Linearized Liquefaction Process by Kalman Filter
Publication: Journal of Geotechnical Engineering
Volume 112, Issue 2
Abstract
Sand liquefaction is a very important problem during earthquake excitation. This paper details the development of equivalent linearization theory for sand, based on both the extended Kalman filter and the weighted global iteration method, and shows how this theory can be used to analyze liquefaction. The equivalent linearization model presented in this paper is very simple and numerically efficient. This numerical model for liquefaction allows direct determination of progressive pore‐water pressures. The model requires a relatively small number of parameters in comparison to an effective stress model by Finn et al. (13). The pattern of progressive pore‐water pressure based on the equivalent linearization law agrees reasonably well with Finn's model based on effective stress analysis for the dynamic response of saturated sand. However, the equivalent linearization law is computationally less efficient and a simple tool for evaluating progressive pore‐water pressure during earthquake motions.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bažant, Z. P., and Krizek, R. J., “Endochronic Constitutive Law for Liquefaction of Sand,” Journal of Engineering Mechanics Division, ASCE, Vol. 102, Apr., 1976, pp. 225–238.
2.
Beck, J. L., and Jennings, P. C., “Structural Identification using Linear Models and Earthquake Records,” Earthquake Engineering and Structural Dynamics, Vol. 8, 1980, pp. 145–160.
3.
Belieau, J. G., “Identification of Viscous Damping in Structures from Modal Information,” Journal of Applied Mechanics, Transactions ASME, 1976–6.
4.
Caravani, P., and Tomson, W. T., “Identification of Damping Coefficients in Multidimensional Linear Systems,” Journal of Applied Mechanics, Transactions ASME, 1974–6.
5.
Caravani, P., Watson, M. L., and Tomson, W. T., “Recursive Least Squares Time Domain Identification of Structural Parameters,” Journal of Applied Mechanics, Transactions ASME, 1977–3.
6.
Carmichael, D. G., “The State Estimation Problem in Experimental Structural Mechanics,” Proceedings of the 3rd International Conference on Application of Statistics and Probability in Soil and Structural Engineering, Sydney, Australia, 1979, pp. 802–815.
7.
Distefano, N., and Rath, A., “System Identification in Nonlinear Structural Seismic Dynamics,” Computer Methods Applied Mechanics and Engineering, 5, 1975, pp. 353–372.
8.
Distefano, N., and Rath, A., “Sequential Identification of Histeretic and Viscous Models in Structural Seismic Dynamics,” Computer Methods in Applied Mechanics and Engineering, 6, 1975, pp. 219–232.
9.
Distefano, N., and Pardo, B. P., “System Identification of Frames under Seismic Loads,” Journal of Engineering Mechanics Division, ASCE, Apr., 1976.
10.
Finn, W. D. L., Byrne, P. M., and Martin, G. R., “Seismic Response and Liquefaction of Sands,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 102, No. GT8, Aug., 1976, pp. 841–856.
11.
Finn, W. D. L., and Bhatia, S., “Endochronic Theory of Sand Liquefaction,” Proceedings, 7th. World Conference on Earthquake Engineering, Istanbul, Vol. 3, 1980, pp. 149–153.
12.
Finn, W. D. L., Lee, K. W., and Martin, G. R., “An Effective Stress Model for Liquefaction,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT6, June, 1977, pp. 517–533.
13.
Ghaboussi, J., and Dikmen, S. U., “Liquefaction Analysis of Horizontally Layered Sands,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT3, Mar., 1978, pp. 341–356.
14.
Halder, A., and Tang, W. H., “Probabilistic Evaluation of Liquefaction Potential,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT2, Feb., 1979, pp. 145–162.
15.
Hardin, B. O., and Drnevich, V. P., “Shear Modulus and Damping in Soils: Design Equations and Curves,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. SM7, Proc. Paper 9006, July, 1972, pp. 667–692.
16.
Hoshya, M., and Saito, E., “Structural Identification by Extended Kalman Filter,” The Journal of Engineering Mechanics Division, ASCE, Vol. 110, No. 12, Dec., 1984, pp. 1757–1770.
17.
Jazwinski, A. H., “Stochastic Processes and Filtering Theory,” Academic Press, 1970.
18.
Kagawa, T., and Kraft, L. M., “Modeling the Liquefaction Process,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 107, No. GT12, Dec., 1981.
19.
Kalman, R. E., “A New Approach to Linear Filtering and Prediction Problems,” Journal of Basic Engineering, Transaction, ASME, Vol. 83, 1960, pp. 35–45.
20.
Kalman, R. E., and Bucy, R. S., “New Results in Linear Filtering and Prediction Theory,” Journal of Basic Engineering, Transaction, ASME, Vol. 83, 1961, pp. 95–108.
21.
Kawa, I., and McNiven, H. D., “Investigation of the Elastic Characteristics of a Three‐Story Steel Structure Using System Identification,” Earthquake Engineering and Structural Dynamics, Vol. 10, 1982, pp. 433–445.
22.
McVerry, G. H., “Structural Identification in the Frequency Domain from Earthquake Records,” Earthquake Engineering and Structural Dynamics, Vol. 8, 1980, pp. 161–180.
23.
Seed, H. B., and Lee, K. L., “Liquefaction of Saturated Sands During Cyclic Loading,” Journal of the Mechanics and Foundations Division, ASCE, Vol. 93, No. SM3, Proc. Paper 5233, May, 1967, pp. 83–108.
24.
Seed, H. B., and Idriss, I. M., “Influence of Soil Conditions on Ground Motions During Earthquakes,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 95, No. SM1, Proc. Paper 6347, Jan., 1969, pp. 99–137.
25.
Shinozuka, M., Yun, C.‐B., and Imai, H., “Identification of Linear Structural Dynamics Systems,” Journal of Engineering Mechanics Division, ASCE, June, 1982.
26.
Yun, C.‐B., and Shinozuka, M., “Identification of Nonlinear Structural Dynamics,” Journal of Structural Mechanics, Vol. 8, No. 2, 1980, pp. 187–203.
27.
Zienkiewicz, O. C., Chang, C. T., and Hinton, H., “Nonlinear Seismic Response and Liquefaction,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 2, 1978, pp. 381–404.
Information & Authors
Information
Published In
Journal of Geotechnical Engineering
Volume 112 • Issue 2 • February 1986
Pages: 155 - 169
Copyright
Copyright © 1986 ASCE.
History
Published online: Feb 1, 1986
Published in print: Feb 1986
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.