Page 239 - Numerical Analysis and Modelling in Geomechanics

220 I.-M.LEE AND D.-H.KIM

Figure 7.13 Plastic zone assessed by Hoek-Brown’s criterion.
Note
a W.Z. weathered zone.

to be a larger value in the field. Measurement errors of 4, 20 and 30 percent are
considered in this study to evaluate the influence of measurement accuracy on
the magnitude of uncertainty. Table 7.6 shows the reduction of uncertainties from
prior to posterior with the variation of measurement errors in model I–2. The
elastic modulus of the weathered rock layer is more sensitive to the changing of
measurement accuracy.

Concluding remarks
Introduced in this chapter is a new feedback system in which field measurements
and prior information are systematically combined together. The extended
Bayesian method (EBM) was adopted for the feedback analysis. The main
advantage of the extended Bayesian method is the introduction of the
hyperparameter β which is influenced by the sensitivity of the parameters and
uncertainties existing in both the prior information and the measurement. A
small value of β implies that the measurement possesses more weight than the
initially estimated information, and vice versa. Therefore, by observing the value
of β, the relative importance of feedback analysis can be easily seen.

References

Akaike, H., ‘Information Theory and an Extension of the Maximum Likelihood
Principle’, Second International Symposium on Information Theory, 1973,
pp. 267–281.
Beck, J.V. and Arnold, K.J., Parameter Estimation in Engineering and Science, New
York, John Wiley & Sons, 1977.
Cividini, A., Maier, G., and Nappi, A., ‘Parameter Estimation of a Static Geotechnical
Model Using a Bayes’s Approach’, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.,
1983, vol. 20, pp. 215–226.