Analysis Methods

The Methods tab in the Project Settings dialog, allows the user to select:

Analysis Methods

The following limit equilibrium analysis methods are available in Slide:

Any or all of these methods can be selected for a given Slide analysis. When Compute is run, all of the selected analysis methods will be simultaneously run on the model, and results for all methods will be available for viewing in the Slide Interpret program.

An excellent review of limit equilibrium analysis methods for slope stability, can be found in the text by Abramson, Lee, Sharma & Boyce (2001). This includes the equations, theory and assumptions associated with each method.

Janbu Corrected Method

For a given slip surface, the Janbu Corrected safety factor is obtained by multiplying the Janbu Simplified safety factor for the surface, by a modification factor , as follows:

Janbu Corrected Safety Factor = * Janbu Simplified Safety Factor

The modification factor is a function of the slope geometry, and the strength parameters of the soil, as illustrated below.

The Janbu modification factor is an attempt to compensate for the fact that the Janbu Simplified method satisfies only force equilibrium, and assumes zero interslice shear forces. Janbu developed a rigorous procedure, the Janbu Generalized method, satisfying both moment and force equilibrium. By comparing results using both the Janbu Simplified method and the Janbu Generalized method, for homogeneous slopes, Janbu was able to plot a series of curves (see below) described by the following equation:

where the value of varies according to the soil type as follows:

image\janbu_cor2a.gif

Definition of L and d for Janbu corrected method

image\janbu_cor1a.gif

Empirical curves used to compute Janbu correction factor

NOTE that this derivation is based on calculations for a homogeneous (single material) slope. For multiple material slopes, where the slip surface passes through different soil types (for example, c only AND c - f soils), the relationship for c-f soils is used ( = 0.50)

GLE Interslice Force Function

If the GLE analysis method is selected, the user may also specify the Interslice Force Function to be used in the analysis. By default, a Half Sine Interslice Force Function will be in effect, unless the user specifies a different function with the Change button. See the Interslice Force Function topic for details.

Number of Slices

The Number of Slices is the number of vertical slices into which the sliding mass for each slip surface will be divided. The default number of 25 slices is sufficient to obtain an accurate solution for most problems. A large Number of Slices (e.g. greater than 100) is not recommended, since the accuracy of the solution will not necessarily be improved, and computation time and size of the output file is directly proportional to the Number of Slices.

Tolerance

The Tolerance is the difference in safety factor, between two successive iterations of the limit equilibrium analysis procedure, at which the solution is considered to have converged, and the iteration process is stopped. The default value of 0.005 is recommended. Much smaller values will increase the computation time, and may lead to convergence problems. Values greater than 0.01 will speed up the computation, but will lead to less precise values of safety factor.

Maximum Number of Iterations

The Maximum Number of Iterations is the maximum number of iterations allowed in the limit equilibrium analysis, for each slip surface. Although the default value is 50, it should be noted that for a typical problem, only 3 to 4 iterations are required for convergence. If a given slip surface requires more than say, 20 iterations, incorrect material properties, or very low safety factors, may be the cause, and the user should check their model input carefully. If the Maximum Number of Iterations is reached, then the iteration process is terminated for that slip surface, and the last calculated value of safety factor is recorded.

Advanced Convergence Options

Various advanced convergence options relating to the limit equilibrium calculations, are available by selecting the Advanced button within the Methods tab of the Project Settings dialog. This will display another dialog, which makes available the options described below (M_Alpha Check and Tensile Stress check).

M_Alpha Check

The variable m_alpha, is the denominator in the equation which is used to calculate the NORMAL force on the base of a slice, during the limit equilibrium calculations. It is dependent on the angle of the slice base (alpha), the friction angle of the material, and the safety factor F, as follows:

image\eqn_malpha.gif

The factor of safety calculation is sensitive to the value of m_alpha. It has been suggested (Whitman and Bailey, 1967), that if the value of m_alpha goes below 0.2, for any slice, during the limit equilibrium calculations, that the resulting safety factor may be incorrect or misleading. For example:

A more complete discussion of issues related to the variable m_alpha, can be found in Ching and Fredlund, 1983.

So there are numerous reasons to keep track of the value of m_alpha during the stability calculation. To ensure that the value of m_alpha is NOT ALLOWED to go below a value of 0.2, select the checkbox for "Check malpha < 0.2". Any slip surfaces for which malpha < 0.2 (on the final iteration of the limit equilibrium calculation), will be reported as INVALID slip surfaces, with an error code of -112 written to the output file.

Surfaces with an error code of -112, will often be deep-seated slip surfaces, with high negative base angle slices in the passive zone (at the toe of the slope). In some cases, you may wish to calculate a safety factor for these slip surfaces.

A value of malpha < 0.2, DOES NOT NECESSARILY MEAN THAT THE SAFETY FACTOR IS INCORRECT. In most cases, a safety factor can still be calculated (i.e. the limit equilibrium calculation will converge to an answer). If you wish to analyze such surfaces, then clear the "Check malpha < 0.2" checkbox. In this case, malpha is allowed to take on any value, except zero (malpha cannot equal zero, since the entire stability calculation would then abort).

Tensile Stress Check

Negative effective normal stress (i.e. tensile stress) may sometimes be calculated on the base of one or more slices, during the limit equilibrium calculations. This can occur for various reasons, including:

When tensile stresses are calculated, this may affect the validity of the calculated safety factor. Depending on the magnitude of the calculated tensile stress, the resulting slice forces may not be kinematically feasible, and the calculated safety factor may be inaccurate or in the worst case, completely invalid.

By default, the tensile stress check is NOT performed. This means that tensile normal stresses are permitted on the base of any slice.

If you wish to check for the existence of tensile normal stress on slip surfaces, then you can select the checkbox for the Tensile Stress Check option, in the Advanced Convergence Options dialog, within the Methods tab of the Project Settings dialog. You can also specify the "Percentage of Slices" which will be tested. If this checkbox is selected, the Tensile Stress Check will be carried out as follows:

  1. For each slip surface analyzed, the limit equilibrium calculation is allowed to complete, as usual (i.e. a Safety Factor is calculated).

  2. NOTE: the check for Tensile Stress is NOT performed during the iteration process to calculate a Safety Factor. The check is performed on the slip surface AFTER the Safety Factor has been calculated (i.e. after the iteration has converged to a final answer).

  3. The Tensile Stress check is performed on the "Percentage of Slices" specified by the user. The "Percentage of Slices" simply represents the (approximate) number of slices, starting from the TOE of the slip surface, which will be checked for Tensile Stress on the slice base.

  4. FOR EXAMPLE: the default Percentage = 95%. This means that for a typical analysis (e.g. 25 to 30 slices), all slices will be tested for the existence of tensile stress, except for the last 1 or 2 slices, at the CREST of the slip surface (i.e. the last 5% of slices will NOT be tested). The reason for this, is simply that the slices near the crest of a slip surface, are most likely, in reality, to exhibit tension across the base (i.e. these slices may be part of a tension crack zone at the crest of the slope).

  5. The allowable tensile stress on a slice base, depends on the strength criterion of the material at the base of the slice. The allowable tensile stress is ZERO for all strength criteria, except: Hoek-Brown, Generalized Hoek-Brown, and Shear-Normal Function. For these 3 strength models, a finite tensile strength can exist. If the calculated tensile stress is within the tensile strength of the material, then the slice results are still considered valid.

  6. If the calculated tensile stress on the base of a slice, exceeds the tensile strength allowed by the strength criterion, then Error Code -120 will be written to the output file, rather than the safety factor, for that slip surface.

  7. Remember that the Tensile Stress check is only performed on the Percentage of Slices specified, starting from the toe of the slip surface. Tensile stress will be permitted on slices at the crest of the slip surface, if the Percentage of Slices is less than 100%.

Negative Shear Strength Check

Finally, it is important to note the following -- during the limit equilibrium iteration process, a check is ALWAYS performed, to ensure that the SHEAR STRENGTH on the base of any slice, is not allowed to become negative. If a negative shear strength is calculated, the shear strength is automatically set to zero, for the slice. This check is always performed during the analysis, and does NOT depend on the Tensile Stress check, which is performed separately, after the safety factor has been calculated for a slip surface.