Analytical solution for design parameters of model box to simulate seismic spatial variability effect using double-array shaking tables

Based on the multi-point shaking table tests on underground structures, the simulation of the seismic spatial variability effect can be realized by the design of model box, that is, the model container can be used to realize the equivalent transformation from the discrete multi-point shaking of the table into a continuous non-uniform seismic excitation. However, neither analytical solutions nor experimental data are available in the current literatures to obtain the design parameters of the model box. The simplified analysis model and boundary conditions of the model box are established for the typical double-array shaking table test system. According to the integral transformation and residue theorem, the analytical solution for dynamic response of the model box on the double-array shaking tables is derived, and thus the analytical relationship between the dynamic response and the parameters of the model box can be directly expressed from the proposed solution. By taking the continuous non-uniform seismic input as benchmark, the analytical expression for the design parameters of the model box is obtained. Finally, the proposed solution is verified by a series of shaking table tests. The analytical solution can be used for the design of the model box to simulate the seismic spatial variability effect based on double-array shaking tables.