Bridge Abutment Nonlinear Force-Displacement-Capacity Prediction for Seismic Design

Formulation of the mobilized force-displacement-capacity for the seismic design of a bridge abutment–embankment system is presented herein. As part of the seismic design philosophy of bridge structures, a realistic prediction of the abutment–embankment participation should be included in the bridge demand and capacity assessments. The nonlinear force-displacement capacity and/or stiffness of a bridge abutment–embankment system is a function of the abutment height, embankment soil properties (mobilized soil resistance), and the mobilized interface friction angle between the embankment and bridge abutment. A method based on a limit equilibrium logarithmic spiral, method of slices, coupled with characterization of the stress-strain behavior of the soil is employed. The stress-strain characterization relies on standard triaxial test results. The use of Mohr–Coulomb strength criteria based on mobilized strength parameters allows the consideration of a developing mobilized surface via limit equilibrium. The stress-strain behavior of soil in conjunction with the developing (mobilized) abutment–soil resistance surface is evaluated to assess the corresponding displacement. The nonlinear force-displacement response of different types of abutment–soil combinations (sand, clay, and $c\text{-}\varphi$ soil) is assessed. The Mohr–Coulomb strength criteria are used to develop shape function for describing the distribution of the interslice forces between two adjacent slices. Therefore the abutment–embankment lateral force computation and the values and directions of the interslice forces relative to the ever changing (mobilized) soil mass are handled explicitly. That is, the method presented allows simple assessment of the developing (mobilized) logarithmic spiral failure surface and the associated abutment load-displacement response without trial and error procedure. The nonlinear force-displacement-capacity prediction is in very good agreement with the results obtained from small- and full-scale experimental tests in cohesionless and cohesive backfill soils.