## Example

A vertical 4 m high wall is founded on a relatively impervious soil and is supporting soil with the properties < j> ' 40 , c' 0,S 20 , 7sat 20kN m3. The surface of the retained soil is horizontal and is level with the top of the wall. If the wall is subjected to heavy and prolonged rain such that the retained soil becomes saturated and its surface flooded, determine the maximum horizontal thrust that will be exerted on to the wall (i) if there is no drainage system (ii) if there is the...

## Act

If mv and A are assumed constant with depth the equation for p reduces to x A + (l-A)a (4) Poisson's ratio for a saturated soil is generally taken as 0.5 at the stage when the load is applied so a is a geometrical parameter which can be determined, various values for a that were obtained by Skempton and Bjerrum are given in Table 9.4. The value of the pore pressure coefficient A can now be substituted in Equation (4) and a value for i obtained, typical results being Soft sensitive clays...

## Hlq

Fig. 3.35 Space diagonal and octahedral plane. Fig. 3.35 Space diagonal and octahedral plane. cra axial stress on sample due to applied loading (71 < 7a for compression tests and o or for extension tests. Consider again the point P and consider the octahedral plane passing through it. This plane will cut the space diagonal at the point P' such that P' represents the stress system (op, op, where It is seen therefore that it is often convenient to divide a general stress system into two...

## Anchored earth

A further type of earth retaining wall structure was evolved by Murray and Irwin (1981). The system involves the use of metal rods, generally of mild steel, which are placed horizontally within the fill at vertical and horizontal spacings of about 0.6 m or more. The rods, typically 16-20 mm in diameter, have one end formed into a Z or triangular shape which acts as an anchor while the other end has a screwed connection to the facing panel (Fig. 7.19). So far the facing units used have been made...

## B

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## Con

Taking moments about O, the centre of rotation We culr cur0r cur20 for equilibrium Restraining moment cur29 The position of G is not needed, and it is only necessary to ascertain where the line of action of W is. This can be obtained by dividing the sector into a set of vertical slices and taking moments of area of these slices about a convenient vertical axis. With a slip in a cohesive soil there will be a tension crack at the top of the slope (Fig. 5.7) along which no shear resistance can...

## B E

The differences between the various pressure diagrams can be seen in Fig. 6.27d where the three diagrams have been superimposed. It has been found that if the top of a wall moves 0.1 per cent of its height, i.e. a movement of 10 mm in a 10 m high wall, an arching-active case is attained. This applies whether the wall rotates or slides. In order to achieve the totally active case the top of the wall must move about 0.5 per cent, or 50 mm in a 10 m wall. It can therefore be seen that if a...

## Ego

(c) Culmann line diagram Fig. 6.18 Example 6.6. Note If the design had been in accordance with CP2 then the depth of the tension cracks, he should have been evaluated from the formula This value should be used in place of 1.52 m for hc. Analytical solutions with the Coulomb theory are possible but complicated. Kerisel and Absi (1990) published values of the horizontal components of Ka and Kp for a range of values of cf> , (3, 6 and ip to ease calculation. In this section we are concerned with...

## Fag

Fig. 8.7 Variation of the coefficient Nc with depth (after Skempton, 1951). 8.3.4 Summary of bearing capacity formula It can be seen that Rankine's theory does not give satisfactory results and that, for variable subsoil conditions, the slip surface analysis of Fellenius provides the best solution. For normal soil conditions, Equations (6)-(9) can generally be used and may be applied to foundations at any depth in c < f> soils and to shallow foundations in cohesive soils. For deep footings...

## Qxo

With centre C and radius CD draw the circle establishing the points A and B on the x-axis. By scaling, OD resultant stress 10.6kN m2. With protractor, 4> 19 6 55 . OA 0-3 7.6 kN m2 OB en 15 kN m2 It is possible to make a vertical cut in silts and clays and for this cut to remain standing, unsupported, for some time. This cannot be done with a dry sand which, on removal of the cutting implement, will slump until its slope is equal to an angle known as the angle of repose. In silts and clays,...

## Uqh

Fig. 8.7 Variation of the coefficient Nc with depth (after Skempton, 1951). The coefficient Nq allows for the surcharge effects due to the soil above the foundation level and N7 allows for the size of the footing, B. The effect of N7 is of little consequence with clays, where the angle of shearing resistance is usually assumed to be the undrained value, < > u, and assumed equal to 0 , but it can become significant with wide foundations supported on cohesionless soil. Terzaghi's solution for...

## Bearing capacity terms

The following terms are used in bearing capacity problems. Ultimate bearing capacity The value of the average contact pressure between the foundation and the soil which will produce shear failure in the soil. The maximum value of contact pressure to which the soil can be subjected without risk of shear failure. This is based solely on the strength of the soil and is simply the ultimate bearing capacity divided by a suitable factor of safety. The maximum allowable net loading intensity on the...

## C

Fig. 3.9 A cohesive coil, subjected to undrained conditions and zero total normal stress will still exhibit a shear stress, cu. Tf shear stress at failure, i.e. the shear strength c unit cohesion a total normal stress on failure plane ( > angle of shearing resistance. The equation gave satisfactory predictions for sands and gravels, for which it was originally intended, but it was not so successful when applied to silts and clays. The reasons for this are now well known and are that the...

## Consolidation by drainage in two and three dimensions

The majority of settlement analyses are based on the frequently incorrect assumption that the flow of water in the soil is one dimensional, partly for ease of calculation and partly because in most cases knowledge of soil compression values in three dimensions is limited. There are occasions when this assumption can lead to significant errors (as in the case of an anisotropic soil with a horizontal permeability so much greater than its vertical value that the time-settlement relationship is...

## Ccz

Fig. 6.15 The effect of cohesion on active pressure. At depth, h, both soils are subjected to the same major principal stress a 7h. The minor principal stress for the cohesionless soil is < 73 but for the cohesive soil it is only < 73c, the difference being due to the cohesive strength, c, that is represented by the lengths AB or EF. Difference between < 73 and a , HF Hence the active pressure, pa, at depth h in a soil exhibiting both frictional and cohesive strength and having a...

## Design of gravity walls

During the design of gravity walls, the following limit states should be (1) Slip of the surrounding soil (Fig. 7.5a). This effect can occur in cohesive soils and can be analysed as for a slope stability problem. (2) Bearing failure of the soil beneath the structure (Fig. 7.5b). The overturning moment from the earth's thrust causes high bearing pressures at the toe of the wall. These values must be kept within safe limits -usually not more than one-third of the supporting soil's ultimate...

## Determination of the coefficient of consolidation cv from the consolidation test

If for a particular pressure increment applied during a consolidation test the compression of the test sample is plotted against the square root of time, the result shown in Fig. 10.6 will be obtained. The curve is seen to consist of three distinct parts AB, BC and CD. AB (initial compression or frictional lag) A small but rapid compression sometimes occurs at the commencement of the increment and is probably due to the compression of any air present or to the reorientation of some of the...

## Bpv

Fig. 3.32 Typical results from consolidated undrained shear tests on saturated clays. An overconsolidated clay is considerably stronger at a given pressure than it would be if normally consolidated, and also tends to dilate during shear whereas a normally consolidated clay will consolidate. Hence when an over-consolidated clay is sheared under undrained conditions negative pore water pressures are induced, the effective stress is increased, and the undrained strength is much higher than the...

## E E

Similarly, strains on other two planes are - ( + , E E Now it can be shown that, no matter what the stresses on the faces of the cube, the volumetric strain is equal to the sum of the strains on each face. Compressibility of a material is the volumetric strain per unit pressure, i.e. for a soil skeleton, Cc per unit pressure increase Average pressure increase j(cti + ct2 + 03). Therefore, for a perfectly elastic soil E (a 1 + < r2 + C3) 3(1 2 i) E Consider a sample of saturated soil subjected...

## Kqs

Fig. 10.6 Typical consolidation test results. The square root of time 'fitting' method It will be appreciated that the curve described above is an actual consolidation curve and would not be obtainable from one of the theoretical curves of Fig. 10.4, which can only be used to plot the primary compression range. To evaluate the coefficient of consolidation it is necessary to establish the point C, representing 100 per cent primary consolidation, but it is difficult from a study of the test curve...

## Et

The effect of a tension crack can again be allowed for, and in this case The centre of the most critical circle can only be found by trial and error, various slip circles being analysed and the minimum factor of safety eventually obtained. A suitable procedure is suggested in Fig. 5.10. The centre of each trial circle is plotted and the F value for the circle is written alongside it. After several points have thus been established it is possible to draw 'contours' of F values, which are roughly...

## Exercise

A 2.5 kg rammer compaction test was carried out in a 105 mm diameter mould of volume 1000 cm3 and a mass of 1125 g. Test results were Moisture content (per cent) 10.0 11.0 12.0 13.0 14.0 Mass of wet soil and mould (g) 3168 3300 3334 3350 3320 Plot the curve of dry density against moisture content and determine the test value for pjiiias and omc. On your diagram plot the zero and 5 per cent air voids lines (take Gs as 2.65). If the percentage of gravel omitted from the test (particle specific...

## Egs

The ratio, at any given point, of the pore water pressure to the weight of the material acting on unit area above it is known as the pore pressure ratio and is given the symbol ru. (See also Section 5.5.1.) Flow parallel to the surface and at the surface The flow net for these special conditions is illustrated in Fig. 5.3. If we consider the same element as before, the excess pore water head, at the centre of the base of the element, is represented by the height hw in Fig. 5.3. In the figure,...

## Granular materials

Soils such as gravel and sand are collectively referred to as granular soils and normally exhibit only a frictional component of strength. A potential slip surface in a slope of granular material will be planar and the analysis of the slope is relatively simple. However, most soils exhibit both cohesive and frictional strength and pure granular soils are fairly infrequent. Nevertheless a study of granular soils affords a useful introduction to the later treatment of soil slopes that exhibit...

## Rio

Fig. 6.28 Pressure distribution in strutted excavation (after BS 8002 1994). In Fig. 6.28b the shape A'B'C'D' represents, to an enlarged scale, the original form of the surface that has yielded to the position ABCD of Fig. 6.28a the resulting pressure on the back of the wall is roughly parabolic and is indicated in Fig. 6.28c. For design purposes a trapezoidal distribution is assumed, of the form recommended in BS8002 1994 after the work of Terzaghi and Peck (1967), since revised (Terzaghi,...

## Yqe

Re due to Pressure Resultant re due to Pressure Resultant (c) Trapezoidal Fig. 10.2 Forms of initial excess pore pressure. 10.3 Terzaghi's theory of consolidation Terzaghi's first presented this theory in 1925 and most practical work on the prediction of settlement rates is now based upon the differential equation he evolved. The main assumptions in the theory are as follows. (i) Soil is saturated and homogeneous. (ii) The coefficient of permeability is constant. (iii) Darcy's law of saturated...

## Gmt

Figure 3.3a shows a major principal plane, acted upon by a major principal stress, < 71, and a minor principal plane, acted upon by a minor principal stress, 03. By considering the equilibrium of an element within the stressed mass (Fig. 3.3b) it can be shown that on any plane, inclined at angle 9 to the direction of the major principal plane, there is a shear stress, r, and a normal stress, crn. The magnitudes of these stresses are These formulae lend themselves to graphical representation,...

## In situ testing for ultimate bearing capacity

In this test an excavation is made to the expected foundation level of the proposed structure and a steel plate, usually from 300 to 750 mm square, is placed in position and loaded by means of a kentledge. During loading the settlement of the plate is measured and a curve similar to that illustrated in Fig. 8.11 is obtained. On dense sands and gravels and stiff clays there is a pronounced departure from the straight line relationship that applies in the initial stages of loading and the qu...

## Info

(i) Determine the value of the pore pressure coefficient B and state whether or not the soil was saturated. (ii) Plot the variation of deviator stress with strain. (iii) Plot the variation of the pore pressure coefficient A with strain. The soil was partially saturated as B was less than 1.0. Strain ( ) Aud (Act, - A< t3) A A( l Strain ( ) Aud (Act, - A< t3) A A( l

## J

Fig. 10.13 Explicit recurrence formula treatment for an impermeable boundary. derivatives) and rounding-off errors (due to working to only a certain number of decimal places). The size of the space increment, Az, affects both these errors but in different ways the smaller Az is, the less the truncation error that arises but the greater the round-off error tends to become. The value of r is also important. For stability r must not be greater than 0.5 and, for minimum truncation errors, should be...

## L

Inclined loads The usual method of dealing with an inclined line load, such as P in Fig. 8.9, is to first determine its horizontal and vertical components PH and Pv and then, by taking moments, determine its eccentricity, e, in order that the effective width of the foundation B' can be determined, from the formula B' B 2e. The ultimate bearing capacity of the strip foundation (of width B) is then taken to be equal to that of a strip foundation of width B'...

## M

(b) the representative critical state strength. Again, this should ensure a maximum wall displacement of 0.5 per cent wall height, for non-soft and non-loose soils. When considering the design values of wall friction, < 5, and undrained wall adhesion, cw, BS 8002 recommends that the design value be the lesser of the representative value determined by test, or 75 per cent of the design shear strength to be actually mobilised in the soil. Design tan S 0.75 x Design tan < j> Design cw 0.75 x...

## Main types of earth retaining structures

Various types of earth retaining structures are used in civil engineering, the main ones being mass construction gravity walls The last two structures are different from the rest in that the soil itself forms part of these structures. Because of this fundamental difference reinforced soil and anchored earth walls are discussed separately at the end of this chapter. Earth retaining structures are commonly used to support soils and structures to maintain a difference in elevation of the ground...

## Methods of investigating slope stability

Contemporary methods of investigation are based on (a) assuming a slip surface and a centre about which it rotates, (b) studying the equilibrium of the forces acting on this surface, and (c) repeating the process until the worst slip surface is found as illustrated in Fig. 5.5. The worst slip surface is that surface which yields the lowest factor of safety, F where F is the ratio of the restoring Fig. 5.4 Typical rotational slip in a cohesive soil. Fig. 5.4 Typical rotational slip in a cohesive...

## Oc

It can be shown by trigonometry that 6.3.2 Rankine's theory (soil surface sloping at angle (3) This problem is illustrated in Fig. 6.4. The evaluation of Ka may be carried out in a similar manner to the previous case, but the vertical pressure will no longer be a principal stress. The pressure on the wall is assumed to act parallel to the surface of the soil, i.e. at angle to the horizontal. The active pressure, pa, is still given by the expression

## P

Fig. 5.21 Effective stress analysis forces acting on a vertical side. Let the other forces acting on the slice be W weight of slice P total normal force acting on base of slice T shear force acting on base of slice z height of slice b breadth of slice 1 length of BC (taken as straight line) a angle of between P and the vertical x horizontal distance from centre of slice to centre of rotation, O. In terms of effective stress, the shear strength mobilised is Total normal stress on base of slice

## Preface

By the time this book is published later this year, it will be nine years since I wrote the preface to the sixth edition. During this period dramatic changes to the treatment of soil mechanics have been suggested and adopted. Many changes have been created by the draft European Geotechnical Design Code, Eurocode 7 but the results of modern research into soil behaviour have also created changes, which are still continuing. The book includes for the first time an introduction to practical...

## Q

Fig. 13.8 v-lnpf of the values tabulated in Table 13.1. Fig. 13.8 v-lnpf of the values tabulated in Table 13.1. The projection of the critical state line on to the v-p' plane is unfortunately curved but if we consider the projection on to the v In p' plane we obtain a straight line with a slope that can be assumed to be equal to the slope of the normal consolidation line. The values for Pf are tabulated in Table 13.1 and it is a simple matter to obtain a set of lnp'f values so that a v-lnp plot...

## R

(i) Upper part ( ) Lower part In (i) Taking moments about D gives R In (ii) Taking moments about B eliminates PP1 and gives d Fig. 7.13 Fixed earth support method for anchored sheet piled walls. computed by the free earth support method for both the moments in the pile and the tension in the tie can be realistically reduced. The method involves the use of two coefficients, rd and rt, and worked examples illustrating the use of the method have been prepared by Barden (1974). More recently,...

## S

Total settlement of centre of foundation 25 mm Note The Schmertmann approach is now preferred by most engineers to the De Beer and Martens' method. The results from a plate loading test can be used to predict the average settlement of a proposed foundation on granular soil. The test should be carried out at the proposed foundation level and the soil tested must be relatively homogeneous for some depth (not with conditions such as illustrated in Fig. 4.10). If pi is the settlement of the test...

## Site Investigation and Ground Improvement

A site investigation, or soil survey, is an essential part of the preliminary design work on any important structure in order to obtain information regarding the sequence of strata and the ground water level, and also to collect samples for identification and testing. In addition a site investigation is often necessary to assess the safety of an existing structure or to investigate a case where failure has occurred. British Standard Code of Practice BS5930, Site investigations, lists the...

## Strength of Soils

The property that enables a material to remain in equilibrium when its surface is not level is known as its shear strength. Soils in liquid form have virtually no shear strength and even when solid have shear strengths of relatively small magnitudes compared with those exhibited by steel or concrete. To appreciate this section some knowledge of the relevant strength of materials is useful. A brief summary of this subject is set out below. Consider a block of weight W resting on a horizontal...

## Stressstrain relationships

Before commencing a study of the material in this chapter it is best to become familiar with the main terms used to describe the stress-strain relationships of a material. It is useful to begin by examining a typical stress-strain plot obtained for a metal (Fig. 4.1). Results such as those indicated in the figure would normally be obtained by subjecting a specimen of the metal to a tensile test and plotting the values of tensile strain against the nominal values of tensile stress, as the...

## Symbols

Critical state theory is a three-dimensional approach and therefore uses three parameters p and q, the equivalent of the s and t parameters used in Chapter 9, and a third parameter, v, the specific volume, which is defined in Chapter 1 and is the total volume of soil that contains a unit volume of solids. From Chapter 1 v (l + e). As explained in Chapter 3, in the triaxial test, where rrj 03, we can say that foct (a + 20V) Toct y (crj - cr3) In order to avoid the term j 2, p and q were defined...

## The Authors

Smith MSc, PhD, CEng, MICE was formerly Head of Geotechnics and, later, a Senior Research Fellow at Heriot-Watt University, Edinburgh. Ian G.N. Smith BEng, PhD has several years' practical experience in site investigation and is now Lecturer in Geotechnics in the Department of Civil and Transportation Engineering at Napier University, Edinburgh. C.R.I. Clayton, M.C. Matthews & N.E. Simons 0-632-02908-0 hardback Ground Bioengineering Techniques for Slope Protection and Erosion Control...

## The state of stress at a point within a soil mass

A major problem in geotechnical analysis is the estimation of the state of stress at a point at a particular depth in a soil mass. A load acting on a soil mass, whether internal, due to its self weight, or external, due to a load applied at the boundary, creates stresses within the soil. If we consider an elemental cube of soil at the point considered then a solution by elastic theory is possible. Each plane of the cube is subjected to a stress, a, acting normal to the plane, together with a...

## Total stress analysis

This analysis, often called the ( > u 0 analysis, is intended to give the stability of an embankment immediately after its construction. At this stage it is assumed that the soil in the embankment has had no time to drain and the strength parameters used in the analysis are the ones representing the undrained strength of the soil (with respect to total stresses), which are found from either the unconlined compression test or an undrained triaxial test without pore pressure measurements....

## 1

Silty clay Gs 2.7 w 30 k 3 x 10 8m s Silty clay Gs 2.7 w 30 k 3 x 10 8m s Height of clay left above gravel after excavation 8 2 6 m Upward pressure from water on base of clay 10 x 10 100 kN m2 Downward pressure of clay 6 x 19.0 114 kN m2 . Downward forces 114 Factor ol safety Upward forces 110 Downward pressure after construction 114-

## Va

Compressibility of the pore water Cv Consider a saturated soil of initial volume V. Then volume of pore water nV where n porosity. Assume a change in total ambient stress A< 73. Assume that the change in effective stress caused by this total stress increment is Acr'j and that the corresponding change in pore water pressure is Aua. Then, Decrease in volume of soil skeleton QVAct'j Decrease in volume of pore water CvnVAua With no drainage these changes must be equal i.e. The compressibility of...

## W

F .-E c'l + W(cos a - ru sec a) tan 4> ' This formula gives a solution generally known as the conventional method which allows rapid determination of F when sufficient slip circles are available to permit the determination of the most critical. For analysing the stability of an existing tip it should prove perfectly adequate. In the case of an earth embankment F is usually considered to be satisfactory if it is not less than 1.25, and for economic reasons it should not be designed for a...

## Rnk

Considering unit volume, the volume of soil that replaced the gravel X, so Volume of gravel omitted where Gg particle specific gravity of excluded gravel. .'. Difference in volume - (1 - Pd Corrected optimum moisture content w where w the optimum moisture content obtained from the test. Even when a gravel correction is applied compaction test results are not representative for a soil with X much greater than 25 per cent. BS1377 mentions that in such cases the CBR mould (a mould 152 mm in...

## Xf X V k

This equation is Laplacian and involves the two co-ordinate variables xt and z. It can be solved by a flow net provided that the net is drawn to a vertical scale of z and a horizontal scale of 2.22 Calculation of seepage quantities in an anisotropic soil and the only problem is what value to use for k. Using the transformed scale a square flow net is drawn and Nf and Nd obtained. If we consider a 'square' in the transformed flow net it will appear as shown in Fig. 2.25a. The same figure, drawn...

## Y

Fig. 2.6 Element in an orthotopic soil. The component of the hydraulic gradient, ix, at the centre of the element (Note that it is of negative sign as there is a head loss in the direction of flow.) The rate of change of the hydraulic gradient ix along the length of the element in the x direction will be Hence the gradient at the face of the element nearest the origin The gradient at the face furthest from the origin is

## T

Hence the shear stress under a 5 m square foundation can be obtained from the bulb of pressure of shear stress for a circular foundation of diameter 5.64 m. These values can be combined if we proportion them to the respective areas (or lengths) The method is approximate but it does give an indication of the shear stress values.

## Vsl

Note As < 70Ct is also the mean value of the three principal stresses of the applied stress system, then < 70Ct ap. The stress systems applied in the triaxial test have already been discussed The compression test < 71 > < 72 03 or > o'2 o'3 The extension test ctj < 02 03 or a < < r'2 ct'3 The Mohr circle diagrams for the tests are illustrated in Fig. 3.25. Representing < 71 by the symbol oa and representing < 72 and < 73 by the symbol or the plane O01A is designated as...

## Ohc

EXERCISE 4.3 The plan of a foundation is given in Fig. 4.16a. The uniform pressure on the soil is 40kN m2. Determine the vertical stress increment due to the foundation at a depth of 5 m below the point X, using Fig. 4.6. Note In order to obtain a set of rectangles whose corners meet at a point, a section of the foundation area is sometimes included twice and a correction made. For this particular problem the foundation area must be divided into six rectangles (Fig....

## Classification and Identification Properties of Soil

In the field of civil engineering, nearly all projects are built on to, or into, the ground. Whether the project is a structure, a roadway, a tunnel, or a bridge, the nature of the soil at that location is of great importance to the civil engineer. Geotechnical engineering is the term given to the branch of engineering which is concerned with aspects pertaining to the ground. Soil mechanics is the subject within this branch which looks at the behaviour of soils in civil engineering....

## Description

Medium dense to dense red brown silty sand and fine gravel Stiff light brown laminated silty clay, with layers of sand Medium dense becoming dense brown sand Compact brown silty Sand with layers of silty clay Dense grey-brown clayey sand with occasional gravel Hard mottled red-brown, grey and green coarse grained basaltic tuff Soft and medium hard weathered mottled red-brown, grey-green basaltic tuff Hard mottled grey-green basaltic tuff Remarks Penetration test continued beyond normal drive...

## Xyi

Fig. 4.13 Contact pressure distribution under a rigid foundation loaded with a uniform pressure, p. Fig. 4.14 Method for determining subsoil stresses beneath a spoil heap (the effect of siope is of course three-dimensional). Fig. 4.14 Method for determining subsoil stresses beneath a spoil heap (the effect of siope is of course three-dimensional). stresses are obtained by addition (Fig. 4.14). The method can be extended to include earth embankments.

## Lj

Clay cutter Fig. 14.2 Clay cutter and sample tube. of dropping the cutter from some 1.5 to 3 m above the soil and is largely carried out by hand, although this practice is going out of fashion and when site conditions are suitable the operation is often powered. In compact sands and gravels water is generally added if the deposit is not already wet. The material is removed by means of a shell which is dropped in a similar manner to the clay cutter it is fitted with a clack (a hinged lid) that...

## Consolidation during construction

A sufficiently accurate solution is generally achieved by assuming that the entire foundation load is applied halfway through the construction period. For large constructions, spread over some years, it is sometimes useful to know the amount of consolidation that will have taken place by the end of construction, the problem being that whilst consolidating the clay is subjected to an increasing load. Figure 10.9 illustrates the loading diagram during and after construction. While excavation is...

## Twodimensional stress paths

As discussed in Chapter 3, the state of stress in a soil sample can be shown graphically by a Mohr circle diagram. In a triaxial compressive test the axial strain of the test specimen increases up to failure and the various states of stress that the sample experiences from the start of the test until failure can obviously be represented by a series of Mohr circles. The same stress states can be represented in a much simpler form by expressing each successive stress state as a point. The line...

## Jurgenson Stress 1934

Point load (Boussinesq Theory, 1885) The simplest case of applied loading has been illustrated in Example 4.2. However, most loads are applied to soil through foundations of finite area so that the stresses induced within the soil directly below a particular foundation are different from those induced within the soil at the same depth but at some radial distance away from the centre of the foundation. The determination of the stress distributions created by various applied loads has occupied...

## Types of foundations

Often termed a continuous footing this foundation has a length significantly greater than its width. It is generally used to support a series of columns or a wall. Generally an individual foundation designed to carry a single column load although there are occasions when a pad foundation supports two or more columns. This is a generic term for all types of foundations that cover large areas. A raft foundation is also called a mat foundation and can vary from a fascine mattress supporting a farm...

## Residual and critical strength states

The stress conditions that apply at the critical state line represent the ultimate strength of the soil (i.e. its critical state strength) and this is the lowest strength that the soil will reach provided that the strains within it are reasonably uniform and not excessive in magnitude. The residual strength of a soil only operates, in the case of clays, after the soil has been subjected to considerable strains with layers of soil sliding over other layers. It is important that the difference...

## Notation Index

The following is a list of the more important symbols used in the text. A Area, pore pressure coefficient As Area of surface of embedded length of pile shaft B Width, diameter, pore pressure coefficient Cc Compression index, soil compressibility D Diameter, depth factor, embedded length of pile Dc, Dq, D7 Depth factors E Modulus of elasticity, efficiency of pile group lCT Vertical stress influence factor Ka Coefficient of active earth pressure K0 Coefficient of earth pressure at rest Kp...

## The model law of consolidation

If two layers of the same clay with different drainage path lengths H, and H2 are acted upon by the same pressure increase and reach the same degree of consolidation in times ti and t2 respectively, then theoretically their coefficients of consolidation must be equal as must their time factors, Tj and T2 This gives a simple method for determining the degree of consolidation in a layer if the simplifying assumption is made that the compression recorded in the consolidation test is solely due to...

## Numerical determination of consolidation rates

When a consolidating layer of clay is subjected to an irregular distribution of initial excess pore water pressure, the theoretical solutions are not usually applicable unless the distribution can be approximated to one of the cases considered. In such circumstances the use of a numerical method is fairly common. A brief revision of the relevant mathematics is set out below. Assuming that f(x) can be expanded as a power series y f(x) ao + aix + a2x2 + a3x3 + anxn f'(x) ai + 2a2x + 3asx2 + 4a4x3...

## Embedded wall

Embedded walls rely on the passive resistance of the soil in front of the lower part of the wall to provide stability. Anchors or props, where incorporated, provide additional support. These walls are made up from a series of interlocking piles individually driven into the foundation soil. Most modern sheet pile walls are made of steel but earlier walls were also made from timber or precast concrete sections and may still be encountered. There are two main types of sheet pile walls cantilever...

## Operative values for f and c for passive pressure

It is generally agreed that, for passive pressures in a granular soil, the operative value of (f> is lower than 4> u the peak triaxial angle obtained from drained tests, particularly for high values of < j> t. With a granular soil fa is most often estimated from the results of some in situ test such as the standard penetration test. It is suggested therefore that values for fa to be used in the determination of passive pressure values, can be obtained from Fig. 6.31 (which is a modified...

## Effective stress analysis

The methods for analysing a slip circle that have been discussed so far can be used to give an indication of the factor of safety immediately after construction has been completed, but they are not applicable in the case of an existing embankment if water pressures are present. However, if an analysis is carried out in terms of effective stress then it can be used to determine F after drainage has occurred or for any intermediate value of ru between undrained and drained, such an analysis...

## Bscs Classification System Chart

A BS cone penetrometer test was carried out on a sample of clay with the following results Cone penetration (mm) 16.1 17.6 19.3 21.3 22.6 Moisture content ( ) 50.0 52.1 54.1 57.0 58.2 The results from the plastic limit test were Test no. Mass of tin Mass of Mass of (g) wet soil + tin dry soil + tin Determine the liquid limit, plastic limit and the plasticity index of the soil. Solution The plot of cone penetration to moisture content is shown in Fig. 1.6. The liquid limit is the moisture...

## Soil Mechanics Calculations

From the force diagram, maximum Pa 190 kN m run of wall, acting at 6 to the normal to the wall. .'. Maximum horizontal thrust on back of wall 190 cos 10 187 kN m run of wall. (b) Coefficients Ka and Kac (Table 6.1) can be obtained by linear interpolation For Cw Cu 1.0 and 0 20 Ka 0.48 for 6 0 For Cw Cu 1.0 and 0 20 Ka 0.40 for < 5 0 .-. Ka 0.44 For Cw Cu 1.0 and 0 20 Kac 1.96 for 8 0 For cw cu 1.0 and 0 20 Kac 1.59 for < 5 0 (20 x 3.75 x 0.44) - (10 x 1.78) 15.2kN m2 20(5 + 3.75)0.44 - 17.8...

## Analytical methods for the determination of the ultimate bearing pressure of a foundation

The ultimate bearing capacity of a foundation is given the symbol qu and there are various analytical methods by which it can be evaluated. As will be seen, some of these approaches are not all that suitable but they still form a very useful introduction to the study of the bearing capacity of a foundation. Consider an element of soil under a foundation (Fig. 8.1). The vertical downward pressure of the footing, qu, is a major principal stress causing a corresponding Rankine active pressure, p....

## British Steel Piling Earth Pressure

By factoring the strength parameters, Ka is increased and Kp is decreased leading to modified pressure distributions relative to those obtained using the gross pressure method. This is advocated by British Steel in the British Steel Piling Handbook (1997) where the net horizontal pressure distribution is used (Fig 7.8f)- The pressure distribution is derived by subtracting the active earth and water pressures from the passive earth and water pressures.

## Contents

1 Classification and Identification Properties of Soil 1 1.1 Agricultural and engineering soil 1 1.2 Engineering definitions 2 1.5 Common types of soil 15 1.6 Soil classification and description 15 1.8 Soil physical relations 30 Exercises 31 2 Soil Water, Permeability and Flow 34 2.2 Flow of water through soils 36 2.3 Darcy's law of saturated flow 37 2.4 Coefficient of permeability (k) 37 2.5 Determination of k in the laboratory 38 2.6 Determination of k in the field 41 2.8 General differential...

## N

Very loose loose medium dense very dense that the significant factors affecting the N value are the relative density of the soil and the value of the effective overburden pressure removed. Various workers have investigated this problem Coffmann (1960), Bazaraa (1967), but the method proposed by Thorburn (1963) now seems to have gained general acceptance, at least in the UK. Thorburn assumed that the original Terzaghi and Peck relationships between N and the relative density corresponded to an...

## Dzi

Tendency of overconsolidated clays towards critical state The question must now be asked Do undrained and drained stress paths for heavily overconsolidated clays reach the critical state line as do normally consolidated and lightly overconsolidated clays In an ideal situation the stress paths of heavily overconsolidated clays will reach the Hvorslev surface and then will continue to move up this surface to the critical state line. But ideal situations rarely occur and a more realistic picture...

## Usa

Commerce Place 350 Main Street Maiden, MA 02148 5018 (Orders Tel 800 759 6102 781 388 8250 Fax 781 388 8255) Login Brothers Book Company 324 Saulteaux Cresent Winnipeg, Manitoba R3J 3T2 (Orders Tel 204 837-2987 Fax 204 837-3116) Blackwell Science Pty Ltd 54 University Street Carlton, Victoria 3053 (Orders Tel 03 9347 0300 Fax 03 9347 5001) A catalogue record for this title is available from the British Library

## Kun

Vesic (1975) suggested that, for the case of a foundation founded in a layer of soft clay which overlies a stiff clay, the ultimate bearing capacity of the foundation can be expressed as where cu the undrained strength of the soft clay and Ncm a modified form of Nc, the value of which depends upon the ratio of the cu values of both clays, the thickness of the upper layer, the foundation depth and the shape and width of the foundation. Values of Ncm are quoted in Vesic's paper. The converse...

## Dolly Pile System

The use of sheet piling, which can be of timber, concrete or steel, for earth retaining structures has been described in Chapter 7. Piled foundations form a separate category and are generally used (i) to transmit a foundation load to a solid soil stratum (ii) to support a foundation by friction of the piles against the soil (iii) to resist a horizontal or uplift load (iv) to compact a loose layer of granular soil. There are two main classes of piles. Derive most of their carrying capacity from...

## Preconsolidation Pressure By British Standard Code

Active earth pressure, 196-8, 211-14, 219-21 activity of a clay, 126, 127 adhesion factor, 303 adsorbed water, 61 aeration zone, 35, 36 air dried soils, 9 air voids line, 388 air voids percentage, 396 allowable bearing pressure, 269, 292, 293, 348, 349 analogy of consolidation settlement, 352 backfill, 223 backfill drainage, 224 back pressure, 102, 103 basalt, 2 base materials, frost susceptibility, 407 bearing capacity coefficients, 275, 279, 280 bearing capacity of a pile, determination of,...

## Construction pore pressures in an earth dam

A knowledge of the induced pore pressures occurring during the construction of an earth dam or embankment is necessary so that stability analyses can be carried out and a suitable construction rate determined. Such a problem is best solved by numerical methods. During the construction of an earth dam (or an embankment) the placing of material above that already in position increases the pore water pressure whilst consolidation has the effect of decreasing it the problem is one of a layer of...

## Bnx

The values of M, N, T and A vary with the type of soil. From Figs 13.6 and 13.8 we see that the values for remoulded Weald clay are approximately M 0.85 N 2.13 T 2.09 and A 0.10. 13.7 Representation of triaxial tests in p'-q-v space The results of drained and undrained triaxial compression tests can be represented in the three-dimensional stress space p'-q-v. For both tests the sample is first consolidated to some point A on the normal consolidation curve corresponding to some particular value...

## Hpw

A (1 p2)(Np,B, + Np2B2 + Np3B3) 3 j)5QQC)75 ( -76 x 50 + -56 x 50 + 0.64 x 30) 1.28m Fox (1948) showed that for deep foundations (z > B) the calculated immediate settlements are more than the actual ones, and a reduction may be applied. If z B the reduction is approximately 25 per cent, increasing to about 50 per cent for infinitely deep foundations. Most foundations are shallow, however, and although this reduction can be allowed for when a layer of soil is some depth below a foundation, the...

## Soil Mechanics 2 Worked Examples

An 8 m thick layer of silty clay is overlaying a gravel stratum containing water under artesian pressure. A stand-pipe was inserted into the gravel and water rose up the pipe to reach a level of 2 m above the top of the clay Fig. 2.12 . The clay has a particle specific gravity of 2.7 and a natural moisture content of 30 per cent. The permeability of the silty clay is 3.0 x 10 8 m s. It is proposed to excavate 2 m into the soil in order to insert a wide foundation which, when constructed, will...

## E P Curve Overconsolidated Clay

By way of illustration let us use the test results of Example 9.4 together with the following information Original dimensions of test sample 75 mm diameter, 20 mm thickness Mass of sample after removing complete from consolidation apparatus at end of test and drying in oven 135.6 g. Ms 135.6 g A x 752 4418 mm2 Hs -- 11.58mm Hence the void ratio to pressure relationship can be found. Pressure kN m2 Thickness H e - Note Such close agreement between the two methods for determining the e-p...

## Compaction Mould Less Its Collar And Base

The following results were obtained from a compaction test using the 2.5 kg rammer. Mass of mould wet soil g 2783 3057 3224 3281 3250 3196 Moisture content per cent 8.1 9.9 12.0 14.3 16.1 18.2 The weight of the compaction mould, less its collar and base, was 1130 g and the soil had a particle specific gravity of 2.70. Plot the curve of dry density against moisture content and determine the optimum moisture content. On your diagram plot the lines for 5 per cent and 0 per cent air voids. The...

## Contact pressure

Contact pressure is the actual pressure transmitted from the foundation to the soil. In all the foregoing discussions it has been assumed that this contact pressure value, p, is uniform over the whole base of the foundation, but a uniformly loaded foundation will not necessarily transmit a uniform contact pressure to the soil. This is only possible if the foundation is perfectly flexible. The contact pressure distribution of a rigid foundation depends upon the type of soil beneath it. Figures...

## Z

Fig. 10.19 Popular arrangements of sand drains. Spacing of drains depends upon the type of soil in which they are placed. Spacings vary between 1.5 and 4.5 m. Sand drains are effective if the spacing, a, is less than the thickness of the consolidating layer, 2H. Arrangement of grid sand drains are laid out in either square Fig. 10.19a or triangular Fig. 10.19b patterns. For triangular arrangements the grid forms a series of equilateral triangles the sides of which are equal to the drain...

## The effect of cohesion on passive pressure

Rankine's theory has been developed by Bell 1915 for the case of a frictional cohesive soil. His solution for a soil with a horizontal surface is Pp 7h tan2 Us 1 J 2c tan U5 1 As has been discussed, a clay has a non-linear stress-strain relationship and its shear strength depends upon its previous stress history. Add to this the complications of non-uniform strain patterns within a passive resistance zone and it is obvious that any design approach must be an empirical approach based on...

## Find The Center Of The Critical Circle And Toe Circle Failure

Fig. 5.10 Method for determining the centre of the critical circle. Fig. 5.10 Method for determining the centre of the critical circle. the critical circle will be. Note that the value of F is more sensitive to horizontal movements of the circle's centre than to vertical movements. To determine a reasonable position for the centre of a first trial slip circle is not easy, but a study of the various types of slips that can occur is helpful it should be remembered, however, that the following...

## Review And Exercise Of The Soil Mechanics

In a falling head permeameter test on a fine sand the sample had a diameter of 76 mm and a length of 152 mm with a stand-pipe of 12.7 mm diameter. A stop watch was started when h was 508 mm and read 19.6 s when h was 254 mm the test was repeated for a drop from 254 mm to 127 mm and the time was 19.4 s. Determine an average value for k in m s. A sample of coarse sand 150 mm high and 55 mm in diameter was tested in a constant head permeameter. Water percolated through the soil under a head of 400...

## Soil Water Permeability and Flow

This is the term used to define all water found beneath the Earth's surface. The main source of subsurface water is rainfall, which percolates downwards to fill up the voids and interstices. Water can penetrate to a considerable depth, estimated to be as much as 12000 metres, but at depths greater than this, due to the large pressures involved, the interstices have been closed by plastic flow of the rocks. Below this level water cannot exist in a free state, although it is often found in...

## Settlement of a foundation

Probably the most difficult of the problems that a soils engineer is asked to solve is the accurate prediction of the settlement of a loaded foundation. The problem is in two distinct parts i the value of the total settlement that will occur, and ii the rate at which this value will be achieved. When a soil is subjected to an increase in compressive stress due to a foundation load the resulting soil compression consists of elastic compression, primary compression and secondary compression. This...

## Compaction and Soil Mechanics Aspects of Highway Design

The process of mechanically pressing together the particles of a soil to increase the density compaction is extensively employed in the construction of embankments and in strengthening the subgrades of roads and runways. Many workers in the field talk about consolidating a soil when they really mean compacting it. Strictly speaking, consolidation is the gradual expulsion of water from the voids of a saturated cohesive soil with consequent reduction in volume, whereas compaction is the packing...

## Immediate settlement

If a saturated clay is loaded rapidly, the soil will be deformed during the load application and excess hydrostatic pore pressures are set up. This deformation occurs with virtually no volume change, and due to the low permeability of the clay, little water is squeezed out of the voids. Vertical deformation due to the change in shape is the immediate settlement. This change in shape is illustrated in Fig. 9.1a, where an element of soil is subjected to a vertical major principal stress increase...

## Wa

Fig. 1.10 Water and air contents in a soil. The degree of saturation is simply Volume of water Vw Volume of voids Vv 1.7.3 Particle specific gravity Gs The specific gravity of a material is the ratio of the weight or mass of a volume of the material to the weight or mass of an equal volume of water. In soil mechanics the most important specific gravity is that of the actual soil grains and is given the symbol Gs. From the above definition it is seen that, for a soil sample with volume of solids...

## Soil Mechanics Exercises

A proposed cutting is to have the dimensions shown in Fig. 5.32. The soil has the following properties lt gt 15 , c 13.5 kN m2, 7 19.3 kN m3. Determine the factor of safety against slipping for the slip circle shown i ignoring tension cracks and ii allowing for a tension crack. Answers i 1.7, ii 1.6 EXERCISE 5.2 Investigate the stability of the embankment shown in Fig. 5.33. The embankment consists of two soils, both with bulk densities of 19.3 kN m3 the upper soil has c 7.2kN m2 and 0 30 ,...

## Steinbrenner Soil Mechanics

A 4.5 m square foundation exerts a uniform pressure of 200kN m2 on a soil. Determine i the vertical stress increments due to the foundation load to a depth of 10 m below its centre and ii the vertical stress increment at a point 3 m below the foundation and 4 m from its centre along one of the axes of symmetry. i The square foundation can be divided into four squares whose corners meet at the centre O Fig. 4.7a . ii This example illustrates how the method can be used for points outside the...