隧道初期支护力学分析及参数优化研究
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摘要
初期支护作为隧道工程中最为关键的结构和极为重要的承载单元，对其力学模型的研究长期以来一直是隧道及地下工程界的热点问题。但是，初期支护的工程应用远远超前于理论研究，目前对初期支护的力学问题的研究依然没有完全清晰，在很大程度上仍需进行更深入的理论探讨，同时在隧道工程实践中依然存在潜在风险隐患或过度浪费的现象。因此论文以长江学者和创新团队发展计划资助（IRT1045）和重庆市寸滩隧道工程为依托，采用资料收集整理、理论分析、现场监测与测试以及数值模拟等方法，系统地研究了隧道初期支护结构的受力问题以及应用研究。论文的主要工作如下：
①根据锚固界面层传递界面剪应力的机理，考虑锚杆与围岩间锚固接触界面上变形协调关系，建立了全长锚杆界面剪应力的受力模型，然后将锚杆界面剪应力以体积力的形式引入圆形隧道围岩弹塑性分析中，进而可探讨锚杆支护系统中锚杆受力状态和锚固层界面力学特征以及分析隧道弹塑性围岩介质中的岩体稳定性和支护结构受力机制等问题；并分析了支护时间和锚固层参数对应力分布规律的影响。并结合现场监测锚杆轴力对所提出的锚杆力学模型计算结果进行对比与验证。
②通过对隧道喷射混凝土衬砌的支护机理进行研究，探讨了喷射混凝土的支护作用，并根据隧道工程中喷射混凝土的力学特性，由“围岩—喷层支护”共同体的相互作用特点，并考虑喷层与围岩接触界面上变形协调关系，运用复合曲梁理论建立了喷层与围岩结构的复合承载体的力学模型，可分析喷射砼与围岩界面力的影响，进而探讨喷层结构的力学特征和隧道围岩的稳定性。
③根据喷层受到来自围岩的形变压力，将喷射混凝土层视为弹性地基曲梁，将初期支护中喷层结构按弹性地基曲梁进行计算分析，并以量测的围岩与喷层间的接触应力作为边界条件，来推求喷层结构内力的解析解，可研究隧道实际情况下的喷层结构的应力集中部位。
④通过分析软弱破碎围岩段隧道施工现场钢拱架与喷射混凝土联合支护的特点和受力特性，建立含有钢拱架和喷射砼的隧道复合初期支护的地基曲梁力学模型，然后运用地基曲梁相关理论，以现场监测获取的钢拱架应力值为基本参数来推求出隧道复合初期支护内力解析式，从而可迅速分析软弱破碎围岩段隧道支护力学性能。
⑤对软弱破碎围岩段初期支护中锚杆、喷射混凝土和钢拱架联合支护展开分析，根据围岩与支护相互作用特点，研究多种形式的联合支护作用下形成围岩组合拱的承载体力学模型。从围岩—联合支护断面的几何形状上，将系统锚杆形成围岩拱视为支护外拱，喷层与钢拱架则构成支护内层拱，然后将二者间的组合拱应力进行叠加，能够分析考虑锚、喷、钢架联合支护条件下的围岩变形和联合支护结构承载能力的关系，达到分析“锚喷网+钢拱架”联合支护与围岩相互作用以及承载力的目的。并将上述理论应用于工程实践并且结合数值模拟进行分析。
Initial support would be used as an important construction of tunnel.Themechanical analysis of initial support is one of key problems for tunnel andunderground engeering for long time. However, the engineering application of is farahead of theoretical research of initial support in tunnel. It is not completely clear for thesupporting mechanics, and exit many faults. The paper takes tunnel and undergroundengineering as studying background, to study the mechanics of tunnel initial supportfrom different aspects and different viewpoints, for obtaining the deeply levelsupporting mechanics, and providing theory proofs for tunnel design. Combined withSupported by Program for Changjiang Scholars and Innovative Research Team inUniversity (IRT1045), took Cuntan tunnel in Chongqing as an engineering example, onthe basis of previous research, the mechanical characteristics and action mechanism oftunnel initial support is systemic and thoroughly researched by theory analysis,numerical simulation and in-situ test. The main works and achievement of thesis can bedrawn as follows:
①The bolt’s axial displacement differential equation is established according tothe stress equilibrium in a small section of a rock bolt and the sheart stress transfermechanism of anchorage body interfacial layer between rock bolt and surroundingrock.Then the axial load distribution function and the shear stress distribution functionon the interface of the fully grouted bolt are obtained by solving the differentialequation under the interaction between rock bolt and surrounding rock mass.Thereaction of the shear stress on interface of the fully grouted bolt on the surrounding rockis assumed to be symmetric radial action. The plastic zone radius of circular tunnel forbolt-shotcrete support can be solved by means of Mohr-Coulomb yield condition.On thebasis of the model and function above, the mechanical effect of system for surroundingrock and initial support is analyzed. The selection of supporting time has great influenceon anchoring effect and surrounding rock stability; It is suggested that increasing thethickness of the grout layer properly can decrease efficiently shear stress concentrationat bolt end and also can improve the reinforcement effect of fully grouted rock bolt.
②According to the characteristics of interfacial stess between surrounding rockand shotcrete support,the article established mechanical model of composite curvedbeame for support system of tunnel surrounding rock and shotcrete lining, which considering the interfacial deformation coordination and the effects of bearing arch ofsurrounding rock. Then from static equilibrium of two differential elements, thedifferential equation for the radial displacement of composite curved beam are derivedout. All analytical formulas of both interfacial stress and internal forces betweensurrounding rock and shotcrete lining by arbitary distribution load are derived.And thusthe mechanical condition of interface zone and the stress concentration position areobtained,which is convenient to guideline for assessment of stability of surroundingrock and and prediction of safety. Finally，the analysis of tunnel project excavated bybenth method shows that shotcrete lining made the formation of compressive stresszone in surrounding rock by transferring stress from the interface between surroundingrock and shotcrete,which is beneficial to improve the stability of surrounding rock.
③According to the characteristics of shotcrete layer in initial support and thetheory of circular beam on elastic foundation,based on touch stresses between shotcretelayer and surrounding rock,the analytical solution of internal force is deduced.The stressconcentration position is obtained,which is convenient to make relative safetycountermeasures in the following construction.The analysis of tunnel project excavatedby bench method shows that the analytical expression of solving internal force based ontouch stresses is a new and effective way,so as to provide a more reliable basis for thesafety assessment of tunnel structures.
④Prompt analysis of the internal force of tunnel lining in weak-brokensurrounding rocks is one of key problems for tunnel construction,useful foridentification of construction safety state and evaluation of stability of the supportsystem.Steel arch support would be used as an important primary support of tunnelwhen the surrounding rock is weak and broken.According to its characteristics andmechanical properties in-situ,a mechanical model of steel arch and shotcrete isestablished.Analytical solutions of the internal force of the composite support arededuced based on the theory of circular beam on elastic foundation and steel archstresses measurement.As a result,stress concentrated parts of tunnel lining can bequickly identified.An example of a tunnel excavated by using the bench method verifiedthe method.
⑤The combined support method of rock bolt and shotcrete mesh and steel arch ininitial support of tunnel is widely used soft and broken surrounding rock，but it is verydeficient in understanding on bearing behavior of the combined supporting structure；and it still lacks quantitative analytical formulae especially for bearing capacities of primary supporting and secondary supporting.In allusion to the united supportingcharacteristics of rockbolt，shotcrete layer and steel sets of wall rock，the mechanicalmodel of overlap arch bearing body were put forward based on rock mechanics theory，which are composed with the outer compression arch(bolt supporting)and the innercompression arch(shotcrete and steel arch supporting).By means of elastoplastic theory，formulas of the bearing body of combined support were deduced.Then following theNATM prinsiple to transfer fully the ability of surrounding rock so that the deformationpressure is minimum on the combined support. Through the medium of establishing therelation between support displacement and structure stiffness,by means of optimizationmethod,to adjust support stiffness, finally gives reasonable supporting parameters.
①根据锚固界面层传递界面剪应力的机理，考虑锚杆与围岩间锚固接触界面上变形协调关系，建立了全长锚杆界面剪应力的受力模型，然后将锚杆界面剪应力以体积力的形式引入圆形隧道围岩弹塑性分析中，进而可探讨锚杆支护系统中锚杆受力状态和锚固层界面力学特征以及分析隧道弹塑性围岩介质中的岩体稳定性和支护结构受力机制等问题；并分析了支护时间和锚固层参数对应力分布规律的影响。并结合现场监测锚杆轴力对所提出的锚杆力学模型计算结果进行对比与验证。
②通过对隧道喷射混凝土衬砌的支护机理进行研究，探讨了喷射混凝土的支护作用，并根据隧道工程中喷射混凝土的力学特性，由“围岩—喷层支护”共同体的相互作用特点，并考虑喷层与围岩接触界面上变形协调关系，运用复合曲梁理论建立了喷层与围岩结构的复合承载体的力学模型，可分析喷射砼与围岩界面力的影响，进而探讨喷层结构的力学特征和隧道围岩的稳定性。
③根据喷层受到来自围岩的形变压力，将喷射混凝土层视为弹性地基曲梁，将初期支护中喷层结构按弹性地基曲梁进行计算分析，并以量测的围岩与喷层间的接触应力作为边界条件，来推求喷层结构内力的解析解，可研究隧道实际情况下的喷层结构的应力集中部位。
④通过分析软弱破碎围岩段隧道施工现场钢拱架与喷射混凝土联合支护的特点和受力特性，建立含有钢拱架和喷射砼的隧道复合初期支护的地基曲梁力学模型，然后运用地基曲梁相关理论，以现场监测获取的钢拱架应力值为基本参数来推求出隧道复合初期支护内力解析式，从而可迅速分析软弱破碎围岩段隧道支护力学性能。
⑤对软弱破碎围岩段初期支护中锚杆、喷射混凝土和钢拱架联合支护展开分析，根据围岩与支护相互作用特点，研究多种形式的联合支护作用下形成围岩组合拱的承载体力学模型。从围岩—联合支护断面的几何形状上，将系统锚杆形成围岩拱视为支护外拱，喷层与钢拱架则构成支护内层拱，然后将二者间的组合拱应力进行叠加，能够分析考虑锚、喷、钢架联合支护条件下的围岩变形和联合支护结构承载能力的关系，达到分析“锚喷网+钢拱架”联合支护与围岩相互作用以及承载力的目的。并将上述理论应用于工程实践并且结合数值模拟进行分析。
Initial support would be used as an important construction of tunnel.Themechanical analysis of initial support is one of key problems for tunnel andunderground engeering for long time. However, the engineering application of is farahead of theoretical research of initial support in tunnel. It is not completely clear for thesupporting mechanics, and exit many faults. The paper takes tunnel and undergroundengineering as studying background, to study the mechanics of tunnel initial supportfrom different aspects and different viewpoints, for obtaining the deeply levelsupporting mechanics, and providing theory proofs for tunnel design. Combined withSupported by Program for Changjiang Scholars and Innovative Research Team inUniversity (IRT1045), took Cuntan tunnel in Chongqing as an engineering example, onthe basis of previous research, the mechanical characteristics and action mechanism oftunnel initial support is systemic and thoroughly researched by theory analysis,numerical simulation and in-situ test. The main works and achievement of thesis can bedrawn as follows:
①The bolt’s axial displacement differential equation is established according tothe stress equilibrium in a small section of a rock bolt and the sheart stress transfermechanism of anchorage body interfacial layer between rock bolt and surroundingrock.Then the axial load distribution function and the shear stress distribution functionon the interface of the fully grouted bolt are obtained by solving the differentialequation under the interaction between rock bolt and surrounding rock mass.Thereaction of the shear stress on interface of the fully grouted bolt on the surrounding rockis assumed to be symmetric radial action. The plastic zone radius of circular tunnel forbolt-shotcrete support can be solved by means of Mohr-Coulomb yield condition.On thebasis of the model and function above, the mechanical effect of system for surroundingrock and initial support is analyzed. The selection of supporting time has great influenceon anchoring effect and surrounding rock stability; It is suggested that increasing thethickness of the grout layer properly can decrease efficiently shear stress concentrationat bolt end and also can improve the reinforcement effect of fully grouted rock bolt.
②According to the characteristics of interfacial stess between surrounding rockand shotcrete support,the article established mechanical model of composite curvedbeame for support system of tunnel surrounding rock and shotcrete lining, which considering the interfacial deformation coordination and the effects of bearing arch ofsurrounding rock. Then from static equilibrium of two differential elements, thedifferential equation for the radial displacement of composite curved beam are derivedout. All analytical formulas of both interfacial stress and internal forces betweensurrounding rock and shotcrete lining by arbitary distribution load are derived.And thusthe mechanical condition of interface zone and the stress concentration position areobtained,which is convenient to guideline for assessment of stability of surroundingrock and and prediction of safety. Finally，the analysis of tunnel project excavated bybenth method shows that shotcrete lining made the formation of compressive stresszone in surrounding rock by transferring stress from the interface between surroundingrock and shotcrete,which is beneficial to improve the stability of surrounding rock.
③According to the characteristics of shotcrete layer in initial support and thetheory of circular beam on elastic foundation,based on touch stresses between shotcretelayer and surrounding rock,the analytical solution of internal force is deduced.The stressconcentration position is obtained,which is convenient to make relative safetycountermeasures in the following construction.The analysis of tunnel project excavatedby bench method shows that the analytical expression of solving internal force based ontouch stresses is a new and effective way,so as to provide a more reliable basis for thesafety assessment of tunnel structures.
④Prompt analysis of the internal force of tunnel lining in weak-brokensurrounding rocks is one of key problems for tunnel construction,useful foridentification of construction safety state and evaluation of stability of the supportsystem.Steel arch support would be used as an important primary support of tunnelwhen the surrounding rock is weak and broken.According to its characteristics andmechanical properties in-situ,a mechanical model of steel arch and shotcrete isestablished.Analytical solutions of the internal force of the composite support arededuced based on the theory of circular beam on elastic foundation and steel archstresses measurement.As a result,stress concentrated parts of tunnel lining can bequickly identified.An example of a tunnel excavated by using the bench method verifiedthe method.
⑤The combined support method of rock bolt and shotcrete mesh and steel arch ininitial support of tunnel is widely used soft and broken surrounding rock，but it is verydeficient in understanding on bearing behavior of the combined supporting structure；and it still lacks quantitative analytical formulae especially for bearing capacities of primary supporting and secondary supporting.In allusion to the united supportingcharacteristics of rockbolt，shotcrete layer and steel sets of wall rock，the mechanicalmodel of overlap arch bearing body were put forward based on rock mechanics theory，which are composed with the outer compression arch(bolt supporting)and the innercompression arch(shotcrete and steel arch supporting).By means of elastoplastic theory，formulas of the bearing body of combined support were deduced.Then following theNATM prinsiple to transfer fully the ability of surrounding rock so that the deformationpressure is minimum on the combined support. Through the medium of establishing therelation between support displacement and structure stiffness,by means of optimizationmethod,to adjust support stiffness, finally gives reasonable supporting parameters.
引文
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