Some limitations of the models of limit equilibrium of forces for rock mass joints are discussed here, especially the exclusive use of dimensionless geometric parameters of roughness. A new limit equilibrium model of strain energies for rock joints, which allows the integration together of dilation and amplitude of roughness, is introduced by consideration of strength and deformability features. Important details of parameters of this equation are considered.

1 Introduction

The energies involved in the geomechanical processes of rock mass discontinuities slidings can not be measured either in the laboratory or in the field, but only calculated. But the forces involved in these processes can be measured and calculated. Now with two discontinuities having homothetic asperities, with the same slope but different amplitude (Figure 1), they slide and yield for the same strength as the Patton model and all other models of equilibrium limit of forces assert, wherein the magnitude of amplitude of the roughness is not involved, but only its slope. But the energies involved in the two cases are different. The position energy mobilized by the roughness of greater amplitude is higher than that mobilized in samples with lower asperities.

This creates a terrible paradox that is to be ineffective classic models of limit equilibrium of forces, to the point of being able to doubt of its internal coherence. On the other hand, Figure 2 shows that when the effect of cohesion or of the asperity shear strength is more important, according to models of Patton and Barton (the most important classical limit equilibrium models of forces) the participation of the asperity shear strength is lower, vanishing hyperbolically with increasing σn (Leal-Gomes & Dinis-da-Gama 2014a). At least in matched discontinuities under high average normal stress σn, where the asperities are strongly overlapped and adjusted and the sliding is made with their shear.

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