條形振動夯實造成砂土密度及土壓力變化

國立交通大學

土木工程學系碩士班

碩士論文

條形振動夯實造成砂土密度及土壓力變化

Variation of Soil Density and Earth Pressure

due to a Strip Compaction

研 究 生 : 簡煜倫

指導教授 : 方永壽 博士

條形振動夯實造成砂土密度及土壓力變化

Variation of Soil Density and Earth Pressure due to a Strip Compaction

研 究 生: 簡煜倫

Student：Yu-Lun Chien

指導教授：方永壽 博士

Advisor：Dr. Yung-Show Fang

國 立 交 通 大 學 土 木 工 程 學 系 碩 士 班

碩士論文

A Thesis

Submitted to the Department of Civil Engineering

College of Engineering

National Chiao Tung University

in Partial Fulfillment of the Requirements

for the Degree of

Master of Engineering

in Civil Engineering

September, 2007

Hsinchu, Taiwan, Republic of China

中華民國九十六年九月

條形振動夯實造成砂土密度及土壓力變化

研究生 : 簡煜倫 指導教授 : 方永壽 博士

國立交通大學土木工程學系碩士班

摘要

本論文以實驗方法探討條形振動夯實造成砂土密度和土壓力的變化。本研究 以氣乾之渥太華砂為回填土，回填土高 1.5 公尺。回填土初始相對密度(Dr)為 34%。為了在實驗室模擬雙向平面應變的情況，本研究採用塑膠膜潤滑層來降低 砂土和填砂槽側牆間的摩擦力。本研究進行一連串相關的實驗，來探察振動夯實 對砂土所產生的影響。這些影響包括夯實後土壤表面的沉陷、相對密度的變化和 夯實前後的垂直和側向殘餘土壓力。根據實驗結果，本研究獲得以下幾項結論： 1. 對於疏鬆砂土，土體內的垂直土壓力和水平土壓力可分別以σv =γz 和 Jaky 公式來進行合理的估算。 2. 隨著夯實機夯實趟數的增加，條形夯實區之地表沉陷量隨之增大。地表沉陷量 和夯實趟數之間的關係可以用雙曲線的模式來模擬。 3. 砂土的相對密度變化等高線範圍，會隨著夯實趟數增加而擴大。 4. 垂直土壓力變化量的等高線近似於同心圓的形狀，而殘餘垂直土壓力Δσv會由 圓心區域向外逐漸減少。土體內最大Δσv值會隨著夯實趟數增加而增大。 5. 在夯實機夯實 1 和 2 趟後，殘餘水平土壓力Δσh的等高線會形成兩個較高的應 力區，水平土壓力變化量會由中心區域逐漸減少。然而在夯實機夯實 4 和 8 趟後，殘餘水平土壓力的等高線則近似於一個同心圓的形狀。夯實影響的區域 (Δσh = 0.2 kN/m2 應力等高線) 深度會隨著夯實能量增加而增大。 6. 在夯實一趟後，土壤所受夯實影響的機制可以用基礎下方土壤之局部剪力破壞

的情況來解釋。然而，當夯實趟數增加到 8 趟後，被夯實土壤之機制可用方形 鋼樁以振動打樁機貫入砂質地盤的情況來模擬。

Variation of Soil Density and Earth Pressure

due to a Strip Compaction

Student : Yu-Lun Chien Advisor : Dr. Yung-Show Fang Institute of Civil Engineering

National Chiao Tung University

Abstract

This paper studies the variation of soil density and earth pressure due to the strip compaction with a vibratory compactor. In this study, dry Ottawa sand was used as backfill material, and the height of backfill was 1.5 m. The initial relative density of the backfill (Dr) was 34 %. To simulate a 2-way plane strain condition in the laboratory,

the friction between the soil and sidewalls of the soil bin was reduced as much as possible. Experiments were conducted to investigate the effects of soil densification with a vibratory compactor. The surface settlement and change of relative density were measured after compaction. The vertical and horizontal stresses in the soil mass were measured before and after compaction. Based on the test results, the following conclusions can be drawn.

1. For loose sand, the vertical and horizontal earth pressure in the soil mass could be properly estimated with the equation σv = and Jaky’s equation, respectively. γz

2. The surface settlement increased with the increasing number of passes of the compactor. The relationship between the surface settlement and the number of passes of the compactor could be modeled by the hyperbolic model.

3. After compaction, the range of contours of relative density (Dr = 36 %) would

become larger with increasing number of passes.

decrease gradually from the central region. The vertical stress increment Δσv

increased with increasing number of passages of the compactor.

5. The contours of Δσh formed two circles of high stresses and Δσh decreased

gradually from the center region after the first and the second passes of compactor. The contours of Δσh were analogous to concentric circles after 4 and 8 passes of

the compactor. The depth of the compaction-induced zone increased with increasing compaction energy input.

6. Based on the test results, the mechanism of soils after the first pass of the compactor could be explained by local shear failure. However, the mechanism of soils after 8 passes of the compactor could be simulated by a steel square pile driven in sand with a vibratory hammer.

Acknowledgements

The author wishes to give his sincere appreciation to his advisor, Dr. Yung-Show Fang for his continuous encouragement, enthusiastic support and helpful discussions in the past two years. The author also felt a great gratitude to the members of his supervisory committee, Dr. Ching-Chuan Huang, Dr. Tsang-Jiang Chen for their valuable suggestions.

Appreciation is extended to all my friends and classmates, especially for Mr. Shih-Da Hsu, Mr. Hao-Chen Chang, Mr. Chuan-Te Wu, Mr. Yung-Cheng Cheng, Mr. Pai-Shuo Chen, Mr. Sheng-Feng Huang for their encouragement and assistance. Finally, the author would dedicate this thesis to his parents, sisters and brother for their continuing encouragement and moral support.

Table of Contents

Page

Abstract (in Chinese) ……….. i

Abstract ………..………. iii

Acknowledgements ……… v

Table of Contents ………... vi

List of Tables ……….. ix

List of Figures ………. x

List of Symbols ………... xviii

Chapter 1 Introduction

………... 1

1.1 Objectives of Study ……….. 1

1.2 Research Outline ……….. 2

1.3 Organization of Thesis …..……..……….………. 3

Chapter 2 Literature Review

………... 4

2.1 Earth Pressure At-Rest …………..……….... 4

2.1.1 Coefficient of Earth Pressure At-Rest ……….…... 4

2.1.2 Jaky’s Formula …..……….………...…... 6

2.2 Effects of Soil Compaction on Earth Pressure ………. 7

2.2.1 Study of Duncan and Seed ……….………... 7

2.2.2 Study of Chen ………..………... 9

2.3 Elastic Solutions for a Strip Surface Loading ………... 10

2.4 Ultimate Bearing Capacity of Shallow Footing ……… 11

2.5 Stresses in Soil during Penetration Test ………... 12

Page

Chapter 3 Experimental Apparatus

……….……….. 15

3.1 Soil Bin ……….……….... 15

3.2 Soil Pressure Transducer ……….. 16

3.3 Data Acquisition System ………..……… 17

3.4 Vibratory Compactor ………..……... 17

Chapter 4 Backfill Characteristics

………..…….. 18

4.1 Backfill Properties ………... 18

4.2 Reduction of Wall Friction ………...……… 19

Chapter 5 Test Results for Loose Sand

………..………...………... 21

5.1 Testing Procedure ………. 21

5.2 Distribution of Soil Density ……….. 22

5.2.1 Air-Pluviation of Ottawa Sand ………. 22

5.2.2 Uniformity of Soil Density ……….……….…… 23

5.3 Distribution of Earth Pressures ………. 23

Chapter 6 Surface Settlement and Density Change due

to Compaction

………... 25

6.1 Testing Procedure ………. 25

6.2 Pilot Tests ………... 26

6.3 Surface Settlement ………... 28

6.4 Change of Relative Density ……….. 28

Chapter 7 Change of Vertical Stresses due to Compaction

…... 31

7.1 Testing Procedure ………. 31

7.2 Vertical Stress Distribution under Compaction Strip ………….……... 32

Page

Chapter 8 Change of Horizontal Stresses due to Compaction

... 34

8.1 Horizontal Stress Distribution under Compaction Strip ………... 34

8.2 Horizontal Stress Change on Intermediate Principal Plane ………….. 35

8.3 Mechanism of Soils under Strip Compaction ………... 36

8.3.1 Mechanism after First Pass of Compactor …... 36

8.3.2 Mechanism after 8 Passes of Compactor ………... 37

Chapter 9 Conclusions

………... 39

References ………... 40

Tables ………. 44

Figures ……….... 49

Appendix A: Calibration of Soil Pressure Transducers ……….. 149

Appendix B: Operation of Softwares Surfer 8 and Grapher 7 ……….... 163

Appendix C: Test Results at Grid Points ……… 173

Appendix C1: Relative Density of Sand at Grid Points ………. 174

Appendix C2: Δσv in Soil Mass at Grid Points ………... 178

List of Tables

Number Page

2.1 Terzaghi’s Bearing Capacity Factors (after Kumbhojkar,1993) ……... 44 3.1 Technical Information of the Eccentric Motor ……….. 45 4.1 Properties of Ottawa Sand (after Hou, 2006) ……… 46 6.1 Relationship between the Surface Settlement and Number of Pass

(a) Smax divided into Five Equal Parts and the Corresponding Number

of Passes

(b) 1, 2, 4, and 8 Compactor Passes and Corresponding Surface

Settlement ………... 47 6.2 Differences between Test Results from the Laboratory

List of Figures

Number Page

1.1 Compaction of Soil with Vibratory Compactor ………...……. 49 2.1 Development of in-situ Stresses ……… 50 2.2 Principal Stresses in a Soil Element ……….. 51 2.3 Jaky’s Formulation of the Relationship between Ko on OC and φ

Mobilized in OAB (after Mesri and Hayat, 1993) ……… 52 2.4 Basic Components of Hysteretic Ko-Loading/Unloading Model

(after Duncan and Seed, 1986) ………. 53 2.5 Comparison between Final Pressure Distributions Based on ………...

Incremental Analysis and Hand Solution (after Duncan and Seed, 1983) 54 2.6 Distribution of Horizontal Earth Pressure after Compaction

(after Chen, 2002) ………. 55 2.7 Horizontal Earth Pressure Estimated with Various Methods after

Compaction (after Chen, 2002) ………. 56 2.8 Uniform Vertical Loading on an Infinite Strip ……….. 57 2.9 Stress beneath a Strip (after Jurgenson, 1934) ……….. 58 2.10 Bearing Capacity Failure in Soil under a Rough Rigid Continuous

Foundation (after Terzaghi, 1943) ……… 59 2.11 Definition of Failure Mode (after Vesic, 1973) ………. 60 2.12 Mode of Foundation Failure in Sand (after Vesic, 1973) ……….. 61

Number Page 2.13 Bearing Capacity Failure in Soil (after Vesic, 1973) ……… 62 2.14 Ultimate Load-Carrying Capacity of Pile (after Meyerhof, 1976) …... 63 2.15 Variation of the Maximum Values of Nq* with Soil Friction Angle φ’

64 (after Meyerhof, 1976) ………

2.16 Influence Zone Assumed for Piles in Sand (after Yang, 2006) ………. 65 2.17 Mean Range of Influence Zone for Pile in Clean Sand

(after Yang, 2006) ………. 66 2.18 Growth Curves for a Silty Clay – Relationship between Dry Unit

Weight and Number of Passes of Three-Wheel Roller Compactor

(after Johnson and Sallberg, 1960) ……….. 67 2.19 Vibratory Compaction of a Sand - Variation of Dry Unit Weight with

Number of Roller Passes; Thickness of Lift = 2.45 m

(after D’Appolonia, Whitman and D’Appolonia, 1969) ………... 68 3.1 NCTU Non-Yielding Retaining-Wall Facility (after Chen, 2002) …… 69 3.2 Soil-Pressure Transducer (Kyowa BE-2KCM17) (after Chen, 2002) .. 70 3.3 Data Acquisition System ………... 71

3.4 Side-View of Vibratory Soil Compactor ………... 72 3.5 Vibratory Soil Compactor ………. 73 3.6 Eccentric Motor with Eccentric Steel Plate (Mikasa KJ75)

Number Page 3.7 Vertical Dynamic Force Generated by Compactor as a Function of No.

of Eccentric Plate (after Chen, 2002) ……… 75

4.1 Grain Size Distribution of Ottawa Sand (after Hou, 2006) ………….. 76

4.2 Shear Box of Direct Shear Test Device(after Wu, 1992) ……….. 77

4.3 Relationship between Unit Weight γ and Internal Friction Angle φ (after Chang, 2000) ………... 78

4.4 Lubrication Layer on the Walls ………. 79

4.5 Schematic Diagram of Sliding Block Test (after Fang et al., 2004) … 80

4.6 Sliding Block Test Apparatus (after Fang et al., 2004) ………. 81

4.7 Variation of Interface Angle with Normal Stress(after Fang et al., 2004) 82 5.1 Relationship among Slot Opening, Drop Height, and Relative Density (after Ho, 1999) ………. 83 5.2 Method to Control Drop Height = 1.0 m ……….. 84

5.3 Method to Control Slot Opening = 15 mm ………... 85

5.4 Pluviation of Ottawa Sand into Soil Bin ………... 86

5.5 Dimensions of Soil Density Cup (after Ho, 1999) ……… 87

Numbe Page

5.7 Soil Density Cups Buried at Different Elevations ……… 89

5.8 Arrangement of Soil Density Cups at Same Elevation ………. 90

5.9 Density Control Test (a) Placement of Density Cup; (b) Measurement of Soil Mass in Cup …………. 91

5.10 Distribution of Soil Density for Loose Sand ………. 92

5.11 Locations of SPT to Measure Distribution of Vertical Earth Pressure .. 93

5.12 Placement of SPT in Soil Mass ………. 94

5.13 Photograph of SPT used to Measured Vertical Stress ………... 95

5.14 Distribution of Vertical Earth Pressure ………. 96

5.15 Locations of SPT to Measure Distribution of Horizontal Earth Pressure 97 5.16 Photograph of SPT used to Measured Horizontal Stress ……….. 98

5.17 Distribution of Horizontal Earth Pressure ………. 99

6.1 Testing Procedure of Strip Compaction ……… 100

Number Page

6.3 Definition of X-Y-Z Axes, XZ, YZ, and XY - Plane ……… 102

6.4 Surface of Backfill: (a) before Compaction; (b) after Compaction …. 103

6.5 Measurement of Surface Settlement on (a) XZ – Plane; (b) YZ - Plane 104 6.6 Surface Settlement along Compaction Lane with Regions of Sidewall Effects ………... 105

6.7 Surface Settlement along Compaction Lane after Compactor ……….. 106

6.8 Hyperbolic Model to Estimate Surface Settlement S as a Function of No. of Passes of Compactor ……….. 107

6.9 Surface Movement of Settlement Trough after First Pass of Compactor 108 6.10 Surface Settlement of Compaction Lane after 1, 2, 4 and 8 Passes of Compactor ………. 109

6.11 Surface Settlement along Compaction Lane after First Pass of Compactor ……… 110

6.12 Surface Settlement along Compaction Lane after 1, 2, 4 and 8 Passes of Compactor ………. 111

6.13 Locations of Density Cups (Side - View) ………. 112

6.14 Locations of Density Cups (Top - View) ……….. 113

6.15 Locations of Soil Density Cups at Same Elevation ……….. 114

Number Page 6.17 Contours of Relative Density after 1 – Pass of Compactor ………….. 116 6.18 Contours of Relative Density after 2 – Passes of Compactor ………... 117 6.19 Contours of Relative Density after 4 – Passes of Compactor ………... 118 6.20 Contours of Relative Density after 8 – Passes of Compactor ………... 119 6.21 Comparison between Test Results from Laboratory and Test Results

from Field (Johnson et al., 1960) ………. 120 6.22 Comparison between Test Results from Laboratory and Test Results

from Field (D’Appolonia et al., 1969) ……….. 121 7.1 Locations of SPT to Measure Variation of Vertical Stress under

Compaction Strip ……….. 122

7.2 Distribution of Vertical Stress under Compaction Strip ……… 123 7.3 Change of Vertical Stresses under Compaction Strip ………... 124 7.4 Locations of SPT to Measure Δσv due to Compaction (Side - View) 125

7.5 Locations of SPT to Measure Δσv due to Compaction (Top - View) 126

7.6 Locations of SPT at Same Elevation ………. 127 7.7 Δσv at Grid Points after 1 – Pass of Compactor ……… 128

Number Page

7.9 Contours of Δσv after 2 – Passes of Compactor ……… 130

7.10 Contours of Δσv after 4 – Passes of Compactor ……… 131

7.11 Contours of Δσv after 8 – Passes of Compactor ……… 132

8.1 Locations of SPT to Measure Variation of Horizontal Stress under Compaction Lane ……….. 133

8.2 Distribution of Vertical Stress under Compaction Lane ………... 134

8.3 Change of Horizontal Stresses under Compaction Lane ……….. 135

8.4 Locations of SPT to Measure Δσh due to Compaction (Side - View) ... 136

8.5 Locations of SPT to Measure Δσh due to Compaction (Top - View) … 137

8.6 Locations of SPT at Same Elevation ………. 138

8.7 Δσh at Grid Points after 1 – Pass of Compactor ……… 139

8.8 Contours of Δσh after 1 – Pass of Compactor ………... 140

8.9 Contours of Δσh after 2 – Passes of Compactor ………... 141

8.10 Contours of Δσh after 4 – Passes of Compactor ………... 142

Number Page 8.12 Comparison between Change of Relative Density after 1 Pass of

Compactor in This Study and Vesic’s Theory (1973) ………... 144 8.13 Bearing Capacity Failure in Soil (after Vesic, 1973) ……… 145 8.14 Comparison between Test Results and Local Shear Failure

(Vesic, 1973) ………. 146

8.15 Influence Zone Assumed for Piles in Sand (after Yang, 2006) ………. 147 8.16 Comparison between Test Results and Influence zone for Piles in Sand

List of Symbols

B = Width of Vibratory Soil Compactor

Cu = Coefficient of Uniformity

Df = Distance Form Ground Surface to the Bottom of Shallow Foundation

Dr = Relative Density of Soil

dL = Distance from Left Sidewall

dM = Distance from Model Sidewall

ds = Element Strip of Width

δw = Angle of Wall Friction

E _{= Young’s Modulus}

emax = Maximum Void Ratio of Soil

emin = Minimum Void Ratio of Soil

ε = Normal Strain

φ = Effective Stress Friction Angle

φ’ = Effective Stress Friction Angle for Local Shear Failure

Gs = Specific Gravity of Soil

γ = Unit Weight of Soil

γd = Dry Unit Weight of Soil

γd,max = Maximum Dry Unit Weight Measured in Tests

Ka = Coefficient of Active Earth Pressure

Ko = Coefficient of Earth Pressure At-Rest

Kp = Coefficient of Passive Earth Pressure

ν = Poisson’s Ratio

Ν = Number of Passes of Compactor

qult = Ultimate Bearing Capacity of Soil

S = Surface Settlement

σ1 = Major Principal Stress

σ3 = Minor Principal Stress

σcyc = Compaction Loading

σh = Effective Horizontal Stress

Δσh = Change of Horizontal Stress

σn = Normal Stress

σv = Effective Vertical Stress

Chapter 1

Introduction

In the construction of highway embankments, earth dams, and many other engineering structures, engineers will compact loose soils to increase their unit weights. The objective of the compaction operation is to improve the engineering properties of soil such as increasing the fill bearing capacity or reducing settlement. In various methods of compaction, vibratory compactions are used mostly for the densification of granular soils as shown in Fig. 1.1. Before compaction, the vertical earth pressure is calculated by the equation

z

v γ

σ = , and the horizontal earth pressure is estimated with Jaky’s formula. Many researchers had conducted studies regarding soil compaction, however most of their investigating were focused on compaction-induced stresses. It should be mentioned that the effects of compaction on a soil mass are not limited to stress change only. This study discusses the compaction-induced effects on a loose sandy soil which includes: (1) the surface settlement; (2) the change of relative density; (3) the change of vertical stresses; and (3) the change of horizontal stresses in the soil mass. Based on the experimental evidence, the mechanism of soil behavior under compaction is preposed.

1.1 Objectives of Study

Compaction is a particular kind of soil stabilization methods and it is one of the oldest methods for improving existing soil or man-placed fills. To analyze the residual

lateral earth pressure induced by soil compaction, several methods of analysis have been proposed by Rowe (1954), Broms (1971), Ingold (1979), Duncan and Seed (1986), Peck and Mesri (1987) and other researchers. However, little information regarding the mechanism of the compacted soil has been reported. From a practical point of view, this study simulates the strip compaction with a vibratory compactor on the surface of a loose granular soil in the field. The tests results include the change of soil density and the change of stress in the soil mass due to compaction. Based on the test data, the mechanism of the compacted soil due to the strip compaction on the surface of a sandy soil mass is proposed. All experiments mentioned in this study were conducted in the National Chiao Tung University (NCTU) non-yielding retaining wall facility that is described in Chapter 3. The horizontal and vertical stresses were measured with the soil pressure transducers (SPTs) which were embedded in the backfill.

1.2 Research Outline

This research utilizes the NCTU model wall facility to investigate the effects of compaction. The review of at-rest earth pressure theories and compaction-induced stresses are summarized in Chapter 2. Details of the experimental apparatus for this study are discussed in Chapter 3. The characteristics of backfill and the method used to reduce the sidewall friction are introduced in Chapter4. Chapter 5 discusses the test results for loose sand before compaction.

To investigate effects of compaction, the backfill was prepared by air-pluviated method and then compacted with a vibratory compactor. To decide the procedure of compaction, pilot tests were carried out and introduced in Chapter 6. Test results regarding surface settlement and change of relative density after 1, 2, 4 and 8 passes of

the vibratory compactor on the sand compaction line are reported in Chapter 6. Chapter 7 and Chapter 8 discuss the change of vertical stress and horizontal stress due to compaction, respectively. Based on the test results, the mechanism of the compacted soil as a result of the strip compaction is proposed.

1.3 Organization of Thesis

This paper is divided into the following parts:

1. Review of past investigations regarding soil compaction (Chapter 2) 2. Description of experimental apparatus (Chapter 3)

3. Characteristics of the backfill and the soil bin (Chapter 4) 4. Experimental results for loose sand (Chapter 5)

5. Surface settlement and density change due to compaction (Chapter 6) 6. Change of vertical stresses due to compaction (Chapter 7)

7. Change of horizontal stresses, and the mechanism of failure (Chapter 8) 8. Conclusions (Chapter 9)

Chapter 2

Literature Review

The Jaky’s formula (1944) is commonly used to calculate the earth pressure at-rest. To improve the engineering properties, contractors are generally required to compact the loose soils to increase their unit weights and reducing settlements. Previous studies associated with the compaction-induced effects such as the change of soil density, the change of stresses in the soil mass and mechanism of soils under compaction are discussed in this chapter.

2.1 Earth Pressure At–Rest

2.1.1 Coefficient of Earth Pressure At–Rest

As shown in Fig. 2.1(a), a soil element A located at depth z is compressed by the overburden pressure σv =γz. During the formation of the deposit, the

element A is consolidated under the pressure σv. The vertical stress induces a

lateral deformation against surrounding soils due to the Poisson’s ratio effect. Over the geological period, the horizontal strain is kept to be zero and the surrounding soil would develop a lateral stress to counteract the lateral deformation. A stable stress state will develop that the principal stresses acts

1

σ and σ ₃ on the vertical and horizontal planes, as shown in Fig. 2.1(b). The soil in a state of static equilibrium condition is commonly termed as the

vertical stress σv is defined as the coefficient of earth pressure at-rest, Ko, or v h o K σ σ = (2.1) z γ

since σv = , then σh =Koγz, where γ is the unit weight of soil.

For an isotropic soil element shown in Fig. 2.2, if the soil behaved as an ideal elastic material, based on the mechanics of materials, the lateral strain εy

can be expressed as:

( x z) y y E E σ σ ν σ ε = − + (2.2) or h ( _{h v}) h E E σ σ ν σ ε = − + (2.3) where E is the elastic modulus and ν is the Poisson’s ratio of the soil.

Base on the definition of the at-rest condition, the lateral strain would be zero under the application of stress state and the . Then the Eq. 2.3 can be written as:

v o h K σ σ = _h = 1 (K_{o v} − K_{o v} − _v)=0 E σ ν σ νσ ε (2.4) ν ν − = 1 o K (2.5)

It should be mentioned that Eq. 2.5 is applicable for the isotropic and elastic materials only. However, the behavior of soil element is more complex and far from these assumptions. It is evident that the relationship between Ko and

elastic parameter, ν of Eq. 2.5 is obsolescent for predicting in-situ horizontal stress.

2.1.2 Jaky’s Formula

Several scholars attempted to set up a theoretical relationship between the strength properties of a soil and Ko. The empirical relationship to estimate Ko of

coarse-grained soil is discussed in the following section.

Mesri and Hayat (1993) reported that Jaky (1944) established a relationship between Ko and maximum effective angle of internal friction φ by analyzing a

talus of granular soil freestanding at the angle of repose. Jaky (1944) supposed that the angle of repose is analogous to the angle of internal friction φ. This is reasonable for sediment, normally consolidated material. Jaky (1944) reasoned that the sand cone OAD in Fig. 2.3 is in a state of equilibrium and its surface and inner points are motionless. The horizontal pressure acting on the vertical plane OC is the earth pressure at-rest. Slide planes exist in the inclined sand mass. However, as OC is a line of symmetry, shear stresses can not develop on it. Hence OC is a principal stress trajectory. Based on the equations of equilibrium, Jaky expressed the coefficient of earth pressure at-rest Ko with the

angle of internal friction, φ :

φ φ φ sin 1 sin 3 2 1 ) sin 1 ( + + − = o K (2.6)

In 1948, Jaky presented a modified simple expression given by Eq. 2.7. Ko =1−sinφ (2.7)

Mayne and Kulhawy (1982) reported that, the approximate theoretical relationship for Ko for normally consolidated soils supposed by Jaky appears

valid for cohesionless soils. Using Jaky’s equation to estimate the in-situ lateral earth pressure is reliable for most engineering purposes.

2.2 Effects of Soil Compaction on Earth Pressure

Compaction a soil can produce a stiff, settlement-free and less permeable mass. It is usually accomplished by mechanical means that cause the density of soil to increase. At the same time the air voids are reduced. It has been realized that the compaction of the backfill material has an important effect on the earth pressure.

Several theories and analytical methods have been proposed to analyze the residual lateral earth pressures induced by soil compaction. Most of these theories introduce the idea that compaction represents a form of overconsolidation, where stresses resulting from a temporary or transient loading condition are retained following removal of this load.

2.2.1 Study of Duncan and Seed

Duncan and Seed (1986) presented an analytical procedure for evaluation of peak and residual compaction-induced stresses either in the free field or adjacent to vertical, non-deflecting soil-structure interfaces. This procedure employs a hysteretic Ko

-loading model shown in Fig. 2.4. The model is adapted to incremental analytical methods for the evaluation of peak and residual earth pressures resulting from the placement and compaction of soil. When the surcharge is applied on the soil surface, it will increase the vertical stress and the horizontal stress. In Fig. 2.4, as the virgin loading is applied on the soil, both σv and σh increase along the Ko -line (Ko = 1-sinφ).

virgin unloading path. As virgin reloading was applied again, the increment of earth pressure is less than that induced by the first virgin loading.

The hysteretic model may be applied to the analysis of compaction as represented by a transient, moving surficial load of finite lateral extent by directly modeling loading due to increased overburden as an increase in vertical effective stress (Δσ’v). To model

compaction loading in terms of the peak virgin, compaction-induced horizontal stress increase (Δσ’h,vc,p) is defined as the horizontal effective stress which would be induced

by the most critical positioning of the compactor. The Δσ’h,vc,p could be evaluated by

the simple elastic analysis if the soil had been previous uncompacted (if the soil had no “lock-in” residual stresses due to previous compaction). While the hysteretic model is applied to the analysis of compaction loading cycle, the Δσ’h,vc,p should be transformed

to an equivalent peak vertical load increment (Δσ’v,e,p) calculated as

o p vc h p e v K ' , , ' , , σ σ = Δ Δ (2.8) It is important to note the peak compaction loading must be based on directly calculated lateral stress increase rather than directly calculated peak vertical stress increase multiplied by Ko, Ka or some other coefficient. Seed and Duncan (1983)

concluded that either in the free field, or at or near vertical, nondeflecting soil/structure interfaces, Δσ’h,vc,p resulting from surficial compaction loading can be calculated

directly by simple elastic analysis. The parameter of Poisson’s ratio, ν for surficial compaction loading may be chosen according to the empirically derived relationship

(0.5 ) 2 1 o o ν ν ν = + − (2.9) where o o o K K + = 1 ν

Ko = 1-sinφ

Seed and Duncan (1983) also brought up a simple hand calculation procedure which results in good agreement with the incremental procedure described above. In Fig. 2.5, it is apparent the simple hand solution has a good agreement with the incremental procedure.

2.2.2 Study of Chen

Chen (2002) reported some experiments in non-yielding retaining wall at National Chiao Tung University to investigate influence of earth pressure due to vibratory compaction. Air-dry Ottawa sand was used as backfill material. Vertical and horizontal stresses in the soil mass were measured in loose sand and compacted sand. Based on his test results, Chen (2002) proposed the following conclusions: (1) after compaction, the lateral stress measured near the top of backfill is almost identical to the passive earth pressure estimated with Rankine theory. The compaction-influenced zone rises with rising compaction surface. Below the compaction-influenced zone, the horizontal stresses converge to the earth pressure at-rest, as indicated in Fig. 2.6; (2) when total (static + dynamic) loading due to the vibratory compacting equipment exceeds the bearing capacity of foundation soils, the mechanism of vibratory compaction on soil can be described with the bearing capacity failure of foundation soils; (3) the vibratory compaction on top of the backfill transmits elastic waves through soil elements continuously. For soils below the compaction-influenced zone, soil particles are vibrated. The passive state of stress among particles is disturbed. The horizontal stresses among soil particles readjust under the application of a uniform overburden pressure and constrained lateral deformation, and eventually converge to the at-rest state of stress.

Chen’s test results were compared with the design recommendations proposed by NAVFAC DM-7.2 (1982), Duncan and Seed (1986), Peck and Mesri (1987), and Duncan et al. (1991) as shown in Fig. 2.7. Parameter values used in the stress calculation including the unit weight γ, relative Dr, internal friction angle φ, wall

friction angle δ, and cyclic compaction stress σcyc are shown in Fig. 2.7. The horizontal

pressure distribution suggested by the Navy Design Manual DM-7.2 was based on the analytical method proposed by Ingold (1979). The pressure distribution calculated with the method proposed by Duncan et al. (1991) was obtained from the design chart for vibratory plates with a cyclic compaction stress q = 34.9 kN/m2 (5 psi).

In Fig. 2.7, Chen’s test data are in good agreement with the proposed design methods. The horizontal stresses in the uppermost compacted lift are equal to or slightly less than the passive Rankine pressure. However, at a lower depth, the Chen’s test data are apparently lower than the calculated horizontal stresses. It is important that the application of Chen’s test findings are limited to estimating the horizontal stresses acting on a non-yielding wall induced by a small size vibratory hand tamper.

2.3 Elastic Solutions for a Strip Surface Loading

A simple equation to calculate the lateral pressure increase due to a uniform vertical strip surcharge was mentioned by Jurgenson (1934). Fig. 2.8 shows the case where a uniform vertical load of q per unit area is acting on a flexible infinite strip on the surface of a semi-infinite elastic mass. To obtain the stresses at a point P(x,z), consider an elementary strip of width ds loaded at a distance s from the centerline of the load. The load per unit length of this elementary strip is q.ds, and the strip loading can be approximated as a line load.

[

α sinαcos(α 2δ)

π

σ_x = q − +

]

(2.13)

The expression for σz given can be presented in a simplified form　

[

α sinαcos(α 2δ)

π

σ_z = q + +

]

( 2.14)

where α and δ are the angle indicated in Fig. 2.8.

The contours of σx/ q andσz/ q due to the surface strip loading are shown in Fig.

2.9. The units of X and Y axes are the distance from center of the soil bin dividing by the half width of foundation (B/2).

2.4 Ultimate Bearing Capacity of Shallow Footing

Terzaghi (1943) suggested that the failure surface in soil at an ultimate load for a continuous strip footing was similar to Fig. 2.10. The effect of soils above the bottom of the footing may be assumed to be replaced by an equivalent surcharge, q = γDf (where γ is the unit weight of soil). The failure zone under

the footing can be separated into three parts: (1) the triangular zone ACD immediately under the footing; (2) the radial shear zones ADF and CDE, with the curves DE and DF being arcs of a logarithmic spiral; and (3) two triangular Rankine passive zones AFH and CEG. Using equilibrium analysis, Terzaghi expressed the ultimate bearing capacity as:

q_u c N_c qN_q γBN_γ

2 1 ' + +

= (2.15) where c’=cohesion of soil

γ = unit weight of soil q = γDf

Nc, Nq, Nγ = bearing capacity factors that are nondimensional and are

functions only of the soil friction angle φ’

Table. 2.1 shows the variation of Nc, Nq, and Nγ with the soil friction φ’

(after Kumbhojkar, 1993).

For footings that exhibit the local shear failure mode for strip footing in soils, Terzaghi (1943) suggested the following modified as:

γ γBN qN N c q_{u c q} 2 1 ' 3 2 _{+ +} = (2.16) , , and , the modified bearing capacity factors, can be calculated by using the bearing capacity factor equations (for Nc, Nq, and Nγ, respectively) by

replacing φ by ' c N Nq' ' γ N ) tan 3 2 ( tan ' φ = −1 _{φ .}

Vesic (1963) conducted several laboratory load-bearing tests on circular and rectangular plates supported by soil at various relative densities of compaction. On the basis of experimental results, Vesic (1973) defined the three types of the bearing capacity failure mode including general shear failure, local shear failure and punching shear failure. Fig. 2.11 indicates the typical load-settlement relationship for these failure modes. The failure modes are dependent on the relative density of soil and the depth of embedment Df as shown in Fig. 2.12. In Fig. 2.13, Vesic (1973) suggested that

as the loaded soil fails, the composite failure surface would develop along bcde and acd1e1. The stresses of sand in zone I belong to active state. Zone II is known as the

zone of radial shear, and zone III is identical to the passive Rankine zone.

2.5 Stresses in Soil during Penetration Test

shown in Fig. 2.14. The ultimate load-carry capacity Qu of a pile is given by the

equation:

Qu =Qp +Qs (2.17)

where Qp = load-carrying capacity of the pile point

Qs = frictional resistance (skin friction) derived from the soil-pile

interface

The point bearing capacity (Qp) of a pile in sand generally increases with the

depth of pile in the bearing stratum. Meyerhof (1976) suggested the Qp in sand

by the equation as:

_' * (2.18) q p p p p A q A q N Q = =

where Ap = area of pile tip

qp = unit point resistance

' = effective vertical stress at the level of the pile tip q

* = the bearing capacity factors

q N

In Fig. 2.15, Meyerhof (1976) suggested the relationship between and soil friction angle φ’.

*

q N

Yang (2006) proposed an analytical method to estimate the influence zone surrounding the tip of a loaded pile in sand. In the framework of the cavity expansion theory and a confined local failure mechanism, explicit expressions are derived. The sizes of the upward and downward influence zone are properly linked with the angle of shearing resistance, the stiffness, the volumetric strain, and the mean effective stress of the sand at the pile tip. Based on a series of parametric analyses, the mean range of the influence zone is suggested. Fig. 2.16 shows that the confined local failure mechanism

provides a fairly good prediction for the end-bearing capacity of displacement piles in sand. For piles in clean sand, the influence zone above the pile tip is between 1.5D and 2.5D and the zone below the tip ranges from 3.5 to 5.5D as shown in Fig. 2.17, where D is pile diameter.

2.6 Density Change due to Compaction

In the field, the factors affecting compaction include the thickness of lift, the intensity of pressure applied by the compacting equipment, and the area over which the pressure is applied. During compaction, the dry unit weight of soil is affected by the number of roller passes. Johnson and Sallberg (1960) used 84.5 kN (19kip) three-wheel roller to compact a silty clay in 229 mm (9 in) loose layers at different moisture contents. The test results shows the growth curve that indicated the dry unit weight of a soil at a given moisture content increases to a certain point with the number of roller passes in Fig. 2.18.

In Fig. 2.19, D’Appolonia et.al. (1969) reported the distribution of the unit weight of soil with depth for a poorly graded dune sand, for which compaction was achieved by a vibratory drum roller. Vibration was produced by mounting an eccentric weight on a single rotating shaft within the drum cylinder. The weight of the roller used for this compaction was 55.6 kN (12.5 kip), and the drum diameter was 1.19 m (47 in). The lifts were kept at 2.44m (8ft). The dry unit weight of compacted soil increased with the number of roller passes. However, the rate of increase in unit weight gradually decreases after about 15 passes. The dry unit weight and hence the relative density Dr

reached maximum values at a depth of about 0.5 m (1.5 ft) and gradually decreased at lesser depths. This decrease occurs because of the lack of confining pressure toward the surface.

Chapter 3

Experimental Apparatus

To investigate the effects of vibratory compaction on the vertical and horizontal stresses in a cohesionless soil mass, the instrumented non-yielding model retaining wall facility at National Chiao Tung University (NCTU) was used. This chapter introduces the NCTU non-yielding retaining wall facilities and the vibratory compactor used to densify the loose backfill. The NCTU non-yielding retaining wall facilities consist of three components: (1) the soil bin, (2) soil pressure transducers, and (3) the data acquisition system (Chen and Fang, 2002). The details of the foregoing apparatuses are described in the following sections.

3.1 Soil Bin

To simulate a plan strain condition for model test, the soil bin is designed to minimize the lateral deflection of sidewalls. In Fig. 3.1, the soil bin was fabricated of steel plates with inside dimensions of 1500 mm × 1500 mm × 1600 mm. The soil bin was divided into two parts to discuss in the following section: (1) model wall, and (2) sidewall and end wall.

The model wall shown in Fig. 3.1 is 1500 mm-wide and 1600 mm-high, and 45 mm-thick. To achieve at-rest condition, the wall material should be nearly rigid. It is hoped that the deformation of the wall could be neglected with the application of earth pressure. As indicated in Fig. 3.1, twenty-four 20 mm-thick steel columns were welded

to the four sidewalls to reduce any lateral deformation during loading. In addition, twelve C-shaped steel beams were also welded horizontally around the box to further increase the stiffness of the box.

Assuming a 1.5 m-thick cohesionless backfill with a unit weight γ = 17.1 kN/m3

, and an internal friction angle φ = 41o

was pluviated into the box. A 45 mm-thick solid steel plate with a Young’s modulus of 210 GPa was chosen as the wall material. The estimated deflection of the model wall would be only 1.22 × 10-3 mm. Therefore, it can be concluded that the lateral movement of the model wall is negligible and an at-rest condition can be achieved.

The end-wall and sidewalls of the soil bin were made of 35 mm-thick steel plates. Outside the steel walls, vertical steel columns and horizontal steel beams were welded to increase the stiffness of the end-wall and sidewalls. If the soil bin was filled with dense sand, the estimated maximum deflection of the sidewall would be 1.86 × 10-3 mm. From a practical point of view, the deflection of the four walls around the soil bin can be neglected.

3.2 Soil Pressure Transducer

To investigate the distribution of stress in the backfill, an series of soil pressure transducers (Kyowa BE-2KCM17, capacity = 98.1 kN/m2) as shown in Fig. 3.2 was used. The transducers were buried in the soil mass to measure the variation of vertical and horizontal earth pressure during the filling and compaction process. The five radial extensions projected from the transducer are used to prevent possible rotation of the transducer due to filling and compaction. The effective diameter of the transducer is 22 mm and its thickness is 6 mm.

3.3 Data Acquisition System

A data acquisition system was used to collect and store the considerable amount of data generated during the tests. In the Fig. 3.3, the data acquisition system is composed of the following four parts: (1) dynamic strain amplifiers (Kyowa: DPM601A and DPM711B); (2) AD/DA card (NI BNC-2090); and (3) Personal Computer. The analog signals from the sensors were filtered and amplified by the dynamic strain amplifiers. Then, the analog experimental data were digitized by an A/D-D/A card. The digital signals were then transmitted to the personal computer for storage and analysis.

3.4 Vibratory Compactor

To simulate compaction of backfill in the field, the vibratory compactor shown in Fig. 3.4 and Fig.3.5 was made by attaching an eccentric motor (Mikasa Sangyo, KJ75-2P) to a 0.225 m × 0.225 m steel plate. Fig. 3.6 shows that the eccentric force can be controlled by adjusting the number of eccentric steel plates attached to the rotating shaft of motor. For this study, a total of sixteen eccentric plates (8+8) were used. The detailed information regarding the eccentric motor is listed in Table 3.1. Fig. 3.7 shows the dynamic vertical force Fd measured with a load cell placed under the

base plate of the vibratory compactor with 16 eccentric plate, the corresponding Fd =

1.648 kN. With the static mass of the compactor (w = mg = 0.119 kN), the cyclic vertical force (static + dynamic) was 1.767 kN. The measured frequency of vibration was 44 Hz. Assuming the distribution of contact pressure between the base plate (0.225 m × 0.225 m )and soil is uniform, the cyclic normal stress σcyc applied on the surface of

soil would be 34.9 kN/m2 (5.06 psi). It should be mentioned that the distribution of contact pressure between the foundation and soil varies with the stiffness of the footing. If the footing is perfectly rigid, the static contact pressure on the footing increases from zero at the edge to a maximum at the center.

Chapter 4

Backfill Characteristics

The characteristics of the backfill and the method to reduce the wall friction are introduced in this chapter.

4.1 Backfill Properties

Air-dry Ottawa silica sand (ASTM C-778) was used as the backfill material in all experiments. Physical properties of the soil are summarized in Table 4.1. Grain-size distribution of the backfill is shown in Fig. 4.1. The major reasons to select Ottawa sand as the backfill material are listed below.

1. Its round shape, which avoids effect of angularity of soil grains.

2. Its uniform distribution of grain size (coefficient of uniformity Cu = 1.78), which

avoids the effects due to soil gradation.

3. High rigidity of solid grains, which reduces possible disintegration of soil particles under loading.

4. Its high permeability, which allows fast drainage and therefore reduces water pressure behind the wall.

To establish the relationship between unit weight of backfill γ and its internal friction angle φ, direct shear tests have been conducted. The shear box used has a square (60 mm ×60 mm) cross-section, and its arrangement is shown in Fig. 4.2. Before shearing, Ottawa sand was air-pluviated into the shear box and then compacted to the desired density. Details of the technique to control soil density are discussed in section 5.1.

Chang (2000) established the relationship between the internal friction angle φ and unit weight γ of Ottawa sand as shown in Fig. 4.3. It is obvious from the figure that soil strength increases with increasing soil density. For the air-pluviated backfill, the empirical relationship between soil unit weight γ and φ angle can be formulated as follows

φ = 6.43γ- 68.99 (4.1) where

φ = angle of internal friction of soil (degree)

γ = unit weight of soil (kN/m3)

Eq. (4.1) is applicable for γ= 15.45 ~ 17.4 kN/m3 only.

4.2 Reduction of Wall Friction

To constitute a plane strain condition for model wall tests, the shear stress between the backfill and wall should be minimized to nearly frictionless. To reduce the friction between wall and backfill, a lubrication layer fabricated with plastic sheets was furnished for all experiments. Two types of plastic sheeting, one thick and two thin plastic sheets, were adopted to reduce the interface friction. All plastic sheets were hung vertically on four walls before the backfill was deposited as shown in Fig. 4.4.

Multiple layers of thin plastic sheets (without any lubricant) were used by McElroy (1997) for shaking table tests of geosynthetic reinforced soil (GRS) slopes. Burgess (1999) used three thin plastic sheets to reduce side wall friction in full-scale GRS wall tests. The wall friction angle was approximately 15° as determined by the shear box tests. In this study, two thin (0.009 mm-thick) and one thick (0.152 mm-thick) plastic sheet were adopted for the earth pressure experiments. The friction angle δw developed

between the plastic sheets and steel sidewall could be determined by the sliding block test. A schematic diagram and a photograph of the sliding block test proposed by Fang

et al. (2004) are illustrated in Fig. 4.5 and Fig. 4.6. The wall friction angle δw for the

sliding block test was determined using the basic principles of physics. Fig. 4.7 shows the variation of friction angle δw as a function of the normal stress σn for the plastic

sheet method (1 thick + 2 thin sheeting) used in this study. The measured friction angle with this method is about 7.5°. It is clear in Fig.4.7 that the interface friction angle δw is

nearly independent of the applied normal stress σn. This constancy is an important

advantage in establishing the input soil properties for analytical models that might be used to analyze the experimental results. For all experiments in this paper, the lubrication layer wall applied on four walls as indicated in Fig. 4.4. The plastic sheets not only can help to reduce the friction angle between the wall and the backfill. The plastic sheets can also help to reduce the reflection of elastic waves transmitted to the soil-wall boundaries during compaction.

Chapter 5

Test Results for Loose Sand

This chapter introduces the distribution of soil density, horizontal and vertical stresses in the loose sand backfill before compaction. The sections discussed included: (1) the method to prepare the loose backfill; (2) the method to control soil density; (3) the measured distribution of soil density in loose sand; and (4) the distribution of earth pressure in loose sand.

5.1 Testing Procedure

The testing procedures adopted for this study for the measurement of relative density and stresses in the loose backfill are briefly described below.

For the measurement of the relative density:

(1) Sand pluviated into the soil bin by controlling the drop height of soil and slot opening of the sand hopper.

(2) Density cups placed at the different elevations and locations.

(3) After the soil had been filled up to 1.5 m from the bottom of the soil bin, soil density cups were dug out from the soil mass carefully.

(4) The weight of the cup and soil was measured and recorded. For the measurement of the earth pressures:

(1) Sand pluviated into the soil bin by controlling the drop height of soil and slot opening of the sand hopper.

(2) Placed the SPTs at the desired locations.

(3) When the backfill was filled up to 1.5 m, the earth pressures were recorded and stored.

5.2 Distribution of Soil Density

5.2.1 Air-Pluviation of Ottawa Sand

To achieve a uniform soil density in the backfill, Ottawa sand was deposited by air-pluviation method into the soil bin. The air-pluviation method had been widely used for a long period of time to reconstitute laboratory sand specimens. Rad and Tumay (1987) reported that pluviation is the method that provides reasonably homogeneous specimens with desired relative density. Lo Presti et al. (1992) reported that the pluviation method could be performed for greater specimens in less time.

Das (1994) suggested that relative densities of 15~50%, and 70~85% are defined as loose and dense condition, respectively. To achieve loose backfill (Dr = 32%), Chen

(2002) adopted the drop height of 1.0 m and hopper slot opening of 15 mm. According to the test results, Ho (1999) established the relationship among slot opening, drop height, and density as shown in Fig. 5.1. As a result, the drop height of 1.0 m and hopper slot-opening of 15 mm are selected to achieve the loose backfill for testing in this study. Fig. 5.2 shows the method to control the drop height = 1.0 m. In the picture, a 1.0 m-long rope was hung from the hopper to the surface of the soil to control the drop distance of soil. In Fig. 5.3, the soil hopper that lets the sand pass through a calibrated slot opening (15 mm) at the lower end was used for the spreading of sand. The raining of the Ottawa sand into soil bin is shown in Fig. 5.4.

5.2.2 Uniformity of Soil Density

To observe the distribution of soil density in the soil bin, the soil density cups were made. The soil density control cup made of acrylic is illustrated in Fig. 5.5 and Fig. 5.6. During the preparation of soil specimen, density cups were buried in the soil mass at different elevations and different locations in the backfill as shown in Fig. 5.7 and Fig. 5.8. After the soil had been filled up to 1.5 m from the bottom of the soil bin, soil density cups were dug out from the soil mass carefully. Fig. 5.9(a) shows the density cup was placed in the soil bin and Fig. 5.9(b) shows the weight of the cup and soil was measured with an electrical scale. The distribution of soil density with depth for loose sand is shown in Fig. 5.10. The mean relative density is Dr = 34.1 % with the standard

deviation of 2.4%. The soil density distribution was reported by Chen (2002). The test results are in fairly good agreement with data. The backfill achieved with the air-pluviation method was loose, Dr = 15%~50% as suggested by Das (1994).

5.3 Distribution of Earth Pressure

For comparison purposes, at the beginning of this study, experiments were conducted to investigate the stresses in an uncompacted backfill. Fig. 5.11 shows the location of soil pressure transducers to measure the distribution vertical earth pressure

σv with depth. The method to confirm the location and depth of the SPT in the soil

mass is shown in Fig. 5.12. Fig. 5.13 shows the photograph of SPT used to measure vertical stress in the soil mass. After the backfill had been filled up to 1.5 m thick, the vertical earth pressure σv measured in the soil mass was illustrated in Fig. 5.14.

Obviously, the vertical pressure increased with increasing depth and the test data were in good agreement with the equation σv = γz, where γ is the unit weight of the backfill.

earth pressure σh were shown in Fig. 5.15. Fig. 5.16 shows the photograph of SPT used

to measure horizontal stress in the soil mass. The distribution of horizontal earth pressure σh with depth was illustrated in Fig. 5.17. In the figure, the earth pressure

profile induced by the 1500 mm-thick loose backfill was approximately linear and was in good agreement with the Jaky’s equation. Mayne and Kulhawy (1982), Mesri and Hayat (1993) reported the Jaky’s equation is suitable for backfill in its loosest state. From a practical point of view, it may be concluded that for a loose backfill, the vertical and horizontal earth pressure in the soil mass can be properly estimated with the equation σv = and Jaky’s equation, respectively. γz

Chapter 6

Surface Settlement and Density Change

due to Compaction

This chapter introduces the pilot tests to determine the program of compaction tests. The surface settlement and change of soil density due to vibratory compaction are discussed in the following sections.

6.1 Testing Procedure

The testing procedures adopted for the measurement of the surface settlement and change of the relative density due to compaction are briefly described below.

(1) Sand pluviated into the soil bin by controlling the drop height of soil and slot opening of the sand hopper.

(2) Density cups placed at the different elevations and locations.

(3) After the soil had been filled up to 1.5 m from the bottom of the soil bin, level the surface of the backfill.

(4) After the first pass of the vibratory compactor, remove the compactor. (5) Measured the surface settlement on the XZ and YZ – plane..

(6) Soil density cups were dug out from the soil mass carefully. Weight of the cup and soil was measured and recorded.

compactor to 2, 4, and 8 passes.

6.2 Pilot Tests

To investigate the effects of compaction on the surface of a sandy backfill with a vibratory compactor, a series of pilot tests were conducted at the beginning. The results of the pilot tests can help a researcher to set up the testing program.

The testing procedure of strip compaction was indicated in Fig. 6.1. The vibratory compactor was pulled over the compaction lane from the left sidewall to the right sidewall for the first pass as shown in Fig. 6.2. Then the vibratory compactor was turned around 180 degrees to compact the backfill at the second pass from the right to the left sidewall. As the end, the backfill below the compaction lane had been densified with eight passes of the vibratory compactor. Each pass was about 1.5 m-long and lasted a duration of 70 seconds.

Under a plane strain condition, there was zero lateral strain in the longitudinal direction, and the shear stress on the intermediate principal plane was by definition equal to zero. To simulate a plane strain condition in the NCTU non-yielding retaining wall facilities, the frictional resistance between the soil and the sidewalls should be minimized as much as possible. For all experiments in this paper, the lubrication layers were applied on both sidewalls as indicated in Fig. 6.3. As a result, in Fig. 6.3, the XZ – plane became the intermediate principal plane as shown in Fig. 6.3. For all tests in this study, the effects of compaction were observed on the XZ – plane. To reduce the friction on the model wall and the end wall, the lubrication layers were also hung on them. The plastic sheets not only can help to reduce the friction between the wall and the backfill. The plastic sheets can also help to reduce the reflection of elastic waves transmitted to the soil-wall boundaries during compaction.

compaction, a settlement trough was induced apparently on the surface of the backfill. The method to measure surface settlement on the XZ and YZ – planes was shown in Fig. 6.5(a) and (b), respectively. To determine the amount of compaction for testing, the surface settlement of the compaction lane was investigated in pilot tests.

Because of the sidewall friction, the surface settlement measured near the sidewall was less than the average settlement indicated in Fig. 6.6. Based on the test results, sidewall effects were limited to the regions about 300 mm from the sidewalls.

Fig. 6.7 shows the compaction-induced surface settlement increased with the increasing number of passes of the compactor. Based on the test results, a hyperbolic model relationship between surface settlement S and number of passes N was established as shown in Fig. 6.8. The surface settlement S was the average settlement of the seven points (point B to H) shown in Fig. 6.7. In Fig. 6.8, the data points obtained from tests 0701 and 0703 indicated that the test results were quite reproducible. Based on the test results, the hyperbolic model was established to estimate the surface settlement S as a function of No. of passes of the compactor.

The relationship can be expressed as: (6.1) N N S 0241 . 0 0178 . 0 + =

where S = surface settlement in mm

N = number of passes of the compactor

The asymptote of the hyperbolic model was Smax = 41.5 mm. Table 6.1(a) shows that

the Smax was divided into five equal parts and their corresponding number of pass was

obtained. In the field, at least 1 – pass of compactor would be carried out to compact the loose backfill. In Table 6.1(a), 0.6Smax is related to 1.11 pass of the compactor.

applications. Therefore, 1 – pass of the compactor would be the minimal. From a practical point of view, while the numbers of passes of the compactor were doubled, the compaction-induced effects would be concerned by engineers. Table 6.1(b) shows the surface settlement corresponding to 1, 2, 4, and 8 passes. The effects of compaction associated with 1, 2, 4 and 8 passes of the compactor were discussed in this study.

6.3 Surface Settlement

Before compaction, the height of backfill was 1.5m and the surface of the backfill was horizontal. After the first pass of the compactor, Fig. 6.9 shows the average settlement of the compaction lane was approximately 18.75 mm. The surface settlement was about 8.3% of the width of the vibratory compactor (S/B = 8.3%). Heaving of sand at the both edges of the compactor lane was observed in Fig. 6.9. Fig. 6.10 shows the surface settlement profiles after 1, 2, 4 and 8 passes of the compactor. It is obvious in the figure that the surface settlement increased with the increasing compaction effort.

Fig. 6.11 shows the surface settlement along the compaction lane after the first pass of the compactor. After compactor was pulled horizontally by the operator on the compaction lane, the surface settlement was not uniform. The settlements measured near the sidewall were less than the average surface settlement. Except the regions of sidewall effect, the surface settlement was in fairly agreement with the average settlement of 21.8 mm. Fig. 6.12 shows the surface settlement increased with the increasing number of passes of the compactor.

6.4 Change of Relative Density

sand specimen (Dr=34%) was prepared testing. To investigate the change of relative

density due to compaction, many soil density cups were embedded in the backfill to measure the local densities at different locations. To constitute the grid points for density measurements, the density cups were placed densely as shown in Fig. 6.13 and Fig. 6.14. The technique to control the location of density cup was described in section 5.2.2. Fig. 6.15 shows the locations of soil density cups placed at the same elevation. After the desired number of compactor passages, the soil density cups were dug out from the soil mass and measured carefully.

The relative density of sand at the grid points after the first passage of the compactor is indicated in Fig. 6.16. By using the Golden Software Surfer 8, the values of Dr at

grid points were converted into a Grapher Grid file. The Grapher Grid file included the test data of relative density. Opening the file with the program Golden Software Grapher 7, the contours of relative density after the first passage of the compactor can be obtained as illustrated in Fig 6.17. The detail operation of the softwares Surfer 8 and Grapher 7 are illustrated in Appendix B. The value of Dr of sand at the grid points after

2, 4, and 8 passes of compactor are listed in Appendix C1.

Fig. 6.17 shows the contours of relative density in soil mass after the first passage of the compactor. Before compaction, the backfill has a uniform relative density of 34%. The soil density became quite dense (Dr=64%) under the vibratory compactor, and the

soil density decreased gradually with the distance from the compactor. From the relative density of 34% to 65%, the effects of vibratory compaction on soil density were quite obvious right below the compactor. As the number of passes increased to 2, 4, and 8 passes, more compaction energy was transmitted to the soil. In Fig. 6.18, Fig. 6.19, and Fig. 6.20, the region of dense sand (Dr=60%~80%) expanded with the

increasing number of the compactor passes. The maximum relative density below the compactor was 68%, 72%, and 75%, respectively. The relative density 64%, 68%, 72%

and 75% are correspond to the dry unit weight 16.3 kN/m3, 16.4 kN/m3, 16.5 kN/m3 and 16.6 kN/m3, respectively.

Fig. 6.21 shows the relationship between dry unit weight and number of passes of the compactor in this study. Johnson and Sallberg (1960) used 84.5 kN (19kip) three-wheel roller to compact a silty clay in 229 mm (9 in) loose layers at different moisture contents. The tests results in this study were in fairly good agreement with the tests result in the field reported by Johnson et al. (1960).

Fig. 6.22 shows the comparison between the tests results obtained from this study and the test results obtained from the field reported by D’Appolonia (1969). The obvious difference is the depth of the maximum dry unit weight. D’Appolonia et al. (1969) proposed that the less value of γ near the surface was relative to the lack of confining pressure. However, based on the test results in this study, the lack condition didn’t appear. The dry unit weight decreased gradually with the distance from the compactor. The vibratory compactor put the vertical energy into the sand and the vibratory compactor compress sand coercively. In Table 6.2, it shows the difference between the laboratory tests in NCTU and the field tests from D’Appolonia et al. (1969)

Chapter 7

Change of Vertical Stresses due to

Compaction

This chapter reports the variation of vertical earth pressure Δσv in a

cohesionless soil mass due to compaction. The following sections include the distribution of vertical stress under the compaction lane and the vertical stress change Δσv in the soil mass due to the compaction.

7.1 Testing Procedure

The testing procedures adopted for the measurement of change of the stresses after compaction are briefly described below.

(1) Sand pluviated into the soil bin by controlling the drop height of soil and slot opening of the sand hopper.

(2) SPTs placed in the soil bin at the different elevations and locations. (3) After the soil had been filled up to 1.5 m from the bottom of the soil bin,

level the surface of the backfill.

(4) After the first pass of the compactor, remove the vibratory compactor. (5) The test data were recorded and stored.

(6) Repeated steps (1) through (5), change the number of passes of the compactor to 2, 4 and 8 passes.