地震作用下三维接触面单元弹塑性模拟方法
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摘要
为了模拟非连续结构面、接触面等在地震荷载作用下的动力响应,在弹塑性框架内建立了一种新的三维接触面弹塑性模型,该模型能够综合考虑应变率和塑性损伤对接触面强度的影响。在弹性阶段,采用双曲线函数来描述接触面的非线性应变过程。在塑性阶段,考虑了应变率和损伤对接触面强度的影响,对带拉伸截止限的莫尔库伦准则进行了修正,并且基于塑性一致性条件,推导了塑性应变增量的求解过程。通过与试验数据对比,验证了模型的合理性。将该模型写入到有限元计算程序中,并应用于典型地下工程数值计算,结果表明:与等效连续模型相比,该模型计算的梁体主应力减小了约7.6%,长锚杆承担了更多的荷载;梁体变形量增加了1~2 mm,说明接触面的存在减小了围岩对岩锚梁的约束作用,降低了其在地震荷载作用下的稳定性。
In order to simulate the dynamic response of discontinuous structural plane or interface under seismic load,a new 3-D interface elastoplastic model is established within the elastoplastic framework,in which the effects of strain rate and plastic damage on the strength of the interface are comprehensively considered. In the elastic phase,the process of the non-linear strain of the interface is described with hyperbolic function. In the plastic phase,the effects of strain rate and damage on the strength of the interface are considered,while the Mohr Coulomb criterion with stretch cutoff limit is revised and the solving process of the plastic strain increment is deduced based on the plastic consistency condition. Compared with the relevant experimental data,the reasonability of the model is verified. Through putting the model into the relevant finite element calculation program and applying it to the numerical calculation for typical underground project,the result shows that compared with the equivalent continuum model,the principal stress of the beam calculated by the model is decreased by about 7% with long anchor-rod for bearing more load,while the deformation of the beam is increased by 1 ~ 2 mm,which is indicated that the existence of the interface reduces the constraint effect from the surrounding rock on the rock-anchored beam,thus decreases its stability under the seismic load.
In order to simulate the dynamic response of discontinuous structural plane or interface under seismic load,a new 3-D interface elastoplastic model is established within the elastoplastic framework,in which the effects of strain rate and plastic damage on the strength of the interface are comprehensively considered. In the elastic phase,the process of the non-linear strain of the interface is described with hyperbolic function. In the plastic phase,the effects of strain rate and damage on the strength of the interface are considered,while the Mohr Coulomb criterion with stretch cutoff limit is revised and the solving process of the plastic strain increment is deduced based on the plastic consistency condition. Compared with the relevant experimental data,the reasonability of the model is verified. Through putting the model into the relevant finite element calculation program and applying it to the numerical calculation for typical underground project,the result shows that compared with the equivalent continuum model,the principal stress of the beam calculated by the model is decreased by about 7% with long anchor-rod for bearing more load,while the deformation of the beam is increased by 1 ~ 2 mm,which is indicated that the existence of the interface reduces the constraint effect from the surrounding rock on the rock-anchored beam,thus decreases its stability under the seismic load.
引文
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[19]王爱文,潘一山,赵宝友.冲击载荷下锚杆—围岩结构冲击失效机制的数值分析[J].地震工程学报,2017,39(3):417-424.
[20]赵坚,李海波.莫尔—库伦和霍克—布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2):171-176.
[21]朱泽奇,盛谦,冷先伦,等.大型地下洞室群关键块体地震响应分析[J].岩石力学,2010,31(2):254-259.
[22]张志国.地下洞室群地震响应数值分析方法研究[D].武汉:武汉大学,2012.
[23]李海波,冯海鹏,刘博.不同剪切速率下岩石节理的强度特性研究[J].岩石力学与工程学报,2006,25(12):2435-2440.
[24]李海波,刘博,冯海鹏,等.模拟岩石节理试样剪切变形特征和破坏机制研究[J].岩石力学与工程学报,2008,29(7):1741-1752.
[25]崔新壮,陈士海,刘德成.在裂隙岩体中传播的应力波的衰减机理[J].工程爆破,1999,5(1):18-21.
[2]DESAI C S,ZAMAN M M.Thin layer element for interfaces and joints[J].International journal for number and analytical methods in geomechanics,1984,8(1):19-43.
[3]PLESHA M E.Constitutive models for rock discontinuities with dilatancy and surface degradation[J].International journal for numerical and analytical methods in geomechanics,1987,11(5):345-363.
[4]BEER G.An isoparametric joint/interface element for finite element analysis[J].International journal for numerical method in engineering,1985,21(1):585-600.
[5]BOUZID D A,TILIOUINE B.Exact formulation of interface stiffness matrix for axi-symemetric bodies under noaxi-symmetric loading[J].Computers and geotechnics,2004,31(2):75-87.
[6]CHEN Juntao,YANG Yang,YE Chao,et al.Three-dimensional numerical analysis of compound lining in complex underground surge-shaft structure[J].Mathematical problems in engineering,2015,2015:1-10.
[7]BANDIS S C,LUMSDEN A C,BARTON N R.Fundamentals of rock joint deformation[J].International journal of rock mechanics and mining sciences and geomechanics abstracts,1983,20(6):249-268.
[8]MALAMA B,KULATILAKE P.Models for normal fracture deformation under compressive loading[J].International journal of rock mechanics and mining sciences,2003,40(6):893-901.
[9]SUN Z.Fracture mechanics and tribology of rocks and rock joints[D].Lulea:Lulea University of Technology,1983.
[10]李夕兵,王卫华,马春德.不同频率荷载作用下的岩石节理本构模型[J].岩石力学与工程学报,2007,26(2):247-253.
[11]尹显俊,王光纶.岩体结构面法向循环加载本构关系研究[J].岩石力学与工程学报,2005,24(7):1158-1163.
[12]HUANG T H,CHANG C S,CHAO C Y.Experimental and mathematical modeling for fracture of rock joint with regular asperities[J].Engineering fracture mechanics,2002,69:1977-1996.
[13]WANG J G,ICHIKAWA Y,LEUNG C F.A constitutive model for rock interfaces and jonts[J].International journal of rock mechanics and mining sciences,2003,40:41-53.
[14]GRASSELLI G,EGGER P.Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters[J].International journal of rock mechanics and mining sciences,2003,40:25-40.
[15]尹显俊,王光纶,张楚汉.岩体结构面切向循环加载本构关系研究[J].工程力学,2005,22(6):97-103.
[16]王小威,陈俊涛,谢金元,等.地下厂房岩锚梁接触面非线性有限元模拟方法[J].四川大学学报(工程科学版),2017,49(4):70-77.
[17]CLOUGH G W,DUNCAN J M.Finite element analysis of retaining wall behavior[J].Journal of soil mechanics and foundation division,1973,99(4):1657-1672.
[18]肖明.地下洞室围岩稳定与支护数值方法研究[D].武汉:武汉大学,2002.
[19]王爱文,潘一山,赵宝友.冲击载荷下锚杆—围岩结构冲击失效机制的数值分析[J].地震工程学报,2017,39(3):417-424.
[20]赵坚,李海波.莫尔—库伦和霍克—布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2):171-176.
[21]朱泽奇,盛谦,冷先伦,等.大型地下洞室群关键块体地震响应分析[J].岩石力学,2010,31(2):254-259.
[22]张志国.地下洞室群地震响应数值分析方法研究[D].武汉:武汉大学,2012.
[23]李海波,冯海鹏,刘博.不同剪切速率下岩石节理的强度特性研究[J].岩石力学与工程学报,2006,25(12):2435-2440.
[24]李海波,刘博,冯海鹏,等.模拟岩石节理试样剪切变形特征和破坏机制研究[J].岩石力学与工程学报,2008,29(7):1741-1752.
[25]崔新壮,陈士海,刘德成.在裂隙岩体中传播的应力波的衰减机理[J].工程爆破,1999,5(1):18-21.