giáo trình nền móng của đại học xây dựng bản tiếng anh

12 Figure 2-14 Bearing capacity failure in soil under a rough rigid continuous strip foundation .... Figure 2-11: Linear distribution of contact pressure 2.3.1 Contact Pressure Distribut

NGUYEN BAO VIET

LE THIET TRUNG

NATIONAL UNIVERSITY OF CIVIL ENGINEERING

DIVISION OF SOIL MECHANICS AND FOUNDATION ENGINEERING

F O U N D A T I O N E N G I N E E R I N G

( F O R T H E E N G L I S H C O U R S E )

CONTENTS

CONTENTS i

LIST OF FIGURES iii

PREFACE v

CHAPTER 1: INTRODUCTION 1

CHAPTER 2: SHALLOW FOUNDATIONS 3

2.1 Introduction 3

2.2 Main Components of Shallow Foundations 5

2.3 Contact Pressure Distribution beneath Base of Footing 7

2.3.1 Contact Pressure Distribution of Spread Footing 9

2.3.2 Contact Pressure Distribution of Wall Footing 10

2.3.3 Net Load Applied on Footing Base 10

2.3.4 Vertical Stress Increase 10

2.4 Ultimate Bearing Capacity of Shallow Foundation 12

2.4.1 General 12

2.4.2 Terzaghi‘s Bearing Capacity Theory 13

2.4.3 The General Bearing Capacity Equation 17

2.4.4 General Bearing Capacity Equation in Practice 19

2.4.5 Safety Factor and Allowable Load-Bearing Capacity 20

2.4.6 Bearing Capacity of Layered Soils: Stronger Soil underlain by Weaker Soil 20

2.5 Shallow Foundation Design 21

2.5.1 Introduction 21

2.5.2 Design Procedure for Shallow Foundation 21

2.5.3 Geotechnical Analyses and Design 22

2.5.4 Structural Footing Design 25

CHAPTER 3: SOIL IMPROVEMENT 30

3.1 Sand Replacement 31

3.2 Sand Compaction Piles 32

3.2.1 Characteristics of Sand Compaction Piles 34

3.2.2 Sand Compaction Pile Working Procedure 35

3.2.3 Applied Assumptions in Calculation of Sand Compaction Piles 36

3.2.4 Principle of Sand Compaction Pile Analyses 36

3.2.5 Plan layout and Distance of Sand Compaction Pile 37

3.2.6 Estimation of Improved Soil Properties 41

3.3 Vibroflotation 42

3.4 Blasting 44

3.5 Precompression 44

3.6 Stone Columns 45

3.7 Dynamic Compaction 46

3.8 Jet Grouting 48

3.9 Recommendation of Improvement Methods for Soils 49

CHAPTER 4: PILE FOUNDATIONS 50

4.1 Definitions and classifications 50

4.1.1 Definitions 50

4.1.2 Classifications of piles 52

4.1.3 Advantages and disadvantages of different pile material 58

4.2 Constitution of a Prefabricated Reinforced Concrete Pile 62

4.3 Bearing Capacity of a Single Pile 66

4.3.1 Definitions 66

4.3.2 Pile axial bearing capacity 66

4.4 Design of Low Pile Cap Foundation 74

4.4.1 Design hypotheses 74

4.4.2 Material selection for pile and pile cap 74

4.4.3 Pile dimension selection and pile load capacity calculation 75

4.4.4 Pile quantity and pile arrangement 75

4.4.5 Verification of load applied to pile 76

4.4.6 Verification of the resistance of bearing stratum 77

4.4.7 Calculation of pile foundation settlement 78

4.4.8 Pile cap height 78

4.4.9 Verification of pile when transportation and positioning 81

4.4.10 Selection of hammer for driven piles 82

REFERENCES 83

LIST OF FIGURES

Figure 2-1 (a) Strip foundation under a wall (b) Strip foundation under columns

(c) Spread foundation (d) Mat foundation (1) Footing (2) Wall (3)

Column 3

Figure 2-2 Examples of spread foundations 3

Figure 2-3 Examples of shallow foundations (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform 4

Figure 2-4 Examples of mat foundations (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat 4

Figure 2-5 A typical cross section of spread footing 5

Figure 2-6 Reinforcement of a spread footing 6

Figure 2-7 Behavior of foundations with connecting beams 6

Figure 2-8 Ground beam and footing reinforcements 7

Figure 2-9 Settlement profile and contact pressure in sand: (a) flexible foundation; (b) rigid foundation 8

Figure 2-10: Settlement profile and contact pressure in clay: (a) flexible foundation; (b) rigid foundation 8

Figure 2-11: Linear distribution of contact pressure 9

Figure 2-12 2:1 method of finding stress increase under a foundation 11

Figure 2-13 Nature of bearing capacity failure in soil: (a) general shear failure: (b) local shear failure; (c) punching shear failure 12

Figure 2-14 Bearing capacity failure in soil under a rough rigid continuous (strip) foundation 14

Figure 2-15 Bearing capacity of a strip foundation on layered soil 20

Figure 2-16 Two-way shear calculation 26

Figure 2-17 Wide-beam shear calculation 27

Figure 2-18 Flexure reinforcement calculation 28

Figure 3-1 (a) Completed sand replacement (b) Partial sand replacement 31

Figure 3-2 Sand compaction pile test of Basore and Boitano (1969): (a) Layout of the compaction piles; (b) Standard penetration resistance variation with depth and S’ 33

Figure 3-3 Sand compaction pile mandrel tip 34

Figure 3-4 Characteristic of sand compaction piles for a spread footing 35

Figure 3-5 Sand compaction pile working procedure 36

Figure 3-6 Principle of sand compaction pile analyses 37

Figure 3-7 Compaction area for (a) strip footing and (b) spread footing 38

Figure 3-8 Plan layout of sand compaction piles (a) equiangular triangle (b) Square 40

Figure 3-9 Vibroflotation unit 42

Figure 3-10 Compaction by the vibroflotation process 43

Figure 3-11 Principles of precompression 44

Figure 3-12 Sand drain 45

Figure 3-13 Prefabricated vertical drain (PVD) 45

Figure 3-14 (a) Stone columns in a triangular pattern; (b) stress concentration due to change in stiffness 46

Figure 3-15 Rig of Dynamic compaction 47

Figure 3-16 Dynamic compaction, working procedure 47

Figure 3-17 Effects of soil Improvement by Dynamic compaction & Vibroflotation 48

Figure 3-18 Jet grouting 49

Figure 3-19 Site improvement methods as a function of soil grain size 49

Figure 4-1: Low pile cap foundation – High pile cap foundation 52

Figure 4-2: Steel pile cross section 53

Figure 4-3: End bearing pile 54

Figure 4-4: Friction or Cohesion pile 54

Figure 4-5: under-reamed base enlargement to a bore-and-cast-in-situ pile 55

Figure 4-6: Concrete driven piles system 56

Figure 4-7: Drilling auger types: short section – single flight – double flight 57

Figure 4-8: Bored pile phasing: Site preparation – Positioning – Excavation – Rebar installation – Conrete pouring – Pile completion 58

Figure 4-9: Different cross section of piles 63

Figure 4-10: Detailed design of prefabricated reinforced concrete pile 63

Figure 4-11: Cross section of a square pile 64

Figure 4-12: Stirrup bar: separate bar and spriral bar 64

Figure 4-13: Details of pile toe 64

Figure 4-14: Steel grid at pile top – Hook rebar 64

Figure 4-15: Steel plate at the pile top 65

Figure 4-16: Details of pile connection 65

Figure 4-17: s c kháng bên qci và s c kháng m i qcn trong thí nghi m CPT 68

Figure 4-18 Typical static load test arrangement showing instrumentation 70

Figure 4-19: Two P-S curves types (a, b) and T-S curve (c) 71

Figure 4-20: Piles arrangement in side view 75

Figure 4-21: Piles arrangement in plan view 76

Figure 4-22: Equivalent raft 77

Figure 4-23: damage pile cap by column 79

Figure 4-24: damage of pile cap by pile reaction 80

Figure 4-25: Rebar area calculation schemas 81

Figure 4-26: Pile transportation verification 81

Figure 4-27: Pile positioning verification 82

PREFACE

Soil mechanics and foundation engineering have developed rapidly during the last fifty years Intensive research and observation in the field and the laboratory have refined and improved the science of foundation design

This text book of ―Foundation Engineering‖ is edited for undergraduate civil engineering students, who have passed the soil mechanics course, which is a prerequisite for the foundation engineering course The text is composed of four chapters with examples and problems, and an answer section for selected problems The chapters are mostly devoted to the geotechnical aspects of foundation design and briefly described as follows

Chapter 1 of introduction gives an overview of foundation engineering

Chapter 2 presents on the concept of shallow foundation and focus analyses and design of spread footing and wall trip footing on several types of sub-soils The structural design of footing according to the Vietnamese codes also mentioned in detail

in this chapter

Chapter 3 introduces various types of soil improvement in that sand cushion and sand compaction piles are concentrated in analyses and design also

Chapter 4 is dedicated for deep foundation of prefabricated piles The estimation

of geotechnical and in structural bearing capacity of piles is mentioned based on both theories and practices Structural pile-cap design is an important content in this chapter

After this course, the students can get the basic knowledge in foundation engineering They could calculate and design foundation in some simple cases This is the first step for an engineer in geotechnical and foundation engineering

Thanks are due to all members of Geotechnical and Foundation Engineering Division of National University of Civil Engineering for their help and encouragements during the preparation of this text

I am also grateful for several helpful suggestions of Prof Vu Cong Ngu and Assoc Prof Pham Quang Hung

Dr Nguyen Bao Viet

Dr Le Thiet Trung

CHAPTER 1: INTRODUCTION

All structures resting on the earth must be carried by an interface element called foundation A foundation is the lowest part of a structure that transmits to, and into, the underlying soil or rock all loads of the super-structure and also its self-weight

The term super-structure is commonly used to describe the engineered part of the system bringing loads to the foundation, or substructure especially for buildings and bridges However, foundations also may carry only machinery, support industrial equipment (pipes, towers, and tanks) act as sign base, and the like Therefore it is better to describe a foundation as a part of the engineered system that interfaces the load-carrying component to the ground

It is evident that a foundation is the most important part of the structures or engineering system

The design of foundations of structures such as buildings, bridges, and dams generally requires knowledge of such factors as:

(a) The load that will be transmitted by the superstructure to the foundation system,

(b) The requirements of the local building code,

(c) The behavior and stress-related deformability of soils that will support the foundation system, and

(d) The geological conditions of the soil under consideration

To a foundation engineer, the last two factors are extremely important because they concern soil mechanics

The geotechnical properties of a soil such as its grain-size distribution, plasticity, compressibility, and shear strength can be assessed by proper laboratory testing In addition, recently emphasis has been placed on the in situ determination of strength and deformation properties of soil, because this process avoids disturbing samples during field exploration

However, under certain circumstances, not all of the needed parameters can be or are determined, because of economic or other reasons In such cases, the engineer must make certain assumptions regarding the properties of the soil To assess the accuracy

of soil parameters whether they were determined in the laboratory and the field or whether they were assumed the engineer must have a good grasp of the basic principles of soil mechanics At the same time, he or she must realize that the natural soil deposits on which foundations are constructed are not homogeneous in most cases Thus, the engineer must have a thorough understanding of the geology of the area that

is, the origin and nature of soil stratification and also the groundwater conditions Foundation engineering is a clever combination of soil mechanics, engineering geology, and proper judgment derived from past experience To a certain extent, it may be called an art When determining which foundation is the most economical, the engineer must consider the superstructure load, the subsoil conditions, and the desired tolerable settlement

(1) Shallow foundations

(2) Deep foundations

Spread footings, wall footings, and mat foundations are all shallow foundations In most shallow foundations, the depth of embedment can be equal to or less than three to four times the width of the foundation Pile and drilled shaft foundations are deep foundations They are used when top layers have poor load-bearing capacity and when the use of shallow foundations will cause considerable structural damage or instability The separation is not strict but in the point of view of a foundation engineer, in analysis and design of a shallow foundation, vertical friction between the foundation and soils is neglected

CHAPTER 2: SHALLOW FOUNDATIONS

2.1 Introduction

Shallow foundations, often called footings, are usually embedded about a meter or

so into soil One common type is the spread footing which consists of strips or pads of structural materials which transfer the loads from walls and columns to the soil or bedrock

Another common type of shallow foundation is the slab-on-grade foundation where the weight of the building is transferred to the soil through a concrete slab placed at the surface Slab-on-grade foundations can be reinforced mat slabs, which range from 25 cm to several meters thick, depending on the size of the building

Concrete is almost universally used for footings because of its durability in a potential hostile environment and for economy

Figure 2-1 shows some shallow foundations including strip footings (a) and (b); spread footing (c); and mat foundation (d) Furthermore, in Figure 2-2 there are several common types of spread footing consist of constant footing (a); stepped footing (b); and sloped footing (c)

Figure 2-1 (a) Strip foundation under a wall (b) Strip foundation under columns (c) Spread foundation (d) Mat foundation (1) Footing (2) Wall (3) Column

Figure 2-2 Examples of spread foundations

Various types of shallow foundation which could be used in practice such as combined

or connected footings and mat foundations are illustrated in Figure 2-3 and Figure 2-4

Figure 2-3 Examples of shallow foundations (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform

Figure 2-4 Examples of mat foundations (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of

mat

2.2 Main Components of Shallow Foundations

A shallow foundation basically consists of the following components:

- Leveling concrete

- Footings (single, strip, and mat)

- Ground beams

- Vertical supported structures such as columns, walls

Figure 2-5 show a typical reinforced concrete footing The concrete used for foundation should not be less than B20 and reinforcement should not be less than 10 Just based on soil, leveling concrete is the lowest layer with at least 100mm thick Leveling concrete creates a clean flat platformso that concrete work for the foundations could be carried out fluently The concrete used for leveling normally is B7.5 with course aggregate of 4x6 rock

Footings would be flat, step or slope as shown in Figure 2-2 with the minimum thickness would be required as 150mm but 200mm is preferred in practice Footing reinforcements shown in Figure 2-5 to resist tensile stress induced in the footing For spread and wall strip footing, basically upper (top) reinforcement, hairpin and chair bar are not necessary

A rebar spacer is a device that secures the reinforcing steel is assembled in place prior to the final concrete pour so that cover depth normally of 50mm is assured The spacers are left in place for the pour to keep the reinforcing in place, and become a permanent part of the structure Rebar spacer would be made of concrete or plastic

Figure 2-5 A typical cross section of spread footing

Figure 2-6 illustrates rebar placement for a spread footing and supported column

It should be noted that in case of stepped or sloped footing, footing‘s neck would be required The neck should be normally enlarged about 50mm for every directions of the column Sometimes column rebars need a hook so that they could stand on the lower (bottom) reinforcements layer

Figure 2-6 Reinforcement of a spread footing

Figure 2-7 Behavior of foundations with connecting beams

Figure 2-8 Ground beam and footing reinforcements

Generally, it is useful to place connecting beams at the foundation because they carry the horizontal shear forces and prevent damage from differential settlements Connecting beam is also called ground beam because of the location the beams placed Figure 2-7 shows the behavior of spread footings tied together with ground beams Reinforcement for ground beam and footings are shown in Figure 2-8

2.3 Contact Pressure Distribution beneath Base of Footing

The stress distribution under even symmetrically loaded footing is not uniform following researches of Schultze (1961), Barden (1962) and Borowicka (1963) The actual stress distribution depends on both footing rigidity and subsoil For footing on loose sand the grains near to edge tend to displace laterally, whereas interior soil is relatively confined Figure 2-9 shows the general diagram of the stress distribution for both flexible and rigid shallow foundation on granular soil

The theoretical pressure distribution for the general case of rigid footing on cohesive soils is shown on Figure 2-10(b) The high edge pressure may be explained

by considering that edge shear must occur before any settlement can take place Since soil has low rupture strength, and most of footings are of intermediate rigidity, it is very not likely that high edge shear stresses are developed

The pressure distribution beneath most footings will be rather indeterminate because of the interaction of the footing rigidity with the soil type, state, and time response to stress For this reason it is common practice to use linear pressure distribution of Figure 2-11 beneath foundations whose rigidity are large enough such

as spread footings and strip footings under wall Some of field measurements reported indicated this assumption is adequate

Figure 2-9 Settlement profile and contact pressure in sand: (a) flexible foundation;

(b) rigid foundation

Figure 2-10: Settlement profile and contact pressure in clay: (a) flexible foundation;

(b) rigid foundation

Figure 2-11: Linear distribution of contact pressure

2.3.1 Contact Pressure Distribution of Spread Footing

A footing carrying a single column is called spread footing, since its function is to

―spread‖ the column load laterally to the soil so that the stress intensity is reduced to a value that soil can safely carry These members sometimes called single or isolated footings Since the footings are subjected to moments in addition to vertical load, as shown in Figure 2-11, distribution of the contact pressure by the foundation on soil is not uniform The nominal distribution of the pressure is:

Eq 2-1

Eq 2-2

Eq 2-3

Where: N is vertical axial force at footing level;

N0 is vertical axial force at the ground level;

, weight of footing and soil above footing

(concrete) and soil above footing

Mx, My are moments at footing level;

l, b are dimensions of spread footing

2.3.2 Contact Pressure Distribution of Wall Footing

Wall footings serve a similar purpose of spreading the wall load to the soil

Because of their long shape (ratio of length (l) to width (b) greater than 7), the footings

theoretically are considered as one-way structure In reality, when the wall is high enough so its internal resistance moment of the long axis is large then the bending of the wall and also the footing could be ignored

The distribution of the contact pressure is:

Eq 2-4

Eq 2-5

Eq 2-6

Where: N is vertical axial force distributed for 1m long at footing level;

N0 is vertical axial force distributed for 1m long at the ground level;

, weight of footing and soil above footing for 1m long;

M is moments distributed for 1m at footing level;

b is width of footing wall

2.3.3 Net Load Applied on Footing Base

The net load applied on footing base is determined as the total stress at the footing base level extract the geostatic (over-burden) stress at the base level

Eq 2-7

Where ’tb = effective unit weight of soils above footing base level

2.3.4 Vertical Stress Increase

2.3.4.1 Method based on Boussineq Equation

One of the most common methods to estimate stress increase  at a depth under a foundation from the net applied load ( p) is Boussineq Equation based on Theory of Elasticity which have been mentioned at chapter 4 of the Soil mechanics text book To obtain the result, the load is assumed act on a homogenous, isotropic, weightless, and elastic half-space of soil

Certainty the increase stress, , is varies from point to point in the soil space but

in the engineering point of view, in conservative side, at each level  should be considered at the center of the foundation where it gets maximum value To deal this problem, an equivalent uniform distribution of load of p should be used as net applied load General equation based on chapter 4 of soil mechanics text book to get the increase stress is

Where k = loading factor depending on the shape of foundation base and the depth of considered point

2.3.4.2 Simple Equivalent Method (2:1Method)

Figure 2-12 2:1 method of finding stress increase under a foundation

Foundation engineers often use an approximate method to determine the increase

in stress with depth caused by the construction of a foundation The method is referred

to as the 2:1 method (See Figure 2-12) According to this method, the increase in stress

at depth z is

Eq 2-9 and Eq 2-10 are based on the assumption that the stress from the foundation spreads out along lines with a vertical-to-horizontal slope of 2:1

Some authors have proposed the slope angle be anywhere from 30o to 45o In Vietnam, 30o is default for that angle It should be noted that 2:1 method is widely used over the world because of simplicity and conservative result

p

2.4 Ultimate Bearing Capacity of Shallow Foundation

2.4.1 General

To perform satisfactorily, shallow foundations must have two main characteristics:

1 They have to be safe against overall shear failure in the soil that supports them

2 They cannot undergo excessive displacement, or settlement (The term excessive is relative, because the degree of settlement allowed for a structure depends on several considerations.)

The load per unit area of the foundation at which shear failure in soil occurs is called the ultimate bearing capacity, which is the subject of this part

Figure 2-13 Nature of bearing capacity failure in soil: (a) general shear failure: (b)

local shear failure; (c) punching shear failure

Consider a strip foundation with a width of b resting on the surface of a dense sand

or stiff cohesive soil, as shown in Figure 2-13(a) Now, if a load is gradually applied to the foundation, settlement will increase The variation of the load per unit area on the

foundation p with the foundation settlement is also Figure 2-13 failure in the soil

supporting the foundation will take place, and the failure surface in the soil will extend

to the ground surface This load per unit area is usually referred to as the ultimate bearing capacity of the foundation When such sudden failure in soil takes place, it is called general shear failure

If the foundation under consideration rests on sand or clayey soil of medium compaction Figure 2-13 (b), an increase in the load on the foundation will also be accompanied by an increase in settlement However, in this case the failure surface in the soil will gradually extend outward from the foundation, as shown by the solid lines

in Figure 2-13 (b) When the load per unit area on the foundation equals movement of the foundation will be accompanied by sudden jerks A considerable movement of the foundation is then required for the failure surface in soil to extend to the ground surface (as shown by the broken lines in the figure) The load per unit area at which

this happens is the ultimate bearing capacity, p gh Beyond that point, an increase in load will be accompanied by a large increase in foundation settlement The load per

unit area of the foundation, p gh(1), is referred to as the first failure load (Vesic, 1963)

Note that a peak value of p is not realized in this type of failure, which is called the

local shear failure in soil

If the foundation is supported by a fairly loose soil, the load–settlement plot will

be like the one in Figure 2-13 (c) In this case, the failure surface in soil will not extend

to the ground surface Beyond the ultimate failure load, p gh, the load–settlement plot will be steep and practically linear This type of failure in soil is called the punching shear failure

2.4.2 Terzaghi’s Bearing Capacity Theory

Terzaghi (1943) was the first to present a comprehensive theory for the evaluation

of the ultimate bearing capacity of rough shallow foundations According to this theory, a foundation is shallow if its depth, (Figure 2-14), is less than or equal to its width Later investigators, however, have suggested that foundations with equal to 3 to

4 times their width may be defined as shallow foundations

Terzaghi suggested that for a continuous or strip foundation (i.e., one whose width

to length ratio approaches zero), the failure surface in soil at ultimate load may be assumed to be similar to that shown in Figure 2-14 (Note that this is the case of general shear failure, as defined in Figure 2-14a.) The effect of soil above the bottom

of the foundation may also be assumed to be replaced by an equivalent surcharge, (where is a unit weight of soil) The failure zone under the foundation can be separated into three parts (see Figure 2-14):

2 The radial shear zones ADF and CDE, with the curves DE and DF being arcs

of a logarithmic spiral

3 Two triangular Rankine passive zones AFH and CEG

Figure 2-14 Bearing capacity failure in soil under a rough rigid continuous (strip)

foundation

The angles CAD and ACD are assumed to be equal to the soil friction angle ’

Note that, with the replacement of the soil above the bottom of the foundation by an equivalent surcharge q, the shear resistance of the soil along the failure surfaces GI and HJ was neglected

Using equilibrium analysis, Terzaghi expressed the ultimate bearing capacity in the form

Where: c’ = cohesion of soil

 = unit weight of soil

Eq 2-14

Where Kp = passive pressure coefficient

The variations of the bearing capacity factors defined by Eq 2-12, Eq 2-13, and

Eq 2-14 are given in Table 2-1

Table 2-1 Terzaghi‘s Bearing Capacity Factors

To estimate the ultimate bearing capacity of square and circular foundations, Eq 2-11 may be respectively modified to

In Eq 2-15, b equals the dimension of each side of the foundation; in Eq 2-16, b

equals the diameter of the foundation

For foundations that exhibit the local shear failure mode in soils, Terzaghi suggested the following modifications to Eq 2-11, Eq 2-15, and Eq 2-16:

 for strip foundation Eq 2-17

N’ , N’q, and N’c, the modified bearing capacity factors, can be calculated by using the bearing capacity factor equations (for N , Nq, and Nc, respectively) by replacing ’ by ’’ = tan-1(2/3tan’) The variation of and with the soil friction angle

is given in Table 2-2

Table 2-2 Terzaghi‘s Modified Bearing Capacity Factors

Terzaghi‘s bearing capacity equations have now been modified to take into account the effects of the foundation shape depth of embedment and the load inclination This is given in the next section Many design engineers, however, still use Terzaghi‘s equation, which provides fairly good results considering the uncertainty of the soil conditions at various sites

2.4.3 The General Bearing Capacity Equation

The ultimate bearing capacity Eq 2-11, Eq 2-15, and Eq 2-16 are for continuous, square, and circular foundations only; they do not address the case of rectangular foundations Also, the equations do not take into account the shearing resistance along the failure surface in soil above the bottom of the foundation (the portion of the failure surface marked as GI and HJ in Figure 2-14) In addition, the load on the foundation may be inclined To account for all these shortcomings, Vesic (1973) suggested the following form of the general bearing capacity equation:

In this equation:

c’ = cohesion;

q = effective stress at the level of the bottom of the foundation;

 = unit weight of soil;

b = width of foundation (= diameter for a circular foundation);

s(.) = shape factors;

d(.) = depth factors;

i(.) = load inclination factors;

b(.) = tilted base inclination factors;

g(.) = ground inclination factors;

N , Nq, and Nc = bearing capacity factors

The equations for determining the various factors given in Eq 2-20 are described briefly in the sections that follow Note that the original equation for ultimate bearing capacity is derived only for the plane-strain case (i.e., for continuous foundations) The shape, depth, load inclination, tilted base inclination, and ground inclination factors are empirical factors based on experimental data

The basic nature of the failure surface in soil suggested by Terzaghi now appears

to have been borne out by laboratory and field studies of bearing capacity (Vesic, 1973) It can be shown that

Shape, Depth, load Inclination, tilted Base inclination, and Ground inclination Factors

Where Q0 = shear force at column base level

N0 = axial force at column base level

F = foundation base area

cg = cohesion between footing base and the soil under

since the angle opposite to combination of axial force N0 and shear force Q0)

Where:  is angle between the grounds surface to horizontal

Table 2-3 Bearing capacity factors for the general equations

2.4.4 General Bearing Capacity Equation in Practice

In practice, most of shallow foundations based on flat ground with base inclination equal zero, for simplicity Eq 2-20 can be reformed into the following equation in that factors of depth, load inclination might be neglected

Where sc, sq, q are shape factors as mentioned above but for simplicity, some engineers have used following alternative relations

2.4.5 Safety Factor and Allowable Load-Bearing Capacity

Calculating the gross allowable load-bearing capacity, [p] , of shallow foundations requires the application of a factor of safety (FS) to the gross ultimate bearing capacity, or

Eq 2-25

The factor of safety, FS, should be 2~3 in most cases

2.4.6 Bearing Capacity of Layered Soils: Stronger Soil underlain by Weaker Soil

The bearing capacity equations presented in the above section involve cases in which the soil supporting the foundation is homogeneous and extends to a considerable depth The cohesion, angle of friction, and unit weight of soil were assumed to remain constant for the bearing capacity analysis However, in practice, layered soil profiles are often encountered In such instances, the failure surface at ultimate load may extend through two or more soil layers, and a determination of the ultimate bearing capacity in layered soils can be made in only a limited number of cases This section features the procedure for estimating the bearing capacity for layered soils in which stronger soil underlain by weaker soil

Figure 2-15 shows a strip foundation supported by a stronger soil layer, underlain

by a weaker soil that extends to a great depth The physical parameters of the two soil layers are also written down in the Figure

In this case, the stronger soil could be failed cause of contact foundation ptb, and

on the other hand, the weaker soil could be failed by the load just above that layer at depth of hm_tđ

Figure 2-15 Bearing capacity of a strip foundation on layered soil

Bearing capacity of foundation at footing base level (the stronger soil) could be calculated easily by the normal approaches described in the above sections (Eq 2-11,

Eq 2-15, and Eq 2-16 or Eq 2-20 or Eq 2-24) On the other hand, bearing capacity of the weaker soil could be done by the same way with an equivalent foundation of footing dimensions are extended follows 2:1 method and the embedded depth is calculated as

Where: hm_tđ = embedded depth of equivalent foundation

hm = embedded depth of foundation

H = Thickness of the soil from footing level to the weaker soil

2.5 Shallow Foundation Design

3 Foundation structure needs to be available for both conditions of strength and serviceability

2.5.2 Design Procedure for Shallow Foundation

a) Soil base design

1 Choose embedded depth of footing;

2 Determine dimensions of footing;

3 To calculate the contact pressure;

4 Check for bearing capacity and economy conditions;

5 To calculate settlement and differential settlement;

6 Serviceability condition check;

b) Structural footing design

7 Choose structural materials for footing (type of concrete and reinforcement)

8 Determine thickness of footing base, h;

9 Check for bearing capacity of shear;

10 Flexural design for footing base;

11 Technical drawings

2.5.3 Geotechnical Analyses and Design

2.5.3.1 Strength design of the Subsoil

a) Embedded depth of footing

Embedded depth of footing would be decided based on the following guidelines:

1 The footing must be laid on a steady strong soil and should be above underground water level

2 The shallower the better for the construction work of foundation but it should

be deep enough for satisfying architect requirements

Depth of footing depends on soil strata it lay on Basically, there are three types of soil strata and see how to deal with each case

(a) All soil layers are strong;

This case is most easy and convenient to give a decision The footing depth normally is about 1.0~1.5m since the lateral load is small the depth may be lesser

(b) Weak soil of upper layer and strong soil of the lower;

When the weak layer is small (less than 3m) the most common method is eliminate the weak soil replace them by a strong material such as sand and set the footing on that Since the thickness is larger (3~5m) the improvement of the soil such as soil replacement, sand compaction piles … should be applied

(c) Strong soil at first, then weak layer and finally strong soil again at the lowest

If the first strong layer is thick enough then this case is similar to the (a) case When the first strong layer is not so thick then the footing might place on the first but the depth should be as small as possible In this case bearing capacity of foundation must be carefully considered for both strong and weak layers In bad way, if the first soil is thin then it becomes near case (b)

b) Dimensions of footing

To determine the footing dimensions play an important role in the foundation design procedure The size of footing affect significantly to the strength and serviceability design of the foundation The size should be large enough to satisfy the technical requirements but not so large to agree with economic condition

Firstly, an arbitrary value of foundation width, b0, should be chosen That is entire

of the first step for strip footing but for spread footing, the length (l0 >b0) must be assumed also Normally l0 follows the larger of the bending moments and may be estimated by relation l0 = b0 where = Mx/My  2 For example, in Figure 2-11 l0 (L)

is in Y direction according to case of Mx > My In case of unique moment, l0 = b0where = (1+ e ~(1+ 2e) and e is a ratio of the moment, M, to axial force, N; (e= M/N)

c) Calculation of contact pressure

According to load and action codes, a structure must sustain several types of loading such as static load, live load, wind load, earthquake load, flood load, and so

on Basically, nominal loads are decided on the code To determine the loads applying

on a structure component (foundation, in this case) a combination process must be carried out, of course, according to the code instruction The loads can be divided into two categories as follows

- Un-factored loads combined with no factors are based on the nominal values only For foundation design un-factored loads are used for bearing capacity check and also for settlement estimation

The un-factored loads normally displayed by symbol of tc for example , Hence the contact pressure under footing comes from un-factored combination, ptb, pmax, pmin are obtained from Eq 2-1 to Eq 2-6 in that ,

are replaced by , respectively

- Factored loads combination in which the nominal values are multiplied with the factors in the code These combinations are applied for structural foundation design The stresses used for structural footing design must be based on factored load combinations, but due to the self-balance the weight of footing and the soil above footing are not involved in the calculation If factored loads are , then the pressure under footing comes from factored combination, p0tb, p0max, p0min are computed from the equations modified from section 2.3

For spread footings:

d) Check for technical and economic conditions

The contact pressures, ptb, pmax, pmin must be satisfied technical conditions

Eq 2-33

In case both conditions of Eq 2-34 are not satisfied, works in the step (2) should

be done again with advised smaller dimensions It should be noted that, in practice, 20% is completely acceptable instead of 5% of idealization

2.5.3.2 Serviceability conditions of the Soil

a) Stress induced Settlement

Stress induced settlement, pgl, is the net applied stress on soil of the un-factored combination loads Based on Eq 2-7, the expression as follow

Eq 2-35

Where ptb is contact pressure obtained from Eq 2-1 or Eq 2-4 with

un-factored combination loads

’tb = effective unit weight of soils above footing base level

b) To calculate settlements

The approaches to estimate settlement of soil under the load have been described

in detail on the Soil mechanics book or any text books of geotechnical engineering A review is presented as follows

Settlement for homogenous soil strata

If net applied load is small, the relation of p–S is linear, hence using the

assumption that the soil medium is an elastic, homogeneous, isotropic, and infinite medium In practice, since a soil stratum is homogenous, the theory of elastic would be applied

semi-For rectangular foundation:

Eq 2-36

Where const influenced by shape of footing l/b (rigid foundation);

b = width of footing;

0 = Poisson‘s ratio;

E0 = Elastic modulus of the soil

pgl = Net applied load of the un-factored combination

Settlement of multi-layers soil strata

For multi-layers soil strata, settlement of footing is estimated by accumulating settlement of appropriate soil layers in the effective depth The settlement calculation

is expressed as follow:

Eq 2-37

Where Si = settlement of a sub-layer which could be calculated based on

results of oedometer test Refer to section 5.3 of the Text book

of Soil mechanics

c) To calculate differential settlements

The differential settlements between two points (center of footings) are defined as follow

Eq 2-38

Where Si, Si+ 1 = settlement of footing number i and i+ 1

Li~i+ 1 = distance between the two points

d) Serviceability condition check

The estimated settlements and differential settlements must be in range required in the code The relations could be expressed as

Eq 2-39

The allowable settlement, [S] , and allowable differential settlements, [ S] of framed building of reinforced concrete are 8.0cm and 0.002 respectively, according to the Vietnamese code If material for the frame is steel then the allowable ones are 12.0cm and 0.004 For detail, refer to TCVN 205-1998, appendix H

2.5.4 Structural Footing Design

Dimensions of a footing are controlled by the allowable soil pressure On the other hand, footing thickness h is usually decided by shear stresses In addition, footing must have strength to resist the bending moment induced by contact pressure of soil

2.5.4.1 Shear strength design of footing

Footing must be considered in both ways: (1) shear forces of two-way action and (2) wide-beam Two-way action shear always controls the depth for centrally loaded square footing Wide-beam shear may control the depth for rectangular footings when l/b ratio is greater than about 1.2 and may control for other l/b ratios when there are overturning or eccentric loadings

a) Two-way action shear

A shear force acting on edge faces of the frustum in the Figure 2-16 of two-way action based on the equilibrium theory

Eq 2-40

Where ltb = min { lc+ h0; 0.5(lc+ l) }; btb = min { bc+ h0; 0.5(bc+ l) };

bc,lc = dimensions of column according to b, l of footing

N0tt = Axial force at column base level of factored combinations;

p0tb is calculated by Eq 2-27 or Eq 2-30

Figure 2-16 Two-way shear calculation

Shear strength of footing must be strong enough to resist the shear force of way action Normally structural footing design uses no reinforcement for shear therefore footing need an enough thickness for shearing

a = concrete cover, normally equals of 50mm;

Rbt = allowable tension strength of footing concrete

Eq 2-42

Where lđt = 0.5(l - lc);

b = width of foo`ting;

p0max, p0min are determined in part c) of section 2.5.3.1

Figure 2-17 Wide-beam shear calculation

The thickness of footing also must suit with wide beam shear condition In practice, the following equation is usually used to

Eq 2-43

Where btb = min { bc+ h0; 0.5(bc+ b) };

h0 = effective height of footing;

Rbt = tension strength of footing concrete

Thickness of a wall strip footing is controlled by wide-beam shear in the short direction Calculation process would be carried out by the same way as that described above Actually, this is plane strain problem then to analyze a wall strip footing, a unit length of the footing would be consider Thickness of the wall works as short dimension of column bc, and in the long direction, dimension of the wall and dimension of footing all are unit (1.0)

c) Thickness footing design procedure

- Chose a value of footing thickness, h;

- Determine concrete cover, a then calculate effective height h0 = h – a;

- Types of concrete and reinforcement used for footing should agree with suggestions in section 2.2

- The effective thickness h0 must be satisfied the shear conditions expressed by

Eq 2-41 and Eq 2-43; if not, a larger value of footing thickness, h, is advised

- The thickness must not so close to the minimum thickness based on shear check because the thicker of footing the more rigid and lesser reinforcement of foundation

2.5.4.2 Flexural strength design of footing

Figure 2-18 Flexure reinforcement calculation

Flexural reinforcements of footing are calculated based on a console beam model fixed at the edge of column sustain the soil reactions pressures Reinforcements in the long and short direction are computed by the bending moment at section I-I, II-II respectively

According to reinforcement concrete code for flexural structures, the reinforcement could be calculated by the following simplified equation

Where h0 = the effective height of footing;

Rs = allowable tensile strength of reinforcement;

M = the bending moment

Eq 2-44

In case of no moment action then the soil pressures are uniform and the bending moments could be calculated by the following equations:

Where lco = lng = 0.5( l - lc ) console span in long direction;

lco= bng = 0.5( b-bc ) console span in short direction;

Eq 2-45

Since the footing subjected moments, M, as shown in Figure 2-18, the soil pressures are distributed in trapezoid then the bending moments could be calculated by the following equations:

is set according to the minimum requirement of the codes

Having obtained the required reinforcement area, an engineer should be place the reinforcements into the footing by indicate size and distances of them Note that, the minimum reinforcement ratio and size, distance of reinforcement bars are basically stipulated in the codes

All the information of footing must be described in drawings detailed so that site engineer could do construction work without any additional comments of designer except some of extraordinary works

CHAPTER 3: SOIL IMPROVEMENT

In many areas of Vietnam especially in coastal Hong River and Me Kong delta, certain soils make the construction of foundations extremely difficult For example, expansive or collapsible soils may cause high differential movements in structures through excessive heave or settlement Foundation engineers must be able to identify difficult soils when they are encountered in the field Although not all the problems caused by all soils can be solved, preventive measures can be taken to reduce the possibility of damage to structures built on them This chapter outlines introduce some methods for soil improvement before construction of foundations

Function of a foundation is to transfer the structural loads from a building safely into the ground A backyard tool shed may need only wooden skids to spread its load across an area of ground surface, whereas a house would need greater stability and consequently its foundation should reach the underlying soil that is free of organic matter A larger and heavier building of masonry, steel, or concrete would require its foundations to go deeper into earth such that the soil or the rock on which it is founded

is competent to carry its massive loads; on some sites, this means going a hundred feet

or more below the surface Because of the variety of soil, rock, and water conditions that are encountered below the surface of the ground and the unique demands that many buildings make upon the foundations, foundation design is a highly specialized field of geotechnical engineering

The soil at a construction site may not always be totally suitable for supporting structures such as buildings, bridges, highways, and dams For example, in granular soil deposits, the in situ soil may be very loose and indicate a large elastic settlement

In such a case, the soil needs to be densified to increase its unit weight and thus its shear strength Sometimes the top layers of soil are undesirable and must be removed and replaced with better soil on which the structural foundation can be built The soil used as fill should be well compacted to sustain the desired structural load Compacted fills may also be required in low-lying areas to raise the ground elevation for construction of the foundation

Soft saturated clay layers are often encountered at shallow depths below foundations Depending on the structural load and the depth of the layers, unusually large consolidation settlement may occur Special soil improvement techniques are required to minimize settlement Improving in situ soils by using additives is usually referred to as stabilization

Various techniques are used to

1 Reduce the settlement of structures

2 Improve the shear strength of soil and thus increase the bearing capacity of shallow foundations

3 Increase the factor of safety against possible slope failure

4 Reduce the shrinkage and swelling of soils

This chapter discusses some of the general principles of soil improvement, such as compaction, vibroflotation, precompression, sand drains, wick drains, stabilization by admixtures, jet grouting, and deep mixing, as well as the use of stone columns and sand compaction piles in weak clay to construct foundations

In case soil strata have weak soil of upper layer and strong soil of the lower and when the weak layer is small (less than 3m) or the upper layer is not so weak, the most common method is eliminate all or part of the weak soil then replace them by strong material such as sand Footings are set on the strong replacement

Figure 3-1 (a) Completed sand replacement (b) Partial sand replacement

The filled soils normally compacted by layers of 300~500mm to ensure the quality

as designed request Sands from small to medium are widely used as replacement materials so in Vietnam this method is also called ―sand cushion‖ The properties of filled sand listed as follow would be easily achieved with not so hard effort of compaction

- Natural weight unit,  = 18kN/m3

0.5hđb

hđ

weak

soil

stiff soil

- Internal friction angle,

- Deformation modulus, E0 = 16MPa

The filled sand must be thick enough to reduce the pressures at the footing to a bearable pressure of the weak soil at the end of sand cushion The problem requires the bearing capacity consideration of layered soils mentioned at section 2.4.6 Note that the sand cushion is taken into account as the stronger layer and the soil underneath the sand cushion is the weaker layer The pressure acting on the weaker layer consists of two components (1) total vertical overburden (geostatic) pressure mentioned in the Soil mechanics text book (2) vertical stress increment described in section 2.3.4

On the other hand, with the thick enough of sand cushion, foundation settlement could be reduced significantly The settlement must satisfy at least the serviceability conditions discussed in section 2.5.3.2

It should be noted that in construction work of soil replacement, the original soil would be removed by excavation therefor the engineer should estimate the soil slope

of the excavation The slope could be predicted empirically, approximately vertical to horizontal ratio, m = 1:1 to 1.5:1 is applied

3.2 Sand Compaction Piles

Compaction piles are displacement piles can be driven into the ground in order to increase the density of the soil The soil is densified by both the actual displacement of the soil and the vibration of the ground that occurs during the driving process In addition, there must be relatively close spacing of the piles in order to provide meaningful densification of soil between the piles

Sand compaction piles are one of compaction piles They can be used in sites to improve stability, control liquefaction, and reduce the settlement of various structures Built in soft clay, these piles can significantly accelerate the pore water pressure-dissipation process and hence the time for consolidation

Sand piles were first constructed in Japan between 1930 and 1950 (Ichimoto, 1981) Large-diameter compacted sand columns were constructed in 1955, using the Compozer technique (Aboshi et al., 1979) The Vibro-Compozer method of sand pile construction was developed by Murayama in Japan in 1958 (Murayama, 1962)

Sand compaction piles are constructed by driving a hollow mandrel with its bottom closed during driving (see Figure 3-3) On partial withdrawal of the mandrel, the bottom doors open Sand is poured from the top of the mandrel and is compacted

in steps by applying air pressure as the mandrel is withdrawn The piles are usually 0.40 to 0.76m in diameter and are placed at about 1.5 to 3m center to center The pattern of layout of sand compaction piles is shown as Figure 3-2(a) for equiangular triangle Sometimes, square layout is used for the sand piles

Basore and Boitano (1969) reported a case history on the densification of a granular subsoil having a thickness of about 9 m at the Treasure Island Naval Station

in San Francisco, California, using sand compaction piles The sand piles had diameters of 356 mm Figure 3-2(a) shows the layout of the sand piles The spacing,

S’, between the piles was varied The standard penetration resistances, N60, before and after the construction of piles are shown in Figure 3-2(b) (see location of SPT test in Figure 3-2(a))

From this figure, it can be seen that the effect of densification at any given depth decreases with the increase in S’ (or S’/D) These tests show that when S’/D exceeds

about 4 to 5, the effect of densification is practically negligible

Figure 3-2 Sand compaction pile test of Basore and Boitano (1969): (a) Layout of the compaction piles; (b) Standard penetration resistance variation with depth and S’

Figure 3-3 Sand compaction pile mandrel tip

To improve soil by sand compaction piles, the engineer needs to consider:

- Diameter of the piles

- Length of the piles

- Plan layout and distance among the piles

- Determine the improved soil properties

3.2.1 Characteristics of Sand Compaction Piles

Sand compaction piles are circular with diameter  of 400  600mm, 400mm is widely used in Viet Nam;

Length of the piles, L, must be deep enough in order to improve the soils influenced by loading When the effective depth Hn of soil is deeper than that of weak soil then the pile length should be controlled by depth of the weak soil hy In the other case, L should be controlled by Hn The length L could be expressed as follow (see Figure 3-4)

Properties of the sand compacted piles would be collected as sand replacement methods mentioned above as follows

- Natural weight unit,  = 18kN/m3

- Internal friction angle,  = 30o

- Deformation modulus, E0 = 16MPa