基于Marc二次开发实现粘弹性人工边界和振型分解反应谱法

新版《水电工程水工建筑物抗震设计规范》（NB35047-2015）中规定:"抗震设防类别为甲类的混凝土坝应考虑远域地基的辐射阻尼效应"。针对通用商业有限元软件Marc在振型分解反应谱法中的不足，且缺少时程分析法中模拟地基辐射阻尼效应的粘弹性人工边界，采用Fortran语言编制相应的独立程序及二次开发程序，以便在Mrac软件中精确实现新规范要求下的混凝土坝抗震安全评价。数值算例和工程实例分析结果验证了基于Marc二次开发实施思路和自编程序的正确性；重力坝抗震薄弱部位主要为坝体断面突变处，考虑无限地基的辐射阻尼效应后，坝体地震动力响应明显下降。

Viscoelastic artificial boundary and response spectral method of mode decomposition based on Marc second development

According to the new code for seismic design of hydraulic structures for hydropower projects (NB35047-2015), the radiation damping effect of the distant foundation should be considered for concrete dams with seismic fortification A-class. However, the general commercial finite element software Marc cannot directly output the stress response when using response spectral method of mode decomposition, and lacks the viscoelastic artificial boundary for simulating the radiation damping effect of foundation in time history analysis. In order to evaluate seismic performance of concrete dams under the new specification by Marc software, realization methods of the viscoelastic artificial boundary and the response spectral method of mode decomposition based on Marc are proposed, and the corresponding independent programs and second development programs are compiled based on the Fortran language. Results of both numerical simulation and engineering analysis verified the correctness of the implementation ideas and the compiled programs. The seismic weak parts of gravity dams are mainly the abrupt change of the section of dam body, and the seismic dynamic response of the dam body decreases obviously when considering the radiation damping effect of the infinite foundation.