Parameter Optimization of Rock Failure Criterion Using Error-in-Variables Approach
Publication: International Journal of Geomechanics
Volume 11, Issue 1
Abstract
Parameters of rock failure criteria are estimated using an optimization procedure based on appropriate objective function. In the development of objective function, it is assumed that the independent variables are free from errors. But, as measurement error is attributed to equipment and random testing effects, all the measuring variables may have some error. In such cases, a statistical approach known as error-in-variables (EIVs) method has been proposed in literature. In EIV, the parameter vectors and reconciled values of the measured variables are estimated. The parameter estimation of such problem is associated with increase in dimensions of the optimization problems, and due to chosen nonlinear models, the resulting optimization problem is generally nonconvex. In the present study, the EIV approach has been applied for estimation of rock strength parameter for multiaxial rock failure criteria using evolutionary optimization algorithms. The rock strength parameters and the mean square error values so obtained have been compared with that obtained from least square and reweighted least-square methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aubertin, M., Li, L., Simon, R., and Khaifi, S. (1999). “Formulation and application of a short-term strength criterion for isotropic rocks.” Can. Geotech. J., 36(5), 947–960.
Bard, Y. (1974). Nonlinear parameter estimation, Academic, New York.
Das, S. K. (2005). “Slope stability analysis using genetic algorithm.” Electron. J. Geotech. Engrg., 10, Bundle A.
Das, S. K., and Basudhar, P. K. (2006). “Comparison study of parameter estimation techniques for rock failure criterion.” Can. Geotech. J., 43(7), 764–771.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms, Wiley, Chichester, U.K.
Desai, C. S. (2001). Mechanics of materials and interfaces: A disturbed state concept, CRC, Boca Raton, Fla.
Desai, C. S., and Chen, J. Y. (2006). “Parameter optimization and sensitivity analysis for disturbed state constitutive model.” Int. J. Geomech., 6(2), 75–88.
Domer, B., Raphael, B., Shea, K., and Smith, I. F. C. (2003). “A study of two stochastic search methods for structural control.” J. Comput. Civ. Eng., 17(3), 132–141.
Esposito, W. R., and Floudas, C. A. (1998). “Parameter estimation in nonlinear algebraic models via global optimization.” Comput. Chem. Eng., 22(1), S213–S220.
Feng, X. T., Li, S., Liao, H., and Yang, C. (2002). “Identification of non-linear stress-strain-time relationship of soils using genetic algorithm.” Int. J. Numer. Analyt. Meth. Geomech., 26(8), 815–830.
Gau, C. -Y., and Stadtherr, M. A. (2002). “Deterministic global optimization for error-in-variables parameter estimation.” AIChE J., 48(6), 1192–1197.
Goh, A. T. C. (1999). “Genetic algorithm search for critical slip surface in multiple-wedge stability analysis.” Can. Geotech. J., 36(2), 382–391.
Goldberg, D. E. (1989). Genetic algorithm in search, optimization, and machine learning, Addison-Wesley, Reading, Mass.
Jade, S., and Sitharam, T. G. (2003). “Characterization of strength and deformation of jointed rock mass based on statistical analysis.” Int. J. Geomech., 3(1), 43–54.
Karakus, M., Kumral, M., and Kilic, O. (2005). “Predicting elastic properties of intact rocks from index tests using multiple regression modeling.” Int. J. Rock Mech. Min. Sci., 42(2), 323–330.
Li, L., Gamache, M., and Aubertin, M. (2000). “Parameter determination for nonlinear stress criteria using a simple regression tool.” Can. Geotech. J., 37(6), 1332–1347.
Li, L., Lee, P. K. K., Tsui, Y., Tham, L. G., and Tang, C. A. (2003). “Failure process of granite.” Int. J. Geomech., 3(1), 84–98.
Liu, M. D., and Carter, J. P. (2003). “General strength criterion for geomaterials.” Int. J. Geomech., 3(2), 253–259.
McCombie, P., and Wilkinson, P. (2002). “The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis.” Comput. Geotech., 29(8), 699–714.
Pal, S., Wathugala, G. W., and Kundu, S. (1996). “Calibration of a constitutive model using genetic algorithm.” Comput. Geotech., 19(4), 325–348.
Phoon, K. -K., Kulhawy, F. H., and Grigoriu, M. D. (1995). “Reliability based design of foundations for transmission line structures.” Rep. TR-105000, Electric Power Research Institute, Palo Alto, Calif.
Ponterosso, P., and Fox, D. S. J. (2000). “Optimization of reinforced soil embankment by genetic algorithm.” Int. J. Numer. Analyt. Meth. Geomech., 24(4), 425–433.
Raphael, B., and Smith, I. F. C. (2003). “A direct stochastic algorithm for global search.” Appl. Math. Comput., 146(2–3), 729–758.
Rousseeuw, P. J. (1998). “Robust estimation and identifying outliers.” Handbook of statistical method for engineers and scientists, H. M. Wadsworth, ed., McGraw-Hill, New York.
Shah, S., and Hoek, E. (1992). “Simplex reflection analysis of laboratory strength data.” Can. Geotech. J., 29(2), 278–287.
Simpson, A. R., and Priest, S. D. (1993). “The application of genetic algorithms to optimization problem in geotechnics.” Comput. Geotech., 15(1), 1–19.
Varadarajan, A., Sharma, K. G., Desai, C. S., and Hashemi, M. (2001). “Constitutive modeling of a schistose rock in the Himalaya.” Int. J. Geomech., 1(1), 83–107.
Yu, M. H. (2002). “Advances in strength theories of materials under the complex stress state in the 20th century.” Appl. Mech. Rev., 55(3), 169–218.
Yu, M. H., Zan, Y. W., Zhao, J., and Yoshimine, M. (2002). “A unified strength criterion for rock material.” Int. J. Rock Mech. Min. Sci., 39(8), 975–989.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 11 • Issue 1 • February 2011
Pages: 36 - 43
Copyright
© 2011 ASCE.
History
Received: Nov 8, 2009
Accepted: Apr 5, 2010
Published online: Apr 12, 2010
Published in print: Feb 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.