The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Abstract Knowledge of the spacing and size of discontinuities in a rock mass is of considerable importance for the prediction of rock behaviour. The characteristics of discontinuities can be estimated using scanline surveys but the precision of the estimates must be obtained and the bias caused by linear sampling must be eliminated before they can validly be used. Initially, an expression is presented which gives the degree of confidence that can be assigned to the measured mean discontinuity spacing. A reduced form of this expression is obtained for cases where the discontinuity spacings follow the negative exponential distribution. The precision of discontinuity frequency and RQD estimates is also explained. The distribution of trace lengths produced by the intersection of planar discontinuities with a planar rock face is used to determine the distribution of trace lengths, the distribution of semi-trace lengths and the distribution of censored semi-trace lengths intersected by a randomly located scanline. Comparison of the actual and sampled distributions demonstrates the bias introduced by scanline sampling of trace lengths. Relations between the distributions can be used to produce analytical or graphical methods of estimating mean trace length from censored measurements at exposures of limited extent.

Estimation discontinuity spacing and trace length using scanline surveys

http://uu.diva-portal.org/smash/get/diva2:1153724/FULLTEXT01

The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks

Flood susceptibility mapping using novel ensembles of adaptive neuro fuzzy inference system and metaheuristic algorithms.

Monte Carlo simulation (MCS) provides a conceptually simple and robust method to evaluate the system reliability of slope stability, particularly in spatially variable soils. However, it suffers from a lack of efficiency at small probability levels, which are of great interest in geotechnical design practice. To address this problem, this paper develops a MCS-based approach for efficient evaluation of the system failure probability P f , s of slope stability in spatially variable soils. The proposed approach allows explicit modeling of the inherent spatial variability of soil properties in a system reliability analysis of slope stability. It facilitates the slope system reliability analysis using representative slip surfaces (i.e., dominating slope failure modes) and multiple stochastic response surfaces. Based on the stochastic response surfaces, the values of P f , s are efficiently calculated using MCS with negligible computational effort. For illustration, the proposed MCS-based system reliab...

http://swrh.whu.edu.cn/dianqing/images/pdf-files/2015-Efficient_System_Reliability_Analysis_of_Slope_Stability_in_Spatially_Variable_Soils_Using_Monte_Carlo_Simulation.pdf

Efficient System Reliability Analysis of Slope Stability in Spatially Variable Soils Using Monte Carlo Simulation

Analysis of damage mechanisms and optimization of cut blasting design under high in-situ stresses

The key to three-dimensional discontinuous deformation analysis (3D DDA) is a rigorous contact theory that governs the interaction of many three-dimensional blocks. This theory must provide algorithms to judge contact types and locations and the appropriate state of each contact, which can be open, sliding or locked. This paper presents a point-to-face contact model, which forms a part of the contact theory, to be used in 3D DDA. Normal spring, shear spring and frictional force submatrices are derived by vector analysis and the penalty method. Also given are the “open-close” iteration criteria and operations performed for different changes in contact state. Sliding at a contact can occur in any direction parallel to the contact face, as opposed to one of two directions in two-dimensional DDA. This point-to-face contact model has been implemented into a 3D DDA computer program, and numerical results from several test cases demonstrate the validity of the model and the capability of the program.

A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis

In this study, shear tests on artificial rock joints with different roughness were conducted under five normal stress levels. Test results showed that the shear strength of rock joints had a positive correlation with roughness and the applied normal stress. Observation of joint specimens after shear tests indicated that asperity damage was mainly located in the steep areas facing the shear direction. The damaged joint surfaces tend to be rough, which implies that tensile failure plays an important role in shear behavior. As a result of the anisotropic characteristic of joint roughness, two quantitative 2D roughness parameters, i.e., the revised root-mean-square of asperity angle tan−1(Z
 2r) and the maximum contact coefficient C
 m, were proposed considering the shear direction. The proposed roughness parameters can capture the difference of roughness in forward and reverse directions along a single joint profile. The normalized tensile strength and the proposed roughness parameters were used to perform a rational derivation of peak dilatancy angle. A negative exponential-type function was found to be appropriate to model the peak dilatancy angle. Using the new model of peak dilatancy angle, we obtained a new criterion for peak shear strength of rock joints. The good agreement between test results and predicted results by the new criterion indicated that the proposed criterion is capable of estimating the peak shear strength of rock joints. Comparisons between the new criterion and published models from available literature revealed that the proposed criterion has a good accuracy for predicting the peak shear strength of joints investigated in this study.

Laboratory Investigation on Shear Behavior of Rock Joints and a New Peak Shear Strength Criterion

Three-dimensional numerical manifold method for unconfined seepage analysis is proposed in this article. By constructing hydraulic potential functions of the manifold element, the element conductivity matrix and the global simultaneous equations for unconfined seepage analysis are derived in detail. The algorithm of locating the free surface and the formula for seepage forces are also given. Three-dimensional manifold method employs the tetrahedral mathematical meshes to cover the whole material volume. In the iterative process for locating the free surface, the manifold method can achieve an accurate seepage analysis of the saturated domain below the free surface with mathematical meshes unchanged. Since the shape of manifold elements can be arbitrary, the disadvantage of changing the permeability of transitional elements cut by the free surface in the conventional Finite Element Method (FEM) is removed, and the accuracy of locating the free surface can be ensured. Furthermore, the seepage force acting on the transitional elements can be accurately calculated by the simplex integration. Numerical results for a typical example demonstrate the validity of the proposed method.

Qinghui Jiang

Papers

Analysis of damage mechanisms and optimization of cut blasting design under high in-situ stresses

A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis

Laboratory Investigation on Shear Behavior of Rock Joints and a New Peak Shear Strength Criterion

Modeling Unconfined Seepage Flow Using Three-Dimensional Numerical Manifold Method

A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis