Probabilistic geotechnical analysis

Elastic superiposition

Status: Beta

Principal Author: Johan Wesseloo

Contributing Authors: Chun Wei Ho, Paul Harris

Development support: Initial developed under the Ground Support Systems Optimisation, Phase 1

Citation: Wesseloo, J., Harris, P.C. and Ho, C.W. (2017) mXrap software app, Elastic Stress Superimposition position version 1. Perth, Western Australia: The Australian Centre for Geomechanics, University of Western Australia.

Description: The app uses the principal of elastic superimposition to calculate the elastic stress conditions around an opening for any given stress state. Six unit stress analysis is performed in 3rd party software and the results imported into the app. The results of the unit analyses are used to calculate the final 3D stress state for any input stress state and the strength factor around openings can be calculated for any stress state and strength properties. Input stress and strength properties can be specified as distributions and the probabilistic analysis performed. Available probabilistic methods are, Monte Carlo, Response surface method, Point Estimate Method and the Response influence factor method.

The principle of elastic superimposition and the approach implemented in this app is discussed in the following paper:

Wesseloo, J 2016, ‘The use of elastic superposition as part of a multi-tiered probabilistic ground support design approach’, in E Nordlund, TH Jones & A Eitzenberger (eds), Eighth International Symposium on Ground Support in Mining and Underground Construction, 12-14 September 2016, Luleå, Sweden, Luleå University of Technology, pp. 9.

(a) σ1 = 50 MPa, dip of σ1 = 0°

(b) σ1 = 50 MPa, dip of σ1 = 0°

(c) σ1 = 40 MPa, dip of σ1 = 0°

Figure 1: Strength factor calculated for three different stress states using stress superposition post processing

Figure 2: Strength factor calculated for three different stress states using stress superposition post‑processing