6.1. Requirements imposed by the integration on the numerical models
A numerical model of the rockmass response to loading is suitable for a functional integration with observational seismic data when:
` it implements a reasonable approximation of the fundamental relationships between the relevant physical degrees of freedom.
` it is designed to solve a forward problem about the evolution of the physical state of the rock under the given initial and boundary conditions.
` it can convert the data about a real seismic event into a corresponding addition to the loading at the correct moment of time.
` it can itself emulate seismic events in a way which allows for calibration of the model to the observed local seismicity.
` it must have an adequate resolution in the size, location and time of modelled events.
` the computer code must run sufficiently fast so that the numerical clock does not lag behind the physical clock.
6.2. Numerical models that are suitable for seismic integration
6.2.1. Existing models
The “classic” tool for the analysis of stress distribution problems in tabular mining has been the displacement discontinuity method (DDM). It is possible to use this numerical framework for the integration of seismic activity by allocating slip patches to appropriate regions of defined fault planes, according to the observed record of seismic event sequences. Each slip area can be made to conform to the observed seismic moment and forward assessment of future seismic activity can be made at any stage of the integration cycle. This approach is constrained, at present, to the analysis of static deformation problems but is accessible to most of the current 3D-DDM software available in South Africa. Additional interface computer codes for automatic conversion of recorded event moments to slip plane positions may be required.
The static DDM models can be used to model fault creep by postulating laws that define the fault creep rate in terms of the shear loading stress. Regions of each fault surface can be assigned different material properties to designate asperities or creeping “gouge” material. As stress accumulates on the asperities, these will be broken at intermittent intervals. This process can be used to replicate some aspects of the statistical nature of seismic activity. Event frequency-magnitude statistics will be controlled by the asperity density and strength, as well as the characteristic relaxation time, of the fault creep law.
At present, the incorporation of an observed event may be incompatible with the existing stress state over the selected fault position. Future studies will have to be directed to devising strategies to treat these incompatibilities in a systematic manner.
6.2.2. Future model development
Future developments should explore the possibility of formulating a fully dynamic version of the DDM to allow dynamic fault slip and the accompanying wave propagation effects. This would have to be integrated with slow creep dominated deformations and would allow a much richer incorporation of waveform characteristics into the integration process. Difficulties relating to the numerical stability of 3D dynamic DDM models have to be resolved.
Hybrid methods, such as the Integrated Damage Rheology Model (IDRM) described in this report, hold promise for the detailed dynamic simulation of complex seismic source processes and their integration with mine planning. At the quasi-dynamic level damage rheology modelling is conceptually well-suited for integration with real seismic data by converting seismic events into corresponding additional loading on the rockmass.
Non-linear continuum models, such as the finite element method (FEM) or other forms of finite difference models, may also prove to be suitable tools for developing a hybrid seismic damage model. In these cases, numerical strategies have to be used to treat absorbing boundary problems for mining applications.
6.3. Recommendations for integration in practice
Integrated numerical models of rockmass response to loading have serious advantages compared to models which are not capable of assimilating seismic data in real time, and will inevitably become an industry standard for mining design and production planning. The methodologies for using integrated numerical models will eventually crystallise from the experience of employing such models for practical problem-solving but even at this very preliminary stage one can make some recommendations in this respect:
` the initial state of the modelled rockmass should be specified as accurately as possible.
` it must be ensured that high-quality seismic data exists, or will be provided, for the location and time-interval of interest.
` the numerical model has to be set up for the required resolution with respect to both the real and the modelled seismicity, while staying within the available computational resources (computer memory and CPU speed), and ensuring that the numerical time-stepping is faster than the pace of physical time.
` the loading on the studied rockmass, due to the existing and planned mining, has to be estimated as accurately as possible.
` The perturbations to the physical state of the modelled material, caused by the real seismic activity in the area, have to be quantified so that they can be introduced in the running model as an input at the appropriate time.
What can reasonably be expected from an integrated monitoring-modelling system? First and foremost, the integration of data with modelling will improve the reliability of the forecasts about the evolution of the physical state of a particular volume of rock, subjected to a variable loading due to specified mining activity, and the actual local seismicity. In particular, the data generated by an integrated monitoring-modelling system should, when analysed, allow definite statements to be made about:
` the elastic and plastic deformation within the modelled volume of rock at a particular moment of time.
` the distribution of static stress at a particular moment of time.
` the level of micro-seismic activity within the modelled volume of rock.
` the rockmass stability and, in particular, any expected loss of stability of the modelled rockmass.
A conceptual view of the integration of seismic monitoring with numerical modelling for the needs of the mining industry is the first step towards developing the new generation of mining design and planning tools. This development is not a matter for the distant future but has
already started. Even at this very early stage it has become evident that a data-driven numerical model has considerable advantages over its non-integrated counterpart.