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Backward erosion piping (BEP) has been recognised as a major cause of failures in water-retaining structures. However, the fundamental mechanisms controlling the phenomenon are not well understood. This research applies the theory of rate processes to develop a constitutive relationship between energy density of the seepage flow and the erosion rate of soils during the evolution of BEP. The resulting equation is used to analyse four datasets of previously reported experimental observations. The mechanical parameters estimated through the proposed model fall into the ranges of values that were reported in the literature. To validate the proposed approach, the constitutive model was incorporated into a multiphase numerical framework to simulate evolution of BEP in embankment soil and compared with reported experimental observations. The numerical framework with the proposed constitutive model is shown to be capable of reproducing both the observed evolution of local hydraulic gradients and pipe progression in the structure. 

ABSTRACT Backward erosion piping (BEP) is a significant contributor to failures in global flood protection infrastructure, yet it remains among the least understood geotechnical phenomena, particularly concerning the fundamental mechanisms driving its initiation. This study focuses on the development of a novel stochastic framework for the prediction of critical hydraulic gradients causing BEP initiation. The novelty of the study lies in the following: (1) the development of a grain‐scale probabilistic model based on fundamental mechanisms by means of the theory of rate processes, (2) quantification of the influence of soil variability on BEP initiation probability by introducing an initiation probability function, and (3) an analytical framework reconciling grain kinetics of BEP initiation with the Weibull distribution. A particle‐scale BEP initiation probabilistic model is first established based on fundamental grain kinetics under seepage flow by using the theory of rate processes. To investigate how soil variability influences initiation, a stochastic dual random lattice modeling framework is exercised, complemented by direct x‐ray computed tomography measurements of soil variability conducted on sand samples. The analytical probabilistic model for BEP initiation closely aligns with the Weibull distribution, also demonstrating that soil variability influences both the scale and shape parameters of the distribution. This work establishes the linkage between probability of BEP initiation as described by the theory of rate processes and phenomenological Weibull statistics. Findings presented herein bring the potential to develop a multiscale probabilistic framework by means of Weibull statistics for evaluating the probability of BEP initiation at multiple scales. 

ABSTRACT Backward erosion piping (BEP) is a leading internal erosion mechanism for flood protection system failures. A model capable of predicting critical hydraulic conditions for BEP initiation at multiple scales while also incorporating soil variability is a pressing need. This study formulates and validates a novel multiscale probabilistic BEP initiation framework with incorporation of soil variability. The framework is based on a grain‐scale probabilistic model and the weakest link theory, and the theory of rate processes. The multiscale framework proposed herein is validated through a wide range of available experimental data from independent sources, encompassing tests performed at multiple scales. Following calibration with small‐scale experimental data, the model demonstrates accurate prediction of critical hydraulic gradients at larger scales (3–6 orders of magnitude difference), including the ability to capture the grain size dependence of BEP initiation and providing uncertainty estimates. A systematic analysis is performed to uncover the effects of different soil properties on multiscale critical hydraulic conditions.