岩石弹塑性应力-渗流-损伤耦合模型研究(Ⅰ):模型建立及其数值求解程序
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摘要
在地下水渗流场、应力场、损伤场的耦合作用下更易造成隧道围岩坍塌或涌水等灾害。首先,将围岩材料视作各向同性连续介质,基于Drucker-Prager准则建立岩石弹塑性损伤本构模型,采用完全隐式返回映射算法实现弹塑性损伤本构方程的数值求解。其次,以上述研究为基础根据岩石处于弹塑性状态时渗透系数动态演化公式,建立岩石弹塑性应力-渗流-损伤耦合模型,并给出三场耦合情况下的数值求解迭代方法。针对耦合模型中涉及参数较多且不易测定的问题,基于差异进化算法原理建立智能反分析方法,对耦合模型中的损伤参数进行反演。最后,利用C++语言编制相应的岩石弹塑性应力-渗流-损伤耦合程序和参数反演程序,利用所编程序进行以下计算:(1)对智能反分析程序的性能、正确性进行分析,对比不同差异策略、交叉因子、变异因子的反演精度和收敛速度。(2)分别采用弹性模型和弹塑性损伤模型进行隧道围岩位移场、应力场的计算。(3)不考虑力学作用的情况下进行孔隙水压力、渗流量的计算。(4)采用所建耦合模型计算得到隧道围岩应力场、渗流场以及损伤场的相互影响规律。研究结果表明,基于差异进化算法的智能反分析程序能够较好地解决耦合模型中损伤参数不易确定的难题,为实际工程中获得不易测定的计算参数提供了有效的方法,同时所建立的耦合模型通过应力、渗流和损伤的相互作用更能够真实地反映出岩石材料的宏观破坏现象,所编计算程序能够模拟地下水渗流场、应力场、损伤场之间的耦合特性,为受地下水影响严重的工程建设提供了方法,研究结论为后期对实际隧道工程进行耦合计算奠定基础。
It is more likely to cause the collapse of tunnel surrounding rock and water disasters under the action of the coupling effect of the groundwater seepage field, the stress field and the damage field. First of all, surrounding rock is regarded as the isotropic continuum material, and the elastoplastic damage constitutive model of rock is established based on the Drucker Prager criterion. The fully implicit return mapping algorithm is adopted to achieve the numerical solution of elastoplastic damage constitutive equations.Secondly, according to the dynamic evolution formula of permeability coefficient in elastoplastic state based on the above research,the elasoplastic stress-seepage-damage model of rock is established; and the coupling solving iterative method of many fields is presented. Back analysis program is compiled on the basis of the principle of differential evolution algorithm in order to solve the problem that elastoplastic damage model involves many parameters and not easy to determine, and the damage parameters are inversion; Finally, the corresponding coupling program of the elastoplastic stress-seepage-damage is compiled and parameters inversion program are compiled using C++ language respectively. The following calculations are conducted by using the programs:(1)The performance and the correctness of the intelligent back analysis program are analyzed, comparing the inversion accuracy and the convergence rate of the differences between the different strategies, the cross factors and the variation factors.(2) The calculationresults of the displacement field and the stress field by the elastic model and the elastoplastic model are compared.(3) The pore water pressure and the seepage flow are calculated without considering the effect of mechanics.(4) The interaction rules of the stress field,the seepage field and the damage field of tunnel surrounding rock are calculated using the coupling model. The results show that the problem of damage parameters which is difficult to determine can be better to solve in damage model by the back analysis program based on differential evolution algorithm. It provides effective method for the calculation parameters are acquired not easily determined in practical engineering. At the same time, the macro failure of rock material can be more realistically reflect through the interaction of the stress, the seepage and the damage of the built coupling model. The calculation program which provides a method for the engineering construction affected by groundwater severely can simulate the coupling characteristics of the groundwater seepage field, the stress field and the damage field. The study of this paper lays a solid foundation for the coupling calculation of the later period for actual tunnel engineering.
It is more likely to cause the collapse of tunnel surrounding rock and water disasters under the action of the coupling effect of the groundwater seepage field, the stress field and the damage field. First of all, surrounding rock is regarded as the isotropic continuum material, and the elastoplastic damage constitutive model of rock is established based on the Drucker Prager criterion. The fully implicit return mapping algorithm is adopted to achieve the numerical solution of elastoplastic damage constitutive equations.Secondly, according to the dynamic evolution formula of permeability coefficient in elastoplastic state based on the above research,the elasoplastic stress-seepage-damage model of rock is established; and the coupling solving iterative method of many fields is presented. Back analysis program is compiled on the basis of the principle of differential evolution algorithm in order to solve the problem that elastoplastic damage model involves many parameters and not easy to determine, and the damage parameters are inversion; Finally, the corresponding coupling program of the elastoplastic stress-seepage-damage is compiled and parameters inversion program are compiled using C++ language respectively. The following calculations are conducted by using the programs:(1)The performance and the correctness of the intelligent back analysis program are analyzed, comparing the inversion accuracy and the convergence rate of the differences between the different strategies, the cross factors and the variation factors.(2) The calculationresults of the displacement field and the stress field by the elastic model and the elastoplastic model are compared.(3) The pore water pressure and the seepage flow are calculated without considering the effect of mechanics.(4) The interaction rules of the stress field,the seepage field and the damage field of tunnel surrounding rock are calculated using the coupling model. The results show that the problem of damage parameters which is difficult to determine can be better to solve in damage model by the back analysis program based on differential evolution algorithm. It provides effective method for the calculation parameters are acquired not easily determined in practical engineering. At the same time, the macro failure of rock material can be more realistically reflect through the interaction of the stress, the seepage and the damage of the built coupling model. The calculation program which provides a method for the engineering construction affected by groundwater severely can simulate the coupling characteristics of the groundwater seepage field, the stress field and the damage field. The study of this paper lays a solid foundation for the coupling calculation of the later period for actual tunnel engineering.
引文
[1]贾善坡,陈卫忠,于洪丹,等.泥岩隧道施工过程中渗流场与应力场全耦合损伤模型研究[J].岩土力学,2009,30(1):19-26.JIA Shan-po,CHEN Wei-zhong,YU Hong-dan,et al.Research on seepage-stress coupling damage model of boom clay during tunneling[J].Rock and Soil Mechanics,2009,30(1):19-26.
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[5]冉启全,顾小芸.油藏渗流与应力耦合分析[J].岩土工程学报,1998,20(2):69-73.RAN Qi-quan,GU Xiao-yun.Coupling analysis of multiphase flow and stress for oil reservoir[J].Chinese Journal of Geotechnical Engineering,1998,20(2):69-73.
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[7]杨天鸿,唐春安,朱万成,等.岩石破裂过程渗流与应力耦合分析[J].岩土工程学报,2001,23(4):489-493.YANG Tian-hong,TANG Chun-an,ZHU Wan-cheng,et al.Coupling analysis of seepage and stresses in rock failure process[J].Chinese Journal of Geotechnical Engineering,2001,23(4):489-493.
[8]张巍,肖明,范国邦.大型地下洞室群围岩应力-损伤-渗流耦合分析[J].岩土力学,2008,29(7):1813-1818.ZHANG Wei,XIAO Ming,FAN Guo-bang.Stressdamage-seepage coupling analysis of surrounding rock of large-scale underground caverns[J].Rock and Soil Mechanics,2008,29(7):1813-1818.
[9]刘仲秋,章青.考虑渗流-应力耦合效应的深埋引水隧洞衬砌损伤演化分析[J].岩石力学与工程学报,2012,31(10):2147-2153.LIU Zhong-qiu,ZHANG Qing.Damage evolution analysis of permeable lining of deep diversion tunnel based on seepage-stress coupling theory[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(10):2147-2153.
[10]沈振中,张鑫,孙粤琳.岩体水力劈裂的应力-渗流-损伤耦合模型研究[J].计算力学学报,2009,26(4):523-528.SHEN Zhen-zhong,ZHANG Xin,SUN Yue-lin.Research on stress-seepage-damage coupling model of hydraulic fracturing for rock mass[J].Chinese Journal of Computational Mechanics,2009,26(4):523-528.
[11]赵延林,王卫军,黄永恒,等.裂隙岩体渗流-损伤-断裂耦合分析与工程应用[J].岩土工程学报,2010,32(1):24-32.ZHAO Yan-lin,WANG Wei-jun,HUANG Yong-heng,et al.Coupling analyssis of seepage-damage-fracture in fractured rock mass and engineering appliaction[J].Chinese Journal of Geotechnical Engineering,2010,32(1):24-32.
[12]毛昶熙,段祥宝,李祖贻.渗流数值计算与程序应用[M].南京:河海大学出版社,1999.
[13]叶源新,刘光廷.岩石渗流应力耦合特性研究[J].岩石力学与工程学报,2005,24(14):2518-2525.YE Yuan-xin,LIU Guang-ting.Research on coupling charcateristics of fluid flow and stress within rock[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(14):2518-2525.
[14]TAYLOR D W.Fundamentals of soil mechanics[M].New York:John Wiley&Sons.,1948.
[15]SAMARASINGHE A M,HUANG Y H,DRNEVICH V P.Permeability and consolidation of normally consolidated soils[J].Journal of the Geotechnical Engineering Division,1982,108(6):835-850.
[16]LOUSI C.Rock hydraulics[M]//Rock Mechanics[M].New York:Elsevier Science,1974.
[17]NELSON R A.Fracture permeability in porous reservoirs:Experimental and field approach[D].Texas:Department of Geology,Texas A and M University,1975.
[18]沈新普,泽农·慕容子,徐秉业,等.岩石材料弹塑性正交异性损伤耦合本构理论[J].应用数学和力学,2001,22(9):927-933.SHEN Xin-pu,ZENON Mroz,XU Bing-ye,et al.Constitutive theory of plasticity coupled with orthotropic damage for geomaterials[J].Applied Mathematics and Mechanics,2001,22(9):927-933.
[19]王军祥,姜谙男.岩石弹塑性损伤本构模型建立及在隧道工程中的应用[J].岩土力学,待刊.WANG Jun-xiang,JIANG An-nan,Elastoplastic damage constitutive model of rock considering the action of the pore water pressure and numerical algorithm[J],Rock and Soil Mechanics,in press.
[20]STORN R,PRICE K.Differential evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces[R].Berkeley:International Computer Science Institute,1995.
[2]李根,唐春安,李连崇.水岩耦合变形破坏过程及机理研究进展[J].力学进展,2012,42(5):593-619.LI Gen,TANG Chun-an,LI Lian-chong.Advances in rock deformation and failure process under water-rock coupling[J].Advances in Mechanics,2012,42(5):593-619.
[3]陈平,张有天.裂隙岩体渗流与应力耦合分析[J].岩石力学与工程学报,1994,13(4):299-308.CHEN Ping,ZHANG You-tian.Coupling analysis of seepage/stress for jionted rock[J].Chinese Journal of Rock Mechanics and Engineering,1994,13(4):299-308.
[4]王媛.多孔介质渗流与应力的耦合计算方法[J].工程勘察,1995,(2):33-37.WANG Yuan.A coupling calculating method of seepage and stress of porous media[J].Geotechnical Investigation&Surveying,1995,(2):33-37.
[5]冉启全,顾小芸.油藏渗流与应力耦合分析[J].岩土工程学报,1998,20(2):69-73.RAN Qi-quan,GU Xiao-yun.Coupling analysis of multiphase flow and stress for oil reservoir[J].Chinese Journal of Geotechnical Engineering,1998,20(2):69-73.
[6]杨延毅,周维垣.裂隙岩体的渗流-损伤耦合分析模型及其工程应用[J].水利学报,1991,19-27,35.YANG Yan-yi,ZHOU Wei-yuan.A coupled seepagedamage analysis model for jointed rock masses and its application to rock engineering[J].Journal of Hydrauing Engineering,1991,19-27,35.
[7]杨天鸿,唐春安,朱万成,等.岩石破裂过程渗流与应力耦合分析[J].岩土工程学报,2001,23(4):489-493.YANG Tian-hong,TANG Chun-an,ZHU Wan-cheng,et al.Coupling analysis of seepage and stresses in rock failure process[J].Chinese Journal of Geotechnical Engineering,2001,23(4):489-493.
[8]张巍,肖明,范国邦.大型地下洞室群围岩应力-损伤-渗流耦合分析[J].岩土力学,2008,29(7):1813-1818.ZHANG Wei,XIAO Ming,FAN Guo-bang.Stressdamage-seepage coupling analysis of surrounding rock of large-scale underground caverns[J].Rock and Soil Mechanics,2008,29(7):1813-1818.
[9]刘仲秋,章青.考虑渗流-应力耦合效应的深埋引水隧洞衬砌损伤演化分析[J].岩石力学与工程学报,2012,31(10):2147-2153.LIU Zhong-qiu,ZHANG Qing.Damage evolution analysis of permeable lining of deep diversion tunnel based on seepage-stress coupling theory[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(10):2147-2153.
[10]沈振中,张鑫,孙粤琳.岩体水力劈裂的应力-渗流-损伤耦合模型研究[J].计算力学学报,2009,26(4):523-528.SHEN Zhen-zhong,ZHANG Xin,SUN Yue-lin.Research on stress-seepage-damage coupling model of hydraulic fracturing for rock mass[J].Chinese Journal of Computational Mechanics,2009,26(4):523-528.
[11]赵延林,王卫军,黄永恒,等.裂隙岩体渗流-损伤-断裂耦合分析与工程应用[J].岩土工程学报,2010,32(1):24-32.ZHAO Yan-lin,WANG Wei-jun,HUANG Yong-heng,et al.Coupling analyssis of seepage-damage-fracture in fractured rock mass and engineering appliaction[J].Chinese Journal of Geotechnical Engineering,2010,32(1):24-32.
[12]毛昶熙,段祥宝,李祖贻.渗流数值计算与程序应用[M].南京:河海大学出版社,1999.
[13]叶源新,刘光廷.岩石渗流应力耦合特性研究[J].岩石力学与工程学报,2005,24(14):2518-2525.YE Yuan-xin,LIU Guang-ting.Research on coupling charcateristics of fluid flow and stress within rock[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(14):2518-2525.
[14]TAYLOR D W.Fundamentals of soil mechanics[M].New York:John Wiley&Sons.,1948.
[15]SAMARASINGHE A M,HUANG Y H,DRNEVICH V P.Permeability and consolidation of normally consolidated soils[J].Journal of the Geotechnical Engineering Division,1982,108(6):835-850.
[16]LOUSI C.Rock hydraulics[M]//Rock Mechanics[M].New York:Elsevier Science,1974.
[17]NELSON R A.Fracture permeability in porous reservoirs:Experimental and field approach[D].Texas:Department of Geology,Texas A and M University,1975.
[18]沈新普,泽农·慕容子,徐秉业,等.岩石材料弹塑性正交异性损伤耦合本构理论[J].应用数学和力学,2001,22(9):927-933.SHEN Xin-pu,ZENON Mroz,XU Bing-ye,et al.Constitutive theory of plasticity coupled with orthotropic damage for geomaterials[J].Applied Mathematics and Mechanics,2001,22(9):927-933.
[19]王军祥,姜谙男.岩石弹塑性损伤本构模型建立及在隧道工程中的应用[J].岩土力学,待刊.WANG Jun-xiang,JIANG An-nan,Elastoplastic damage constitutive model of rock considering the action of the pore water pressure and numerical algorithm[J],Rock and Soil Mechanics,in press.
[20]STORN R,PRICE K.Differential evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces[R].Berkeley:International Computer Science Institute,1995.
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