Summary
This paper presents closed-form solutions for the stress field induced by gravity in anisotropic and stratified rock masses. These rocks are assumed to be laterally restrained. The rock mass consists of finite mechanical units, each unit being modeled as a homogeneous, transversely isotropic or isotropic linearly elastic material. The following results are found. The nature of the gravity induced stress field in a stratified rock mass depends on the elastic properties of each rock unit and how these properties vary with depth. It is thermodynamically admissible for the induced horizontal stress component in a given stratified rock mass to exceed the vertical stress component in certain units and to be smaller in other units; this is not possible for the classical unstratified isotropic solution. Examples are presented to explore the nature of the gravity induced stress field in stratified rock masses. It is found that a decrease in rock mass anisotropy and a stiffening of rock masses with depth can generate stress distributions comparable to empirical hyperbolic distributions previously proposed in the literature.
Similar content being viewed by others
References
Amadei, B., Savage, W. Z., Swolfs, H. S. (1987): Gravitational Stresses in Anisotropic Rock Masses. Int. J. Rock Mech. Min. Sci. vol. 24, No. 1, pp. 5–14.
Amadei, B., Savage, W. Z. (1985): Gravitational Stresses in Regularly Jointed Rock Masses. Proc. Int. Symposium on Fundamentals of Rock Joints. Bjorkliden, Ove Stephansson, Centek Publ. (Eds.), pp. 463–473.
Brown, E. T., Hoek, E. (1978): Trends in Relationships Between Measured In Situ Stresses and Depth. Int. J. Rock Mech. Min. Sci.,15, (no. 4), 211–215.
Gerrard, C. M. (1975): Background to Mathematical Modelling in Geomechanics: The Role of Fabric and Stress History. Proc. Int. Symp. on Numerical Methods, Karlsruhe, 33–120.
Gibson, R. E. (1974): The Analytical Method in Soil Mechanics. 14th Rankine Lecture. Geotechnique,24, (no. 2), 115–140.
Haimson, B. C., Rummel, F. (1982): Hydraufracturing Stress Measurements in the Iceland Research Drilling Project Drillhole at Reydasfjordur, Iceland. J. of Geophysical Research,87, (no. B8), 6631–6649.
Lekhnitskii, S. G. (1963): Theory of Elasticity of an Anisotropic Elastic Body. Holden Day, Inc., San Francisco.
Lempriere, B. M. (1968): Poisson's Ratios in Orthotropic Materials, J. Am. Inst. Aeroaut. Astronaut.,6 (no. 11), 2226–2227.
Lerau, J., Saint Leu, C., Sireys, P., (1981): Anisotropie de la Dilatance des Roches Schisteuses. Rock Mechanics,13, 185–196, in French.
Lin, W., Heuze, F. E. (1986): “In-Situ Dynamic Moduli of Mesaverde Rocks, Compared to Static and Dynamic Laboratory Moduli.” Proc. 27th Rock Mechanics Symposium, University of Alabama, June (AIME, Littleton, CO). Also Lawrence Livermore National Laboratory Report UCRL-94075.
Love, A. E. H. (1927). A Treatise on the Mathematical Theory of Elasticity. 4th Ed., Dover, New York.
Pickering, D. J. (1970): Anisotropic Elastic Parameters for Soil. Geotechnique,20 (no. 3), 271–276.
Salamon, M. D. G. (1968): Elastic Moduli of a Stratified Rock Mass. Int. J. Rock Mech. Min. Sci.,5, 519–527.
Savage, W. Z., Swolfs, H. S., Powers, P. S. (1985): Gravitational Stresses in Long Symmetric Ridges and Valleys. Int. J. Rock Mech. Min. Sci.,22 (no. 5), 291–302.
Swolfs, H. S. (1984): The Triangular Stress Diagram — A graphical representation of crustal stress measurements. Geological Survey Professional Paper No. 1291, 19 pp., Washington.
Terzaghi, K., Richart, F. E. (1952): Stresses in Rock About Cavities. Geotechnique,3, 57–90.
Tremmel, E., Widmann, R. (1970): Das Verformungsverhalten von Gneis. Proc. 2nd Cong. ISRM, Belgrade,1, 567–575.
Wardle, L. J., Gerrard, C. M. (1972): The Equivalent Anisotropic Properties of Layered Rock and Soil Masses. Rock Mechanics,4, 155–175.
Warpinski, N. R., Branagan, P., Wilmer, R. (1985): In-Situ Stress Measurements at U.S. DOE's Multiwell Experiment Site, Mesaverde Group, Rifle Colorado. J. of Petroleum Technology, March, pp. 527–536.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Amadei, B., Swolfs, H.S. & Savage, W.Z. Gravity-induced stresses in stratified rock masses. Rock Mech Rock Engng 21, 1–20 (1988). https://doi.org/10.1007/BF01019673
Issue Date:
DOI: https://doi.org/10.1007/BF01019673