Page 196 - Numerical Analysis and Modelling in Geomechanics
P. 196
BACK ANALYSIS OF GEOTECHNICAL PROBLEMS 177
Note, however, that the covariance matrix of the measurements still affects the
covariance matrix associated with the best estimate of the parameters. In fact eq.
(6.23) becomes,
(6.28)
where
(6.29)
The influence of the measurement errors on the results of back analysis has been
discussed in [9] and [14] with reference to a simple rock mechanics problem.
The first study is based on the mentioned Monte Carlo or simulation approach,
while the second adopts the Bayesian procedure. To compare the results of the
two approaches, eqs. (6.27) and (6.29) were adopted in the Bayesian solution
procedure, instead of eqs. (6.18) and (6.23), since no a priori information can be
introduced in the “simulation” back analysis.
The results of the two studies showed that both approaches lead practically to
the same results, in terms of the relationships between the resolution of the
measuring devices and the uncertainty of the estimated parameters. However, the
computer time required by the simulation process is appreciably larger than that
required by the Bayesian back analysis.
Figure 6.1 Construction sequence of the railroad tunnel.
