Capturing Failure Planes in a Numerical Model

Two conditions must be met to capture failure planes in a numerical model; the first condition is implementing a constitutive model (material behavior) that can simulate loss of strength as a function of strain. The second one is having fine-enough computational units, i.e. grid size. The first allows the localization of deformation to be captured and the second provides a grid size in the range of the localization phenomenon.

Here is an example of the formation of shear bands in a triaxial experiment at confining pressure of 25 MPa. The proper pre and post-peak stress-strain behavior is captured. 

The same material properties are then used to simulate breakouts observed in images around a 7.5 cm diameter borehole at depth. This allows a back analysis to narrow down the ranges of estimated in-situ stresses. Such model has been done here with a grid size as small as 0.4 mm. 

Similar study can be conducted on a rock slope. With a numerical model, that has such capabilities, slope instability can be modeled and failure plane can be captured. In addition, material properties can be back-calculated if a failure has already occurred. Such material properties can then be used to forecast any potential slope failure in the future. The mesh size in this case does not have to be as small as what is required for the simulation of a triaxial experiment or a borehole breakout. 

Below is the last example showing the development of (shear and tensile) fractures around a larger excavation at depth, like shaft sinking. Such simulation can be used for making timely and cost-effective decision on the selection of temporary ground support and permanent liner.