岩体脆性破裂失稳临界应力特征重正化群研究
摘要
岩体通常是由节理和岩桥组成,大量岩体工程破坏和失稳多是由于系统中较硬介质突然脆性破坏所致.把岩体脆性破坏过程看作一个逾渗相变过程,假定岩体细观微元体强度服从Weibull分布,基于系统在逾渗阈值处有尺度不变的性质,利用重正化群方法在求得一维和二维条件下系统逾渗阈值的基础上,首次研究了三维重正化群条件下岩体脆性破坏在逾渗阈值附近的临界特性,为相关问题三维重正化群研究提供了解析解参考,并揭示了如下规律:(1)维数一定时,逾渗阈值p*随着形状参数m的增大呈减小趋势;当形状参数m一定且m较小时,逾渗阈值p*随着维数增加而降低;当形状参数m一定且m较大时,逾渗阈值p*随着维数增加呈逐渐增大趋势.(2)形状参数m一定时,关联临界指数ν随着维数增加呈降低趋势;维数为1时,关联临界指数ν随着形状参数m的增大呈衰减趋势,而对于二维、三维的情况,其随着形状参数m的增大基本呈增大趋势.(3)对于一维、二维情况而言,体积膨胀点与峰值强度点所对应的应力之比σcd/σf随着形状参数m的增大呈减小趋势,三维则正好相反,σcd/σf随着形状参数m的增大呈增大趋势.特别需要指出的是,在维数、形状参数m一定时,σcd/σf为定值,说明对于特定的岩石破裂过程,其膨胀点处应力与峰值应力之间存在某种联系,可能遵循一定的规律,这对于宏观岩石破裂现象(诸如边坡失稳、岩爆、地震等)的预测具有一定的启示意义.
Rock mass usually is composed of joints and rock bridges,many failure cases of rock mass engineering were induced by the sudden brittle failure of rock bridges.In this paper,the percolation model of brittle failure was established firstly and supposing the strength distribution of rock obeyed weibull function,then the percolation thresholds of one-dimension and two-dimension models were computed by the renormalization group methods.Furthermore,the critical state features of the three-dimension percolation model were studied for the first time and the results indicated:(1)with the dimension of renormalization group fixed,the percolation threshold p* decreases when the shape parameter m increases;with m fixed and it is smaller,p* decreases when the dimension of renormalization group increases;with m fixed and it is larger,p* increases when the dimension of renormalization group increases;(2)with m fixed,the correlative length index ν decreases with the increasing dimension of renormalization group.For one-dimension renormalization group,correlative length index ν decreases with the increasing m;For two-dimension and three-dimension renormalization group,the index ν increases with the increasing m;(3)For one-dimension and two-dimension renormalization group,the stress ratio between volume dilatant point and peak point,σcd/σf,decreases with the increasing m;however,for three-dimension renormalization group,σcd/σf increases with the increasing m.Especially speaking,with the dimension of renormalization group and m fixed,σcd/σf is a definite value,which means that there exists a certain law between the stress at the expansion point and peak stress in the process of rock failure.Maybe it has certain significance for the forecast of the macro rock rupture phenomena(such as slope instability,rock burst,earthquake,etc.).
Rock mass usually is composed of joints and rock bridges,many failure cases of rock mass engineering were induced by the sudden brittle failure of rock bridges.In this paper,the percolation model of brittle failure was established firstly and supposing the strength distribution of rock obeyed weibull function,then the percolation thresholds of one-dimension and two-dimension models were computed by the renormalization group methods.Furthermore,the critical state features of the three-dimension percolation model were studied for the first time and the results indicated:(1)with the dimension of renormalization group fixed,the percolation threshold p* decreases when the shape parameter m increases;with m fixed and it is smaller,p* decreases when the dimension of renormalization group increases;with m fixed and it is larger,p* increases when the dimension of renormalization group increases;(2)with m fixed,the correlative length index ν decreases with the increasing dimension of renormalization group.For one-dimension renormalization group,correlative length index ν decreases with the increasing m;For two-dimension and three-dimension renormalization group,the index ν increases with the increasing m;(3)For one-dimension and two-dimension renormalization group,the stress ratio between volume dilatant point and peak point,σcd/σf,decreases with the increasing m;however,for three-dimension renormalization group,σcd/σf increases with the increasing m.Especially speaking,with the dimension of renormalization group and m fixed,σcd/σf is a definite value,which means that there exists a certain law between the stress at the expansion point and peak stress in the process of rock failure.Maybe it has certain significance for the forecast of the macro rock rupture phenomena(such as slope instability,rock burst,earthquake,etc.).
引文
[1]Broadbent S R,Hammersly J M.Percolation processes.Ⅰ.Crystals and mazes[J].Proceedings of the CambridgePhilosophical,1957,53(3):629-641
[2]柯善明,顾浩鼎,翟文杰.地震活动的逾渗模型及临界状态的研究[J].地震学报,1999,21(4):379-386Ke Shanming,Gu Haoding,Zhai Wenjie.Study on percolation model and critical state in earthquake[J].ActaSeismological Sinica,1999,21(4):379-386
[3]吴忠良.逾渗模型的地震学含义[J].地球物理学进展,1992,7(4):38-45Wu Zhongliang.Implication of percolation model in seismology[J].Progress in Geophysics,1992,7(4):38-45
[4]Bebbington M,Ver-Jons D,Zheng X.Percolation theory:A model of rock fracture[J].Geophysical Journal International,1990,100(2):215-220
[5]Chelidze T L.Percolation and fracture[J].Physics of the Earth and Planetary Interiors,1982,28(2):93-101
[6]彭自正,王殚业,许云廷,等.逾渗与岩石破裂的计算机模拟研究[J].西北地震学报,1996,18(1):22-28Peng Zizheng,Wang Danye,Xu Yunting,et al.A computer simulation study on percolation and rock fracture[J].Northwestern Seismological Journal,1996,18(1):22-28
[7]金乾坤,杨永琦.岩石爆破损伤断裂中的逾渗行为[J].金属矿山,1996,(3):11-14Jin Qiankun,Yang Yongqi.Percolation behavior in the damage fracture of rock blasting[J].Metal Mine,1996,(3):11-14
[8]金乾坤,杨永琦.岩石爆破逾渗模型[J].爆破,1996,13(2):7-11Jin Qiankun,Yang Yongqi.Percolation model of rock blasting[J].Blasting,1996,13(2):11-14
[9]梁正召,唐春安,唐世斌,等.岩石损伤破坏过程中分形与逾渗演化特征[J].岩土工程学报,2007,29(9):1386-1391Liang Zhengzhao,Tang Chunan,Tang Shibin,et al.Characteristics of fractal and percolation of rocks subjected touniaxial compression during their failure process[J].Chinese Journal of Geotechnical Engineering,2007,29(9):1386-1391
[10]冯增朝,赵阳升,文再明.煤岩体孔隙裂隙双重介质逾渗机制研究[J].岩石力学与工程学报,2005,24(2):236-240Feng Zengchao,Zhao Yangsheng,Wen Zaiming.Percolation mechanism of fractured coal rocks as dual-continua[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(2):236-240
[11]冯增朝,赵阳升,吕兆兴.强随机分布裂隙介质的二维逾渗规律研究[J].岩石力学与工程学报,2006,25(S2):3904-3908Feng Zengchao,Zhao Yangsheng,Lu Zhaoxing.Research on laws of 2D percolation of fully random distribution fracturemedia[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(S2):3904-3908
[12]吕兆兴,冯增朝,赵阳升.孔隙介质三维逾渗机制数值模拟研究[J].岩石力学与工程学报,2007,26(S2):4019-4023LüZhaoxing,Feng Zengchao,Zhao Yangsheng.Numerical simulation of 3D percolation mechanism in porous media[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(S2):4019-4023
[13]Ravi V,Michael B H.Direct imaging of the percolation network in a three-dimensional disordered conductor-insulatorcomposite[J].Physical Review Letters,1995,75(24):4433-4436
[14]Wu J J,Mclachlan D S.Percolation exponents and thresholds obtained from the nearly ideal continuum percolationsystem graphite-boron nitride[J].Physical Review(B),1997,56(3):1236-1248
[15]Daniel T.Simulation of percolation on massively-parallel computers[J].International Journal of Modern Physics(C),2001,12(6):871-878
[16]杨进,杨祖宝,何延才.Monte Carlo重正化群方法计算逾渗模型的临界指数[J].计算物理,1994,11(1):113-117Yang Jin,Yang Zubao,He Yancai.The calculation of critical parameters for the site percolation problem by Monte Carlorenormalization group[J].Chinese Journal of Computational Physics,1994,11(1):113-117
[17]Madden T R.Microcrack connectivity in rocks:A renormalization group approach to the critical phenomena of conductionand failure in crystalline rocks[J].Journal of Geophysical Research,1985,88(B1):585-592
[18]Allegre C J,Mouel J L Le,Provost A.Scaling rules in rock fracture and possible implication for earthquake prediction[J].Nature,1982,297:47-49
[19]Smalley R F,Turcotte D L,Salla A Solla.A renormalization group approach to the stick slip behavior of faults[J].Journal of Geophysical Research,1985,90(B2):1894-1900
[20]陈忠辉,谭国焕,杨文柱.岩石脆性破裂的重正化研究及数值模拟[J].岩土工程学报,2002,24(2):183-187Chen Zhonghui,Tan Guohuan,Yang Wenzhu.Renormalization study and numerical simulation on brittle failure of rocks[J].Chinese Journal of Geotechnical Engineering,2002,24(2):183-187
[21]秦四清,徐锡伟,胡平,等.孕震断层的多锁固段脆性破裂机制与地震预测新方法的探索[J].地球物理学报,2010,53(4):1001-1014Qin Siqing,Xu Xiwei,Hu Ping,et al.Brittle failure mechanism of multiple locked patches in a seismogenic fault systemand exploration on a new way for earthquake prediction[J].Chinese Journal of Geophysics,2010,53(4):1001-1014
[22]秦四清,王媛媛,马平.崩滑灾害临界位移演化的指数律[J].岩石力学与工程学报,2010,29(5):873-880Qin Siqing,Wang Yuanyuan,Ma Ping.Exponential laws of critical displacement evolution for landslides and avalanches[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):837-880
[23]秦四清,薛雷,王媛媛,等.对孕震断层多锁固段脆性破裂理论的进一步验证及有关科学问题的讨论[J].地球物理学进展,2010,25(3):749-758Qin Siqing,Xue Lei,Wang Yuanyuan,et al.Further verifications on the brittle failure theory of multiple locked patchesalong a seismogenic fault system and discussions on some science issues[J].Progress in Geophysics,2010,25(3):749-758
[24]Weibull W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,18(3):293-297
[25]Brace W F,Paulding B W.Dilatancy in the fracture of crystalline rocks[J].Journal of Geophysical Research,1966,71(16):3939-3953
[26]Martin C D,Chandler N A.The progressive fracture of Lac du Bonnet granite[J].International Journal of RockMechanics and Mining Sciences,1994,31(6),643-659pbpb
[2]柯善明,顾浩鼎,翟文杰.地震活动的逾渗模型及临界状态的研究[J].地震学报,1999,21(4):379-386Ke Shanming,Gu Haoding,Zhai Wenjie.Study on percolation model and critical state in earthquake[J].ActaSeismological Sinica,1999,21(4):379-386
[3]吴忠良.逾渗模型的地震学含义[J].地球物理学进展,1992,7(4):38-45Wu Zhongliang.Implication of percolation model in seismology[J].Progress in Geophysics,1992,7(4):38-45
[4]Bebbington M,Ver-Jons D,Zheng X.Percolation theory:A model of rock fracture[J].Geophysical Journal International,1990,100(2):215-220
[5]Chelidze T L.Percolation and fracture[J].Physics of the Earth and Planetary Interiors,1982,28(2):93-101
[6]彭自正,王殚业,许云廷,等.逾渗与岩石破裂的计算机模拟研究[J].西北地震学报,1996,18(1):22-28Peng Zizheng,Wang Danye,Xu Yunting,et al.A computer simulation study on percolation and rock fracture[J].Northwestern Seismological Journal,1996,18(1):22-28
[7]金乾坤,杨永琦.岩石爆破损伤断裂中的逾渗行为[J].金属矿山,1996,(3):11-14Jin Qiankun,Yang Yongqi.Percolation behavior in the damage fracture of rock blasting[J].Metal Mine,1996,(3):11-14
[8]金乾坤,杨永琦.岩石爆破逾渗模型[J].爆破,1996,13(2):7-11Jin Qiankun,Yang Yongqi.Percolation model of rock blasting[J].Blasting,1996,13(2):11-14
[9]梁正召,唐春安,唐世斌,等.岩石损伤破坏过程中分形与逾渗演化特征[J].岩土工程学报,2007,29(9):1386-1391Liang Zhengzhao,Tang Chunan,Tang Shibin,et al.Characteristics of fractal and percolation of rocks subjected touniaxial compression during their failure process[J].Chinese Journal of Geotechnical Engineering,2007,29(9):1386-1391
[10]冯增朝,赵阳升,文再明.煤岩体孔隙裂隙双重介质逾渗机制研究[J].岩石力学与工程学报,2005,24(2):236-240Feng Zengchao,Zhao Yangsheng,Wen Zaiming.Percolation mechanism of fractured coal rocks as dual-continua[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(2):236-240
[11]冯增朝,赵阳升,吕兆兴.强随机分布裂隙介质的二维逾渗规律研究[J].岩石力学与工程学报,2006,25(S2):3904-3908Feng Zengchao,Zhao Yangsheng,Lu Zhaoxing.Research on laws of 2D percolation of fully random distribution fracturemedia[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(S2):3904-3908
[12]吕兆兴,冯增朝,赵阳升.孔隙介质三维逾渗机制数值模拟研究[J].岩石力学与工程学报,2007,26(S2):4019-4023LüZhaoxing,Feng Zengchao,Zhao Yangsheng.Numerical simulation of 3D percolation mechanism in porous media[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(S2):4019-4023
[13]Ravi V,Michael B H.Direct imaging of the percolation network in a three-dimensional disordered conductor-insulatorcomposite[J].Physical Review Letters,1995,75(24):4433-4436
[14]Wu J J,Mclachlan D S.Percolation exponents and thresholds obtained from the nearly ideal continuum percolationsystem graphite-boron nitride[J].Physical Review(B),1997,56(3):1236-1248
[15]Daniel T.Simulation of percolation on massively-parallel computers[J].International Journal of Modern Physics(C),2001,12(6):871-878
[16]杨进,杨祖宝,何延才.Monte Carlo重正化群方法计算逾渗模型的临界指数[J].计算物理,1994,11(1):113-117Yang Jin,Yang Zubao,He Yancai.The calculation of critical parameters for the site percolation problem by Monte Carlorenormalization group[J].Chinese Journal of Computational Physics,1994,11(1):113-117
[17]Madden T R.Microcrack connectivity in rocks:A renormalization group approach to the critical phenomena of conductionand failure in crystalline rocks[J].Journal of Geophysical Research,1985,88(B1):585-592
[18]Allegre C J,Mouel J L Le,Provost A.Scaling rules in rock fracture and possible implication for earthquake prediction[J].Nature,1982,297:47-49
[19]Smalley R F,Turcotte D L,Salla A Solla.A renormalization group approach to the stick slip behavior of faults[J].Journal of Geophysical Research,1985,90(B2):1894-1900
[20]陈忠辉,谭国焕,杨文柱.岩石脆性破裂的重正化研究及数值模拟[J].岩土工程学报,2002,24(2):183-187Chen Zhonghui,Tan Guohuan,Yang Wenzhu.Renormalization study and numerical simulation on brittle failure of rocks[J].Chinese Journal of Geotechnical Engineering,2002,24(2):183-187
[21]秦四清,徐锡伟,胡平,等.孕震断层的多锁固段脆性破裂机制与地震预测新方法的探索[J].地球物理学报,2010,53(4):1001-1014Qin Siqing,Xu Xiwei,Hu Ping,et al.Brittle failure mechanism of multiple locked patches in a seismogenic fault systemand exploration on a new way for earthquake prediction[J].Chinese Journal of Geophysics,2010,53(4):1001-1014
[22]秦四清,王媛媛,马平.崩滑灾害临界位移演化的指数律[J].岩石力学与工程学报,2010,29(5):873-880Qin Siqing,Wang Yuanyuan,Ma Ping.Exponential laws of critical displacement evolution for landslides and avalanches[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):837-880
[23]秦四清,薛雷,王媛媛,等.对孕震断层多锁固段脆性破裂理论的进一步验证及有关科学问题的讨论[J].地球物理学进展,2010,25(3):749-758Qin Siqing,Xue Lei,Wang Yuanyuan,et al.Further verifications on the brittle failure theory of multiple locked patchesalong a seismogenic fault system and discussions on some science issues[J].Progress in Geophysics,2010,25(3):749-758
[24]Weibull W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,18(3):293-297
[25]Brace W F,Paulding B W.Dilatancy in the fracture of crystalline rocks[J].Journal of Geophysical Research,1966,71(16):3939-3953
[26]Martin C D,Chandler N A.The progressive fracture of Lac du Bonnet granite[J].International Journal of RockMechanics and Mining Sciences,1994,31(6),643-659pbpb
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