Physics-informed probabilistic models for peak pore pressure and shear strain in layered, liquefiable deposits

In this paper probabilistic models are developed for estimating the peak excess pore pressure ratio (⁠$ru$⁠) and peak shear strain (⁠$γmax$⁠), which control liquefaction triggering, in layered granular soils under earthquake loading. The models are developed using non-linear regression applied to a database of 167 352 results from one-dimensional, non-linear, effective stress, site response analyses. A pseudo-parametric regression strategy is adopted to account for the theoretical upper bound on $ru$ at a value of 1. The models include the influence of variables that are specific to the individual layer, to the soil profile and to the ground motion, as well as layer-to-layer interaction and the relationship between $ru$ and $γmax$⁠. The variability around model predictions is decomposed, and the relative contributions of layer-, profile- and ground motion-specific parameters are evaluated. Epistemic uncertainty related to soil model selection, calibration and validation is also addressed. The total uncertainty around model predictions ranges from 0·5 to 1·6 in natural log units, with smaller values for scenarios that are of particular engineering interest (e.g. high $ru$⁠). Finally, the proposed models are used to estimate the probability of liquefaction triggering for case studies from the 2010–2011 Canterbury earthquake sequence. The results are shown to compare favourably with existing deterministic and probabilistic methods in terms of their ability to distinguish between cases where liquefaction was observed in both the Darfield and Christchurch earthquakes and those where no liquefaction was observed in either event.