Finite Element Method (FEM) - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 254

10.5.4 Simulation of Support Measures
A realistic simulation of support measures in finite element stability analyses is required
to account for the rock-support interaction adequately. In the following, some sugges-
tions are given in this respect.
Shotcrete
In order to assess the efficiency of shotcrete as a support measure during the stages of
excavation of an underground opening or a construction pit the stress-strain behavior
of the young shotcrete, which is, up to an age of 24 h, referred to as “green shotcrete”,
is essential. The stress-strain behavior of green shotcrete according to Hesser (2000) is
characterized by
- hardening (increasing of Young's modulus and strength) with time,
- creep ability decreasing with time,
- nonlinear creep disproportionate to increasing load.
In finite element stability analyses the development of Young's modulus with time as
well as creep and shrinkage are generally not taken into account. Instead, the shotcrete
is assumed to be elastic, exhibiting an equivalent modulus to account for hardening
after application as well as creep and shrinkage.
The interpretation of monitoring results in different tunneling projects by means of
back analyses has shown that a Young's modulus of E = 15,000 MPa can be used as
an equivalent modulus for the shotcrete. This corresponds to the 24-hour-value of con-
crete according to CEB (1978) and Weber (1979). However, in cases where the shotcrete
is already loaded at a particularly young age due to short pullout lengths and early
closing of the invert, values of 1000 MPa to 7500 MPa for the equivalent modulus of
shotcrete have proven to be more realistic (John et al. 2002, Wittke et al. 2002).
The loading of the shotcrete membrane is significantly dependent on the ratio of the mod-
uli of the rock mass and the shotcrete. The larger this ratio is, the greater is the proportion
of the rock mass pressure that the rock mass has to carry, provided that the rock mass
behaves widely elastic after excavation and support. The deformation, and thus the loading
of the shotcrete membrane, decreases with increasing Young's modulus of the rock mass.
Steel sets
Steel sets only become fully effective as a support if they form a closed ring. In this way
they are often used as support in mining without additional support measures.
In tunneling, the load-bearing behavior of steel sets is based on their bond with the
shotcrete membrane. Immediately after the steel set is installed and covered with
shotcrete, when the shotcrete still has a very low Young's modulus, it is mostly the
steel set that carries the loads resulting from rock mass pressure. Since steel sets
are usually installed close to the temporary face, initially their loading is general-
ly small. With progressing hardening of the shotcrete with time the strength and
thus the bearing capacity of the shotcrete membrane increases. Finally, when the
shotcrete has fully hardened, the normal stiffness of the steel sets can be neglected
compared to that of the shotcrete membrane (Wittke et al. 2002). As a consequence,