Abstract: 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.

Key words: multidirectional earthquake loading, ratio of equivalent number of strain cycle, computation model