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Response spectrum-based seismic response of bridge embankments

A single degree of freedom model is presented for calculating the free-field seismic response of bridge embankments due to horizontal ground shaking using equivalent linear analysis and a design response spectrum. The shear wave velocity profile, base flexibility, 2D shape, and damping ratio of the embankment are accounted for in the model. A step-by-step procedure is presented for calculating the effective cyclic shear strain of the embankment, equivalent homogeneous shear modulus and damping ratio, fundamental period of vibration, peak crest acceleration, peak shear stress profile, peak shear strain profile, equivalent linear shear modulus profile, and peak relative displacement profile. Model calibration and verification of the proposed procedure is carried out with linear, equivalent linear, and nonlinear finite element analysis for embankments with fundamental periods of vibration between 0.1 and 1.0 s. The proposed model is simple, rational, and suitable for practical implementation using spreadsheets for a preliminary design phase of bridge embankments.