Construction of simplified design p–y curves for liquefied soils

Abstract

In practice, laterally loaded piles are most often analysed using a 'beam-on-non-linear-Winklerfoundation' approach, whereby the soil-structure interaction is modelled by means of p-y curves. Although well-calibrated p-y curves exist for non-liquefied soils (e.g. soft clay and sand), the profession still lacks reliable p-y curves for liquefied soils. In fact, the latter should be consistent with the observed strain-stiffening behaviour exhibited by liquefied samples in both element and physical model tests. It is recognised that this behaviour is induced by the tendency of the liquefied soil to dilate upon undrained shearing, which ultimately results in a gradual decrease in excess pore pressure, and consequent increase in stiffness and strength. The aim of this paper is twofold. First, it proposes an easy-to-use empirical model for constructing stress-strain relationships for liquefied soils. This only requires three soil parameters which can conveniently be determined by means of laboratory tests. Second, it introduces a method for the construction of p-y curves for liquefiable soils from the proposed stress-strain model, based on the scaling of stress and strain into compatible soil reaction p and pile deflection y, respectively. The scaling factors for stress and strain are computed following an energy-based approach that is analogous to the upper-bound method used in classical plasticity theory. To validate the proposed p-y curves, results from a series of centrifuge tests are employed to back-calculate p-y curves for liquefied soils. The latter are compared with those obtained from the proposed method and the conventional p-multiplier approach.

Lateral Behavior of Pile Foundations during Partial Liquefaction

“…It is interesting to that the API (2000) and P-multiplier (Brandenberg, 2005) approaches yield similar peak BM pattern along the depth of the pile. However, the bilinear model proposed by Lombardi et al (2016) predicted a fixed moment at the bottom unlike the other two approaches along with the zero BM being shifted to much deeper elevation (1.5 m from surface) due to the zero initial stiffness of the model. Figure 10 compares the peak BM profile along the depth for 25% and 50% liquefaction levels along with the traditional approaches with the shake table results.…”

“…The resulting P-Y curves at 25% and 50% liquefaction are shown in Figure 8. The traditional P-Y curves were also developed based on three approaches, API 2007, p-mulitplier of 0.33 based on Brandenberg (2005) and fully liquefied condition based on Lombardi et al, (2016). All the P-Y curves developed along with the proposed partially liquefied curves are shown in Figure 8.…”

“…In addition, the P-Δ effect is also considered during the loading. Figure 9 (a), (b) and (c) present the bending response of the single pile with the soil pile interaction modelled using the API (2000), P-multiplier and post liquefaction bilinear model by Lombardi et al, (2016) respectively, at different pseudo-static loading conditions. It is interesting to that the API (2000) and P-multiplier (Brandenberg, 2005) approaches yield similar peak BM pattern along the depth of the pile.…”

“…However, this approach lacks the basic representation of post liquefied behavior of soils-strain hardening with zero initial stiffness. More recently, Lombardi et al, (2016) proposed a bilinear Winkler spring approach considering the zero initial stiffness and strain stiffening behavior for liquefied soils, Figure 1 (d). It is important to note that the behavior of sandy soils during partial liquefaction (0<Ru<1.0) is neither analogous to nonliquefied nor to fully liquefied conditions, and is therefore the application of any of the above approaches in estimating the bending response of piles in partial liquefaction can be questionable.…”

The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure Mechanisms, Analysis, Re-Qualification

“…Similarly, the post-liquefaction behaviour of sands observed in element tests by [104,105]. Lombardi et al [106] and Dash et al [107] adopted a new set of p-y curves that can be obtained by modifying the conventional p-y curves (for non-liquefied soils) in such a way that replicates the strain hardening behaviour with practically-zero stiffness at low strain.…”