Swell Pressures and Retaining Wall Design In

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SWELL PRESSURES AND RETAINING WALL DESIGN

IN EXPANSIVE SOILS

Thesis

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Master of Science in Civil Engineering

Eman M.S. Mansour

Dayton, Ohio

December, 2011

SWELL PRESSURES AND RETAINING WALL DESIGN

IN EXPANSIVE SOILS

Name: Mansour, Eman M. S.

APPROVED BY:

Ömer Bilgin, Ph.D., P.E. Steven L. Donaldson, Ph.D. Advisory Committee Chairman Committee Member Assistant Professor Assistant Professor Department of Civil and Department of Civil and Environmental Engineering Environmental Engineering & Engineering Mechanics & Engineering Mechanics

Elias A. Toubia, Ph.D. Committee Member Assistant Professor Department of Civil and Environmental Engineering & Engineering Mechanics

John G. Weber, Ph.D. Tony E. Saliba, Ph.D. Associate Dean Dean, School of Engineering School of Engineering & Wilke Distinguished Professor

ABSTRACT

SWELL PRESSURES AND RETAINING WALL DESIGN

IN EXPANSIVE SOILS

Name: Mansour, Eman M. S.

University of Dayton

Advisor: Dr. Ömer Bilgin, P.E

Expansive soils cause damages to civil engineering structures in various parts of the world, because they swell when absorb water and shrink when they dry out.

Additional stresses applied to the structures due to the swell pressures are important in explaining some of the damages to the structures in expansive soils. Therefore, the prediction of the swell pressures and taking them into consideration in the design of retaining structures is needed. In other words, if these pressures are not included in the design, the stability of the structure will be reduced, potentially to the point of failure.

Retaining walls in expansive soils are subjected to uplift forces and friction forces due to the swelling of surrounding soil. More importantly, the walls are also subjected to swell pressures tending to cause additional deformations and bending.

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In this study, the relationship between the index properties and swelling characteristic of expansive soils is examined. The earlier studies showed that an increase in dry density and plasticity index of the soil cause an increase in swell pressure, while a decrease in natural moisture content cause an increase in swell pressure.

The process of swelling and shrinking is a cyclic behavior and continues for many years. Thus, when the expansive soils are present behind retaining walls, traditional lateral earth pressures cannot be used to estimate total pressures acting on the retaining structure. In this study, a new proposed method developed to predict potential swell pressures and to use in the design of retaining walls. A parametric study performed to study the effect of swell pressures on the design of anchored sheet pile walls constructed in expansive soils. The parametric study results show that, based on the soil properties and wall geometry, the expansive soils can significantly affect the design of retaining structures. More importantly, ignoring the effect of expansive soils on retaining walls would result in under design and unsafe structures. In addition, it was comparing between the proposed swell pressure method and the constant swell pressure method, the different between those methods, the previous method (constant swell pressure method) did not consider the changing in plasticity index and the moisture content. On the other hand, the proposed method takes in the account the changing in each of plasticity index and the moisture content that play important roles in the swell pressure.

ACKNOWLEDGEMENTS

I would like to express my sincerest thanks to my advisor, Prof. Bilgin for his professional guidance, invaluable advice, encouragement, and support through the course of this work.

My thankfulness goes to Dr. Richard Tseng (Bowser-Morner, Inc.) and Ben

Glascoe (Department of Civil Engineering) for their assistance; also I would also like to thank Bill Meers and Mary Lou Meers for their help and kindness.

Gratitude expressed to my husband, Osama for his unwavering support, belief in me and, above all, patience during these most challenging last few years.

Special thanks are extended to my family for their constant encouragement, and moral support without which this study would not be done.

TABLE OF CONTENTS

ABSTRACT...... iii ACKNOWLEDGEMENTS...... v LIST OF FIGURES...... x LIST OF TABLES...... xii CHAPTER 1: INTRODUCTION...... 1 1.1 General...... 1 1.2 Research Objectives...... 3 1.3 Organizational Outline...... 4 CHAPTER 2: OVERVIEW OF EXPANSIVE SOILS AND THEIR BEHAVIOR...... 5 2.1 Introduction ...... 5 2.2 Classification Procedures for Expansive Soils ...... 5 2.2.1 Mineralogical identification ...... 6 2.2.2 Indirect measurement ...... 6 2.2.2.1 Index property method ...... 6

2.2.2.2 PVC method ...... 10

2.2.2.3 Activity method ...... 11

2.2.3 Direct measurement ...... 12 2.2.3.1 Improved swell oedometer test ...... 12

2.2.3.2 Constant volume test ...... 13

2.2.3.3 Swell overburden test ...... 13

2.3 Suction in Expansive Soils...... 13 2.4 Swelling Behavior of Expansive Soil...... 14 2.5 Methods Used to Predict the Amount of Swell ...... 16 2.5.1 Empirical methods ...... 16 2.5.2 Oedometer tests ...... 17 2.5.3 Suction test ...... 17 2.5.3.1 The filter paper method ...... 17

2.5.3.2 Psychrometers technique ...... 18

2.5.3.3 Tensiometers ...... 19

2.5.3.4 Pressure plate and pressure membrane ...... 19

2.5.3.5 Thermal conductivity sensors ...... 20

2.6 Damage Caused by Expansive Soils ...... 21 2.6.1 Crack pattern ...... 23 2.6.2 Flatwork on expansive soil ...... 25 2.7 Expansive Soil Movements ...... 25 2.7.1 Vertical movements ...... 27 2.7.1.1 Cyclic heave and shrinkage ...... 27

2.7.1.2 Progressive swelling beneath the center of the structure ...... 27

2.7.1.3 Slab-on-grade foundation on expansive soil ...... 28

2.7.2 Lateral movements ...... 29 CHAPTER 3: RETAINING WALLS AND CONVENTIONAL WALL DESIGN...... 31 3.1 Introduction ...... 31 3.2 Lateral Earth Pressure for Retaining Walls ...... 32 3.2.1 Lateral earth pressure at rest ...... 35 3.2.2 Active lateral earth pressure ...... 36 3.2.3 Passive lateral earth pressure ...... 38 3.3 Retaining Walls Design ...... 38

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CHAPTER 4: DETERMINATION OF SWELL PRESSURES FOR RETAINING WALLS...... 48 4.1 Introduction ...... 48 4.2 Active Zone ...... 49 4.3 Backfill Behind Retaining Wall ...... 51 4.4 Swell Pressure ...... 53 4.4.1 Swell pressure measured in the laboratory and in the field...... 54

4.4.2 Models developed by various researchers for swell pressure ...... 56 4.5 Estimating Swell Pressures ...... 58 4.5.1 Swell pressure and Erzin & Erol (2007) method ...... 58 4.5.1.1 Swell pressure versus dry density ...... 59

4.5.1.2 Swell pressure versus moisture content ...... 61

4.5.2 Swell pressure and constant pressure (Fredlund and Rahardjo) method (1993) ...... 63 4.5.3 Erzin & Erol versus Fredlund & Rahardjo method ...... 64 CHAPTER 5: SOIL PRESSURES AND RETAINING WALL DESIGN...... 67 5.1 Introduction ...... 67 5.2 Proposed Method for Swell Pressures Acting on the Wall ...... 67 5.3 Wall and Soil Profiles Studied ...... 68 5.3.1 Parameters used in this study ...... 69 5.3.1.1 Moisture content ...... 69

5.3.1.2 Density ...... 69

5.3.1.3 Plasticity index ...... 70

5.3.1.4 Lateral earth pressure coefficients ...... 70

5.3.1.5 Internal friction angle...... 70

5.3.1.6 Undrained shear strength ...... 71

5.4 Fredlund and Rahardjo (1993) vs. Proposed Method...... 72 5.4.1 Design of anchored sheet piles using constant swell pressure method (Fredlund and Rahardjo 1993)...... 72

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5.4.2 Design of anchored sheet piles using proposed swell pressure method ...... 74 CHAPTER 6: PARAMETRIC STUDY AND ANALYSIS OF RESULTS...... 78 6.1 Introduction ...... 78 6.2 Anchor Sheet Pile Design Sample Calculations ...... 79 6.2.1 Retaining wall case study for H = 5 m ...... 79 6.2.1.1 Design calculations for non-expansive soil ...... 79

6.2.1.2 Design calculations using constant swell pressure method ...... 82

6.2.1.3 Design calculations using proposed method ...... 85

6.3 Results of the Parametric Study ...... 89 6.3.1 Effect of plasticity index ...... 91 6.3.2 Effect of wall height ...... 94 6.4 Effect of Moisture Content ...... 96 6.5 Effect of Dry Density ...... 97 CHAPTER 7: CONCLUSIONS...... 99 REFERENCES...... 101

LIST OF FIGURES

Figure 1.1 Locations of expansive soils around the world ...... 2 Figure 1.2 Locations of expansive soils in the U.S……………………...... …2 Figure 2.1 Classification chart for swelling potential……………………………...... 11 Figure 2.2 Expansive soil caused severe heaving of sidewalk……………………...... 24 Figure 2.3 Severely inwardly displaced foundation due to lateral pressure from wetting of expansive soil ………....…………..……..……………………………………...... 24 Figure 2.4 Cracks in the wall ………..………………....…………………………....…. 24 Figure 2.5 Typical cracking of expansive soil...... 26 Figure 2.6 Center-Lift and Edge-Lift deformation configurations...... 29 Figure 2.7 The collapse of a retaining wall that has a clay backfill...... 30 Figure 3.1 (a) Earth pressure at rest (b) active earth pressure (c) passive earth pressure..32 Figure 3.2 Rankine active force and point of application…………………………...…...33 Figure 3.3 Coulomb active force and point of application………………...... …….....34 Figure 3.4 Coulomb’s active pressure…………………………………...……..………..37 Figure 3.5 Types of retaining walls…………………………………...... …………....40 Figure 3.6 Typical sheet pile construction methods…………………………...... …..….42 Figure 3.7 The deformation and moment distribution of the sheet piles……..…...... 43 Figure 3.8 Anchored sheet-pile wall penetrating sand…………...... ……...…..…...44 Figure 3.9 Anchored sheet-pile wall penetrating clay…………….………...……..….....46 Figure 4.1 Water content profiles in the active zone………………...... 49 Figure 4.2 Seasonal water content profile……...... …...... 50

Figure 4.3 Seasonal water content profile with change in depth…...... 51 Figure 4.4 Overburden and constant swell pressure distributions versus depth...... 52

Figure 4.5 Relative variations in field water content wN with depth Z above the water table...... …..…………...... ….....53 Figure 4.6 Correct the swell pressure…………………..……...... ……………...... ….…54 Figure 4.7 Relation between lateral swell pressure and void ratio………..…..……...... 55 Figure 4.8 Components of swell pressure in a particular direction……..…...... ……....56 Figure 4.9 Effect of dry density on swell pressure…...... 59 Figure 4.10 w = 15% vs. w =25% at same dry density...... 61 Figure 4.11 Effect of moisture content on swell pressure...... 62 Figure 4.12 ρ =1.5 g/cm3 vs. ρ =1.8 g/cm3 at same moisture content...... 63 Figure 4.13 Effect of dry density on swell pressure...... 64 Figure 4.14 Erzin & Erol method vs. Fredlund and Rahardjo method at constant dry density...... 65 Figure 4.15 Erzin & Erol method vs. Fredlund and Rahardjo method at constant moisture content...... 66 Figure 5.1 Undrained versus drained conditions...... 72 Figure 5.2 Scheme for Fredlund and Rahardjo method for anchored sheet piles and expansive soils...... 73 Figure 5.3 Scheme for proposed method for anchored sheet piles and expansive soil.....76 Figure 6.1 Case study at H= 5m before applying the swell pressure...... 82 Figure 6.2 Case study at H= 5m for constant swell pressure...... 85 Figure 6.3 Case study at H= 5m for the proposed method...... 89 Figure 6.4 Proposed method for different height...... 92 Figure 6.5 Constant swell pressure method for different height...... 93 Figure 6.6 Proposed method for different plasticity index...... 94 Figure 6.7 Constant swell pressure method for different plasticity index...... 95 Figure 6.8 Effect of moisture content on the proposed method...... 96 Figure 6.9 Effect of dry density on the proposed method...... 97

LIST OF TABLES

Table 2.1 Classification of expansive soils ……………….…....……………...... ….7 Table 2.2 Soil expansivity prediction by liquid limits and plasticity index ...... ….....7 Table 2.3 Expansive soil classification based on Atterberg limits …...... …...... …8 Table 2.4 Classification of swelling soils ……………………...………...... ….8 Table 2.5 Liquid limit range and site classification ……....……...…….……...... 9 Table 2.6 Soil expansivity prediction by shrinkage limits and linear shrinkage….....9 Table 2.7 Classification of expansive soils based on previous studies……….....…10 Table 2.8 Values of PVC rating ………………………………..………....…….....11 Table 5.1 Classification of swelling soils………………………..…...………….....70 Table 6.1 Properties considered for the present case study before applying the swell pressure...... 80 Table 6.2 Properties considered for the present case study at constant swell pressure………...... 83 Table 6.3 Properties considered for the present case study at constant swell pressure………...... ….86 Table 6.4 Non-expansive soils (PI=0)………………………….. ………………....89 Table 6.5 Constant swell pressure method…………………………...…….…..…..90 Table 6.6 The proposed method………………………………………………..…..90 Table 6.7 The constant swell pressure method vs. the proposed method (% change relative to non-expansive soils)…………………... ……. ………………………..91 Table 6.8 Comparing between Figure 6.8 vs. Figure 6.9…………....……………..98

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CHAPTER 1

INTRODUCTION

1.1 General

Expansive soils include clays and very fine silts which shrink as their moisture content decreases and swell as their moisture content increases. Expansive soils are found in many arid and semiarid areas in worldwide such as Australia, Canada, China, India,

South Africa, and the United States. The locations of these soils around the world and in the United State are shown in Figure 1.1 and Figure 1.2, respectively. An expansive or swelling soil is a natural, highly dispersed, and highly plastic soil that typically contains clay mineral such as montmorillonite that attracts and absorbs water. These clays are very sensitive to drying or wetting, these soils will tend to expand as they absorb water and will shrink as water is drawn away.

Figure 1.1 Locations of expansive soils around the world (Chen 1975)

Figure 1.2 Locations of expansive soils in the U.S. (US Army Engineer 1975)

Engineering geological properties of expansive soil including the swelling, shrinkage, and mechanical properties are closely related to their origin, geological time, geological process, material source and composition, and microstructure type. The 2

geological times of the expansive soil is an important factor influencing the engineering properties. Expansive soils have diverse origins, mainly including lacustrine, alluvial, eluvial, and pluvial origins. In addition, soil found in two or more modes can exist, such as alluvial-pluvial, eluvial-pluvial. In general, the pluvial soil is lower, lacustrine soil is higher, eluvial and alluvial soils are diverse in shrinkage and swelling (Miao et al. 2007).

Swelling in expansive clays is complex and a result of changes in the soil water system. When water is introduced in the environment, clay soils adsorb water more than sandy and gravelly soils causing extensive damage to civil engineering structures. Chen

(1975) estimated that the annual cost to repair buildings, roads and other structures built on expansive soils were expected to be more than $10 billion in 1975. In 2004, the annual cost of expansive soil damage in the U.S. was estimated to be more than $25 billion

(Wray and Meyer 2004).

Retaining walls constructed on expansive soils are subjected to uplift forces and friction forces due to swelling of the soil. More importantly they are also subjected to horizontal swelling pressures causing horizontal deformations and bending. Foundations of these structures require reasonably accurate predictions of the expected movements and pressures of the expansive soils in order for the walls to be designed accurately and safely. The prediction of pressures exerted by the swelling of the soil is needed to provide an important guideline for the design of retaining structures.

1.2 Research Objectives

The main objectives of this research study are to investigate the effect of expansive soils on retaining walls, to develop models to predict swell pressures acting on retaining

walls, and to develop a design method to be used for retaining wall design in expansive soils.

1.3 Organizational Outline

This chapter, Chapter 1, is the introduction. Chapter 2 presents provides an overview on the expansive soils and their behavior. Chapter 3 provides general information about retaining walls and different types of these walls. In addition, it explains the traditional method used to design retaining walls in non expansive cohesive and granular materials. Construction method for anchored sheet piles is presented based on the conventional methods. Chapter 4 includes the literature review of numerous studies to estimate the swelling pressure in the laboratory and in the field. The swelling pressure calculations and measurement are presented. The active zone definition and values are described. Estimating swelling pressure based on index property for the empirical equation and the constant swell pressure are summarized. In Chapter 5, the new proposed method for design of anchored sheet piles in expansive soils is presented.

Chapter 6 presents the results of a parametric study performed to study the effect of expansive soils in anchored sheet pile wall design. Chapter 7 presents the conclusions of this research and recommendations for future study.

CHAPTER 2

OVERVIEW OF EXPANSIVE SOILS AND THEIR BEHAVIOR

2.1 Introduction

Over the years, expansive soils have received the attention of many researchers studying the behavior of expansive soils and their damage to engineered structures, such as buildings, roadways, and retaining walls. Many factors have an effect on the characteristics of expansive soil, including the horizontal pressure applied to foundation walls, water content, dry density, liquid limit, and plasticity index.

2.2 Classification Procedures for Expansive Soils

An expansive soil can be identified by the potential of the soil to swell independently of field conditions such as water content and surcharge pressure. The potential for swell depends on many factors: 1) amount and type of clay mineral; 2) soil structure, such as particle arrangement, bonding, and fissures; and 3) nature of the pore fluid and exchangeable cations. Chen (1975) found that there are different methods of identifying potentially expansive soils. The first, mineralogical identification can be useful in the evaluation of the material but is not sufficient itself when dealing with natural soils. Another method is indirect measurements, such as the index property

method, including Atterberg limits tests, linear shrinkage tests, free swell tests, PVC method, and activity method. The third method is direct measurement in the laboratory.

The test performed for direct measurement is simple and the equipment is not expensive.

2.2.1 Mineralogical identification

The mineralogical composition of expansive soils has an important bearing on the swelling potential. There are a lot of factors contribute to the swelling potential of the clay like the negative electric charges on the surface of the clay mineral, the strength of the interlayer bonding, and the cation exchange capacity . Therefore, it is claimed by the clay mineralogists that the swelling potential of any clay can be evaluated by identifying of the constituent mineral through the following methods: X-ray Diffraction, Differential

Thermal Analysis, Dye Adsorption, Chemical Analysis, and Electron Microscope

Resolution. These different mineralogical identification methods are important in a research laboratory in exploring the basic properties of clays; however, they are impractical and uneconomical for practicing engineers (Chen 1975).

2.2.2 Indirect measurement

There are several indirect measurement methods used to predict swell potential of expansive soils and these methods are summarized below.

2.2.2.1 Index property method

The Atterberg limits test has been commonly used because they are relatively inexpensive and fast compared to many other tests. In the early 1970s, the Federal

Housing Administration (FHA) (1973), San Francisco Insuring Office, classified the

degree of expansiveness of soils according to their plasticity index (PI) and liquid limit

(LL). The plasticity index is defined as the range of water content over which a soil behaves plastically and the liquid limit is defined as the water content (in percent) of a soil at which soil behavior changes from plastic to liquid (ASTM D4318 2010). The classification of expansive soils by FHA/HUD is given in Table 2.1 (Meehan and Krap

1994).

Table 2.1 Classification of expansive soils (FHA/HUD 1973) Plasticity Liquid Soil Classification index limit group Non-expansive 0-6 0-25 A Marginal 6-10 25-30 B Moderately expansive 10-25 30-50 C Highly expansive > 25 > 50 D Expansive claystone > 50 > 70 E

Chen (1975) demonstrated that plasticity index and liquid limit are useful indices for determining the swelling characteristics of expansive soil as following in Table 2.1:

Table 2.2 Soil expansivity prediction by liquid limits and plasticity index (Chen 1975) Degree of expansion Liquid limit Plasticity index Low < 30 0 - 15

Medium 30 - 40 10 - 35

High 40 - 60 20 - 55

Very high > 60 > 35

Snethen et al. (1977) re-evaluated the criteria for predicting soil swell behavior and found that the liquid limit, plasticity index, and soil suction at natural moisture content were good indicators of potential swell. The resulting classification system is shown in Table 2.3.

Table 2.3 Expansive soil classification based on Atterberg limits (Snethen et al. in 1977) Potential swell Liquid Plasticity Natural soil Potential swell classification limit index suction

Low < 50 < 25 < 1.5 < 0.5

Marginal 50 – 60 25 - 35 1.5 - 4 0.5 – 1.5

High > 60 > 35 > 4 > 1.5

The Department of Army (1983) also classified the potential of swell according to their Atterberg limits as shown in Table 2 4.

Table 2.4 Classification of swelling soils (Department of Army 1983) Plasticity Liquid limit Potential Natural soil Classification index (%) (%) swell, Sp(%) suction, tsf Low < 25 < 50 < 0.5 < 1.5

Marginal 25-35 50-60 0.5-1.5 1.5-4.0

High > 35 > 60 >1.5 > 4.0

If the liquid limit is less than 40 percent and the plasticity index is less than 15 percent are essentially nonexpansive (Department of Army 1983).

Kay (1990) showed that liquid limit is a sufficiently good indicator of shrink- swell response for natural soil in spite of the fact that the test is conducted on remolded soil. He classified the site based on LL range in accordance with Table 2.5.

Table 2.5 Liquid limit range and site classification (Kay 1990) Site classification Liquid limit range

S (slightly expansive) < 20

M (moderately expansive) 20-40

H (highly expansive ) 40-70

E (extremely expansive) >70

Altmeyer (1955) suggested a guide to determination of potential expansiveness for various values of shrinkage limits and linear shrinkage as given in Table 2.6.

Table 2.6 Soil expansivity prediction by shrinkage limits and linear shrinkage (Altmeyer 1955) Shrinkage limit as Linear shrinkage as a Degree of expansion a percentage percentage Critical < 10 > 8

Marginal 10 - 12 5-8

Non- critical > 12 0-5

According to the previous tables, it can be summarized the classification of expansive soils based on the following table

Table 2.7 Classification of expansive soils based on previous studies

Classification Plasticity index (%) Liquid limit (%) Non-expansive 0-6 0-25 Low < 25 25-50 Marginal 25-35 50-60 High > 35 > 60

Holtz and Gibbs (1956) suggested that soils having free swell value, which is the difference between the final and the initial volume expressed as a percentage of initial volume in the swell test, as low as 100% can cause considerable damage to lightly loaded structures, and soils having free swell value below 50% seldom exhibit appreciable volume change even under very light loadings.

2.2.2.2 PVC method

The determination of the potential volume change (PVC) of soil is obtained by doing a swell index test on the soil and then plotting relative values of the swell index with PVC. The swell index test is essentially a measurement of the pressure exerted by a sample of compacted soil when it tries to swell against a restraining force after being wetted. The PVC method can be used in the field or the laboratory. Swelling categories based on the PVC method is given in Table 2.8 (Lambe 1961). It should be pointed out that the PVC meter test should be used only as a comparison between various swelling soils (Chen 1975).

Table 2.8 Values of PVC rating (Lambe 1961)

Category PVC rating

Very critical > 6

Critical 4 - 6

Marginal 2 - 4

Non- critical < 2

2.2.2.3 Activity method

As proposed by Seed et al. (1962), the activity based on remolded artificially prepared soils was defined by Equation 2.1. The proposed classification chart based on the activity and the percent clay fraction is shown in Figure 2.1:

where

P.I = plasticity index (%)

C = the percentage clay size finer than 0.002 mm

Figure 2.1 Classification chart for swelling potential (Seed et al.1962) 11

2.2.3 Direct measurement

The most satisfactory and convenient method to classifying potential expansive soils is by direct measurement. There are different oedometer swell tests have been developed for the identification of expansive soils, and most common methods include improved swell oedometer (free swell) test, constant volume swell test, and swell overburden test. The swell pressure can be evaluated easily through this method (Chen

1975 and Erol1987). These tests are defined in ASTM D4546 (2003) as given in the following.

2.2.3.1 Improved swell oedometer test

In the improved swell oedometer test (ISO), it is allowed the sample to swell freely in a vertical direction under a seating load. Then water is added and the sample swells under the load. After swelling, the sample is further loaded until the initial void ratio is reached. Then the specimen is rebounded in decrements and the final void ratio is measured. The swell pressure is defined as the pressure required re-compressing the fully swollen sample to its original volume. The amount of swell is calculated from the following relationship

where

eo = initial void ratio

ef = final void ratio

ΔH = heave 12

H = layer thickness.

2.2.3.2 Constant volume test

In the constant volume test (CVS), the sample is immersed and at the same time the swelling of sample is prevented by adding loads at regular intervals. Swell pressure can be defined as the maximum applied stress required maintaining a constant volume.

2.2.3.3 Swell overburden test

During this test, the sample is loaded dry to predetermined surcharge pressure then the sample is immersed and allowed to swell until primary swell is completed. After that, the sample is loaded until it reaches its original height. Unloading can be performed to obtain rebound characteristics until equilibrium swell is obtained.

2.3 Suction in Expansive Soils

The variations in the environmental conditions such as temperature and humidity influence the swell potential by changing the suction potential of unsaturated expansive soils. So, suction measurements are important for better characterization of heave and shrink potentials of expansive soils. Soil suction is commonly referred to as the free energy state of water, and the suction associated with the movement of water in the liquid and vapor phases are called the matric and total suction. The total suction is equal to the sum of the matric and osmotic suctions. Matric suction is the attraction of water to the soil particle surfaces and depends on pore size distribution. Osmotic suction of the pore fluid is evaluated as the difference between dissolved salts concentration of the pore water and reservoir water salinity. The total suction is related to the water vapor pressure 13

in the air space of the soil. Many factors such as, initial density and water content, permeability, cracks, rainfall infiltration, and evaporation influence the distribution of soil suction (Linchang and Xin 2004).

Earlier studies indicated that there is a strong dependence of the soil suction on the type of the clay mixtures and water content, increasing in the bentonite content or reducing the water content resulting in higher equilibrium suction (Erzin and Erol 2007).

2.4 Swelling Behavior of Expansive Soil

Evaluation of swelling characteristics of expansive soils, namely, swell potential and swell pressure, is important for the design of foundations. Previous investigations have indicated that some factors influence swell potential and swell pressure, such as type and amount of clay, stress history, nature of pore fluid, temperature, volume change permitted during swell pressure measurements, and time (Nayak and Christensen 1971).

Nayak obtained the following equations by the method of least squares to calculate the swell potential and swell pressure for expansive soil.

(i) For swell potential

2.3 where

Sp = predicted value of swelling potential

wi = initial moisture content

(ii) For swell pressure

2.4

where

Pp is the predicted value of swell pressure in psi.

The definition of swell pressure for undisturbed soils is that the pressure required keeping the volume of a soil as constant at its natural dry density. For remolded soils, the swell pressure is the pressure that is required to keep the volume of a soil at its maximum proctor density constant (Fadol and Ke-xu 2004). The definition of swell potential introduced by Seed et al. (1962), is the percentage of swell of a laterally confined sample on soaking under 1 psi surcharge, after being compacted to maximum density at optimum water content in the standard AASHO compaction test.

Rao et al. (2004) indicated that the swell potential and swell pressure depends on index properties clay content and placement conditions such as initial dry unit, initial water content, and initial surcharge pressure. It was observed that the higher the initial dry unit weight, the greater swell potential and swell pressure. Both swell potential and swell pressure decrease with increasing initial water content. In addition, increase in surcharge pressure reduces the amount of swell potential. Liquid limit (LL) and plasticity index (PI) are important factors to predict the swell potential of the soil. In addition, LL of the clay mixtures is more sensitive to the changes in the clay mineralogy than plastic limit (PL) implying that it is at the LL where most changes due to temperature are likely to occur (Erzin and Erol 2007).

Soil scientists recognize that shrink–swell behavior can best be predicted by examining a combination of physical chemical and mineralogical soil properties. While the shrinkage characteristics of a soil depend on the grain-size distribution, and type of clay mineral, swelling is caused by a number of additional phenomena including the

elastic rebound of the soil grains, the attraction of the clay minerals for water, the electrical repulsion of the clay particles and their adsorbed cation, and the expansion of air trapped in the soil voids. Swelling and shrinkage of expansive soils take place between a lower and upper limit of water content, this lower limit is less than the shrinkage limit, and the upper limit is less than the full saturation condition. The swelling index, which is the difference between the water content at the upper and the lower swelling limit, decreases with the increase of the applied vertical pressure. The shrinkage behavior increases with the number of wetting and drying cycles, it also increases with the increase of initial water content, dry unit weight, and applied vertical pressure (Dif and Bluemel 1991).

2.5 Methods Used to Predict the Amount of Swell

The prediction of heave has received more attention than any other analysis associated with swelling soils. Hence, many investigators have proposed methods for predicting heave. The empirical methods and analytical methods including oedometer methods and suction methods are most common methods used to identify soils that might swell and to evaluate the amount of swell that may occur.

2.5.1 Empirical methods

Earlier methods predicted heave in ways to imply various degrees of accuracy in term of low, medium, high, and very high, as described in section 2.2.2.1.

2.5.2 Oedometer tests

There are different analytical methods to predict the amount of swell described in section 2.2.3.

2.5.3 Suction test

Soil suction has been introduced in section 2.3. Tests associated with the soil suction provide a better characterization of the behavior of expansive soils. Suction testing measures the free energy content of soil water (pore pressure of the soil). The soil suction tests are less time consuming as compared to oedometer tests and the measured data are applicable to a wide range of moisture content conditions (Erzin and Erol 2007).

There are several soil suction measurement instruments used by soil scientists and engineers, such as filter paper, psychrometers, tensiometers, pressure plate, and thermal conductivity sensors. Each method has its own limitations. Psychrometers are less sensitive in the low suction range, require frequent recalibration, are sensitive to the temperature of surrounding environment, require frequent maintenance, and can only measure total suction. Tensiometers function in low suction range and require daily maintenance. The filter paper method is regarded as a reliable test method for the measurement of the matric and total suctions of soil sample in the laboratory. Pressure plates, membranes, and thermal conductivity sensors can only measure the matric suction

(Manosuthkij et al. 2008).

2.5.3.1 The filter paper method

In geotechnical engineering field, many researchers, such as Gardner (1937), used the filter paper for measuring soil suction because of its advantages over other suction 17

measurement devices; the filter paper method is an inexpensive and relatively simple laboratory test method although this test required longer times for equilibrium to occur.

The moisture in a filter material will reach equilibrium with the surrounding environment either through vapor (total suction measurement) or liquid (matric suction measurement) flow. Initially dry filter paper of prescribed mass (and size) is calibrated to give matric or total suction. At equilibrium, the suction value of the filter paper and the soil will be equal. After equilibrium, the water content of the filter paper disc is measured. Then, by using the appropriate filter paper calibration curve, the suction value of the soil is estimated (ASTM D5298).

2.5.3.2 Psychrometers technique

There are two main types of psychrometers; namely, thermocouple psychrometers and thermistor or transistor psychrometers. The thermocouple psychrometers can be used either in the field or in the laboratory, and Spanner (1951) was the first researcher introduced this technique. A thermocouple (electrical circuit with two dissimilar conductors) is used to determine the relative humidity, and it can be used to measure total suctions between 100 and 8000 kPa.

The transistor psychrometer has been developed in Australia to effectively replace the thermocouple psychrometers for total suction measurement. It can be used to measure suction pressures to negative 90 kPa. Richards (1965) showed that transistor psychrometers have a better capability of measuring total suction at lower levels when compared with other psychrometric methods. The equipment for psychrometric technique is expensive and subject to damage in inexperienced hands.

2.5.3.3 Tensiometers

As Pan et al. (2010) stated, tensiometers are normally used for directly measuring the negative pore water pressure of soil. The basic principle is that the pressure of water contained in a high air entry material will come to equilibrium with the soil water pressure making it possible to measure negative soil water pressures. Since a true semi- permeable membrane for soluble salts does not exist in a tensiometer, the effect of the osmotic component of suction is not measured. Thus, the measurement only provides the value of the matric suction component in the soil. A small ceramic cup is attached to a tube filled with deaired water which is connected to a pressure measuring device. Then the ceramic cup and tube is saturated by filling with water and applying a vacuum to the tubing. The ceramic tip is allowed to dry to reduce the water pressure in the sensor and any air bubbles that appear are removed.

The limitation is that air in the sensor will result in less negative measurements of the pore water pressure for the following reasons: air comes out of solution as the water pressures decrease, air in soil can diffuse through the ceramic material, and water vaporizes (cavitations) as the soil water pressure approaches the vapor pressure of water at the ambient temperature (Pan et al. 2010).

2.5.3.4 Pressure plate and pressure membrane

The pressure plate and pressure membrane methods were developed in the soil science field to study the water uptake and retention of soils. The main components of the pressure plate and membrane apparatus are pressure chamber, porous ceramic plate or cellulose membrane, and air compressor. The main difference between the pressure plate

and pressure membrane devices is the former for the pressure plate uses a ceramic porous disk that can be used for pressures up to 150 kPa and pressure membrane uses cellulose membranes with which pressures can be extended up to 10,000 kPa. The ceramic disks are rigid enough to carry the soil specimens on them, but a support is provided for the highly flexible membrane (Bulut 2001).

It should be noted that there are some procedures before each test, the porous plate or the membrane is completely saturated with distilled water and then sealed within the pressure chamber along with the soil specimens which rested on the surface of the plate or membrane. With the influence of the applied air pressure, the moisture inside the soil specimen and the ceramic plate or the membrane is expelled out and collected in a graduated cylinder until the equilibrium is reached between the soil sample and the applied air pressure. At equilibrium, the suction inside the soil sample equals the applied air pressure. The air pressure is then released and the moisture content of the soil sample is determined (Bulut 2001).

2.5.3.5 Thermal conductivity sensors

Thermal conductivity sensor was introduced by Baver (1939). A thermal conductivity sensor employs a porous block, typically ceramic, as a medium to measure matric suction indirectly. The basic principle is if a matric suction gradient exists between the soil and porous block, water flux will occur until their suctions are equal. The thermal conductivity of the block consists of the thermal conductivity of the solid and the fluid

(air or/and water) that fills the voids in the porous block. As the moisture content of the porous block increases, the thermal conductivity of the block increases. The moisture

content of the block is measured by heating the porous block with a heater embedded in the center of the porous block and measuring the temperature rise during heating. The temperature rise which is related to the thermal conductivity of the porous medium and the moisture content can then be used as an index of matric suction in the soil. The time to equilibrate depends on the temperature gradient and the hydraulic conductivity of the porous medium and surrounding soil.

The attractiveness of the thermal conductivity soil suction sensor lies primarily in its ability to produce a reasonably reliable measurement of soil suction over a relatively wide range of suctions and the measurements are essentially unaffected by the salt content of the soil. Another advantage of thermal conductivity sensors is their versatility and ability to be connected to a data acquisition system for continuous and remote monitoring. There have been numerous shortcomings and difficulties experienced with previously developed versions of thermal conductivity suction sensors. These difficulties can be identified as: low strength and poor durability of the ceramic tip, insensitivity and inaccuracy particularly in the higher range of suctions, and poor stability of the electronic signal (Bulut 2001).

2.6 Damage Caused by Expansive Soils

During the last few decades damage due to swelling action has been observed clearly in the semi-arid climate. A "semi-arid" climate can be described as a climate that has periods of rainfall followed by long periods of no rainfall. So, because of the conditions of this climate soil becomes wet and swells. The response of expansive soils in the form of swelling and shrinkage due to changes in water content is expressed as

heaving and settlement of lightly loaded geotechnical structures such as pavements, railways, roadways, foundations and channel or reservoir linings. According to Chen

(1975), expansive soil damages exceed the combined average annual damages from floods, hurricanes, earthquakes, and tornados.

In expansive soil areas, the soils are generally stiff, and the chance of lightly loaded structures cracking due to settlement is more common. However, there are many cases where heavy cracks have appeared in the basement walls that were not caused by foundation heaving but by earth pressure exerted on the wall, generally compounded by seepage pressure. In most cases where vertical or horizontal cracks developed in the basement wall, earth pressure problems are suspect. Diagonal cracks that develop below windows and above doors are a strong indication of swelling movement (Chen 1975).

The weight of the structure has a significant impact in suppressing or leveling out the differential ground profile which would result from the moisture changes in the soil alone. In particular, swelling movements are often largely suppressed because the wet swelling soil has a relatively low stiffness. Cases of damage due to cyclic movements appear to be less common than those due to either swelling or shrinkage although there are some reports of extensive damage, such as roadway and ground movement due to seasonal climate changes, and severe cracks because of swelling during rainy periods and shrinkage during dry periods. Climatic conditions, wet seasons followed by warm, and dry seasons are most favorable to cyclic movements (Lambe 1960). Foundation movements for structures founded on expansive soils are reflected as cracks which are explained in the following.

2.6.1 Crack pattern

Cracks caused by swelling soils have the same general pattern as settlement cracks, although swelling cracks are generally wide at the top and narrow at the bottom.

Clays are probably the greatest factors in the rate of swelling. Clays will shrink until the shrinkage limit is reached. Even as the moisture content decreases below the shrinkage limit, there is probably still the development of additional cracks as the clay dries.

Because clays are the greatest factors in the rate of swelling, the more cracks in the clay, the greater the pathways for water to penetrate the soil, and the quicker the rate of swelling (Day 1999).

Types of cracks sustained by structures due to differential heave of foundation expansive soils include:

1. Cracks in grade beams, expansive overburden foundation soils can exert enough pressure on the bottom of beams to crack and cause complete failure where voids are not provided. Differential movement between two supporting points can cause cracks in grade beams.

2. Cracks in walls, differential foundation movement and rigid walls cause cracks in the wall.

3. Cracks in pier shafts, expansion of materials through which insufficiently reinforced pier shafts pass, and upward forces exerted on pier shafts by skin friction developed by surrounding expansive soils, cause cracks from induced tension (Johnson and Stroman

1976). Figures 2.2 through 2.4 below illustrate some examples.

Figure 2.2 Expansive soil caused severe heaving of sidewalk (http://www.jeffersonconservationdistrict.org/biochar.html)

Figure 2.3 Severely inwardly displaced foundation due to lateral pressure from wetting of expansive soil (http://www.hieofcolorado.com/work.html)

Figure 2.4 Cracks in the wall http://princeofpunjab.blogspot.com/2011/04/weaknesses-are-cracks-in-our-egos-wall.html

2.6.2 Flatwork on expansive soil

As mentioned previously, expansive soils will expand when given access to water and shrink when they dry out causing cyclic movements of flatwork. Flatwork used to describe appurtenant structures that surround a building such as concrete walkways, slab, driveways and other flat surface for which a finishing is usually required, to separate away from the structure. This lateral movement of flatwork away from the structure is known as "walking." Because flatwork only supports its own weight, so as the flatwork walks away from the house, these appurtenant structures, which coverage for additional buildings on the same property as the principal insured buildings, are pulled laterally and frequently damaged. It was found from the field experiments that most lateral movement of flatwork on expansive soils occurs during the wet periods. With each additional wet period, the flatwork continues to move up and away from the structures. During the dry period, the flatwork does not return to the original position, and then in the next wet period, the clay causes the flatwork to move again. These cycles of wetting and drying cause progressive movement of flatwork away from the structure (Day 1992).

2.7 Expansive Soil Movements

The problem of expansive soils was brought to the attention of the engineers as early as 1950. Severe foundation movement problems were recorded in many parts of the world (Chen 1975). The walls placed on these soils will experience the movements.

Depending on the magnitude, these soil and wall movement can cause additional stresses on the wall and can cause cracks on the walls, and affect the highway, basement floors, pipelines, or other structures. In addition, cyclic and continued expansive soil movements

may result in wall failure, either serviceability or structural failure. In the field, expansive soils can be recognized in dry season by the deep cracks, which are the result of foundation movement caused by swelling soils as shown in Figure 2.5.

Figure 2.5 Typical cracking of expansive soil (Silberstein 2011)

Soil movement creates horizontal and vertical stresses. Horizontal and vertical movements in expansive soils are reversible, dynamic processes under natural field conditions. Vertical soil movement is a function of soil depth, soil water content, and rainfall, while horizontal soil movement is not related to soil depth, but related to soil water content and rainfall. Vertical movement decreased with depth because of decreased swelling and shrinking (Cheng and Pettry 1993).

Movements caused by the volumetric shrink and swell of expansive clays have the most pronounced impact on light structures, though differential wetting and drying at the edge of structures or hillside creep may cause horizontal movements as well (Meehan and Krap 1994). Expansive soil movements occur due changing in soil suction. As a soil

dries, the soil suction increases and the soil shrink. While wetting of soils causes decrease in soil suction and causes swell (Masia et al. 2003).

2.7.1 Vertical movements

2.7.1.1 Cyclic heave and shrinkage

Cyclic heave and shrinkage is type of expansive soil vertical movement which affects the perimeter of the foundation, by uplifting the edge of the structure or shrinking away from it. For example, the perimeter of a pavement or slab-on-grade foundation will heave during the rainy season and then settle during the drought if the clay dries out. This causes cycles of up and down movement, causing cracking and damage to the structure

(Sattler and Fredlund 1990; Day 1999; Day 2000).

2.7.1.2 Progressive swelling beneath the center of the structure

As Day (2000) stated, two ways that moisture can accumulate underneath structures are by thermal osmosis and capillary action. It has been noted that water at higher temperature than its surroundings will migrate in the soil towards the cooler area to equalize the thermal energy of the two areas, this process known as thermal osmosis.

Because of capillary action, moisture can move upward through soil, where it will evaporate at the ground surface. But when a structure is constructed, it acts as a ground surface barrier, reducing or preventing the evaporation of moisture. It is the effect of thermal osmosis and the evaporation barrier due to the structure that causes moisture to accumulate underneath the center of the structure. A moisture increase will result in swelling of expansive soils (Day 1999; Day 2000).

2.7.1.3 Slab-on-grade foundation on expansive soil

A slab-on-grade, which is concrete slab foundation built on ground level, should be designed to resist two types of expansive soil movement: the short-term cyclic heave and shrinkage around the perimeter of the foundation and the long-term progressive swelling beneath the center of the slab (Day 1994).

The amount of cyclic heave and shrinkage depends on the change in moisture content below the perimeter footing. Cyclic heave and shrinkage around the perimeter of the slab is a seasonal or short-term condition. The progressive heave of the center of the slab is a long-term condition because the maximum value may not be reached until many years after construction (Day 1994).

Another type of foundation for expansive soil is the post-tensioned slab-on-grade.

The design of a post-tensioned slab-on-grade required to construct a slab foundation that is strong enough and rigid enough to resist the expansive soil forces. The structural engineer must design the foundation for two conditions: (1) "Center lift" (also called center heave or doming) is the long-term progressive swelling beneath the center of the slab, and (2) "edge lift" (also called edge heave or dishing) is the short-term cyclic heave beneath the perimeter of the foundation as shown in Figure 2.6 (Day 1994).

Figure 2.6 Center-Lift and Edge-Lift deformation configurations (Day 1994)

2.7.2 Lateral movements

It is an important to consider lateral movement in the design of basements and retaining walls, especially if the clay backfill is compacted below optimum moisture content, seepage of water into the clay backfill causes horizontal swell pressure well in excess of at-rest value. Figure 2.7 shows the collapse of a retaining wall that has a clay backfill (Day 1999; Day 2000).

Figure 2.7 The collapse of a retaining wall that has a clay backfill (Dave 2010)

As mentioned above in section 2.6.2, shrinkage and swelling in expansive soils cause a cycle of movement, then causing walking or flatwork, so it is obvious that the

cyclic heave and shrinkage is also part of lateral movement of expansive soils.

CHAPTER 3

RETAINING WALLS AND CONVENTIONAL WALL DESIGN

3.1 Introduction

Most retaining walls constructed with a foundation avoids the use of cohesive materials as the backfill behind these structures, because expansive soils usually create many problems including settlements, swelling potential, and additional lateral earth pressures. Lateral earth pressures can cause damage and can increase significantly after construction if the clay were to swell behind the wall. The main reason that cohesive materials are used as backfill is to produce an economical wall design by using the local cohesive soils instead of transporting the granular materials that may not be available locally (Symons et al. 1989).

When the walls built are in-situ walls, such as slurry or sheet pile walls used as excavation support system, then choosing the material behind the wall is not optional.

The walls in these situations are exposed to the natural soils in the ground at the wall location and those natural soils may be expansive soils.

Traditional design methods using non-expansive cohesive backfill do not consider the lateral swelling pressure that may occur due to the wetting of expansive soils. The

magnitude of potential lateral swell pressure can be estimated and added to the conventionally derived lateral pressure (Sorchan and Ryabova 1988; Sorchan and Kim

1995; Clayton et al. 1991; Thomas et al. 2009). So, total lateral pressure for retaining walls on expansive soils consists of lateral traditional earth pressure, surcharge pressure, and lateral swelling pressure (Sapaz 2004; Thomas et al. 2009).

The calculation for traditional design methodology for retaining wall structures using granular and cohesive backfill materials is the same for hydrostatic and surcharge loads, and for the point of application of the resultant active lateral pressures. However, due to the low angle of internal friction exhibited by clay soils, higher lateral earth pressures exist when cohesive soils are used as backfill. In addition, the presence and the nature of cohesion forces require more in-depth analysis (Thomas 2008).

3.2 Lateral Earth Pressure for Retaining Walls

There are three different conditions of lateral earth pressures acting on retaining walls depend on the movements experienced by the wall on which the pressure is acting as shown in Figure 3.1 (Das 2004 and 2007).

Figure 3.1 (a) Earth pressure at rest (b) active earth pressure (c) passive earth pressure (Das 2004)

For active and passive lateral earth pressure, there are two widely used theories, namely

Rankine Earth Pressure and Coulomb Earth Pressure theories.

The Rankine Theory assumes:

- There is no friction between the wall and soil,

- The wall is vertical,

- Lateral pressure is located at one-third of the height above the base of the wall as shown in Figure 3.2,

- The point of application for Rankine force at the backside of the soil wedge, and it intersects the wall at distance H1/3 from the base of the wall as shown in Figure 3.2.

(a) Horizontal Backfill (b) Inclined Backfill

Figure 3.2 Rankine active force and point of application

where

Pa = Rankine active force (kN/m)

H = wall height (m)

α = the angle of inclination of ground surface above the horizontal.

The Coulomb Theory is more applicable to general conditions as it does not have some of the assumptions that Rankine Theory used. In Coulomb theory:

- There is friction between the wall and soil and takes this into account by using soil-wall friction angle of δ,

- Lateral pressure is not limited to vertical walls,

- The point of application for Coulomb calculation is a point on the backside of the wall, and the line of action of the resultant force (Pa) will act at distance H1/3 above the base of the wall as shown in Figure 3.3

(a) Vertical Wall Face (b) Inclined Wall Face

Figure 3.3 Coulomb active force and point of application where

Pa = Coulomb active force (kN/m)

δ = friction angle

3.2.1 Lateral earth pressure at rest

At-rest conditions occur when the wall is restrained from the movement such as along a basement wall. The pressure acting on the back of the wall is described in terms of the coefficient of lateral earth pressure at rest, K0.

For normally consolidated clays and granular soils the relation for K0 is

K0 = 1 – sin’ 3.1 where

K0 = “at rest” lateral earth pressure coefficient

’ = soil friction angle.

For overconsolidated clays, K0 is given as

0.5 K0,overconsolidated = K0,normally consolidated *(OCR) 3.2 where

OCR = the overconsolidation ratio which is defined as the ratio of the maximum effective consolidation stress and the effective overburden stress

The total lateral earth force at rest, P0, per unit wall length is then given by:

3.3

where

 = unit weight (kN/m3)

3.2.2 Active lateral earth pressure

For active conditions, the wall tends to move away from the soil, such as typical retaining walls. As the wall moves away from the soil as shown in Figure 3.1, the vertical stress v’ remains the same, but the horizontal stress h’ decreases.

The horizontal stress at depth z in granular soils, h’ is

3.4

where

2 v’ = vertical stress (kN/m )

Ka = active lateral earth pressure coefficient

And for cohesive soils,

 h ' Ka v '2c' Ka 3.5

where

c’ = cohesion (kPa)

Rankine in 1857 proposed that the active pressure coefficient, Ka, for horizontal backfill against a frictionless wall is

1 sin' Ka  1 sin' 3.6

For inclined ground surface behind the wall, Rankine’s active pressure coefficient becomes

3.7 where 36

’ = soil friction angle.

α = the angle of inclination of ground surface above the horizontal.

In 1776, Coulomb proposed a theory for calculating the lateral earth pressure on retaining walls considering the wall friction, inclined back wall, and sloped ground surface behind the wall as shown in Figure 3.4. Active lateral earth pressure coefficient,

Ka is given by

where

’ = effective angle of friction

δ = wall friction angle

α = slope inclination

β = back face inclination of the structure

Figure 3.4 Coulomb’s active pressure

3.2.3 Passive lateral earth pressure

When the wall is pushed against the mass of soil as shown in Figure 3.1, v’ remains the same, but h’ increases. The horizontal stress at depth z in granular soils is

 h ' K P v ' K P z 3.9 where

Kp = passive lateral earth pressure coefficient

And for cohesive soils,

 h ' K P v '2c' K P 3.10

For Rankine passive pressure coefficient, KP is

1 sin' K P  1 sin' 3.11

For inclined backfill wall, Rankine’s passive pressure coefficient is

3.12

Coulomb’s passive lateral earth pressure coefficient is

3.3 Retaining Walls Design

Retaining walls are also known as lateral earth support systems are constructed to resist lateral earth pressures. They are very common structures used in many construction projects. Most common materials used for retaining walls are: 38

-Wood sheets;

- Steel and plastic interlocking sheets;

- Reinforced concrete sheets;

- Precast concrete elements;

- Closely spaced in-situ soil-cement piles;

-Wire-mesh boxes.

There are many types of retaining walls, but the most common types are shown in

Figure 3.5 (Das 2007):

1.Gravity retaining walls are made from plain concrete or stone masonry, unreinforced

concrete, or reinforced concrete. These walls can be used in both cut and fill

applications. They depend on their mass or weight to resist the pressure exerted by the

earth behind them. The gravity wall type includes rigid gravity walls, mechanically

stabilized earth (MSE) walls, and prefabricated modular gravity walls.

2.Semigravity walls are constructed of reinforced concrete. They can be used in both cut

and fill applications. Semigravity walls are similar to gravity walls, but this type of the

retaining wall minimizes the size of the wall section because it will use a small amount

of steel for the construction.

3.Cantilever retaining walls are built of reinforced concrete in both the footing and wall

structures. The cantilever is the most common type of retaining wall and is used for

heights up to 8 m.

4. Counterfort retaining walls are similar in construction to cantilever walls expect these

type of retaining walls have thin vertical concrete slabs known as counterforts that join

the wall and the base slab together.

5. Sheet piling retaining walls are usually built in relatively soft soils; including

expansive soils, and tight spaces. Sheet piles are also used for temporary structures,

such as braced cuts. In addition, they can be used for different purpose, like excavation

support system, floodwalls that can increased by soft soil layers below the tip of the

wall, and cut-off walls under dams (Bilgin et al. 2011). Sheet pile walls are divided into

two basic categories: cantilever, which is used for moderate height about 4.5 m or less,

and anchored sheet pile walls which are used for heights exceeding 4.5 m (ASCE

1994).

(e) Sheet piling walls

Figure 3.5 Types of retaining walls (Das 2007)

Types of wall installation can induce the additional movements of walls, one of these walls installation sheet pile walls. The sheet pile walls are flexible walls and have relatively much lower system stiffness comparing with other in-situ walls (Clough and

Rourke 1990). Because the movement beneath the excavation may be an issue in soft clays, so our objective in this study will focus only in the effect of expansive clays on sheet pile walls.

There are many types of material used for sheet pile walls as summarized in the following (ASCE 1994): a) Heavy-gauge steel is the most common material used for sheet pile walls due to its

relative light weight. Additionally, it provides a long service life from field

observations and has low costs compared to other types. b) Light-gauge steel has low-section moduli and very low moments of inertia in

comparison to heavy-gauge steel. Light-gauge piling should be considered for

temporary or minor structures. c) Wood sheet pile walls should be restricted to short to moderate wall heights and

used only for temporary structures. d) Concrete sheet pile walls are capable of providing a long service life under normal

circumstances but have relatively high initial costs. Past experience indicates this

pile can induce settlement in soft foundation materials. This type is more difficult to

install than steel piling. e) Light-gauge aluminum sheet piling has a relatively low-section modulus and

moment of inertia necessitating tiebacks for most situations.

Anchored sheet pile construction methods

An anchored sheet-pile wall is constructed as shown in the Figure 3.6 below. Depending

on the original ground surface elevation, there are two methods for construction of

anchored sheet pile namely, excavation and backfilled methods.

Figure 3.6 Typical sheet pile construction methods (Bilgin 2010)

There are two conventional methods used in the design of Anchored sheet pile

walls; free earth support and fixed earth support methods. Figure 3.7 shows the

deformation and moment distribution of the sheet piles for the two methods. The free

earth support method assume that embedment of the retaining wall is free to move to

certain distance under the action of lateral earth pressure. While the fixed earth support

method is to assume the embedment of the retaining wall is fixed at a point below the

excavation surface (Ou 2006). The free earth support method requires smaller penetration

depth and it is more commonly used because of its simplicity compared to fixed earth method (Das 2007).

(a) Free earth support method (b) Fixed earth support method

Figure 3.7 The deformation and moment distribution of the sheet piles (Das 2007)

Free earth support method for walls in granular soils

In this method, it assumed the active pressures at the back of the wall and the passive pressures at the front of the wall. The net pressure diagram under these conditions is shown in Figure 3.8. The submerged unit weight of soil is considered the calculations for the soils below the groundwater level.

Figure 3.8 Anchored sheet-pile wall penetrating sand (Das 2007)

The anchored sheet pile design performed to obtain three main parameters; Wall penetration depth, anchor force, and maximum bending moment. The wall penetration depth determines the total pile length to be installed, anchor force is used for anchor design, and the maximum bending moment is used to select pile profile for the wall. The free earth design method, using Figure 3.7, is outlined in the following:

1- Anchor force or tension in the tie rod per unit length of the wall:

3.14

where

P = area of the pressure diagram ACDE

Ka = active lateral earth pressure coefficient by Rankine or Coulomb method

Kp = lateral passive earth pressure coefficient by Rankine or Coulomb method

The Rankine earth pressure is based on the assumption that the wall is frictionless; on the other hand, Coulomb theory takes wall friction into the consideration.

’= effective unit weight of soil = sat - w

L4 is calculated by taking the moment about point O’ by using Equation 3.15 and trial and error.

2- The theoretical depth:

Dtheoretical = L3+L4 3.16

Where σ’2 = the stress at point D (kPa)

The theoretical depth is increased by about 30-40% for actual construction for a factor of safety, so

Dactual = 1.3 to 1.4 Dtheoretical 3.18

3- The maximum moment to which the sheet pile will be subjected to occurs at a depth

between z = L1 and z = L1+L2. The depth z is the location of maximum bending

moment where the shear is zero. So the maximum moment is calculated as:

= 0 3.19

Once the value of z is determined, then it can be calculated the magnitude of the maximum moment.

Free earth support method for walls in cohesive soils

Net pressure diagram acting on the wall where cohesive soils are present below the dredge line is shown in Figure 3.9.

Figure 3.9 Anchored sheet-pile wall penetrating clay (Das 2007)

The design steps for this case are outlined below using the notation given in Figure 3.9:

1- Anchor force or tension in the tie rod per unit length of the wall:

where

P1 = area of the pressure diagram ACDE

F = anchor force per unit length of the sheet-pile wall

2- The theoretical depth of penetration:

The theoretical depth is increased by about 30-40% for actual construction as mentioned before, to be more conservative by applying this safety factor, so

Dactual = 1.3 to 1.4 Dtheoretical 3.22

3- The maximum moment to which the sheet pile will be subjected to occurs at a depth

between z = L1 and z = L1+L2. The depth z is the location of maximum bending

moment where the shear is zero. So the maximum moment is calculated as:

= 0 3.23

CHAPTER 4

DETERMINATION OF SWELL PRESSURES FOR RETAINING WALLS

4.1 Introduction

The phenomenon of soil swelling and the potential for structural damage has been recognized for many years. Chen (1988) reported that structural distress due to expansive cohesive soils had been found in several areas in the U.S. and many other countries around the world. Retaining structures and buried structures, such as foundation piles and buried conduits, are subjected to uplift and friction forces due to the process of swelling and shrinking due to expansive soil. They are also subjected to horizontal swell pressures causing additional horizontal wall deformations and bending.

Replacing expansive soils with non-expansive ones may offer a simple solution to eradicate expansive soil problems. However, this method is unsustainable today as it produces waste soils, consumes significant amount of resources, and expensive. As conventional backfill materials are becoming more scarce and costly, removing and replacing the expansive soils may not be a viable option for many projects. Therefore, determining and modeling the swell pressures acting on the retaining walls is the first important step in the wall design to have safe and sustainable structures.

4.2 Active Zone

Active zone is the thickness of the soil layer in which the moisture content changes occur. The hydrostatic water content profile indicates a negative pore water pressure above the groundwater table that varies linearly with height above the groundwater level. The temperature affects the migration of water as shown in Figure 4.1.

(Nelson and Miller 1992)

Figure 4.1 Water content profiles in the active zone (Nelson and Miller 1992)

The depth of active zone is a very important in the design of a foundation system for expansive soils. It was found that the range of the active zone is about 4.5 to 6 m

(Nelson and Miller 1992; Som and Das 2003). While the Department of the Army (1983) indicated the active zone depth to be about 3-6 m, Overton et al. (2001) said this depth can extend for much greater than 6 m.

In arid and semiarid locations, water content will increase with depth until a point at which the water content becomes constant with depth. Also Nelson and Miller (1992) developed a plot showing water content as a function of depth in Colorado over several wet and dry seasons. They concluded that it can be estimated the active zone for any site based on plotting the depth versus moisture content as shown in Figure 4.2.

Figure 4.2 Seasonal water content profile (Nelson and Miller 1992)

In cases where the soil is not uniform with the depth or if several strata exist, the differences in soil types can be compensated for by plotting water content (w) divided by plasticity index (PI) as shown in Figure 4.3.

Figure 4.3 Seasonal water content profile with change in depth (Nelson and Miller 1992)

In the above Figure, the depth of the soil is not uniform, so by plotting a graph between depth and (w / PI), the active zone, which is the point at the depth becomes constant with moisture content, is equal 6 m (20 ft). Although these values are not exactly close, they provide a reasonable estimate for the active zone. In current study, the depth of the active zone is assumed to be 5 m (15 ft).

4.3 Backfill Behind Retaining Wall

A presence of expansive soils behind the retaining structures generates very large lateral swell pressure. Based on Thomas et al. (2009), there is no accepted method to estimate the distribution of lateral swell pressure that could be induced by using expansive soil cohesive backfill in retaining walls. Although Fredlund and Rahardjo

(1993) and Rae et al. (1988) assumed that the corrected swell pressure, which is equal to

the sum of the overburden pressure and the matric suction equivalent, is constant with depth as shown:

Figure 4.4 Overburden and constant swell pressure distributions versus depth

(Fredlund and Rahardjo in 1993)

The corrected swell pressure (Ps) is:

Ps = ρ.g.H 4.1 where

ρ = density of the soil which is assumed to remain constant (kg/m3)

g = gravitational acceleration (9.81 m/s2)

H = active depth (m)

However, expansive soils undergo volume changes upon wetting and drying.

These soils occur in an active zone as shown in Figure 4.5

Figure 4.5 Relative variations in field water content wN with depth Z above the water table

(Bowles 1996)

Figure 4.5 shows that soil near the ground surface dries during the summer season. When the rain comes, the soil becomes wet, increasing the moisture content and causing soil to swell and develop swell pressures.

4.4 Swell Pressure

Swell pressure is the required pressure to prevent volume change of the sample, or the pressure that requires returning the specimen back to its original state after swelling

(Som and Das 2003). Numerous studies in the past have tried to developed methods to predict swell pressure; some from laboratory tests and some from field measurements.

4.4.1 Swell pressure measured in the laboratory and in the field

There were several research studies performed in the laboratory to measure the swell pressure. These studies indicated that the swell pressure depends on various factors, such as type of equipment, density, initial moisture content, and the clay friction (Katti et al. 2002). Ali and Elturabi (1984) used two testing methods to measure the swell pressure of expansive soils, constant volume method and the oedometer method. Their results indicated that the oedometer methods give higher swell pressure values than the constant volume method. Shuai and Fredlund (1998) measured the swell pressure by different oedometer tests and the range of their results was 210 to 320 kPa at moisture content of

26%. Robertson and Wagener (1975) measured the swell pressure in the field at different initial moisture contents between 10 to 16% and the field swell pressures were between

60 to 90 kPa. However, Fredlund (1983) explained that laboratory tests to measure the swell pressure may not represent the actual swell pressure in the field and should be corrected as shown in Figure 4.6.

Figure 4.6 Correct the swell pressure (Fredlund 1983) 54

Katti et al. (2002) found a relationship between lateral swell pressure and void ratio for different types of expansive soil. Figure 4.7 show that there is an increase in the lateral swell pressure with decreases the void ratio.

Figure 4.7 Relation between lateral swell pressure and void ratio (Katti et al. 2002)

Katti et al. (2002) also found the swell pressure that is measured in any particular direction is the sum of the components of the forces exerted by the individual particles per unit area as shown in Figure 4.8.

Figure 4.8 Components of swell pressure in a particular direction (Katti et al. 2002)

Joshi et al. (1980) and Katti et al. (2002) concluded that the swell pressure in both vertical and lateral direction observed in the laboratory investigations is the same because of random orientation of particles.

4.4.2 Models developed by various researchers for swell pressure

Based on their research studies several researchers developed empirical equations to determine swell pressure. In these empirical equations index properties that are believed to have significance for swelling are used as independent variables. Komornik and David (1969) proposed statistical analysis on 200 natural (undisturbed) samples to estimate the logarithm of the swell pressure based on the following equation:

where

2 Ps = swell pressure kg/cm ,

LL = liquid limit (%),

3 d = natural dry density of soil kg/m , and

w = natural moisture content (%).

According to this equation, the coefficient of the correlation, R was found to be

0.6. In addition, they have concluded that the swell pressure increases with an increase in initial density and liquid limit, but with a decrease in moisture content.

Erzin and Erol (2007) investigated the effect of different empirical equations in a wide range of expansive soil properties to calculate the swell pressure and compared these equations with the measured swell pressures by oedometer tests. They found that the following equations have strong correlations between the logarithms swell pressure and the soil properties, R =0.96 and 0.97, respectively. Also these equations have a good agreement between the measured and predicted swell pressures.

For 0 < Ps ≤ 100 kPa;

Log Ps = - 3.72 + 0.0111 PI + 2.077 d + 0.244 log s 4.3

For100 < Ps ≤ 350 kPa;

Log Ps = - 16.31 + 0.0330 PI + 8.253 d + 0.829 log s 4.4

If the suction measurements are not available, then the equation for the correlation between the soil suction, s, and the soil properties given in the following:

Log s = 2.02 + 0.00603 PI – 0.0769 w 4.5 57

2 3 Where Ps in kg/cm ; PI and w in percent; d in g/cm ; s in bar. Erzin and Erol concluded that the swell pressure can be predicted by the initial soil suction and the two soil properties, plasticity index and dry density, using simpler techniques than the oedometer tests in shorter time.

Lytton et al. (2005) indicated that swelling near the surface acts like passive earth pressure behavior and the values of total lateral earth pressure coefficient K0 vary between 0.0 and passive earth pressure levels.

In this study, the swell pressures of expansive soils were developed using Erzin and Erol’s equations (Equations 4.3, 4.4, and 4.5) and the swelling near the surface acts like passive earth pressure behavior in parametric study of retailing wall analyses.

4.5 Estimating Swell Pressures

Relationships between swell pressure and different parameters have been investigated in this study based on Erzin and Erol (2007) equations (4.3, 4.4, and 4.5) and

Fredlund and Rahardjo (1993) equation (4.1).

4.5.1 Swell pressure and Erzin & Erol (2007) method

The effect of several parameters on the swell pressures are given in the following sections. Based on previous studies that showed the swell pressures in the field did not exceed than 100kPa (Robertson and Wagener 1975), so the swell pressures are limited to

100 kPa in next figures, in addition, the negative values for swelling pressures do not consider in this study because of the shrinkage. In other words, negative values mean no swell pressures.

4.5.1.1 Swell pressure versus dry density

As indicated by Erzin and Erol (2007), the dry density of the soil is one of the factors which affect the swelling characteristic of expansive soils

a) w = 10% b) w = 15%

c) w = 20% d) w = 25%

Figure 4.9 Effect of dry density on swell pressure 59

where

Ps = swell pressure (kPa)

w = moisture content (%)

PI = plasticity index (%)

ρ = dry density (g/cm3)

The swell pressure and the dry density (Figure 4.9) at constant moisture content

(w %) for different ranges of plasticity index (PI), low , marginal ,and high plasticity shows that the swell pressure increases with increasing the dry density and PI. For ρ =

1.65 g/cm3 and w = 25%, there is not swell pressures at low plasticty . If we compared between w =25 % and 15% at ρ = 1.65 g/cm3 , and low plasticity as shown in Figure

4.10, this means we have same volume of soild as shown in the following scheme.

Volume of solid at w =25 % equal to the volume of solid at w =15%, but volume of water at w = 25% is bigger than the volume of water at w =10% , in this case there will be no space for the expansive soil to expand. So, the pressure will shrink at w ≥ 25%. As a results, there will not be swell pressure.

Figure 4.10 w = 15% vs. w =25% at same dry density

4.5.1.2 Swell pressure versus moisture content

Moisture content is also another factor which plays a role in swell characteristics of expansive soils. Graphs are plotted to show the relationship between the moisture content and swell pressure for the entire range of PI at constant dry density. The results show that there is a tendency of decreasing swell pressure with increment of moisture content, however swell pressure increases as PI increases (Figure 4.11).

a) ρ = 1.5g/cm3 b) ρ = 1.65g/cm3

c) ρ = 1.8g/cm3 Figure 4.11 Effect of moisture content on swell pressure

At low dry density there are not swell pressure values at low plasticity index. If we compared between ρ =1.5 and 1.8 g/cm3 at w = 10%, and low plasticity, this means 62

volume of soild at ρ =1.8 g/cm3 is bigger than volume of soild at ρ =1.5 g/cm3 as shown in the following scheme. Volume of water in both cases are equal, in this case at higher ρ, this means the soild is more compacted, so there will be a liitle space for the expansive soil to expand.causeing higher swell pressure (Figure 4.12).

Figure 4.12 ρ =1.5 g/cm3 vs. ρ =1.8 g/cm3 at same moisture content

4.5.2 Swell pressure and constant pressure (Fredlund and Rahardjo) method (1993)

In this method, the only variable is the dry density, so one graph is drawn to study the relationship between the swell pressure and different dry density values. Figure 4.13 shows that the swell pressure, which is constant through the depth of active zone, increases as the dry density of the soil increases.

Figure 4.13 Effect of dry density on swell pressure

4.5.3 Erzin & Erol versus Fredlund & Rahardjo method

Figure 4.14 (a, b, and c) shows the effect of moisture content for both methods.

And Figure 4.15 (a, b, c, and d) shows the effect of dry density for both methods. At

Erzin & Erol method, there are different values of swell pressure and these pressures are increasing with decreasing moisture content and increasing dry density. However, for

Fredlund and Rahardjo method the swell pressures are constant for a given dry density values and are independent of moisture content and plasticity index.

a) ρ = 1.5g/cm3 b) ρ = 1.65g/cm3

c) ρ = 1.8 g/cm3

Figure 4.14 Erzin & Erol method vs. Fredlund and Rahardjo method at constant dry density

a) w =10% b) w =15%

c) w =20% d) w =25%

Figure 4.15 Erzin & Erol method Vs Fredlund and Rahardjo method at constant moisture content

CHAPTER 5

SOIL PRESSURES AND RETAINING WALL DESIGN

5.1 Introduction

This chapter explores the determination of the magnitude and the distribution of swell pressures to be used in the design of anchored sheet pile walls. A new method to estimate the swell pressures acting on the wall is developed and proposed to be used in design. The steps used in designing anchored sheet pile walls and for the analyses results presented in Chapter 6 for the proposed method and the constant swell pressure method

(Fredlund and Rahardjo’s 1993) are presented in this chapter.

5.2 Proposed Method for Swell Pressures Acting on the Wall

As presented in Chapter 4 the following equation was developed by Erzin and

Erol (2007) to calculate the swell pressures when the swell pressures are less than 100 kPa:

Log Ps = - 3.72 + 0.0111 PI + 2.077 d + 0.244 log s 5.1 where

s = soil suctions (bar)

Log s = 2.02 + 0.00603PI – 0.0769W 5.2

PI = plasticity index (%)

3 d = dry density (g/cm )

w = moisture content (%)

Several measurements of swell pressures indicated that they usually do not exceed

100 kPa (Robertson and Wagener 1975, Hong 2008). The swell pressures that are measured in the field are more representative of actual conditions than the values obtained from the laboratory tests (Fredlund in 1983); the swell pressures in this study are limited to 100 kPa. In addition, Lytton et al. (2005) indicated that swelling near the surface acts like passive earth pressure behavior. The new method is proposed using these criteria mentioned above to calculate the swell pressures acting on retaining walls when expansive soils are present behind the wall.

5.3 Wall and Soil Profiles Studied

The behavior of anchored sheet pile walls have been studied in the past for granular and cohesive soils (ASCE 1994; Das 2007; Bilgin 2011). While sheet pile walls less than 3-4.5 m can be cantilever, higher walls require anchors (ASCE 1994). Since single level anchor sheet pile walls are studied in this study, three different wall heights

(5, 7.5, and 10 m) were considered. The walls higher than 10-12 m usually require multiple levels of anchors. The groundwater table was always assumed to be at 5 m below the ground surface, i.e. top of the wall.

A study performed by Bilgin and Erten (2009) showed that to have minimum lateral wall movement and soil settlements, the anchor should be installed at approximately 0.25H depth from the top of wall, where H is the wall height. So, the

anchor location was fixed at 25 percent of the wall height below the top of wall in all the cases analyzed in this study. By using the free-earth support method, the walls were first designed assuming the soils are non-expansive and the depth of penetration, axial anchor force, and maximum wall bending moments were determined. Then the walls were designed using various levels of expansive soils and the depth of penetration, axial anchor force, and maximum wall bending moments were determined for these cases.

5.3.1 Parameters used in this study

5.3.1.1 Moisture content

This current research suggests that the range of moisture contents between 10 to

25 percent based on previous researches, and the approximate average value that will be considered is 15 percent.

5.3.1.2 Density

For the unit weight (ϒ), it is assumed to be 20 kN/m3

For the dry density

5.3 where

ρ = the density of the material, and it is assumed based on the average value

between 1.5 to 1.8 =1.65 g/cm3

g is acceleration due to gravity ( m/s2)

w = moisture content (%)

5.3.1.3 Plasticity index

As mentioned in chapter 2, classification of swelling soils based on entire range of plasticity index as shown in Table 2.4 is repeated in Table 5.1

Table 5.1 Classification of swelling soils (Department of Army 1983) Plasticity index Liquid limit Potential Natural soil Classification (PI) (%) (LL) (%) swell, Sp(%) suction, tsf Low < 25 < 50 < 0.5 < 1.5

Marginal 25-35 50-60 0.5-1.5 1.5-4.0

High > 35 > 60 >1.5 > 4.0

Therefore, in this study different plasticity index ranges from low to high swelling will be considered as the following:

PI = 10% for low potential expansive soils

PI = 30% for marginal potential expansive soils

PI = 70% for high potential expansive soils

5.3.1.4 Lateral earth pressure coefficients

The lateral earth pressure coefficients were selected based on Coulomb theory as explained in Chapter 3.

5.3.1.5 Internal friction angle

According to Lytton et al. (2005), the effective angle of frication can be calculated based on the plasticity index as the following equation

’ = 0.0016PI 2 − 0.3021PI + 36.208 5.4

PI = plasticity index

5.3.1.6 Undrained shear strength

According to Kang et.al (2011), there are some empirical correlations between PI and the undrained shear strength ratio (Su / σv’) such as Skemton (1957) and Chandler

(1988), their equations were to calculated the undrained shear strength based on PI for normal and over consolidation clay as the following:

Su / σv’ = 0.11+0.0037 PI 5.5 where

Su = undrained shear strength (kPa)

σv’ = effective overburden stress = .z (kPa)

 = unit weight (g/cm3)

Equation 5.5 will be used in the design of anchored sheet piles based on different ranges of plasticity index.

Expansive soil as mentioned before is unsaturated soil, so it is acceptable at the active zone to assume drained conditions. However, close to the ground surface where the change in moisture content is maximum and soil is almost fully saturated to have the full swelling potential, the undrained soil conditions will develop when the maximum swell pressures are acting on the wall. The calculations performed to look at the comparative analysis of drained versus undrained conditions close to ground surface indicate that the undrained condition results in more pressures and therefore is more conservative than the drained condition, as shown in Figure 5.1 .

In this study, it was found that the maximum swell pressure occurs at the depth

(z), where is z ≤ 1.61 m, as will be presented later in next chapter. So, as a result from 71

plotting the undrained and drained condition (Figure 5.1), it can be seen at z ≤ 1.61 and

PI=70 % (for example), the area under the undrained condition is bigger than the drained condition, so as considering the undrained condition, it will be more safety factor in the calculation at the active zone.

Figure 5.1 Undrained versus drained conditions

5.4 Fredlund and Rahardjo (1993) vs. Proposed Method

5.4.1 Design of anchored sheet piles using constant swell pressure method (Fredlund and Rahardjo 1993)

In Fredlund and Rahardjo method, which hereinafter will be referred to as constant swell pressure method, it is assumed that the swell pressure is constant with depth. In this study, the swell pressures will be estimated from the equation of constant swell pressures on anchored sheet piles, then add this magnitude to the conventionally 72

derived lateral earth pressure. So, total lateral pressure for anchored sheet piles on expansive soils will be calculated from lateral earth pressure and constant swell pressure as in the following scheme.

(a) H = 5 m

(b) H > 5 m

Figure 5.2 Scheme for Fredlund and Rahardjo method for anchored sheet piles and expansive soils where

F = Anchor force (kN/m) 73

Ps = Swell pressure (kPa)

H = wall height = h1+h2 (m)

D = penetration depth (m)

h1 = the depth from the ground level to the water table (m)

h2 = the depth from the water table to the dredge line (m)

σ’1 = stress at point A (kPa)

σ’2 = stress at point B (kPa)

l1 = the depth from the ground level to the anchor force level = 0.25H

l2 = the depth from the anchor force level to the water table = h1-l1

WT = water table level

DL = dredge line

Based on previous research, the depth of active zone, ranged between 10 to 20 ft

(3.05 to 6.1 m). So an average active zone depth of 5 m height from the ground surface to the water table level will be assumed. Therefore, the distribution in the swell pressure will be acting in this depth and it will be always in this study at height = 5 m.

5.4.2 Design of anchored sheet piles using proposed swell pressure method

During this study, an anchored sheet pile wall design method including the swell pressures for expansive soils is proposed as given in the following steps:

1- Calculate the swell pressure at constant dry density and moisture content, but at the

entire range of plasticity from Erzin and Erol’s equation for Ps ≤ 100 kPa.

2- As mentioned in previous chapters, it will be assumed that the swell pressure at the

surface acting like passive behavior, and the moisture content is greater at the surface

than the bottom, so swell pressure also will be greater at the surface.

3- According to Lytton et al. (2005), the confining pressure (σc) = (σv+ 2σH)/3, in which

σv (vertical stress) = .z , and σH (horizontal stress) = .z + 2Su

From above, σc = .z + (4/3) Su

where

Su = undrained shear strength (kPa)

3  = unit weight (kN/m )

4- If Ps > σc, this means the pressure at swelling (σs) = .z + 2Su, but if Ps < σc this means

the pressure at swelling (σs) = Ps

5- To calculate the depth (z), the equation of confining pressure will be equal to the

equation of swell pressure.

6- Then considering the additional forces due to the swell pressures calculate the depth of wall penetration, axial anchor force, and maximum bending moment.

(a) H = 5 m

(b) H > 5 m

Figure 5.3 Scheme for proposed method for anchored sheet piles and expansive soils

A parametric study performed to look at the effect of expansive soils on anchored sheet pile wall design, using the both pressure diagrams given above, is presented in the next chapter.

CHAPTER 6

PARAMETRIC STUDY AND ANALYSIS OF RESULTS

6.1 Introduction

A parametric study is performed to investigate the effect of expansive soil swell pressures on anchored sheet pile wall design is presented in this chapter. The new proposed swell pressures as given in Chapter 5 were used in the analyses. The wall design parameters, such as wall penetration depth, anchor force, and wall bending moments were compared to non-expansive soils to evaluate the effect of swell pressures on wall design. The design parameters obtained using proposed swell pressures were also compared to the results obtained by using constant swell pressure method given in the literature. The parametric study included the wall heights ranging from 5 to 10 m.

There were 21 anchored sheet pile wall cases analyzed in this study as described previously. Three of these cases were analyzed for non-expansive soils and the rest of them were analyzed with swell pressures indicating presence of expansive soils behind the wall. The detailed discussion of the analyses performed and the results obtained are presented in this chapter.

6.2 Anchor Sheet Pile Design Sample Calculations

The current section explains a set of sample calculations pertaining to case studies for both methods. The subsequent calculations for determining the quantities of density and moisture content are based on the average values below as stated in Chapter 5.

Average moisture content, w (%) = 15%

3 Average dry unit weight (dry density), d (from equation 5.3) = 18.61 kN/m

Unit weight,  = 20 kN/m3

6.2.1 Retaining wall case study for H = 5 m

The case study for wall height of 5 m was selected because the effect of expansive soils on wall bending moments, anchor forces, and depth of penetration is more significant at small wall heights as will be presented later in this chapter. Based on models developed in Chapter 5, the design calculations for this case study are performed to present the anchored sheet pile behavior in expansive soils.

6.2.1.1 Design calculations for non-expansive soil

The properties of this case study as shown in Figure 6.1 that were used in design of anchored sheet pile are given in Table 6.1, where

' = 0.0016PI2 − 0.3021PI + 36.208

δ/' = 0.67

PI = plasticity index = 0 for non-expansive soil

Table 6.1 Properties considered for the present case study before applying the swell pressure

Property Description Value Unit ' effective angle of fiction 36.21 degree δ wall friction angle 24.259 degree H Wall height 5 m back face inclination of the β 0 degree structure α slope inclination 90 degree 3 d dry density 18.61 kN/m  unit weight 20 kN/m3 the depth from the ground level to h 5 m 1 the water table the depth from the water table to h 0 m 2 the dredge line The depth from the ground level l 1.25 m 1 to the anchor force level = 0.25H the depth from the anchor force l2 3.75 m level to the water table = h1-l1

Ka active earth pressure coefficient 0.232

Kp passive earth pressure coefficient 5.751 W.T water table level

D.L dredge line

The calculations (see Table 6.1 for property descriptions):

' 2 σ1 =Ka*d*H = 0.232*18.61*5 = 21.682 kN/m where Ka is based the Coulomb method as given in Chapter 3

L3 = σ1/('(Kp/F.S.-Ka)) where Kp is based the Coulomb method as given in Chapter 3

A factor of safety, F.S., of 2.0 is used for passive earth pressure. 80

3 The effective unit weight, ' = - w = 20 -9.81 = 10.19 kN/m

So, L3 = 21.682/ [10.19*(11.5/2 – 0.232)] = 0.386 m

The force P1 (Area of the pressure diagram AO’B) = 0.5*σ'1*H = 0.5*21.682*5 =

54.205 kN/m

The force P2 (Area of the pressure diagram ABC) = 0.5* σ'1* L3 = 0.5*21.682*0.386 =

4.180 kN/m

By taking the moment about point O (ΣMO = 0) yields

2 P1*[(H*2/3)-l1] + [P2*(L3/3+l2)]-[(0.5*(Kp/F.S-Ka)*'*L4 )*(2/3*L4+L3+l2)] = 0

By trial and error, it can be calculated that L4 is equal to 0.980 m

The depth of wall penetration, D = L3 + L4 = 1.37 m

2 So, P3 = 0.5*(Kp/F.S - Ka)* '*L4 = 27.00 kN/m

From horizontal force equilibrium ΣFH = 0

F- P1 - P2 + P3 →the anchor force, F= 31.38 kN/m

The maximum moment (zero shear) will be between H < x < H+L3 (Figure 6.1). Using a new coordinate system x for zero shear gives

2 0.5 -Ka*d*x /2+F=0→ x= ((F*2)/ (d*Ka)) = 3.81 m

And the stress at the depth x

2 σ1x = Ka*d*x = 16.50 kN/m

The magnitude of the maximum moment may now be obtained

Mmax= - 0.5* σ1x *x*(x/3) +F*(x-l1) = 40.37 kN.m/m

Figure 6.1 Case study at H= 5m before applying the swell pressure

6.2.1.2 Design calculations using constant swell pressure method

In this method, the design swell pressure is based on constant dry density. The wall height is equal to the depth of the active zone, which is equal to 5 m. Table 6.2 and

Figure 6.2 illustrate the properties of this case study.

Table 6.2 Properties considered for the present case study at constant swell pressure

Property Description Value Unit ' effective angle of fiction 22.90 degree δ wall friction angle 15.34 degree H Wall height 5 m back face inclination of the β 0 degree structure α slope inclination 90 degree 3 d dry density 18.61 kN/m  unit weight 20 kN/m3 the depth from the ground level to h 5 m 1 the water table the depth from the water table to h 0 m 2 the dredge line The depth from the ground level l 1.25 m 1 to the anchor force level = 0.25H the depth from the anchor force l2 3.75 m level to the water table = h1-l1

Ka active earth pressure coefficient 0.391

Kp passive earth pressure coefficient 1.758 W.T water table level

D.L dredge line

The calculations (see Table 6.2 for property descriptions):

' 2 σ1 =Ka*d*H = 0.391*18.61*5 = 36.409 kN/m where Ka is based the Coulomb method as given in Chapter 3

L3 = σ1/ ('(Kp/F.S-Ka)) where Kp is based the Coulomb method as given in Chapter 3

A factor of safety, F.S., of 2.0 is used for passive earth pressure.

3 The effective unit weight, ' = - w = 20 -9.81 = 10.19 kN/m

So, L3 = 36.409/ [10.19*(3.52/2 – 0.391)] = 2.613 m

The force P1 (Area of the pressure diagram AO’B) = 0.5*σ'1*H = 91.02 kN/m

The force P2 (Area of the pressure diagram ABC) = 0.5* σ'1* L3 = 47.58 kN/m

By taking the moment about point O (ΣMO = 0) yields

P1*((2*H/3)-l1) + [P2*(L3/3) +l2))] + [Ps*H*(Ls-l1)]-[P3*(((2/3)*L4) + L3+l2)] = 0 where Ps is obtained from Fredlund and Rahardjo’s equation (constant swell pressure), as stated in chapter 5

Ps = ρ.g.H = 1.65*9.81*5 = 80.93 kPa

By trial and error, it can be calculated L4 which equal 3.84 m

The depth of wall penetration, D = L3 + L4 = 6.45 m

2 So, P3 = 0.5*(Kp / F.S- Ka)* '*L4 = 102.72 kN/m

For equilibrium analysis ΣFH = 0

F- P1 - P2 + P3 - Ps→ the anchor force, F= 440.55 kN/m

According to the maximum moment (zero shear) will be between H < x < H+L3

(Figure 6.2). Using a new coordinate system x for zero shear gives

2 -Ka*d*x /2+F – Ps*x = 0

By trial and error, x = 4.52 m

2 And the stress at the depth x, σ1x = Ka**x = 32.4 kN/m

The magnitude of the maximum moment may now be obtained

Mmax= - 0.5* σ1x *x*(x/3) +F*(x-l1) –Ps*(x/2) = 501.68 kN.m/m

Figure 6.2 Case study at H= 5m for constant swell pressure

6.2.1.3 Design calculations using proposed method

In this method, the design calculations are performed using average values of dry density and moisture content. The design is for soil with high plasticity index, PI= 70%.

Table 6.3 and Figure 6.3 illustrate the properties of this case study.

Table 6.3 Properties considered for the present case study at constant swell pressure

Property Description Value Unit ' effective angle of fiction 22.90 Degree δ wall friction angle 15.34 Degree H Wall height 5 M back face inclination of the β 0 Degree structure α slope inclination 90 Degree 3 d dry density 18.61 kN/m  unit weight 20 kN/m3 the depth from the ground level to h 5 M 1 the water table the depth from the water table to h 0 M 2 the dredge line The depth from the ground level l 1.25 M 1 to the anchor force level = 0.25H the depth from the anchor force l2 3.75 M level to the water table = h1-l1

Ka active earth pressure coefficient 0.391

Kp passive earth pressure coefficient 1.758 W.T water table level

D.L dredge line

The calculations (see Table 6.3 for property descriptions):

' 2 σ1 =Ka*d*H = 0.391*18.61*5 = 36.409 kN/m where Ka is based the Coulomb method as given in Chapter 3

L3 = σ1/ ('(Kp /F.S-Ka)) where Kp is based the Coulomb method as given in Chapter 3

The F.S for the passive earth pressure coefficient = 2

3 The effective unit weight, ' = - w = 20 -9.81 = 10.19 kN/m

So, L3 = 36.409/ [10.19*(3.52 / 2 – 0.391)] = 2.613 m

The force P1 (Area of the pressure diagram AO’B) = 0.5*σ'1*H = 91.02 kN/m

The force P2 (Area of the pressure diagram ABC) = 0.5* σ'1* L3 = 47.58 kN/m

To calculate the undrained shear strength (Su) from equation 5.5 that stated in chapter 5

Su / σv’ = 0.11+0.0037 PI

It is assumed Su at the active zone, at H=5 m, so by taking the average of Su between the ground surface and H= 5, and at PI = 70%

Su = 18.45 kPa where σv’ = effective overburden stress = .z (kPa)

z = (Ps-4/3Su) / (+Ps/H) = 1.51 m where Ps is obtained from Erzin and Erol’s equation at PI= 70% that stated in chapter 5

Log Ps = - 3.72 + 0.0111 PI + 2.077 d + 0.244 log s

Log s = 2.02 + 0.00603PI – 0.0769W as stated in chapter 5 s = soil suctions (bar)

PI = plasticity index (%)

3 d = dry density (g/cm ) w = moisture content (%)

2Su = 2*18.45 = 36.9 kPa

2Su+.z = 36.9 + 20*1.51 = 67.03 kPa

By taking the moment about point O (ΣMO = 0) yields

P1*((2*H/3) - l1) + P2*(L3/3) + l2)-[2Su*z*(z/2+R)]-[((2Su+.z) - (2Su))*0.5*z*(z/3+R)] +

[(2Su+.z)*0.5*(H-z)*(E-R)] = 0

where

R = l1-(z/2)

E = (H-z)/3

By trial and error, it can be calculated L4 which equal 3.05 m

The depth of wall penetration, D = L3 + L4 = 5.67 m

2 So, P3 = 0.5*(Kp / F.S - Ka)* '*L4 = 64.80 kN/m

For equilibrium analysis ΣFH = 0

F= P1+P4- P5 + (2Su*z) + [((2Su+d.z)-(2Su))*0.5*z] + [(2Su+ d.z)*0.5*(H-z)] → the anchor force, F= 268.75 kN/m

The maximum moment (zero shear) will be between H < x < H+L3. (Figure 6.3). Using a new coordinate system x for zero shear gives

2 -0.5*Ka**x +F - (2Su*z)-[((2Su+ . z)-(2Su))*0.5*z]-[M*0.5*(x-z)]-[N*(x-z)] where

M = [(2Su+  .z)*(x-z)] / (H-z)

N= (2Su+  .z)-M

By trial and error, x= 4.89 m

And the stress at the depth x

2 σ1x = Ka**x = 35.64 kN/m

The magnitude of the maximum moment may now be obtained

Mmax = - 0.5*σ1x*x*(x/3)+F*(x-l1)-[2Su*z*(x-z/2)]-[((2Su1+d .z)-(2Su))*0.5*z*(x-

(2/3)*z)]-[M*0.5*(x-z)*(2/3*(x-z))]-[N*(x-z)*(x-z)/2)] = 258.30 kN.m/m

Figure 6.3 Case study at H= 5m for the proposed method

6.3 Results of the Parametric Study

The results obtained from the proposed method and the constant swell pressure method is summarized in the following tables.

Table 6.4 Non-expansive soils (PI=0)

Depth of wall Anchor force, F Max moment, H (m) penetration, D (kN/m) M , (kN.m/m) (m) max 5 1.37 31.38 40.37 7.5 1.89 67.50 124.60 10 2.39 112.11 261.02

Table 6.5 Constant swell pressure method 1. After applying the swell pressure, for low potential expansive soils (PI= 10%) Depth of wall Anchor force, F Max moment, M H (m) max penetration, D (m) (kN/m) (kN.m/m) 5.0 2.96 360.63 292.49 7.5 2.90 454.97 309.47 10.0 3.16 537.47 328.49

2. After applying the swell pressure, for marginal potential expansive soils (PI= 30%) Depth of wall Anchor force, F Max moment, M H (m) max penetration, D (m) (kN/m) (kN.m/m) 5.0 4.13 389.48 362.99 7.5 4.37 489.79 399.61 10.0 4.97 586.63 514.50

3. After applying the swell pressure, for high potential expansive soils (PI= 70%) Depth of wall Anchor force, F Max moment, M H (m) max penetration, D (m) (kN/m) (kN.m/m) 5 6.45 440.55 501.77 7.5 7.42 559.82 639.39 10 8.76 686.29 982.63

Table 6.6 The proposed method 1. After applying the swell pressure, for low potential expansive soils (PI= 10%) Depth of wall Anchor force, F Max moment, M H (m) max penetration, D (m) (kN/m) (kN.m/m) 5 1.88 72.33 55.76 7.5 2.50 118.64 153.90 10 3.12 173.64 315.78

2. After applying the swell pressure, for marginal potential expansive soils (PI= 30%) Depth of wall Anchor force, F Max moment, M H (m) max penetration, D (m) (kN/m) (kN.m/m) 5 3.07 136.34 105.03 7.5 3.96 199.37 241.83 10 4.90 276.28 476.86 90

3. After applying the swell pressure, for high potential expansive soils (PI= 70%) Depth of wall Anchor force, F Max moment, M H (m) max penetration, D (m) (kN/m) (kN.m/m) 5 5.67 268.75 258.30 7.5 7.01 432.84 463.50 10 8.66 483.51 915.90

Table 6.7 The constant swell pressure method vs. the proposed method (% change relative to non-expansive soils) PI =10% % Change % Change Depth of Depth of Anchor Max. Anchor Max. H (m) wall wall force moment force moment penetration penetration Constant swell pressure method The proposed method 5 117.00 1049.13 624.55 37.92 130.48 38.13 7.5 53.27 574.00 148.38 32.12 75.76 23.52 10 32.50 379.41 25.85 30.83 54.88 20.98 PI =30% 5 202.79 1141.07 799.18 125.17 334.44 160.17 7.5 131.18 625.58 220.72 108.97 195.35 94.09 10 108.11 423.25 97.11 105.18 146.44 82.69 PI =70% 5 372.57 1303.78 1142.96 315.46 756.37 539.86 7.5 292.29 729.33 413.17 270.61 541.22 272.00 10 267.05 512.15 276.46 262.87 331.28 250.90

The proposed method was compared with the previous research by Fredlund and

Rahardjo (1993) (constant swell pressure) as the following:

6.3.1 Effect of plasticity index

The depth of wall penetration, anchor forces, and the wall bending moments obtained from the free earth support method using the constant swell pressure method,

and the proposed method at different plasticity index, PI are shown in Figures 6.4 and

Figure 6.5.

a) Change in the depth of wall penetration

b) Change in the anchor force

c) Change in the moment

Figure 6.4 Proposed method for different height 92

a) Change in the depth of wall penetration

b) Change in anchor force

c) Change in moment

Figure 6.5 Constant swell pressure method for different height

The results presented in Figures 6.4 and 6.5 show that there is an increase in depth of wall penetration, anchor force, and wall bending moment as the plasticity index increases for both methods. Increases in anchor forces and bending moment obtained

using the proposed method is smaller than the results obtained using the constant swell pressure method. However, the change in the depth is approximately the same in both methods.

6.3.2 Effect of wall height

The depth of wall penetration, anchor forces, and wall bending moment, obtained from the analysis of all cases using the proposed and the constant swell pressure methods are shown in Figures 6.6 and 6.7.

a) Change in depth of wall penetration b) Change in anchor force

c) Change in moment

Figure 6.6 Proposed method for different plasticity index

a) Change in depth of wall penetration

b) Change in anchor force

c) Change in moment

Figure 6.7 Constant swell pressure method for different plasticity index

Figures 6.6 and 6.7 show that the change in anchor force, moment, and the depth decrease with increases in the height in both methods, indicating that the effect of expansive soils on the depth of wall penetration, anchor forces, and the wall bending moments is more significant for relatively shorter walls. The decreases in anchor forces and bending moment are smaller than the ones calculated from the constant swell pressure method, although the change in the depth is approximately the same in both methods.

6.4 Effect of Moisture Content

In order to study the effect of the moisture content on the amount of swell pressure for the proposed method, different moisture contents at the same dry density that was used in the parametric study (ρ = 1.65 g/cm3) are plotted on the graph in Figure 6.8.

Figure 6.8 Effect of moisture content on the proposed method

As is shown in Figure 6.8 at the same dry density, soils with moisture content w

=10% and plasticity index PI=36%; w =15% and PI= 44%; w = 20% and PI=50%; and w 96

= 25% and PI=58% would result in same swell pressures and therefore almost very similar wall design parameters for the depth of wall penetration, anchor forces, and the wall bending moments.

6.5 Effect of Dry Density

Figure 6.9 shows the effect of dry density on the swell pressure for the proposed method.

Figure 6.9 Effect of dry density on the proposed method

The results of the Figure 6.9 show that the swell pressure at a constant moisture content of w =15%, soils with dry density ρ =1.5g/cm3 and plasticity index PI=72%; ρ

=1.65g/cm3 and PI= 44%; and ρ=1.8g/cm3 and PI=20 would result in same swell pressures and therefore almost very similar wall design parameters for the depth of wall penetration, anchor forces, and the wall bending moments.

Therefore, it can be concluded that, the results of anchor force, wall bending moment, and depth of penetration at the average value of w =15%, and ρ = 1.65 g/cm3 97

will have similar results in case using any value from Figure 6.8 and 6.9. For example, in this current study, the analysis and design of anchored sheet pile is done by considering w

= 15%, ρ= 1.65g/cm3, so if these values used to calculate the swell pressure from Figure

6.11 and 6.12 as shown in the following table.

Table 6.8 Comparing between Figure 6.8 vs. Figure 6.9

Figure 6.11 Figure 6.12

Ps= 44 kPa Ps= 44 kPa 3 ρ =1.65 g/cm w = 15% w = 15% PI= 44% ρ=1.65 g/cm3 PI= 44%

w = 20% PI = 50% ρ=1.8 g/cm3 PI = 20%

It can be seen, there will be same swell pressure if the values in Table 6.8 are used. As a result, the depth of wall penetration, anchor forces, and the wall bending moments will be similar with considering the other properties, including ’, δ, Ka, and

Kp.

CHAPTER 7

CONCLUSIONS

In this study, a new proposed method is developed to analyze and design retaining walls in expansive soils. Empirical equations were used in the developed method to determine the expansive soil swell pressures. The conclusions and recommendations drawn from this study are given in the following sections.

1. Expansive soil swell pressures depend on soil’s dry density and plasticity index. The swell pressures increase with increasing dry density and plasticity index.

2. The swell pressures also depend on the moisture content of the soil and the swell pressure increases with decreasing moisture content.

3. The swell pressures calculated by using the empirical equations given by Erzin & Erol

(2007) method compared with the constant swell pressures given by Fredlund and

Rahardjo (1993) show that at high dry density, the magnitude of swell pressures by Erzin

& Erol method are smaller than the magnitude of the swell pressures which were calculated by the constant swell pressure method.

4. The design calculations with the new proposed swell pressure distribution diagram have shown that the changes in anchor force, and wall bending moments are smaller than the ones calculated from the constant-swell pressure method, although the change in the depth of wall penetration is approximately the same in methods, the proposed method and 99

constant swell pressure method.

5. In both methods, there is an increase in the depth of wall penetration, anchor force, and wall bending moments with an increase in the plasticity index.

6. The effect of expansive soils on the depth of wall penetration, anchor force, and wall bending moment is more significant at small wall height for the proposed method and constant swell pressure. For the proposed method, the change in anchor force at height =

5 m equal 700% while at height = 10 m, the change equal 300%. So, there is about 400 % increase on anchor force as increasing the height.

7. The presence of expansive soils behind an anchored sheet pile wall significantly affects the depth of wall penetration, anchor force, and wall bending moments. The effect is much more significant for relatively shorter walls.

The results of this study show that considering the effect of expansive soils and designing for the potential swell pressures may result in very heavy designs. When highly expansive soils are present, wall design with multi levels of anchors, instead of single level anchor, can help to eliminate heavy anchor designs and use of large pile profiles. As mentioned earlier, the expansive soil behavior is observed within the active zone depth.

The active zone depth varies depending on the project location; however the published data indicates that the average depth is about 5 m. Instead of designing retaining walls for expansive soil swell pressures, especially when the soils are highly expansive, it may be more economical to remove the top a few meters of existing expansive soils and replacing them with non-expansive soils. There are also expansive soil chemical treatments available which are designed to reduce the expansion potential. Treatment with “lime” or Calcium Oxide is the most traditional treatment method.

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