裂隙岩体损伤流变模型研究及其工程应用
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摘要
裂隙岩体力学特性及其时效特征的研究一直为岩石力学与工程界所关注。本文综合应用岩石损伤力学、岩石流变力学、数值计算等理论方法,对裂隙岩体损伤流变耦合本构方程及工程应用做了一些初步的探讨。
首先,针对裂隙岩体结构特征,从几何损伤的角度,引入了一个二阶张量来描述裂隙面对岩体的劣化效应。以裂隙面面积、裂隙面方向、裂隙面间距及密度作为损伤变量的主要影响因素,将多组裂隙面在各截面上的损伤贡献进行叠加来近似描述多组裂隙面的各向异性损伤。以西原模型作为描述岩体力学时效特性的基本模型,并通过对应原理将一维形式的西原模型流变本构方程转化为三维形式。最后根据等效应变假设,将二阶损伤张量引入流变本构方程,得到了基于西原模型的三维粘弹塑性损伤本构方程。
在VC++6.0环境下,以FLAC3D Version 2.1数值计算通用软件为开发平台,编写了上述本构模型的程序块,实现了该软件本构模型的二次开发,并阐述了二次开发程序块的运行原理。
最后,运用开发的本构模型,对双江口水电站地下洞室群开挖过程及围岩稳定性进行了粘弹塑性损伤分析,并与弹塑性计算进行了比较,从对比结果来看模型基本上是合理的。同时,根据计算结果,为地下洞室群的长期稳定性及安全性,提出了一些合理的建议。
The study on the mechanics and time-dependent feature of fractured rock mass is always an important subject of rock mechanics and engineering. Based on the theoretical method of rock damage mechanics, rock rheological mechanics and numerical calculation, this paper makes a preliminary study on the damge and rheology coupled model of fractured rock mass and its engineering application.
First, according to the structural characteristics of fractured rock mass and the geometric damage theory, we cite a second-order damage tensor to describe the deterioration of rock mass due to cracks. Taking the crack area, direction, space and density as the major influencing factors of the damage variable, we stack the damage contribution of groups of cracks on each section to describe the anisotropic damage approximatively. The Nishihara model is taken as the basic model to study the time-dependent characteristics of rock mass. And its one-dimensional constitutive equation is transformed into three-dimensional form. Eventually, by introducing the second-order damage tensor into the rheological constitutive equation on the basis of the equivalent strain hypothesis, the three-dimensional viscoelastic-plastic damage constitutive equation is deduced.
Taking FLAC3D Version2.1 as the development platform, we compile the above constitutive model on the VC++6.0 environment, and realize the secondary development of FLAC3D. The operation principles of secondary development program is also described.
In the end, the surrounding rock stability of the underground cavern group of Shuangjiangkou hydropower station is analysed by using the development program. And the results are compared with the ones obtained from the computation with elastic-plastic model. According to the comparative results, the model is basically reasonable. Meanwhile, some rational suggestions are put forward for the long-term stability and security of underground cavern group.
首先,针对裂隙岩体结构特征,从几何损伤的角度,引入了一个二阶张量来描述裂隙面对岩体的劣化效应。以裂隙面面积、裂隙面方向、裂隙面间距及密度作为损伤变量的主要影响因素,将多组裂隙面在各截面上的损伤贡献进行叠加来近似描述多组裂隙面的各向异性损伤。以西原模型作为描述岩体力学时效特性的基本模型,并通过对应原理将一维形式的西原模型流变本构方程转化为三维形式。最后根据等效应变假设,将二阶损伤张量引入流变本构方程,得到了基于西原模型的三维粘弹塑性损伤本构方程。
在VC++6.0环境下,以FLAC3D Version 2.1数值计算通用软件为开发平台,编写了上述本构模型的程序块,实现了该软件本构模型的二次开发,并阐述了二次开发程序块的运行原理。
最后,运用开发的本构模型,对双江口水电站地下洞室群开挖过程及围岩稳定性进行了粘弹塑性损伤分析,并与弹塑性计算进行了比较,从对比结果来看模型基本上是合理的。同时,根据计算结果,为地下洞室群的长期稳定性及安全性,提出了一些合理的建议。
The study on the mechanics and time-dependent feature of fractured rock mass is always an important subject of rock mechanics and engineering. Based on the theoretical method of rock damage mechanics, rock rheological mechanics and numerical calculation, this paper makes a preliminary study on the damge and rheology coupled model of fractured rock mass and its engineering application.
First, according to the structural characteristics of fractured rock mass and the geometric damage theory, we cite a second-order damage tensor to describe the deterioration of rock mass due to cracks. Taking the crack area, direction, space and density as the major influencing factors of the damage variable, we stack the damage contribution of groups of cracks on each section to describe the anisotropic damage approximatively. The Nishihara model is taken as the basic model to study the time-dependent characteristics of rock mass. And its one-dimensional constitutive equation is transformed into three-dimensional form. Eventually, by introducing the second-order damage tensor into the rheological constitutive equation on the basis of the equivalent strain hypothesis, the three-dimensional viscoelastic-plastic damage constitutive equation is deduced.
Taking FLAC3D Version2.1 as the development platform, we compile the above constitutive model on the VC++6.0 environment, and realize the secondary development of FLAC3D. The operation principles of secondary development program is also described.
In the end, the surrounding rock stability of the underground cavern group of Shuangjiangkou hydropower station is analysed by using the development program. And the results are compared with the ones obtained from the computation with elastic-plastic model. According to the comparative results, the model is basically reasonable. Meanwhile, some rational suggestions are put forward for the long-term stability and security of underground cavern group.
引文
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[2]Goodman R E,Shi G.Block theory and its application to rock engineering[M].PREN TICE-HAN INC,1985.
[3]Shi Genhua.Discontiunous deformation analysis-A new numerical model for the statics and dynamics of block systems[M].Ph D thesis,Dept of Civil Engineering,U C Berkeley,1988.
[4]Horri H,Nemat-Nasser S.Overall moduli of solids with micro cracks in rocks:Load induced anisotropy[J].J Mech and Phys Solids,1983,31:155-177.
[5]Cai Metc.A constitutive model and FEM analysis of jointed rockmasses[J].Int J Rock Mech Min Sci & Goemech Abstr,1993,Vol.30.
[6]Margolin L G.Elastic moduli of a cracked body[J].Int J Frac,1983,Vol.22.
[7]Yoshiaki Okui,Hideyuki Horii and Narioki Akiyama.A continuum theory for solids containing microdefects[J].Int J Engng Sci,1993,Vol.31,No.5.
[8]朱维申,王平.节理岩体的等效连续模型与工程应用[J].岩土工程学报,1992,Vol.14,No.2.
[9]张明焕,汤任基.裂纹与弹性夹杂的相互影响[J].应用数学和力学,1995,Vol.16,No.4.
[10]Rabotnov Y N.On the equations of state for creep[J].Progress in Applied Mechanics,1963,307-315.
[11]Janson J,Hult J.Fracture mechanics and damage mechanics,a combined approach[J].J de Mech Appl,1977,1(1),59-64.
[12]Krajcinovic D.Constitutive theories for solids with defective micro-structrue[C].Damage mechanics and continuum modeling,New York:ASCE,1985,39-56.
[13]Krajcinovic D,Sumaral D.A mecsomechanical model for brittle deformation processes:Part Ⅰ and Part Ⅱ[J].ASME J Appl Mech,1989,56:51-62.
[14]Krajcinovic D,Basista M,Sumaral D.Micromechanically inspired phenomenological damage model[J].ASME J Appl Mech,1991,58:305-310.
[15]Hult J.Effect of voids on creep rate and strength[C].Damage mechanics and continuum modeling,New York:ASCE,1985,13-24.
[16]Atkinson B K,Meredith P G.The theory of subcritical crack growth with applications to minerals and rocks[C].Fracture Mechanics of Rock.London:Academic press,1987,111-166.
[17]杨光松.损伤力学与复合材料损伤[M].北京:国防工业出版社,1995.
[18]Murakami S.Anisotropic aspects of material damage and application of continuum damage mechanics[C].Springer-Verlay Wien-New York,1987,91-134.
[19]She W,Peng L H,Yue Y G et al.Elastic damage and energy dissipation in anisotropic solid material[J].Fracture Mech,1987,33(2).
[20]Chen X F,Lu Y B,Lee H.An endochronic plastic theory with anisotropic damage[J].Fracture Mech,1989,32(4).
[21]Tzou D Y,Chen E P.Mesocrack damage induced by a macro-crack in heterogeneous materials[J].Fracture Mech,1991,39(2).
[22]Kyoya T et al.A damage mechanics theory for discontinuous rock mass[C].5th Int Conf Numer in Geomech,1985,469-480.
[23]Kyoya T et al.A damage mechanics analysis for underground excavation in jointed rock mass[C].Proc Int Syrup On Engng In Complex Rock Formations,Beijin:1985,506-513.
[24]Kawamoto T et al.Deformation and fracturing of discontinuous rock mass and damage mechanics theory[J].Int J Numer Anal Mechods Geomech,1988,12:1-30.
[25]Zhang W H,Valliappan S.Analysis of random anisotropic damage.Mechanics problems of rock mass,Part Ⅰ Proba-bilistic Simulation,Part Ⅱstatistical estimation rock Mech[J].Rock Engng,1990,23:241-259.
[26]Swoboda G,Yang Q.Damage propagation model and its application to rock engineering problems[C].Int Congress on rock mechanics proceeding,Tokyo,Japan,1995,159-163.
[27]谢和平.大理岩微观断裂的分形模型研究[J].科学通报,1989,34(5).
[28]谢和平,高峰.岩石类材料损伤演化的分形特征[J].岩石力学与工程学报,1991,10(1):1-9.
[29]谢和平,Sanderson D J,Peacock D C P.雁型断裂分形模型和能量耗散[J].岩土工程学报,1994,16(1):1-7.
[30]凌建明.节理岩体损伤力学及时效损伤特征的研究[D].上海:同济大学博 士学位论文,1992.
[31]凌建明,蒋爵光,傅永胜.非贯通裂隙岩体力学特性的损伤力学分析[J].岩石力学与工程学报,1992,11(4):373-383.
[32]叶黔元.岩石的内时损伤本构模型[C].第四届全国岩土力学数值方法与解析方法会议论文集,武汉:武汉测绘科技大学出版社,1991,85-90.
[33]卢应发,葛修润.岩石损伤本构理论[J].岩土力学,1990,11(2):67-71.
[34]吴澎,周维垣.节理岩体的损伤模型及非线性有限元分析[J].岩石力学与工程学报,1988,7(3).
[35]孙卫军,周维垣.裂隙岩体弹塑性损伤本构模型[J].岩石力学与工程学报,1990,9(2):108-119.
[36]李广平,陶振宇.真三轴条件下的岩石细观损伤力学模型[J].岩土工程学报,1995,17(1):24-31.
[37]杨延毅.节理裂隙岩体损伤-断裂力学模型及其在岩体工程中的应用[D].北京:清华大学博士学位论文,1990.
[38]李新平,朱维申.多裂隙岩体的等效弹性损伤模型及有限元分析[C].第四届全国岩土力学数值分析与解析方法讨论会论文集,武汉:武汉测绘科技大学出版社,1991,1-7.
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