Finite Element Method (FEM) - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 271

Figure 10.45 Principal normal stresses and plastic zones (Wittke 1990)
Figure 10.46 (right) shows the calculated vertical displacements along the two
vertical sections and the vault arch for cases 4 and 5. The reduced lateral sup-
port due to the open vertical joints does not considerably affect the calculated
displacements in the elastic analyses (cases 1 and 4). However, if the strength and
the corresponding viscoplastic behavior of the rock mass are taken into account
the reduced lateral support leads to increased displacements and to an increased
bending of the shotcrete membrane. Thus, small horizontal in-situ stresses may
cause failure of the shotcrete membrane due to bending. The stress resultants in
the shotcrete membrane calculated for cases 4 and 5 shows the large influence of
the reduced strength of the discontinuities (Fig. 10.47).
The analyzed load-bearing behavior of the rock mass and the shotcrete membrane
during an advancing vault excavation with open invert in a horizontally bedded and
vertically jointed rock mass is summarized in Fig. 10.48. When the shear strength of
the vertical joints and the horizontal stresses are small, the excavation of the tunnel
may lead to stepped failures and thus to a disintegration of the structure of the rock
mass above the vault. As a consequence, the arching effect around the opening is
reduced to a very limited amount and thus the shotcrete has to carry a large portion
of the overburden (Fig. 10.48, left).