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# Strength Reduction Analysis

The Strength Reduction option in the Project Settings dialog allows you to perform a finite element slope stability analysis using the Shear Strength Reduction (SSR) method. For an overview of the SSR method in RS2 see the Shear Strength Reduction Overview topic.

To enable the Shear Strength Reduction method:

1. Select the Determine Strength Reduction Factor check box on the Strength Reduction page of the Project Settings dialog.
2. You may customize the analysis parameters described below, or use the default values.

## Initial Estimate of SRF

The initial estimate of the Strength Reduction Factor for the first iteration of the SSR analysis. By default this is set to 1.

## Automatic Step Size

The Step Size is the difference in the Strength Reduction Factor between two iterations of the SSR analysis.

If Step Size = Automatic (this is the default selection), an appropriate Step Size is automatically determined by RS2, and may vary from iteration to iteration (i.e. it may increase or decrease between any two iterations).

### TOLERANCE (SRF)

If Step Size = Automatic, the Tolerance (SRF) determines the convergence (end of analysis) for the SSR method. The Tolerance (SRF) is implemented as follows:

1. When the difference in SRF between two iterations of the SSR method is LESS THAN the Tolerance (SRF), AND...
2. The Stress Analysis has converged for the SSR iteration with the lower SRF, but does NOT converge for the SSR iteration with the higher SRF, THEN...
3. The SSR analysis is deemed to have converged. The critical value of SRF is the SSR iteration with the lower SRF.

## Custom Step Size

If Step Size = Custom, this allows the user to define the Step Size and Final SRF values. In conjunction with the Initial Estimate of SRF value (see above), this fully determines the number of iterations and the value of SRF at each iteration.

With the Custom Step Size option, the Step Size is uniform and increases monotonically between the Initial SRF and Final SRF values.

With the Custom Step Size option, the Critical SRF is simply the lowest value of SRF for which the Stress Analysis converged (i.e. equilibrium was achieved).

The following advanced SSR analysis options can be configured by selecting the Advanced button under the Strength Reduction tab in Project Settings.

### REDUCE NUMBER OF ITERATIONS AFTER FAILURE

By default, RS2 will automatically reduce the maximum number of iterations allowed for the stress analysis, if failure occurs (i.e. the model becomes unstable and convergence is not achieved), for a given iteration of the SSR analysis. This decreases the required computation time, and generally does not affect the final results of the SSR analysis.

If you do NOT want RS2 to automatically reduce the maximum number of iterations after failure, then clear this check box. RS2 will then always use the same value for the maximum number of iterations allowed for convergence of the stress analysis, regardless of whether or not failure has occurred for a given iteration of the SSR analysis. In some cases this may improve the accuracy of the SSR analysis. However this will depend on your particular model. If you are uncertain about the SSR analysis results, you can try re-running the analysis with this check box turned OFF, to see if this has any effect on the results. In general this will increase the required computation time.

### CONVERGENCE PARAMETERS

By default RS2 will automatically determine appropriate convergence parameters (Tolerance, Maximum Number of Iterations, Convergence Type) for the SSR stress analysis. If the SSR convergence is set to default then it will use the same criteria with the option in the Stress Analysis menu. If desired, the convergence parameters can be user-defined by selecting the User Defined Convergence Parameters option. The following convergence parameters can be user defined:

### TOLERANCE (STRESS ANALYSIS)

The definition of this parameter is the same as described for the Tolerance parameter in the Stress Analysis (Project Settings) topic. The only difference is that this Tolerance value applies to the RS2 stress analyses which are computed during each iteration of the SSR analysis.

### MAXIMUM NUMBER OF ITERATIONS

The definition of this parameter is the same as described for the Maximum Number of Iterations parameter in the Stress Analysis (Project Settings) topic. The only difference is that this value applies to the RS2 stress analyses which are computed during each iteration of the SSR analysis.

### CONVERGENCE TYPE

In RS2, you may choose either Enhanced Absolute Energy, Square Root Energy, Absolute Force & Energy, Absolute Energy, or Comprehensive as the convergence criterion used for the finite element stress analysis. For details see the Stress Analysis or Convergence Criteria document in the RS2 theory section.

## Coupled Formulation

If you are performing coupled analysis (Biot theory) then you can use a coupled formulation for the SSR analysis by selecting the Coupled Formulation check box. This option is only enabled if the Solid-Fluid Interaction option on the General page of the Project Settings dialog is set to Coupled (Biot).