Thermal damage constitutive model for rock considering damage threshold and residual strength

Abstract

With the gradual depletion of mineral resources in the shallow part of the earth, resource exploitation continues to move deeper into the earth, it becomes a hot topic to simulate the whole process of rock strain softening, deformation and failure in deep environment, especially under high temperature and high pressure. On the basis of Lemaitre’s strain-equivalent principle, combined with statistics and damage theory, a statistical constitutive model of rock thermal damage under triaxial compression condition is established. At the same time, taking into account the existing damage model is difficult to reflect residual strength after rock failure, the residual strength is considered in this paper by introducing correction factor of damage variable, the model rationality is also verified by experiments. Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure, initiation, expansion, penetration, and the formation of macro-cracks under coupled effect of temperature and confining pressure. Rock thermal damage shows logistic growth function with the increase of temperature. Under the same strain condition, rock total damage decreases with the rise of confining pressure. By studying the electron microscope images (SEM) of rock fracture, it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite. The model parameter F reflects the average strength of rock, and M reflects the morphological characteristics of rock stress–strain curves. The physical meanings of model parameters are clear and the model is suitable for complex stress states, which provides valuable references for the study of rock deformation and stability in deep engineering.

Keywords

rock damage model / temperature effect / confining pressure / damage threshold / residual strength

References

[1] Al-ShayeaN A, KhanK, AbduljauwadS N. Effects of confining pressure and temperature on mixed-mode (I-II) fracture toughness of a lime-stone rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2000, 37(4): 629-643

[2] ZhaoY-s, WanZ-j, FengZ-j, YangD, ZhangY, QuFang. Triaxial compression system for rock testing under high temperature and high pressure [J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 52: 132-138

[3] YinT-b, WangP, LiX-b, ShuR-h, YeZ-yuan. Effects of thermal treatment on physical and mechanical characteristics of coal rock [J]. Journal of Central South University, 2016, 22(3): 2336-2345

[4] GautamP K, VermaA K, MaheshwarS, SinghT N. Thermomechanical analysis of different types of sandstone at elevated temperature [J]. Rock Mechanics and Rock Engineering, 2016, 49(5): 1985-1993

[5] LiM, MaoX-b, CaoL-l, PuH, MaoR-r, LuA-hong. Effects of thermal treatment on the dynamic mechanical properties of coal measures sandstone [J]. Rock Mechanics and Rock Engineering, 2016, 49(9): 3525-3539

[6] YangS-q, RanjithP G, JingH-w, TianW-l, JuYang. An experimental investigation on thermal damage and failure mechanical behavior of granite after exposure to different high temperature treatments [J]. Geothermics, 2017, 65: 180-197

[7] ZhaoY S, WanZ J, FengZ J, XuZ H, LiangW G. Evolution of mechanical properties of granite at high temperature and high pressure [J]. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 2017, 3(2): 199-210

[8] YinT B, WangP, LiX B, ShuR H, YeZ Y. Effects of thermal treatment on physical and mechanical characteristics of coal rock [J]. Journal of Central South University, 2016, 23: 2336-2345

[9] DougillJ W, LauJ C, BurtnJ. Toward a theoretical model for progressive failure and softening in rock, concrete and similar materials [J]. Mechanics in Engineering, 1976, 102: 333-355

[10] LiP, RaoQ-h, LiZ, MaW-b, MaBin. Thermal-hydro-mechanical coupling damage model of brittle rock [J]. Journal of Central South University, 2014, 21(3): 1136-1141

[11] LiuX S, NingJ G, TanY L, GuQ H. Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading [J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 85: 27-32

[12] VanD V, ArashM, GiangD N, AbdulH S. A thermodynamics-based formulation for constitutive modelling using damage mechanics and plasticity theory [J]. Engineering Structures, 2017, 143: 22-39

[13] CerfontaineB, CharlierR, CollinF, TaiebatM. Validation of a new elastoplastic constitutive model dedicated to the cyclic behaviour of brittle rock materials [J]. Rock Mechanics and Rock Engineering, 2017, 50(10): 2677-2694

[14] SaharaD P, SchoenballM, GerolymatouE, KohlT. Analysis of borehole breakout development using continuum damage mechanics [J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 97: 134-143

[15] CaoW-g, ZhaoM-h, LiuC-xue. Study on the model and its modifying method for rock softening and damage based on weibull random distribution [J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(19): 3226-3231

[16] ChenJ-w, YangC-h, GaoX-p, LiX-h, JiangD-yi. Study on the couple damage of temperature and mechanics for salt rock [J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(11): 1986-1991

[17] LiX, CaoW-g, SuY-hua. A statistical damage constitutive model for softening behavior of rocks [J]. Engineering Geology, 2012, 143–144: 1-17

[18] ZhangH-m, LeiL-n, YangG-she. Damage model of rock under temperature and load [J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(2): 3391-3396

[19] LiY-w, JiaD, RuiZ-h, PengJ-y, FuC-k, ZhangJun. Evaluation method of rock brittleness based on statistical constitutive relations for rock damage [J]. Journal of Petroleum Science and Engineering, 2017, 153: 123-132

[20] DengJ, GuD-sheng. On a statistical damage constitutive model for rock materials [J]. Computers & Geosciences, 2011, 37(2): 122-128

[21] LiuS, XuJ-yu. Analysis on damage mechanical characteristics of marble exposed to high temperature [J]. International Journal of Damage Mechanics, 2015, 24(8): 1180-1193

[22] ZhaoH, ShiC-j, ZhaoM-h, LiX-bing. Statistical damage constitutive model for rocks considering residual strength [J]. International Journal of Geomechanics, 2017, 17(1): 04016033

[23] CaiM-f, HeM-c, LiuD-yanRock mechanics and engineering [M], 2002, Beijing, Science Press

[24] LemaitreJ. How to use damage mechanics [J]. Nuclear Engineering and Design, 1984, 802233-245

[25] CaoR-l, HeS-h, WeiJ, WangFang. Study of modified statistical damage softening constitutive model for rock considering residual strength [J]. Rock and Soil Mechanics, 2013, 34(6): 1652-1660

[26] XuX-l, GaoF, ZhangZ-zhen. Influence of confining pressure on deformation and strength properties of granite after high temperatures [J]. Chinese Journal of Geotechnical Engineering, 2014, 36(12): 2246-2252

[27] XuX-l, GaoF, ZhangZ-zhen. Thermomechanical coupling damage constitutive model of rock based on the Hoek–Brown strength criterion [J]. International Journal of Damage Mechanics, 2018, 27(8): 1213-1230

[28] XuX-l, KarakusM. A coupled thermo-mechanical damage model for granite [J]. International Journal of Rock Mechanics and Mining Sciences, 2018, 103: 195-204

[29] MogiK. On the pressure dependence of strength of rocks and the coulomb fracture criterion [J]. Tectonophysics, 1974, 21(3): 273-285