隧道围岩与支护结构的相互作用研究
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摘要
围岩与支护结构的相互作用问题一直是隧道工程稳定性的难点问题,而围岩与支护结构接触界面的力学性质是围岩与支护结构相互作用的核心问题,接触面模拟的合理与否对接触面上的应力分布以及支护结构和围岩的受力、变形都将产生重要的影响。
目前,对于围岩与支护结构的相互作用问题,关于初期支护与二次支护(模注混凝土)间的接触面的问题研究较多,但对于新奥法锚喷支护喷射混凝土与围岩间的接触面的问题研究不多,普遍认为喷射混凝土能够与围岩形成较稳定的整体,共同工作。本文针对这一问题,以某一实际工程为背景,对隧道围岩与锚喷初期支护结构相互作用中涉及到的一些问题进行了较深入的研究。主要的研究内容和取得的成果如下：
(1)深入研究围岩与初期支护结构间接触界面的力学性质,建立接触面弹塑性分析的有限元模型,参考嵌岩桩桩端摩阻力的计算方法得出接触面切向剪应力的限值；
(2)研究围岩与初期支护结构界面间的约束程度对围岩与支护结构相互作用的影响,利用ABAQUS软件建立全约束和考虑摩擦的两种三维有限元分析模型,模拟隧道是的施工过程,得到围岩与初期支护结构在开挖过程中的位移以及应力的变化情况。比较两个模型的计算结果发现,引入接触面,通过界面间的摩擦考虑相互作用会减小支护结构的受力,增大围岩的应力和位移,使围岩与支护结构的受力更为均匀；
(3)对两种计算模型,研究锚喷支护的设计参数(包括锚杆长度、锚杆间距以及喷层厚度)的变化对围岩和支护结构应力以及位移的影响,发现一味地通过增加锚杆长度或加大喷层厚度的方法来提高对围岩的支护效果,效果不大。所以,应合理考虑锚喷支护的设计参数,提出设计的优化方案；
(4)对两种计算模型,不同埋深下的有限元分析结果比较,得到隧道围岩稳定性及衬砌受力和埋深的一般性关系；
(5)分析接触面摩擦系数的取值对围岩与锚喷支护结构相互作用的影响,发现随着摩擦系数的增加,接触面的切向应力增大,接触压力除拱底测点由于拱起效应加大而减小外,其余测点均增大。
As a tough problem in the tunneling stability, the interaction of the surrounding rock and the supporting structure considers the mechanical properties on the interface as the core issue. Reasonable simulation of the interface has great influences both on the stress distribution of the interface and also on the force and displacement of the surrounding rock and the supporting structure.
At present, as a problem of the interaction of the surrounding rock and the supporting structure, one aspect referring the interface of the initial and the secondary support has been well studied, while another aspect is ignored for a long time which refers the interface of the shotcrete and the surrounding rock during the new Austrian method. It is generally considered that the shotcrete and the surrounding rock could work as a stable integrity. Based on the background of a practical project, this paper studies further on the problem referring to the interaction of the tunnel surrounding rock and the initial support and obtains some achievements as following:
(1) Deeply studied the mechanical properties of the surrounding rock and supporting structure, established the elastic-plastic finite element model of the interface, and figured out the limit of the tangential shearing referring to the calculation method of the frictional resistance of the rock-embedded pile.
(2) The influences of the constraint degree on the interface between the surrounding rock and the initial support were researched. Two different 3D finite element models, one is constraining strictly, another is taking interface friction into account, were established using ABAQUS software to simulate the construction process and obtained the deformation and resistance of the surrounding rock and lining. It was found that the friction on the interface would decrease the resistance of the supporting structure, increase the stress and displacement of the surrounding rock, and even the stress of the surrounding rock and supporting structure up.
(3) The finite element analysis also researches on the influence of the design parameters on the stress and displacement of the surrounding rock and the supporting structure containing the length and the distance of the bolt and the thickness of the shotcrete. It shows that lengthening the bolt or thickening the shotcrete separately influent the support structure little. As a result, the design parameters should be comprehensively considered to get an optimization design.
(4) Comparing the result of the two finite element models, it was found that the relationship between the stability of the surrounding rock and the resistance of the lining and the embedded depth.
(5) After researching on the influence of the friction coefficient on the interaction of the surrounding rock and the supporting structure, it was found that, as the increasing of the friction coefficient, the tangential shearing would increase and the pressure would also increase except the bottom of the arc due to the arching effect.
目前,对于围岩与支护结构的相互作用问题,关于初期支护与二次支护(模注混凝土)间的接触面的问题研究较多,但对于新奥法锚喷支护喷射混凝土与围岩间的接触面的问题研究不多,普遍认为喷射混凝土能够与围岩形成较稳定的整体,共同工作。本文针对这一问题,以某一实际工程为背景,对隧道围岩与锚喷初期支护结构相互作用中涉及到的一些问题进行了较深入的研究。主要的研究内容和取得的成果如下：
(1)深入研究围岩与初期支护结构间接触界面的力学性质,建立接触面弹塑性分析的有限元模型,参考嵌岩桩桩端摩阻力的计算方法得出接触面切向剪应力的限值；
(2)研究围岩与初期支护结构界面间的约束程度对围岩与支护结构相互作用的影响,利用ABAQUS软件建立全约束和考虑摩擦的两种三维有限元分析模型,模拟隧道是的施工过程,得到围岩与初期支护结构在开挖过程中的位移以及应力的变化情况。比较两个模型的计算结果发现,引入接触面,通过界面间的摩擦考虑相互作用会减小支护结构的受力,增大围岩的应力和位移,使围岩与支护结构的受力更为均匀；
(3)对两种计算模型,研究锚喷支护的设计参数(包括锚杆长度、锚杆间距以及喷层厚度)的变化对围岩和支护结构应力以及位移的影响,发现一味地通过增加锚杆长度或加大喷层厚度的方法来提高对围岩的支护效果,效果不大。所以,应合理考虑锚喷支护的设计参数,提出设计的优化方案；
(4)对两种计算模型,不同埋深下的有限元分析结果比较,得到隧道围岩稳定性及衬砌受力和埋深的一般性关系；
(5)分析接触面摩擦系数的取值对围岩与锚喷支护结构相互作用的影响,发现随着摩擦系数的增加,接触面的切向应力增大,接触压力除拱底测点由于拱起效应加大而减小外,其余测点均增大。
As a tough problem in the tunneling stability, the interaction of the surrounding rock and the supporting structure considers the mechanical properties on the interface as the core issue. Reasonable simulation of the interface has great influences both on the stress distribution of the interface and also on the force and displacement of the surrounding rock and the supporting structure.
At present, as a problem of the interaction of the surrounding rock and the supporting structure, one aspect referring the interface of the initial and the secondary support has been well studied, while another aspect is ignored for a long time which refers the interface of the shotcrete and the surrounding rock during the new Austrian method. It is generally considered that the shotcrete and the surrounding rock could work as a stable integrity. Based on the background of a practical project, this paper studies further on the problem referring to the interaction of the tunnel surrounding rock and the initial support and obtains some achievements as following:
(1) Deeply studied the mechanical properties of the surrounding rock and supporting structure, established the elastic-plastic finite element model of the interface, and figured out the limit of the tangential shearing referring to the calculation method of the frictional resistance of the rock-embedded pile.
(2) The influences of the constraint degree on the interface between the surrounding rock and the initial support were researched. Two different 3D finite element models, one is constraining strictly, another is taking interface friction into account, were established using ABAQUS software to simulate the construction process and obtained the deformation and resistance of the surrounding rock and lining. It was found that the friction on the interface would decrease the resistance of the supporting structure, increase the stress and displacement of the surrounding rock, and even the stress of the surrounding rock and supporting structure up.
(3) The finite element analysis also researches on the influence of the design parameters on the stress and displacement of the surrounding rock and the supporting structure containing the length and the distance of the bolt and the thickness of the shotcrete. It shows that lengthening the bolt or thickening the shotcrete separately influent the support structure little. As a result, the design parameters should be comprehensively considered to get an optimization design.
(4) Comparing the result of the two finite element models, it was found that the relationship between the stability of the surrounding rock and the resistance of the lining and the embedded depth.
(5) After researching on the influence of the friction coefficient on the interaction of the surrounding rock and the supporting structure, it was found that, as the increasing of the friction coefficient, the tangential shearing would increase and the pressure would also increase except the bottom of the arc due to the arching effect.
引文
[1]陈秋南,张永兴.隧道工程[M].北京：机械工业出版社,2007
[2]王建宇.地下工程锚喷支护原理和设计[M].北京：中国铁道出版社,1980
[3]山地宏志,樱井春辅.隧道结构优化应变控制法[J].土木学会论文集,1982,317：93-100
[4]于学馥,轴变论与围岩变形破坏的基本规律[J].铀矿冶,1982,01：22-28
[5]陆家梁.软岩巷道支护技术[M].长春：吉林科学技术出版社,1995
[6]何满潮,孙晓明.中国煤矿软岩巷道工程支护设计与施工指南[M].北京：科学出版社,2004
[9]李春林.都汶公路龙溪隧道支护结构力学行为研究[D].成都理工大学硕士学位论文,2008
[7]徐干成,白洪才,郑颖人,刘朝.地下工程支护结构[M].北京：中国水利水电出版社,2002
[8]李志业,曾艳华.地下结构设计原理[M].成都：西南交通大学出版社,2003
[10]宋丽霞,陶平强.隧道围岩稳定性数值模拟研究现状与发展方向[J].矿业快报,2007,6(6)：16-20
[11]徐军,郑颖人.隧道围岩弹塑性随机有限元分析及可靠度计算[J].岩土力学,2003,24(1)：70-74
[12]张华兵,倪玉山,赵学勐.黄土隧道围岩稳定性粘弹塑性有限元分析[J].岩土力学,2004(增刊)：247-250
[13]胡文清,郑颖人,钟昌云.木寨岭隧道软弱围岩段施工方法及数值分析[J].地下空间,2004,24(2)：194-197
[14]师金锋,张应龙.超大断面隧道围岩的稳定性分析[J].地下空间与工程学报,2005,1(2)：227-241
[15]刘刚,宋宏伟.围岩松动圈影响因素的数值模拟[J].矿冶工程,2003,1：1-3
[16]李德海,王东攀,高保彬.围岩粘弹性模型有限元模拟分析[J].矿冶工程,2005,1：1-8
[17]Kim K, Yao C Y. Effect of micromechanical property variation on fracture processes in simple tension [A]. In:Daemon Sed. Rock Mechanics [C]. Rotterdam:A.A. Balkema,1995,471-476
[18]Fairhurst C. Geomaterials and recent development in micromechanical numerical
models [J]. News Journal,1997,4(2):11-14
[19]Schalagen E, van Mier J GM. Simple lattice model for numerical simulation of fracture of concrete materials and structures [J]. Materials and Structures,1992, 25:534-542
[20]P.Kumar. In finite Elements for Numerical Analysis of Underground Excavations [J]. Tunnelling and Underground Technology,2000,15(1):117-124
[21]朱合华,陈清军,杨林德.边界元法及其在岩土工程中的应用[M].上海：同济大学出版社,1997
[22]K. J. Shou. A Three-Dimensional Hybrid Boundary Element Method for Non-Linear Analysis of a Weak Plane Near an Underground Excavation [J]. Tunnelling and Underground S pace Technology,2000,15(2):215-226
[23]王志亮,李筱艳.某隧道工程的参数反演及围岩稳定边界元分析[J].岩土工程技术,2001,3：176-179
[24]徐干成.粘弹性边界元法预测锚喷支护隧道围岩稳定性[J].岩土力学,2001,22(1)：12·15
[25]Cundall P A. A computer model for simulating progressive large scale movements in blocky systems [A]. Proceedings of the Symposium of the International Society of Rock Mechanics [C]. Nancy, France,1971,12-8
[26]Wang G Numerische Untersuchungen Zum Bruchund Verformung sverhalten Von Gekltlfteten Gebirgsbreichen Beim Tunnelbau [M].[S.l.]:Veroffentlichungen des Institutsur Geotechnik der Technischen Universitat Bergakademie Freiberg, Heft, 2001
[27]Hart R, Cundall P A, Lcmos J Formulations of three-dimensional distinct element model PARTII:Mechanical calculation of a system composed of many polyhedral blocks. International Journal of Rock Mechanics and Mining Sciences,1988 (3)
[28]王涛,陈晓玲,杨建.基于3DGIS和3DEC的地下洞室围岩稳定性研究[J].岩石力学与工程学报,2005,24(19)：3476-3481
[29]王贵君.节理裂隙岩体中不同埋深无支护暗挖隧洞稳定性的离散元法数值分析[J].岩石力学与工程学报,2004,23(7)：1154-1157
[30]Charles Fairhurst, Juemin Pei. A Comparison Between the Distinct Element Method and the Finite Element Method for Analysis of the Stability of an Excavation in Jointed Rock [J]. Tunnelling and Underground Space Technology, 1990,5(1):111-117
[31]胡夏嵩,赵法锁.低地应力区地下洞室初始和二次应力离散元模拟[J].金属矿 山,2004,11：18-21
[32]高谦,乔兰,吴顺川,杨素贞.地下工程系统分析与设计[M].北京：中国建材工业出版社,2005
[33]梁旭黎,李冬霞,李源.隧道围岩与支护结构相互作用的弹塑性分析[J].山西建筑,2008,34(6)：22-30
[34]张明聚,张文字,杜修力.近接桥桩暗挖隧道支护结构内力监测分析[J].北京工业大学学报,2008,34(8)：830-835
[35]Goodman R F, Taylor R L, Brekke T L. A model for themechanics of jointed rock [J]. Journal of Soil Mechanicsand Foundation Engineering Division, ASCE,1968, 94(3):637-660
[36]Clough G W, Duncan J M. Finite Element Analysis of Retaining Wall Behavior [J]. Joural of Soil Mechanics and Foundations Division, ASCE,1971,97(SM12): 1657-1674
[37]陈慧远.摩擦接触单元及其分析方法[J].水利学报,1985(4)：44-50
[38]Boulon M, Nova R. Modeling of Soil Structure Interface Behavior:A Comparison Between Elasto-Plastic and Rate-Type Laws[J]. Computers and Geotechnics, 1990(9):21-46
[39]殷宗泽,朱泓,许国华.土与结构材料接触面的变形及其数学模拟[J].岩土工程学报,1994,16(3)：14-22
[40]卢廷浩,鲍伏波.接触面薄层单元耦合本构模型[J].水利学报,2000(2)：71-75
[41]安关锋,高大钊.接触面弹粘塑性本构关系研究[J].土木工程学报,2001,34(1)：88-91
[42]栾茂田,武亚军.土与结构间接触面的非线性弹性-理想塑性模型及其应用[J].岩土力学,2004,25(4)：507-513
[43]张嘎,张建民.粗粒土与结构接触面受载过程中的损伤[J].力学学报,2004,36(3)：322-327
[44]彭丽敏,刘小兵.隧道工程[M].湖南：中南大学出版社,2009
[45]麦倜曾,张玉军.锚固岩体力学性质的研究[J].工程力学,1987,4(1)：106-116
[46]李晓红.隧道新奥法及其量测技术[M].北京：科学出版社,2002
[47]孟丽娟.围岩与衬砌的相互作用[D].华北水利水电学院,2005
[48]陈玉祥,王霞,刘少伟.锚杆支护理论现状及发展趋势探讨[J].西部探矿工程,2004,16(10)：11-16
[49]董方庭,宋宏伟.巷道围岩松动圈支护理论.煤炭学报,1994,2：21-31
[50]曹金凤,石亦平.ABAQUS有限元分析常见问题解答[M].北京：机械工业出版 社,2009
[51]ABAQUS Analysis User's Manual (v6.9-1)
[52]卢廷浩,刘祖德.高等土力学[M].北京：机械工业出版社,2006
[53]过镇海,张秀琴.单调荷载下的混凝土应力-应变曲线实验研究[J].建筑结构学报,1982,3(1)：1-12
[54]过镇海,时旭东.钢筋混凝土原理和分析[M].北京：清华大学出版社,2003
[55]李淑春,刁波,叶英华.反复荷载作用下的混凝土损伤本构模型[J].铁道科学与工程学报,2006,3(4)：21-28
[56]过镇海,王传志.多轴应力下混凝土的强度和破坏准则研究[J].土木工程学报,1991,24(3)：1-14
[57]中国建筑科学院主编.GB50010-2001混凝土结构设计规范[S].北京：中国建筑工业出版社,2002
[58]赵腾伦.ABAQUS6.6在机械工程中的应用[M].北京：中国水利水电出版社,2007
[59]李学文,陈万吉.三维接触问题的非光滑算法[J].计算力学,2000,1：43-49
[60]黄琛,陈志远.用罚函数法处理三维变厚度节理元嵌入接触问题[J].汕头大学学报(自然科学版),2002,17(4)：17-23
[61]JGJ94-94建筑桩基技术规范[S].北京：中国建筑科学研究院,1995
[62]乔伟.地下工程围岩与支护结构相互作用接触机理研究[D].西安科技大学,2007
[63]中华人民共和国水利部、建设部主编.GB50218-94工程岩体分级标准[S].北京：中国建筑工业出版社,1995
[2]王建宇.地下工程锚喷支护原理和设计[M].北京：中国铁道出版社,1980
[3]山地宏志,樱井春辅.隧道结构优化应变控制法[J].土木学会论文集,1982,317：93-100
[4]于学馥,轴变论与围岩变形破坏的基本规律[J].铀矿冶,1982,01：22-28
[5]陆家梁.软岩巷道支护技术[M].长春：吉林科学技术出版社,1995
[6]何满潮,孙晓明.中国煤矿软岩巷道工程支护设计与施工指南[M].北京：科学出版社,2004
[9]李春林.都汶公路龙溪隧道支护结构力学行为研究[D].成都理工大学硕士学位论文,2008
[7]徐干成,白洪才,郑颖人,刘朝.地下工程支护结构[M].北京：中国水利水电出版社,2002
[8]李志业,曾艳华.地下结构设计原理[M].成都：西南交通大学出版社,2003
[10]宋丽霞,陶平强.隧道围岩稳定性数值模拟研究现状与发展方向[J].矿业快报,2007,6(6)：16-20
[11]徐军,郑颖人.隧道围岩弹塑性随机有限元分析及可靠度计算[J].岩土力学,2003,24(1)：70-74
[12]张华兵,倪玉山,赵学勐.黄土隧道围岩稳定性粘弹塑性有限元分析[J].岩土力学,2004(增刊)：247-250
[13]胡文清,郑颖人,钟昌云.木寨岭隧道软弱围岩段施工方法及数值分析[J].地下空间,2004,24(2)：194-197
[14]师金锋,张应龙.超大断面隧道围岩的稳定性分析[J].地下空间与工程学报,2005,1(2)：227-241
[15]刘刚,宋宏伟.围岩松动圈影响因素的数值模拟[J].矿冶工程,2003,1：1-3
[16]李德海,王东攀,高保彬.围岩粘弹性模型有限元模拟分析[J].矿冶工程,2005,1：1-8
[17]Kim K, Yao C Y. Effect of micromechanical property variation on fracture processes in simple tension [A]. In:Daemon Sed. Rock Mechanics [C]. Rotterdam:A.A. Balkema,1995,471-476
[18]Fairhurst C. Geomaterials and recent development in micromechanical numerical
models [J]. News Journal,1997,4(2):11-14
[19]Schalagen E, van Mier J GM. Simple lattice model for numerical simulation of fracture of concrete materials and structures [J]. Materials and Structures,1992, 25:534-542
[20]P.Kumar. In finite Elements for Numerical Analysis of Underground Excavations [J]. Tunnelling and Underground Technology,2000,15(1):117-124
[21]朱合华,陈清军,杨林德.边界元法及其在岩土工程中的应用[M].上海：同济大学出版社,1997
[22]K. J. Shou. A Three-Dimensional Hybrid Boundary Element Method for Non-Linear Analysis of a Weak Plane Near an Underground Excavation [J]. Tunnelling and Underground S pace Technology,2000,15(2):215-226
[23]王志亮,李筱艳.某隧道工程的参数反演及围岩稳定边界元分析[J].岩土工程技术,2001,3：176-179
[24]徐干成.粘弹性边界元法预测锚喷支护隧道围岩稳定性[J].岩土力学,2001,22(1)：12·15
[25]Cundall P A. A computer model for simulating progressive large scale movements in blocky systems [A]. Proceedings of the Symposium of the International Society of Rock Mechanics [C]. Nancy, France,1971,12-8
[26]Wang G Numerische Untersuchungen Zum Bruchund Verformung sverhalten Von Gekltlfteten Gebirgsbreichen Beim Tunnelbau [M].[S.l.]:Veroffentlichungen des Institutsur Geotechnik der Technischen Universitat Bergakademie Freiberg, Heft, 2001
[27]Hart R, Cundall P A, Lcmos J Formulations of three-dimensional distinct element model PARTII:Mechanical calculation of a system composed of many polyhedral blocks. International Journal of Rock Mechanics and Mining Sciences,1988 (3)
[28]王涛,陈晓玲,杨建.基于3DGIS和3DEC的地下洞室围岩稳定性研究[J].岩石力学与工程学报,2005,24(19)：3476-3481
[29]王贵君.节理裂隙岩体中不同埋深无支护暗挖隧洞稳定性的离散元法数值分析[J].岩石力学与工程学报,2004,23(7)：1154-1157
[30]Charles Fairhurst, Juemin Pei. A Comparison Between the Distinct Element Method and the Finite Element Method for Analysis of the Stability of an Excavation in Jointed Rock [J]. Tunnelling and Underground Space Technology, 1990,5(1):111-117
[31]胡夏嵩,赵法锁.低地应力区地下洞室初始和二次应力离散元模拟[J].金属矿 山,2004,11：18-21
[32]高谦,乔兰,吴顺川,杨素贞.地下工程系统分析与设计[M].北京：中国建材工业出版社,2005
[33]梁旭黎,李冬霞,李源.隧道围岩与支护结构相互作用的弹塑性分析[J].山西建筑,2008,34(6)：22-30
[34]张明聚,张文字,杜修力.近接桥桩暗挖隧道支护结构内力监测分析[J].北京工业大学学报,2008,34(8)：830-835
[35]Goodman R F, Taylor R L, Brekke T L. A model for themechanics of jointed rock [J]. Journal of Soil Mechanicsand Foundation Engineering Division, ASCE,1968, 94(3):637-660
[36]Clough G W, Duncan J M. Finite Element Analysis of Retaining Wall Behavior [J]. Joural of Soil Mechanics and Foundations Division, ASCE,1971,97(SM12): 1657-1674
[37]陈慧远.摩擦接触单元及其分析方法[J].水利学报,1985(4)：44-50
[38]Boulon M, Nova R. Modeling of Soil Structure Interface Behavior:A Comparison Between Elasto-Plastic and Rate-Type Laws[J]. Computers and Geotechnics, 1990(9):21-46
[39]殷宗泽,朱泓,许国华.土与结构材料接触面的变形及其数学模拟[J].岩土工程学报,1994,16(3)：14-22
[40]卢廷浩,鲍伏波.接触面薄层单元耦合本构模型[J].水利学报,2000(2)：71-75
[41]安关锋,高大钊.接触面弹粘塑性本构关系研究[J].土木工程学报,2001,34(1)：88-91
[42]栾茂田,武亚军.土与结构间接触面的非线性弹性-理想塑性模型及其应用[J].岩土力学,2004,25(4)：507-513
[43]张嘎,张建民.粗粒土与结构接触面受载过程中的损伤[J].力学学报,2004,36(3)：322-327
[44]彭丽敏,刘小兵.隧道工程[M].湖南：中南大学出版社,2009
[45]麦倜曾,张玉军.锚固岩体力学性质的研究[J].工程力学,1987,4(1)：106-116
[46]李晓红.隧道新奥法及其量测技术[M].北京：科学出版社,2002
[47]孟丽娟.围岩与衬砌的相互作用[D].华北水利水电学院,2005
[48]陈玉祥,王霞,刘少伟.锚杆支护理论现状及发展趋势探讨[J].西部探矿工程,2004,16(10)：11-16
[49]董方庭,宋宏伟.巷道围岩松动圈支护理论.煤炭学报,1994,2：21-31
[50]曹金凤,石亦平.ABAQUS有限元分析常见问题解答[M].北京：机械工业出版 社,2009
[51]ABAQUS Analysis User's Manual (v6.9-1)
[52]卢廷浩,刘祖德.高等土力学[M].北京：机械工业出版社,2006
[53]过镇海,张秀琴.单调荷载下的混凝土应力-应变曲线实验研究[J].建筑结构学报,1982,3(1)：1-12
[54]过镇海,时旭东.钢筋混凝土原理和分析[M].北京：清华大学出版社,2003
[55]李淑春,刁波,叶英华.反复荷载作用下的混凝土损伤本构模型[J].铁道科学与工程学报,2006,3(4)：21-28
[56]过镇海,王传志.多轴应力下混凝土的强度和破坏准则研究[J].土木工程学报,1991,24(3)：1-14
[57]中国建筑科学院主编.GB50010-2001混凝土结构设计规范[S].北京：中国建筑工业出版社,2002
[58]赵腾伦.ABAQUS6.6在机械工程中的应用[M].北京：中国水利水电出版社,2007
[59]李学文,陈万吉.三维接触问题的非光滑算法[J].计算力学,2000,1：43-49
[60]黄琛,陈志远.用罚函数法处理三维变厚度节理元嵌入接触问题[J].汕头大学学报(自然科学版),2002,17(4)：17-23
[61]JGJ94-94建筑桩基技术规范[S].北京：中国建筑科学研究院,1995
[62]乔伟.地下工程围岩与支护结构相互作用接触机理研究[D].西安科技大学,2007
[63]中华人民共和国水利部、建设部主编.GB50218-94工程岩体分级标准[S].北京：中国建筑工业出版社,1995