What are the possibilities of applying computerised interactive graphics to analyse the stability of underground excavation? What are the obstacles to such an extension of the work done to date?

Reply by Cundall

In the equation solving part of the technique the assumption is made that the deformation of the intact rock is small compared with the deformation along the surfaces between rock blocks. Deep underground, with high stresses and large deformations of the entire rock, the method breaks down. It might be applicable down to medium stress range. It could be used in the destressed region in the neighbourhood of a large underground opening, in conjunction with the finite element method applied to regions further back from the opening. Question by Barton (for Cundall, Voegele and Fairhurst ) It appears that with non-planar Joints drawn on the cathode ray screen, sliding can occur by a process of maximum dilation in which no failure disparities occur. This corresponds to shearing under gross stresses with hard, competent Joint walls. In underground excavation, such Joints would probably stabilize any possible collapse due to their dilation of normal stress induced properties, as is observed in practice. The question concerns rock slopes in which one set of identical non-planar Joints dips unfavourably towards the slope face. Unlike the underground example, this situation is unconfined. Shear displacement can occur along the non-planar Joints without necessarily causing a general rise in normal stress across the dilating Joints. If either a linear or a curved shear failure criterion is used, failure, if it occurs at all, will tend to occur on the lowest Joint exposed at the toe, since shear strength is more likely to be exceeded at the higher stress level. The question is: where will failure occur? With a linear friction shear failure criterion, it appears that failure is equally possible on any of the unfavourable Joints. Would the interactive graphics technique show failure on the lowest Joint, or another single Joint, or on all Joints simultaneously if the friction angle were set low enough to allow sliding?

Reply by Cundall

This sort of situation has been investigated by first setting high friction on all Joints and then reducing friction until failure occurs. The effect will be the same for each Joint since there is no cohesion; there is no dimensionality. Consequently, on each Joint there will be an imbalance of forces. The bottom block will see an imbalance and will start to move. The next block will see the same imbalance and will also move, in approximately the same motion as the first block. Hence it appears that the whole system would move simultaneously, one block on top of another, and over one another when the first block reaches the bottom. Similar behaviour was observed the analysis of a dam foundation in a system of cross Joints. Deformations were non-uniform. The dam itself had moved up slightly. An enormous tension crack had opened giving rise to many simultaneous Joint movements.

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