**Uncertainty quantification for granular materials with a stochastic
discrete element method**

DY Liu and MZ Lyu, COMPUTERS AND GEOTECHNICS, 161, 105560 (2023).

DOI: 10.1016/j.compgeo.2023.105560

Significant uncertainty exists in granular materials, as demonstrated by experimental and simulation studies. Quantifying this uncertainty by integrating refined discrete element analysis with direct stochastic simulation is challenging due to computational cost constraints. To this end, the probability density evolution method (PDEM) is introduced to propose the methodology of stochastic discrete element analysis. The objective of this paper is to develop a formulation of the stochastic discrete element method (DEM) on uncertainty quantification for granular materials. First, the uncertainty characterization of inter-particle friction coefficients (& mu;) is performed via experimental data, resulting in the identification of an optimal probability distribution. Second, the 100 representative deterministic points of basic random variables are selected for subsequent DEM shearing simu-lation until the critical state. Third, the PDEM is developed to obtain the probability density function (PDF) surface representing the system's performance, thus offering a comprehensive prediction of uncertainty for granular materials. The results show that the uncertainty of & mu; propagates to the behavior of granular materials. Utilizing the stochastic DEM methodology clarifies which behavior parameters exhibit significant randomness and which possess negligible randomness. Notable uncertainties are observed in large strain macro-scale behavior and the proportion of inactive particles. It can be inferred that conventional methods that neglect probability distributions might produce spurious results. Moreover, the influence of uncertainties on granular material behavior varies depending on the its shearing state and related soil parameters. In contrast, limited uncertainties are identified for the randomness of small strain stiffness, and the randomness on the particle scale stress transmission shape is also limited. This study marks the initial application of the PDEM in geotechnical engineering, suggesting that considering probability density evolution could enhance geotechnical engineering design. The current study highlights the necessity of using statistical methods to assess key geotechnical parameters.

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