Numerical Stress Modelling

Overview

Click to Enlarge The geometry of mining excavations and mining rate are the major factors driving stress change in mines. These stress changes in-turn affect seismicity. Modelling stress changes and then comparing expected and observed seismicity leads to a better understanding of the state of the rock mass. Our aim is to integrate modelling results with existing stability analysis techniques to improve seismic hazard assessment.

As integration is a relatively new field of research we choose to develop our own numerical stress modelling codes rather than purchase existing software The experience gained developing our own codes gives us a deep understanding of the advantages and limitations of each modelling technique, enabling us to use the most appropriate tool for the job and quickly modify the code when it becomes necessary.

Numerical Modelling Code

Our most mature code is ISSM, an implementation of the boundary element method. ISSM can model both tabular and volumetric excavations over large areas very efficiently. The Material Point Method (MPM) is a domain method capable of simulating large deformations and wave propagation which we use to perform tunnel damage modelling. Most failure criteria used in stress modelling are not suitable for modelling seismicity. Research shows that approaches based on damage rheology can successfully model seismicity.

We have developed the Integrated Damage Rheology Model (IDRM) to model seismicity. IDRM theory is grounded in thermodynamics and can model all stages of brittle rock deformation.
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Integrated Static Stress Model

Click to EnlargeISSM is our own implementation of the indirect boundary element method. It models the rock mass as a linear elastic continuum but can also model the following non-linear behaviour:

It is 5X faster than similar commercial tools and has been multi-threaded to take advantage of multi-core computers. We offer routine modelling services and some consultancy based on ISSM, and also use this as a base for combination with other modelling techniques – for example, a MPM zone embedded within an ISSM model for providing a non-linear high-deformation region within the realistic stress environment of a large mine.

Integrated Damage Rheology Model

Click to EnlargeIDRM can model the approach to brittle failure and recovery thereafter. At different scales this could represent the model analogue of either acoustic emission or seismic events Stable fracturing where an increase in load is required for crack propagation Healing of cracks under confining stress The Kaiser effect where under cyclic loading/unloading acoustic emission is only observed at stress levels larger than previously experienced Seismic and aseismic potency release
 

Material Point Method

Originally developed by Sulsky, Chen and Schreyer to simulate impact and penetration in solid dynamics problems, IMS implemented MPM in order to side-step mesh entanglement problems caused by large deformations. It also has the advantage of being based on the physics of solid mechanics, which allows one to use familiar concepts:

MPM models the material as Lagrangian particles that are free to move through an Eulerian reference grid: Equations of motion are solved on the reference grid