Parametric Study of Steel-Lined pressure Shafts in Anisotropic Rock
Steel-lined pressure tunnels and shafts are used to convey water from the reservoir to the turbines in high-head hydroelectric power plants. An axisymmetrical multilayer model is of-ten considered by engineers for the design of the steel liner. Stresses and deformations can then be computed with a closed-form analytical solution in isotropic rock. When the rock is anisotropic, the lowest elastic modulus of the rock measured in situ is often considered in the analytical solu-tion, which is regarded as conservative. In this work, the behaviour of steel liners in anisotropic rock was studied systematically by means of the Finite Element Method (FEM). The materials, namely steel, backfill concrete, near-field rock and far-field rock were modelled as linear and elas-tic, and a tied contact was assumed between the layers. The influence of geometrical and material parameters under a quasi-static internal water pressure was studied through an extensive para-metric study. It was observed that, compared to the corresponding results in isotropic rock, maxi-mum stresses in the steel-liner can be reduced up to 25% when anisotropy is considered. On the contrary, the maximum stresses in the far-field rock can be largely underestimated, namely up to 65%.
Gravitational stresses in anisotropic rock masses
Abstract This paper presents closed-form solutions for the stress field induced by gravity in anisotropic rock masses. These rocks are assumed to be laterally restrained and are modelled as a homogeneous, orthotropic or transversely isotropic, linearly elastic material. The analysis, constrained by the thermodynamic requirement that strain energy be positive definite, gives the following important result: inclusion of anisotropy broadens the range of permissible values of gravity-induced horizontal stresses. In fact, for some ranges of anisotropic rock properties, it is thermodynamically admissible for gravity-induced horizontal stresses to exceed the vertical stress component; this is not possible for the classical isotropic solution. Specific examples are presented to explore the nature of the gravity-induced stress field in anisotropic rocks and its dependence on the type, degree and orientation of anisotropy with respect to the horizontal ground surface.
Les fuites des galeries en charge en terrain sec. Rôle de revêtement, des injections, du terrain
Author's report is the latest in a series of research reports published in La Houille Blanche over a period of more than ten years in collaboration with other authors on the subject of unlined power tunnel equilibrium, among which notably on the theoretical and experimental research carried out on the unlined shaft at the Capivari power plant, which operates under a world record static pressure of 450 metres. In the most frequent cases, and as a general rule whenever possible, power tunnels are installed at sufficient depth underground to ensure that the groundwater pressure exceeds the tunnel pressure so that, if anything, the tunnel receives water from its environment when in service. Tunnels in a permeable medium not containing pressurized groundwater are a different case, however, as leakage is the only form of exchange that is liable to take place. This is the subject of Author's report, in which he attempts to calculate the possible leakage rates and establish how leakage can best be reduced in the first part of the report, the theoretical characteristics of flow originating in the assumed homogeneous and isotropic rock medium as a result of tunnel pressure are determined and several leakage rate formulae derived, which allow for permeability of the surrounding medium and the presence or absence of tunnel lining. Next, the forces causing leakage head loss are investigated, and it is shown that the resulting deformation of the tunnel lining will eventually crack it, thus considerably impairing its effectiveness in limiting losses (although this might be avoided by a very heavy lining, Author considers this to be a costly and somewhat doubtful solution). The only thing left, therefore, is to rely on ground impermeability to provide an effective barrier. This can be improved by grouting, but the effectiveness of present methods is restricted to fairly definite limits associated with operational difficulties or deformation of the ground, even after grouting. As a final conclusion, therefore, ideal impermeability of the considered type of structure would appear to be unattainable, except if there were a strict ruling that power tunnels only be sited in areas known to contain a rock aquifer, i.e. beyond the stope of the present study.