Discrete element method has been widely adopted to simulate processes that are challenging to continuum-based approaches. However, its computational efficiency can be greatly compromised when large number of particles are required to model regions of less interest to researchers. Due to this, the application of DEM to boundary value problems has been limited. This paper introduces a three-dimensional discrete element–finite difference coupling method, in which the discrete–continuum interactions are modeled in local coordinate systems where the force and displacement compatibilities between the coupled subdomains are considered. The method is validated using a model dynamic compaction test on sand. The comparison between the numerical and physical test results shows that the coupling method can effectively simulate the dynamic compaction process. The responses of the DEM model show that dynamic stress propagation (compaction mechanism) and tamper penetration (bearing capacity mechanism) play very different roles in soil deformations. Under impact loading, the soil undergoes a transient weakening process induced by dynamic stress propagation, which makes the soil easier to densify under bearing capacity mechanism. The distribution of tamping energy between the two mechanisms can influence the compaction efficiency, and allocating higher compaction energy to bearing capacity mechanism could improve the efficiency of dynamic compaction.
Existing research on DEM vertical accuracy assessment uses mainly statistical methods, in particular variance and RMSE which are both based on the error propagation theory in statistics. This article demonstrates that error propagation theory is not applicable because the critical assumption behind it cannot be satisfied. In fact, the non‐random, non‐normal, and non‐stationary nature of DEM error makes it very challenging to apply statistical methods. This article presents approximation theory as a new methodology and illustrates its application to DEMs created by linear interpolation using contour lines as the source data. Applying approximation theory, a DEM's accuracy is determined by the largest error of any point (not samples) in the entire study area. The error at a point is bounded by max(|δnode|+M2h2/8) where |δnode| is the error in the source data used to interpolate the point, M2 is the maximum norm of the second‐order derivative which can be interpreted as curvature, and h is the length of the line on which linear interpolation is conducted. The article explains how to compute each term and illustrates how this new methodology based on approximation theory effectively facilitates DEM accuracy assessment and quality control. 相似文献