基于比例边界有限元法的高混凝土坝系统建模与非线性地震响应研究

混凝土坝‐地基‐库水相互作用系统在地震作用下的损伤破坏研究一直是水工结构抗震领域的热点，其精确性与高效计算是其中的主要挑战，决定着大坝抗震安全评价的正确性与可信度。比例边界有限元法（SBFEM）的半解析特点，使其对于求解无限域和应力奇异性等方面具有特殊的优越性。本项目拟考虑基于标量波动方程的库水与混凝土坝耦合作用，建立基于矢量波动方程的大坝‐地基动力相互作用的高阶时域模型及非一致性地震动输入方法，构建基于SBFEM的远域辐射阻尼高阶边界模型；构建基于损伤能量释放率的混凝土弹塑性损伤本构模型及其SBFEM非线性求解方法；将所构建的边界模型与本构模型集成组装为综合应用程序/软件，对强震作用下系统的非线性动力响应与损伤特性进行数值模拟，并与其他现行理论与方法进行对比研究。项目成果有助于进一步提高地震作用下的大坝‐地基‐库水体系无反射边界的模拟精度、准确模拟混凝土坝地震动响应与损伤特性。

The studies on the damage and failure of the concrete dam-foundation-reservoir interaction system under earthquakes have always been a hot topic in the field of seismic resistance of hydraulic structures. Its accurate and efficient calculation is the main challenge, which determines the correctness and credibility of the seismic safety evaluation for the concrete dams. Due to the unique semi-analytical characteristics, the scaled boundary finite element method (SBFEM) has the special advantages in solving the problems of infinite domains, stress singularities, etc. This proposal aims to consider the coupling of reservoir water and concrete dam based on the scalar wave equation, develop a high-order time-domain model for dam-foundation dynamic interaction based on the vector wave equation and its nonuniform seismic input mechanism, construct a high-order boundary model of far-field radiation damping based on the scaled boundary finite element method. Then, it intends to establish an elasto-plastic damage constitutive model for the dam concrete based on damage energy release rate and its SBFEM nonlinear solution method. Finally, it plans to integrate the high-order boundary model and the elasto-plastic constitutive model into a comprehensive computer program/software, analyze the nonlinear seismic responses and damage characteristics of the system and compare the results with those of other existing theories and methods. The results of this proposal are expected to further improve the simulation accuracy of the nonreflecting boundary in the dam-foundation-reservoir water system and accurately simulate the seismic responses and damage characteristics of concrete dams.