MULTI SCALE, NON-LINEAR ANALYSIS
Advances in computational efficiency and capacity mean that significant improvements in modelling practice for mines are possible. Perhaps the most significant improvement will come from a move towards calibrated, multi-scale non-linear modelling.
Many mine deformation modelling approaches assume physical phenomena of different length scales cannot, or do not affect each other. This assumption is made to overcome computing limitations, as it allows smaller, detailed sub-models of areas of interest to be analysed using simplified boundary conditions. The central idea is that gross deformation simulated at one scale, relying on a set of simplified material assumptions, can be used to frame the loading system, or boundary conditions for a smaller length scale model incorporating a more advanced material model.
It is common for example, for elastic, regional-scale geological models to be employed to set fixed boundary conditions for simple plastic, mine-scale models, and for these models to drive the boundaries of detailed, excavation-scale models with advanced constitutive behaviour. The practice is very widespread, but it has many complications. The most important is that yield or large strain at any boundary between length scales, or model boundaries, violates the assumption that yield mechanisms at different length scales are sufficiently decoupled. The damage on the shorter length scales is needed to properly develop the yield at the larger length scales and the only computational solution is multi-scale analysis.
Figure: Example of a multi-scale, strain softening, dilatant simulation incorporating more than 10 Million degrees of freedom. Only the drive scale analysis of steel arches used a sub modelling approach.
Massive, strain softening, dilatant analysis is the most obvious approach for multi-scale analysis in rock, but previously this was out of reach for most mines. Now, using off-the-shelf strain-softening, dilatant Finite Element (FE) codes and parallel computing, models with more than 10 million degrees of freedom and higher order elements are frequently being employed in both small and large projects. Run and build times for very large, life-of-mine, mine scale problems using codes such as Abaqus on multi-processor machines are short enough to allow application in roles very similar to that usually fulfilled by much simpler, but less featured 2D and elastic analysis on mine sites.
A large number of projects around the world are taking advantage of multi-scale analysis. The greatest improvements have been the rationalisation of the use of sub-models and a major step change in the ability to correctly replicate displacements (at all length scales). This opens up mine modelling to greater rigour in calibration and an immediate consequence is the ability to use velocity, displacement and rock damage as criteria for stability. Over a short time this can lead to an order of magnitude change in the value of field measurements and mines will invest much more in instrumentation, monitoring and simulation aided engineering.
In the Figure, results from a single model step for a strain-softening, dilatant FE model of a block cave underneath an existing sub-level cave are shown. The intent of this model was to replicate deformation induced between the two operations as the block cave propagates. Importantly, this model was calibrated using measurements from each length-scale of interest in the model. Achieving a similar level of precision at each successive length-scale confirmed that the fundamental mechanisms of damage and deformation were captured.
Drive deformation is simulated in sufficient detail to allow displacement driven, post failure sub-model analysis of steel arches and concrete linings, the stability of pillars in the main model can be directly interpreted and on a much larger scale and the interaction between the two caves can be forecast at monthly intervals. The massive multi-scale approach was not only efficient, but essential to capture the mechanisms of damage and deformation that affect stability at each length-scale.
This particular model employed approximately 10E6 Degrees of freedom, only higher-order elements, 119 discrete excavation steps and was run in Abaqus Explicit on a 32 CPU machine in approximately 24 hours. An interesting feature was the discrete modelling of faults using contact discontinuities, very similar in nature to discrete elements.
This is just one example, but it shows that far from a being a burden, higher standards for numerical modelling are possible using today’s technology.