Constitutive Model for Rocks
Publication: Journal of Geotechnical Engineering
Volume 113, Issue 5
Abstract
A constitutive model based on the theory of plasticity is proposed and used to characterize stress‐deformation behavior of rocks. It allows for factors such as hardening, volume changes, stress paths, cohesive and tensile strengths, and variation of yield behavior with mean pressure. It is applied to characterize behavior of three hard rocks: Sandstone, Westerly Granite, and Dunham Dolomite. The constants for the model are determined from series of available laboratory tests conducted under different initial confinements and stress paths obtained by using multiaxial and cylindrical triaxial testing devices. The model is verified with respect to observed laboratory responses. Overall, the proposed model is found suitable to characterize the behavior of the rocks and involves less or equal number of constants compared to available models of similar capabilities and is easier to implement in (numerical) solution procedures.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Brown, E. T., and Michelis, P. N., “A Critical State Yield Equation for Strain Softening Rock,” Proceedings, 19th U.S. Symposium on Rock Mechanics, Lake Tahoe, Nev., 1978, pp. 515–519.
2.
Desai, C. S., “A General Basis for Yield, Failure and Potential Functions in Plasticity,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 4, 1980, pp. 361–375.
3.
Desai, C. S., and Faruque, M. O., “A Constitutive Model for (Geologic) Materials,” Journal of Engineering Mechanics Division, ASCE, Vol. 110, No. 9, Sep., 1984, pp. 139–1408.
4.
Desai, C. S., and Siriwardane, H. J., Constitutive Laws for Engineering Materials, Prentice‐Hall, Englewood Cliffs, N.J., 1984.
5.
Desai, C. S., Somasundaram, S., and Frantziskonis, G., “A Hierarchical Approach for Constitutive Modelling of Geologic Materials,” International Journal of Numerical and Analytical Methods in Geomechanics, Vol. 10, No. 3, 1986.
6.
DiMaggio, F. L., and Sandler, I. S., “Material Model for Granular Soil,” Journal of the Engineering Mechanics Division, ASCE, Vol. 97, No. 3, 1971, pp. 935–950.
7.
Dragon, A., and Mroz, Z., “A Continuum Model for Plastic‐Brittle Behavior of Rock and Concrete,” International Journal of Rock Mechanics, Mining Science & Geomechanics Abstracts, Vol. 16, 1979, pp. 253–259.
8.
Georgiannopolous, N., and Brown, E. T., “The Critical State Concept Applied to Rock,” International Journal of Rock Mechanics, Mining Science & Geomechanics Abstracts, Vol. 15, 1978, pp. 1–10.
9.
Goodman, R. E., Introduction to Rock Mechanics, John Wiley & Sons, New York, N.Y., 1980.
10.
Hannat, D. J., “Nomograms for the Failure of Plain Concrete Subjected to Short‐Term Multiaxial Stresses,” The Structural Engineer, Vol. 52, 1974, pp. 151–165.
11.
Ichikawa, Y., et al., “Brittle‐Fracture of a Tuffaceous Rock and Plasticity Theory,” Proceedings, International Conference on Constitutive Laws for Engineering Materials, C. S. Desai and R. H. Gallagher, Eds., Tucson, Ariz., 1982, pp. 349–355.
12.
Isenberg, J., and Bagge, C. F., “Analysis of Steel‐Lined Penetration Shafts for Deeply Buried Structures,” Proceedings, Symposium on Applications of the Finite Element Method in Geotechnical Engineering, Vicksburg, Miss., 1972, pp. 1145–1164.
13.
Jaeger, J., and Cook, N. G. W., Fundamentals of Rock Mechanics, Chapman & Hall, London, U.K., 1976.
14.
Kim, M. K., and Lade, P. V., “Modelling Rock Strength in Three Dimensions,” International Journal of Rock Mechanics, Mining Science & Geomechanics Abstracts, Vol. 21, 1984, pp. 21–23.
15.
Kovari, K., Hagedorn, H., and Fritz, P., “Parametric Studies as a Design Aid in Tunnelling,” Proceedings, 2nd International Conference on Numerical Methods in Geomechanics, ASCE, Vol. II, Blacksburg, Va., 1976, pp. 773–790.
16.
Kulhawy, F. H., “Stress Deformation Properties of Rock and Rock Discontinuities,” Journal of Engineering Geology, Vol. 9, 1975, pp. 327–350.
17.
Lade, P. V., “Three‐Parameter Failure Criterion for Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 108, No. 5, May, 1982, pp. 850–863.
18.
Mitchell, J. K., “The Properties of Cement‐Stabilized Soils,” Proceedings, Workshop on Materials and Methods for Low Cost Road, Rail and Reclamation Works, Leura, Australia, 1976, pp. 365–404.
19.
Mogi, K., “Effect of the Intermediate Principal Stress on Rock Failure,” Journal of Geophysical Research, Vol. 72, 1967, pp. 5117–5130.
20.
Nishida, T., Esaki, T., Aoki, K., and Kimura, T., “On the Stress Loci by Strain Controlled Tests on Sandstone under Generalized Triaxial Stress,” Proceedings, 6th Japan Symposium on Rock Mechanics, Japan, 1984, pp. 43–48.
21.
Price, A. M., and Farmer, I. W., “Application of Yield Models to Rock,” International Journal of Rock Mechanics, Mining Science & Geomechanics Abstracts, Vol. 16, 1979, pp. 157–159.
22.
Price, A. M., and Farmer, I. W., “The Hvorslev Surface in Rock Deformation,” International Journal of Rock Mechanics, Mining Science & Geomechanics Abstracts, Vol. 18, 1981, pp. 229–234.
23.
Reyes, S. F., and Deere, D. U., “Elasto‐Plastic Analysis of Underground Openings by the Finite Element Method,” Proceedings, 1st International Congress on Rock Mechanics, Vol. II, Lisbon, Portugal, 1966.
24.
Salami, M. R., “Constitutive Modelling of Concrete and Rock under Multiaxial Compressive Loadings,” thesis presented to the University of Arizona, at Tuscon, Ariz., in 1986, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
25.
Schofield, A. N., and Wroth, C. P., Critical State Soil Mechanics, McGraw‐Hill, London, U.K., 1968.
26.
Zienkiewicz, O. C., Valliappan, S., and King, I. P., “Elasto‐Plastic Solutions of Engineering Problems—‘Initial Stress’ Finite Element Method,” International Journal of Numerical Methods in Engineering, Vol. 1, No. 1, 1969.
Information & Authors
Information
Published In
Journal of Geotechnical Engineering
Volume 113 • Issue 5 • May 1987
Pages: 407 - 423
Copyright
Copyright © 1987 ASCE.
History
Published online: May 1, 1987
Published in print: May 1987
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.