measurements of modulus of deformation are time- consuming, costly and difficult to monitor. Due to this reason, deformation modulus is often estimated by indirect methods. Many research workers have developed empirical correlations based on the available in-situ data and these have been presented in subsequent sections in this chapter.

2.2 EXISTING FIELD METHODS The various in-situ methods for determination of deformation modulus are uniaxial jacking test, radial jacking test, borehole jack test, plate jacking test, plate load test, Goodman jack test, flat jack test, cable jacking tests, dilatometer tests etc. In-situ tests are usually conducted in special test adits or drifts excavated by conventional drill and blast methods, having a span of about 2 m and a height of 2.5 m. The length of such adits varies according to local conditions from 10. m to several hundred meters. Initial preparations for conducting tests at each test site are time consuming. The interpretation of measured in-situ data is another difficult and a very

5 crucial aspect. Plate jacking test, plate loading test and Goodman jack test are frequently used to determine the modulus of deformation in the field. Their brief description is given below: i) Plate jacking test (PJT): In this test, two areas in the test adit, diametrically opposite, are loaded simultaneously using flat jacks positioned across the test drift as shown in Fig. 2.1. The plates are subjected to cyclic loading. Rock displacements are measured in bore holes behind each loaded area with the help of multiple point borehole extensometers. The test determines how in-situ rock / rock mass reacts to controlled loading and unloading cycles. Deformation moduli, creep and rebound are estimated from the response of rock mass, i.e. stress vs. deformation curve obtained for different loading and unloading cycles. These tests are easier to conduct, relatively cheaper, and simpler. ii) Plate loading test (PLT): While the plate jacking test records the displacements in drill holes beyond the loading assembly of flat jacks, the plate loading test measures the displacements at the loading surface of the rock, as shown in Fig. 2,1. The main disadvantage of this test is that displacements are measured at the loaded surface which comes under the zone damaged due to blasting during excavation. Hence, this results in an estimated value of deformation modulus. iii) Goodman jack test: Goodman jack consists of two curved rigid bearing plates of angular width 900, which can be forced apart inside an NX size bore hole by a number of pistons. Two transducers mounted at either end of the 20 cm long bearing plates measure the displacement as shown in Fig. 2.1. This test gives better representation of deformability of rock mass, as it can record deformation of much larger volume of rock mass around the drift /tunnel. The limitation of this test is that it is difficult to conduct and is very expensive. In addition to these three tests, the following in situ deformation tests are conducted: • Flat jack tests • Cable jacking tests • Radial jack tests • D ilato meter tests • Pressure chamber

6 The plate loading test (PLT) involves application of cyclic loads to the rock surface by means of hydraulic or flat jacks, and then measurement of the subsequent deformations. Thus, the response of the rock mass to loading and unloading is evaluated. Blasting strongly influences the PLT as the damage from blasting is significant particularly near the surface of the adits. This is the primary reason why modulus determined on basis of surface displacements by PLT generally gives much lower values than displacements measurements in drill holes in the PJT. Therefore PIT based on borehole displacement measurements is better suited for in-situ deformation measurements. In PJT, the modulus value increases with the increase in applied pressure during the measurement. This is due to the closure of cracks or joints in the rock mass under stress, making the material stiffer at higher stresses. The first cycle should never be considered for the determination of the modulii values, as most of the closure of joints takes place during this process. The analysis of field test results is usually carried out assuming that the rock mass displays linearly elastic behavior when subjected to applied loads Furthermore, because of the complexity of the tests and sophisticated nature of the equations used in the analysis of the test results, assumptions are often made about the rock-mass deformability in order to reduce the number of elastic constants that need to be determined.

2.3 REVIEW OF EARLIER WORK Due to the difficulties encountered during the in-situ tests, some empirical relations between the deformation modulus and the rock mass properties have been developed for the indirect estimation of the deformation modulus. The indirect procedures for estimating the deformation modulus are simple and can be used readily, especially as compared to the in-situ tests. Many research workers have related the deformation modulus with the rock mass classification systems such as RMR, Q, GSI, RMi etc. Various empirical correlations have been presented in Table 2.1 along with the required parameters and respective limitations. Most authors have developed the expressions on basis of field test data reported by Bieniawski (1978) and Serafim and Pereira (1983).

7 Table 2.1 Empirical Expressions for Estimating Modulus of Deformation

ReqRequired S. Author Expression Limitations parameters No.

1 Bieniawski RMR E.— 2RMR-100 RMR > 50 (1978)

2. Serafim and RMR E. = 101uviR-t0)b40 RMR < 50 Pereira(1983)

3 V. K. Mehrotra RMR E. = 10(RMR-25)140 (1992)

4. Grimstad and Q Em = 25 logio Q Q>1 Barton (1993)

5. Clerici (1993) - E. = Er Star X Em dyn / Er dyn -

6. Palmstrom RMi Em= 5.6 RMi° 375 RMi>0.1 (1995)

a, <100 7 Hoek and GSI and 0, Em = ( ac /100)0 51 0(GS 1-10)/40 Brown (1998) MPa

8. Read et al. RMR (1999) E., - 0.1(RMFt/10)3 -

( 0 I -- 2 GSI 105 0.02+ 75+25D-GST _

Hoek and I 4- e " 9. Diederichs (2005) / D 1- - E; and GSI E, 0.02 + 40,1521, oc, - 1+ e " i

8 These expressions give a reasonable fit to the field data, except for the exponential expressions. Exponential expressions give poor estimates of the deformation modulus for massive rock because of the poorly defined asymptotes. In Table 2.1,

En, = Modulus of deformation of rock mass in GPa Efin -Rock mass modulus in MPa = Intact rock modulus RMR = Rock Mass Rating system (Bieniawski, 1973) Q = Q system (Barton et al., 1974) oe = Uniaxial compressive strength (in MPa) of intact rock measured on 50 mm diameter samples RMi = Rock Mass index (Palmstrom, 1995) GSI = Geological Strength Index (Hoek and Brown, 1998)

Er dyn = Dynamic elasticity modulus of intact rock

Er stat = Static elasticity modulus of intact rock

Em dyn = Dynamic in situ deformation modulus

D = Load distribution factor

The use of more than one indirect procedure has been proposed by many authors, so that the results obtained can be compared and their reliability can be checked. The RMR system has probably been used most frequently for the estimation of deformation modulus. The reliability of an empirical relation depends on the number and quality of the data employed. In addition, all empirical relations are open to the improvement as a result of inflow of new data. For their empirical equation, Hoek and Brown (1998) stated that, as more field evidence is gathered, it may be necessary to modify the relation. This statement is valid for all empirical approaches.

2.4 CRITICAL COMMENTS

➢ Plate jacking test (PIT) with borehole ektensometer measurement: the deformations are measured inside the drill hole from the damaged zone towards the undisturbed rock masses.

9 > Plate loading test (PLT) with surface measurement: The lower value of deformation modulus measured at the rock surface in these tests can be explained by the fact that these measurements are made in the damaged zone from blasting. > Goodman jack test (GJT) performed inside the drill hole: The Goodman jack tests have also been found to give lower values of the modulii because, in hard rock, the loading platens deform, the primary reason being that the displacement devices record the increase in borehole diameter plus the deformation of loading plates. > The values of En, in massive rock based on RMR give significantly higher values for all the rock strengths than En, calculated from laboratory test adjusted for scale effect. > As the Q system does not require the rock strength as input parameter, En, based on Q system for massive rock masses has the same value for all rock strengths. For an less than about 150 MPa, the value has been found to be considerably higher than the value of En, estimated from laboratory tests adjusted for scale effect. > The values of En, for massive rock mass obtained from the RMi equation have also been found higher than the values based from the laboratory test results adjusted for the scale effect, especially for weak rocks (an < 10 MPa). However, RMi estimates give the best results out of the three systems in massive rock. > The simplified Hoek and Diederichs (2005) expression can only be used when GSI (or RMR or Q) data are available. However, the more detailed Hoek and Diederichs (2005) expression can be used where reliable estimates of the intact rock modulus or intact rock strength are available. The values of modulus of deformation measured by the Goodman jack test (GJT) and the plate loading test (PLT) are generally lower. Usually these should be multiplied by a factor, Rp = 2.5 for the purpose of comparison of results from PJT. > Due to the closing of cracks and joints in the damaged and distressed zone, the modulus value increases with the increase in applied pressure. Therefore, the values for the highest test pressures, 4 - 6 MPa, both for the plate jacking tests

10 (PJT) and for Goodman jack tests (GJT) should be used. For the same reason, the deformations in the first cycle should not be included in the measurements. ➢ The plate jacking test (PJT) has been found to give the best in situ measurement results as compared to those of plate loading tests (PLT) and Goodman jacking tests (GJT). > All empirical models depend on number and the quality of the data employed. Therefore, before using empirical relations for the design purposes, it must be checked with the other empirical expressions or in situ data or both.

2.5 JUSTIFICATION OF PROBLEM Above review of literature suggests that estimation of deformation modulus from in-situ measurements is based on the assumption that rock mass behaves elastically and also these methods are time consuming, expensive and difficult to conduct. This suggests that there is a need to include in the analysis the more realistic behaviour of rock mass i.e. elasto-plastic behaviour. Therefore an attempt has been made in this study to simulate one of the in-situ tests i.e. plate jacking test using the finite element method so that nonlinear and elasto-plastic behaviour of rock mass can be taken in to account while determining modulus of deformation. Software package ANSYS has been used for analyzing the problem considered.

2.6 OBJECTIVES AND SCOPE OF WORK The present study is concerned with the prediction of modulus of deformation from the actual behaviour of rock mass. Numerical simulation of plate jacking test has been carried out for five different dam sites. Specifically, the following objectives have been defined for the present study: > To simulate the in-situ plate jacking test for different site conditions. > To generate the load intensity vs. strain curves of the rock mass for plate jacking test. > To predict the modulus of deformation from generated curves and compare with those obtained from in-situ plate jacking tests.

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12 CHAPTER-III

FIELD GEOLOGICAL DATA

3.1 IMPORTANCE OF GEOLOGY Geological investigations are of help to understand the physical environment in which major infrastructures are developed. These assist in overcoming the major challenges posed by ground conditions on projects such as motorways, underground openings, water supplies, wind energy, waste management and offshore construction. These provide major opportunities not only to improve cost efficiencies and minimize delays, but also to avoid subsequent construction defects and liability claims. Knowledge of geology plays a crucial role in the management of projects that are to be completed successfully on time and within the budget and also is very useful in assessing the risk arising from the uncertainty about ground conditions. At early feasibility stage of a project, the likely problems stemming from the ground conditions will need to be assessed on the basis of published and local information, together with experience of the site and type of the project. It is at this stage that the engineering geologist can have a significant influence on the project, indicating the potential hazards and their consequences on the economy of design, methods of construction and expected performance of the works. The vital importance of engineering geological input is usually appreciated at the starting stage of the project, but it is the next stage, the construction work, that a further valuable contribution can be made. For underground constructions, the aim of geological investigations is to develop knowledge of the rock masses for many operations like blasting, drilling etc. For estimating modulus of deformation especially from indirect methods, knowledge of engineering geology is a basic requirement to know the RMR, Q, RMi and GSI. Mehrotra (1992) performed plate jacking tests at different sites and estimated engineering parameters of rock mass. In the present work, the geology of these sites has been used to simulate plate jacking test using FEM. The details of geology of these sites are presented in subsequent sections.

13 3.2 GEOLOGY OF JAMRANI DAM SITE The Jamrani dam project comprises of construction of a 150 m high roller compacted concrete dam across the river Gola at Jamrani village about 10 km upstream of Kathagodam in the state of Uttarakhand. The dam site is located on the lower Shiwalik rocks of Kumaun Himalaya which consists of sandstone with alternative bands of siltstone and claystone. The rock mass is traversed by a number of joints. There are five prominent joint sets out of which four intersect, resulting in the formation of rock wedges which are likely to cause problems in abutment stripping. The dam site lies in an active seismic belt and was affected by earthquakes in various parts of Kumaun and adjacent seismic belt at frequent intervals. Rock slides have been observed on the abutments. However, major slope slides have been observed on the left abutment due to undermining of the toe at river bed level. At some locations, the sandstone has been found to be very soft and weathered. On being immersed in water, it disintegrates rapidly into small pieces and loses its strength. The geological section along the Jamrani dam project has been presented in Fig. 3.1.

3.3 GEOLOGY OF KOTLIBHEL DAM SITE The project involves the construction of a 210 m high earth-rock fill dam on river Ganga with an installed capacity of 1000 MW. The dam derives its importance for the fact that it has been constructed to serve as a balancing reservoir for a number of projects planned in upper reaches of Ganga valley together with partial flood protection woks in this region. The dam site area is located in quite a complex geology with repeated folding and faulting. There are alternate bands of soft and hard quality rocks in the dam foundation area. A major fault has been mapped on the left bank which is exposed on the upstream side passing through the left abutment on the river bed towards downstream. Presence of soft pockets or local shear zones has been found to be evident. Studies indicated the presence of limestone, breccia and slate as basic rocks. At few places, calcium carbonate was found to have been deposited within the joints of cavities. Figure 3.2 depicts the geological section along the Kotlibhel dam project.

14 3.4 GEOLOGY OF LAKHWAR DAM SITE The Lakhwar dam project envisages construction of a 204 m high gravity dam across river Yamuna and a 3X100 MW installed capacity underground power house near village Lakhwar. At the dam site, the river flows through a narrow gorge and the side hills are fairly high. The rock formation in the region where Lakhwar dam was proposed to be located comprises of phyllites, slates, quartzites and limestones which form the Southern limb of a major syncline. These rocks were intruded by a number of minor basic trap rock bodies. The Lakhwar dam is located across one such intruded body of basic rock. The trap was generally coarse grained and highly jointed. On the left abutment an outcrop of slates and quartzites was enclosed on three sides by the trap forming a rock body. On the right abutment, the band of trap rock containing a number of joints in different directions was observed. The joint surfaces were mostly fresh, but few of them displayed slight alternation also. In the foundation of overflow section, the trap was underlined by crushed and thinly foliated slates of indefinite thickness at a depth of 30-40 m below the toe region. Figure 3.3 shows the overflow section of the Lakhwar dam

33 GEOLOGY OF SRINAGAR HYDEL DAM SITE Srinagar hydroelectric project comprises of a 90 m high concrete gravity dam on river Alakhnanda near Srinagar town in the state of Uttarakhand and a surface power house with an installed capacity of 330 MW. The spillway has been accommodated in the darn body itself due to non-availability of sufficient suitable space on the left bank. The project was located within the rocks of Dudatoli and Garhwal groups, separated by a major tectonic lineament called Srinagar thrust. The dam was located in a complex folded, sheared and fractured sequence of quartzites and basic rock belonging to the Garhwal group. The dam area exposed a sequence of complexly folded quartzite and metabasic rock. The generation was identifiable in the field in both the rock units. The cross section of the deepest block showing foundation geology of Srinagar dam has been presented in Fig. 3.4.

15 3.6 GEOLOGY OF TEHRI DAM SITE Tebri dam project was taken up for utilizing the vast potential of river Bhagirathi, a tributary of Ganga, for irrigation and generation of power. It comprises of 260.5 m high earth and rock fill dam across river Bhagirathi near Tehri town in Uttarakhand. Tehri dam project is located in the Lesser Himalaya. The rock formation at the dam site is phyllites of Chandpur series which are banded in appearance. The bands are comprised of argillaceous and arenaceous materials, which have been classified in to three groups as Grade I Phyllites, Grade Il Phyllites and Grade III Phyllites. Grade I and Grade II Phyllite units which form about 70 percent of the foundation area were nearly of the same quality so far as deformability characteristics and permeability are concerned. The core recovery of phyllites of grades I and II was found to increase with depth. After a depth of 10 in, the core recovery was generally above 50 percent. There are number of shear zones in the Tehri gorge which have crushed rock and are expected to be relatively more pervious. In many cases, the shear zones are filled with clay. Figure 3.5 shows the geology along the dam axis. Brief summery of details of these five major hydroelectric projects in the lesser Himalayan has been presented in Table 3.1.

Table 3.1 Details of Hydro-Electric Projects in Lesser Himalaya

S. Dam General Project Dominant Location Elevation No Rock(s) Type Height (m) (m) Sandstone, Concrete Lower 615.00 1. JAMRANI 150 Clay stone Gravity Siwalik Earth Shale Ganga 2. KOTHLIBHEL and 210 370.00 Limestone' Valley Rock fill Trap, Arch Yamuna 3. LAKHWAR 204 620.00 Slate Gravity Valley Quartzite, Concrete Ganga 4. SRINAGAR 90 545.00 Metabasic Gravity Valley 1r Earth Ganga Phyllites and 260.5 610.00 5. TEHRI Valley Rock fill

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21 CHAPTER-IV

FIELD GEOTECHNICAL DATA

4.1 IMPORTANCE OF GEOTECHNICAL DATA The need of the geotechnical data was once relatively not so sophisticated and was keyed primarily to site selection and design. The methods of investigation were simple as well, because construction techniques were readily adaptable to adverse conditions. Current and developing underground construction methods are not so forgiving; they demand greater attention to the collection of geological information to permit their efficient and economic use as an integral part of modern and future practice. A technically sound and thorough geotechnical site investigation program is an essential ingredient for obtaining the lowest cost of underground construction. To accomplish that end, the program must not only be optimal in design for the particular conditions at site, but must also be sensitive to the required refinements in the scope of traditional data, data reporting, and data interpretation, in order to take full advantage of the new cost reducing construction methods, equipments, and concepts in project design. Along with fairer tunneling cost, greater project suitability, longevity, and safety can be achieved due to availability of proper geotechnical data. The ultimate goal which is to determine, with reasonable accuracy, the nature of subsurface formations and how they will react or behave during tunneling, comes at highly variable costs. The knowledge and skills necessary to achieve sound and thorough geotechnical investigation are not possessed by all the investigators. Therefore, the designer or contractor in charge of obtaining the geotechnical data should be responsible for evaluating the investigator's capability to conduct an effective exploration program and to know when special skills or additional knowledge may be needed. The geotechnical site investigation must provide data to encourage safe and economical design; to assist the contractor in analyzing the feasibility, costs, procedures, and equipment for construction; to enable the owner to prepare contract and bid documents that accurately reflect and provide equitable methods for resolution of potential areas of contingent costs, The geotechnical site investigation must answer or

22 assist in answering, the designer's question of the loads for which the structure must be designed; the contractor's questions of what type of ground is to be excavated, how it will behave during construction, which method is suitable to build the structure, and how much it will cost; and the owner's questions of whether the budget is adequate and the schedule can be met. The ultimate goal of the geotechnical investigation must be an understanding of the behavior of the soil and rock/ rock mass The geotechnical site investigation is not an isolated part of the design and construction processes; nor is it only an early part of basic feasibility decision making. Rather, it must and should serve as a continuous resource throughout the design, construction and operation processes. In the present work field geotechnical data from five different sites (Mehrotra, 1992) have been used for the analysis.

4.2 ROCK MASS PROPERTIES The in-situ tests were carried out for finding out RMR and Q and also standard laboratory tests were carried out for Poisson's ratio, modulus of elasticity and uniaxial compressive strength by Mehrotra (1992). The summary of results of in-situ and laboratory investigations is given in Table 4.1.

4.3 MODULUS OF DEFORMATION

4.3.1 Details of Field Tests Extensive field tests were carried out by Mehrotra (1992) to estimate the engineering parameters of different rock masses encountered at various project sites. The nature of the rock mass varies from place to place and from project to project due to variation in moisture conditions, effect of anisotropy, the stress environment in rocks and also other unknown geological conditions. Uni-axial jacking test, on 60 cm diameter plates, were conducted in exploratory drifts excavated at each project site to determine the behaviour of rock mass during loading and unloading cycles. In order to assess modulus anisotropy, tests were conducted in horizontal as well as in vertical directions. Figure 4.1 shows the lest set up of equipment for conducting a uni-axial jacking test in the drift.

23 Table 4.1 Summary of Results of In-Situ and Laboratory Investigations (Mehrotra, 1992)

Uni-axial Modulus of Compressive Poisson's Rock Type RMR Elasticity, Q Strength, Ratio (MPa) (MPa)

D 1.75 - 2.90 0.7 - 2.0 20 - 45 32.00-75.00 0.30 - 0.36 Sandstone S 1.20 0.2 27 24.00-48.00

D 1.43 - 3.67 0.7 - 1.8 24-38 - Claystone S

D 0.98 - 7.80 0.3 - 3.9 18 - 45 1.00-38.00 0.39 Slates S 1.09 - 3.60 0.1 - 2.1 23-42 0.00-20.50

D 1.98 - 13.00 1.7 - 11.7 30 - 61 98.00-196.50 0.24 - 0.27 Trap S 1.60 - 9.70 1.2-13.2 43-64 71.50-163.00

D 2.22 - 2.95 0.9 - 1.5 25 - 30 16.80-37.00 0.36 Shale S 1.09 - 1.15 0.1 - 0.2 23 - 25 12.50-30.50

D 0.55 - 4.80 0.1 - 4.0 11 - 53 21.00-49.00 0.32 Limestone S 16.00-40.00

1) 4.38 - 7.11 3.3 - 4.7 37 - 60 70.90-104.00 0.29 Metabasic S 3.39 - 5.73 2.5 - 3.0 49 63.00-88.50

D 0.98-14.37 0.3 - 19.0 27 - 71 67.00-128.00 0.33 Quartzite S 1.78 - 6.52 1.2 - 4.9 37 - 58 54.50-112.00

D 0.73 - 4.13 0.3 - 4.1 18 - 50 38.00-133.00 0.24 - 0.32 Phyllite S 1.25 - 5.14 0.3 - 6.5 31 - 61 25.50-95.50

D- Natural moisture condition, S- Saturated condition

24 It was assumed that the plate settlement was about half of the total deflection between top and the bottom plates. Investigations were carried out with an object to estimate the following properties concerning the rock mass: 1. Modulus of deformation and Modulus of elasticity 2. Cohesion(c) and angle of internal friction (et). 3. Rock mass classification using following approaches; (i) RMR system of Bieniawski (1973) (ii) Q-system of Barton et al. (1974) The laboratory tests performed on shale, claystone and slates were not successful because the specimens fractured during initial stages of loading. Under saturation, most of the specimens of slate, shale, claystone and sandstone crumbled and could not be tested.

4.3.2 Test Data (Mehrotra, 1992) Uniaxial jacking tests were carried out at different locations for each dam project site. Loading intensity vs displacement curves have been plotted for different RMR values. Curves were plotted for 2 cycles. Figures 4.2 - 4.5 show the plots for different RMR values and for different project sites.

4.3.3 Interpretation of Test Data The geological conditions were different at different project sites. Further, variation was also observed within a particular project site. This variation was of the order of 17-64 in terms of RMR and 0.5 GPa — 12 GPa in terms of the modulii. The following empirical relation has been proposed by Mehrotra (1992) based on the in-situ tests (Figs. 4.2 — 4.5)

(RMR 25)

Ed= 10 40 GPa (4.1)

The relationship yields the prediction with an error of 20.8 percent as shown in Fig.4.6. The modulii, data obtained in the saturated rock mass have been presented as curve-2 in Fig. 4.6. For rock masses at a natural moisture content of the order of 5 percent, RMR was estimated by taking into account the condition of ground water having

25 the rating 10 (for damp rock mass). For rock masses at saturation moisture content, the rating was taken as 7 (for wet mass). These values of RMR were chosen as per the suggestions given by Bieniawski (1978) for various conditions. The effect of saturation has been observed to be more predominant in poor rocks than in fair quality rocks. In case of poor rocks, the reduction in modulus of deformation (Ed) was found to be around 90% as the moisture condition changed from natural to saturated. However, this reduction was about 70% in case of fair quality rocks. This was expected because R&M. was generally less in argillaceous rocks with water sensitive minerals in lesser Himalaya. Figure 4.6 shows the RMR values plotted against the modulus of deformation (Ed) for RMR values from 17 to 64. Curve 1 corresponds to data based on rock mass tested at natural moisture content and curve 2, to data of saturated rock mass. Bieniawski (1978) correlated the values of modulus of deformation through the geomechanical classification of hard rocks as shown by curve 3. For poor quality rock masses, Serafim and Pereira (1983) proposed an overall correlation which is shown by the curve 4 in Fig.4.6.

4.4 CONCLUDING REMARKS Following concluding comments can be offered from the test data presented: • Mehrotra (1992) proposed an empirical correlation between modulus of

deformation, Ed and RMR. The values of Ed were estimated by conducting in-situ tests for different sites having different RMR values. • This correlation has a prediction error of 20.8 %. • Degree of saturation has a considerable influence on values of modulus of deformation which were found to reduce by 90 % and 70 % for poor rock masses respectively as the rock mass condition changes from natural moisture condition to saturated condition.

70.0

60.0

Maximum stress 5060 kg/cm? i 50,0

rh cr+ E d t•-• 11650 14o/cm2 40,0

30.0

20.0

10,0 1 — 4.175mm I/ F4.4" r* 0.95mm

010 2-0 4.0 6,0 8.0 10.0 12,0 14.0 Deformation mm--4.•

Fig. 4.2 Typical Pressure-Settlement Curve for Poor Quality Rock Mass (RMR=25) Obtained from Uni-axial Jacking Test (Mehrotra, 1992)

28 45.0 Max. stress 42.44 ligiern2

40.0- E d s 13840 kg Tem2

35.0

30.0- t 4 ry Eu 75.01

10.0

15.0.

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Deformation mm

Fig. 4.3 Typical Pressure-Settlement Curve for Poor Quality Rock Mass (RMR=31) Obtained from Uni-axial Jacking Test (Mehrotra. 1992)

29 701-

60.0-

Max. stress 5307 k9/Cm2 A 50,0- Ed =29/200 kg /cm 2

Si I 30.0 -

20,0— A.

10,0 1,880m 775mm iv/ A --L-1.125mm -- /

A 040 1-.11 A 0 0.5 1.0 1.5 2.0 2.5 3.0 3 655 40

Deformation , mm •••••41••

Fig. 4.5 Typical Pressure - Settlement Curve for Fair Quality Rock Mass (RMR=54) Obtained from Uni-axial Jacking Test (Mehrotra, 1992)

31 The load has been uniformly distributed on to the surface area of the rock mass through this plate. 2-D quadratic 8-noded solid elements (PLANE-82) have been considered for modeling the rock mass.

5.2.1 PLANE82 Element Description (ANSYS 10.0): PLANE 82 is a higher order version of the 2-D, four-node element (PLANE 42). It provides more accurate results for mixed (quadrilateral-triangular) automatic meshes. The 8-noded element is defined by eight nodes having two degrees of freedom at each node: translations in the nodal x and y directions. The element can be used as a plane element or as an axisymmetric element. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.

5.2.2 Description of Model A model has been developed to simulate the plate jacking tests conducted on rock mass using ANSYS. As the problem is axi-symmetric in nature, one particular plane has been considered. Figure 5.1a shows geometrical idealization and complete discretization (mesh) of rock mass considered around the area loaded by flat jacks. Fig. 5.1b shows the close up view of the mesh in the proximity of the loaded area. The total number of elements used in the finite element mesh for simulating plate jacking test is 1445 and total number of nodes involved is 4500.

5.3 BOUNDARY CONDITIONS The horizontal displacements (in X-direction) at boundaries of rock mass parallel to Y-direction have been constrained. The vertical displacements (in Y-direction) at boundary (away from loading region) parallel to X-direction have been constrained. The total number of boundary nodes in the mesh is 115. The boundary conditions have been presented in Fig. 5.2.

5.4 LOADING Loading has been applied to rock mass through the loading plate. To simulate plate jacking test conditions, cyclic loads have been applied in 2-5 cycles depending upon the rock mass parameters. The load in a particular cycle has been applied in increments

as indicated in Fig. 5.4. In the former case (external cone), cone circumscribes the hexagonal pyramid, and the material constants a and k as obtained by Zienkiewicz (1983) are given by: 2 sin 0 a — (5.2a) -‘5 (3 — sin 0) 6 c cos 0 k (5.2b) -Z (3 — sin 0) The latter case results in an inner cone and the corresponding material constants are given by: 2 sin 0 a — (5.3a) (3 + sin 0) 6 c cos 0 k — (5.3b) „II (3 + sin 0) The geometric representation of Mohr-Coulomb and Drucker-Prager yield surfaces in principal stress space and 7- plane has been shown in Figs. 5.3 and 5.4 respectively. However, since the values of c and 0 are determined by using conventional triaxial compression tests, the material constants are different from those determined for plane strain condition. Under the conventional triaxial compression condition, the values of a and k can be expressed as: 2 sin 0 a — (5.4a) 75 (3 — sin 0) 6 c cos 0 k — (5.4b) V3 (3 — sin 0)

For plane strain condition, the constants are given by: tan 0 a — (5.5a) (9 +12 tan2 0)2 k— 33c (5.5 b) (9+12 tan2 0)2

36 The two material parameters a and k for Drucker-Prager model can be determined from the slope and the intercept of the failure envelope plotted in ./1 — (J2)2 space as shown in Fig.5.5. When a = 0 (i.e. e = 0), this surface reduces to Von-Mises surface as shown in Fig. 5.6.

5.7 PLASTIC STRESS - STRAIN RELATIONS - FLOW RULE Plastic stress-strain relations may be written (v = 1/2 for constant-volume plastic deformation) as de," = dA[cri --(a2 +a,)] do f = d — z (al +a3 )] (5.6a) de3 = d4a; —(cr,+a2 )]

The plastic strain increment de' is related to the stresses by a proportionality factor, dl . The factor, is not a material constant and is a positive quantity. Equations 5.6a may be further expressed by using the deviatoric stresses a, a2 and a; . By taking the first of Equation 5.6a as

del = —am )—(a2 +a,)+o-„,]

= dit[o-;-4(cr;+a,)] = dyl.[T3 o-;—(cr; + a; + cr;)]

Since by definition cr, +a; +a3 = 0, this reduces to:

3 de° = — d Ao- 2 t Equations 5.6a thus take the from: de" de' de' 3 .2 3 = ctet (5.6b) C2 C3 2 which implies that the plastic-strain increments are proportionally related to the deviatoric stress components and not to the total stresses. This is consistent with the assumption that plastic deformation is independent of the hydrostatic stress component, an, . The plastic stress-strain relations as given by Equations 5.6 are often referred to as the Levy-Mises plastic flow rule. Such relations are still not complete since

37 the proportionality factor, dX is yet to be determined. This plastic multiplier is expressed as —

[dZ° dA-3 (5.6c) 2 CT where, de is equivalent plastic strain increment and a is equivalent stress. Equations 5.6 imply that the principal directions of plastic strain increments coincide with the principal directions of stresses. If the ratios, a; : a2 : cr; remain unchanged during the entire loading path, then the ratios between plastic strain increments, del : del' :deg' will also remain constant and this condition is known as proportional loading. In such cases, the flow rule Equations 5.6b can be integrated to give

n p 3 E =£ I = E I = A cr1 (5.6d) 0-2 1 0-3 1 2 where the total plastic strains are used instead of their increments.

5.8 SOLUTION ALGORITHM ANSYS 10.0 employs Newton-Raphson procedure to solve the set of simultaneous equations resulting from finite element discretization process. This procedure has been described as follows: 5.8.1 Overview

The finite element discretization process yields a set of simultaneous equations: [K] {u} = {Fa} (5.7) where [K] = coefficient matrix {u} = vector of unknown DOF (degree of freedom) values {Fa } = vector of applied loads If the coefficient matrix [K] is itself a function of the values of unknown DOF, then Equation 5.7 is a nonlinear equation. The Newton-Raphson method is an iterative process of solving the nonlinear equations and can be written as

[KT] {Au,}={P}-{Fr} (5.8)

{uiti} = {u, } + {Au,} (5.9) where [KT ] = Jacobian matrix (tangent matrix) = subscript representing the current equilibrium iteration {Fr} = vector of residual loads corresponding to the element internal forces.

Both [KT] and {F"} are evaluated based on the values given by {ni}. The right- hand side of Equation 5.8 is the residual or out of balance force vector; i.e., the amount of force by which the system is out of equilibrium or the amount of force which is yet to be equilibrated. Single solution iteration is depicted graphically in Fig. 5.7. In a structural analysis, [KT] is the tangent stiffness matrix, {u,} is the displacement vector and {F," } is the restoring force vector calculated from the element stresses. More than one Newton-Raphson iteration is needed to obtain a converged solution (Figs. 5.7, 5.8). The general algorithm proceeds as follows: i. Assume {uo}. {uo} is usually the converged solution from the pervious time step. For the first time step, {uo} = {0}.

ii. Compute the updated tangent matrix [KT] and the restoring load {F"} from

configuration {u,}. iii. Calculate {Au, } from Equation 5.8.

iv. Add {Au,} to {ni} in order to obtain the next approximation {u,,} (Equation 5.9).

v. Repeat steps ii to iv until convergence is obtained. Figure 5.8 shows the solution of the next iteration (i+1). The subsequent iterations would proceed in a similar manner. The solution obtained at the end of the iteration process would correspond to load level, {F'}. The final converged solution would be in equilibrium, such that the restoring force vector, {F,"} (computed from the current stress state) would equal the applied load vector, {F'}. None of the intermediate solutions would be in equilibrium.

39 If the analysis included path-dependent nonlinearities (such as plasticity), then the solution process requires that some intermediate steps be in equilibrium in order to correctly follow the load path. This is accomplished effectively by specifying a step-by- step incremental analysis; i.e., the final load vector {F' } is reached by applying the load in increments and performing the Newton-Raphson iterations at each step. [KL]{Atii}={F7}-{F,M (5.10)

where [IC] = tangent matrix for time step n, iteration i

{F° } = total applied force vector at time step, n

= restoring force vector for time step n, iteration, i.

This process is the incremental Newton-Raphson procedure and has been shown in Fig 5.9. The Newton-Raphson procedure guarantees convergence if and only if the solution at any iteration {u,} is near the exact solution. Therefore, even without a path- dependent nonlinearity, the incremental approach is sometimes required in order to obtain a solution corresponding to the final load level. When the stiffness matrix is updated, every iteration (as indicated in Eqn 5.8 and Eqn 5.10) in the process is termed as a full Newton-Raphson solution procedure (NROPT, FULL or NROPT, UNSYM). Alternatively, the stiffness matrix could be updated less frequently using the modified Newton-Raphson procedure (NROPT,MODI). Specifically, for static analysis, it would be updated only during • the first or second iteration of each sub step, respectively. Use of the initial-stiffness procedure (NROPT, NIT) prevents any updating of the stiffness matrix, as shown in Fig. 5.10. In a multi- status element in the model, however, it would be updated at iteration in which it changes the status, irrespective of the Newton-Raphson option. The modified and initial-stiffness Newton-Raphson procedures converge more slowly than the full Newton-Raphson procedure, but they require fewer matrix reformulations and inversions. A few elements form an approximate tangent matrix so that the convergence characteristics are somewhat different. In the present study, full Newton-Raphson solution procedure has been adopted.

40 5.8.2 Convergence The iteration process described in the previous section continues until convergence is achieved. The maximum number of permissible equilibrium iterations is performed in order to obtain the convergence. Convergence is assumed when, II{R}I < eRkef (Out-of-balance convergence) (5.11)

I I { Au, I I < tau pe (DOF increment convergence) (5.12) where {R} is the residual force vector which is equal to - {R} = {F:}-{r} (5.13) which is the right-hand side of Equation 5.8. {Au, } is the DOF increment vector, eR and

eu are tolerances and R ref and uref are reference values (VALUE on the CNVTOL). I I ei is a vector norm; that is, a scalar measure of the magnitude of the vector (defined below). Convergence, therefore, is obtained when the size of the residual is less than a tolerance factor times a reference value and/or when the size of the DOF increment is less than a tolerance times a reference value. The default is to use out-of-balance convergence checking only. The default tolerance values are 0.001 (for both eu and E R ).

5.8.3 Line Search Algorithm The line search option (accessed with LNSRCH command) attempts to improve a Newton-Raphson solution {Au; ) by scaling the solution vector by a scalar value termed as the line search parameter. Consider Equation 5.9, namely {u,,,}={u,}±{Au,} (5.14)

In some solutions, the use of the full {Au, } leads to solution instabilities. Hence, if the line search option is used, Eqn 5.14 has been modified to : {u,,,}={u,}4-s{Au,} (5.15) where s is the line search parameter defined by 0.05 < s < 1.0. s is automatically determined by minimizing the energy of the system, which reduces to finding the zero of the nonlinear equation:

41 gs ({Fa }-{F" (s{Aui })}) (5.16) where, gs = gradient of the potential energy with respect to s. The scaled solution (Au; is used to update the current DOF values

{Au,,,} in Equation 5.9 and the next equilibrium iteration is performed.

5.8.4 Program Developed in ANSYS 10.0 for Present Study The above sections explained the algorithm which is in-built in ANSYS 10.0 to solve a set of non-linear equations resulting from finite element process. For present study, the load has to be applied in cyclic manner with different values of modulus of elasticity for loading and unloading processes. As ANSYS 1. 0.0 does not have an in-built option for the same, this has been incorporated with the combined use of available commands and features of ANSYS 10.0 package. The complete solution program for the simulation of plate jacking test on rock mass has been presented in APPENDIX - I. This deals with the analysis of rock mass having properties as existed at Jamrani Dam site; however, by varying input parameters, the same can become applicable for any type of rock mass.

42 Table.5.1Ro ckMass Properties of allPro ject Sites C4 LI CI-I Z I:4 Load. Intensity, Z 0 d c>, o^ 0 U -E; t GZ E e GIS a 0 0 A z

Project Site Type of MPa CA

Rock . ...--.. ram /1 S P-4 0.i h5 C7- OS ...... ' 0 el ctl cr, 1, .-■ * Len c--4 * -I- l'Il

P a rn 0 —, 0 0 r; 6 en en en cp 0 0 N In 00 't N N In In it O 0 In r`). 0 ,--, V Tr VD • • •

JAMKAN1 o N • 0 op -er o 0 I 0 '1" a \ c:, N v) 0 In In 0 00 cl d- In N N N 4 oo 00 Clay stone cp vi Tr -4 - •

a (21 1/40 N N kr) (••••• 0 CP‘ 6 In N N N t tr.' , CV 0 0 o In N N ct V N o -- , I I i -

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44 Fig. 5.1(b). Zoomed View of Finite Element Mesh near the Loaded Area

45 H. A.

Drucktr-Prager Surface.

Mohr-Coulomb Surface

c cot

H.A. — Hydrostatic Axis

Fig. 5.3. Geometrical Representation of Mohr-Coulomb and Drucker-Prager Yield Surfaces in Principal Stress Space

Mohr-Coulomb Criterion

Line of Pure Drucker-Prager Shear (0 = 0) Criterion

Fig.5.4. Two-Dimensional r - Plane Representation of Mohr-Coulomb and Drucker-Prager Yield Criteria

47 Fig.5.5. Drucker-Prager Yield Criterion in Terms of Stress Variants

,„11. A. - G 3 Drucker-Prager (.> 0) Criterion —a 3 I

Von Mises(4 = 0) Criterion

43- cco

Fig.5.6 Drucker-Prager and Von-Mises Yield Surfaces in Principal Stress Space

48 Fig.5.7 Newton-Raphson Solution-One Iteration

Fig.5.8 Newton-Raphson Solution-Next Iteration

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Fig.5.9 Incremental Newton-Raphson Procedure

Fig.5.10. Initial - Stiffness Newton — Raphson Solution

50 CHAPTER-VI

DISCUSSION OF RESULTS

6.1 GENESIS OF THE PROBLEM Attempt has been made herein to simulate, through finite element analysis, the rock mass surrounding the plates in a plate jacking test which is conducted in a test adit for predicting the stress dependent values of modulii of deformation. Elasto-plastic analysis has been carried out for different cycles of loading and unloading applied during the test. The results of the analysis have been presented in the form of loading intensity versus the corresponding strains for 2nd and the 5th cycles of loading. Values of modulii of deformation have been obtained from these curves for different stress ranges and for different cycles of loading. As per the current practice in vogue, a unique value of modulus of deformation is normally recommended for the purpose of design. This corresponds to the 2" or 5th cycle of loading. However, the rock mass experiences different cycles of loading in the field under different sets of conditions. For example: i) virgin rock mass in the field is already in a state of stress called as the in-situ stress. When an opening is excavated in this rock mass, there occurs a redistribution of stresses in rock mass surrounding this opening. When an additional tunnel is excavated in the vicinity of this opening, there is again a redistribution of stresses around the existing opening. This is the third cycle of stress which the rock mass surrounding the earlier opening experiences whereas the new opening experiences only the second cycle; ii) If the underground structure in the field involves a large cavern, which is excavated, say by multiple drift method, the rock mass surrounding the cavern is subjected to a large number of cycles. It is obvious that material behavior during all these cycles would be elasto-plastic and not elastic whereas the current practice is to estimate the modulus of deformation using the expressions from the Theory of Elasticity. This appears to be somewhat erroneous. The work in this thesis is therefore based on the Theory of Cyclic Plasticity. It is based on the concept that the value of modulus of deformation which should be used in design should, really speaking, correspond to the actual number of cycles to

51 which the rock mass is going to be subjected to in the field. The cycle for which the modulus of deformation should be estimated for use in design shall vary from one situation to the other as stated above. In the present study, especially for the sake of comparison, values of applied load intensity while simulating the field tests, have been kept the same during the first two loading cycles as was done by Mehrotra (1992) while conducting the tests at different dam sites. These load intensities corresponding to various loading cycles have already been presented in Table 5.1. Application of loading, while conducting the tests at different dam sites, was done in two cycles only (Mehrotra, 1992). However, in the present study, number of loading cycles has not been fixed to two. In case the rock mass is able to sustain load intensity over and above that applied during the field tests, the present analysis takes care of the same in terms of more number of loading cycles. It has been observed that rock mass at Jamrani dam site could sustain higher load intensity and so 5 cycles of loading and unloading could be applied. However, for all other dam sites, the rock mass could not undergo more than 2 cycles of loading and unloading. The divergence has been observed during 3rd loading cycle for all dam sites except for Jamrani dam site.

6.2 VERIFICATION OF THE SOLUTION ALGORITHM The solution algorithm has been developed for simulating plate jacking test conditions and analyzing the surrounding rock mass considering the elasto-plastic behaviour. Verification of algorithm developed for the purpose has been done by loading the rock mass in such a way that the response of rock mass remains within the elastic region. The deformation obtained from present study has been compared with the elastic solution available for a circular loaded region. Integrating Boussinesq's solution over circular loaded area, the expression for the elastic settlement at the centre of circular footing at the surface is obtained as q d (1-u2 ) w — (Poulos & Davis, 1974) (6.1)

where, q is the load intensity, d, the diameter of footing, Li, the Poisson's ratio and E, the modulus of elasticity.

52 Figure 6.1 depicts the variation of deformation with load intensity obtained from the present study for same values of loading and unloading modulus of elasticity for the parameters shown in the figure. From Fig. 6.1, the deformation of 0.75 mm has been obtained for a load intensity of 6.0 MPa. However, using Eqn 6.1, the deformation corresponding to same load intensity would be 0.82 mm. The difference in these two results has been found to be of the order of about 10% which may be due to the fact that elasto-plastic behaviour of rock mass has been considered in the present analysis although the loading is in elastic range. This verifies the developed solution algorithm, as for all practical purposes this difference in results from two different approaches is acceptable.

6.3 LOAD INTENSITY VERSUS STRAIN RESPONSE OF JAMRANI DAM SITE Variation of stress and deformation in the width direction has been presented in Fig. 6.2(a) and Fig. 6.2(b) respectively. The parameters used in the analysis have been derived from Mehrotra (1992) and presented in respective figures. The vertical stress has been found to reduce by 45% towards the edge of the plate, however the reduction in vertical deformation has been found to be 20%. It is clear from the figure that plate deforms almost uniformly indicating that its behaviour is similar that of a rigid plate. Figure 6.3a displays the variation of vertical stress along the line of symmetry (central line of rock mass). The figure reveals the fact that influence of load intensity reduces with increasing distance from the point of application of load and becomes almost zero at larger distances. Figure 6.3(b) presents the variation of vertical deformation along the central line of plate for the parameters shown in the figure. It has been observed that vertical deformation reduces with increase in distance from the point of application of load and tends to be zero at greater distances. Plastic strain comes into picture when the rock mass exceeds its yield stress. The spread of plastic zone has been shown in Fig. 6.4 for parameters, Eloading = 2000 MPa,

Ennloading = 2500 MPa, µ = 0.33, c = 0.33 MPa and o = 45°. Plastic zone has been found to spread with increase in the load intensity. Deformations in rock mass under different load

53 intensities have been presented in Fig 6.5 for the same set of parameters as mentioned above. Variation of strain, at the excavated surface of rock mass at centre of plate, has been presented, with applied load intensity for natural moisture condition in Fig. 6.6(a) and Fig. 6.6(b) for 2 and 5 cycles of loading respectively. The maximum load intensity corresponding to first two load cycles (Fig. 6.6a) has been kept to be the same as used by Mehrotra (1992) during his field tests. The strain has been obtained with respect to the width of loading plate. Variation of strain with load intensity for saturated condition of rock mass, for 2 and 5 cycles of loading, have been presented in Fig. 6.7(a) and Fig. 6.7(b) respectively. As the rock mass at the dam site possesses high cohesion, it has sustained the applied load till the load intensity reached a value of 12.75 MPa in natural condition. Hence, it was possible to analyze the rock mass till 5 loading cycles. Linear load intensity versus strain response has been observed for the first 2-cycles of loading. In saturated condition, the solution converged just after 2 cycles, which indicated that the strength of rock mass reduced significantly when it is fully saturated.

6.4 LOAD INTENSITY VERSUS STRAIN RESPONSE OF KOTLIBHEL DAM SITE Figures 6.8(a) and 6.8(b) depict the variation of strain at surface of rock mass at centre of loading plate with applied load intensity when rock mass is in natural moisture condition and saturated condition respectively at Kotlibhel dam site. For natural moisture condition, the rock mass has been first subjected to a load intensity of 2.7 MPa corresponding to which the resulting strain was 0.984 x 10-3. After unloading, rock mass has been reloaded to 5.06 MPa for which the corresponding strain level has been found to be 2.3 x10-3. Rock mass has been subjected to further loading after the unloading in 2" cycle and the failure has been observed at a load intensity of 6.0 MPa in the form of divergence. For saturated condition, the failure has been observed at a load intensity of 5.25 MPa during the third loading cycle as shown in Fig. 6.8(b).

54 6.5 LOAD INTENSITY VERSUS STRAIN RESPONSE OF LAKHWAR DAM SITE The load intensity vs. strain response in natural moisture and saturated conditions of rock mass has been presented in Figs. 6.7(a) and 6.7(b) respectively for Lakhwar dam site. Rock mass has been observed to fail at a load intensity of 6.75 MPa and 4.5 MPa for natural moisture and saturated conditions respectively during the third loading cycle for the parameters shown in respective figures. As rock mass possess higher values of modulii of elasticity, the strains have been observed to be relatively less.

6.6 LOAD INTENSITY VERSUS STRAIN RESPONSE OF SRINAGAR HYDEL DAM SITE Variation of strain at surface of rock mass at centre of loading plate with load intensity in natural moisture condition has been presented in Fig. 6.10(a). Figure 6.10(b) shows similar variation for the saturated condition. Here also, the failure has been observed during the third loading cycle. The failure load intensity has been found to be 7.5 MPa and the corresponding strain has been observed to be 2.11 x 10-3 for natural moisture condition.

6.7 LOAD INTENSITY VERSUS STRAIN RESPONSE OF TERRI DAM SITE ZONE The load intensity vs. strain response for natural moisture and saturated conditions at Tehri dam site has been presented in Figs. 6.11(a) and 6.11(b) respectively. The load intensity at failure has been observed to be 5.25 MPa and 4.5 MPa for the respective conditions. Shear strength of rock mass at this site was less and so higher values of strains have been observed as compared to strains obtained in case of Lakhwar and Srinagar hydel dam sites.

55 6.8 ESTIMATION OF LOADING AND UNLOADING MODULII FOR DIFFERENT CYCLES OF LOADING The values of modulus of deformation have been evaluated for loading and unloading of each loading cycle for different stress ranges. These have been found to vary with different stress ranges due to nonlinearity in the behaviour of rock mass. For a particular stress range, the modulus of deformation has been calculated by taking the ratio of the difference of load intensities and the difference of corresponding strains at two extremes of considered stress range. Tables 6.1 and 6.2 give the modulii values for natural moisture and saturated conditions respectively at various dam sites considered in the present study, for different stress ranges during various loading and unloading cycles. From these summarized results, it has been observed that values of modulus of deformation significantly reduce as the condition of rock mass changes from natural moisture condition to saturated condition. This reduction has been observed to vary from 15% to 65% for different dam sites.

6S COMPARISON OF MODULII WITH THE FIELD TEST DATA The deformation modulus was obtained by Mehrotra (1992) using Boussinesq's rigid punch equation as given below:

u2 )P Edm (1— (6.2) (5 12) where, P represents the normal load; u, the Poisson's ratio; m, a constant = 0.96 for circular plate; A, the area of the plate and 6, the deformation corresponding to load P. The value of S used in the above expression was obtained the from stress-deformation response observed in plate jacking tests conducted by Mehrotra (1992) at various dam sites. The procedure adopted by Mehrotra (1992) to obtain modulus of deformation has been explained in Fig.6.12. An attempt has been made herein to compare the Values of modulus of deformation obtained in the present study with those obtained by Mehrotra (1992) and have been presented in Tables 6.1 and 6.2 for natural moisture and saturated conditions respectively It has been clear that the values of modulii of deformation obtained in the

56 present study are quite different from those obtained by Mehrotra (1992). Generally, present study provides higher values of modulus of deformation. Modulii values computed by Mehrotra (1992) correspond to 2 cycles of loading and unloading. Moreover, Mehrotra (1992) assumed elastic behaviour of rock mass while analysing his field test data and obtaining the modulus of deformation. However, the present study considers a more realistic i.e. elasto-plastic r of the rock mass. This may be the reason why the results from these two approaches have been found to be so different from each other.

6.10 CONCLUDING REMARKS Following generalized conclusions have been drawn from the consideration of the elasto-plastic response of rock mass in plate jacking tests to cyclic plasticity: ■ The solution algorithm developed in this study successfully simulates the plate jacking test conditions. ■ The load intensity at failure has been found to be the highest in case of Jamrani dam site (12.75 MPa). For Kotlibhel, Lakhwar, Srinagar hydel and Mini dam sites, the failure load intensity in natural moisture condition has been observed as 6.00 MPa, 6.75 MPa, 7.5 MPa and 5.25 MPa respectively. ■ Modulus of deformation has been found to reduce significantly as rock mass approaches a fully saturated condition and this reduction can be to the extent of 65% which is quite significant so as to influence the design. ■ Values of deformation moduli obtained in the present study have been found to be quite different from those obtained by Mehrotra (1992). This may be due to the fact that both approaches assume different behaviour of rock mass. ■ This analysis also provides an alternate method of predicting the modulus of deformation of rock mass in situations where the field conditions are very difficult and do not permit conducting a plate jacking test in the field.

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Eunloading = 4000 MPa 6 c = 0.50 MPa = 40° = 0.30 d = 600 mm 5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 8 Deformation (mm)

Fig 6.1 Load intensity vs Deformation Response for Verification of Solution Algorithm

Distance from centre of plate along its width (mm) 0 50 100 150 200 250 300

AMR =27

Eloading = 2000 MPa Eunloading = 2500 MPa c = 0.33 MPa o = 45° =0.33

12 -

Fig. 6.2(a) Variation of Vertical Stress Along the Plate Width for Jamrani Dam Site

Distance from centre of plate along its width (mm)

0 50 100 150 200 250 300 0 1 RMR = 27 Blanding = 2000 MPa Eunloading = 2500 MPa c = 0.33 MPa = 45° = 0.33

5 .

Fig.6.2(b) Variation of Vertical Deformation Along Plate Width for Jamrani Dam Site

63 Vertical stress (MPa) 0 2 4 6 8 10 12 14

E 1000 - o t 2000 RMR = 27

CU T _Flouting = 2000 MPa " Eunloading r- 2500 MPa 2 o- 3000 c = 0.33 MPa

• • = 45° tCC:;; sto 4000 - = 0.33

5000

Fig. 6.3(a) Variation of Vertical Stress Along Line of Symmetry for Jamrani Dam Site

Vertical deformation (mm)

0 1 2 3 4

o. E o 1000 -1 tal

5 2000 RMR = 27 ELoming = 2000 MPa 5 c8 Eunloading = 2500 MPa 0 3000 c = 0.33 MPa <.)(1) C o = 45° ed = 0.33 .4 C:Z 4000

5000

Fig. 6.3(b) Variation of Vertical Deformation Along Line of Symmetry for Jamrani Dam Site

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I NODAL SOLUTION NS YS JUN 17 2007 8T1/•16 18:14:06 SUB •7 TIM215.05 us (AVG) ASYSflO DM( .1_554 SIM —.6552-04 SEX -1.554

-.1002,114 .34320 .1044.) 1.111 1.341 .1111St .11411S 1.[O,

Fig.6.5. Deformations in Rock Mass at Different Load Increments for Jam ran Dam Site (contd...) (Bloating = 2000 MPa, Eunioadmg = 2500 MPa, µ = 0.33, c = 0.33 MPa and ei = 45°)

66 NODAL SOLUTION ANSYS STEP-16 JUN 17 2007 SUB fl2 18:14:28 TIO3=15.6 UY MOM RSYS=0 Dort =2.465 SUN s-.4491-03 SOX =2.465

-.44360 .747421 1.4ff 1.141 1.131 .247441 .421271 1.417 1.4114

L NODAL SOLUTION ANSYS sT1D..14 JUN 17 2007 SOH -16 18:14:53 Tffi-15.8 UT IAVGY ASYSE0 ONX 3_407 NO -_4401-03 SEX =3_407

-.440E-01 . 1.514 t.til 7.027 .174112 1.11, 1.051 1.17 1.447

Fig.6.5. Deformations in Rock Mass at Different Load Increments for Jamrani Dam Site (Flooding = 2000 MI); Eunloading = 2500 MPa, g = 0.33, c = 0.33 MPa and 0 = 45°)

67 14

RMR = 31 12 - Eioading = 2000 MPa = 2500 MPa c = 033 MPa = 45° 10 - =0.33

0 1 2 3 4 5 6 7 8 Strain X 10-3

Fig. 6.6(b) Load Intensity vs Strain Response at Jamrani Dam Site for 5-cycles of Loading (Natural Moisture Condition)

69 4.5 RMR = 28

4 Eioading = 1200 MPa Eunfoading = 1500 MPa c = 0.29 MPa 3.5 - = 40° 1 = 0.35

3- cc;

F? 2.5 a

1.5 -

0.5 -

0 0.5 1 1.5 2 2.5 3 3.5 Strain X 10-3

Fig. 6.7(a) Load intensity vs Strain Response at Jamrani Dam Site for 2-Cycles of Loading (Saturated Condition)

70 7

RMR =27 Eloading = 2200 MPa 6 Eunloading = 2775 MPa c = 0.195 MPa = 40° = 0.32 5 11

0 0.5 1 1.5 2 2.5 3 3 5

Strain X 10-3

Fig. 6.8(a) Load Intensity vs Strain Response at Kotlibhel Dam Site for 2-Cycles of Loading (Natural Moisture Condition)

72 6 RMR --- 24

Eloading = 1100 MPa = 1375 MPa 5 Eunloading c = 0.18 MPa 0 = 38° 11. = 0.34

0 1 2 3 4 5

Strain X 10-3

Fig. 6.8(b) Load intensity vs Strain Response at Kotlibhel Dam Site for 2-Cycles of Loading (Saturated Condition)

4.5 - RMR =51 Eloading = 3000 MPa Eunloading = 3750 MPa 4 = 0.20 MPa erC = 35° = 0.32 3.5 - ictc cL.., 3 c

2.5 - N -o

Q 2 l

1.5 -

0.5 -

0 0.5 1 1.5 2 Strain X 10-3

Fig. 6.9(b) Load Intensity vs Strain Response at Lakhwar Darn Site for 2-Cycles of Loading (Saturated Condition)

75 7

RMR = 42 fianding = 2800 MPa 6 Funloading = 3500 MPa c = 0.23 MPa = 380 = 0.28

) Pa

M 4 ( ity s ten

In 3 - d a Lo

0 0 0.5 1 1.5 2 2.5 3 Strain X 10-3

Fig. 6.10(b) Load Intensity vs Strain Response at Srinagar Dam Site for 2-Cycles of Loading (Saturated Condition)

77 RIV1R = 27 4.5 - Blooding = 1500 MPa Elmloading = 1875 MPa 4- c = 0.18 MPa _ 350

= 0.30 3.5 -

2.5 - 02

7:3 0 1-1 1.5 -

1 -

0.5 -

0 1 2 3 4 5 Strain X 10-3

Fig. 6.11(b) Load Intensity vs Strain Response at Tehri Dam Site for 2-Cycles of Loading (Saturated Condition)

79 Sires ra•ra,

40.0

35.0

30.11

11 e 20.0

% 15-0

10.0

5.0 8- 343rarni So 3.(.6mm

0'0 1--- o-- , r. D 1'0 , . 2'0 3.0 ire 5.0 60 PO 80 Oct orina tIon, mm......

E 0 P (Boussinescrs rigid DirCII equation) VATh g/2-

0460-0.04/x42-44x2B2S Ed e Vidfra x (0,3/2 1 el 133870 k9/a+

Fig. 6.12 Method for Calculating Modulus of Deformation from Test Data (Mehrotra, 1992)

80 CHAPTER-VII

CONCLUSION

7.1 SUMMARY OF WORK DONE The present study is aimed at predicting modulus of deformation of rock mass by considering elasto-plastic behaviour of rock mass and using the Theory of Cyclic Plasticity. The available literature related to the problem considered has been reviewed which included experimental studies as well as empirical correlations. The geological and geotechnical data for five different dam sites have been considered (Mehrotra, 1992) for the purpose of analysis. Simulation of plate jacking tests and analysis of rock mass in these test conditions have been carried out using finite element approach with the help of ANSYS 10.0 software package. Simulation has been done for five dam sites and the modulus of deformation has been evaluated corresponding to different loading and unloading cycles for different stress ranges. These values have been compared with those obtained from the analysis of available field test data (Mehrotra, 1992).

7.2 CONCLUSIONS Based on the results of elasto-plastic finite element analysis of rock mass in plate jacking test conditions, following generalized conclusions have been drawn: i) Present study takes care of the elasto-plastic behaviour of rock mass under plate jacking test conditions and is based on Theory of Cyclic Plasticity. ii) Failure load intensity and modulus of deformation are greatly affected by both geological as well as geotechnical parameters. iii) Degree of saturation has a significant bearing upon the values of modulus of deformation. Modulus of deformation reduces with increase in degree of saturation. iv) The values of modulus of deformation obtained in the present study do not match with those obtained from the analysis of field test data (Mehrotra, 1992) due to the

81 fact that present study considers elasto-plastic behaviour of rock mass however, Mehrotra (1992) assumed this to be elastic. v) The analysis provides an alternative to the estimation of modulus of deformation in situations where the field conditions are very difficult and prohibit conducting a plate jacking test in an adit.

7.3 SCOPE FOR FUTURE WORK The present study can be improved in predicting the response of rock mass by incorporation of following suggestions:

i) Consideration of response of joints sets, their orientation and characteristics. ii) Extension of present analysis to 3-D situations. iii) Simulation of other in-situ tests for better prediction of modulus of deformation. iv) Development of sophisticated computer program to incorporate different stress- strain relationship during any loading/unloading cycle.

82 REFERENCES

1. Adnan, J. Z., 2004. Finite element analysis of shallow foundations for eccentric inclined loads", Ph.D Thesis, Department of Civil Engineering, Indian Institute of Technology Roorkee, 2. Bieniawski, Z.T., 1978. Determining rock mass deformability: experience from case histories", Int. J. Rock Mechanics & Mining. Sci. Geomechanics Abstr. 15, 237. 3. Clerici, A., 1993. Indirect determination of the modulus of deformation of rock masses-case histories. Proc. Conf. Eurock 1993, pp. 509-517. 4. CSMRS (Central Soils and Material Research Station), Manual on Rock Mechanics; CBPI, New Delhi, May, 1988. 5. Drucker, D. C. and Prager, W., 1952. Soil mechanics and plasticity analysis on limit design. Q. Appl. Math., 10, pp. 157-165. 6. Gokceoglu, C., Sonmez, H. and Kayabasi, A., 2003. Predicting the deformation moduli of rock masses. Int. J. Rock Mech. Min. Sci.40, 701-710. 7. Grimstad, E. and Barton, N., 1993. Updating the Q-system for NMT. Proc. Int. Symp. on Sprayed Concrete, Fagernes, Norway 1993. Norwegian Concrete Association, Oslo 20 pp. 8. Hoek, E. and Brown, E. T., 1997. Practical estimates of rock mass strength. Int. J. Rock Mech. Min. Sci. 34:1165-1186. 9. Hoek, E. and Diederichs, M. S., 2005. Empirical estimation of rock mass modulus. Int. J. Rock Mech. Min. Sci. 43: 203-215 10. ISRM, 1979. Suggested methods for determining in situ deformability of rock. Int. J. Rock Mechanics Miner. Sci. Geomechanics Abstr.16 (3), 195-214. 11. Kayabasi, A., Gokceoglu, C. and Ercanoglu, M., 2003. Estimating the deformation modulus of rock masses: a comparative study. Int. J. Rock Mech. Min. Sci.40, 55-63. 12. Mehrotra, V. K., 1992. Estimation of engineering parameters of rock mass. Ph.D Thesis, Department of Civil Engineering, Indian Institute of Technology Roorkee, India.

83 13. Palmstrom, A. and Singh, R., 2001. The deformation modulus of rock masses- comparisons between in situ tests and indirect estimates. Tunneling and Underground Space technology 12:115-131. 14. Poulos, H. G. and Davis, E. H., 1974. Elastic solutions for soil and rock mechanics, Canada, Rainbow-Bridge Book Company. 15. Ragab, A. R. and Bayoumi, S. E., 1998. Engineering solid mechanics: fundamentals and applications. Boca Raton, FL, CRC Press. 16. Read, S. A. L., Richards, L. R. and Perrin, N. D., 1999. Applicability of the Hoek—Brown failure criterion to New Zealand greywacke rocks. In: Vouille, G., Berest, P., editors. Proceedings of the ninth international congress on rock mechanics, Paris, August, vol. 2; 1999. p. 655-60. 17. Serafim, J.L. and Periera, J.P., 1983. Consideration of geomechanics classification of Bieniawski. Proc. Int. Symp. on Engineering Geology and Underground Constructions, pp. 1133-1144 18. Singh, B., Viladkar, M. N., Samadhiya, N, K. and Mehrotra, V. K., 1997. Rock mass strength parameters mobilised in tunnels. Tunneling and Underground Space Technology 12(1). 19. Verman, M., Singh, B., Viladkar, M. N. and Jethwa. J.L., 1997: Effect of tunnel depth on modulus of deformation of rock mass. Rock Mechanics and Rock Engineering, 30(3), 121-127 20. Zienkiewicz, 0. C., 1983. The finite element method in engineering and science. McGraw Hill, New Delhi, India

84 APPENDIX-I

PROGRAM DEVELOPED FOR SIMULATING PLATE JACKING TEST

The program developed for simulating the plate jacking test conditions for Jamrani dam site with rock mass under natural moisture condition is presented below. However, this program is quite general enough for the analysis of any type of rock mass just by providing corresponding rock mass properties and applied load intensity for various cycles.

/NOPR /PMETH,OFF,0 KEYW,PR_SET,1 KEYW,PR_STRUC,1 KEYW,PR_THERM,0 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 KEYW,MAGHFE,0 KEYW,MAGELC,O KEYW,PR_MULTI,0 KEYW,PR_CFD,0 /GO /COM, Structural ET,1,PLANE82 KEYOPT,1,3,1 KEYOPT,1,5,0 KEYOPT,1,6,0

! Variables ROCKMODULUS_L=2000 ROCKMODULUS_U=2500 ROCKPOISSON=0.33 CONCMODULUS=27386 CONCPOISSON=0.17 MPTEMP„,„„, MPTEMP,1,0 MPDATA,EX,1„ROCKMODULUS_L MPDATA,PRXY,1„ROCKPOISSON

85 PrEt,ipp,1„, 113MOID IF ,1,1,0.33 TTIMOIDIF,1,2,45 1-13MODIF,1,3,0 MP-TEMP „ „ „ „ MPTEMP, I ,0

MPTEMP„„„„ IVIPTEMP,1,0 MP ITYALTA.,E,C,2 „ col-4cm or)T_TLAIS MPIDATA,PEOCY,2„CO-NICPOISSONT MP TEMP „ „ „ „ MP TEMP, 1 ,0

MP'TEMP„„„„ MPT'EMP,1,0 IVIPIDAT'A,,EX,3„R_OCKMODULTJS_TJ MPIDATA„PRiCY,3„R_OtC1CPOIS SON

TEI,DP,3„, TIEIMOT)IF, 1 , 1 ,0 _33 TT3MOID IF ,1,2,45 TTIMOL)IF,1,3,0 MP 1 _El\ 4P, „ „ , MP'TEMP,1,0

! Geometry 1C„13,0„ K„4500,0„ IC„4500,4500„ IC„0,4500„ K„300,0„ K„300,-25„ IC„0,-25„ IC„2250,0„ K„2250,2250„ IC„0,2250„ K„4500,2250„ IC„2250,4500„ LSTR, 10, 9 LSTR, 9, 8 LSTR, 8, 2 LSTR, 2, 11 LSTR, 11, 9

86 LSTR, 11, LSTR, 3, 12 12, 9 LSTIR, 12, 4 LSTR, 4, 10 LSTR, 10, 1 LSTR, 6, 5 LSTR, 6, 7 LSTR, 7, 1 LSTR, 1, 8

/AUT 0,1 /REP, FAS T FLST,2,4,4 FITE1v1,2,10 FITE1v1,2,9 FITEN/1,2,8 FITEM,2,1 AL„P51X FLST,2,4,4 FITEM,2,7 FITEM,2,6 FI'TElvf,2,5 FIT'EN4,2,8 A.L„P51X FLST,2,4,4 FI-TEN4,2,1 FITE1v1,2,2 FITEM,2,15 FITEM,2,11 ALPS 1C FLST,2,4,4 FITElv1,2,5 FITEM,2,4 FITEN4,2,3 FITEM,2,2 A.1L,P51X LSTR, 5, 1 FLST,2,4,4 FITEN4,2,12 FITEM,2,13 FITEM,2,16 FITE,1v1,2,14 AL,P5 13C FEST',2,4,5,ORDE,2 FITEN/1,2,1

87 FITEM,2,-4 AADD,P51X FLST,2,2,5,ORDE,2 FITEM,2,5 FITEM,2,-6 A CLUE,P51X

Meshing FL,ST,5,4,4,ORDE,4 FITEM,5,3 FITE M,5,6 FITEM,5,-7 FITEM,5,1 0

LSEL, „P51X

CM SEL..„_X LES IZE,__V1„ ,15,1„ „1 FEST,5,2,4,ORDE,2 F1TEM,5,4 FITEM,5,9 C Y,L,INTE LSEL,„ „P51X CM,_Y1 ,LINE CMSEL,„ Y L,ESIZE, 1, „20,1, , ,1 FL,ST,5,1,4,01213E,1

CM,__Y, LINE ESEE„ „P51X Y1,ErN-E CNISEL,„_Y „30,1„ „1 FLST,5,1,4,4DRI3E,1 Frrsm, 5,1

LSEL„ „P51X CM, YI,LINTE CMSEL,„_Y ,25,1„ „1 FLST,5,1,4,OR_DE,1 FITEIV1,5,16

ESEL,„ „P51X CM,Y1,1-FINIE

88 CMS EL, _V LESIZE, _V 1 , „ 5, 1 „ „ 1 1‘.4 SHAPE, 0,2L)

CM,Y,AR_EA A SEL, „ 1 CM,_Y 1 ,AREA CITICMS1-1,1AR_EA' CM S EL AIVIESH,_Y 1 CMIDELE,_Y- CMIDELE,y 1 C MID EL,E,LY2 OP LOT OPLOT

TYPE, 1 MAT, 2 REAL, ES VS, 0 SECIW , FLST,5,1,4,ORDE,1 FITEM, 5,13 CNL,_Y,LINE L S EL, , ,P5 1 X 1 ,LINIE CMSEL„ Y- L,ESIZE, „5,1 , , ,1 ELS , 2,4, ORIDE,2 FITEM,5, 12 FITEM,5, 14

LSEL, „ ,P51 X , LINE CMSEL.„_V LESIZE, „ ,2, 1 „ „ 1 CIVI,±Y,.AREA ASEL, „ 5 CM,±Y 1 „AREA C HKIVI S H A.Ft EA' CMSEL, S, A_ME S 1-1,_ Y 1

C MIDELE,_1( 1 CMIDELE,_V2

89 !Boundary Conditions !Displacement boundary conditions

FINISH /SOL FL,ST1,2,4,4,0aDlE,4

FITE11.4,2,6 FITEM,2,10

/GO 131_,,P51„LIX, FL-ST',2,2,4,0Ft_DE,2

FITEM,2,9 /GC) DL,,P51X„LTY, FINISH

!Application of cyclic load and Solution !Loading of -1 st cycle /SOL ANTYPE„,0

FL-S-F,2,1,4,01ZDE,1 FrTEIVI,2,13 SFL.,,P513C,PR_ES,2.8, INTSIJI3ST,10,10,10 OLTER_ES,E,RASE OUTRES,ALL,ALL LeNISRCI-1,1 CINTNITOL„F„0.001,2,0.01, CNV701_,L1„0_001,2, FTIME,4 L.SWRITE,1 ESSOE:VE,1,1,1

!Unloading of 1st cycle

*DO,COLTNITT4,1,1435,1 MPCI-10,3,COUTh1/41-1-1■1, * EN OD 0 ALLS

90 /SOL ANTYPE,O,0 N1,0E0M,1 FLSIT,2,1,4,ORDE,1 FIT'EM,2,13 SFL,,P51X,PR_ES,2.8, N S LIB ST,1,1,1,0N OLJTRES,ER__ASE °UTILES ,ALL,A.L,L, LINTS RCH,1 CNVTOL,F „O. 001,2,0. 01, CNVTOL,,LJ„0.001,2, ,

LS WRITE,2 LSSOLVE,2,2,1

/SOL, ANTYPE,OPE,0 NL0E0N1,1 FLST",2,1,4,01WE,1 FITEM,2,13 SFL,P51X,PR_ES,O, SUB ST,5,5,5, ON OUTRES,ERASE OUTRES,ALL,,A LE ENSRCH,1 CNVTOL, F„0.001,2,0 .01, CNATT OL,LT„ 0 . 001,2„ !TIME,4 LS WR_ITE,3 LSSOLVE,3,3,1

Loading of 2nd cycle

* DO, CO UNTN,1, 1435 , I MPCH0,1,CO UNT1\T, * ENIDD 0 ALLS

/SOL ANTYPE,O NL0E0M,1 FLST,2,1,4,ORDE,1 FITENI,2,13 SFL,P51X,PRES,4.244, NSUBST,10,10,10,0INI

91 OUTRES,ERASE OUTRES,A.LL,ALL, UNSRCH,1 CNVTOL„F„0.001,2,0.01, CNVTOL,U„0.001,2„ !TINIE,4 L,SWRITE,4 LSSOLVE,4,4,1

!Unloading of 2nd cycle

*DO,COUNTN,1,1435,1 NIPCF10,3,COUNTN, * EN ID 0 ALLS

/SOL ANTYPE,0 NLGEON1,1 FLST,2,1,4,ORDE,1 FITEM,2,13 SFL„P51X,PRES,4,244, NSUBST,1,1,1,ON OUTRES,ERASE OLITRES,AL,L„ALL, LNSRCH,1 CNVTOL,F„0.001,2,0_01, CNVTOL,U„0.001,2„ !TIIVIE,4 1_,SWRITE,5 LSSOLVE,5,5, I

/SOL, ANTYPE,O NLGEOM, I FLST,2,1,4,ORDE,1 FITEM,2,13 SFL,P51X,PRES,O, NSUBST,5,5,5,ON OUTRES,ERASE OUTRES,ALL,,ALL, LNSRCH, I CNVTOL,,F„0.001,2,0 _01, CNV1-01_,,U„0.001,2, !TIME,4

92 LSWRITE,6 LSSOLVE,6,6,1

!Loading of rd cycle

*DO,COLTNTN,1,1435,1 MPCHG,1,COLTNTN, *ENDDO ALLS /SOL ANTYPE,O NLGEOM,1 FLST,2,1,4,ORDE,1 FITEM,2,13 SFL,P51X,PRES,6, NSUBST,10,10,10,0N OUTRES,ERASE OUTRES,ALL,ALL LNSRCH,1 CNVTOL,F„0.001,2,0.01, CNVTOL,U„0.001,2„ !TIME,4 LS WRITE,? LSSOLVE,7,7,1

!Unloading of 314 cycle

*DO,COLINTN,1,1435,1 MPCHG,3,COUNTN, *ENDDO ALLS

/SOL ANTYPE,O NLGEOM,1 FLST,2,1,4,ORDE,1 FITEIV1,2,13 SFL,P51X,PFtES,6, NSUBST,1,1,1,ON OUTRES,ERASE OUTRES,ALL,ALL ENS RCH,1 CNVTOL,F „0.001,2,0 _01, CNVTOL,U„0.001,2„ !TIME,4 LSWRITE,8

93 LSSOLVE,8,8,1

/SOL, ANTYPE,O INILOE0M,1 FLST,2,1,4,0R_DE,1 FITEM,2,13 SFL,P51X,PRES,O, NSUBST,5,5,5,0N OUTRES,ERASE OUTR_ES,AL,L„ALL,

CNIVTOL,F„0.001,2,0 .01, CNV TC>L„ „ 0. 001 ,2 „

LSWRITE,9 LS SOLVE,9,9,1

!Loading of 4th cycle

*1)0,C OUNTN,1,1435,1 MPC1-1G,I,CouNMT, *ENDIDO ALLS

/SOL ANT YP E, 0 NLGEOIV1,1 FLST,2,1,4,0R_DE,1 FITEM,2,13 SFL,P51X,PR_ES,8, NSUBST,20,20,20,4D/NT OUTR_ES,ERASE OUTRES,ALL, A EL LEN S R_CH,1 CNVT101_,,F„0.001,2,0.01, CNVT'OL,U„0.001,2„ ! LS WR_ITE,10 LS SOLVE,10,10,1

!Unloading of 4th cycle

*IDO,COUNTN,1,1435,1 1V1PCH0,3,COLTNETN, *ENDIDO

94 ALLS

/SOL, ANTYPE,O NLGEOM,1 FES'T,2,1,4,ORDE,1 F1TEM,2,13 SFL,P51X,PRES,8, NSUBST,1,1,1,ON OUTRES ,ERASE, OUTRES,ALL,ALL LNSRCH,1 CINTV'T'OLY„0.001,2,0.01, CNVTOL,U„0.001,2„ TIME,4 LSWRITE,11 LSSOLVE,1 1,1 I,1

/SOL, ANTYPE,O NEGEOM,1 FEST,2,1,4,0R3DE,1 FITEM,2, 13 SFL„P51X,PR_ES,O, NSUBST,5,5,5,ON OUTRES,ERASE OUTRES,ALL,ALL LNSRCH,1 CNVTOL„F„0.001,2,0.01, CNV TOL ,LJ „O. 001,2 „ !TEVIE,4 1_,SWRITE,12 L,SSOLVE,12,12,1

!Loading of 5th cycle

*IDO,COUNITN,1,1435,1 MP CH 0, I , C 0 UNTN, *ENDDO ALLS

/SOL, ANTYPE,O NLOEOM,1 FES T,2, I ,4,ORDE,1

95 FITEIN4,2,13 S FL, P51X,PRES ,10, IV SUB s-r,20,20,20,01\I 0151-12ES, ERASE OUTRE S 1-1■1 S12.C1-1, 1 C1NT VTOL,F, 0_001,2 ,0 _ 01 , CIWT 1_,,U,0.001 , 2 „ f LS WRITE, 13 L.SSOLATE,13,13,1

!Unloading of 5Th cycle

*1:040,COLTI■TY14,1,1435,1 1\4P CFI G,3 , C 01.31■1-TINT, EINTDDO ALI- S

/SOL, AINTTYPE,0 1■11_,GE C11\4,1 FLST,2,1,4,0R_OE,1 FITE1\4,2,13 SFL„P51X,PR_ES,10, TVS unST,1, I ,1,01■1 OUTRES,ERASE OUTRES,A&.L,ALL LINISR C1-1, ON,/ L„F „ O. 001 ,2,0. 01 , Ci■T VTO „0_001,2 „ ! LS WRITE, 14 L./SSCIT.-ATE, I 4,14,1

IS OE ANT E,0 NIECE01\4,1 FLST,2,1,4, OftrIE,1 FIT'Ely1,2,13 SFL,P51X,PRES,O, NSUBST,5,5,5,ON OUT RES ,ERASE OLVTICE S,A1-1-, L,1_, LINT S R_CI-I,1 CI\T\PTOL,F„0.001,2,0 _01,

96 CNVTOL,U„0.001,2„ !TIME,4 LSWRITE,15 LSSOLVE,15,15,1

!Loading of till Convergence

*DO,COUNTN,1,1435,1 MPCHG,1,COUNTN, *ENDDO ALLS

/SOL, ANT YPE,0 NLGEOM,1 ELS 7;2,1,4,ORIDE,1 FITEM,2, 13 SFL,P51X,PRES,15, NSUBST,20,20,20,ON OUTRES,ERASE °LITRES ,ALL,ALL LNSRCH,1 CNVTOL,F„0.001,2,0.01, CNVTOL,U„0.001,2„ !TIME,4 LSWRITE,16 LSSOLVE,16,16,1