准各向同性裂隙岩体中有效动弹性参数与弹性波速关系的研究
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摘要
从弹性波在介质中传播的特点和弹性波法在岩体工程中的实际应用情况方面,分析了弹性波在含裂隙岩体介质中的传播特征。将岩体中裂隙呈随机分布的裂隙岩体似为准各向同性裂隙岩体,根据能量平衡原理、岩石断裂力学理论和卡氏最小功能定理(Castiglano’stheorem),确定了准各向同性裂隙岩体的有效动弹性参数(E、ν、G)与裂隙密度参数(Xv)的数学关系。在此基础上,根据各向同性介质中传播的弹性波理论,建立了准各向同性裂隙岩体中弹性波速(Vp、Vs)和Vp/Vs与裂隙密度参数(Xv)之间的关系。理论研究表明,在此裂隙岩体中,有效动弹性参数和弹性波速与裂纹密度参数之间相互的关系均近似成倒数函数的非线性关系;裂隙密度参数增加,有效动弹性模量(E)也减少,弹性波速(Vp,Vs)也减小;在裂隙密度参数较小时,此裂隙岩体的有效弹性模量和弹性波速随裂隙密度参数的变化较大,说明裂隙体的有效弹性参数和弹性波速对裂隙体非常敏感。
According to the characteristic of elastic waves propagation in medium and the application of elastic wave method in rock mass engineering, the paper has analyzed the characteristic of elastic waves propagation in cracked rock masses. It has put out the relationship of effective dynamic parameters of elasticity ( E ,ν , G ) and crack density parameters, according to the principle of energy balance, rock rupture mechanics and Castiglano’s theorem, by looking the cracked mass with random cracks as quasi-isotropic cracked mass. On this basis, and through the theory of elastic wave propagation in isotropic medium, it has made out the relationship between the elastic wave velocity and crack density parameters. The theoretical research has shown that, in this kind of cracked rock masses, it will be nonlinear relationships between the effective dynamic parameters of elasticity and wave velocities and the crack density parameter; and with the increase of crack density parameter, the effective dynamic modulus of elasticity and the elastic wave velocities decrease; and at the same time, when the crack density parameter is very small, the effective dynamic modulus of elasticity and the elastic wave velocities change with the crack density parameter much more, which has explained the sensitivity of effective elastic parameters and elastic wave velocities to cracked rock masses.
According to the characteristic of elastic waves propagation in medium and the application of elastic wave method in rock mass engineering, the paper has analyzed the characteristic of elastic waves propagation in cracked rock masses. It has put out the relationship of effective dynamic parameters of elasticity ( E ,ν , G ) and crack density parameters, according to the principle of energy balance, rock rupture mechanics and Castiglano’s theorem, by looking the cracked mass with random cracks as quasi-isotropic cracked mass. On this basis, and through the theory of elastic wave propagation in isotropic medium, it has made out the relationship between the elastic wave velocity and crack density parameters. The theoretical research has shown that, in this kind of cracked rock masses, it will be nonlinear relationships between the effective dynamic parameters of elasticity and wave velocities and the crack density parameter; and with the increase of crack density parameter, the effective dynamic modulus of elasticity and the elastic wave velocities decrease; and at the same time, when the crack density parameter is very small, the effective dynamic modulus of elasticity and the elastic wave velocities change with the crack density parameter much more, which has explained the sensitivity of effective elastic parameters and elastic wave velocities to cracked rock masses.
引文
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[16]Hudson J A.Overall elastic properties of isotropic materials with arbitrary distribution of circular cracks[J].Geophys.J.Int.,1990,102:465-469.
[17]Zimmerman R W.The effect of microcracks on the elastic moduli of brittle materials[J].J.Mater.Scl.Lett.,1985.
[18]王宏图,鲜学福.复杂应力条件下岩石弹性波的传播特性[J].重庆大学学报,1989,12(4):204-207.WANG Hong-tu,XIAN Xue-fu.Characteristic of spread of elastic wave of rock under intricacy stress[J].Journal of Chongqing University,1989,12(4):204-207.
[2]Gaviglio P.Longitudinal waves propagation in a Limestone:The relationship between velocities and density[J].Rock Mech.Rock Eng,1989,22(4):290-299.
[3]李纪汉.温度对岩石的弹性波速和声发射的影响[J].地震学报,1986,8(3):242-245.LI Ji-han.Effect of temperature on elasticity wave velocity and voice launching of rock[J].Journal of Earthquake,1986,8(3):242-245.\
[4]史謌,沈文略,杨东全.岩石弹性波速度和饱和度、孔隙流体分布的关系[J].地球物理学报,2003,46(1):138-142.SHI Ge,SHEN Wen-lue,YANG Dong-quan.The relationship of wave velocities with saturation and fluid distribution in pore space[J].Chinese Journal of Geophysics,2003,46(1):138-142.
[5]刘祝萍,吴小薇,楚择涵.岩石声学参数的实验测量及研究[J].地球物理学报,1994,37(5):659-666.LIU Zhu-ping,et al.Laboratory study of acoustic parameters of rock[J].Chinese Journal of Geophysics,1994,37(5):659-666.
[6]首培.地震波在工程中的应用[M].北京:地质出版社,1982.SGOU Pei.Application of Earthquake Wave in Enginee-ring[M].Beijing:Geological Press,1982.
[7]高龙生.中国大陆岩石标本在高压下的弹性波速的研究[J].地球物理学报,1975,8(1):26-38.GAO Long-sheng.Study on elasticity wave velocity of rock of China mainland under high pressure[J].Chinese Journal of Geophysics,1975,8(1):26-38.
[8]吴少武.应用声波法研究围岩的应力状态[J].地震,1984,6:12-19.WU Shao-wu.Study the stress state of wall rock used by voice wave method[J].Earthquake,1984,6:12-19.
[9]罗淦堂等.岩石温度对纵波速度的影响[J].岩土工程学报,19857(5):80-84.LUO Jin-tang,et al.Effect of temperature of rock on vertical wave velocity[J].Journal of Rock and Soil Engineering,1985,7(5):80-84.
[10]Zimmerman R W,King M S.Propagation of acoustic waves through cracked rock[A].Proc.26th.U.S.on Rock Mechanics[C].[s.l.]:[s.n.],1985,739-745.
[11]O’connell.Seismic velocities in dry and saturated cracked solids.J.Geophys.Res.,1974,97:5412-5426.
[12]Willis J R.A polarization approach to the scattering of elastic waves-I:Scattering by a single inclusion[J].J.Mech.Phys.Solids,1980,28:287-305.
[13]沈联蒂,史謌.流体饱和度、频率、流体类型对岩石弹性波速度影响的实验研究[J].地球物理学报,1992,35(增刊):322-331.SHEN Lian-di,et al.Laboratory study of effect of saturation and frequency of liquid&styles of liquid on elasticity wave velocity of rock[J].Chinese Journal of Geophysics,1992,35(Supp):322-331.
[14]Irwin G R.Analysis of stresses and strains near the ends of a crack traversing a plate[J].J.Appl.Mech.,1975,24:261-364.
[15]Sih G C.Handbook of Stress Intensity Factors.Institute of Fracture and Solid Mechanics[M].Bethlehem:Lehigh University,1973.
[16]Hudson J A.Overall elastic properties of isotropic materials with arbitrary distribution of circular cracks[J].Geophys.J.Int.,1990,102:465-469.
[17]Zimmerman R W.The effect of microcracks on the elastic moduli of brittle materials[J].J.Mater.Scl.Lett.,1985.
[18]王宏图,鲜学福.复杂应力条件下岩石弹性波的传播特性[J].重庆大学学报,1989,12(4):204-207.WANG Hong-tu,XIAN Xue-fu.Characteristic of spread of elastic wave of rock under intricacy stress[J].Journal of Chongqing University,1989,12(4):204-207.
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