Rock-Joint Micromechanics: Relationship of Roughness to Closure and Wave Propagation
Publication: International Journal of Geomechanics
Volume 11, Issue 6
Abstract
The closure behavior of rock joints is intimately related to joint roughness. Here we utilize a micromechanical approach that explicitly considers asperity interactions on joint surfaces to study the rock-joint closure and wave propagation behavior. Elastic deformations and inelastic frictional sliding are considered at inclined asperity contacts. Rock-joint roughness is modeled through distributions of asperity heights and asperity contact orientations. The micromechanical approach developed in this paper establishes the link between the rock-joint closure behavior, the initial overlap of the joints, the asperity height distribution parameters, and the average asperity slope. The model is verified by comparison with experimental measurements. Subsequently a parametric study is performed. The results show that rock joints with the same roughness can exhibit a range of closure behavior depending upon initial overlap and rock intrinsic friction. Therefore, unique descriptions of rock-joint closure behavior are elusive. Finally, the model-predicted nonlinear normal and shear stiffness are used to investigate the reflection and transmission of plane waves at rock joints.
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References
Achenbach, J. D. (1973). Wave propagation in elastic solids, North-Holland, New York.
Adler, R. J., and Firman, D. (1981). A non-Gaussian model for random surfaces.” Philos. Trans. R. Soc. A, 303(1479), 433–462.
Bandis, S., Lumsden, A. C., and Barton, N. R. (1981). “Experimental studies of scale effects on the shear behavior of rock joints.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 18(1), 1–21.
Boitnott, G. N., Biegel, R. L., Scholz, C. H., Yoshioka, N., and Wang, W. (1992). “Micromechanics of rock friction 2. Quantitative modeling of initial friction with contact theory.” J. Geophys. Res., 97(B6), 8965–8978.
Brown, S. R., and Scholz, C. H. (1985). “Closure of random elastic surfaces in contacts.” J. Geophys. Res., 90, 5531–5545.
Brown, S. R., and Scholz, C. H. (1986). “Closure of rock joints.” J. Geophys. Res., 91, 4939–4948.
Dong, J. J., and Pan, Y. W. (1996). “A hierarchical model of rough rock joints based on micromechanics.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33(2), 111–123.
Greenwood, J. A., and Williamson, J. B. P. (1966). “Contact of nominally flat surfaces.” Proc. R. Soc. London, Ser. A, 295(1442), 300–319.
Gu, B., Suarez-Rivera, R., Nihei, K. T., and Myer, L. R. (1996). “Incidence of Plane Waves upon a fracture.” J. Geophys. Res., 101(B11), 25337–25346.
Hills, D. A., Nowell, D., and Sackfield, A. (1992). Mechanics of elastic contacts, Butterworth, Newton, MA.
Johnson, K. L. (1985). Contact mechanics, Cambridge University Press, New York.
Kendall, K., and Tabor, D. (1971). “An ultrasonic study of area of contact between stationary and sliding surfaces.” Proc. R. Soc. London, Ser. A, 323(1554), 321–340.
Malama, B., and Kulatilake, P. H. S. W. (2003). “Models for normal fracture deformation under compressive loading.” Int. J. Rock Mech. Min. Sci., 40(6), 893–901.
Mindlin, R. D., and Deresiewicz, H. (1953). “Elastic spheres in contact under varying oblique forces.” J. Appl. Mech., 20(3), 327–344.
Misra, A. (1997). “Mechanistic model for contact between rough surfaces.” J. Eng. Mech., 123(5), 475–484.
Misra, A. (1999). “Micromechanical model for anisotropic rock joints.” J Geophys Res, 104, 23175–23187.
Misra, A. (2002). “Effect of asperity damage on shear behavior of single fracture.” Eng. Fracture Mech., 69(17), 1997–2014.
Misra, A., and Marangos, O. (2008). “Micromechanical model of rough contact between rock blocks with application to wave propagation.” Acta Geophysica, 56(4), 1109–1128.
Murty, G. S. (1975). “A theoretical for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastic half-space.” Phys. Earth Planet. Inter., 11(1), 65–79.
Murty, G. S., and Kumar, V. (1991). “Elastic wave propagation with kinematics discontinuity along a non-ideal interface between two isotropic elastic half-spaces.” J. Nondestruct. Eval., 10(2), 39–53.
Nayak, P. R. (1971). “Random process model of rough surfaces.” J. Lubr. Technol., 93(3), 398–407.
Nakagawa, S., Nihei, K. T., and Myer, L. R. (2004). “Plane wave solution for elastic wave scattering by heterogeneous fracture.” J. Acoust. Soc. Am., 115(6), 2761–2772.
Pecorari, C. (2003). “Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact.” J. Acoust. Soc. Am., 113(6), 3065–3072.
Pyrak-Nolte, L. J., Myer, L. R., and Cook, N. G. W. (1990). “Transmission of seismic waves across single natural fractures.” J. Geophys. Res., 95(B6), 8617–8638.
Rokhlin, S. I., and Wang, Y. J. (1991). “Analysis of boundary conditions for elastic wave interaction with an interface between two solids.” J. Acoust. Soc. Am., 89(2), 503–515.
Schoenberg, M. (1980). “Elastic wave behavior across linear slip interfaces.” J. Acoust. Soc. Am., 68(5), 1516–1521.
Swan, G. (1983). “Determination of stiffness and other joint properties from roughness measurements.” Rock Mech. Rock Eng., 16(1), 19–38.
Swan, G., and Zongqi, S. (1985). “Prediction of shear behavior of joints using profiles.” Rock Mech. Rock Eng., 18(3), 183–212.
Wriggers, P. (2002). Computational contact mechanics, Springer, New York.
Xia, C. C., Yue, Z. Q., Tham, L. G., Lee, C. F., and Sun, Z. Q. (2003). “Quantifying topography and closure deformation of rock joints.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 40(2), 197–220.
Yamada, K., Takeda, N., Kagami, J., and Naoi, T. (1978). “Mechanisms of elastic contact and friction between rough surfaces.” Wear, 48(1), 15–34.
Yoshioka, N. (1994). “Elastic behavior of contacting surfaces under normal loads: A computer simulation using three-dimensional surface topography.” J. Geophys. Res., 99(B8), 15549–15560.
Yoshioka, N., and Scholz, C. H. (1989). “Elastic properties of contacting surfaces under normal and shear loads, 1, Theory.” J. Geophys. Res., 94(B12), 17681–17690.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 11 • Issue 6 • December 2011
Pages: 431 - 439
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jul 13, 2009
Accepted: Apr 28, 2010
Published online: May 1, 2010
Published in print: Dec 1, 2011
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