Closed-Form Force-Displacement Backbone Curves for Bridge Abutment-Backfill Systems

The abutment-soil-structure-interaction plays a significant role in the global response of bridge structures. This paper presents nonlinear closed-form formulas to describe force-displacement backbone curves of bridge abutments with typical backfill soils. The original closed-form formulas are modified Hyperbolic Force-Displacement ("HFD") equations developed to simulate the results of two field abutment tests for an abutment wall height of 5.5 feet. To extend the formulas to be applicable to abutment walls with other heights, a series of analyses are performed using the limit-equilibrium method that implements mobilized Logarithmic-Spiral failure surfaces coupled with a modified Hyperbolic soil stress-strain behavior ("LSH" model). The limit-equilibrium method with LSH model, which is a relatively simple approach, has been verified through analyses using a complex finite element model and also has been validated by abutment and pile cap field tests conducted on various typical structure backfills. Based on the results of the analyses, two height adjustment factors are derived for typical sandy and clayey backfill soils. The recommended closed-form formulas are the products of the original closed-form formulas and the height adjustment factors. The formulas are simple enough to be used by the practicing engineers and are capable of capturing the major characteristics of the force-displacement backbone curves.