An Elasto-Plastic Damage Model for Rocks Based on a New Nonlinear Strength Criterion

Rock Mechanics and Rock Engineering - Tập 51 - Trang 1413-1429 - 2018
Jingqi Huang1,2, Mi Zhao3, Xiuli Du3, Feng Dai4, Chao Ma3, Jingbo Liu2
1School of Civil and Environmental Engineering, University of Science and Technology Beijing, Beijing, China
2Department of Civil Engineering, Tsinghua University, Beijing, China
3Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, China
4State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and Hydropower, Sichuan University, Chengdu, China

Tóm tắt

The strength and deformation characteristics of rocks are the most important mechanical properties for rock engineering constructions. A new nonlinear strength criterion is developed for rocks by combining the Hoek–Brown (HB) criterion and the nonlinear unified strength criterion (NUSC). The proposed criterion takes account of the intermediate principal stress effect against HB criterion, as well as being nonlinear in the meridian plane against NUSC. Only three parameters are required to be determined by experiments, including the two HB parameters σc and m i . The failure surface of the proposed criterion is continuous, smooth and convex. The proposed criterion fits the true triaxial test data well and performs better than the other three existing criteria. Then, by introducing the Geological Strength Index, the proposed criterion is extended to rock masses and predicts the test data well. Finally, based on the proposed criterion, a triaxial elasto-plastic damage model for intact rock is developed. The plastic part is based on the effective stress, whose yield function is developed by the proposed criterion. For the damage part, the evolution function is assumed to have an exponential form. The performance of the constitutive model shows good agreement with the results of experimental tests.

Tài liệu tham khảo

Al-Ajmi AM, Zimmerman RW (2005) Relation between the Mogi and the Coulomb failure criteria. Int J Rock Mech Min Sci 42(3):431–439 Al-Rub RKA, Kim SM (2010) Computational applications of a coupled plasticity–damage constitutive model for simulating plain concrete fracture. Eng Fract Mech 77(10):1577–1603 Benz T, Schwab R, Kauther RA, Vermeer PA (2008) A Hoek–Brown criterion with intrinsic material strength factorization. Int J Rock Mech Min Sci 45(2):210–222 Brown ET (1993) The nature and fundamentals of rock engineering. In: Hudson JA, Brown ET, Fairhurst C, Hoek E (eds) Compressive rock engineering—principle, practice and projects, vol 1. Pergamon Press, Oxford, pp 1–23 Cai M (2010) Practical estimates of tensile strength and Hoek–Brown strength parameter mi of brittle rocks. Rock Mech Rock Eng 43(2):167–184 Chang C, Haimson B (2000) True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite. J Geophys Res 105(B8):18999–19013 Chen L, Shao JF, Huang HW (2010) Coupled elastoplastic damage modeling of anisotropic rocks. Comput Geotech 37(1):187–194 Cheng X, Wang J (2016) An elastoplastic bounding surface model for the cyclic undrained behaviour of saturated soft clays. Geomech Eng 11(3):325–343 Chiarelli AS, Shao JF, Hoteit N (2003) Modeling of elastoplastic damage behavior of a claystone. Int J Plast 19(1):23–45 Cicekli U, Voyiadjis GZ, Al-Rub RKA (2007) A plasticity and anisotropic damage model for plain concrete. Int J Plast 23(10):1874–1900 Colak K, Unlu T (2004) Effect of transverse anisotropy on the Hoek–Brown strength parameter ‘mi’ for intact rocks. Int J Rock Mech Min Sci 41(6):1045–1052 Colmenares LB, Zoback MD (2002) A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 39(6):695–729 Desai CS (2001) Mechanics of materials and interfaces: the disturbed state concept. CRC Press, New York Drucker DC, Prager W, Greenberg HJ (1952) Extended limit design theorems for continuous media. Q Appl Math 9(4):381–389 Du XL, Lu DC, Gong QM, Zhao M (2009) Nonlinear unified strength criterion for concrete under three-dimensional stress states. J Eng Mech 136(1):51–59 Eberhardt E (2012) The Hoek–Brown failure criterion. Rock Mech Rock Eng 45(6):981–988 Grassl P, Jirásek M (2006) Damage–plastic model for concrete failure. Int J Solids Struct 43(22):7166–7196 Haimson B, Chang C (2000) A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite. Int J Rock Mech Min Sci 37(1):285–296 Haimson B, Rudnicki JW (2010) The effect of the intermediate principal stress on fault formation and fault angle in siltstone. J Struct Geol 32(11):1701–1711 Hoek E (2006) Rock engineering-course notes by Evert Hoek, 2006 edn. http://www.rocscience.com/hoek/PracticalRockEngineering.asp Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186 Hoek E, Carranza-Torres C, Corkum B (2002) Hoek–Brown failure criterion, 2002 edn. In: Proceedings of NARMS-Tac, vol 1, pp 267–273 Hu C, Liu H, Huang W (2012) Anisotropic bounding-surface plasticity model for the cyclic shakedown and degradation of saturated clay. Comput Geotech 44:34–47 Jaiswal A, Shrivastva BK (2012) A generalized three-dimensional failure criterion for rock masses. J Rock Mech Geotech Eng 4(4):333–343 Jia Y, Song XC, Duveau G, Su K, Shao JF (2007) Elastoplastic damage modelling of argillite in partially saturated condition and application. Phys Chem Earth 32(8):656–666 Jiang H, Xie YL (2012) A new three-dimensional Hoek–Brown strength criterion. Acta Mech Sin 28(2):393–406 Jiang H, Zhao J (2015) A simple three-dimensional failure criterion for rocks based on the Hoek–Brown criterion. Rock Mech Rock Eng 48(5):1807–1819 Jiang H, Wang X, Xie Y (2011) New strength criteria for rocks under polyaxial compression. Can Geotech J 48(8):1233–1245 Kawamoto T, Ichikawa Y, Kyoya T (1988) Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory. Int J Numer Anal Methods 12(1):1–30 Kohgo Y, Nakano M, Miyazaki T (1993) Verification of the generalized elastoplastic model for unsaturated soils. Soils Found 33(4):64–73 Lade PV (1997) Modelling the strengths of engineering materials in three dimensions. Mech Cohe Frict Mater 2(4):339–356 Lee YK, Pietruszczak S, Choi BH (2012) Failure criteria for rocks based on smooth approximations to Mohr–Coulomb and Hoek–Brown failure functions. Int J Rock Mech Min Sci 56:146–160 Li X, Cao WG, Su YH (2012) A statistical damage constitutive model for softening behavior of rocks. Eng Geol 143:1–17 Linker MF, Dieterich JH (1992) Effects of variable normal stress on rock friction: observations and constitutive equations. J Geophys Res 97(B4):4923–4940 Lu DC, Ma C, Du XL, Jin L, Gong QM (2016a) Development of a new nonlinear unified strength theory for geomaterials based on the characteristic stress concept. Int J Geomech 17:04016058 Lu DC, Du XL, Wang GS, Zhou AN, Li AK (2016b) A three-dimensional elastoplastic constitutive model for concrete. Comput Struct 163:41–55 Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proc Jpn Soc Civ Eng 232:59–70 Matsuoka H, Yao Y, Sun D (1999) The Cam-clay models revised by the SMP criterion. Soils Found 39(1):81–95 Melkoumian N, Priest SD, Hunt SP (2009) Further development of the three-dimensional Hoek–Brown yield criterion. Rock Mech Rock Eng 42(6):835–847 Mogi K (1967) Effect of the intermediate principal stress on rock failure. J Geophys Res 72(20):5117–5131 Mogi K (1971) Fracture and flow of rocks under high triaxial compression. J Geophys Res 76(5):1255–1269 Mogi K (2007) Experimental rock mechanics. Taylor and Francis, London Pan XD, Hudson JA (1988) A simplified three dimensional Hoek–Brown yield criterion. In: ISRM international symposium. International Society for Rock Mechanics Perras MA, Diederichs MS (2014) A review of the tensile strength of rock: concepts and testing. Geotech Geol Eng 32(2):525–546 Priest SD (2005) Determination of shear strength and three-dimensional yield strength for the Hoek–Brown criterion. Rock Mech Rock Eng 38(4):299–327 Priest S (2012) Three-dimensional failure criteria based on the Hoek–Brown criterion. Rock Mech Rock Eng 45(6):989–993 Saksala T (2010) Damage–viscoplastic consistency model with a parabolic cap for rocks with brittle and ductile behavior under low-velocity impact loading. Int J Numer Anal Methods 34(13):1362–1386 Shao JF, Jia Y, Kondo D, Chiarelli AS (2006) A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions. Mech Mater 38(3):218–232 Shen J, Karakus M (2014) Simplified method for estimating the Hoek–Brown constant for intact rocks. J Geotech Geoenviron Eng 140(6):04014025 Single B, Goel RK, Mehrotra VK, Garg SK, Allu MR (1998) Effect of intermediate principal stress on strength of anisotropic rock mass. Tunn Undergr Space Technol 13(1):71–79 Takahashi M, Koide H (1989) Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m. In: ISRM international symposium. International Society for Rock Mechanics Voyiadjis GZ, Taqieddin ZN, Kattan PI (2008) Anisotropic damage–plasticity model for concrete. Int J Plast 24(10):1946–1965 Xie N, Zhu QZ, Xu LH, Shao JF (2011) A micromechanics-based elastoplastic damage model for quasi-brittle rocks. Comput Geotech 38(8):970–977 Yao YP, Wang ND (2013) Transformed stress method for generalizing soil constitutive models. J Eng Mech 140(3):614–629 Yao YP, Zhou AN, Lu DC (2007) Extended transformed stress space for geomaterials and its application. J Eng Mech 133(10):1115–1123 Yoshimine M (2006) 3-D Coulomb’s failure criterion for various geomaterials. In: Geomechanics II: testing, modeling, and simulation, pp 71–86 You MQ (2009) True-triaxial strength criteria for rock. Int J Rock Mech Min Sci 46(1):115–127 Yu MH, Zan YW, Zhao J, Yoshimine M (2002) A unified strength criterion for rock material. Int J Rock Mech Min Sci 39(8):975–989 Zhang L (2008) A generalized three-dimensional Hoek–Brown strength criterion. Rock Mech Rock Eng 41(6):893–915 Zhang L, Zhu H (2007) Three-dimensional Hoek–Brown strength criterion for rocks. J Geotech Geoenviron 133(9):1128–1135 Zhang Q, Zhu HH, Zhang LY (2013) Modification of a generalized three-dimensional Hoek–Brown strength criterion. Int J Rock Mech Min Sci 59:80–96 Zhou CY, Zhu FX (2010) An elasto-plastic damage constitutive model with double yield surfaces for saturated soft rock. Int J Rock Mech Min Sci 47(3):385–395 Zhou H, Jia Y, Shao JF (2008) A unified elastic–plastic and viscoplastic damage model for quasi-brittle rocks. Int J Rock Mech Min Sci 45(8):1237–1251 Zhou H, Bian HB, Jia Y, Shao JF (2013) Elastoplastic damage modeling the mechanical behavior of rock-like materials considering confining pressure dependency. Mech Res Commun 53:1–8