# SSR

Rocscience has also written papers on Shear Strength Reduction, and links to these papers are provided below.

Investigating the Performance of the Shear Strength Reduction (SSR) Method on the Analysis of Reinforced Slopes

The Shear Strength Reduction Method for the Generalized Hoek-Brown Criterion

The papers below, from RocNews, also discuss SSR.

A New Era in Slope Stability Analysis: Shear Strength Reduction Finite Element Technique

Unique Shear Strength Slope Stability Features in RS2

## General

What are some general guidelines for carrying out an SSR analysis?

The following are a few things to keep in mind when carrying out an SSR analysis in RS2:

• Relevant tutorials: SSR Tutorial and SSR Search Area Tutorial
• Use 6-noded triangles for an SSR analysis
• If material properties are set to zero, this can cause numerical issues
• The first thing to check when doing an SSR analysis is the Shear Strength Reduction Graph, and you should be looking for displacements taking off, diverging from the elastic part of the graph
• Even for 6-noded triangles there can be mesh sensitivity, so always be mindful of this
• It is recommended to use both Slide and RS2 to properly judge the factor of safety of a slope
• In an SSR analysis, both the peak and residual strengths are reduced for a particular SRF value. Residual values are used after failure of the material
• The displacements at any stage of an SRF analysis are the displacements you would see if you reduced the strength of the in situ material by that SRF factor
• The Stage Settings option in the Data menu allows you to set any reference stage, if desired, to view differential data between any two stages of a multi-stage model. For an SSR analysis, if the reference stage is used, all the results are based on the difference between any SRF stage and the initial stage. So, the model results of SRF=1 should equal the results of the initial stage. The true displacements from an SSR analysis will be displayed if the reference stage is not used.
• A pin at the edge of the model is preferable to a roller when doing SSR analyses, particularly if the boundary is close. If rollers a used, the failure surface can propagate along the external boundary since it is in essence a frictionless, cohesionless surface.
• Before doing an SSR analysis on a multi-stage model, one should always do the model without SSR first

How do I include joints in the SSR analysis?

In order to do this, you need to turn on SSR for the particular joint. If this is not done, the strength of the joint is not reduced as part of the SSR analysis.

In older versions of RS2 (earlier than version 11 (or M+), it has been found that when using joint elements (either for rock slopes or when using structural interfaces when modeling geotextiles), a lower tolerance should be used. Joint elements also tend to take more iterations to converge. However, an improvement has been made in the M+ release and the default setting should be appropriate (for more details please see the Joint Verification Manual)

Can SSR analysis be done for tunnels?

We have used SSR analyses for slopes only, not for underground excavations/tunnels. However, there are people who have used SSR for such analyses.

The following comments are from Evert Hoek regarding the use of SSR in tunneling design (comments are from 2009):

I have thought a great deal about the possible role of SSR in tunnel design and I am afraid that I fail to see much future for it other than that it provides another interesting number. The practicality of tunnelling requires the designer to start off with a number of common sense questions that determine the methods that are best suited to providing a reliable and practical solution. These questions include the nature of the rock mass and in situ stress field and, as a consequence, the most likely failure modes; the method and sequence of excavation and the constraints imposed by this method on the support systems that can be used; the influence of groundwater on the design (for example whether the lining is leaky or impermeable); the role of time (creep and rock deterioration) on the response of the rock mass around the tunnel and the sensitivity of surface structures above the tunnel on the permissible subsidence and tilt. Each underground structure is unique and it is important to determine which of the factors listed above, or others, will dominate the design. There is no single magic bullet for tunnel design and it is usually a combination of methods that provide a number of quantified responses which then have to be assessed as to their adequacy to meet the over design requirements. In some cases these requirements may be dictated by national codes or guidelines.

It is very difficult to see where a "factor of safety" determined by SSR fits into this scheme of things. In fact, it does not answer any of the questions outlined above and the number arrived at may or may not have any physical significance. The sequence of failure, if it occurs, can be adequately assesses by means of the normal pi or modulus reduction techniques that we employ. I always set maximum displacements as the background screen and add failure indicators and boundary displacements. If I am using rock bolts I look at the axial loads in the bolts and whether any portions of the bolts have failed and if I am installing a lining I look at the support capacity plots. For near surface tunnels I look at surface displacements.

Can SSR be used in an axisymmetric model?

Yes, SSR is supported in axisymmetric mode. A pdf comparing plane strain and axisymmetric SSR analyses of a slope can be downloaded here.

## Results Interpretation

What is the critical SRF?

The Critical SRF is identical to the Factor of Safety in limit equilibrium slope stability analyses (Slide2). A value of 1.0 means the slope is in a state of limit equilibrium and that any reduction in shear strength will result in failure of the slope. You do not design for a factor of safety of 1.0 unless you are using limit states and factoring input parameters (Eurocode). Design values for slope stability analyses are up to the user and depend on the type of slope and consequences of failure.

If you are looking for guidelines on what factors of safety to use, a suggested reference is John Read and Peter Stacey's book, "Guidelines for Open Pit Design". This book contains typical safety factors for use in design.

How do I interpret the SRF value and the displacements that result from SSR analysis?

The critical SRF value is a global factor of safety similar to the Factor of Safety computed by a limit-equilibrium program. It is recommended to do a limit-equilibrium analysis as well.

The displacement data within a slope, for a particular SRF, are relative to SRF=1.0. To get absolute values of displacement, as are plotted in the shear strength reduction plot, go to the Data>Stage Settings menu option in the Interpreter. In the Stage Settings dialog, define the Reference stage as not used. Remember, displacements for SRF values represent the displacement if you reduce the shear strength in the slope by a particular SRF value. They are not the in situ values.

The examples shown below are taken from the Shear Strength Reduction tutorial.

Displacements for SRF=1.15 relative to SRF=1

Displacements for SRF=1.15 (Reference Stage not used)

What does it mean if the critical SRF calculated is less than 1?

For one stage models, RS2 accurately computes models with SRF or FS less than 1. For multi-stage models, if and only if all stages leading up to the last stage converge is the solution accurate. RS2 uses the stress state from the end of the second last stage as the initial stress state for the SSR analysis. So if it is invalid (due to non-convergence) the SSR analysis will not be correct. There are numerous examples of one stage models with SRF<1 in the Slope Stability Verification Manuals.