Numerical Modeling of Brittle Rock Failure under Dynamic Loading
N. Golchinfar and M. Cai
Bharti School of Engineering, Laurentian University, Sudbury, Ontario, Canada P3E 2C6
Tunnels in deep mines are subjected to high static stresses. Fracture and failure of the rock
mass around an opening can result from high mining-induced stresses, which may lead to
large deformations. In burst-prone grounds, seismicity can cause additional dynamic loading
which may increase the stress around the tunnel. When the stress reaches the rockmass
strength, rockmass fracturing can occur and rockburst may result. The support installed in the
tunnel must be capable of holding the failed rock in the failure zone. One method to estimate
the support capacity under dynamic loading is the energy approach based on the estimation of
the maximum ejection velocity (Stacey & Ortlepp, 1993), the other relies on a reasonable
estimate of the ultimate depth and extent of the failed zone under both static and dynamic
loading conditions.
Accurate estimation of the depth of failure is a challenging task. An empirical relationship
between the depth of failure and the stress level was established for brittle rocks (Eq. (1),
from case studies of observed depth of failure (Kaiser, et al., 1996; Martin, et al., 1999). The
effect of dynamic stress wave loading can be considered by superimposing the static and
dynamic stresses (Kaiser, et al., 1996).
df
a
 1.25
 max
 0.51  0.1
c
(1)
where d f : depth of failure, a : tunnel radius,  max : maximum tangential stress,  c : uniaxial
compressive strength
With the advance in numerical modeling, it is now possible to produce accurate results and
consider the effect of dynamic loading on stress changes around the opening directly. Vasak
and Kaiser (1995) simulated the effect of seismic waves on rock failure in a tunnel using
FLAC with a strain-softening model. By using a brittle model, Golchinfar and Cai (2012)
successfully simulated the depth of failure of the Mine-by tunnel under static loading. The
strength parameters assigned to the brittle model are more realistic with peak and residual
strength envelopes largely defined by cohesion strength and frictional strength components,
respectively.
In the present study, the effect of dynamic stress wave loading on the depth of failure around
excavations is investigated using the brittle model. The calculated depth of failure by the
numerical model is compared with the empirical approach in which the dynamic loading is
considered by adding a dynamic stress increase to  max in Eq. (1).
This research contributes to a more accurate simulation of the failure zone resulting from
dynamic loading generated from a remote seismic event, making it possible to design safe and
cost-effective rock support system in burst-prone grounds.
1.
References:
Golchinfar, N. & Cai, M., 2012. Modeling depth of failure using brittle morh-coulomb failure
model. Edmonton, Alberta, 21st Canadian Rock Mechanics Symposium.
Hajiabdolmajid, V., Kaiser, P. & Martin, C., 2002. Modelling brittle failure of rock.
International Journal of Rock Mechanics & Mining Sciences, 39(6), pp. 731-741.
Kaiser, P., Dwayne, D. T. & McCreath, D., 1996. Drift support in burst-prone ground.
Martin, C., Kaiser, P. & McCreath, D., 1999. Hoek-Brown parameters fro predicting the
depth of brittle failure around tunnels. canadian geotechnical Journal, pp. 136-151.
Stacey, T. R. & Ortlepp, W. D., 1993. Rockburst mechanisms and tunnel support in rockburst
conditions. Ostrava, Czech Republic, s.n., p. September .
Vasak, P. & Kaiser, P., 1995. Tunnel stability assessment during rockbursts, Montreal,
Quebec: CAMI '95, 3rd Canadian conference on computer applications in the mineral
industry.
Keywords: Numerical modeling, Dynamic loading, Depth of failure, Brittle failure,
Rockburst
To be submitted to: 23rd World Mining Congress and Expo 2013, August 11-15, 2013,
Montréal, QC Canada.