A numerical procedure for determination of hydraulic uplift pressures/forces due to reservoir water on 3-dimensional foundation rock blocks in concrete dam foundations is presented. The procedure is implemented in a commercially available computer program, FLAC3D (
imensions). A sample problem is included to illustrate the use of the procedure.
Concrete dams are generally founded on sound rock formations. However, these rocks are traversed by discontinuities which render the rock mass vulnerable to sliding failure under loading from the dam, hydraulic uplift pressures due to the reservoir water, and earthquake induced perturbations in the foundation-dam-reservoir system. In a rigorous sense, the foundation-dam-reservoir system should be analyzed as one problem in engineering mechanics; however, in dam engineering practice, the problem is often solved piecemeal, that is, the stability of the foundation is analyzed separately from that of the dam. As such, the pressures/forces exerted by the dam and reservoir water on the foundation rock blocks are needed to perform stability assessment of the foundation. The scope of this paper is limited to the determination of uplift forces on the foundation rock blocks due to the reservoir water. The numerical model is three-dimensional (3-D), and the procedure presented is implemented in a commercially available computer program, FLAC3D -
imensions . FLAC3D is a three-dimensional explicit finite-difference program for engineering mechanics computations and has a built-in programming language, FISH, to facilitate user-defined uses of the program.
The problem of determining hydraulic uplift pressures/forces on foundation rock blocks is relatively simple. The adaptation of the procedure in FLAC3D was for reasons of convenience, and the computer instructions were written in FISH. However, the ideas and the proposed procedure can be implemented in other computer programs.
To our awareness, there is a general lack of reporting in the literature of the procedure(s) used for determining hydraulic uplift pressures/forces on foundation rock blocks. In the Bureau of Reclamation, this task has been carried out with the aid of Keyblock Module  to identify rock blocks vulnerable to sliding failure, AutoCAD  to define 3-D geometry, and MathCAD  to carry out numerical computations. However, this practice has been tedious, time consuming, and has the potential for errors in results due to coarseness of the discretization. These issues/concerns provided the motivation to seek alternative means to compute hydraulic uplift pressures/forces on the foundation rock blocks effectively and efficiently.
For ease of presentation, the nomenclature shown in figure 1(a) is used in this paper. A volume element
(available in full pape)
is defined by nodes and faces in a 3-D orthogonal coordinate system. Each face of a volume element is a quadrilateral bounded by four nodes, and lies in one plane. Thus, a general representation of a 3-D volume element is via a brick with 8-nodes and 6- faces, see figure 1(b). Different shapes of a 3-D volume element are achieved by adjusting the spatial locations of surrounding nodes.