Civil Engineering Reference
In-Depth Information
9.2.2 Influence of Topography
Topography can considerably influence the in-situ stress state due to gravity, particular-
ly near the ground surface.
In order to evaluate the in-situ stress state below long topographic structures such as
slopes, cliffs, ridges and valleys two-dimensional analytical solutions have been devel-
oped. The solutions for V-notch valleys, small slopes, ridges and valleys as well as for
vertical cliffs with regular topography provided by Voight (1966a), McTigue & Mei
(1981), Savage et al. (1985), Savage & Swolfs (1986), McTigue & Mei (1987) and Savage
(1993) are based on isotropic rock mass behavior. Gravity-induced stresses in long sym-
metric ridges and valleys, assuming transversely isotropic rock mass behavior, are pre-
sented by Liao et al. (1992) and Pan et al. (1994). Pan & Amadei (1993) and Pan et al.
(1995) applied an analytical method for the in-situ stress determination of rock masses
with irregular topography assuming anisotropic rock mass behavior. By this method
irregular topography is accounted for by superposition of symmetric ridges and valleys.
However, the application of these analytical solutions, even to rock masses with regular
topography, is cumbersome. Therefore, it is recommended to evaluate the in-situ stress
state due to gravity influenced by the topography with the aid of the finite element
method (FEM) that is dealt with in Chapter 10.
This can be achieved with relatively low computational effort as in the example of a sym-
metric series of ridges and valleys with infinite length illustrated in Fig. 9.4. The rock mass
with a unit weight of
γ
= 25 kN/m3 is assumed to be isotropic and elastic (E = 2000 MPa,
ν
= 0.2, Fig. 9.4). In this case the analysis can be restricted to a computation section
bounded by the two planes of symmetry marked in Fig. 9.4, the ground surface and a
lower horizontal plane.
Figure 9.4
Isotropic, elastic rock mass with regular topography, computation section, boundary
conditions and parameters (Wittke 1990)
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