9

Soil Mechanics C R I Clayton MSc, PhD, CEng, MICE Reader in Geotechnical Engineering, University of Surrey

Contents 9.1

The basics of soil behaviour 9.1.1 Effective stress 9.1.2 Shear strength 9.1.3 Permeability 9.1.4 Consolidation

9/3 9/3 9/3 9/4 9/5

9.2

Design and limit states in soil mechanics and foundation engineering

Appendix 9.1 A9.1.1 A9.1.2 A9.1.3 A9.1.4 A9.1.5

Laboratory testing of soils Soil classification: physical Soil classification: chemical Soil compaction Strength tests Consolidation tests

9/29 9/30 9/32 9/32 9/33 9/34

9/6

Appendix 9.2 A9.2.1

Pile capacities Groups of piles

9/35 9/35

Appendix 9.3 A9.3.1 A9.3.2 A9.3.3 A9.3.4 A9.3.5 A9.3.6 A9.3.7 A9.3.8 A9.3.9 A9.3.10

Ground improvement Drainage and water lowering Vertical drains to accelerate settlement Exclusion of groundwater Injection processes: grouting Reinforced earth Geotextiles Ground anchors Deep ground improvement Shallow compaction Soil stabilization

9/37 9/37 9/39 9/39 9/40 9/41 9/42 9/42 9/42 9/43 9/43

9.3

Foundations 9.3.1 Bearing capacity of shallow foundations 9.3.2 Bearing capacity of deep foundations 9.3.3 Settlement 9.3.4 Settlement of granular soils 9.3.5 Depth corrections

9/7 9/7 9/9 9/10 9/15 9/16

Earth pressure 9.4.1 Active and passive conditions 9.4.2 Active pressure 9.4.3 Passive resistance 9.4.4 Distribution of pressure 9.4.5 Strutted excavations 9.4.6 Anchored bulkheads 9.4.7 Overall stability

9/17 9/17 9/18 9/20 9/20 9/20 9/21 9/22

9.5

The stability of slopes 9.5.1 Stability analysis

9/22 9/23

9.6

Seepage and flow nets 9.6.1 Construction of flow nets 9.6.2 Examples of hydraulic problems by flow nets

9/27 9/28

Definitions of terms used in soil mechanics

9/29

9.4

9.7

References

9/44

Bibliography

9/45

Acknowledgements

9/45

9/29

This page has been reformatted by Knovel to provide easier navigation.

9.1 The basics of soil behaviour In engineering terms, soil is the generally softer, weaker and more weathered material overlying rock. All soils consist of solid particles assembled in a relatively loose packing. The voids between the particles may be filled completely with water (fully saturated soils) or may be partly filled with water and partly with air (partly saturated soils). Soil and rock materials can, very simply, be divided into the groups shown in Table 9.1. The primary engineering problems which we attempt to solve in soil mechanics are those of predicting the strength, compressibility and time-dependent compression of soil materials. For this it is necessary to understand the principle of effective stress. 9.1.1 Effective stress Soil can be considered as a two-phase system consisting of a solid phase—the skeleton of soil particles—and a fluid phase— water plus air in a partly saturated soil, and water alone in a saturated soil. It follows that the normal stress across a plane within a soil mass will have two components: (1) an intergranular pressure, known as the effective pressure or effective stress; and (2) a fluid pressure known as the pore pressure or neutral pressure u. The sum of these will constitute the total normal stress. The volume change characteristics and the strength of a soil are controlled by the effective stress, the pore pressure being significant only in so far as it determines the magnitude of the effective stress for a given total stress. The simplest illustration of pore pressure and effective stress is given by consideration of the vertical stresses acting on a horizontal plane at a depth h under equilibrium conditions with a horizontal water table. The total vertical stress a is given by the weight per unit area of soil and water above the plane: o = yh

(9.1)

where y is the bulk density of the soil, i.e. its total weight/unit volume (see section 9.7 for a definition of terms). The pore pressure will be the water pressure, and if the plane is at a depth hw below the water table then u = hw-yw. The effective vertical stress is the difference between these: a' = a- u

The excess pore pressure, positive or negative, will dissipate with time, the rate at which equilibrium pore pressure conditions are re-established being governed by the permeability of the soil. In coarse grained granular soils, such equilibrium conditions will be achieved immediately and changes in effective stress are equal to changes in total stress. At the other limit, with clays of low permeability, equilibrium conditions may take considerable time, up to tens of years, to be re-established. The relation between pore pressure change and the change in principal stresses can be expressed by the use of pore pressure parameters A and B. The basic relationship is in terms of the major and minor principal stresses, a, and a,: Au = B[Aa, + A(Aa1 - Aa,)]

(9.3)

It is also useful to relate the pore pressure change to the change in deviator stress (Ao\ — Aa,) alone and also to the change in the major principal stress (AaJ. For these purposes, two further parameters A and B are used as follows: Au = B-Aa, + A (Aa} — Aa,)

or Au = B-Aa,

^^

If the soil structure behaved in an elastic manner, the values of the pore pressures could be established theoretically, e.g. A would have a value of 1/3. However, soils behave nonelastically and A can have values ranging between +1.3 and -0.7 (values at failure in a triaxial compression test). Typical values of the pore pressure parameters are given by Bishop and Henkel.2 For a full discussion of the parameters see Skempton.1 It is the effective stress, rather than the total stress, which controls the key properties of strength and compressibility and, to a certain extent, permeability.

9.1.2 Shear strength Shear strength of a soil is commonly thought of as having two components: cohesion and frictional resistance. Clays are often described as cohesive soils in which the shear strength or cohesion is independent of applied stresses, and sands and gravels are described as noncohesive or frictional soils in which the shearing resistance along any plane is directly proportional to the normal stress across that plane:

(9.2)

s=p-tan In partly saturated soils, there is a pore air pressure wa as well as a pore water pressure MW and the effective stress Equation (9.2) is then modified as follows: a = (a - ua) + x(u.d - uJ

The concepts of cohesion and friction were combined in Coulomb's equation for the shear strength of soil:

(9.2a)

The parameter % is related to the degree of saturation Sr. For full saturation, /= 1 and Equation (9.2a) reduces to (9.2). Equation (9.2a) is rarely used in practice. A change in total stresses arising from a change in external loading conditions will give rise to a change Au in pore pressure.

(9.5)

s = c+p-tan

(9.6)

where c is the cohesion and is the 'angle of internal friction'. Such simple concepts are, however, inadequate to deal with the complex problem of the shear strength of soils. The early history of the study of shear strength is somewhat confused.

Table 9.1 A simple grouping for soils and rocks

Organic materials, e.g. peat Cohesive materials, e.g. clay Granular soils, e.g. silts, sands and gravels Rocks

Strength

Compressibility

Speed of drainage

Very low Low-medium Medium-high Very high

Very high High Low Very low

Generally rapid Slow Very rapid Often rapid

Attempts were made to represent the shear strength of a soil by the envelope to a Mohr circle diagram of stress,3 the intercept on the vertical axis being taken as cohesion c, and the slope of the envelope being taken as the friction angle (f>. It was found that, except in sands and gravels, the results for a given soil varied considerably depending on the test procedure used, particularly the rate of testing and the conditions of drainage of the specimens during test. However, following the realization that the strength of a soil is governed by the effective stress, it was possible to achieve a better understanding of the shear strength characteristics of soils. The shear strength can be expressed as: Tf=c' + (a-u)tan'

(9.7)

where c' and ' the angle of shearing resistance and u the pore water pressure. The Mohr circle diagram can be plotted in terms of effective stress, with c' as the cohesion intercept and ' as the slope of the envelope (Figure 9.1). In terms of effective principal stresses in the Mohr diagram the Coulomb failure criterion may be expressed as: (cr; - CT^) = sin (f>'(o\ + crj) - 2c' cos '

(9.8)

and if c' is zero, then: a; = )/(l+O

The solution of the consolidation equation has been given by Taylor3 and values have been tabulated for the degree of consolidation U against the time factor T, where: T=cvt/H2

9.1.4 Consolidation

cJ2u/dz2 = du/dt

where e is the void ratio and p the effective pressure.

(9.18)

(9.19)

and H is the length of the drainage path. Values of cv and mv are determined by laboratory tests known as oedometer, or consolidation, tests. The relationship between the degree of consolidation, C/, and the time factor T is dependent on the initial distribution of excess pore water pressure. Figure 9.3 gives a plot of U against / for various ratios of the initial excess pore pressure at the top and bottom of the compressible stratum w,/M 2 . The cases given are all for single drainage. For double drainage (i.e. where drainage can take place at the top and bottom of the layer) values corresponding to uju2 — I can be used for all ratios of initial pore pressure, but it should be noted that in the double drainage case, H is taken as only half of the layer thickness. One-dimensional drainage is seldom fully realized in practice and for important calculations, particularly where the loaded area is small in comparison with the thickness of the compressible stratum, two- or three-dimensional consolidation should be considered.6-7 Furthermore, in many deposits, lateral permeability can be up to two orders greater than vertical owing to the presence of a laminar structure of thin layers and partings of silt and fine sand. This will have a very marked effect on rate of consolidation.8 Problems involving a number of layers having different consolidation characteristics have been solved numerically using the finite-difference method.9 Methods of test to obtain the soil parameters described in the previous sections are detailed in Appendix 9.1.

Consolidation U (%)

Values of V

Time factor 7" Figure 9.3 Values of time factor T 9.2 Design and limit states in soil mechanics and foundation engineering

(4) Geotechnical calculation, associated with changes in structural design, to achieve maximum economy while avoiding unacceptable behaviour of the structure.

Unlike virtually all other materials dealt with by civil engineers during the course of their work, soil is naturally occurring. It is inherently variable, not only from site to site but also at different levels and plan locations at any one site. The extent of its variability can be judged by examining the typical limits of some of its most important properties:

Table 9.2 Ground problems and low-rise building. (After Building Research Establishment (1987) Site investigation for low-rise building: desk studies. BRE Digest Number 318. HMSO, London)

Undrained shear strength cu Coefficient of permeability k Coefficient of compressibility m v

5-300 kN/m 2 10 2-10"10 m/s 0.01-3.00 m 2 /MN

If the variability of soil is to be understood and allowed for, then a knowledge of geology and the processes leading to the formation and induration of the soil will be important. For any single soil type it is rarely reasonable to assume that the soil is uniformly variable, in the sense of conforming to a single Gaussian distribution for a given soil property, or that the full ranges of its properties are known. The basic steps involved in soil mechanics design are: (1) Arbitrary division of the soil into layers thought to have similar engineering behaviour. This process is carried out during site investigation (see Chapter 11, and Clayton, Simons and Matthews10) using sample description and classification testing. Approximate assessment of the principal soil mechanics parameters (e.g. undrained strength) for each soil group. (2) Envisaging all the mechanisms by which the structure-soil combination may lead to a limit state for the structure (e.g. the structure may fail to perform as required because of foundation bearing capacity failure, excess differential settlement, chemical attack on foundations, etc.). Table 9.2 lists some of these factors as they affect low-rise construction. (3) Testing of soil, both in situ and in the laboratory, to obtain detailed parameters suitable for sound geotechnical engineering calculations in order to assess the risk of 'failure' by all of the mechanisms envisaged in (2) above.

Differential settlement or heave of foundations (or floor slabs) Soft spots under spread footings on clays Growth or removal of vegetation on shrinkable clays Collapse settlements on pre-existing made ground Mining subsidence Self-settlement of poorly compacted fill Floor slab heave on unsuitable fill material Soil failure Failure of foundations on very soft subsoil Instability of temporary or permanent slopes Chemical processes Groundwater attack on foundation concrete Reactions due to chemical waste or household refuse Variations during construction Removal of soft spots to increase depth of footings Dewatering problems Piling problems

Geotechnical engineers recognize an important division between soils which drain rapidly (e.g. silts, sands, gravels) and those which are slow-draining (e.g. clays and clayey soils). In the case of free-draining, noncohesive soils the important consequence of their rapid dissipation of excess pore water pressures is that they undergo increasing effective stress as load is applied; therefore, their strength increases as shear stresses brought about by loading also increase. The consequence is that when foundations are placed on granular soils, bearing capacity is rarely a problem.

Cohesive soils, on the other hand, do not drain rapidly; loading or unloading leads to excess pore water pressures which may take years to dissipate. For these materials the geotechnical engineer recognizes two types of loading which lead to critical conditions at two different times during the life of the structure. Consider an element of soil beneath a foundation constructed on a clay foundation. As the loads are applied to the foundation during the relatively rapid process of constructing the superstructure of the building, the shear stress applied to the soil is increased. Because of the increase in load applied to the soil, excess pore pressures develop. Because clay is slow-draining, the excess pore pressures do not dissipate significantly, the effective strength does not change, and the shear strength of the soil remains constant. Thus, the factor of safety against bearing capacity failure decreases up to the end of the construction (Figure 9.4(a)), after which it increases. Normal practice, for almost all cases where a load increase is applied to the soil, is therefore to calculate a so-called 'short-term' factor of safety using the initial undrained shear strength of the soil combined with the structural loads and bearing pressures expected from the completed structure. In those cases where unloading takes place (Figure 9.4(b)), the same logic leads to the conclusion that the critical time may be many years after the end of construction, in the 'long-term', once the pore pressures once again come to equilibrium. Examples, of unloading situations include excavated slopes and retaining walls. In these cases, the shear strength used in calculations must take into account the changes in pore pressure and effective stress that have occurred. For this reason, longterm calculations are carried out using effective strength parameters.

9.3 Foundations There are two ways in which a foundation can fail to perform satisfactorily: (1) by shear failure; and (2) by settlement. In the first case, a surface of rupture is formed in the soil, the foundation settles considerably and probably tilts to one side and heaving of the soil occurs on one or both sides of the foundation. In the second case, failure of the soil in shear does not occur, but-the existing deformations are large enough to cause failure of the structure which the foundation is supporting. Failure by settlement is therefore a function of the particular structure as well as the underlying soil. Skempton and Macdonald11 have given a criterion for framed buildings based on angular distortion which is expressed by the ratio of differential settlement, 6, to the distance /, between two points, usually the column positions. From a detailed study of field data, a limiting value of djI= 1/300 has been determined. More flexible structures, oil tanks for example, may undergo considerably greater settlements without sustaining damage. On the other hand, some sensitive machinery and stiff reinforced concrete slabs will tolerate very little settlement (see Chapter 17). The ultimate bearing capacity of a foundation is the value of the net loading intensity at which the ground fails in shear. Before discussing bearing capacity, several definitions are necessary. (1) The gross loading intensity, /?, is the pressure due to the applied load and the total weight of foundation, including any backfill above the foundation. (2) The net loading intensity, /?„, is the gross foundation pressure less the weight of material (soil and water) displaced by the foundation (and by the backfill above the foundation). Alternatively, the net pressure can be considered as equal to

the gross pressure less the total overburden pressure, Pn=P- P0(3) The safe bearing pressure is the ultimate bearing capacity divided by the factor of safety, qs = qJF. (4) The allowable bearing pressure, ?a, is less than, or equal to, the safe bearing capacity, depending on the settlements which are expected and which can be tolerated. The term 'presumed bearing value' was introduced in CP 2004,l2 and was defined as the net loading intensity considered appropriate to the particular type of ground for preliminary design purposes. Table 9.3 gives the current presumed bearing values from BS 8004.13 9.3.1 Bearing capacity of shallow foundations There are two groups of methods of determining ultimate bearing capacity: (1) analytical methods; and (2) graphical methods. The graphical methods are very flexible and will cover any conditions likely to be found in practice, but they are rather cumbersome in use. The analytical techniques, which are only strictly applicable in cases in which the soil is uniform, are quicker and easier to use, and therefore are the most often used. The most general formula for the ultimate bearing capacity of a strip footing is that of Terzaghi,14 which in terms of effective stress is: •-EO^M";

, ~ . (934) Q A

where zx is the thickness of the xth layer, Jav is the average vertical stress increase in the jcth layer due to foundation or embankment loading, Cc is the compression index, e0 is the initial voids ratio of the jcth layer, and P'0 is the initial effective vertical stress at the centre of the .xth layer.

Angle of shearing resistance 0 (deg) Figure 9.6 Berezantsev's bearing capacity factor /Vq

Net pressure q Heave

The increase in vertical stress at any level, due to a flexible foundation or embankment loading, can be obtained from elastic theory. Boussinesq25 gave the following equation for the vertical stress increase at depth z due to a point load P on the surface of a semi-infinite solid:

'