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Analysis Options: Solution Method
There are two solution methods used in RocSupport to compute
the Ground Reaction Curve for the tunnel: the Duncan Fama solution,
Duncan Fama (1993) and
the Carranza-Torres solution, Carranza-Torres
(2004). Both are closed-form solutions but with slightly different
approaches and assumptions.
The Duncan Fama solution is based on the Mohr-Coulomb failure criterion
of the rock mass, while the Carranza-Torres solution is based on
the Generalized Hoek-Brown criterion. The latter also takes into
account dilation and residual strength parameters.
Project Settings dialog.
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Analysis Options: Long Term Ground
Reaction Curve
The RocSupport solution methods compute the Ground Reaction
Curve based on initial assumed material properties and loading conditions.
To account for long term tunnel behaviour (e.g. rock mass property
deterioration, re-establishment of groundwater regimes, creep, etc.),
a strength reduction factor can be applied to obtain a long term Ground
Reaction Curve, (Hoek (2003).
If you select the “Plot Long Term Curve” checkbox in Project
Settings and enter a % reduction factor, this will be applied to the
strength and modulus parameters of the rock. Both short and long term
Ground Reaction Curves will then be computed, as shown in the following
figure.
Ground reaction curves. Short term (lower curve) and long
term (upper curve).
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Analysis Options: Deterministic/Probabilistic
In Project Settings you may select either Deterministic or Probabilistic
analysis. For a Deterministic analysis, all input values are assumed
to be exactly known, resulting in a unique ground reaction curve and
factor of safety for the support system.
For a Probabilistic Analysis, you may enter statistical distributions
for input parameters (e.g. Tunnel and Rock Parameters). This results
in a distribution of safety factors, from which a probability of
failure for the support system can be calculated. See the RocSupport
Probabilistic
Analysis page for more information.
Probabilistic analysis option in Project Settings.
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Analysis Options: References
Carranza-Torres, C., (2004) Elasto-plastic solution of tunnel problems
using the
generalized form of the Hoek–Brown failure criterion. International
Journal
of Rock Mechanics and Mining Sciences, Proceedings of the ISRM SINOROCK
2004
Symposium, edited by J.A. Hudson and Xia-Ting Feng, Volume 41, Issue
3, Pages 349-545.
Duncan Fama M. E., (1993) Numerical Modeling of Yield Zones in
Weak Rock. In: Hudson JA, editor. Comprehensive Rock Engineering,
2. Oxford: Pergamon, 1993. p. 49-75.
Hoek, E., (2003) Personal communication.
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