Browse > Article
http://dx.doi.org/10.7474/TUS.2017.27.4.243

Failure Function of Transversely Isotropic Rock Based on Cassini Oval  

Lee, Youn-Kyou (Department of Coastal Construction Engineering, Kunsan National University)
Publication Information
Tunnel and Underground Space / v.27, no.4, 2017 , pp. 243-252 More about this Journal
Abstract
Since the failure behavior of transversely isotropic rocks is significantly different from that of isotropic rocks, it is necessary to develop a transversely isotropic rock failure function in order to evaluate the stability of rock structures constructed in transversely isotropic rock masses. In this study, a spatial distribution function for strength parameters of transversely isotropic rocks is proposed, which is based on the Cassini oval curve proposed by 17th century astronomer Giovanni Domenico Cassini to model the orbit of the Sun around the Earth. The proposed distribution function consists of two model parameters which could be identified through triaxial compression tests on transversely isotropic rock samples. The original Mohr-Coulomb (M-C) failure function is extended to a three-dimensional transversely isotropic M-C failure function by employing the proposed strength parameter distribution function for the spatial distributions of the friction angle and cohesion. In order to verify the suitability of the transversely isotropic M-C failure function, both the conventional triaxial compression and true triaxial compression tests of transversely isotropic rock samples are simulated. The predicted results from the numerical experiments are consistent with the failure behavior of transversely isotropic rocks observed in the actual laboratory tests. In addition, the simulated result of true triaxial compression tests hints that the dependence of rock strength on intermediate principal stress may be closely related to the distribution of the microstructures included in the rock samples.
Keywords
Strength anisotropy; Transversely isotropy; Mohr-Coulomb criterion; Cassini oval;
Citations & Related Records
Times Cited By KSCI : 8  (Citation Analysis)
연도 인용수 순위
1 Attewell, P.B. and M.R. Sandford, 1974, Intrinsic shear strength of a brittle, anisotropic rock - I experimental and mechanical interpretation, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 11, 423-430.   DOI
2 Choi, M.J. and H.S. Yang, 2005, Anisotropic analysis of tunnel in transversely isotropic rock, Tunnel & Underground Space, Korean Society for Rock Mechanics, 15, 391-399.
3 Donath, F.A., 1961, Experimental study of shear failure in anisotropic rocks, GSA Bull., 72(6), 985-989.   DOI
4 Donath, F.A., 1964, Strength variation and deformational behavior in anisotropic rock. In "State of stress in the Earth's crust", W.R. Judd Ed., New York, Elsevier, 281-298.
5 Duveau, G., J.F. Shao and J.P. Henry, 1998, Assessment of some failure criteria for strongly anisotropic geomaterials, Mech. Cohesive-Frictional Mat., 3, 1-26.   DOI
6 Weisstein, E.W., 2005, "Cassini ovals", From MathWorld - A Wolfram Web Resource, http://mathworld.wolfram.com/CassiniOvals.html
7 Kwasniewski, M., 1993, Mechanical behavior of anisotropic rocks, In "Compressive rock engineering", J.A. Hudson Ed., Oxford, Pergamon, 1, 285-312.
8 Ingraham, M.D., K.A. Issen and D.J. Holocomb, 2013, Response of Castlegate sandstone to true triaxial states of stress, J. Geophys. Res. Solid Earth, 118, 536-552.   DOI
9 Jaeger, J.C., 1960, Shear failure of anisotropic rocks, Geol. Mag., 97, 65-72.   DOI
10 Jung, J., C. Heo and S. Jeon, 2013, Study on hydraulic fracturing in transversely isotropic rock using bonded particle model, Tunnel & Underground Space, Korean Society for Rock Mechanics, 23, 470-479.   DOI
11 Lee, Y.K., 2007, Prediction of strength for transversely isotropic rock based on critical plane approach, Tunnel & Underground Space, Korean Society for Rock Mechanics, 17, 119-27.
12 Lee, Y.K. and S. Pietruszczak, 2008, Applicaiton of critical plane approach to the prediction of strength anisotropy in transversely isotropic rock masses, Int. J. Rock Mech. & Min. Sci., 45, 513-523.   DOI
13 Lee, Y.K. and B.H. Choi, 2011, Anisotropic version of Mohr-Coulomb failure criterion for transversely isotropic rock, Tunnel & Underground Space, Korean Society for Rock Mechanics, 21, 174-180.
14 Lee, Y.K., 2013, Intermediate principal stress dependency in strength of transversely isotropic Mohr-Coulomb rock, Tunnel & Underground Space, Korean Society for Rock Mechanics, 23, 383-391.   DOI
15 Lee, Y.K., 2015, Simulation of polyaxial tests using a failure condition for transversely isotropic rocks, Geosystem Engineering, 18, 29-37.   DOI
16 Park, C.W., C. Park, Y.B. Jung and E.S. Park, 2010, Application of suggested equations to determine the elastic constants of a transversely isotropic rock from single specimen, Tunnel & Underground Space, Korean Society for Rock Mechanics, 20, 153-168.
17 Lee, Y.K., 2016, Spatial distribution functions of strength parameters for simulation of strength anisotropy in transversely isotropic rock, Tunnel & Underground Space, Korean Society for Rock Mechanics, 26, 100-109.   DOI
18 Ma, X. and B.C. Haimson, 2016, Failure characteristics of two porous sandstones subjected to true triaxial stresses, J. Geophys. Res. Solid Earth, 121, 6477-6498.   DOI
19 Mogi, K., 2007, Experimental rock mechancis, pp.361, Balkema, London.
20 Park, C.W., C. Park and Y.B. Jung, 2012, Experimental study on the elastic constants of a transversely isotropic rock by multi-specimen compression tests, Tunnel & Underground Space, Korean Society for Rock Mechanics, 22, 346-353.   DOI
21 Park, C.W., C. Park, J.W. Park and Y.B. Jung, 2016, Mathematical understanding of the Saint-Venant approximation in analysis of a transversely isotropy, Tunnel & Underground Space, Korean Society for Rock Mechanics, 26, 363-374.   DOI
22 Pietruszczak, S. and Z. Mroz, 2001, On failure criteria for anisotropic cohesive-frictional materials, Int. J. Numer. Anal. Meth. Geomech., 25, 509-524.   DOI
23 Ramamurthy, T., 1993, Strength and modulus responses of anisotropic rocks, In "Compressive rock engineering", J.A. Hudson Ed., Oxford, Pergamon, 1, 313-329.
24 Saroglou, H. and G. Tsiambaos, 2008, A modified Hoek-Brown failure criterion for anisotropic intact rock, Int. J. Rock Mech. & Min. Sci., 45, 223-234.   DOI