According to classical critical state theory (CST) of granular mechanics, two conditions on the stress ratio and void ratio are satisfied when reaching and maintaining a critical state (CS). Therefore, CST dictates the necessity of these two conditions although their sufficiency has not been demonstrated, but only assumed. The present work challenges this assumption based on the results of a virtual two-dimensional (2D) discrete element method (DEM) experiment. The virtual sample is first brought to CS and then rotation of the principal axes (PA) of stress is imposed while keeping stress principal values fixed. The rotation induces a void ratio reduction and thus, abandonment of CS, despite the fact the two CST conditions are satisfied at the initiation of the rotation process, since the stress principal values remain fixed and the void ratio is at its critical state value for the given fixed pressure. The recently proposed anisotropic critical state theory (ACST) remedies this incompleteness of CST by enhancing its two conditions by a third, related to the critical state value of a fabric anisotropy variable, defined as the trace of the product of the fabric anisotropy tensor and the loading direction tensor. This third condition is violated by the stress PA rotation and can explain the aforementioned void ratio reduction. ACST can also explain various other response characteristics that cannot be addressed by classical CST with no fabric anisotropy consideration. In conclusion, the three conditions of ACST are shown to be both necessary and sufficient for reaching and maintaining CS.

Coal mines produce large amounts of excavated waste soils, known as spoils. These materials can cover vast areas, are typically dumped in heaps without any treatment, and are difficult to exploit for engineering purposes because of their significant variability. Efficient exploitation of spoil heaps poses engineering challenges, related mainly to the involved degree of uncertainty. A small number of studies have attempted to characterize the geotechnical properties of spoil material; however, there remains a considerable gap in understanding how to deal with spoil materials in the context of sustainable development and civil infrastructure design. In this work, a systematic effort is made to quantify the uncertainty of the geotechnical properties of a particular spoil heap. Laboratory test results based on an extended investigation of a spoil material originating from lignite coal mines are gathered in one database and thoroughly analyzed. The results reveal and quantify the significant spoil material variability, which is contrasted against data for common soils, while a systematic approach is proposed for spoil material characterization.