WEEK 13 Soil Behaviour at Very Large Strains 19. Residual strength Starting from soil behaviour at very small strains (less than 0.001%), now we have come to that at very large strains, where the strength peak is passed and the residual strength is observed. In the Critical State concept, we assume that soil eventually reaches the Critical State where no change in the stress and no change in the soil volume are associated to each other. However, this is not the end of story for soils with large clay fractions. The shear strength continues to decrease for larger shear strain without volume change. In this section, let us study (i) why the residual strength appears (ii) how to measure it (iii) why it matters Peak strength Strain hardening Strain softening Critical State? Residual strength γ (After Skempton, 1985) O-C: Over-consolidated N-C: Normally-consolidated 1
19-1. Mechanism of strength mobilisation at very large strains As we looked at in the photos shown in Week 1 (they are shown here again), clay particles generally have flaky, flat shapes, while sand particles are rounder. Clay (London Clay; Gasparre et al., 2007) Sand (Reigate Sand; Fonseca, 2011) At very large strains, the arrangement of sand/silt/gravel particles reaches a stable state (i.e. the Critical State), where no further dilatancy occurs, and the shear deformation /displacement is caused by the rotation of the particles. In clays, however, particle reorientation occurs along the shear plane until the particles are aligned in parallel to the shear plane. At this state, the friction coefficient is very small; in the London Clay, for example, it can go down to as small as φ = 7 o (Garga, 1970). This is significantly smaller than the values normally associated with the Critical State (20-30 o ) σ σ Critical State residual state Critical State at large strain Reorientation Granular soils (Sand/silt/gravel) Clay Residual state at very large strain 2
If the slip surface is observed after shear, it is shiny and polished. Such surfaces are called slickensides, and exist naturally where slope failures and tectonic shear caused large displacement in high-plasticity clays. It is the proof of the clay particle reorientation. Slickensides (Lambe & Whitman, 1969) Influence of clay fraction on the Critical State and residual strength (Lupini et al., 1981; the diagram taken from Skempton, 1985) Note: In the British Standards, a clay particle is defined by <2 µm, not by <5µm as in the JIS. So the clay fraction shown here is the percentage of the particles smaller than 2 µm. In the results shown below, note the slow but consistent reduction in the strength even at very large displacement. (After Skempton, 1985) 3
19-2. Measuring residual strength The previous diagram indicates that very large displacement is required to observe a residual state. We come across an obvious problem if we adopt usual procedures in triaxial tests or direct shear tests; the specimen gets separated after a certain amount of displacement! σ γ To counter this problem, two techniques are commonly adopted. One is the reversal shear box technique, and the other is ring shear testing. The reversal shear box technique applies cyclic loading to the specimen using conventional direct shear apparatus. The cumulative displacement (counting positive in both directions) is taken as the total shear displacement. The deficiency in this method is that, each time a loading reversal takes place, the partially-orientated clay particles are disturbed, and the eventual, truly residual state is hard to reach. See the example below how the loading reversals lead to overshooting of the strain-softening stress-strain curves. σ (After Ramiah & Purushotharamaj, 1971) 4
The ring shear technique avoids the problem by the virtue of its geometry, although it has a disadvantage that the amount of displacement is not uniform across the radius. (After Bishop et al., 1971) 19-3. Practical significance of residual strength The residual strength is relevant to any geotechnical problem which involves large shear deformation, but it is particularly helpful in explaining long-term slope failures. For slope failures that were actually observed, the angle of shear resistance mobilised at the time of failure can be back-caluculated from the soil s unit weight, ground water condition, slope angle, etc. In many cases, it is smaller than the peak angle of shear resistance, and normally lies somewhere between the peak and residual strength. Simplest example: Failure of infinitely long, saturate slope (see your undergraduate textbook) i F γ tanφ γ = φ = tan 1 γttani γttani γ F =1 at failure : Effective unit weight of soil γ t : Total unit weight of soil This experience is explained by progressive failure of soil occurring under strain-softening conditions (Skempton, 1964; Bjerrum, 1967). Note that the slope failures discussed in this section are not those caused by short-term mechanisms such as earthquake motions or intense rainfall. Long-term slope failures develop over many years, with their consequences normally noticed when they reach the ultimate state of instability. 5
The exact mechanism and process of progressive failure are not well understood, but it can be considered as a sort of instability problem deriving from non-uniformity along the slip surface. Imagine, the peak strength is passed along a certain section (AB) of the slip surface earlier than the remaining part of the surface. Because of the stress reduction along AB, the remaining part needs to take larger stress. This leads to local failure at another section CD (which is likely (but not necessarily) to be neighboring AB). And so on and so on hence the name progressive. Rest Peak strength CD AB A C B D Residual strength γ The slip surface therefore cannot mobilise the peak strength at once. But it is not until the overall displacement becomes very large that the residual strength is mobilised uniformly along the whole section of the slip surface; Hence the earlier statement that backcalculated strength normally lies between the peak and residual values. The table shows the analysis results from some case studies in the UK. The parameter R indicates the proportion of the slip surface segment that is in the residual state at failure (R=1 means 100% residual state, while R=0 means 100% peak state). Note also that it may take years for progressive failure to occur in low-permeability clays. Note: The R values here may be under-estimated because the testing techniques described earlier were not fully developed and hence the achieved displacement in this study may not have been sufficient to observe the residual state. (After Skepmton, 1964) 6
The sketches shown here are from Skempton (1964) (two cases from the previous table), illustrating the slip surfaces. (R=1.12) (R=0.56) So, after all, what strength parameter should we be using for analysing slope stability? Unfortunately, there does not seem to be a clear-cut answer to this question. However, probably we should at least keep in mind that adopting the peak shear strength of highly brittle (i.e. strain-softening) soils for design involves potential risks. 7
References Bishop, A.W., Green, G.E., Garga, V.K., Andresen, A. and Browns, J.D. (1971): A new ring shear apparatus and its application to the measurement of residual strength, Geotechnique 21(4) 273-328. Bjerrum, L. (1967) Progressive failure in slopes of overconsolidated plastic clay and clay shales, Journal of the Soil Mechanics and Foundation Division, ASCE 93(SM5) 3-49. Fonseca, J. (2011) The evolution of morphology and fabric of a sand during shearing, PhD Thesis, Imperial College. Gasparre A., Nishimura, S., Coop, M.R., and Jardine, R.J. (2007) The influence of structure on the behaviour of London Clay, Géotechnique 57(1) 19-31. Garga, V.K. (1970): Residual shear strength under large strains and the effect of sample size on the consolidation of fissured clay, PhD Thesis, Imperial College, University of London. Lambe, T.W. and Whitman, R.V. (1969) Soil Mechanics Wiley. Lupini, J.F., Skinner, A.E. and Vaughan, P.R. (1981) The drained residual strength of cohesive soils, Geotechnique 31(2) 181-213. Ramiah, B.K. and Purushothamaraj, P. (1971) Effect of initial structure on the residual strength of Kaolinitic clay, Soils and Foundations 11(4) 15-23. Skempton, A.W. (1964) The Long-term stability of clay slopes, the 4th Rankine Lecture, Geotechnique 14(2) 77-101. Skempton, A.W. (1985) Residual strength of clays in landslides, folded strata and the laboratory Getechnique 35(1) 3-18. 8