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Direct model calibration on a fault using Map3Di

For a fault slip calibration one would define the location of the structure from intersections,seismicity and geological interpretation (as before), then integrate the effect of the seismicityassociated with the fault to determine the distribution of slip on the fault surface. This slip is thenapplied in Map3Di as a prescribed non-homogeneous shear discontinuity. The slip is

accumulated as seismicity occurs and used to further load the model.

As a demonstration of how the Map3Di analysis would proceed, consider the example shownbelow. The location of a fault structure has been defined and is shown with the seismicity.

The seismicity associated with the fault is then integrated to determine the distribution of slip onthe fault surface that is implyed.

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This slip is then applied directly into the Map3Di numerical model as a prescribed non-homogeneous shear discontinuity. A stress analysis can now be conducted to simulate theinteraction between the slip implied by the seismicity and the stoping (and any other featuresincorporated into the model, e.g. slipping faults, dykes etc.). Below, a model has been runwithout modelling the fault (the fault could also be modelled if desired), but including slip implied

by the seismicity. In this figure, the excess shear stress

|| - ntan()

at the location of the fault surface is presented (using a 20 friction angle).

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The results show that over most of the fault surface, there is little or no excess shear stress andhence no further potential for slip at these locations (although additional slip could be induced ifother parts of the fault were to slip). However at a few locations (to the front and right of the leftmost stope) there is still considerable excess shear stress. This could indicate that the fault ishung up at these locations. Alternatively, this may simply be a result of improperly distributing

the slip over the fault plane. In either case, there is considerable potential for slip yet theseismicity has not indicated that this has occurred. Part of the value in applying this procedure isto identify such areas. Further study of this location (including a detailed review of the seismicityand perhaps an in situ investigation) is certainly warranted.

Note that by applying this procedure we have bypassed the trial and error back-analysis stageand thus reduced the amount of engineering effort required to calibrate our model. Once theprescribed shear discontinuity is applied we have by definition a model that matches previouslyobserved behaviour, and we are in a better position to make forward predictions.

This goes along way towards satisfying our first calibration objective: to bring the model to astate most representative of the currently observed conditions. By calibrating our numericalmodel using seismic loading we can actually bring the model into an initial state much closer toin situ conditions then we could ever hope to achieve by the trial and error approach. Non-uniform slip distributions over a fault surface, derived from the observed seismicity, have beendirectly imposed into the numerical model. The amount of trial and error that would be requiredto determine this shear strength distribution would be formidable.

We can now take this procedure one step further. We can use these results as a direct back-analysis method. This would proceed by subdividing the fault into small elements and back-calculating the shear strength in each element that is required to bring about the specified slip

j= tan-1

(||/n)

This is illustrated below where the friction angle distribution necessary to resist slip is presented.

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The results show that over most of the fault surface, a nearly constant friction angle ofapproximately 20 is required. However in front of the left most stope a very high value isrequired to resist slip. This suggests that the fault has hung up at this location. It is possible thatan asperity due to some local bend, wave or offset in the fault is responsible for this. Additionalin situ investigation would be advised to verify this.

We are now in a position to build a non-linear fault model with this heterogeneous shearstrength distribution. Such a model would deform to match the slip distribution observed fromthe seismicity. We now have a model that not only matches previously observed behaviour, butis also calibrated with the exact strength distribution required to evolve to this known state. Thisdoes two things for us: it gives us a calibrated model to make forward predictions with, andthrough repeated back-analyses allows us to test how well our model matches previouslyobserved behaviour.

This goes along way towards satisfying both of our calibration objectives: to bring the model to astate most representative of the currently observed conditions, and characterization ofgeological features. It is clear that the resulting model is far better calibrated to observed in situconditions than one could ever hope to achieve by using a best-fit homogeneous strengthassumption. A homogeneous strength assumption would not allow for simulation of the

observed asperity.

It must be emphasized that this procedure constitutes identification of flaws in the rockmass. Inthis case, microseismic activity is not only being used to identify the presence of these flaws, butalso characterize the behaviour and impose the effect implied by the seismicity into the model.This technique provides a unique opportunity for construction of mine wide stability models

incorporating major structural features.

Download example (smn.zip 41 KB)smn.zipcontains the model and seismic events pictured

above.

1. Unzip smn.zipto create smn.001and smn.ms

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2. To display these results in Map3D, use File > Open Analysis Resultsandselect smn.001

3. To load the seismic events, use the Visualizationfunction and specify the user fileand smn.ms.

4. To display the seismic events, clicking the Plotbutton.5.

These can be contoured by checking Contoured Colours, then clickingthe Plotbutton.6. These can be scaled to the magnitude by checking Scaled Radius, then clicking

the Plotbutton.

7. A plane can be fitted through the data by selecting Plane > Linear Regression, thenselecting Sum in Voxel.