Considerations of similitude
From the foregoing section it was seen that a given soil shear test specimen may have many strengths depending on whether the test specimen is undrained or drained, and whether the shearing takes place before, during or after either consolidation or swelling. In addition, the measurement of strength in shear tests is in¯uenced signi®cantly by test type, e.g. triaxial, in situ shear vane, plate bearing, penetrometer, etc.; sampling disturbance; size of test specimen or test zone; orientation of the test specimen or test zone, i.e. the effects of anisotropy; time to undrained failure; time between sampling and testing (Simons and Menzies, 2000).
The selection of appropriate shear strength data for the prediction of ®eld stability therefore requires some guiding principle unless empirical corrections based on experience are to be made. Apart from such corrections the use of shear test data in stability analyses is appropriate only provided there is similitude between the shear test model, the analytical model and the ®eld prototype. The ®rst steps, therefore, in ensuring similitude between test model and ®eld prototype require that:
. prior to testing the effective stresses and structural con®guration of the test specimen or zone are identical to those in situ before testing disturbance, i.e. the soil specimen or zone is undisturbed
. the size of the test specimen or test zone is representative of the soil in the mass
. during the test the structural distortions and rates of distortion of the soil mass are similar to those which would arise in the ®eld
. at failure in the test, the distortions and rates of distortion of shear surfaces are similar to those which would arise in a full-scale failure. Finally, of course, the principle of similitude requires a realistic analyti- cal model in which the shear test data may be used to give an estimate of the stability of the ®eld prototype. Of considerable importance in this respect is the phenomenon of progressive failure.
Short term and long term stability
The stability of foundations and earthworks in saturated ®ne-grained soil is time dependent. This is because the average sizes of the inter- connecting pores are so small that the displacement of pore water is retarded by viscous forces. The resistance that a soil offers to water ¯ow may be measured in terms of the soil permeability, which is the velocity of ¯ow through the soil under a unit hydraulic gradient.
Permeability is the largest quantitative difference between soils of different time dependent stability (Bishop and Bjerrum, 1960). Asand and a normally-consolidated clay, for example, may have similar effective stress shear strength parameters c0and tan 0but the permeability of the clay is several orders of magnitude lower. The stability of the clay is thus time dependent whereas the more permeable sand reacts to loading changes almost immediately.
If saturated clay is loaded, as may occur in soils supporting building foundations and earth embankments, an overall increase in mean total stress occurs. 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 in pore pressure. 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 thus occurs in the short term undrained condition when the strength is lowest.
If saturated clay is unloaded, as may occur in an excavation or cutting, an overall reduction in mean total stress occurs. In a ®ne-grained soil like clay, the viscous resistance to pore water ¯ow prevents the soil structure, relieved of some of its external loading, from rapidly expanding by sucking in pore water from the surrounding soil. With time, this suction is dissipated by drainage into the area of lowered pore pressure from the surrounding area of relatively higher pore pressure unaffected by the excavation. This ¯ow of pore water causes an increase in soil volume in the zone of in¯uence, soil swelling and soil structure softening. The minimum factor of safety occurs at the equilibrium long term condi- tion when the strength is lowest.
Whether the soil is loaded or unloaded, the stability is generally repre- sented in terms of a factor of safety that is the integrated amount by which the available soil strength may be reduced around a hypothetical shear surface before limiting equilibrium occurs. If a ®eld failure occurs the factor of safety is unity and the average in situ shear strength may be estimated from a back-analysis of the slipped mass. At the design stage, however, it is rare that such conveniently apt and accurate shear strength data are available. It is more usual to rely on small-scale measurements of shear strength. It is necessary to determine which of the various methods of in situ and laboratory shear strength determinations are appropriate to the stability problem considered.
Shear test data applicable to the loading condition
The loading case gave a critical stability condition in the short term, the minimum strength and factor of safety occurring at the end of loading. 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 shape of the soil structure. Eventually the changes in structural con®guration may no longer produce a stable condition and the conse- quent 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 conditioned by the preloading in situ stresses) and its undrained reaction to deformation. A®rst step in meeting the complex similitude require- ments is to ensure that the shear test is effectively undrained.
The undrained shear test may be used to give a direct measure of shear strength, namely the undrained shear strength su, or it may be used to give an indirect measure of shear strength if the pore water pressures are measured by providing c0 and tan 0. It is therefore possible to analyse the stability of the loaded soil by:
. using the undrained shear strength suin a total stress analysis, or by . using the effective stress shear strength parameters c0and tan 0in an
effective stress analysis.
The effective stress analysis requires an estimation of the end of construction pore pressures in the failure zone at failure, whereas the total stress analysis requires no knowledge of the pore pressures whatso- ever.
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 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 so that in the short term it is completely undrained. Pre-failure and failure distortions of the soil mass in the ®eld are, by implication if not in 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.
Shear test data applicable to the unloading condition
The unloading case gives a critical stability condition in the long term, the minimum strength and lowest factor of safety occurring some consider- able time after the end of unloading or construction. It may be readily seen that the long term case approximates to a drained condition in that the pore pressure reduction generated by the unloading is gradually redistributed to the equilibrium pore pressures determined by the steady state ground water levels. Of course the redistribution of pore pressure (under no further change in loading) is accompanied by a change in effective stress as the soil structure swells towards its long term con®guration.
The hydraulic gradient causing the ¯ow of pore water into the expand- ing soil structure is itself reduced by the ¯ow, thus giving an exponential decay in the ¯ow rate. The fully softened structural con®guration is thus approached very slowly indeed. If the long term equilibrium structure is just weak enough for a failure to occur then, in this special case, the long term factor of safety is unity. Here the effective stresses and hence strength are determined by the equilibrium pore pressures (Fig. 1.10, curve A).
If a model shear test is to be used to provide appropriate shear strength data with which to analyse the stability of this condition, then the simili- tude requirements could indicate the use of a slow or drained test. The drained shear test may be used to give a direct measure of shear strength or it may be used to give an indirect measure of shear strength by provid- ing c0and tan 0. Using the effective stress shear strength parameters c0 and tan 0 in an effective stress analysis requires an estimation of the pore pressures. In the special case of limiting equilibrium in the long term, the pore pressures are ®xed by the steady state ground water levels. The analysis may therefore simply proceed on that basis.
For the more general case where the real long term factor of safety is less than unity, i.e. a failure occurs before the pore pressures have reached their equilibrium value (Fig. 1.10, curve B), the instability is still predicted
by an effective stress analysis using the long term equilibrium pore pressure distribution. If the long term factor of safety is less than unity then it becomes unity and instability arises some time prior to the long term condition. The effective stress analysis based on the equilibrium pore pressure thus provides a real check on stability even when the actual failure may occur before pore pressure equilibrium is reached and before the soil behaviour is fully modelled by the drained shear test.