Analysis of seismic earth pressures on flexible underground box structures

The seismic response of underground structures is controlled by a combination of kinematic and inertial soil-structure interaction. Kinematic interaction arises from differences in the displaced shape of the underground structure relative to the free-field soil, while inertial interaction arises from mass being accelerated by earthquake ground motion. Kinematic interaction is typically the dominant source of SSI for underground structures, though inertial interaction could be significant when above ground structural components are attached to the walls. This paper presents kinematic Winkler based analytical solutions of a centrifuge testing program involving an underground box structure bolted to the base of the model container and embedded in dry sand. The model was shaken by a sequence of earthquake ground motions. Input parameters include (i) the free-field soil profile (shear wave velocity and mass density), (ii) the flexural stiffness of the wall, (iii) rotational and translational stiffnesses at the base and top of the wall, and (iv) the ground surface motion. The soil stiffness is assumed to vary with depth according to a power law. The measured surface motion is deconvolved in the frequency domain to obtain depth-dependent displacements that are compatible with the soil profile, and these displacements are utilized as inputs to the Winkler model. The soil stiffness is set to be compatible with mobilized free-field strain levels in accordance with a modulus reduction and damping curve (i.e., the analysis is equivalent-linear). Results are presented in terms of the measured versus predicted earth pressure distributions mobilized at the soil-wall interface and the bending strains mobilized in the wall. Standard of practice procedures in which an inertial force is imposed on an active wedge are also performed. Agreement between measured and predicted quantities is significantly better for the kinematic SSI analytical solution than for standard of practice procedures.