NUMERICAL ANALYSIS OF ANCHORED CONCRETE PILE WALL:

A CASE STUDY

A MASTERS THESIS

in

Civil Engineering

Atlm University

by

KIVAN SNCL

SEPTEMBER 2006

NUMERICAL ANALYSIS OF ANCHORED CONCRETE PILE WALL:

A CASE STUDY

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

ATILIM UNIVERSITY

BY

KIVAN SNCL

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

THE DEPARTMENT OF CIVIL ENGINEERING

SEPTEMBER 2006

Approval of the Graduate School of Natural and Applied Sciences

_____________________

Prof. Dr. Seluk Soyupak

Director

I certify that this thesis satisfies all the requirements as a thesis for the degree of Master of Science.

_____________________

Prof. Dr. Erol Ulu

Head of Department

This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Science.

_____________________

Dr. Y. Dursun Sar

Supervisor

Examining Committee Members

Dr. B. Sadk Bakr _____________________

Dr. M. Serdar Nalakan _____________________

Dr. Y. Dursun Sar _____________________

iii

ABSTRACT

NUMERICAL ANALYSIS OF ANCHORED CONCRETE PILE WALL:

A CASE STUDY

Sincil, Kvan

M.S., Civil Engineering Department

Supervisor: Dr. Y. Dursun Sar

September 2006, 109 pages

This thesis reviews the numerical analysis of anchored concrete pile walls

and comparison of field measurements and numerical values in terms of the stability

of the structure and soil. The deep excavation supported by anchored pile walls,

namely Gazino Station excavation, Ulus-Keiren Metro project. After an extensive

literature review on anchors, anchored structures and deep excavations, the

excavation of Gazino Station is described and modelled and analyzed by FEM

program Plaxis. Special emphasis was given to selection of soil parameters for

numerical analysis, since these parameters play a key role in the success of the

analysis.

The numerical analysis results tend to overestimate the measured lateral

wall deflections above the excavation level, the numerical analysis proves to be quite

satisfactory for considering the preliminary analysis of the concrete pile wall with

and without anchorage. The results can be accurate if more extensive and attentive

field and laboratory will be carried out together with numerical modeling.

Keywords: Numerical Analysis, Anchor, Pile Wall, Lateral Wall Deflection, Lateral

Earth Pressure, Settlement

iv

Z

ANKRAJLI KAZIK DUVARLARIN SAYISAL ZMLENMES:

DURUM ANALZ

Sincil, Kvan

Yksek Lisans, naat Mhendislii Blm

Tez Yneticisi: Dr. Y. Dursun Sar

Eyll 2006, 109 sayfa

Bu tez, ankrajl kazk duvarlarn saysal analizi ile yerinde lmler ile

saysal verilerin, st yap ve zemin stabilitesi asndan karlatrlmasn

iermektedir. Ulus-Keiren Metro projesi almalar kapsamnda, Gazino stasyonu

derin kazs ankrajl kazk duvarlar ile desteklenmitir. Ankrajlar, ankrajl yaplar ve

derin kazlar ile ilgili detayl bir literatr taramasnn ardndan, bahsedilen Gazino

stasyonu kazs, Plaxis isimli bir sonlu elemanlar program kullanlarak modellenmi

ve analiz edilmitir. Saysal analizde kullanlacak olan zemin parametreleri yntemin

baarsnda anahtar rol oynadndan, bu parametrelerin seimine nem verilmitir.

Saysal analiz sonular kaz seviyesinin stndeki yatay duvar

deplasmanlarn llenden daha byk, kaz seviyesinin altndaki deplasmanlar ise

llenlerden daha kk bulma olaslna ramen, saha lmlerindeki dalm ve

gvenilirlilik dikkate alndnda saysal analiz sonular tatminkar olarak

deerlendirilmitir. Zemin parametrelerinin seiminde yardmc olacak daha detayl

ve zenli saha ve laboratuvar deneyleri saysal modellemelerle desteklendiinde

sonular daha doru ve geerli olacaktr.

Anahtar Kelimeler : Saysal Analiz, Ankraj, Kazk, Kazk Yanal Yerdeitirmesi,

Yanal Zemin Basnc, Oturma

v

ACKNOWLEDGMENTS

I express sincere appreciation to my supervisor Dr. Y. Dursun Sar for his guidance

and insight throughout the research. Thanks also to Murat ilsal and for his

technical assistance.

I would also like to thank to Dr. Sadk Bakr and Dr. M. Serdar Nalakan for their

support, encouragement, insight and guidance during this study.

To my family and friends for their technical assistance, and for their continuous

support and patience during this period.

vi

TABLE OF CONTENTS

ABSTRACT iii

Z iv

ACKNOWLEDEGMENTS v

TABLE OF CONTENTS vi

LIST OF TABLES ix

LIST OF FIGURES xi

LIST OF ABBREVIATIONS xv

CHAPTER

1. INTRODUCTION....................................................................................... 1

1.1.Statement of the Problem................................................................. 3

1.2.Scope and Outline of the Thesis...................................................... 4

2. BACKGROUND INFORMATION AND LITERATURE SURVEY........ 6

2.1.Ground Anchors............................................................................... 6

2.1.1. The Terminology......................................................... 9

2.1.2. Anchors in Sands......... ............................................... 11

2.1.3. Anchors in Stiff Clays................................................. 12

2.2. Fundamentals of Anchored Walls.................................................. 16

2.2.1. Working Principles..................................................... 16

2.3. Anchor Wall Characteristics and Applicability............................... 16

2.3.1. Anchored Sheet Pile Walls..........................................16

2.3.2. Anchored Soldier Pile Walls....................................... 17

2.4. Examples of Anchored Walls......................................................... 18

2.5. Estimation of Lateral Stresses and Deformations of Piles.....................22

2.5.1. General Requirements................................................ 22

2.5.2. Initial Stresses............................................................. 22

2.5.3. Constitutive Equations................................................ 23

2.5.4. Boundary Conditions.................................................. 23

2.6. Lateral Earth Pressure.................................................................... 24

2.7. Active and Passive Earth Pressures................................................ 25

2.8. Coefficient of Earth Pressure......................................................... 26

vii

2.9. The Rankine Theory....................................................................... 27

2.10. The Coulomb Theory . 28

2.11. Earth Pressure Coefficient when At-Rest...................................... 29

2.12. Wall Friction.................................................................................. 30

2.13. Elastic Analysis.............................................................................. 30

2.13.1. Linear Analysis........................................................... 31

2.14. Analysis of Anchored Walls by Finite-Element Methods. 35

2.14.1. Advantages and Limitations....................................... 35

2.14.2. Statement of a Model.................................................. 35

2.14.3. Examples of Finite Element Analysis......................... 36

3. FIELD STUDIES...... .................................................................................. 50

3.1. Geological Studies......................................................................... 51

3.2. Laboratory Studies......................................................................... 52

3.3. Geotechnical Evaluation................................................................ 54

3.3.1. General Geology......................................................... 54

3.3.2. Local Geology............................................................. 55

4. MODELLING OF GAZNO STATION ANCHORED PILE WALL........58

4.1. Layout Plan of Gazino Station....................................................... 58

4.2. Prediction of Soil and Rock Properties of the Model.................... 60

4.3. Geometry Model............................................................................ 73

4.4. Material properties of the Model.................................................. 74

4.5. Mesh Generation of the Model...................................................... 79

4.6. K0 Procedure in Plaxis................................................................... 81

4.7. Calculations.................................................................................... 83

4.7.1. Required Results......................................................... 83

4.7.2. Case Studies................................................................ 83

4.7.3. Model Results.............................................................. 84

4.7.3.1.Pile Wal Laterall Displacements............... 84

4.7.4. Stress Strain Relation.............................................. 86

4.7.4.1.Mohr Coulomb Model............................. 86

4.7.5. Settlements at the surface behind pile wall... 95

4.7.6. Anchor Forces.. 96

4.7.7. Safety Analysis.. 97

viii

4.7.8. Active & Passive Earth Pressures 99

4.7.9. Heave of the Soil in front of the Wall 101

5. RESULTS & DISCUSSION.................. 102

5.1. Lateral Deflection of Pile Wall...................................................... 102

5.2. Stress Strain Behavior................................................................. 102

5.2.1. Non-Anchored Behavior... 102

5.2.2. Anchored Behavior... 103

6. CONCLUSION............................................................................................104

REFERENCES............................................................................................ 107

ix

LIST OF TABLES

TABLE

2.1. Typical Flowchart and Procedure Leading to Finite-Element Analysis..... 36

3.1. Boring Logs and Depths at the Subway Route........................... 51

3.2. Jetting Water Test Results for Gazino Station ... 53

3.3. Soil Mechanics Laboratory Test Results 53

3.4. Weight per Unit Volume () and Uniaxial Compressive Strength (UCS) Test Results..........70 4.1. Consistency of clays and approximate correlation to the standard penetration number, N (Das, 1984)...63

4.2. Typical ground parameters (Carter&Bentley, 1991)... 63

4.3. Soil classification and CPT-SPT correlations (Lunne, Robertson&Powell, 1997)... 66

4.4. Estimation of constrained modulus, M, for clays (Lunne,Robertson%Powell,1997). 67

4.5. Empirical values for , Dr, and unit weight of granular soils based on the SPT at about 6 m depth and normally consolidated (Bowles, 1988)...................... 70 4.6 Relation between N-values, relative density, and angle of friction in sands (Das, 1984)..................................................................................................... 70 4.7. Soil and interface properties.. 75 4.8. Properties of the pile (beam).75

4.9. Properties of the pile cap (beam)........ 75

4.10. Properties of the anchor rod (node-to-node anchors)..78

4.11. Property of the grout body (geotextile).. 78

x

4.12. Stress-Strain Values foe selected points at each case.. 90

4.13. Anchor Forces... 96

4.14.... Msf values for Gazino Station at excavation stages. 98

4.15. Comparison of FEM and Rankine Results 100

xi

LIST OF FIGURES

FIGURES

2.1. Schematic presentation of a ground anchor showing the three main

components (Xanthakos, 1991)................................................................... 7

2.2. Ground anchor use for retaining wall support (Hanna, 1982)Use of ground

anchors for rock slope stabilization (Hanna, 1982)..................................... 7

2.3. Ground Anchors (a) grouted mass formed by pressure injection,

(b) grout cylinder, (c) multiple under-reamed anchor 12

2.4. Use of ground anchors for rock slope stabilization (Hanna, 1982). 14

2.5. Cheurfas Dam in Algeria: a) general plan; b) section through main structure

showing the anchorage.(Xanthakos, 1991).. 15 2.6. Excavation for subway construction in Munich; inclined bored pile wall

strutted at the top and anchored in the lower levels. (Littlejohn, 1982)... 18

2.7. Typical section, deep excavation for building in Stockholm

(Littlejohn, 1982)..... 19

2.8. Protection of excavation from groundwater and uplift by lowering

the water table permanently within the excavation area . 20

2.9. Roche Building; typical cross section for the basement excavation.

(Fenoux, 1971).21

xii

2.10. Active and Passive Zone.............................................................................. 26

2.11. Active Earth Pressure Angular Parameters .. 27

2.12. Lateral pressure distribution for different boundary conditions, wall,

condition of no lateral yield (Morgenstern and Eisenstein, 1970). 32

2.13. Lateral pressure distribution for different boundary conditions, wall of

Fig2.12; pressure diagrams for wall yielding 0.0025H towards active state.

(Morgenstern and Eisenstein, 1970) 34

2.14. Anchored wall in clay; (a) section through wall;

(b) soil data and prestressed diagram. (Tsui, 1973) 37

2.15. Construction sequence; Finite element analysis of the anchored wall of

Fig.2.14 (Tsui, 1973)... 38

2.16. Detail Wall and ground movements predicted by finite-element analysis; tied-

back wall of Fig2.14. (Tsui, 1973)... 39

2.17. Lateral earth pressure predicted by finite-element analysis, and appearance

pressure diagrams, tied-back wall of Fig.2.14. (Tsui, 1973)....... 39

2.18. Lateral earth pressure behind a flexible wall predicted by finite-element

analysis; prestressed tied- back wall. (Clough and Tsui, 1974)... 40

2.19. Plan of site showing layout of anchored wall

(Barla and Mascardi, 1974) 41

2.20. Vertical section along anchored retaining wall showing various stages of

excavation (After Barla and Mascardi, 1974). 42

xiii

2.21. Vertical cross-section through the anchored wall

(After Barla and Mascardi, 1974).... 43

2.22. Anchored diaphragm wall for CPF building, Singapore

(After Littlejohn and MacFarlane, 1974).. 43

2.23. Arrangement of ground anchors to support deep Excavation for Subway

Station in Munich (After Ostermayer, 1974)............................................... 44

2.24. Cross Section... 46

2.25. Measured and predicted behavior of Section A-A walls early stages of

excavation................................................................................................... 47

2.26. Measured and predicted behavior of Section B-B walls early stages of

excavation.................................................................................................... 48

2.27. Shear stress-strain behavior of Hardening Soil (HS) model

(Schanz et al., 1999)........................ 49

3.1 The route of Ulus-Keiren Metro Project.................................................. 50

3.2 Main geological map of Ankara.................................................................. 54

3.3 General Geology of Gazino Station............................................................. 57

4.1 Plan view of Gazino Station........................................................................ 59

4.2 A-A section view of the Gazino Station................................................... 60

4.3 Drilling Log Sheet SPT and Pressuremeter Test Results............................. 62

xiv

4.4 Relationships between angle of shearing resistance and plasticity index

(Carter&Bentley, 1991)..................................................................................64

4.5 Correlation between angle of shearing resistance and plasticity index for

normally consolidated clays (Bowles, 1988)................................................. 65

4.6 The variation of f2 = 1/mv with plasticity index (Stroud, 1974)..................... 65

4.7. Plot of standard penetration resistance vs. angle of friction for granular

soils (Das, 1983).71

4.8. Correlation of standard penetration resistance (NAVFAC DM-7.1)........... 72

4.9. Modeled Section.......................................................................................... 74

4.10. Position of nodes and stress points in a 3-node beam element 76

4.11. Plaxis Model... 79

4.12. FEM Results of Pile Wall lateral deflection for each excavation stage.. 85

4.13. Comparison of Pile Cap lateral displacement with and without anchors 86

4.14. Engineering Stress-Strain Curve 87

4.15. - graph and Mohr-Coulomb Failure Envelope as h increasing... 87

4.16. Plastic points occured after Case 3.............................................................. 88

4.17. Selected Stress-Points for Stress-Strain Values........................................... 89

4.18. Stress-Strain behavior of the clusters (after case 3)..................................... 91

4.19. Plastic Points occured after case 6............................................................... 92

4.20. Comparison of stress-strain relation of fill layer

with and without anchors............................................................................. 93

4.21. Principal effective stresses at the final stage (Case 6) 95

4.22. The subsidence at point J... 95

4.23. Active and Passive thrusts on the wall.. 99

4.24. Rankine and FEM result for active and passive earth pressure distribution.. 100

4.25. Computed Heave in front of the Wall 101

xv

LIST OF ABBREVIATIONS

A Ratio of normal pressure at interface to effective overburden pressure B Bearing capacity factor,

Be Width of Excavation BS British Standards

Ca Shaft Adhesion Cu Shear Strength Cub Undrained shear strength at proximal end of fixed anchor

c Effective cohesive strength(Cohesion)

D Diameter of fixed anchor

d Diameter of borehole

Dr Relative Density DIN Deutsches Institut fr Normung

E Youngs Modulus of Elasticity

EA Normal Stiffness

EI Bending Stifness

xvi

Ed Drained Youngs Modulus of Elasticity

G Elastic Shear Modulus

h Depth of overburden Ic Consistency Index ISRM International Society for Rock Mechanics

Ko Coefficient of lateral pressure at rest

KA Coefficient of lateral pressure at active state KP Coefficient of lateral pressure at passive state L Fixed anchor length LL Liquid Limit l Length of Shaft m Natural Moisture Content

mv Coefficient of volume of compressibility

Nc Bearing capacity factor

OCR Overconsolidation Ratio

PL Plastic Limit PI Plasticitiy Index PH Lateral Earth Pressure Pv Vertical Earth Pressure Qf Ultimate load capacity of anchor Qult Ultimate bond or skin friction at rock/grout interface

xvii

qc Measured cone resisitance

SPT, N Standard penetration number

USC Unitied Soil Classification

W Weight per unit volume

Skin friction coefficient Embankment Level The unit weight of soil

Strain

hmax Maximum lateral wall displacement vmax Maximum vertical wall displacement(Settlement)

' Angle of shearing resistance for effective stress

Internal Friction Angle of the Soil

Mohr-Coulomb Principle Stress of the Soil

f Shear Strength of the Soil

M Skin Friction

Wall Friction

Poisson's Ratio

Angle of dialatancy

1

CHAPTER I

INTRODUCTION

Anchor piles and ground anchors have been used in civil works for a long period of

time and a considerable amount of technical study have been performed and these

studies revealed significant technical knowledge and construction expertise. The

digging of an excavation in the ground causes stress changes in the ground. These

stress changes indicates a variety in the stress distribution particularly around the

excavation. These stress changes caused by the roof and wall pressures due to the

excavation bring out the displacements around the excavation which can cause the

deformations and loosening of soil especially on the surface of the slope, retaining

walls and cliff walls. One of the most important cases is to control these

displacements and deformations with the help of some excavation supports. The

greatest use of prestressed anchors with piles is in the support of both temporary and

permanent excavations.

The main purpose in an excavation is to help rock to support itself. The subject of

piling and ground anchoring can be considered in some details and one of the

important subjects is the displacement of the anchor piles due to the excavation and

by applying anchorage the deformations and soil movements can be kept under

control. Load-deformation behavior of anchor piles and anchors is a straightforward

topic to discuss but also a general look to examine in detail some various factors. The

performance of an anchored structure depends on how the anchor develops load.

Another important case is the load testing of anchors to understand the behavior of

the anchors in different types of rock and soil. In another words load testing is the

accepted method for checking the performance and suitability of anchors. Within the

load testing procedures there are interrelated factors to be considered which are the

anchor materials, the ground itself and stressing equipment. There are also suggested

methods for anchorage testing which have to be considered during the test

procedures. For an anchor to function, it has to be displaced relative to the medium in

2

which it is installed. However, it does not have to be prestressed and there are many

instances where non-prestressed anchors or tension piles are used.

While following a suggested method for anchorage testing there are also certain

parameters to consider which are; fixed anchor length, free anchor length, fixed

anchor diameter, shaft diameter, shaft length, etc. also the parts of the anchor that are

interacted with the ground.

The method of anchor stressing is usually by direct pull from a hydraulic jack. A

torque wrench is occasionally used. Details of stressing and the suggested methods

are clearly defined by ISRM: Rock Anchorage Testing. Some useful guidance is also

given by Littlejohn&Bruce (1976).

Today there are some forms of anchor test in use and useful general guidance on

such tests is given by Ostermayer (1974, 1976) and DIN 4125. There are also many

other guidance on such tests and they all have some recommendations for ground

anchors testing. (DIN, BS, S1A 191, French Code, German Code, Bureau Securitas,

etc.)

There are also some other ground exploration and site investigations are needed

which are required before designing the anchored structure. The general geology of

the site and the topographical features affect the design and construction. Details of

the various soil and rock strata and ground water tables may affect the anchorage

during construction. By means of some laboratory tests on the soil and rock samples,

in-situ tests, soil and rock mechanics investigations will also help to select the proper

anchorage.

Today a large number of stabilization methods are available. Within this study the

behavior of the anchor pile wall is investigated and a FEM analysis is carried out.

The design methods are also considered but no attempt has been made to describe

design methods. The main objective is to investigate the anchored pile wall behaviors

and to expose some reasonable result parameters for the subway station construction

according to a failure criterion (Mohr-Coulomb) and Rankines Active&Passive

earth pressure theory. Geological and design parameters and considerations, the

3

observed anchored pile wall behaviors, anchor prestress results are obtained from the

designer and consultant and the study is performed by constituting a theoretical

model and this model is incorporated into a Windows based program called Plaxis.

Plaxis has been used to investigate pile wall behaviors, stabilization and a FEM

analysis of the study with the design considerations and field observations.

1.1. Statement of the Problem

When the ground is excavated the main matter is the stabilization of the walls around

the opening in case of the stability of the superstructure and the other structures

which are constructed before. (e.g. buildings next to the cliff walls, motorways above

a tunnel, etc.)

There are also some natural effects which can always present instability problems

and have to be considered before the stabilization study. The most important

considerations are quantification of the ground material, particularly joints and

fissures, understanding of the water pressures, weathered or unweathered rock

conditions, landslide and earthquake conditions, etc. A detailed geological study is

also required to figure out these parameters and to make a decision about the

stabilization method of the ground. When the effect of the stabilization is considered

the study about the stabilization method becomes more important to determine the

optimum design, construction and cost studies.

There are many stabilization methods available in civil and mining constructions.

The most used excavation supports are rock bolts and ground anchorages. There are

also many types of bolt and anchor types and during this study some of the anchor

types will be mentioned and as pointed out previously the anchor piles will be

considered and the behavior of the anchored pile and excavation walls will be

investigated in the scope of stabilization. The study will make progress within the

field studies, observations and numerical analysis study results.

4

To determine the parameters of the soil due to the Mohr-Coulomb criteria during

excavation and to study the interaction of these parameters is very important to

estimate the problems which can occur during the excavation like landslide, slope or

failure increase of strain, etc. During the construction of the anchor piles and anchors

these parameters have to be studied carefully and one of the most important subjects

is the anchor arrangement and spacing of anchors which can cause failures that are

mentioned above unless it is designed and constructed properly.

1.2. Scope and Outline of the Thesis

Investigation of the stabilization problems that are mentioned above is possible with

the determination of the design parameters and interaction of the parameters which

effects the deformations into the ground during the excavation and stabilization

studies.

In this study the displacements of the anchored pile wall is investigated which are

constructed at the Gazino Station for the stabilization of the excavation. The

deformations into the ground and the anchorage method and testing procedures are

studied and investigated to bring up a conclusion. The anchorages are applied for the

stabilization after the piles are constructed and the constructing of anchor rows and

testing procedures were still on process.

No stabilization problems encountered during the construction of Gazino Station but

the unpredicted deformations and displacements on the pile walls and on the cap of

piles may occur and these cause unforeseen circumstances on the walls and in the

support of permanent excavation.

The data and parameters which are obtained from the field studies will be evaluated

in all manner of how are the deformations effects. Thus by using the whole field data

and study results the probable but unpredictable anchor and ground failures can be

estimated.

5

In this study which the anchor type, anchor arrangement, pile designs, geological

considerations, field and laboratory studies, anchor testing procedures are predicted

and certain, the main objective is to investigate the anchored pile wall stability and

evaluation of the behavior by using the Mohr-Coulomb and Rankine theory. A FEM

analysis and an evaluation of field measurements are considered in the manner of the

stabilization of the deep excavation.

In the first chapter, the problem is defined and a scope of the thesis is described.

Chapter Two gives the background information and some literature survey about the

anchored pile wall applications and there are also some definitions given in this

chapter.

Chapter Three describes the field studies performed within the study of Metro

Project and some test results are also given.

Chapter Four gives the modeling and calculation results and some brief explanations

about the calculation results.

Chapter Five gives discussion of the results.

Finally, conclusions derived from this study and the recommendations for further

studies are provided in Chapter Six.

6

CHAPTER II

BACKGROUND INFORMATION AND LITERATURE SURVEY

2.1. Ground Anchors

A ground anchor normally consists of a high tensile steel cable or bar, called the

tendon, one end of which is held securely in the soil by a mass of cement grout or

grouted soil: the other end of the tendon is anchored against a bearing plate on the

structural unit to be supported. The main application of ground anchors is in the

construction of tie-backs for diaphragm or pile walls. Other applications are in the

anchoring of structures subjected to overturning, sliding or buoyancy, in the

provision of reaction for in-situ load tests and in pre-loading to reduce settlement.

Ground anchors can be constructed in sands (including gravelly sands and silty

sands) and stiff clays, and they can be used in situations where either temporary or

permanent support is required (Craig R.F. , 1978).

Anchors transmit tensile forces into the rock mass. They are inserted into boreholes

and bonded to the rock by grout or other chemicals. Their action is twofold. Firstly,

on tensioning an anchor or rock bolt, the stress field is modified in the vicinity of the

anchor. Secondly, where a tensioned anchor is holding a block of rock in its original

position it also acts as a preventative measure against the further disintegration of the

rock.

A ground anchor functions as load carrying element, consisting essentially of a steel

tendon inserted into suitable ground formations in almost any direction. Its load-

carrying capacity is generated as resisting reaction mobilized by stressing the ground

along a specially formed anchorage zone. (Xanthakos, 1991)

This arrangement is shown schematically in Fig.2.1 together with the basic

components of the system. These components include the head, the free length, and

the bond length. The latter is intended to interact with the enveloping ground

7

materials in order to transfer the load; whereas the free length remains unbonded and

thus free to move within the soil environment.

Fig.2.1

Schematic presentation of a ground anchor showing the three main components (Xanthakos, 1991)

Fig.2.2

Ground anchor use for retaining wall support (Hanna, 1982)

8

As structural devices, anchors usually are attached to ground supports at their head.

The anchor tendon is installed in special boreholes in a wide variety of soils or rock.

The grouted length of tendon, through which force is transmitted to the surrounding

soil, is called the fixed anchor length. The length of tendon between the fixed anchor

and the bearing plate is called the free anchor length: no force is transmitted to the

soil over this length. For temporary anchors the tendon is normally greased and

covered with plastic tape over the free anchor length. This allows for free movement

of the tendon and gives protection against corrosion. For permanent anchors the

tendon is normally greased and sheathed with polythene under factory conditions: on

site the tendon is stripped and de-greased over what will be the fixed anchor length.

The ultimate load which can be carried by an anchor depends on the soil resistance

(principally skin friction) mobilised adjacent to the fixed anchor length. (This, of

course, assumes that there will be no prior failure at the grout-tendon interface or of

the tendon itself). Anchors are usually prestressed in order to reduce the movement

required to mobilise the soil resistance. Each anchor is subjected to a test loading

after installation: temporary anchors are usually tested to 1-2 times the working load

and permanent anchors to 1-5 times the working load. Finally, prestressing of the

anchor takes place. Creep displacements under constant load will occur in ground

anchors. A creep coefficient, defined as the displacement per unit log time, can be

determined by means of a load test. It has been suggested that this coefficient should

not exceed 1 mm for 1-5 times the working load.

A comprehensive ground investigation is essential in any location where ground

anchors are to be employed. The soil profile must be determined accurately, any

variations in the level and thickness of strata being particularly important. In the case

of sands the particle size distribution should be determined, in order that permeability

and grout acceptability can be estimated. The relative density of sands is also

required to allow an estimate of to be made. In the case of stiff clays the undrained

shear strength should be determined.

9

2.1.1. The Terminology

Within this chapter some special terms are defined and a brief explanation for each

term is given by Hobst&Zajic.

The anchoring of structures to rock or soil ensures their mutual interconnection. This

interconnection, which is capable of transferring tensile and shear forces, solely

dependent on the use of anchors, a system of which forms the total anchorage.

An anchor is a device with a static function, transferring forces in a given direction

from the structure to the rock or soil.

The anchor head is situated at the external end of the anchor; from it the prestressing

of the anchor is carried out, and when connected it transmits the anchoring forces to

the structure.

The anchor tendon connects the anchor head with the root. The tendon usually

allows, by virtue of its elastic deformation, the prestressing of the anchor during

anchoring.

The anchor root is situated at the subterranean end of the anchor, and transfers the

tensile forces from the tendon to the ground. The root must be adequately fixed in the

ground for this purpose.

The free length of an anchor (tendon) is determined by the distance between the

starting point of the fixing of the tendon in the anchor root, and the fixing point of

the tendon in the anchor head.

The fixed portion (root) of the anchor in the rock or soil is determined by the length

along which the force within the anchor is transferred to the ground.

A temporary anchor has a service life not exceeding two years.

A permanent anchor has a service life more than two years.

10

A prestressed anchor is permanently tensioned due to the elastic extension of the

tendon over its free length.

A non-prestressed anchor is one that is left without prestressing, or one that cannot in

any case be prestressed because it is fixed in the ground along its entire length.

The prestressing of an anchor is a process in which a tensile force is introduced.

The anchoring force is the force which is transmitted by the anchor to the ground.

The working load of an anchor is the force which the anchor should be capable of

transmitting continuously throughout its service life.

The admissible load of an anchor is determined by the upper limit of its bearing

capacity, computed or ascertained during tests with subtraction of a safety margin.

A testing load is a short-term loading to which the test anchor is subjected in order to

check the quality of its manufacture and establish its maximum load.

The (limit) bearing capacity of an anchor is that load under which the resistance of

any functional part of the system (ground, anchor, anchored structure) fails and the

anchor ceases to function.

The safety factor is the ratio of the limit load or limit deformation load of the anchor

and of its admissible or working load.

11

2.1.2. Anchors in Sands

In general the sequence of construction is as follows. A cased borehole (diameter

usually within the range 75 125 mm) is advanced through the soil to the required

depth. The tendon is then positioned in the hole and cement grout is injected under

pressure over the fixed anchor length as the casing is withdrawn. The grout

penetrates the soil around the borehole, to an extent depending on the permeability of

the soil and on the injection pressure, forming a zone of grouted soil, the diameter of

which can be up to four times that of the borehole (Fig.2.3a). Care must be taken to

ensure that the injection pressure does not exceed the overburden pressure of the soil

above the anchor, otherwise heaving of fissuring may result. When the grout has

achieved adequate strength the other end of the tendon is anchored against the

bearing plate. The space between the sheathed tendon and the sides of the borehole,

over the free anchor length, is normally filled with grout (under low pressure): this

grout gives additional corrosion protection to the tendon.

The ultimate resistance of an anchor to pull-out is equal to the sum of the side

resistance and the end resistance of the grouted mass. The following theoretical

expression was proposed by Littlejohn:

( )

+

+= 224

tan2

dDh

BDLL

hAQ f pi (2.1)

where

Qf : ultimate load capacity of anchor, [kN] A : ratio of normal pressure at interface

to effective overburden pressure, [-] : unit weight of soil [kN/m3] B : bearing capacity factor, [-] h : depth of overburden, [m] L : fixed anchor length, [m] D : diameter of fixed anchor, [m] d : diameter of borehole [m]

12

Fig2.3

Ground Anchors (a) grouted mass formed by pressure injection, (b) grout cylinder, (c) multiple under-reamed anchor.

It was suggested that the value of A is normally within the range 1 to 2. The factor B

is analogous to the bearing capacity factor Nq in the case of piles and it was

suggested that the ratio Nq/B is within the range 1-3 to 1-4, using the Nq values of

Berezantzev, Khristoforov and Golubkov. However, the above expression is unlikely

to represent all the relevant factors in a complex problem.

The ultimate resistance also depends on details of the installation technique and a

number of empirical formulae have been proposed by specialist contractors, suitable

for use with their particular technique.

2.1.3. Anchors in Stiff Clays

The simplest construction technique for anchors in stiff clays is to auger a hole to the

required depth, position the tendon and grout the fixed anchor length using a tremie

pipe (Fig.2.3b). However, such a technique would produce an anchor of relatively

low capacity because the skin friction at the grout-clay interface would be unlikely to

exceed 0,3Cu (i.e. =0,3). (Cu : shear strength, : side resistance(skin friction

coefficient))

13

Anchor capacity can be increased by the technique of gravel injection. The augered

hole is filled with pea gravel over the fixed anchor length, then a casting, fitted with

a pointed shoe, is driven into the gravel, forcing it into the surrounding clay. The

tendon is then positioned and grout is injected into the gravel as the casing is

withdrawn (leaving the shoe behind). This technique results in an increase in the

effective diameter of the fixed anchor (of the order of 50%) and an increase in side

resistance: a value of of around 0,6 can be expected. In addition there will be some

end resistance. The borehole is again filled with grout over the free anchor length.

Another technique employs an expanding cutter to form a series of enlargements (or

under-reams) of the augered hole at close intervals over the fixed anchor length

(Fig.2.3c): the cuttings are generally removed by flushing with water. The cable is

then positioned and grouting takes place. A value of of around 0-8 can be assumed

along the cylindrical surface through the extremities of the enlargements.

The following design formula can be used for anchors in stiff clays:

cuuf N)Cd(Dpi

piDLCQ 22 -4

+= (2.2)

where,

Qf : ultimate load capacity of anchor [kN] L : fixed anchor length [m] D : diameter of fixed anchor [m] d : diameter of borehole [m] : skin friction coefficient [-] Nc : bearing capacity factor(generally assumed to be 9).

The design of underground and ground structures has been almost exclusively an

area reserved for the experienced practical engineer. Although the importance of the

subject and the standing of the science of soil mechanics there is still not sufficient

courses in soil and/or rock mechanics in Civil Engineering departments.

The excavations which are performed in soils and/or rocks cause the stress changes

and effect the stress distribution in the ground. These stress changes formed

significantly around the excavation walls and by means of the displacements around

14

the excavation these stresses effects the stress-strain relationship that is supposed to

be linear at these points.

Fig. 2.4

Use of ground anchors for rock slope stabilization (Hanna, 1982)

Anchoring in the ground fulfils three basic functions (Hobst&Zajic, 1983):

- It establishes forces which act on the structure in a direction towards the point

of contact with the rock or soil.

- It establishes stress acting on the ground, or at least a reinforcement of the

rock medium through which the anchor passes if non-prestressed anchorage

is used.

- It establishes prestressing of the anchored structure itself, when the anchors

pass through this structure.

Historically, the origin of anchorages can be traced to the end of last century.

Frazer (1874) has described tests on wrought-iron anchorages for the support of a

canal bank along the London Birmingham railway. Anderson (1900) has

documented the use of screw piles to restrain floor slabs against flotation.

15

One of the earliest and most impressive applications was the strengthening of the

Cheurfas dam in Algeria, pioneered by Coyne in 1934. This gravity structure, shown

in Fig.2.5 was built of conventional masonry materials in 1880 but was partially

destroyed in 1885 following a serious flood. The dam was rebuilt in 1892, but in the

early 1930s it showed signs of foundation instability. Structural integrity was

restored by the use of vertical 1000 ton capacity anchors placed at 3.5 m intervals,

and then stressed by hydraulic jacks between the crest of the dam and the lower part

of the cable head.

The manufacture of dependable high-tensile steel wire and strand together with

improvements in grouting and drilling methods led to the postwar development of

ground anchors mainly in France, Germany, Sweden and Switzerland, and later

England. During the 1950s anchors were first used to support deep excavations.

Today, anchorage practice is common in most parts of the world, including the

United States, for both rock and soils, and current methods can produce high-

capacity anchors in stiff clays as well as in fine sands and silts. (Xanthakos, 1991)

Fig.2.5

Cheurfas Dam in Algeria: a) general plan; b) section through main structure showing the anchorage.

(Xanthakos, 1991)

16

2.2. Fundamentals of Anchored Walls

2.2.1. Working Principles

Anchored walls provide the support of vertical or near-vertical excavations. In

general, excavation in soil mass causes unloading and local yielding of the soil. If the

opening is deep enough a shear surface develops, resulting in some form of shear

failure. A retaining wall is constructed against the excavation face to limit unloading

of the soft ground and inhibit formation of a failure surface. The wall is acted upon

by an active stress environment, and unless it is stable a resisting force must be

introduced, for example, in the form of anchors, to provide the conditions of stability.

On the other hand, movement (vertical or horizontal) must be restrained and

confined within allowable limits.

The mechanism of an anchored wall is thus complex since the ground, wall and

anchors must interact and work together in order to resist earth pressure loads and

surcharges developing during and after construction, and restrict deformations to

acceptable values. As the wall deflects toward the excavation under the lateral

loading, the anchor stretches and initiates the load transfer in the fixed zone. The

fixity imposed on the anchorage by the soil restraints further wall deflection. This

movement is further controlled if anchors are prestressed.

2.3. Anchor Wall Characteristics and Applicability

2.3.1. Anchored Sheet Pile Walls

These are suitable in soft clays, organic materials, and dilatant soils of low

plasticity. Steel sheeting forms a seal at the base of the excavation if it is driven to

interlock. The system provides resistance to ground movement, particularly below

excavation level, but its inherent flexibility makes sheet piling more suitable for

relatively shallow excavations or where some ground movement can be tolerated.

In hard ground or where boulders and other obstructions are encountered, driving

sheet piling can be difficult and even impossible. In congested sites, depth limitations

may be imposed by available headroom, whereas noise and vibrations are

objectionable and may impose the use of silent pile drivers (Hunt, 1974). Sheet-pile

walls are relatively expensive, but some of the cost is recovered if the piles can be

pulled out for reuse.

17

Anchored sheet-pile walls have, however, limited load-bearing capacity, a problem

that can be remedied either by extending the sheet piles to full resistance in which

case a deep wall will result, by placing intermittent sections on stilts or other suitable

foundation elements, or by choosing a relatively flat anchor inclination to reduce the

vertical load component. Since sheet-pile walls usually serve temporarily, until the

permanent underground structure is in place, the use of detensionable or extractable

anchors is a normal requirement (Xanthakos, 1991).

2.3.2. Anchored Soldier Pile Walls

These offer flexibility in a variety of ground types except soft clays and loose sands

that have a tendency to run. The system is economically attractive, and represents a

time-tested ground support, adaptable where ground movement can be tolerated and

the ground-water level is controlled by dewatering. Structurally the support is

flexible, and below excavation level it provides limited resistance to ground move-

ment. Like sheet piling, the installation is more economical if the piles can be

withdrawn for reuse. If they are left in place, they may be incorporated in the

permanent structure. Soldier piles are suitable at sites where the presence of

underground utilities does not favor other methods.

Problems may arise if it is necessary to underpin existing foundations or where the

excavation is carried out in water-bearing ground. A usual problem is ground loss in

granular soils associated with preexcavation to install the piles, open lagging or

overcut behind lagging, and surface or groundwater migration. In these conditions,

predraining of saturated soils is essential, particularly if materials have a tendency

to run. Difficulties will also arise if these soils are underlain by rock or by

impervious layers within the proposed excavation depth, since this sequence almost

precludes dewatering to the lowest extent of the water bearing formation. A useful

review of soldier pile systems is provided by Wosser and Darragh (1970), and by

Donolo (1971). Concrete soldier piles with concrete lagging are reportedly popular

in Sweden (Broms and Bjerke, 1973). These are fairly watertight; hence, they are

economical if they can become part of the permanent structure.

18

2.4. Examples of Anchored Pile Walls

An inclined bored pile wall is shown in Fig. 2.6, supporting the excavation for a cut-

and-cover extension of the Munich subway.

Fig.2.6

Excavation for subway construction in Munich; inclined bored pile wall strutted at the top and anchored in the lower levels. (Littlejohn, 1982)

The wall inclination in this case was dictated by tight alignment and minimum

clearance, which precluded the use of other methods for lateral support and

underpinning. This construction was carried out in the following stages:

1. Install bored pile wall with an inclination as shown.

2. Install steel H columns using the prefounded column method.

3. Install temporary decking at street level.

4. Excavate to just above existing foundation and install struts as uppermost

wall bracing.

5. Excavate to first anchor level and install the first row of anchors.

6. Excavate to second anchor level and install the second row of anchors.

19

Prestress anchors at both rows.

7. Excavate to final level.

An anchored cast-in-place diaphragm wall for a deep building excavation in

Stockholm is shown in Fig. 2.7. This design satisfies the following criteria: (a)

feasibility of combining the temporary support with the permanent structure: (b)

protection of the base from groundwater effects, uplift pressures, and bottom

swelling; and (c) feasibility of completing the work without effects that are

detrimental to surroundings. The excavation accommodates a five-story basement

22 m (72 ft) deep, and was carried out without pumping. The wall surrounds the entire

site along its perimeter, and is sealed with rock sockets. A grout curtain formed

below the base seals the excavation and relieves the bottom slab from uplift

pressures. After the permanent interior framing was in place, the four rows of

anchors were destressed. Anchor working load varied from 1000-24000 kN

(225-540 kips).

Fig.2.7

Typical section, deep excavation for building in Stockholm. (Littlejohn, 1982)

20

Foundation slabs and mats must be anchored if they are subjected to an upward

loading originating from uplift or from overturning effects of eccentric forces.

An example where the condition of uplift is remedied without tie-down schemes is

shown in Fig.2.8. In this instance, the anchored perimeter enclosure walls are

extended to an existing impervious layer. This isolation is combined with pumping

inside the excavation to provide permanent groundwater lowering within the

protected area. If a natural impervious layer does not exist close to the base, such a

layer can be created by grouting.

Fig.2.8

Protection of excavation from groundwater and uplift by lowering the water table permanently within the excavation area.

An example of anchored foundation slab is shown in Fig. 2-9 (Fenoux, 1971),

subjected to a hydrostatic head of 8.4 m (almost 28 ft) for a corresponding uplift

pressure of 1.4 kg/cm2 (1700 lb/ft2). The permanent pre-stressed anchors have

working loads 240 tons (540 kips), and a fourfold protection in the free length.

21

Fig.2.9

Roche Building; typical cross section for the basement excavation. (Fenoux, 1971)

The effect of the prestress application and the resulting ground response are fully

confirmed in practice. Prestress causes consolidation, leading to settlement with a

corresponding loss of prestress equivalent to the reduction of elastic extension of the

tendon. However, this process converges rapidly, and equilibrium between the two

phenomena is soon reached. Since the elastic extension of the tendon generally is of

an order of magnitude greater than that of settlement, the state of equilibrium

corresponds to a small loss of prestress.

22

2.5. Estimation of Lateral Stresses and Deformations of Piles

2.5.1. General Requirements

In simple terms, the formulation of the problem of predicting lateral pressures and

deformations is essentially the definition of appropriate boundary values. This

requires knowledge of the initial stress conditions in the ground, the constitutive

relations for the soil, and the correct or the most realistic boundary conditions for

useful results.

2.5.2. Initial Stresses

In sedimentary soil, as the buildup of overburden continues there is vertical

compression of soil because of increase in vertical stress, but there should be no

significant horizontal compression. In this case the horizontal earth stress is less than

the vertical, and for sand deposits formed in this manner K0 usually ranges between 0.4

and 0.5. Thus, for initial loading the expression proposed by Jaky is confirmed by the

majority of investigators (Bishop, 1958) so that

Ko = 1 - sin (2.3)

where Ko :coefficient of lateral pressure at rest

' :angle of shearing resistance for effective stress

However, with the exception of certain soils such as normally consolidated clays,

the initial effective stresses in a given ground are seldom known with confidence.

There is also evidence that the horizontal stress can exceed the vertical if a soil

deposit has been heavily preloaded, as a result of a process where the stress

remained locked and did not dissipate when the preload was removed. The

coefficient Ko may now approach 3, and under certain conditions it may become close

to Kp (Brooker and Ireland, 1965; Skempton, 1961).

23

2.5.3. Constitutive Equations

Although the nature of constitutive equations for sands and normally or lightly

overconsolidated clays prepared in the laboratory is adequately understood, natural

soils or soils placed under field conditions are not always fully represented.

Obviously, natural soils may display anisotropic, nonhomogeneous, and time-

dependent properties. Furthermore, discontinuities give rise to size effects in

response to loading.

2.5.4. Boundary Conditions

These are equally essential for meaningful estimates of lateral stresses and

deformations. They are more reliable if they can represent actual construction

procedures and a pragmatic interaction between structure and soil, including the

anchorage. In the following sections examples are presented demonstrating the

difficulty in prescribing correct boundary conditions for certain categories of

problems. In some instances, these conditions can only be stated in a crude idealized

approximation, even where Ko and constitutive equations are established reliably.

Where the prediction of deformations is essential, the problem is usually approached

with linear elastic theory. If maximum lateral pressure or resistance is the governing

factor, limiting equilibrium methods are typically used to estimate these forces. In

this case little, if any, consideration is or can be given to actual deformations and

associated movement. In other instances, such as braced excavations, movement is

usually reduced if not entirely stopped, and this affects the distribution of

lateral earth stresses. Semi empirical methods are in this case used to arrive

at a reasonable solution. Likewise, anchor prestress and wall stiffness affect

movement and cause changes in the magnitude and distribution of earth

loads.

24

2.6. Lateral Earth Pressure

The lateral earth pressure is linearly proportional to depth and is taken as:

a =K . s . z (2.4)

where:

= lateral earth pressure at a given depth, z.

K = coefficient of lateral earth pressure, to be taken as:

Ka, active, for walls that move or deflect sufficiently to reach

the active conditions

Ko, at rest, for walls that do not deflect or are restrained from

movement

Kp, passive, for walls that deflect or move sufficiently to

reach a passive condition, including integral abutments.

s = soil unit weight

z = depth

The resultant lateral earth load due to the weight of the backfill should be assumed to

act at a height of H/3 above the base of the wall, where H is the total wall height,

measured along a vertical plane extending from the ground surface above the back of

the footing down to the bottom of the footing.

For walls with a total wall height, H, greater than or equal to 5 feet, the horizontal

movement of the top of the wall due to structural deformation of the stem and

rotation of the foundation is sufficient to develop active conditions.

At-rest earth pressures are usually limited to bridge abutments to which

superstructures are fixed prior to backfilling (e.g. rigid frame bridges) or to

cantilever walls where the heel is restrained and the base/stem connection prevents

rotation of the stem.

At the formulation there is a K value (coefficient of lateral earth pressure) which is

obtained from the Rankines Active and Passive Earth Pressure Theory.

25

For normally consolidated clays and granular soils,

K0 = 1 sin (2.5)

For overconsolidated clays,

K0,overconsolidated = K0,normally consolidated OCR 0.5 (2.6)

From elastic analysis,

: Poissons Ratio (2.7)

The K0 is the coefficient when the earth pressure is at rest. As the excavation takes

progress the sheet pile wall tends to move away from the soil.

2.7. Active and Passive Earth Pressures

Active and passive earth pressures are the two stages of stress in soils which are of

particular interest in the design or analysis of shoring systems. Active pressure is the

condition in which the earth exerts a force on a retaining system and the members

tend to move toward the excavation. Passive pressure is a condition in which the

retaining system exerts a force on the soil. Since soils have a greater passive

resistance, the earth pressures are not the same for active and passive conditions.

When a state of oil failure has been reached, active and passive failure zones,

approximated by straight planes, will develop as shown in the following figure (level

surfaces depicted) .

K

-10=

26

Fig. 2.10

Active and Passive Zone

The well known earth pressure theories of Rankine and Coulomb provide

expressions for the active and passive pressure for a soil mass at a state of failure.

2.8. Coefficient of Earth Pressure

The coefficient of earth pressure (K) is the term used to express the ratio of the

lateral earth pressure to the vertical earth pressure or unit weight of the soil. For a

true fluid the ratio would be 1. The vertical pressure is determined by using a fluid

weight equal to the unit weight of the soil: PH = K. PV The basic formulas for

horizontal earth pressures are as follows:

PH = KPV = KH = Lateral earth pressure (2.8)

If a soil has a cohesive value the formula becomes:

PH = KH 2C[K]1/2 (2.9)

There are three ranges of earth pressure coefficients to be considered:

Ka = Coefficient of Active earth pressure (0.17 to 1.0) Kp = Coefficient of Passive earth pressure (1.0 to 10.0) K0 = Coefficient of earth pressure for soils at rest or in place (0.4 to 0.6 for drained soils).

27

The next step is to determine the value of the earth pressure coefficient (K) . This is

accomplished by utilizing the known soil properties and the accepted theories,

formulas, graphs and procedures that are available.

Earth pressure coefficients may also be calculated by acceptable soil mechanics

formulas. Two of the more well known authors are Rankine and Coulomb.

Fig. 2.11

Active Earth Pressure Angular Parameters 2.9. The Rankine Theory

The Rankine theory assumes that there is no wall friction (= 0) the ground and

failure surfaces are straight planes, and that the resultant force acts parallel to the

backfill slope. The coefficients according to Rankine's theory are given by the

following expressions:

[ ][ ]

+

=

2/122

2/122

coscoscos

coscoscoscos

aK (2.10)

[ ][ ]

+=

2/122

2/122

coscoscos

coscoscoscos

pK (2.11)

If the embankment is level ( =0) the equation are simplified as follows:

28

)2/45(tansin1

sin1 2

=+

= oaK (2.12)

)2/45(tansin1

sin1 2

+=+

= opK (2.13)

The Rankine formula for passive pressure can only be used correctly when the

embankment slope angle equals zero or is negative. If a large wall friction value

can develop, the Rankine Theory is not correct and will give less conservative

results. Rankines theory is not intended to be used for determining earth pressures

directly against a wall (friction angled does not appear in equations above). The

theory is intended to be used for determining earth pressures on a vertical plane

within a mass of soil.

2.10. The Coulomb Theory

The Coulomb theory provides a method of analysis that gives the resultant

horizontal force on a retaining system for any slope of wall, wall friction, and slope

of backfill provided . This theory is based on the assumption that soil shear

resistance develops along the wall and failure plane. The following coefficient is for

a resultant pressure acting at angle

{ }{ } { }{ }{ }{ }

2

2

2

)cos()cos(

)sin()sin(1)cos(cos

)(cos

++

++

=

Ka (2.14)

The passive Kp value for sloping embankment is not listed since this value can be

drastically overestimated.

The following coefficients are for a horizontal resultant pressure and a vertical wall:

{ }{ }{ }{ }

2

2

coscos

)sin()sin(1cos

cos

++

=

Ka (2.15)

29

{ }{ }{ }{ }

2

2

coscos

)sin()sin(1cos

cos

++

=

Kp (2.16)

Wall friction angle () varies from 0 to 22o, but is always less than the internal angle

of friction of the soil (). It is accepted practice to assume a value of = 1/3 () to

2/3 ().

If the shoring system is vertical and the backfill slope and wall friction angles are

zero

(, and = 0), Coulomb's equation will be the same as Rankine's for a level

ground condition. Coulomb's pressure distribution has been shown to be essentially

correct for the lateral movements of sheeting of braced cuts which closely

correspond to the conditions of rotation of a wall around its top.

Since wall friction requires a curved surface of sliding to satisfy equilibrium, the

Coulomb formula will give only approximate results as it assumes planar failure

surfaces. The accuracy for Coulomb will diminish with increased depth. For passive

pressures the Coulomb formula can also give inaccurate results when there is a large

back slope or wall friction angle. These conditions should be investigated and an

increased factor of safety considered.

2.11. Earth Pressure Coefficient when At-Rest

The at-rest earth pressure coefficient (Ko) is applicable for, determining the active

pressure in clays for strutted systems. Because of the cohesive property of clay there

will be no lateral pressure exerted in the at-rest condition up to some height at the

time the excavation is made. However, with time, creep and swelling of the clay will

occur and a lateral pressure will develop. This coefficient takes the characteristics of

clay into account and will always give a positive lateral pressure.

=1

Ko (2.17)

= The Poisson's Ratio. It is determined by a Laboratory test

(Maximum value = 0.5)

30

An alternate solution for K0 is to use Jaky's equation:

K0 = 1 - sin ' (2.18)

Where is the effective angle of internal friction and not the total stress value. For

most short tens shoring situations the internal friction angle may be substituted for

.

In general, for a level ground situation, values of K0 vill be greater than Ka. If

movement of a retaining system is severely restricted (approaching a fixed

condition) the active failure wedge cannot fully develop and consideration should be

given to using K0 in lieu of Ka.

For very deep excavations the horizontal movement that can occur is usually less

than that needed to develop active failure condition, therefore K0 values should be

used. It is noted that for deadman anchorages, K0 could be used to calculate the

passive resistance.

2.12. Wall Friction ()

Wall friction angle () varies from 0o to 22o, but is always less than the internal

angle of friction of the soil (). It is accepted practice to assume a value of = 1/3

() to 2/3 () . For systems subject to dynamic loading (adjacent railroads, pile

driving operations, etc.) use = 0. It is important to note that as wall friction

increases, lateral pressures decrease.

2.13. Elastic Analysis

This procedure involves both linear and nonlinear stress-strain relations.

The former requires judgment in selecting the appropriate modulus. Non-

linear analysis on the other hand, should include studies of several stress

paths so that relations can be found that are not unduly restrictive. Linear

analysis can be used to calculate both small and relatively large deformations

by changing the elastic modulus. Problems, however, involving large

31

deformations and simulation of yielding are better approached with nonlinear

models.

2.13.1. Linear Analysis

An excavation with a high factor of safety and small deformations is a good

example for linear analysis. If this excavation is in clay, base failure will

occur under undrained conditions when

bcH = NcSu (2.19)

where bc : bulk density of clay

H :height (or depth) of excavation

Nc : stability number depending on the geometry of the problem

Su :undrained shear strength

Terzaghi and Peck (1968) have introduced the dimensionless number N = H/Su as

an index of probable base failure. If N is about 3-4, some plastic yielding can occur.

According to Alberro (1969). if N is less than 4, pressures and deformations can be

computed using elastic theory. If Nc = 6 is taken as typical for most excavations and

N = 3-4, a criterion is manifested for the applicability (lower bound) of elastic theory

(Morgenstern and Eisenstein, 1970).

Until recently, however, this criterion was limited to excavations in deep soft and

medium clays.

As expected, the calculated lateral pressures for both the rough and the smooth base

are the same as the initial Ko horizontal stresses, since neither lateral nor vertical

displacement has occurred and the presence of excavation has no influence on the

stress environment.

32

Earth pressure distribution for the condition of no lateral yield is shown in Fig. 2.17

together with the pressure distribution when the rigid base is at distance 0.5H and H

beneath the base of excavation. In the latter cases earth pressure distribution changes

significantly, although the wall has not moved, because of the ability and freedom of

materials to flow beneath the wall. This effect is amplified when the rigid base

changes to smooth and is located deeper below excavation level.

Fig.2.12 Lateral pressure distribution for different boundary conditions, wall, condition of no

lateral yield (Morgenstern and Eisenstein, 1970)

Interestingly, the maximum horizontal pressure at the base increases while stresses

at the top reverse to tension.

33

For the same example lateral earth stresses are computed for a wall displacement

toward excavation of 0.0025H, which is less than the displacement necessary for the

active state. The results are shown in Fig. 2.13. The boundary condition along the

rigid base is now most significant when it is close to the base of excavation. As

excavation is carried down to the rigid base the pressure behind the wall is reduced

by 50 percent from the Ko state for the rough base, but only by about 10 percent for

the smooth base. The former larger reduction is partly due to the presence of tension

along the base, which is not feasible in reality. A nonlinear stress distribution is

developed as the rigid base is taken below excavation level.

Likewise, lateral earth stresses are computed for a small displacement 0.0025H

toward the ground approaching the passive state, and are shown in Fig. 2.13. The

passive resistance increases considerably owing to the presence of the rough rigid

base, but the effect of conditions along the rigid base decreases as this base is moved

further down below the excavation. An important conclusion is that earth pressures

in the elastic range are sensitive to changes in lateral deformations when the rough

rigid base is close to excavation level.

34

Fig.2.13

Lateral pressure distribution for different boundary conditions, wall of Fig2.12; pressure diagrams for wall yielding 0.0025H towards active state.

(Morgenstern and Eisenstein, 1970)

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2.14. Analysis of Anchored Walls by Finite-Element Methods

2.14.1. Advantages and Limitations

It is evident from the foregoing that partially integrated techniques inhibit complete

problem formulation since they pursue each phase independently. Thus earth stresses

are determined by limiting theory, support loads are estimated empirically, and

deformations are predicted by statistical data, elastic theory, and one-dimensional

consolidation theory. Limiting equilibrium analysis is simple in predicting collapse

loads for earth-retaining structures but does not predict deformations associated with

limit loads and provides no information for conditions other than those at the limit.

Finite-element analysis, on the other hand, permits solutions based on actual stress-

strain relations, boundary conditions, and constitutive equations. As a predictive

technique it allows consideration of structures with arbitrary shape and flexibility,

complex construction sequence, and heterogeneous soil conditions. Furthermore, it

is possible to analyze seepage loading and nonlinear soil-interface behavior, and also

predict stress changes and deformations for both the soil and the structure for

conditions other than at the limit. If instrumentation is contemplated to monitor

construction, the method becomes valuable in predicting critical phases and

instrumentation requirements, and provides a logical supplement to the process.

The programs typically require soil parameters, some of them not readily available,

which must be determined through extensive soil investigations and laboratory tests.

It is also conceivable that application of soil-structure interaction involves certain

special problems for which solutions are approximated. Other difficulties arise from

the simulation of the relative movement between the soil and the structure, the

special construction sequence that must be modeled, and the numerical problems

that are intensified by the stress-strain pattern of the soil.

2.14.2. Statement of a Model

Table 2.1 shows a typical flow chart incorporated in finite-element analyses. The

chart lists the steps involved in the investigation, each step representing an idealized

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form of the actual problem, so that the work is based on the introduction of certain

assumptions.

TABLE 2.1 Typical Flowchart and Procedure Leading to Finite-Element Analysis

Statement of problem

Idealization of soil and groundwater conditions

Selection of constitutive modeling techniques

Selection of media properties

Assumption of initial stress conditions

Assumption of construction sequence

Drawing of finite-element mesh to accommodate soil conditions,

structural configuration, and construction sequence

Analyses

2.14.3. Examples of Finite-Element Analysis

Figure 2.14 shows an anchored wall supporting an excavation 32.5 ft (10 m) deep

(Tsui, 1973). The soil is homogeneous clay underlain by rock. The wall is a concrete

diaphragm 2 ft (60 cm) thick, and the anchors consist of steel rods, 1 in2 in area,

with the fixed length in rock. The prestress loads are estimated from an apparent

pressure diagram shown in (b). The clay has undrained shear strength increasing

linearly with depth from 500 to 1400 lb/ft2 (2.5-7.0 tons/m2) at the bottom of the

clay layer. The coefficient Ko is taken as 0.85, and the insertion of the wall is

assumed to have no effect on the initial at rest condition. The initial tangent modulus

of the soil is taken as 400 times the undrained shear strength.

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The assumption of plane strain condition is considered valid for a wall 2 ft thick and

anchor spacing less than 10 ft (3 m).

Fig.2.14

Anchored wall in clay; (a) section through wall; (b) soil data and prestressed diagram. (Tsui, 1973)

A nonlinear elastic model is incorporated in the analysis, and tangent modulus

values are obtained for a stress-strain curve represented by a hyperbola. The

interface between the wall and the soil is treated similarly on both sides using a

bilinear stress-strain deformation relationship with initial shear stiffness 50,000 pcf

reduced by a factor of 1000 if the yield strength of the interface is exceeded.

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The construction sequence is simulated by an incremented loading process based on

the nine-step modeling shown in Fig.2.15. Anchor lengths vary from 61.5 to 33.9 ft.

Fig.2.15

Construction sequence; Finite element analysis of the anchored wall of Fig.2.14 (Tsui, 1973)

Figures 2.16 and 2.17 show wall and ground movement and earth pressure

distribution, respectively, for the two prestress levels and with zero prestress, together

with anchor loads corresponding to apparent pressure diagrams. Wall movement

responds consistently to prestress level decreasing almost linearly with the amount of

prestressing.

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Likewise, ground settlement behind the wall decreases as the prestress increases, but

the effect diminishes as the next higher prestress load is introduced. Settlement is thus

reduced more by the first increase than by increases that follow.

Fig.2.16

Wall and ground movements predicted by finite-element analysis; tied-back wall of Fig2.14. (Tsui, 1973)

The predicted earth pressure diagrams shown in Fig.2.17(a) can be compared with the

apparent pressures shown in (b) obtained by distributing the anchor loads over the

appropriate spans. Evidently, the predicted pressures approach the original at-rest

values and exhibit a definite triangular distribution. Interestingly, there are no

pressure bumps at the anchor points.

Fig.2.17

Lateral earth pressure predicted by finite-element analysis, and appearance pressure diagrams, tied-back wall of Fig.2.14. (Tsui, 1973)

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A second example of anchored wall in day modeled by finite-element analysis is

shown in Fig. 2.18 (Clough and Tsui. 1974). Two cases are investigated, one with

four rows and the other with three rows of anchors. The wall is flexible, with

moderate stiffness equivalent to PZ-72 sheeting. The anchor prestress is likewise

obtained from apparent pressure diagrams.

The predicted lateral pressures are more triangular than the design trapezoidal

diagram, and this distribution is consistent with the actual wall movement. In this

example, unlike the previous case, we can notice that the earth pressures tend to

concentrate slightly at each anchor level. This bulging is caused by the wall

flexibility in response to the application of prestress; hence it must be distinguished

from the linear stress distribution observed with the stiff wall. Its effect is to reduce

the bending moments slightly.

Fig.2.18

Lateral earth pressure behind a flexible wall predicted by finite-element analysis; prestressed tied- back wall. (Clough and Tsui, 1974)

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By far the greatest use of prestressed anchors is in the support of both temporary

and permanent excavations. A review is given of several case studies to illustrate

the range of problems that have been solved. This is followed by a survey in

summary form of reported anchor uses.

The construction and behaviour of an anchored wall in Genoa is reported by

Barla and Mascardi (1974). A tall building, sited on sloping ground, required an

excavation up to 34m in depth and within 3 m of existing old properties (Fig.2.21).

Fig.2.19

Plan of site showing layout of anchored wall

(Barla and Mascardi, 1974)

The ground conditions were very complex as revealed by 19 boreholes. A section

along the wall is shown in Fig. 2.20. The wall was formed from 358 bored piles at

0.6 to 0.8 m spacing and strengthened with steel H-beams. This wall was tied

back by 658 anchors, Tirsol type IRP, inclined at 20 to the horizontal with

working loads between 569 and 853 kN. Fourteen rows of steel wale beams linked

the heads of the prestressed anchors to the piled wall, Fig.2.21.

It will be noted that the bored piles were intialty taken to an intermediate level to

ensure that they did not deviate from the vertical, otherwise difficulties would

arise with wale beam attachment. The excavation proceeded step by step as the

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anchors were installed and the order of the main stages of the excavation is given

in Fig.2.22. The initial design was based on a triangular earth pressure

distribution assumption. The excavation process was simulated by a finite element

study. This showed that the most critical zone was an area of stiff silty clay. The

wall was carefully monitored during and after construction and comparisons

made between field measurement and finite element prediction. Very good

agreement was found, thus confirming that a good estimate had been made of the

ground parameters and of the in-situ stress state in the ground.

Fig.2.20

Vertical section along anchored retaining wall showing various stages of excavation

(After Barla and Mascardi, 1974)

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Fig.2.21

Vertical cross-section through the anchored wall (After Barla and Mascardi, 1974)

Fig.2.22

Anchored diaphragm wall for CPF building, Singapore