of clays
Short term stability
`One of the main reasons for the late development of soil mechanics as a systematic branch of civil engineering has been the dif®culty in recognizing that the difference between the shear characteristics of sand and clay lies not so much in the difference between the frictional properties of the component particles, as in the very wide difference ± about one million times ± in permeability. The all- round component of a stress change applied to a saturated clay is thus not effective in producing any change in the frictional component of strength until a suf®cient time has elapsed for water to leave (or enter), so that the appropriate volume change can take place.' Bishop and Bjerrum (1960)
The interaction of soil structure and pore water
The uniquely time dependent engineering behaviour of ®ne-grained saturated soils is derived from the interaction of the compressible struc- tural soil skeleton and the relatively incompressible pore water. Rapid changes in external loading do not immediately bring about a volume change due to the viscous resistance to pore water displacement. There- fore, the soil structural con®guration does not immediately change and thus, by Hooke's Law, the structural loading does not change.
However, while the compressible soil structure requires a volume change to change its loading, the relatively incompressible pore water may change its pressure without much volume change. The external loading change is therefore re¯ected by a change in pore pressure. With time, this `excess' pore pressure will dissipate, volume change occurring by pore water ¯ow until the consequent change in structural con®guration brings the struc- tural loading into equilibrium with the changed external loading.
This process may be examined by the spring±dashpot analogy demon- strated in Fig. 2.1.
The soil structure is modelled by a spring, the soil voids modelled by the chamber under the piston and the soil permeability modelled by the lack
of ®t of the piston in the cylinder ± thus a soil of high permeability is modelled by a piston which allows a lot of leakage whereas a soil of low permeability is modelled by a piston which allows very little leakage. It is assumed the piston is frictionless. Pore pressure is indicated by the water level in a standpipe whose bore is very much less than that of the piston. Initially the piston is uniformly loaded by a loading intensity p including the weight of the piston.
The instant immediately after t 0 rapidly increasing the loading by p, the spring (soil structure) is unaffected because insuf®cient time has elapsed for viscous ¯ow past the piston to reduce the volume of the chamber (pores) under the piston and thus allow the spring to compress further and carry some more load. The loading increment, p, is thus initially carried by an equal increase in pore pressure. As time elapses, ¯ow takes place, the piston displacing downwards, the applied loading increment p being shared between the spring and the pore pressure. The hydraulic gradient causing ¯ow from the area of high pore pressure under the piston to the area of zero pore pressure over the piston, is itself reduced by the ¯ow as the spring is allowed to compress further and take more load. The law of diminishing returns thus applies and there is an exponential decay in pore pressure and change in length of the spring. Ultimately, the pore pressure dissipates to the equilibrium value and the total load is fully supported by the spring.
The loading condition
If a saturated clay is loaded, such as may occur in soils supporting building foundations and earth embankments (Fig. 2.2), an overall increase in mean total stress occurs (Fig. 2.3(a)). In a ®ne-grained soil like clay, the viscous resistance to pore water expulsion prevents the soil structure from rapidly contracting. In the short term loading condition, therefore, there is a change in effective stress due to shear strain only together with an increase Fig. 2.1 Spring±dashpot analogy for soil consolidation
Equilibrium ground water level h P End of loading piezometric level
Fig. 2.2 Pore pressure generated on a potential slip surface by embankment loading
Height of fill Shear stress on slip line through P Time Time Time Time (a) (b) (c) (d) P ore w ater pressure h γw Eff ectiv e stress at P F actor of saf ety Rapid construction Pore pressure dissipation Pore pressure equilibrium at P
Fig. 2.3 Variation with time of the shear stress, local pore pressure, local effective stress, and factor of safety for a saturated clay foundation beneath an embankment ®ll (after Bishop and Bjerrum, 1960)
in pore pressure (Fig. 2.3(b) and (c)). With time, this excess pore pressure is dissipated by drainage away from the area of increased pore pressure into the surrounding area of lower pore pressure unaffected by the construction. This ¯ow of pore water causes a time dependent reduction in volume in the zone of in¯uence, the soil consolidating and the soil structure stiffening, giving rise to decreasing settlement and increasing strength. The minimum factor of safety occurs in the short term undrained condition when the strength is lowest (Fig. 2.3(d)).
In this undrained condition the stressed zone does not immediately change its water content or its volume. The load increment does, however, distort the stressed zone. The effective stresses change along with the change in the shape of the soil structure. Eventually the changes in the structural con®guration may no longer produce a stable condition and the consequent instability gives rise to a plastic mechanism or plastic ¯ow and failure occurs.
The strength is determined by the local effective stresses at failure normal to the failure surfaces. These are conditioned by and generated from the structural con®guration of the parent material (which is itself con- ditioned by the preloading in situ stresses) and its undrained reaction to deformation. A ®rst step, therefore, in ful®lling the complex similitude requirements that accordingly arise is to ensure that the shear test used to ®nd the strength is effectively undrained.
The undrained shear test may be used to give a direct measure of shear strength, namely the undrained shear strengths su, or it may be used to give an indirect measure of shear strength, if the pore water pressures are known together with c0 and tan 0. It is therefore possible to analyse the stability of the loaded soil by:
(i) using the undrained shear strength, su, in a total stress analysis, or (ii) using the effective stress shear strength parameters c0and tan 0in
an effective stress analysis.
The use of (ii) requires an estimation of the end of construction pore pressures in the failure zone at failure, whereas the use of (i) requires no knowledge of the pore pressure whatsoever.
In general civil engineering works, the soil loading change is applied gradually during the construction period. The excess pore pressures generated by the loading are thus partially dissipated at the end of con- struction. The end of construction pore pressures and the increased in situ shear strength can be measured on site if the resulting increased economy of design warrants the ®eld instrumentation and testing. On all but large projects this is rarely the case. In addition, the loading is localized, allowing the soil structure to strain laterally, the soil stresses dis- sipating and the principal stresses rotating within the zone of in¯uence.
In the absence of sound ®eld data on the end of construction shear strengths and pore pressures and in the face of analytical dif®culties under local loading, an idealized soil model possessing none of these dif- ®culties is usually invoked for design purposes. This consists of proposing that the end of the construction condition corresponds to the idealized case of the perfectly undrained condition. Here the soil is considered to be fully saturated with incompressible water and is suf®ciently rapidly loaded that, in the short term, it is completely undrained. Prefailure and failure distortions of the soil mass in the ®eld are, by implication if not by fact, simulated by the test measuring the undrained shear strength. It follows that if the shear strength of the soil structure is determined under rapid loading conditions prior to construction, this undrained shear strength may be used for short term design considerations. No knowledge of the pore pressures is required, the undrained shear strength being used in a total stress analysis (the so-called 0 analysis). A note on the 0 analysis
`It is a simple task to place a clay specimen in a shearing apparatus and cause a shear failure. A numerical value of shearing strength, which has acceptable precision, may readily be obtained if proper technique, a representative sample, and a satisfactory apparatus are used. The point which has too often been insuf®ciently appre- ciated by testing engineers is that the shearing strength, both in the laboratory specimen and in the clay in nature, is dependent on a number of variables. Before meaning can be attached to shearing strengths determined in the laboratory, the engineer who is to inter- pret the test results must have at his command an understanding of the factors or variables on which the strength is dependent, and he must make adjustments for every factor which occurs differently in the test than in nature.'
D. W. Taylor (1948)
The concept of the 0 analysis
The 0 analysis is a stability analysis which derives its name from the total stress interpretation of the unconsolidated±undrained triaxial test. In this test, three test specimens of saturated soil taken from the same core barrel (usually clay, but it may be any soil) are tested in unconsoli- dated±undrained triaxial compression at three different cell pressures. The resulting compression strengths (deviator stresses at failure) are the same because the initial isotropic state of effective stress of each test specimen is unchanged by applying cell pressure. Plotting Mohr's circles in terms of total stress (the effective stresses are not known) give circles of the same diameter (Fig. 2.4). An envelope to the circles is, of course,
a horizontal straight line. Interpreting these results using Coulomb's (1773) equation,
f c tan 2:1
gives f c cu su the undrained shear strength 2:2
and u 0 2:3
This apparent insensitivity of shear strength to loading changes led Skempton (1948) to conclude that shear strength was uniquely dependent on water content and if water content did not change then strength did not change. Accordingly, it was believed at that time that as soil strength was unaffected by loading changes in the short term, the strength measured before construction could be used to predict the stability after construc- tion. Thus, the 0 analysis emerged and appeared to work well for both foundations and cuts. Analysis of failed cuts using the 0
method (Lodalen, Norway; Frankton, New Zealand; Eau Brink,
England) gave factors of safety of unity thereby apparently con®rming the validity of the method. Amazingly, these early case histories gave fortuitously atypical results and it was eventually realized that the critical long term stability of cuts could not be predicted using the 0 analysis because the strength diminishes with long term swelling.
Thus for cuts, long term or `drained'strengths must be used and this can be predicted in terms of effective stress using the Terzaghi±Coulomb equation:
sd c0 ÿ u tan 0 2:4
provided the long term pore water pressures are known (they normally are because the ground water regime, initially disturbed by the construction activity, has regained a steady state).
For foundations, however, critical stability is in the short term because the strength increases with consolidation in the long term. In the short term the pore water pressures are unknown and thus an effective stress analysis cannot be made unless pore pressures can be estimated. Accord- ingly, a 0 analysis must be carried out using the undrained shear strength su.
τ
σ φ = 0
c = su
Fig. 2.4 Unconsolidated±undrained triaxial test Mohr's circles showing 0 failure envelope
The applicability of the 0 analysis
From the principle of effective stress it is known that effective stress (and hence strength) will not change provided the soil structure does not deform. This is the case in the unconsolidated±undrained triaxial test during the cell pressure increment stages which are isotropic. The combi- nation of the undrained condition (no volumetric strain) and the isotropic stress change (no shear strain) ensures no deformation and hence no change in the initial state of effective stress. Thus, the 0 condition corresponds to a `no change in the initial state of effective stress' condition. Of course, the strength of the soil skeleton is mobilized in the unconsolidated±undrained triaxial test by axial deformation changing the effective stresses ± it is just that this strength is dependent on the initial state of effective stress.
From the principle of similitude it follows that the concept inherent in the 0 condition (i.e. no change in strength if initial state of effective stress is unchanged), and demonstrated in the unconsolidated±undrained triaxial test, must be matched to a corresponding ®eld condition if the sumeasured in this way is to be used in a 0 analysis to predict the ®eld stability. This means that the analysis is only wholly appropriate to a ®eld condition where the construction activity is both undrained and causes an isotropic increase in total stress. This occurs in the laboratory, for example, in the oedometer at the instant of loading change. In the ®eld this condition may be approximated by rapid global loading such as may occur in the short term at shallow depth beneath the centre of a wide embankment. Towards the toe of the embankment shear strain will occur with conse- quent change in effective stress, thereby progressively invalidating the concept inherent in the 0 analysis. The extent to which this occurs may or may not be signi®cant. Certainly, where narrow foundations such as strip footings are concerned, shear strains will occur throughout the zone of in¯uence and so make the 0 analysis not strictly appropriate. Accordingly, high factors of safety on shear strength (typically F 3) are taken to deal with this discrepancy and with any other factors causing a lack of similitude.