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Extension fractures are typical for the deformation under low or no confining pressure. They can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. In this article, it is shown that the simple extension strain criterion makes unrealistic strength predictions in biaxial compression and tension. To overcome this major limitation, a new extension strain criterion is proposed by adding a weighted principal shear component to the simple criterion. The shear weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting extension failure modes, which are unexpected in the classical understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain leading to dilatancy. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak stress CP. Different from compressive loading, tensile loading requires only a limited number of critical cracks to cause failure. Therefore, for tensile stresses, the failure criteria must be modified somehow, possibly by a cut-off corresponding to the CI stress. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
Humic substances (HS), as important environmental components, are essential to soil health and agricultural sustainability. The usage of low-rank coal (LRC) for energy generation has declined considerably due to the growing popularity of renewable energy sources and gas. However, their potential as soil amendment aimed to maintain soil quality and productivity deserves more recognition. LRC, a highly heterogeneous material in nature, contains large quantities of HS and may effectively help to restore the physicochemical, biological, and ecological functionality of soil. Multiple emerging studies support the view that LRC and its derivatives can positively impact the soil microclimate, nutrient status, and organic matter turnover. Moreover, the phytotoxic effects of some pollutants can be reduced by subsequent LRC application. Broad geographical availability, relatively low cost, and good technical applicability of LRC offer the advantage of easy fulfilling soil amendment and conditioner requirements worldwide. This review analyzes and emphasizes the potential of LRC and its numerous forms/combinations for soil amelioration and crop production. A great benefit would be a systematic investment strategy implicating safe utilization and long-term application of LRC for sustainable agricultural production.