非一致地震激励下长隧道多尺度动力分析方法

Long tunnels are susceptible to receive irrecoverable damage in recent earthquakes, and non-uniform seismic excitation has great effect on seismic response of long tunnels. However, current traditional methods cannot be used to truly reflect non-uniform seismic response of long tunnels, and research on actually existing multi-scale dynamics is less concerned and still challenged. In this proposal, multi-scale dynamic analysis method for long tunnels subjected to non-uniform seismic excitation is studied in detail. Both the theoretical and numerical techniques are used to facilitate the research, which covering and mixing together with different subjects including tunnel dynamics, earthquake engineering, and multi-scale science. Research contents are listed as: multi-scale modeling method for long tunnels is constructed based on concurrent multi-scale theories, and non-uniform seismic effect is considered to establish an effective discretization method for the multi-scale model; constrained relations are built up to connect different multi-scale subdomains, and the corresponding multi-scale dynamic equations are derived; mixed time step algorithm is proposed to solve the dynamic equations under non-uniform seismic excitation, and the corresponding stability condition and convergence criterion are also deduced with consideration of material nonlinearity; and dynamic damage constitutive model for concrete is presented based on damage theory, which is used to perform multi-scale dynamic analysis of a long tunnel subjected to non-uniform seismic loading. Further accomplishment will be of great benefit to seismic analysis theories and methods of tunnels, and provide instructions for seismic calculation and analysis of long tunnels.

近年长隧道结构震害频发，考虑地震动空间非一致性对长隧道地震响应具有较大影响，但传统方法难以真实反映长隧道的非一致地震响应，对实际存在的多尺度动力问题缺乏研究。本项目以长隧道结构为研究对象，交叉融合隧道动力学、地震工程学及多尺度科学等学科，采用理论分析和数值模拟相结合的研究方法，系统研究非一致地震激励下长隧道多尺度动力分析方法。开展基于并发多尺度原理构造结构多尺度建模方法，提出考虑地震动非一致性的长隧道多尺度模型的有效离散化方法；建立不同尺度域间的约束关系，推导多尺度动力控制方程；提出长隧道多尺度动力问题的混合时步高效算法，建立与材料非线性等因素相对应的计算稳定性条件和收敛准则；采用损伤理论建立混凝土动力损伤本构模型，实现考虑损伤劣化特性的非一致地震激励下长隧道多尺度动力分析。项目研究有助于完善我国地下结构抗震理论和方法，为长隧道结构抗震计算和分析提供科学依据。

本项目的最大创新之处在于将多尺度理论和方法引入到长隧道结构的非一致地震响应激励模拟和实现中。首先，基于并发多尺度原理构建了长隧道多尺度建模方法和动力分析模型，综合考虑地震波频谱、介质视波速和行波效应等影响因素，建立了考虑地震动非一致性的模型空间有效离散化方法；其次，以桥域耦合理论为基础，引入拉格朗日乘子将不同尺度区域之间的约束关系，通过能量势函数隐含到动力方程中，推导出不同尺度域的动力控制方程；再次，基于中心差分法，采用不同时间步长来求解不同尺度域，提出了用于地下结构多尺度分析的混合时间步算法，可以高效求解所建立的多尺度动力耦合体系；最后，以实际工程为应用实例，通过与传统的位移耦合方法的对比分析，说明了该多尺度方法用于地下结构动力分析的可行性以及对消除高频波虚假反射的有效性。本项研究是多尺度理论和方法在长隧道结构抗震分析中的初步探索，有助于完善我国地下结构抗震理论和方法，具有重要的科学理论价值和创新性。