Civil Engineering Reference
In-Depth Information
Also to the nodes on the lateral planes x = 0 and x = L having the same y and z coordi-
nates (e.g. points o and n as well as points p and q) the same displacements are assigned
({
δ
q
}). Such an analysis is also referred to as “pseudo-three-dimen-
sional” (Wittke 2000b).
Increased horizontal stresses in the rock mass, such as that due to tectonics or diage-
netic consolidation (Sections 9.3 and 9.4), can be simulated by imposing horizontal
displacements on the nodes located at vertical boundaries. This can be accomplished by
spring elements with very high spring constants c leading to the requested in-situ stress
state (Fig. 10.17). The horizontal displacement
δ
o
} = {
δ
n
}, {
δ
p
} = {
δ
x
needed to induce a horizontal stress
Δσ
x
in an isotropic, elastic rock mass specified in Fig. 10.17 was introduced in Section
9.3 by Equation (9.7).
If a tunnel is located underneath the groundwater level and there is no seepage flow, the
self-weight of the rock mass below the groundwater table is reduced by the hydrostatic
uplift. Instead of applying uplift forces to the corresponding nodes the unit weight of
the rock mass can be replaced by a reduced unit weight
'.
For a sealed tunnel with a double lining, a sealing is installed between the shotcrete
membrane and the internal lining. The sealing is protected and separated from the
shotcrete membrane by a fleece. Since the shotcrete membrane as well as the fleece are
permeable compared to the internal lining, the water pressure p
w
prevailing in the rock
mass can build up within the fleece along its complete circumference and needs to be
applied to the internal lining (Fig. 10.18).
γ
The situation for a machine-driven tunnel with a segmental lining located un-
derneath the groundwater table is illustrated in Fig. 10.19. Since the annular gap
between the rock mass and the segmental lining is grouted with mortar no water
pressure can act in this gap (Chapter 21). However, the water pressure within the
discontinuities that are located next to the excavation contour is acting on the seg-
mental lining and is increasing with depth. The balance of forces in the radial direc-
tion leads to the result that the same water pressure acts at the segmental lining as
at a sealed reinforced concrete lining (cf. Figs. 10.18 and 10.19). However, this water
pressure approach is only valid if the spacing of the water-filled discontinuities is
small compared with the diameter of the tunnel (Wittke et al. 2004, Wittke et al.
2006). In most practical cases this condition is fulfilled.
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