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Numerische Erfassung der Strömungsvorgänge im geklüfteten Fels

Abstract:

The present work, addressed to practicing engineers, presents a numerical method for studying the changes in the groundwater flow in a porous, a fractured or a fractured-porous medium. Firstly, the state-of-the-art in the area of flow in fractured porous media is presented separately. The division of this chapter reflects three areas in which valuable research work has already been carried out by several researchers: flow in $he whole rock mass, flow in a single fracture and numerical methods. In the fundamental theory the most important flow laws for porous and fractured media are presented. These laws, which are the generalized Darcy-law, flow through two parallel plates and the computation of an equivalent permeability tensor after Snow (1965), can cover many problems encountered in engineering practice. The governing differential equation is derived from the mass conservation and the continuity equation. In particular, in regard to flow in incompletely saturated media, a big idealization of the material properties was necessary. In the incompletely saturated parts of the medium, both the permeability and the storage capacity are dependent on the water pressure and exhibit hysteresis during a wetting-drying cycle. The idealization of these material properties is made by means a linear relationship with respect to the water pressure. For a limited number of cases, it is possible to develop a closed form solution for the differential equation of flow. In this work it is solved for the case of nonsteady one-dimensional flow through a porous medium. The treatment of arbitrary domains and arbitrary boundary conditions is only possible employing a numerical method. In the present work the Finite Element method is used. The basic system of equations and the related element matrices are derived by application of the variational principle on the functional of the flow differential equation. The handling of the two typical boundary conditions for groundwater flow involves the determination of the free surface and the seepage face and leads to an iterative procedure which is unique in the present context, although approaches are contained in the works of Desai (1983) and Neuman (1973). The derived numerical method was implemented in the computer program AQUA-ROCK, which was tested with an exhaustive validation procedure. Computations of well-defined problems were carried out and compared with results obtained in three different ways: the analytical solution (one-dimensional fully saturated non-steady flow), electro-analogue solution (two-dimensional steady state flow through an earth dam after Rushton and Redshaw, 1978) and numerical results of other numerical methods (HYDROCOIN Level 1 Case 2).The program AQUA-ROCK allowed the study of practical problems in the area of rock and underground constructions. First, a parameter study of the flow conditions around a storage cavern in a rock mass is carried out. There the position of the water table is analyzed for several parameters: i.e. the influence of the height of the water table before the cavern was excavated, the influence of recharging wells and the influence of the filling degree of the cavern itself. During the construction of the Munich Subway important dewatering measures were and still are required. In an area, which encloses the subway station Lehel of the line 5/9, the measurements of the water level were evaluated. This was done before, during and after the tunnel passes through the area. Using a simplified model it was possible to reproduce numerically the basic phenomena of the lowering of the groundwater level. However, the very variable hydrogeological conditions in the variable soil could only be considered in a simplified manner: this observation shows clearly the limits of the application of numerical methods. A large field study of the piezometric heads in the rock foundation of the Albigna dam was carried out expressly for this work. It delivered a worthful connection between theory and practice. In a cross-section of block 14 of the dam in five boreholes with total length of 255 meters PIEZODEX measuring devices were installed. In all, the instrumentation comprises 46 measuring intervals, which are made watertight by 39 packers. During the rising of the reservoir level the water pressure was measured in the measuring devices. Essential evaluations are the contour plot of the water heads, the comparison of the reservoir water level evaluation with the water heads and the correlation of the water pressure with the opening of a crack, which was monitored with a sliding micrometer at the same time as the PIEZODEX measurements. Computations which were carried out with the program AQUA-ROCK confirmed the influence of the injection curtain which was inferred from the field observations. The effect of the observed crack on the head distribution has also been confirmed by the numerical study.

Authors:

Arn, Thomas

Index Terms:

rock; TunnelingGroup; Arn, Thomas

Further Information:

Date published: 1989