Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of jointed rocks
Introduction
Rocks encountered in civil and mining engineering applications are, in general, jointed and anisotropic in nature. Their strength, under prevailing confining stress conditions, is needed while analysing problems related to deep tunnels, underground excavations and foundations. The strength of jointed rock, as a whole, depends on strength of the intact rock, joint geometry and surface characteristics of the joints. Depending on joint geometry and joint strength characteristics the rock blocks may undergo sliding, shearing, splitting or rotation at the time of failure. Substantial research has been carried out in past to understand the mechanical behaviour of rock joints [2], [3], [4], [5], [6]. The outcome of these studies may be used to analyse the rock mass behaviour if the joints are modelled explicitly.
Classification approaches [7], [8] consider the rock mass as an equivalent continuum, and the effect of the joints is considered implicitly. These approaches have found wide acceptability in the field. Laboratory studies on rocks and model materials have also been used to represent rock mass as an isotropic or anisotropic equivalent continuum [9], [10], [11], [12], [13]. These equivalent continuum approaches can be used to characterize the rock mass, from which the rock mass strength under unconfined state may be obtained. The effect of confinement (triaxial or polyaxial) may then be included using an appropriate strength criterion. The main objective of the present study is to suggest an approach in which the effect of minor and intermediate principal stress on the strength of jointed rock mass can be obtained with adequate accuracy at any given confining pressure.
The strength behaviour of the rocks is generally expressed by a strength criterion. Mohr–Coulomb strength criterion is the most widely used criterion for intact and jointed rocks as well. As discussed in earlier publication [1], the criterion in its present form suffers from two major limitations: (i) it ignores the non-linearity in strength behaviour, and (ii) the effect of intermediate principal stress is not considered in its conventional form. A non-linear strength criterion for intact rocks was suggested by Singh et al. [1], which is an extended form of the conventional Mohr–Coulomb criterion. The intermediate principal stress was also incorporated in the criterion. Using available extensive data from triaxial and polyaxial tests it was shown that the proposed simple criterion works better than the other popular criteria in vogue. An important advantage of the proposed criterion is that the conventional Mohr–Coulomb shear strength parameters are retained as such. In present paper, the criterion proposed for intact rock [1] is extended to jointed rocks. The applicability of the proposed criterion has been verified by applying it to data base available from literature.
Section snippets
Modified Mohr–Coulomb criterion
The complete derivation of the criterion for intact rocks has already been presented in [1]. The criterion was deduced from Barton's concept of critical state in rocks [14]. Barton [14] states that “critical state for any intact rock is defined as stress condition under which Mohr-envelope of peak shear strength of the rocks reaches a point of zero gradient. This condition represents the maximum possible shear strength of the rock. For each rock, there will be a critical effective confining
Extension to polyaxial stress conditions
The importance of considering the strength of rocks in polyaxial condition has been highlighted in the first part of this study [1]. It has been supported from literature that there is growing concern amongst the geotechnical fraternity about the polyaxial strength of rocks and rock masses. In the following section the modified Mohr–Coulomb criterion has been extended to polyaxial stress conditions and it has been shown that reasonably good estimates of the polyaxial strength of jointed rocks
Limitations and assumptions
The following limitations and assumptions apply to the proposed strength criterion for jointed rocks:
- i.
The suggested criterion is more suitable for those failure patterns where assumption of equivalent continuum is valid, and the equivalent properties are function of intact rock properties and joint characteristics. The joints are assumed to be tight with no infilling. If the joints are filled with gouge material, there will not be any wall-to-wall contact and the gouge material will govern the
Concluding remarks
Rock masses encountered in civil and mining engineering applications are invariably jointed. Mohr–Coulomb linear strength is the most widely used strength criterion to assess the strength behaviour of geological materials. However, in its conventional form, the criterion considers the strength behaviour to be linear and also ignores the effect of the intermediate principal stress. In present study the Mohr–Coulomb criterion has been modified to consider the non-linearity in assessing the
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