加载速率对岩石单轴压缩试验影响的数值模拟研究
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摘要
在单轴压缩数值模拟试验中,加载速率由每次边界条件变化幅度和边界条件变化后的平衡计算时间这两个因素共同控制。同样的加载速率,两个因素的不同组合也会对加载效果有很大的影响。因此,探究以上两因素对岩石单轴压缩数值模拟试验的影响机制,可对高效进行高精度的各加载速率下的数值模拟试验起到积极作用。本文使用MatDEM软件,基于软件自动设定的加载区间以及标准平衡迭代,设置不同的应力施加步数Nd与平衡迭代比率Rb,进行不同加载速率下的数值模拟试验。模拟结果表明:(1)单步加载后平衡迭代次数越多(Rb越大),该步中应力波传播与动能衰减越充分。在最优阻尼条件下,当单步加载后平衡迭代次数等于40次(Rb等于0.8)时,每步加载中动能充分平衡,可以最低计算量取得准静态模拟结果;(2)单步加载应力增量越小(Nd越大),数值模拟试验精度越高;(3)当加载速率一定即计算量相同时,为保证更高的模拟试验精度,应采用低单步应力增量与低单步加载后平衡迭代次数(Nd大、Rb小)的加载方案。本文为定量研究岩石加载速率问题和相关数值模拟提供了参考。
In numerical simulation of uniaxial compression, the loading rate is controlled by the variation range of boundary conditions and the balance time after each change of boundary conditions. At the same loading rate, different combinations of the two factors will have a great different on the loading effect. Therefore, exploring the influence mechanism of the above two factors on the numerical simulation test of rock uniaxial compression can play a positive role in doing the efficient and high-precision numerical simulation test under various loading rates. Using the MatDEM software, based on the loading area and standard equilibrium iteration which set by the software automatically, changing the division number Ndand balance rate Rbto alter the loading rates of the uniaxial compression numerical simulation tests. Through the analysis of the simulation results, the following conclusions can be obtained:(1) After one-step loading, the more number of equilibrium iterations are, the more sufficient the propagation of the stress wave and kinetic energy dissipation is. Under the artificial viscosity determined by the semi-empirical equation, when the number of iterations is equal to 40(Rb equals 0.8), the kinetic energy will decay sufficiently in each step, and the quasi-static simulation results can be obtained with the lowest amount of calculation.(2) The smaller the stress increment of single-step loading is(the greater the Nd), the more accurate numerical simulation results are.(3) When the loading rate is fixed and the amount of calculation is the same, loading schemes with low single-step stress increment and lower balance iteration times(large Ndand small Rb) after single-step loading should be adopted to ensure the accuracy of numerical simulation test. This paper provides a reference for quantitative study of rock loading rate and related numerical simulation.
In numerical simulation of uniaxial compression, the loading rate is controlled by the variation range of boundary conditions and the balance time after each change of boundary conditions. At the same loading rate, different combinations of the two factors will have a great different on the loading effect. Therefore, exploring the influence mechanism of the above two factors on the numerical simulation test of rock uniaxial compression can play a positive role in doing the efficient and high-precision numerical simulation test under various loading rates. Using the MatDEM software, based on the loading area and standard equilibrium iteration which set by the software automatically, changing the division number Ndand balance rate Rbto alter the loading rates of the uniaxial compression numerical simulation tests. Through the analysis of the simulation results, the following conclusions can be obtained:(1) After one-step loading, the more number of equilibrium iterations are, the more sufficient the propagation of the stress wave and kinetic energy dissipation is. Under the artificial viscosity determined by the semi-empirical equation, when the number of iterations is equal to 40(Rb equals 0.8), the kinetic energy will decay sufficiently in each step, and the quasi-static simulation results can be obtained with the lowest amount of calculation.(2) The smaller the stress increment of single-step loading is(the greater the Nd), the more accurate numerical simulation results are.(3) When the loading rate is fixed and the amount of calculation is the same, loading schemes with low single-step stress increment and lower balance iteration times(large Ndand small Rb) after single-step loading should be adopted to ensure the accuracy of numerical simulation test. This paper provides a reference for quantitative study of rock loading rate and related numerical simulation.
引文
黄达,黄润秋,张永兴.2012.粗晶大理岩单轴压缩力学特性的静态加载速率效应及能量机制试验研究[J].岩石力学与工程学报,31(2):245-255.
刘春,施斌,顾凯,等.2014.岩土体大型三维离散元模拟系统的研发与应用[J].工程地质学报,22(s1):551-557.
李海波,王建伟,李俊如,等.2004.单轴压缩下软岩的动态力学特性试验研究[J].岩土力学,25(1):1-4.
李永盛.1995.加载速率对红砂岩力学效应的试验研究[J].同济大学学报:自然科学版,(3):265-269.
索文斌,刘春,施斌,等.2017.深基坑PCMW工法开挖过程离散元数值模拟分析[J].工程地质学报,25(4):920-925.
吴绵拔.1982.加载速率对岩石抗压和抗拉强度的影响[J].岩土工程学报,4(2):97-106.
尹小涛,葛修润,李春光,等.2010.加载速率对岩石材料力学行为的影响[J].岩石力学与工程学报,29(s1):2610-2615.
周辉,杨艳霜,肖海斌,等.2013.硬脆性大理岩单轴抗拉强度特性的加载速率效应研究——试验特征与机制[J].岩石力学与工程学报,32(9):1868-1875.
张学朋,蒋宇静,王刚,等.2016.基于颗粒离散元模型的不同加载速率下花岗岩数值试验研究[J].岩土力学,37(9):2679-2686.
赵振龙,赵坤,王晓.2017.不同加载速率下类煤岩力学特性及损伤演化规律研究[J].煤炭科学技术,45(10):41-47.
Cundall P and Strack O.1979.A discrete element model for granular assemblies[J].Geotechnique,29(1):47-65.
Finch E,Hardy S and Gawthorpe R.2004.Discrete element modelling of c ontractional fa ult-propagation folding above rigid basement fault blocks[J].Journal of Structural Geology,16(4):467-488.
Hardy S and Finch E.2006.Discrete element modelling of the influence ofcover strength on basement-involved fault-propagation folding[J].Tec tonophysics,415(1-4):225-238.
Kumar A.1968.The effect of stress rate and temperature on the strength of basalt and granite[J].Geophysics,33(3):501-510.
Li X B,Lok T S and Zhao J.2005.Dynamic characteristics of granite subjected to intermediate loading rate[J].Rock Mechanics&Rock Engineering,38(1):21-39.
Liu C,Pollard D D and Shi B.2013.Analytical solutions and numerical tests of elastic and failure behaviors of close-packed lattice for brittle rocks and crystals[J].Journal of Geophysical Research:Solid Earth,118(1):71-82.
Liu C,Pollard D D,Gu K,et al.2015.Mechanism of formation of wiggly compaction bands in porous sandstone:2.Numerical simulation using discrete element method[J].Journal of Geophysical Research Solid Earth,120(12):8152-1868.
Liu C,Xu Q,Shi B,et al. 2017.Mechanical properties and energy conversion of 3D close-packed lattice model for brittle rocks[J].Computers&Geosciences,103(C):12-20.
Mora P and Place D.1993.A lattice solid model for the nonlinear dynamics of earthquakes[J].International Journal of Modern Physics C,4(6):1059-1074.
Place D,Lombard F,Mora P,et al.2002.Simulation of the Micro-physics of Rocks Using LSMearth[J].Pure&Applied Geophysics,159(9):1911-1932.
Yin H,Zhang J,Meng L,et al.2009.Discrete element modeling of the faultingin the sedimentary cover above an active salt diaper[J].Journal of Structural Geology,31(9):989-995.
Zhao J, Li H B,Wu M B,et al.1999.Dynamic uniaxial compression tests of a granite[J].International Journal of Rock Mechanics&Mining Sciences,36(2):273-277.
刘春,施斌,顾凯,等.2014.岩土体大型三维离散元模拟系统的研发与应用[J].工程地质学报,22(s1):551-557.
李海波,王建伟,李俊如,等.2004.单轴压缩下软岩的动态力学特性试验研究[J].岩土力学,25(1):1-4.
李永盛.1995.加载速率对红砂岩力学效应的试验研究[J].同济大学学报:自然科学版,(3):265-269.
索文斌,刘春,施斌,等.2017.深基坑PCMW工法开挖过程离散元数值模拟分析[J].工程地质学报,25(4):920-925.
吴绵拔.1982.加载速率对岩石抗压和抗拉强度的影响[J].岩土工程学报,4(2):97-106.
尹小涛,葛修润,李春光,等.2010.加载速率对岩石材料力学行为的影响[J].岩石力学与工程学报,29(s1):2610-2615.
周辉,杨艳霜,肖海斌,等.2013.硬脆性大理岩单轴抗拉强度特性的加载速率效应研究——试验特征与机制[J].岩石力学与工程学报,32(9):1868-1875.
张学朋,蒋宇静,王刚,等.2016.基于颗粒离散元模型的不同加载速率下花岗岩数值试验研究[J].岩土力学,37(9):2679-2686.
赵振龙,赵坤,王晓.2017.不同加载速率下类煤岩力学特性及损伤演化规律研究[J].煤炭科学技术,45(10):41-47.
Cundall P and Strack O.1979.A discrete element model for granular assemblies[J].Geotechnique,29(1):47-65.
Finch E,Hardy S and Gawthorpe R.2004.Discrete element modelling of c ontractional fa ult-propagation folding above rigid basement fault blocks[J].Journal of Structural Geology,16(4):467-488.
Hardy S and Finch E.2006.Discrete element modelling of the influence ofcover strength on basement-involved fault-propagation folding[J].Tec tonophysics,415(1-4):225-238.
Kumar A.1968.The effect of stress rate and temperature on the strength of basalt and granite[J].Geophysics,33(3):501-510.
Li X B,Lok T S and Zhao J.2005.Dynamic characteristics of granite subjected to intermediate loading rate[J].Rock Mechanics&Rock Engineering,38(1):21-39.
Liu C,Pollard D D and Shi B.2013.Analytical solutions and numerical tests of elastic and failure behaviors of close-packed lattice for brittle rocks and crystals[J].Journal of Geophysical Research:Solid Earth,118(1):71-82.
Liu C,Pollard D D,Gu K,et al.2015.Mechanism of formation of wiggly compaction bands in porous sandstone:2.Numerical simulation using discrete element method[J].Journal of Geophysical Research Solid Earth,120(12):8152-1868.
Liu C,Xu Q,Shi B,et al. 2017.Mechanical properties and energy conversion of 3D close-packed lattice model for brittle rocks[J].Computers&Geosciences,103(C):12-20.
Mora P and Place D.1993.A lattice solid model for the nonlinear dynamics of earthquakes[J].International Journal of Modern Physics C,4(6):1059-1074.
Place D,Lombard F,Mora P,et al.2002.Simulation of the Micro-physics of Rocks Using LSMearth[J].Pure&Applied Geophysics,159(9):1911-1932.
Yin H,Zhang J,Meng L,et al.2009.Discrete element modeling of the faultingin the sedimentary cover above an active salt diaper[J].Journal of Structural Geology,31(9):989-995.
Zhao J, Li H B,Wu M B,et al.1999.Dynamic uniaxial compression tests of a granite[J].International Journal of Rock Mechanics&Mining Sciences,36(2):273-277.