A theory of heat extraction from fractured hot dry rock is presented, based on an infinite series of parallel vertical fractures of uniform aperture. Fractures are uniformly spaced and drain heat from blocks of homogeneous and isotropic impermeable rock. Cold water enters at the bottom of each fracture, and solutions are given in terms of dimensionless parameters from which the exiting water temperatures at the top of the fractures can be determined. An example of the application of the theory demonstrates how a multiply fractured system provides a more efficient mechanism for heat extraction than a single fracture in hot dry rock.

The Manifold Method of Material Analysis (MM) with high-order displacement functions has been derived based on triangular meshes for the requirement of high accurate calculations from practical applications. The matrices of equilibrium equations for the second-order MM have been given in detail for program coding. The derivation of the method is made by means of approximation theory and very few new mathematical concepts are used in this paper. So, it may be understood by most engineering researchers. By close comparison with widely used Finite Element Method, the advantages of MM can be seen very clearly in the following aspects: (1) the capability of processing large deformation and handing discontinuities like block oriented Discontinuous Deformation Analysis method; (2) making element meshes easily and (3) using high-order displacement functions easily. The C program codes for the second-order MM has been developed, and it has been applied to the example of a beam bending under a central point loading. The calculated results are quite good in agreement with theoretical solutions. By contrast, the results calculated for the same model by use of the original ÿrst-order MM are far from the theoretical solutions. Therefore, it is important and necessary to develop high-order Manifold Method for the complicated deformation problems. ? 1998 John Wiley & Sons, Ltd.

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Rock masses containing a large number of geological discontinuities (called joints) are treated as homogeneous, anisotropic porous media. A permeability tensor, hydraulically equivalent to a flow network formed by joints, is formulated in terms of two tensors and a nondimensional scalar, both depending only on the geometrical aspects of joints such as the spacing, size, orientation, and aperture. Two‐dimensional numerical analyses on seepage flow through the networks support the validity of the present theory. The information about the geometry of joints, which is obtained from the ventilation drift at Stripa mine, Sweden, is interpreted to give the corresponding permeability tensor. The permeability tensor is compared with the result of the large‐scale hydraulic conductivity test, with the conclusion that it provides a reasonable prediction for the hydraulic properties of Stripa jointed granite.

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SUMMARYThis paper presents a generalized procedure for the identification of rock blocks formed by finite-sized fractures around complex excavations. It was assumed that the study domain could be partitioned into a finite number of subdomains, where each either was, or could be, approximated by a convex polyhedron, and the fractures were finite in size and disc shaped and were defined using the location of the disc center, orientation, radius, cohesion coefficient, and friction angle. These may be either deterministic fractures obtained from a field survey or random fractures generated by stochastic modeling. In addition, the rock mass could be heterogeneous; i.e. the rock matrix and individual fractures could have different parameters in different parts. The procedure included: (1) partitioning of the model domain into convex subdomains; (2) removing noncontributive fractures. A fracture was deemed contributive when it played a part in block formation; i.e. it formed at least one surface with some of the blocks; (3) decomposing the subdomains into element blocks with fractures; (4) restoring the infinite fractures to finite discs; and (5) assembling the modeling domain. Our procedure facilitates robust computational programming, and is flexible in dealing with the problem of a complex study domain and with rock heterogeneity. A computer code was developed based on the algorithm developed in this study. The algorithm and computer program were verified using an analytical method, and were used to solve the problem of block prediction around the underground powerhouse of the Three Gorges Project.

SUMMARYDiscontinuous deformation analysis (DDA), a discrete numerical analysis method, is used to simulate the behaviour of falling rock by applying a linear displacement function in the computations. However, when a block rotates, this linear function causes a change in block size called the free expansion phenomenon. In addition, this free expansion results in contact identification problems when the rotating blocks are close to each other. To solve this problem of misjudgment and to obtain a more precise simulation of the falling rock, a new method called Post-Contact Adjustment Method has been developed and applied to the program. The basic procedure of this new method can be divided into three stages: using the linear displacement function to generate the global matrix, introducing the non-linear displacement function to the contact identification, and applying it to update the co-ordinates of block vertices. This new method can be easily applied to the original DDA program, demonstrating better contact identification and size conservation results for falling rock problems than the original program.