多维地震荷载等效循环周数计算模型

地震波是一种多维的随机荷载，一般在参数测定中应将其转化为等效循环荷载。采用有限元模拟多向地震荷载作用下的砂土动力响应，介绍了弹塑性边界面模型及其参数的含义，阐述了确定参数的方法，选取涵盖大震、中震、近场、远场及不同土质条件的155组多向地震输入时程进行单向、多向加载。利用混合效应回归分析法，建立了多向地震荷载作用下等效循环周数计算模型，分析验证了该模型的准确性。提出了基于等效循环周数比的多维地震荷载作用下等效循环周数计算方法。研究表明：模型预测值能较好地反映等效循环周数实际值的变化趋势；震级和震中距对等效循环周数比影响不明显；砂土特性对等效循环周数比的影响具有主导作用, 在不同震级范围内，等效循环周数比均随着相对密度的增大而增大，对应于相对密度为45%、60%、80%、100%的砂土，等效循环周数比分别近似为1.60、1.85、1.90和2.05。

A computational model for equivalent cyclic number of multidirectional earthquake loading

An earthquake wave is a multidirectional random load, which is commonly converted to an equivalent cyclic load with uniform amplitude for laboratory tests. Dynamic responses of sand subjected to multidirectional earthquake loading are simulated using a FEM code. An elastoplastic boundary surface constitutive model is introduced. The method for determining material parameters is discussed. 155 groups of ground motions with multi-components from far to near field of moderate or strong earthquake events at different site conditions are used as input motions for unidirectional and multidirectional loading. Based on hybrid-effect regression analysis methods, a computation model for equivalent number of uniform strain cycles under the condition of multidirectional earthquake loading is proposed. Capability of the proposed model is clearly shown. Based on the ratio of equivalent cyclic number of strain, a method for computing the equivalent cyclic number of multidirectional earthquake loading is proposed. The results show that the proposed model can well predict the variation trend of the equivalent cyclic number of uniform strain cycles. The ratio of the equivalent cyclic number is trivially affected by the earthquake magnitude and site-to-source distance, though it is significantly influenced by the properties of sand. The ratio of equivalent number of strain cycles increases with the relative density of sand within different scopes of earthquake magnitude. For the sands of relative densities 45%, 60%, 80% and 100%, the mean ratio is about 1.60, 1.85, 1.90 and 2.05, respectively.