For plastic analysis, how do I estimate the residual value of the parameter mi?

On the topic of residual strength, please see the following response from Evert Hoek:

 In response to your question about how Phase2 handles the post failure characteristics of rock masses I have to say that we, the rock engineering community, do not have very good models of this process yet. The process itself is illustrated on page 26 of the chapter on rock mass properties and in the attached pdf file. How you create these responses in Phase2 is presently a matter of judgement rather than science.

 In geneneral, in poor quality rock masses (RMR or GSI < 40) I assume perfectly plastic post failure behaviour which means that the rock mass retains its strength and there is no volume change. This is achieved by using the same properties (mb, s and E) for both peak and residual strength and setting dilation to zero. For better quality harder rock masses I tend to use the Disturbance factor D to achieve a strength and modulus reduction after failure and a tyical D=0.7 value seems to work well in most cases. The second pdf attachment shows this process in Phase2 version 8 where I have used D = 0.7 in the GSI option when specifying rock mass properties in a model. Note that I have left the dilation = 0 since I have never found a satisfactory way of using this parameter.

 A number of researchers are working on this issue of post peak behaviour and I am sure that we will arrive at better solutions in the next few years. Meanwhile, this is the best guidance that I can offer you.

 

There is also a paper by Cai that may be useful:

 Determination of residual strength parameters of jointed rock masses using the GSI system, Cai, M., Kaiser, P.K., Tasaka, Y., Minami, M., 2006, published in International Journal of Rock Mechanics and Mining Sciences 44 (2007) 247-265 Elsevier.