Multiscale Stochastic Modeling of Backward Erosion Piping Initiation, From Grain Kinetics to Weibull Statistics. Part I: Analytical Derivations

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.