Modification of rock failure criteria considering the RMR caused by joints
Introduction
As far as underground extractions are concerned, the support of a mine is undoubtedly one of the main aspects defining its viability. Ultimately, the main element supporting the rock is the pre-existing rock mass itself.
Likewise, the capacity of the rock mass to contend with holes that ensure self-support in the case of mining exploitations through rooms and pillars is the key design element. In fact, the ground support capacity depends on the rock mass strength, which in turn determines both the maximum size of the holes and the size of the pillars in between these.
Therefore, we need some criterion to estimate what degree of stress can produce failure of a rock mass. A failure criterion is a scalar function of the stress tensor [8]. Failure of the material does not take place until the stress working on it does not exceed that of said stress tensor. In other words, while the following inequality remains satisfied:The so-called “failure-envelope” or “limiting surface” is obtained when equality is reached.
As regards the rock mass, most failure criteria are empirical. It is thus necessary to establish a difference between those criteria that are exclusively applicable to intact rock and those that are applicable only to the rock mass itself. Most of the latter are based on the correction of the failure criterion of the intact rock depending on the Bieniawski’s rock mass rating (RMR).
Taking the intact rock as the starting point, we shall now analyse the approach we have taken in order to consider the RMR as a key factor in correcting the behaviour of the rock mass. For this purpose, we shall first examine the methods of Bieniawski–Yudhbir–Kalamaras [5], Sheorey [14] and Hoek–Brown [7]. For the first two methods, we shall analyse an existing inconsistency between the two to then propose a modification of the criteria. For the third method, we shall propose an adjustment of the equations if we use the RMR instead of GSI values. In order to validate our argument, we shall present the results obtained in a marble mine in the North of Spain, which was exploited using the room-and-pillar method.
Appendix A is included at the end of the paper that summarizes the ALMEC program, as well as the way in which the failure criteria used in the numerical modelling of a marble mine have been taken into consideration.
Section snippets
Criteria for the failure of rock masses
Many of the failure criteria for intact rock have been generalised in an attempt to simulate the rock mass behaviour. These generalisations are based on the idea that a rock mass failure envelope must follow the same kind of equation as intact rock and must be corrected according to its quality.
We shall now proceed to briefly describe these three criteria: those of Bieniawski–Yudhbir–Kalamaras, Sheorey and Hoek–Brown.
Based on the Bieniawski criterion for intact rock [2], the following failure
Modification of the failure criteria
Before presenting our proposed modification of the above-explained criterion, an inconsistency arising from a theoretical point of view must be analysed, as it has justified the modifications that will be introduced in this paper. This inconsistency will be exemplified for the first of the above criterion, that of Bieniawski, though the rest of the criteria behave similarly.
Fig. 1 represents the envelope according to the Bieniawski criterion for four rock masses with RMR values of 25, 50, 75,
Application and validation of the modified failure criteria
A failure criteria’s importance lies in the fact that it allows us to predict the real behaviour of the rock mass when it is exposed to a certain state of stress.
In this section, we shall compare the three failure criteria. We shall do so by applying these criteria to a specific mine in order to obtain the one that best fits reality and which can be applied to other mining exploitations. The steps that we have followed in this validation are the following:
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In a mine that has been exploited with
Conclusions
From the application of the failure criteria theory to this case of marble mining by rooms and pillars, the following conclusions can be drawn in the shape of a working methodology:
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First, it is necessary to define the parameters governing the failure of the intact rock. To do so, triaxial type tests are recommended and the adoption of the failure criteria of Hoek–Brown or Sheorey, which are very similar and of proven reliability throughout numerous experiments.
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The RMR of the rock mass must be
Acknowledgements
The authors gratefully acknowledge the support of Paul Barnes and Julia Contreras García for the preparation of this paper in English.
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