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The most common short-term stability problem is the end-of-construction condition for materials which dissipate excess pore pressures slowly in comparison with the rate of construction. In more permeable soils, such as sands and gravels, the period of pore pressure redistribution is very short and, except under conditions of transient loading, stability problems typically will fall into the long-term category. Clays, on the other hand, dissipate excess pore pressures so slowly that the period of pore pressure adjustment may last for months or years after the completion of construction.

A classic problem in short-term stability is the case of a fill constructed on a soft clay foundation as shown in Figure 7(a). This problem is normally analyzed using total stresses and undrained shear strengths, the procedure termed the _u =  0 analysis by Bishop and Bjerrum. The undrained strength  S_u  used in such problems is commonly expressed in terms of the in situ vertical effective stress  '_v  and the overconsolidation ratio (OCR) (e.g. Ladd and Foott, 1974), but in more sophisticated analyses the position of the element on the potential sliding surface should also be taken into account (e.g. Ladd et al., 1977). Cuts in saturated clay, Figure 7 (b), can also be analyzed for short-term stability using the _u =  0 method; however, a long-term effective stress analysis should also be performed as this is usually the more critical case.

The end-of-construction condition for a constructed embankment, Figure 7(c), is also a problem in short-term stability. This problem may be analyzed using total or effective stress methods. The total stress method normally involves determination of the undrained strengths using UU triaxial tests and the effective stress method commonly relies on the use of the procedure for computing pore pressures developed by Hilf (1961). The total stress method is shown in Example 1 for TSLOPE. Johnson (1974) provided a detailed discussion of the relative merits of various approaches to end-of-construction stability problems.

Figure 7 End-of-construction stability problems.

The rapid drawdown condition (Figure 8(a)) is another short-term stability problem. While effective stress analyses could be used for this problem it is more common to use total stress analyses, as illustrated in Example 3i and Example 3ii for TSLOPE. In this example the undrained strength, now termed _ff has been determined as a function of the normal stress at consolidation _fc and the anisotropic consolidation ratio, K_c, using ACU triaxial tests as recommended by Lowe (1967) . While other procedures could also be used for the rapid drawdown problem the Lowe procedure has been widely adopted as a standard procedure. As described by Lowe, the procedure involves conduct of two slope stability analyses--an initial effective stress analysis is conducted for the high water steady state condition in order to obtain the normal and shear stresses on the potential sliding surface for the consolidated condition, and a second total stress analysis is conducted for the low water condition using the appropriate undrained strengths. Lowe used a graphical procedure to do the slope stability analyses and it sometimes seems to be assumed that one has to use this graphical procedure in order to obtain the initial normal and shear stresses. This is of course not correct and the normal and shear stresses at the base of each slice can be obtained more easily using TSLOPE. As explained by Johnson (1974), the total stress approach to rapid drawdown stability problems can lead to a substantial component of the shear strength at low confining pressures resulting from negative pore pressures. The practice of the Corps of Engineers, and others, is therefore to use a combined envelope, normally referred to as an S-R envelope, to avoid reliance on the shear strengths associated with negative pore pressures.

The final case of short-term stability analyses to be discussed are earthquake and post-earthquake stability analyses. In past practice the stability of embankments for earthquake loadings has often been checked by applying a "pseudo-static" horizontal force, specified in terms of a seismic coefficient which is used as a multiplier on the weight of the potential sliding mass. TSLOPE allows the user to specify seismic coefficients but it should be noted that pseudo-static seismic analyses are, in general, so crude as to be worthless. A better procedure that is still less complicated than a full dynamic analysis, is that suggested by Newmark (Newmark, 1965; Pyke, 1982) in which it is necessary to determine the seismic coefficient that reduces the factor of safety to unity. In order to facilitate use of the Newmark method TSLOPE provides options for automatic calculation of this critical seismic coefficient as demonstrated in Example 2 for TSLOPE. In such analyses total unit weights must be used in conjunction with either undrained strengths or drained strengths and steady state plus excess pore pressures at failure. Ideally the undrained strengths or the excess pore pressures at failure will be determined as a function of the initial normal and shear stresses along potential sliding surfaces.

Figure 8 Other short-term stability problems.

Post-earthquake stability analyses are a special case of short-term stability in which no seismic coefficient is applied but the undrained strengths may be reduced in order to account for the effects of excess pore pressures developed during earthquake shaking. This kind of problem is illustrated in TSLOPE Example 4. Note, however, that for dilatant materials, the undrained strengths are largely independent of the pore pressures prior to shearing (e.g. Castro and Christian, 1976) so that the undrained shear strengths after cyclic loading may be essentially the same as those prior to shaking. In any case, one should again use total unit weights in conjunction with undrained strengths or drained strengths and steady state plus excess pore pressures at failure. Again, the undrained strengths or the excess pore pressures at failure should ideally be determined as a function of the initial normal and shear stresses along potential sliding surfaces as well as a cyclic loading which simulates the earthquake loading.

For both earthquake and post-earthquake stability analyses the initial normal and shear stresses along potential sliding surfaces can be obtained by conducting an effective stress analysis of the pre-earthquake condition using TSLOPE, as described previously for rapid drawdown analyses. However, for both earthquake and rapid drawdown analyses the initial normal and shear stresses can also be obtained by use of the finite element method and a comparison of the stresses obtained from finite element and slope stability analyses for use in a post-earthquake stability analysis is shown in Figure 9. Note that the ratio of the shear stress to the normal stress obtained from the slope stability analysis is constant along the sliding surface as a result of the basic assumption in this kind of analysis that the factor of safety is constant along the sliding surface. Note also that this ratio is constant only for materials with no cohesion. Thus the finite element method actually gives more reasonable results but the difference in initial stresses led to a difference in the computed factors of safety of less than 0. 1 for the example shown, and it is likely that the difference in the factors of safety in other cases will also be small.

A final point to note with regard to post-earthquake stability analyses is that while the excess pore pressures induced by cyclic loading may be determined as part of the overall analysis procedure, they cannot or should not be included in the slope stability analysis. For the same reason as discussed previously, excess pore pressures which are specified in the analysis affect only the computation of resisting forces and have no effect on driving forces. Further, if effective stress analyses are conducted, it is generally more reasonable to estimate the excess pore pressures at large strains and to use these in the analysis rather than the excess pore pressures prior to shearing since the computation of the factor of safety is more valid as failure is approached and, from a practical point of view, one wants to know whether large strains and failure can develop, rather than the value of an arbitrarily defined factor of safety for a non-failure condition.

Figure 9 Comparison of initial stresses obtained from finite element and slope stability analysis.

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