饱和地基中隧道纵向地震反应的数值分析
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摘要
由于地震动存在空间变异性，长大隧道沿纵向的地震反应将有较为显著的行波效应，进行隧道纵向地震反应分析是评价其抗震性能的重要方面。而饱和地基为固液两相体，其动力反应较之单相体更为复杂。本文对饱和地基中隧道在非一致地震作用下纵向反应分析的数值方法进行了较为系统的研究，包括饱和多孔介质波动方程及反应特性的梳理、传输边界的研发、非一致地震输入的三维有限元实现、隧道-地基系统动力反应的数值模拟等。取得的主要研究成果如下：
1、对饱和土动力方程及波动传播特点进行了系统的梳理。重点讨论了流体运动方程的建立，指出两相体动力分析时土骨架和孔隙水之间的相互作用包含渗透力和惯性耦合力两项。并进一步澄清，由于惯性耦合力的存在，即使渗透系数无穷大，两类压缩波波速也不会分别等于土骨架和孔隙水单相体中的压缩波波速。
2、采用渗透系数为0时柱面波的u-p方程，推导得出了饱和两相介质无限域时域动力有限元分析的高阶弹簧-阻尼-质量传输边界。数值算例表明只要渗透系数的量级满足u-p方程的适用条件，该高阶传输边界均能给出足够精确的结果。将其直接运用于一般二维平面应变内源波动问题时，只要将传输边界布置在离散射波源稍远的位置，所得计算结果仍足以满足工程问题的精度要求。
3、通过引入精确的人工边界改进了二维平面内自由波场的一维化时域有限元算法。将一维算法得到的自由场反应扩展至三维，基于一致质量有限元平衡方程，给出了通过边界单元节点的自由场位移求取自由波场产生的等效荷载的公式。采用粘弹性边界，通过在人工边界上施加等效荷载实现波动输入。编制FORTRAN辅助程序并借助有限元软件ANSYS，实现了瞬态平面内体波斜入射至成层半空间场地的三维数值模拟，数值算例验证了其精度和有效性。
4、针对饱和地基中长大隧道纵向地震反应数值模拟开展研究。论证了按照非一致地震输入方法计算边界等效荷载，对隧道结构的截断边界不作特殊处理，只需将模型沿隧道纵向取得较长，即可得到满意的精度。研究了体波入射角、隧道刚度对纵向反应的影响，讨论了成层土基中隧道地震反应行波效应的分析方法。
5、对非一致地震作用下港珠澳沉管隧道的动力反应进行了较为系统的数值模拟，重点讨论了沉管隧道采用不同接头类型时接头处的内力及变形规律，对实际工程的抗震性能做出评价。
Due to the spatial variation of earthquake ground motion, there will be travelingwave effect along tunnels in soils. As a two phase material, the dynamic response ofsaturated soil is more complex than one phase material. Therefore, dynamic analysis oflongitudinal tunnel response is an important topic for the seismic performanceevaluation of a tunnel. In this thesis, numerical methods for the analysis of longitudinalresponse of tunnels in saturated soils under asynchronous seismic wave is extensivelystudied, including the clarification of the basic equations for wave propagation andcharacteristics in saturated porous media, development of transmitting boundary,3Dfinite element implementation for asynchronous seismic wave motion and numericalsimulation of seismic response of soil-tunnel system. The main research results are asfollows:
1. Systematically clarification of the dynamic basic formulations and wavepropagation characteristics in saturated soils was carried out with special attention paidto the establishment of pore water motion equation. It is pointed out that in dynamicanalysis of saturated soils the interaction between soil skeleton and pore water consistsof two parts: seepage force and inertial-coupling-force. It is also revealed that due to theexistence of inertial-coupling-force, the speeds of two dilatational waves are not equalrespectively to those in single-phased solid skeleton and pore water, even if thepermeability approaches to infinity.
2. A high-order accurate local time-domain transmitting boundary for simulatingthe transient scalar wave propagation in unbounded saturated porous media, based onthe u-p formulation with an assumption of zero permeability coefficient, is derived fromthe cylindrical elastic wave radiation problem. Good wave-absorbing capabilities of thishigh-order transmitting boundary are demonstrated by several types of numericalexamples. Despite the assumption made in the derivation of this transmitting boundary,results showed that it can provide sufficiently accurate results in case the u-pformulation is applicable. Although numerical results show that direct application of theproposed transmitting boundary to general two dimensional wave problems in infinitesaturated porous media is not so accurate, solutions of acceptable engineering accuracy may still be achieved by setting the transmitting boundary relatively far away from thescatter.
3. By introducing the accurate artificial boundary condition, the1D time domainfinite element method used to calculate the in-plane free field wave motion in elasticlayered half space is improved. The results obtained through1D finite element methodare extended to3D. Based on the consistent mass finite element equilibrium equations,the formula for calculating the equivalent loads generated by the free filed is given,which is expressed by nodal displacements of the element at the boundary.Viscous-spring boundary is used to absorb the scattered wave, and the input of seismicwave motion is realized by applying equivalent loads on the artificial boundary.Through compiling FORTRAN program combined with finite element softwareANSYS,3D numerical simulation of elastic layered half space site response underoblique seismic incidence of in-plane wave is achieved, and its accuracy and validity areproved by numerical examples.
4. Based on the research above, a soil-tunnel structure interaction model wasestablished and research is conducted on the numerical method for longitudinal seismicresponse analysis of tunnels in saturated soils. It is demonstrated that using theequivalent loads calculated from asynchronous seismic waves input method as the inputloads without extral treatment to the truncated boundaries on the tunnel sturcture,satisfactory accuracy can be achieved as long as the model is relatively long along thelongitudinal direction. Numerical examples are given to study the influence of theincident angle and tunnel stiffness on the longitudinal internal force. Analytical methodfor traveling wave effect on tunnels in layered soil foundation under earthquakes is alsobriefly discussed.
5. Based on the background of HK-Zhuhai-Macau immersed tunnel project, theasynchronous seismic analysis of immersed tunnel is presented. Discussion is focusedon the internal force and deformation at the joints of immersed tunnels when differenttypes of joints are adoptted. Safety of the project under seismic load is evaluated.
1、对饱和土动力方程及波动传播特点进行了系统的梳理。重点讨论了流体运动方程的建立，指出两相体动力分析时土骨架和孔隙水之间的相互作用包含渗透力和惯性耦合力两项。并进一步澄清，由于惯性耦合力的存在，即使渗透系数无穷大，两类压缩波波速也不会分别等于土骨架和孔隙水单相体中的压缩波波速。
2、采用渗透系数为0时柱面波的u-p方程，推导得出了饱和两相介质无限域时域动力有限元分析的高阶弹簧-阻尼-质量传输边界。数值算例表明只要渗透系数的量级满足u-p方程的适用条件，该高阶传输边界均能给出足够精确的结果。将其直接运用于一般二维平面应变内源波动问题时，只要将传输边界布置在离散射波源稍远的位置，所得计算结果仍足以满足工程问题的精度要求。
3、通过引入精确的人工边界改进了二维平面内自由波场的一维化时域有限元算法。将一维算法得到的自由场反应扩展至三维，基于一致质量有限元平衡方程，给出了通过边界单元节点的自由场位移求取自由波场产生的等效荷载的公式。采用粘弹性边界，通过在人工边界上施加等效荷载实现波动输入。编制FORTRAN辅助程序并借助有限元软件ANSYS，实现了瞬态平面内体波斜入射至成层半空间场地的三维数值模拟，数值算例验证了其精度和有效性。
4、针对饱和地基中长大隧道纵向地震反应数值模拟开展研究。论证了按照非一致地震输入方法计算边界等效荷载，对隧道结构的截断边界不作特殊处理，只需将模型沿隧道纵向取得较长，即可得到满意的精度。研究了体波入射角、隧道刚度对纵向反应的影响，讨论了成层土基中隧道地震反应行波效应的分析方法。
5、对非一致地震作用下港珠澳沉管隧道的动力反应进行了较为系统的数值模拟，重点讨论了沉管隧道采用不同接头类型时接头处的内力及变形规律，对实际工程的抗震性能做出评价。
Due to the spatial variation of earthquake ground motion, there will be travelingwave effect along tunnels in soils. As a two phase material, the dynamic response ofsaturated soil is more complex than one phase material. Therefore, dynamic analysis oflongitudinal tunnel response is an important topic for the seismic performanceevaluation of a tunnel. In this thesis, numerical methods for the analysis of longitudinalresponse of tunnels in saturated soils under asynchronous seismic wave is extensivelystudied, including the clarification of the basic equations for wave propagation andcharacteristics in saturated porous media, development of transmitting boundary,3Dfinite element implementation for asynchronous seismic wave motion and numericalsimulation of seismic response of soil-tunnel system. The main research results are asfollows:
1. Systematically clarification of the dynamic basic formulations and wavepropagation characteristics in saturated soils was carried out with special attention paidto the establishment of pore water motion equation. It is pointed out that in dynamicanalysis of saturated soils the interaction between soil skeleton and pore water consistsof two parts: seepage force and inertial-coupling-force. It is also revealed that due to theexistence of inertial-coupling-force, the speeds of two dilatational waves are not equalrespectively to those in single-phased solid skeleton and pore water, even if thepermeability approaches to infinity.
2. A high-order accurate local time-domain transmitting boundary for simulatingthe transient scalar wave propagation in unbounded saturated porous media, based onthe u-p formulation with an assumption of zero permeability coefficient, is derived fromthe cylindrical elastic wave radiation problem. Good wave-absorbing capabilities of thishigh-order transmitting boundary are demonstrated by several types of numericalexamples. Despite the assumption made in the derivation of this transmitting boundary,results showed that it can provide sufficiently accurate results in case the u-pformulation is applicable. Although numerical results show that direct application of theproposed transmitting boundary to general two dimensional wave problems in infinitesaturated porous media is not so accurate, solutions of acceptable engineering accuracy may still be achieved by setting the transmitting boundary relatively far away from thescatter.
3. By introducing the accurate artificial boundary condition, the1D time domainfinite element method used to calculate the in-plane free field wave motion in elasticlayered half space is improved. The results obtained through1D finite element methodare extended to3D. Based on the consistent mass finite element equilibrium equations,the formula for calculating the equivalent loads generated by the free filed is given,which is expressed by nodal displacements of the element at the boundary.Viscous-spring boundary is used to absorb the scattered wave, and the input of seismicwave motion is realized by applying equivalent loads on the artificial boundary.Through compiling FORTRAN program combined with finite element softwareANSYS,3D numerical simulation of elastic layered half space site response underoblique seismic incidence of in-plane wave is achieved, and its accuracy and validity areproved by numerical examples.
4. Based on the research above, a soil-tunnel structure interaction model wasestablished and research is conducted on the numerical method for longitudinal seismicresponse analysis of tunnels in saturated soils. It is demonstrated that using theequivalent loads calculated from asynchronous seismic waves input method as the inputloads without extral treatment to the truncated boundaries on the tunnel sturcture,satisfactory accuracy can be achieved as long as the model is relatively long along thelongitudinal direction. Numerical examples are given to study the influence of theincident angle and tunnel stiffness on the longitudinal internal force. Analytical methodfor traveling wave effect on tunnels in layered soil foundation under earthquakes is alsobriefly discussed.
5. Based on the background of HK-Zhuhai-Macau immersed tunnel project, theasynchronous seismic analysis of immersed tunnel is presented. Discussion is focusedon the internal force and deformation at the joints of immersed tunnels when differenttypes of joints are adoptted. Safety of the project under seismic load is evaluated.
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