Environmental Engineering Reference
In-Depth Information
a sensitive analysis on Mohr-coulomb and hoek-Brown
parameters effective in ground response curve
a.R. kargara & R. Rahmanejad
Department of Mining Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
aBsTRacT: convergence-confinement is one of the most popular methods that is applied for analyzing
the interaction of a circular opening in rock masses. it is assumed that circular tunnel excavated in a con-
tinuous, homogeneous, isotropic, initially elastic rock mass subjected to a hydrostatic stress
p
o
.
selecting appropriate failure criteria is very important in the analysis since it affects on plastic zone
and on the resulted displacement and stress field around the opening. some closed-form solutions have
suggested for the ground reaction curve, although they are driven based on elastic-perfectly plastic or
elastic-brittle-plastic models of rock mass behavior.
Brown et al. (1983) proposed a stepwise procedure based on hoek-Brown criterion to solve stress
and displacement around the circular opening for elastic-strain softening model of rock mass behavior.
a similar stepwise procedure was extracted in this study for Mohr-coulomb criterion. Finally a sensitive
analysis was implemented for Mohr-coulomb and hoek-Brown criteria in respect to their parameters.
By comparison of the relative displacement caused by changing strength parameters in hoek-Brown
and Mohr-coulomb criteria, it can be concluded that Mohr-coulomb criterion is more sensitive in respect
of variation of strength parameters of rock mass than hoek-Brown.
1
inTRoDUcTion
angle in the strain softening zone. alonso et al
.
(2003) proposed the self-similarity solution by solv-
ing the system of ordinary differential equations
of equilibrium, persistence, and radial displace-
ment velocity and flow rule. in routine engineering
application, the dilatancy of the rock is assumed
to be constant.
The aim of the present study is to apply a sensi-
tive analysis to strength parameters of hoek-Brown
and Mohr-coulomb criteria and investigating their
effects on the ground reaction curve.
analysis of stresses and displacements around
circular opening that excavated in isotropic rock
masses has been one of the fundamental problems
in geotechnical engineering. Provided that the ini-
tial stress field is hydrostatic, the problem may be
regarded as axisymmetric and an analytical solu-
tion can be found. This solution is useful in various
situations that include the validation of constitutive
models, the stability assessments of circular open-
ings such as borehole and TBM excavated tunnel,
the verification of numerical codes, the construction
of ground-support reaction curves, etc. in order to
obtain ground response curves for circular tunnels, a
number of analytical solutions have been presented
by considering the elastic-perfectly plastic and
elastic-brittle-plastic models of material behavior
with the linear Mohr-coulomb (M-c) and nonlin-
ear hoek-Brown (h-B) criteria (Brown et al
.,
1983;
Detournay, 1986; Wang, 1996; carranza-Torres
and Fairhurst, 1999; sharan, 2003, 2005; carranza-
Torres, 2004; Park and kim, 2006).
For an elastic-strain softening model, Brown
et al. (1983) presented a numerical stepwise pro-
cedure for the stresses and displacements in the
h-B media by assuming the constant value of elas-
tic strain in the plastic region such as that at the
elastic-plastic interface and the constant dilatancy
2
DeFiniTion oF The PRoBleM
Figure 1 shows a circular tunnel is excavated in
a continuous, homogeneous, isotropic, initially
elastic rock mass subjected to a hydrostatic stress
p
o
. The tunnel surface is subjected to an internal
pressure
p
i
. as
p
i
is gradually reduced, the radial
displacement occurs and a plastic region develops
around the tunnel when
p
i
is less than the initial
yield stress.
The material behaviour of elastic-strain softening
model used in this study is shown in Figure 2. There
are three different zones around the tunnel: the elas-
tic zone, the softening zone, and the residual zone.
after initial yielding, the strength of rock drops
gradually with increasing strain and follows the
