Finite-element method for combined calculations of the seepage regime and static performance of a ?concrete-dam/rock-bed? system

Abstract

A number of emergency situations at concrete dams founded on rock beds [t] have forced engineers to consider the problem of the reliability of these beds, which had previously been considered ideal. The unfavorable effects of water percolating into a rock mass, which ultimately led to loss of rock stability, were the case of the two largest catastrophes (Malpass and Vaiont Dams) [1]. The tragic events of these years provided the impetus for the development of methods of mathematical modeling of seepage regimes and the static performance of hydraulic structures and their rock beds. According to the geomechanic concept of rock, which is now widely adopted [15], a rock mass is a set of individual integral blocks of rock, which are separated by systems of differently oriented cracks. The mechanical and seepage properties of this discrete medium are determined by the geometry of its structure and the properties of the blocks and cracks. The complexity of the structure, anisotropy, and nonuniformity of rock have predetermined the widespread use of numeric methods employed at the present time to calculate rock masses and, primarily, the finite-element method (FEM) [2]. Problems involving calculation of the seepage regime of a rock bed and the stress-strain state (SSS) of the structure-rock system are closely related to one another and reqnire combined solution. The permeability of a rock mass and, consequendy, the pattern of seepage in it depend heavily on the SSS. The distribution of seepage potentials determines, in turn, the magnitude and distribution of hydrostatic and hydrodynamic seepage forces, which, together with other loads, form the SSS of the dam/rock-bed system. Two methods are proposed for the combined static and seepage calculations of this system [3, 16] using the FEM. In both methods, similar iteration procedures, the schematic of which is also used in the method under discussion, are employed for combined solution of seepage and static problems. The basic difference in these methods consists in the very model of the material's seepage and mechanical properties, which is incorporated in the calculation. Semenov [3] uses the familiar approach of a quasicontinuum, when broken jointed-block rock is treated as a solid mass with corresponding characteristics "spread" across the area. In this case, the relationship between the permeability of the rock and its deformation is given in the form of experimentally obtained curves. The model of the quasicontinuum, which can be used with success for calculations involving heavily jointed statistically homogeneous rock, may lead, however, to false results in cases of irregular jointing, a sparsely jointed mass with a number of large cracks, etc. Significant difficulties also arise in attempting to model the performance of the contact joint between the dam and bed and other specific structural components within the framework of this approach. The approach used by Brekke et al. [16], where the rock bed is treated as a discrete medium using a special finite element [ 17] to model the static performance of the cracks and contact joint, is free of these drawbacks. Neglecting the permeability of the blocks of rock, the authors consider the seepage of water through the cracks in the bed and contact joint [17]. The described approach adequately reflects the actual geometric structure and properties of the jointed-block rock. Moreover, attempts at detailed reproduction for the solution of a specific problem of the complex geometric structure of the rock mass under investigation give rise to a marked increase in labor outlays for the investigation and are inevitably involved with problems of the reliability of initial information and economic-engineering expediency. This approach to the rock calculation, which, in itself, would ensure the value of both methods, is required to reduce their deficiencies to a minimum. In this sense, a method of investigation would be optimal where two types of models of a discrete medium are used within the framework of a single generalized method of combined static-seepage calculations: quasicontinuous - for the modeling of statistically homogeneous heavily jointed zones of the region under investigation, and integral continuous blocks of rock and individual cracks - for the modeling of the contact joint and individual cracks in