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TSLOPE is used for analyses of circular or non-circular slip surfaces in which the user specifies the potential slip surface and the soil properties along that slip surface. Multiple slip surfaces can be analyzed for a site, the user can test the sensitivity of the results to small shifts in the slip surface and/or the specified soil properties and pore pressures and thus conduct an intelligent search for the critical non-circular slip surface.

The program will search for the critical seismic coefficient, that is the seismic coefficient which reduces the factor of safety to unity.

TSLOPE offers a choice of methods for computing the factor of safety, either Spencer's Method or Morgenstern and Price's Method. Both methods fully satisfy equilibrium conditions. As will be discussed subsequently, there is a marginal increase in accuracy with increasing sophistication as one goes from Spencer to Morgenstern and Price.

The Simplified Bishop Method can be extended to non-circular slip surfaces and is then equivalent to Janbu's Simplified Method but for non-circular slip surfaces there tends to be a greater difference between the results obtained using these methods and methods which fully satisfy equilibrium. Academic studies (e.g. Boutrup et al, 1979; Frodlund et al, 1981) have usually indicated that use of the Simplified Janbu method gives factors of safety 10 or 15 % lower than methods which fully satisfy equilibrium unless a correction factor is applied, but greater differences have been reported in some practical applications. Boutrup et al. (1979) also found that the program STABL2, which uses the Simplified Janbu Method, "may give nonconservative and erroneous results for failure surfaces that intersect the top of the slope at steep angles, and where the strength is defined mainly in terms of the cohesion intercept."

Thus, in TSLOPE, which is primarily intended to be used for the analysis of non-circular slip surfaces, we only offer use of Spencer's Method or the Morgenstern and Price Method, both of which fully satisfy equilibrium. As used in TSLOPE these methods are identical except that for Morgenstern and Price's method the user must specify the relative slopes of the inter-slice forces. Since the user does not normally know how to specify the distribution of the relative slopes of the inter-slice forces, it makes more sense to use Spencer's Method. However, the Morgenstern and Price method should be used when Spencer's Method fails to converge or when Spencer's Method yields an unreasonable line of thrust.

TSLOPE may be used to analyze two-dimensional wedge-type failures in which case the sliding mass is divided into a number of vertical slices rather than the two or three wedges that may be used in hand computations. The obtuse angle at the base of the wedge may, however, have to be rounded off when using TSLOPE in order to obtain convergence of the solution.

This program, like all computer programs, is no smarter than the engineer who uses it. We have tried to make the program reasonably simple to use and to provide clear instructions. However, if you have not previously attempted analyses of the kind performed by the program, you should probably seek advice from someone who has experience with this kind of analysis. You will not obtain the correct answer to the problem you are studying unless the field conditions are adequately represented. Even then you should not assume that you have computed the correct answer. The purpose of analyses such as are conducted with this program should be to obtain insight into an engineering problem, not to obtain numerical values which are taken at face value. For this reason, we have built various options into the program so that you can explore the effects of varying the assumptions made in modeling your problem as well as the effects of varying material properties. However, we cannot guarantee that the program works for all analyses that you try to conduct. We have taken special care in developing the program, but you should run your own check problems before conducting particularly unusual or critical analyses.

The theoretical background to the methods of analysis that are used in TSLOPE and some guidance on limit equilibrium slope stability analyses are provided in the next section of this manual. Detailed descriptions of the use of TSLOPE are provided later. For convenience, the shear strength and pore pressure options available in TSLOPE are summarized in Plate A. These options will be explained in this user's guide.

Plate A Shear strength and pore pressure options in TSLOPE.

The three most important pieces of general guidance on the use of limit equilibrium slope stability analyses are:

1. The selection of soil properties and pore pressures that are used in the analysis is up to you - this is the most important part of any evaluation of slope stability and we cannot program this selection for you.

2. Slope failures often occur on thin layers or planes of weakness that can easily be missed in field investigations.

3. As a result of the conventional manner of defining the factor of safety in limit equilibrium analyses, the calculated factor of safety applies equally to all slices. In reality, the factor of safety against local yield will vary somewhat along the slip surface and the local factors of safety for some slices might be less than unity, even if the overall factor of safety is as high as 1.8 (e.g. Bishop, 1955; Popescu, 1982). Then even the computed average factor of safety may be unrealistically high, because the load carried by individual slices cannot in fact exceed the shear capacity on the base of the slice and, in reality, stress redistribution must occur whenever local factors of safety are less than unity.

In the case of brittle materials, even small external loads can reduce the local factors of safety to less than unity and a progressive failure mechanism may be triggered. This happens, for instance, in overconsolidated clays which exhibit residual shear strengths under drained loadings, and in loose, saturated sands under undrained loadings. As pointed out by Peck (1967) and Bishop (1971), the analysis of progressive failure requires the use of numerical techniques such as the finite element method. However, Bishop (1971) did suggest an approximate method for the analysis of progressive failures which requires the user to guess the distribution of local residual factors around the slip surface. This method can readily be applied using TSLOPE since the user individually specifies the strength parameters at the base of each slice. Guidance on values of the residual strengths of brittle soils is given by Bishop et al. (1971) and Lupini et al. (1981). More accurate progressive failure analyses can be conducted using the static finite element program TELSTA which includes interface elements that allow the shear strength to diminish with increasing deformation. A special purpose version of TELSTA for the analysis of slope stability, TELSLOPE, is under development by TAGAsoft Ltd.

Additional references on the mechanics of limit equilibrium slope stability analyses that are instructive include: Spencer (1969), Wright et al. (1973), Tavenas et al. (1980), and Ting (1982).

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