基于指数准则在莫尔空间对岩石剪切强度的研究
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摘要
岩石是多种矿物颗粒构成的天然材料,内部存在不同尺度的孔隙、裂隙等损伤;岩体工程设计及灾害防治所使用的强度准则仍在研究之中.材料的黏结和摩擦在局部不能同时存在,线性的Coulomb准则仅在小范围内近似描述圆柱试样的常规三轴强度,众多非线性强度准则只是经验公式而缺乏物理背景.作者提出的指数准则可描述岩石剪切破坏时强度与围压的关系;基于对11组试验数据的拟合结果在莫尔应力空间分析黏结力和摩擦力的变化特征:岩石承载的剪切力存在上限即材料的真实黏结力c0;在试验范围内莫尔概念的内摩擦力达到约为0.38c0的峰值,且黏结力在其附近相交.材料真实黏结力与正应力无关,因而名义黏结力表征了完好材料剪切破裂的面积;基于裂隙面积计算的等效摩擦因子随正应力降低,意味着裂隙滑移的爬坡角减小,而后者取决于正应力与真实黏结力的比值.等效摩擦因子与指数准则的材料参数具有确定关系,体现了岩石在压应力作用下剪切破裂的物理背景.
Rocks are natural materials composed of various mineral particles within fissures and pores in different sizes,those result in complicate mechanical properties. Strength criteria for rocks in engineering design and disaster prevention are still an open question. As cohesion and friction in rock do not work simultaneously, the linear Coulomb criterion proposed in 1773 is only reliable to describe pseudo-triaxial compression strength of cylindrical specimen in a small range of confining pressure. Many nonlinear criteria are merely empirical formulas but lack of physical background. The exponential criterion proposed by the author is applicable to fit the relationship between strength and confining pressure of rocks in shear failure; therefore, the cohesion and friction are analyzed in Mohr's stress space on the fitting solutions for eleven rocks. Shear stresses in rock have an upper limit, i.e. the genuine cohesion c_0 of rock; and the internal friction has a peak of about 0.38 c_0, by which intersection of the cohesion and internal friction is. The genuine cohesion is independent to normal stress, so the nominal cohesion of rock specimen represents the shear fracture area of intact material when rock specimen reaches its strength. The equivalent friction factor of slipping fissure decreases with the normal stress, so as the climbing angle that depends on ratio of normal stress to the genuine cohesion. Relationship between the equivalent friction factor and parameters in the exponential criterion reflects the physical background of shear fracture for rock under compressive stresses.
Rocks are natural materials composed of various mineral particles within fissures and pores in different sizes,those result in complicate mechanical properties. Strength criteria for rocks in engineering design and disaster prevention are still an open question. As cohesion and friction in rock do not work simultaneously, the linear Coulomb criterion proposed in 1773 is only reliable to describe pseudo-triaxial compression strength of cylindrical specimen in a small range of confining pressure. Many nonlinear criteria are merely empirical formulas but lack of physical background. The exponential criterion proposed by the author is applicable to fit the relationship between strength and confining pressure of rocks in shear failure; therefore, the cohesion and friction are analyzed in Mohr's stress space on the fitting solutions for eleven rocks. Shear stresses in rock have an upper limit, i.e. the genuine cohesion c_0 of rock; and the internal friction has a peak of about 0.38 c_0, by which intersection of the cohesion and internal friction is. The genuine cohesion is independent to normal stress, so the nominal cohesion of rock specimen represents the shear fracture area of intact material when rock specimen reaches its strength. The equivalent friction factor of slipping fissure decreases with the normal stress, so as the climbing angle that depends on ratio of normal stress to the genuine cohesion. Relationship between the equivalent friction factor and parameters in the exponential criterion reflects the physical background of shear fracture for rock under compressive stresses.
引文
1陈颙,黄庭芳,刘恩儒.岩石物理学.合肥:中国科学技术大学出版社,2009:1-17,160-162(Chen Yong,Wong Tengfong,Liu Enru.Rock Physics.Hefei:Press of University of Science and Technology of China,2009:1-17,160-162(in Chinese))
2尤明庆.完整岩石的强度和强度准则.复旦大学学报(自然科学版),2013,52(5):569-582(You Mingqing.Strength and strength criteria for intact rocks.Journal of Fudan University(Natural Science),2013,52(5):569-582(in Chinese))
3 Mogi K.Experimental Rock Mechanics.London:Taylor&Francis,2007:36-37,83-110,307-320
4 Haimson B.Consistent trends in the true triaxial strength and deformability of cores extracted from ICDP deep scientific holes on three continents.Tectonophysics,2011,503(1-2):45-51
5 Li X,Shi L,Bai B,et al.True-triaxial testing techniques of rocksstate of the art and future perspectives//Kwasniewski M,Li X,Takahashi M(eds).True Triaxial Testing of Rocks.London:CRC Press,2012:3-18
6万征,秋仁东,郭金雪.岩土的一种强度准则及其变换应力法.力学学报,2017,49(3):726-740(Wan Zheng,Qiu Rendong,Guo Jinxue.A kind of strength and yield criterion for geomaterials and its transformation stress method.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):726-740(in Chinese))
7 Gu JF,Chen PH.A failure criterion for isotropic materials based on Mohr’s failure plane theory.Mechanics Research Communications,2018,87(1):1-6
8 Labuz JF,Zeng FT,Makhnenko R,et al.Brittle failure of rock:Areview and general linear criterion.Journal of Structural Geology,2018,112:7-28
9尤明庆.端部效应对岩石真三轴压缩强度的影响.岩石力学与工程学报,2016,35(S1):2 603-2 607(You Mingqing.End effects on strengths of rocks under true triaxial compression.Chinese Journal of Rock Mechanics and Engineering,2016,35(S1):2603-2607(in Chinese))
10范鹏贤,李颖,赵跃堂等.茂木式真三轴试验机的端部摩擦效应.岩石力学与工程学报,2017,36(11):2720-2730(Fan Pengxian,Li Ying,Zhao Yuetang,et al.End friction effect of Mogi type of true-triaxial test apparatus.Chinese Journal of Rock Mechanics and Engineering,2017,36(11):2720-2730(in Chinese))
11 Brady BHG,Brown ET.Rock Mechanics for Underground Mining.Netherlands:Springer,2004:105-107
12 Jaeger JC,Cook NGW,Zimmerman RW.Fundamentals of Rock Mechanics.New York:Wiley-Blackwell,2007:90-95
13 von Karman T.Festigkeitsversuche unter allseitigem Druck.Zeitschrift des Vereines Deutscher Ingenieure,1911,55(42):1749-1757
14 Sinha S,Walton G.A progressive S-shaped yield criterion and its application to rock pillar behavior.International Journal of Rock Mechanics and Mining Sciences,2018,105:98-109
15 Bineshian H,Ghainian A,Bineshian Z.Comprehensive compressive-tensile strength criterion for intact rock.Journal of Rock Mechanics and Geotechnical,2012,4(2):140-148
16 You M.Comparison of the accuracy of some conventional triaxial strength criteria for intact rock.International Journal of Rock Mechanics and Mining Sciences,2011,48(5):852-863
17 Paterson MS,Wong TF.Experimental Rock Deformation-the Brittle Field.Netherlands:Springer,2004:211-232
18 Handin J.On the Coulomb-Mohr failure criterion.Journal of Geophysical Research,1969,74(22):5343-5350
19 Mogi K.On the pressure dependence of strength of rocks and the Coulomb fracture criterion.Tectonophysics,1974,21(3):273-285
20 Savage JC,Byerlee JD,Lockner DA.Is internal friction friction?Geophysical Research Letter,1996,23(5):487-490
21尤明庆.基于粘结和摩擦特性的岩石变形与破坏的研究.地质力学学报,2005,11(3):286-292(You Mingqing.Study of deformation and failure of rock based on properties of cohesion and friction.Journal of Geomechanics,2005,11(3):286-292(in Chinese))
22 You M.True-triaxial strength criteria for rock.International Journal of Rock Mechanics and Mining Sciences,2009,46(1):115-127
23 You M.Three independent parameters to describe conventional triaxial compression strength of intact rocks.Journal of Rock Mechanics and Geotechnical Engineering,2010,2(4):350-356
24关成尧,赵国春,白相东等.断层力学科学范畴、发展脉络评论及未来发展思考.地质力学学报,2018,24(4):555-586(Guan Chengyao,Zhao Guochun,Bai Xiangdong,et al.Review of category and development context of fault mechanics.Journal of Geomechanics,2018,24(4):555-586(in Chinese))
25 Iba?nez JP,Hatzor YH.Rapid sliding and friction degradation:Lessons from the catastrophic Vajont landslide.Engineering Geology,2018,244:96-106
26 Byerlee JD.The frictional characteristics of Westerly granite.[PhDThesis].USA:Massachusetts Institute of Technology,1966
27 Xu SQ,Fukuyama E,Yamashita F,et al.Strain rate effect on fault slip and rupture evolution:Insight from meter-scale rock friction experiments.Tectonophysics,2018,733:209-231
28 Byerlee JD.Friction of rock.Pure and Applied Geophysics,1978,116:615-626
29陶振宇,陈铁民.岩石的基本摩擦角及高压摩擦特性.科学通报,1991(20):1567-1569(Tao Zhenyu,Chen Tiemin.Basic friction angle of rock and friction property under high pressure.Science Bulletin of China,1991(20):1567-1569(in Chinese))
30张磊,刘保国.考虑抗拉强度的岩石强度准则对比分析.工程力学,2016,33(11):201-207(Zhang Lei,Liu Baoguo.A comparison study of rock strength criteria considering tensile strength.Engineering Mechanics,2016,33(11):201-207(in Chinese))
31 Zhang Q,Li C,Quan X,et al.New true-triaxial rock strength criteria considering intrinsic material characteristics.Acta Mechanica Sinica,2018,34(1):130-142
32 You M.Comparison of two true-triaxial strength criteria.International Journal of Rock Mechanics and Mining Sciences,2012,54:114-124
33尤明庆.常规三轴压缩的端部效应及花岗岩强度的研究.岩石力学与工程学报,2018,37(S1):3160-3168(You Mingqing.Study on ends effect in conventional triaxial compression test and the strengths property of granites.Chinese Journal of Rock Mechanics and Engineering,2018,37(S1):3160-3168(in Chinese))
34尤明庆.围压对岩石试样强度的影响及离散性.岩石力学与工程学报,2014,33(5):929-937(You Mingqing.Study on effect of confining pressure on strength and the scatter of rock specimens.Chinese Journal of Rock Mechanics and Engineering,2014,33(5):929-937(in Chinese))
35 Rosengren KJ,Jaeger JC.The mechanical properties of an interlocked low-porosity aggregate.Geotechnique,1968,18(3):317-326
36尤明庆.岩石损伤、黏结和摩擦特性的研究.岩土工程学报,2019,41(3):554-560(You Mingqing.Study on the properties of damage,cohesion and friction for rocks.Chinese Journal of Geotechnical Engineering,2019,41(3):554-560(in Chinese))
37 Sriapai T.True triaxial compressive strengths of Maha Sarakham rock salt.[Master Thesis].Thailand:Suranaree University of Technology,2010:33-36
38 B′esuelle P,Desrues J,Raynaud S.Experimental characterisation of the localization phenomenon inside a Vosges sandstone in a triaxial cell.International Journal of Rock Mechanics and Mining Sciences,2000,37(8):1223-1237
39 Fang Z,Harrison JP.A mechanical degradation index for rock.International Journal of Rock Mechanics and Mining Sciences,2001,38(8):1193-1199
40汪斌,朱杰兵,邬爱清等.高应力下岩石非线性强度特性的试验验证.岩石力学与工程学报,2010,29(3):542-548(Wang Bin,Zhu Jiebing,Wu Aiqing,et al.Experimental validation of nonlinear strength property of rock under high geostress.Chinese Journal of Rock Mechanics and Engineering,2010,29(3):542-548(in Chinese))
41 Gowd TN,Rummel F.Effect of confining pressure on the fracture behavior of a porous rock.International Journal of Rock Mechanics and Mining Sciences,1980,17(2):225-229
42 Schwartz AE.Failure of rock in the triaxial shear test//Proceedings of the 6th US Symposium on Rock Mechanics.Rolla,Missouri,1964:109-151
43 Franklin JA,Hoek E.Development in triaxial testing technique.Rock Mechanics,1970,2(4):223-228
44张顶立.隧道及地下工程的基本问题及其研究进展.力学学报,2017,49(1):3-21(Zhang Dingli.Essential issues and their research progress in tunnel and underground engineering.Chinese Journal of Theoretical and Applied Mechanics,2017,49(1):3-21(in Chinese))
45王启智,李炼,吴礼舟等.改进巴西试验:从平台巴西圆盘到切口巴西圆盘.力学学报,2017,49(4):793-801(Wang Qizhi,Li Lian,Wu Lizhou,et al.Improvement of Brazilian test:From flattened Brazilian disc to grooved Brazilian disc.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):793-801(in Chinese))
46 Carter BJ,Duncan SEJ,Lajtai EZ.Fitting strength criteria to intact rock.Geotechnical and Geological Engineering,1991,9(1):73-81
47 Folta BL.Strength testing under multi-axial stress states.[Master Thesis].USA:The University of Minnesota,2016:42-43
48 Mas D,Chemenda AI.An experimentally constrained constitutive model for geomaterials with simple friction-dilatancy relation in brittle to ductile domains.International Journal of Rock Mechanics and Mining Sciences,2015,77:257-264
49韩文梅,康天合.微凸体对抛光岩石表面静摩擦系数影响试验研究.岩土力学,2013,34(3):674-578(Han Wenmei,Kang Tianhe.Experimental study of influence of asperity on static friction coefficient for polished rock surface.Rock and Soil Mechanics,2013,34(3):674-578(in Chinese))
2尤明庆.完整岩石的强度和强度准则.复旦大学学报(自然科学版),2013,52(5):569-582(You Mingqing.Strength and strength criteria for intact rocks.Journal of Fudan University(Natural Science),2013,52(5):569-582(in Chinese))
3 Mogi K.Experimental Rock Mechanics.London:Taylor&Francis,2007:36-37,83-110,307-320
4 Haimson B.Consistent trends in the true triaxial strength and deformability of cores extracted from ICDP deep scientific holes on three continents.Tectonophysics,2011,503(1-2):45-51
5 Li X,Shi L,Bai B,et al.True-triaxial testing techniques of rocksstate of the art and future perspectives//Kwasniewski M,Li X,Takahashi M(eds).True Triaxial Testing of Rocks.London:CRC Press,2012:3-18
6万征,秋仁东,郭金雪.岩土的一种强度准则及其变换应力法.力学学报,2017,49(3):726-740(Wan Zheng,Qiu Rendong,Guo Jinxue.A kind of strength and yield criterion for geomaterials and its transformation stress method.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):726-740(in Chinese))
7 Gu JF,Chen PH.A failure criterion for isotropic materials based on Mohr’s failure plane theory.Mechanics Research Communications,2018,87(1):1-6
8 Labuz JF,Zeng FT,Makhnenko R,et al.Brittle failure of rock:Areview and general linear criterion.Journal of Structural Geology,2018,112:7-28
9尤明庆.端部效应对岩石真三轴压缩强度的影响.岩石力学与工程学报,2016,35(S1):2 603-2 607(You Mingqing.End effects on strengths of rocks under true triaxial compression.Chinese Journal of Rock Mechanics and Engineering,2016,35(S1):2603-2607(in Chinese))
10范鹏贤,李颖,赵跃堂等.茂木式真三轴试验机的端部摩擦效应.岩石力学与工程学报,2017,36(11):2720-2730(Fan Pengxian,Li Ying,Zhao Yuetang,et al.End friction effect of Mogi type of true-triaxial test apparatus.Chinese Journal of Rock Mechanics and Engineering,2017,36(11):2720-2730(in Chinese))
11 Brady BHG,Brown ET.Rock Mechanics for Underground Mining.Netherlands:Springer,2004:105-107
12 Jaeger JC,Cook NGW,Zimmerman RW.Fundamentals of Rock Mechanics.New York:Wiley-Blackwell,2007:90-95
13 von Karman T.Festigkeitsversuche unter allseitigem Druck.Zeitschrift des Vereines Deutscher Ingenieure,1911,55(42):1749-1757
14 Sinha S,Walton G.A progressive S-shaped yield criterion and its application to rock pillar behavior.International Journal of Rock Mechanics and Mining Sciences,2018,105:98-109
15 Bineshian H,Ghainian A,Bineshian Z.Comprehensive compressive-tensile strength criterion for intact rock.Journal of Rock Mechanics and Geotechnical,2012,4(2):140-148
16 You M.Comparison of the accuracy of some conventional triaxial strength criteria for intact rock.International Journal of Rock Mechanics and Mining Sciences,2011,48(5):852-863
17 Paterson MS,Wong TF.Experimental Rock Deformation-the Brittle Field.Netherlands:Springer,2004:211-232
18 Handin J.On the Coulomb-Mohr failure criterion.Journal of Geophysical Research,1969,74(22):5343-5350
19 Mogi K.On the pressure dependence of strength of rocks and the Coulomb fracture criterion.Tectonophysics,1974,21(3):273-285
20 Savage JC,Byerlee JD,Lockner DA.Is internal friction friction?Geophysical Research Letter,1996,23(5):487-490
21尤明庆.基于粘结和摩擦特性的岩石变形与破坏的研究.地质力学学报,2005,11(3):286-292(You Mingqing.Study of deformation and failure of rock based on properties of cohesion and friction.Journal of Geomechanics,2005,11(3):286-292(in Chinese))
22 You M.True-triaxial strength criteria for rock.International Journal of Rock Mechanics and Mining Sciences,2009,46(1):115-127
23 You M.Three independent parameters to describe conventional triaxial compression strength of intact rocks.Journal of Rock Mechanics and Geotechnical Engineering,2010,2(4):350-356
24关成尧,赵国春,白相东等.断层力学科学范畴、发展脉络评论及未来发展思考.地质力学学报,2018,24(4):555-586(Guan Chengyao,Zhao Guochun,Bai Xiangdong,et al.Review of category and development context of fault mechanics.Journal of Geomechanics,2018,24(4):555-586(in Chinese))
25 Iba?nez JP,Hatzor YH.Rapid sliding and friction degradation:Lessons from the catastrophic Vajont landslide.Engineering Geology,2018,244:96-106
26 Byerlee JD.The frictional characteristics of Westerly granite.[PhDThesis].USA:Massachusetts Institute of Technology,1966
27 Xu SQ,Fukuyama E,Yamashita F,et al.Strain rate effect on fault slip and rupture evolution:Insight from meter-scale rock friction experiments.Tectonophysics,2018,733:209-231
28 Byerlee JD.Friction of rock.Pure and Applied Geophysics,1978,116:615-626
29陶振宇,陈铁民.岩石的基本摩擦角及高压摩擦特性.科学通报,1991(20):1567-1569(Tao Zhenyu,Chen Tiemin.Basic friction angle of rock and friction property under high pressure.Science Bulletin of China,1991(20):1567-1569(in Chinese))
30张磊,刘保国.考虑抗拉强度的岩石强度准则对比分析.工程力学,2016,33(11):201-207(Zhang Lei,Liu Baoguo.A comparison study of rock strength criteria considering tensile strength.Engineering Mechanics,2016,33(11):201-207(in Chinese))
31 Zhang Q,Li C,Quan X,et al.New true-triaxial rock strength criteria considering intrinsic material characteristics.Acta Mechanica Sinica,2018,34(1):130-142
32 You M.Comparison of two true-triaxial strength criteria.International Journal of Rock Mechanics and Mining Sciences,2012,54:114-124
33尤明庆.常规三轴压缩的端部效应及花岗岩强度的研究.岩石力学与工程学报,2018,37(S1):3160-3168(You Mingqing.Study on ends effect in conventional triaxial compression test and the strengths property of granites.Chinese Journal of Rock Mechanics and Engineering,2018,37(S1):3160-3168(in Chinese))
34尤明庆.围压对岩石试样强度的影响及离散性.岩石力学与工程学报,2014,33(5):929-937(You Mingqing.Study on effect of confining pressure on strength and the scatter of rock specimens.Chinese Journal of Rock Mechanics and Engineering,2014,33(5):929-937(in Chinese))
35 Rosengren KJ,Jaeger JC.The mechanical properties of an interlocked low-porosity aggregate.Geotechnique,1968,18(3):317-326
36尤明庆.岩石损伤、黏结和摩擦特性的研究.岩土工程学报,2019,41(3):554-560(You Mingqing.Study on the properties of damage,cohesion and friction for rocks.Chinese Journal of Geotechnical Engineering,2019,41(3):554-560(in Chinese))
37 Sriapai T.True triaxial compressive strengths of Maha Sarakham rock salt.[Master Thesis].Thailand:Suranaree University of Technology,2010:33-36
38 B′esuelle P,Desrues J,Raynaud S.Experimental characterisation of the localization phenomenon inside a Vosges sandstone in a triaxial cell.International Journal of Rock Mechanics and Mining Sciences,2000,37(8):1223-1237
39 Fang Z,Harrison JP.A mechanical degradation index for rock.International Journal of Rock Mechanics and Mining Sciences,2001,38(8):1193-1199
40汪斌,朱杰兵,邬爱清等.高应力下岩石非线性强度特性的试验验证.岩石力学与工程学报,2010,29(3):542-548(Wang Bin,Zhu Jiebing,Wu Aiqing,et al.Experimental validation of nonlinear strength property of rock under high geostress.Chinese Journal of Rock Mechanics and Engineering,2010,29(3):542-548(in Chinese))
41 Gowd TN,Rummel F.Effect of confining pressure on the fracture behavior of a porous rock.International Journal of Rock Mechanics and Mining Sciences,1980,17(2):225-229
42 Schwartz AE.Failure of rock in the triaxial shear test//Proceedings of the 6th US Symposium on Rock Mechanics.Rolla,Missouri,1964:109-151
43 Franklin JA,Hoek E.Development in triaxial testing technique.Rock Mechanics,1970,2(4):223-228
44张顶立.隧道及地下工程的基本问题及其研究进展.力学学报,2017,49(1):3-21(Zhang Dingli.Essential issues and their research progress in tunnel and underground engineering.Chinese Journal of Theoretical and Applied Mechanics,2017,49(1):3-21(in Chinese))
45王启智,李炼,吴礼舟等.改进巴西试验:从平台巴西圆盘到切口巴西圆盘.力学学报,2017,49(4):793-801(Wang Qizhi,Li Lian,Wu Lizhou,et al.Improvement of Brazilian test:From flattened Brazilian disc to grooved Brazilian disc.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):793-801(in Chinese))
46 Carter BJ,Duncan SEJ,Lajtai EZ.Fitting strength criteria to intact rock.Geotechnical and Geological Engineering,1991,9(1):73-81
47 Folta BL.Strength testing under multi-axial stress states.[Master Thesis].USA:The University of Minnesota,2016:42-43
48 Mas D,Chemenda AI.An experimentally constrained constitutive model for geomaterials with simple friction-dilatancy relation in brittle to ductile domains.International Journal of Rock Mechanics and Mining Sciences,2015,77:257-264
49韩文梅,康天合.微凸体对抛光岩石表面静摩擦系数影响试验研究.岩土力学,2013,34(3):674-578(Han Wenmei,Kang Tianhe.Experimental study of influence of asperity on static friction coefficient for polished rock surface.Rock and Soil Mechanics,2013,34(3):674-578(in Chinese))