FLOW AND FRACTURE OF ROCKS UNDER GENERAL TRIAXIAL COMPRESSION

Abstract

Abstract: Recent laboratory studies of the flow and fracture of rocks under general triaxial compression are reviewed. New developments in laboratory techniques have made it possible to measure three principal stresses and strains under general triaxial stress states, in which all three principal stresses are different.Strength and ductility of isotropic rocks are markedly affected not only by the least compression, but also by the intermediate compression although these two effects are rather additional in strength, but opposite in ductility. The experimental results show that dilatancy is highly aniso-tropic under the general triaxial stress states.Deformational properties of anisotropic rocks have been also measured under the general triaxial compression. In this case, the effect of the intermediate compression markedly depends on the orientations of the weak planes.

Key words: imperfect interface, mode-II crack, spring model, Fourier transform, stress intensity factor

K. Mogi. FLOW AND FRACTURE OF ROCKS UNDER GENERAL TRIAXIAL COMPRESSION. Applied Mathematics and Mechanics (English Edition), 1981, 2(6): 635-651.

TrendMD

References

[1] Akai,K.and Mori,H.,Study on the failure mechanism of sandstone under combined compressive stresses(in Japanese),Proc.Japan Sci.Civil.Eng.,147,(1967),pp.11-24.
[2] Bieniawski,Z.T.,Deformational behaviour of fractured rock under multiaxial compression,In:Structure,Solid Mechanics and Engineering Design.Te‘eni,M.(ed.).Proc.Southampton 1969Civil Engineering Materials Conference.London:Wiley-inter-science,(1971),pp.589-598.
[3] Brace,W.F.,Brittle fracture of rocks,In:Proceedings of International Conference on State of Stress in the Earth‘s Crust,edited by W.R.Judd,(1964),pp.111-178,Elsevier,New York.
[4] Handin,J.,Strength and ductility,In:Handbook of Physical Constants.Revised ed.Clark,S.P.(ed.).Geol.Soc.Am.Memoir,97,(1966),pp.223-289.
[5] Handin,J.,D.V.Higgs and J.K.O‘Brien,Torsion of Yule marble under confining pressure,In:Rock Deformation,Geol.Soc.Amer.Mem.79,edited by D.Griggs and J.Handin,(1960),pp.245-274.
[6] Handin,J.,Heard,H.C.and Magouirk,J.N.,Effects of the intermediate principal stress on the failure of limestone,dolomite,and glass at different temperatures and strain rates,J.Geophys.Res.,72,(1967),pp.611-640.
[7] Hojem,J.P.M.and N.G.W.Cook,The design and construction of a triaxial and polyaxial cell for testing rock specimens,S.African Mech,Eng.,18,(1968),pp.57-61.
[8] Hoskins,E.R.,The failure of thick-walled hollow cylinders of isotropic rock.Int.J.Rock Mech.Min.Sci.,6,(1969),pp.99-125.
[9] Jaeger,J.C.and E.R.Hoskins,Rock failure under the confined Brazilian test,J.Geophys.Res.,71,(1966),pp.2651-2659.
[10] Mogi,K.,Some precise measurements of fracture strength of rocks under uniform compressive stress,Rock Mech,Eng.Geol.,4,(1966),pp.41-55.
[11] Mogi,K.,Effect of the intermediate principal stress on rock failure,J.Geophys.Res.,72,(1967),pp.5117-5131.
[12] Mogi,K.,Effect of the triaxial stress system on the failure of dolomite and limestone,Tectonophysics,11,(197la),pp.111-127.
[13] Mogi,K.,Fracture and flow of rocks under high triaxial compression,J.Geophys.Res.,76,(1971b),pp.1255-1269.
[14] Mogi,K.,Fracture and flow of rocks,Tectonophysics,13,(1972a),pp.541-56815Mogi,K.,Effect of the triaxial stress system on fracture and flow of rocks,Phys.Earth Planet.Inter.,5,(1972b),pp.318-324.
[16] Mogi,K.,Rock fracture.Annual Review Earth Planet.Sci.,1,(1973),pp.63-84.
[17] Mogi,K.,Dilatancy of rocks under general triaxial stress states with special reference to earthquake precursors,J.Phys.Earth,25,Suppl.,(1977),pp.S203-S217.
[18] Mogi,K.,K.Igarashi and H.Mochizuki,Deformation and fracture of rocks under general triaxial stress states-anisotropic dilatancy(in Japanese),J.Material Sci.Japan,27,(1978a),pp.148-154.
[19] Mogi,K.,M.Kwasniewki and H.Mochizuki,Fracture of anisotropic rocks under general triaxial compression(in Japanese),Abstract,Seismol.Soc.Japan,1,(1978b),p.225.
[20] Murrell,S.A.F.,The effect of triaxial stress systems on the strength of rocks at atmospheric temperatures,Geophys.J.,10,(1965),pp.231-282.
[21] Niwa,Y.,W.Koyanagi and S.Kobayashi,Failure criterion of lightweight concrete to triaxial compression(in Japanese),Proc.Japan soc.Civil.Eng.,143,(1967),pp.28-35.
[22] Sakurai,S.and S.Serata,Mechanical properties of rock salt under three dimensional loading conditions,Proc.Japan Congr.Tect.Mater.,10th,(1967),pp.139-142.
[23] Von Karman,Th.,Festigkeitsversuche unter allsetigem uruck,Z.Verein Deit.Ingr.,55,(1911),pp.1749-1759

[1]	Huayang DANG, Dongpei QI, Minghao ZHAO, Cuiying FAN, C.S. LU. Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 841-856.
[2]	Yansong WANG, Baolin WANG, Youjiang CUI, Kaifa WANG. Anti-plane pull-out of a rigid line inclusion from an elastic medium [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 809-822.
[3]	Chenxue JIA, Zihao WANG, Donghui ZHANG, Taihua ZHANG, Xianhong MENG. Fracture of films caused by uniaxial tensions: a numerical model [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2093-2108.
[4]	Juan PENG, Dengke LI, Zaixing HUANG, Guangjian PENG, Peijian CHEN, Shaohua CHEN. Interfacial behavior of a thermoelectric film bonded to a graded substrate [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1853-1870.
[5]	Xin ZHANG, Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG. Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1901-1920.
[6]	Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG. Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(11): 1633-1648.
[7]	Xing ZHAO, Zhenghua QIAN, Jinxi LIU, Cunfa GAO. Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 139-156.
[8]	K. K. PANKAJ, S. A. SAHU, S. KUMARI. Surface wave transference in a piezoelectric cylinder coated with reinforced material [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 123-138.
[9]	M. KARIMI, A. GHASSEMI, A. ATRIAN, M. VAHABI. Compensation of stress intensity factors in hollow cylinders containing several cracks under torsion by electro-elastic coating [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(9): 1335-1360.
[10]	M. HAJIMOHAMADI, R. GHAJAR. An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(8): 1103-1118.
[11]	Xinsheng XU, Zhenzhen TONG, Dalun RONG, Xianhe CHENG, Chenghui XU, Zhenhuan ZHOU. Fracture analysis of magnetoelectroelastic bimaterials with imperfect interfaces by symplectic expansion [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1043-1058.
[12]	M. FAKOOR, S. M. N. GHOREISHI. Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(11): 1565-1578.
[13]	S. SINGH, K. SHARMA, R. R. BHARGAVA. Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(11): 1517-1532.
[14]	Tiemei YANG, Weiyang YANG, Junlin LI, Xuexia ZHANG. Analysis on non-oscillatory singularity behaviors of mode Ⅱ interface crack tip in orthotropic bimaterial [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1177-1192.
[15]	Hualiang WAN, Qizhi WANG, Xing ZHANG. Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1689-1706.