Simplified Hybrid $p\text{-}y$ Spring Model for Liquefied Soils

The beam-on-Winkler foundation (BWF) method is a popular analysis approach for computing the lateral pile response resulting from both inertial and kinematic loading. However, there is significant uncertainty regarding how to properly represent the load-resistance (i.e., $p\text{-}y$) behavior of liquefied soils. This confusion stems from the significant variability observed with the phenomenon and the large number of $p\text{-}y$ spring models for liquefied soils that have attempted to account for that variability. In an attempt to develop a practical but broadly applicable approach, a simplified hybrid $p\text{-}y$ spring model is presented. This hybrid model incorporates aspects of existing $p\text{-}y$ spring models for liquefied soil and is applicable to a wide range of soil types, relative densities, pile/shaft diameters, and loading conditions. Comparisons with a variety of published case histories involving single piles indicate that the hybrid $p\text{-}y$ spring model provides reasonable estimates of response for both kinematic and inertial loadings. For approximately 80% of the evaluated loading scenarios, the computed maximum bending moments and the peak pile head displacements were within ±30 and ±25%, respectively, of the measured values. The proposed hybrid $p\text{-}y$ model generally overestimated peak bending moments when considering kinematic loading but tended to underestimate peak bending moments for relatively low loads when considering inertial loading. For computed head displacements less than about 20 cm (7.9 in.), computed head displacements were within ±2.54 cm (1 in.) of measured displacements. For computed head displacements greater than about 20 cm (7.9 in.), head displacements were overestimated in approximately 80% of the loading scenarios.