A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

A new 2D discontinuity roughness parameter and its correlation with JRC

The prime objective of this work is to improve our understanding of the shear behavior of rock joints. Attempts are made to relate the peak shear strength of rock joints with its three-dimensional surface morphology parameters. Three groups of tensile joint replicas with different surface morphology are tested with direct shear tests under constant normal load (CNL) conditions. Firstly, the three-dimensional surface characterization of these joints is evaluated by an improved roughness parameter before being tested. Then, a new empirical criterion is proposed for these joints expressed by three-dimensional quantified surface roughness parameters without any averaging variables in such a way that a rational dilatancy angle function is used instead of $${\text{JRC}} \cdot \log_{10} \left( {{{\text{JCS}} \mathord{\left/ {\vphantom {{\text{JCS}} {\sigma_{\text{n}} }}} \right. \kern-\nulldelimiterspace} {\sigma_{\text{n}} }}} \right)$$
 by satisfying the new peak dilatancy angle boundary conditions under zero and critical-state normal stress (not physical infinite normal stress). The proposed criterion has the capability of estimating the peak shear strength at the laboratory scale and the required roughness parameters can be easily measured. Finally, a comparison among the proposed criterion, Grasselli’s criterion, and Barton’s criterion are made from the perspective of both the rationality of the formula and the prediction accuracy for the three groups of joints. The limitations of Grasselli’s criterion are analyzed in detail. Another 37 experimental data points of fresh rock joints by Grasselli are used to further verify the proposed criterion. Although both the proposed criterion and Grasselli’s criterion have almost equal accuracy of predicting the peak shear strength of rock joints, the proposed criterion is easier and more intuitive from an engineering point of view because of its Mohr–Coulomb type of formulation.

New Peak Shear Strength Criterion of Rock Joints Based on Quantified Surface Description

Relationship between joint roughness coefficient and fractal dimension of rock fracture surfaces

A direct determination of the fractal dimensions of a fracture surface is essential for a better understanding of its complete topographic characteristics. In this paper, a laser profilometer is employed to measure the topography of a rock's fracture surface. With the use of the triangular prism surface area and projective covering methods, the resultant data set enables us to directly determine the fractal dimensions of a rock's fracture surface. Moreover, a new method, referred to as the cubic covering method, is proposed. The theoretical issues of fractal dimension estimation are also discussed.

Direct Estimation of the Fractal Dimensions of a Fracture Surface of Rock

Reassessing the Joint Roughness Coefficient (JRC) Estimation Using Z2

The three-dimensional roughness morphology of joint surfaces affects their mechanical behavior. The one-dimensional joint profiles provide an incomplete and biased characterization of joint surface morphology. A two-dimensional quantitative description of surface roughness is thus needed. This paper extends the Hurst index applied on the one-dimensional profile to the two-dimensional joint surfaces. The two-variable fractal Brownian motion theory is employed successfully to describe the whole degree of roughness on the joint surface. To find this two-dimensional roughness index, two base dimensions and asperity height of the joint surface are enlarged by different ratios to achieve the requirement of statistical self-affinity properties. The Hurst index and thus fractal dimension of two joint surfaces cored from sandstone and schist is examined using the triangular-prism-surface-area method as well as this new method. It is shown that for distinguishing the whole roughness difference between these joint surfaces the new method is better. The asperity height distribution of the joint surface is Gaussian and behaves like a self-affine fractal, while the sampling points are enough. For practical application, a two-dimensional Hurst index H 2D ; that is directly expressed in the form of Fourier series represented by the profiles in two properly orthogonal directions is proposed to describe the anisotropy of a whole joint surface.

S. C. Lo

Papers

Reassessing the Joint Roughness Coefficient (JRC) Estimation Using Z2

Two-dimensional Hurst Index of Joint Surfaces