Estimating Subgrade Reaction Modulus for Transversely Isotropic Rock Medium
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 136, Issue 8
Abstract
Most of the rock medium possesses intrinsic grain orientation or preferred bedding and joint directions, thus requiring the use of at least transverse isotropy to describe its elastic behavior. This paper presents a series of charts, based on extensive finite element parametric studies along with nonlinear regression analysis of FE simulation results, for estimating the subgrade reaction modulus (or initial tangent to the curve) using five elastic constants of a transversely isotropic rock mass. The proper characterization of subgrade reaction modulus is critical for accurate prediction of the elastic lateral deflection of a rock socketed drilled shaft under the applied lateral loads. The sensitivity of the response of a laterally loaded drilled shaft to the degree of anisotropy and orientation of the plane of anisotropy (bedding plane direction of the rock medium) was demonstrated in this paper for an actual lateral load testing case in Ohio. It is highly recommended to use five elastic constants to estimate subgrade reaction modulus of rock medium exhibiting high degree of cross anisotropy.
Get full access to this article
View all available purchase options and get full access to this article.
References
Amadei, B. (1996). “Importance of anisotropy when estimating and measuring in situ stresses in rock.” Int. J. Rock Mech. Min. Sci., 33(3), 293–325.
Amadei, B., Savage, W., and Swolfsh, H. (1987). “Gravitational stresses in anisotropic rock masses.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 24(1), 5–14.
ANSYS 11.0, user manual, vol. IV, theory. (2007). Swanson Analysis Systems Inc., Houston, Pa.
Bowles, J. E. (1988). Foundation analysis and design, 4th Ed., McGraw-Hill, New York, 1004.
Carter, D. P. (1984). “A non-linear soil model for predicting lateral pile response.” Rep. No. 359, Civil Engineering Dept., Univ. of Auckland, New Zealand.
Chen, C. S., Pan, E., and Amadei, B. (1998). “Determination of deformability and tensile strength of anisotropic rock using Brazilian tests.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 35(1), 43–61.
Exadaktylos, G. E. (2001). “On the constraints and relations of elastic constants of transversely isotropic geomaterial.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 38, 941–956.
Gabr, M. A., Borden, R. H., Cho, K. H., Clark, S. C., and Nixon, J. B. (2002). “ curves for laterally loaded drilled shafts embedded in weathered rock.” Rep. No. FHWA/NC/2002-08, North Carolina DOT, North Carolina.
Gerrad, C. M. (1975). “Background to mathematical modeling in geomechanics: The roles of fabric and stress history.” Proc. Int. Symp. on Numerical Methods, Wiley, Karlsruhe, Germany, 33–120.
Guo, W. D. (2001). “Subgrade modulus for laterally loaded piles.” Proc., 8th Int. Conf. on Civil and Structural Engineering Computing, Civil-Comp Press, Stirling, U.K.
Hawk, D. J., and Ho, H. Y. (1980). “A study of the orthotropy of coal and other rock materials.” Final Rep. to U.S. Dept. of Interior and Bureau of Mines, Univ. of Colorado, Boulder, Colo.
Hoek, E. (2002). “Practical rock engineering, 2002 Edition.” ⟨http://www.rocscience.com/roc/Hoek/Hoeknotes2000.htm⟩ (March 2009).
Homand, F., Morel, E., Henry, Y. H., Cuxac, P., and Hammade, E. (1993). “Characterization of the moduli of elasticity of an anisotropic rock using dynamic and static methods.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30(5), 527–535.
Johnston, J., and Christensen, N. (1994). “Elastic Constants and velocity surfaces of indurated anisotropic shales.” Surv. Geophys., 15(5), 481–494.
Justo, J. L., Juston, E., Durand, P., and Azañón, J. M. (2006). “The foundation of a 40-story tower in jointed basalt.” Int. J. Rock Mech. Min. Sci., 43(2), 267–281.
Liang, R. Y., Yang, K., and Nusairat, J. (2009). “ criterion for rock mass.” J. Geotech. Geoenviron. Eng., 135(1), 26–36.
Liao, J. J., Hu, T., and Chang, C. (1997). “Determination of dynamic elastic constants of transversely isotropic rock using a single cylindrical specimen.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 34(5), 837–849.
Liu, W., and Novak, M. (1994). “Dynamic response of single pile embedded in transversely isotropic layered media.” Earthquake Eng. Struct. Dyn., 23, 1239–1257.
Lo, T., Coyner, K., and Toksoz, M. (1986). “Experimental determination of elastic anisotropy of Berea sandstone, Chicopee shale, and Chelmsford granite.” Geophysics, 51(1), 164–171.
Marinos, P., and Hoek, E. (2000). “GSI: A geologically friendly tool for rock mass strength estimation.” Proc., Int. Conf. on Geotechnical and Geological Engineering, GeoEng2000, Technomic Publishers, Melbourne.
Reese, L. C. (1997). “Analysis of laterally loaded piles in weak rock.” J. Geotech. Geoenviron. Eng., 123(11), 1010–1017.
ROCSCIENCE. (2006). “RocLab.” Rocscience, Inc., Toronto, ⟨http://www.rocscience.com⟩ (May 2010).
Sargand, S. M., and Hazen, G. A. (1987). “Deformation behaviour of shales.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 24(6), 365–370.
Shatnawi, E. S. (2008). “Development of criterion for anisotropic rock and cohesive intermediate geomaterials.” Ph.D. dissertation, Univ. of Akron, Akron, Ohio.
SPSS. (2003). SPSS Base 12.0 user’s guide, SPSS Inc., Chicago.
Vesic, A. S. (1961). “Beam on elastic subgrade and the Winkler hypothesis.” Proc., 5th Int. Conf. Soil Mechanics and Foundation Engineering, Vol. 1, 845–850.
Wallace, J. W., et al. (2002). “Cyclic large deflection testing of shaft bridges part II: Analytical studies.” Rep. from California DOT, Calif.
Wittike, W. (1990). Rock mechanics theory and applications with case histories, Springer, Berlin.
Yang, K. (2006). “Analysis of laterally loaded drilled shafts in rock.” Ph.D. dissertation, Univ. of Akron, Akron, Ohio.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Dec 27, 2008
Accepted: Oct 16, 2009
Published online: Oct 22, 2009
Published in print: Aug 2010
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.