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- 1970-1-1
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The “strength reduction technique” is typically applied in factor-of-safety calculations by progressively
reducing the shear strength of the material to bring the slope to a state of limiting equilibrium.
A series of simulations are made using trial values of the factor Ftrial to reduce the cohesion c and
friction angle φ until slope failure occurs. First the code finds a “representative number of steps” (denoted by Nr ), which characterizes the
response time of the system. Nr is found by setting the cohesion to a large value, making a large
change to the internal stresses, and finding how many steps are necessary for the system to return
to equilibrium. Then for a given factor of safety, F, Nr steps are executed. If the unbalanced
force ratio* is less than 10−3, then the system is in equilibrium. If the unbalanced force ratio is
greater than 10−3, then another Nr steps are executed, exiting the loop if the force ratio is less than
10−3. The mean value of force ratio, averaged over the current span of Nr steps, is compared with
the mean force ratio over the previous Nr steps. If the difference is less than 10%, the system is
deemed to be in non-equilibrium, and the loop is exited with the new non-equilibrium F. If the
above-mentioned difference is greater than 10%, blocks of Nr steps are continued until either (1)
the difference is less than 10%, (2) 6 such blocks have been executed or (3) the force ratio is less
than 10−3. The justification for case (1) is that the mean force ratio is converging to a steady value
that is greater than that corresponding to equilibrium; the system must therefore be in continuous
motion. |
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