Energy-related characterizations can provide important information regarding mechanical behavior of rocks. A series of uniaxial compression tests were carried out on intact rock samples obtained from Wyoming, USA. The physical properties of the samples (i.e., porosity and grain size) were first examined. To investigate the fracture behavior of sedimentary rocks, a compilation of published dataset and our experimental data were employed to develop a new approach for estimating uniaxial compressive strength (UCS) based on the amount of energy released during rock deformation, which is known as the rock toughness. The energy release is calculated as the area under the stress-strain curve until the peak stress is reached. This energy shows a strong correlation with the density of the rock. Moreover, a predictive empirical model was proposed to estimate the rock UCS based on the rock toughness. The proposed empirical model was validated by comparing the predicted and measured UCS values of experimentally tested rocks, and the comparison showed a good agreement with a mean bias (the ratio of measured to the predicted compressive strength) of 1.002.

Energy-related characterizations can provide important information regarding mechanical behavior of rocks. A series of uniaxial compression tests were carried out on intact rock samples obtained from Wyoming, USA. The physical properties of the samples (i.e., porosity and grain size) were first examined. To investigate the fracture behavior of sedimentary rocks, a compilation of published dataset and our experimental data were employed to develop a new approach for estimating uniaxial compressive strength (UCS) based on the amount of energy released during rock deformation, which is known as the rock toughness. The energy release is calculated as the area under the stress-strain curve until the peak stress is reached. This energy shows a strong correlation with the density of the rock. Moreover, a predictive empirical model was proposed to estimate the rock UCS based on the rock toughness. The proposed empirical model was validated by comparing the predicted and measured UCS values of experimentally tested rocks, and the comparison showed a good agreement with a mean bias (the ratio of measured to the predicted compressive strength) of 1.002. 1. INTRODUCTION During rock deformation process, energy is released and dissipated according to the law of energy conservation. Released energy is significant in rock engineering designs to improve the effectiveness of their efforts. Moreover, understanding the amount of energy released during deformation under different loadings is important to mitigate slope failures consequences since this energy can facilitate the estimation of the degree of rock damage under compression because fracture development is directly proportional to the amount of the energy released during deformation. From a practical point of view, energy released known as toughness is significantly related to the mechanical behavior of the rock. The total energy is the sum of the elastic strain energy and the dissipated energy. The dissipated energy causes internal damage which reflects new microcracks development and cause strength weakening of the rock, whereas the elastic energy causes overall rock failure. Internal microcracks can expand during deformation process causing the elastic energy stored inside the rock to be released resulting in acoustic emissions. Therefore, a fundamental feature of fracture mechanism lies in developing a relationship between the energy released and the compressive strength of the rock under loading. Also, it is significantly acknowledged to develop a simplified cracking description from which the mechanical and fracture behavior can be derived. In this study, traditional stress-strain curves obtained from uniaxial compression tests are used to estimate the energy released at failure, which is quantified as the area under the stress-strain curve of the rock under compression prior to failure. Also, empirical predictive model that correlates the toughness with the rock UCS was developed to provide a better understanding of the effect of mechanical properties on the fracture behavior. Most failure criteria and theories deal with rocks compressive strength and do not deal directly with fracture processes. Therefore, to fill the gap of knowledge, we herein present a combination of the results of uniaxial compression tests conducted at the University of Wyoming on several sedimentary rocks obtained from Wyoming formations as well as experimental data collected from published literature. Strength and fracture parameters were measured and the stress-strain behavior was examined based on test results. The rock toughness was calculated based on the mechanical response of the rock, and then these values were employed to develop an empirical model to estimate the rock compressive strength. This model was validated by comparing the measured UCS with that estimated based on stress-strain curves. Comparison showed a good agreement with a mean bias (ratio of measured to predicted UCS) of 1.002 indicating that this model can be well used to estimate the UCS. Such results can improve stability analysis of rock structures, where fracture and mechanical behavior play a significant role in rock stability.

Mechanical properties of sandstone, such as compressive strength and young’s modulus, are commonly used in the design of geotechnical structures and numerical simulation of underground reservoirs using models such as the digital groundwater, equivalent porous medium, and Discrete Fracture Network (DFN) models. A better understanding of the mechanical behaviors of sandstone under different loading conditions is imperative when assessing the stability of geotechnical structures. This paper highlights the effect of the physical properties (i.e., porosity, mean grain size) and environmental conditions (i.e., water content and confining stress) on uniaxial compressive strength, triaxial compressive strength, and young’s modulus of sandstone. A series of uniaxial and triaxial compression experiments are conducted on sandstone formations from Wyoming. In addition, experimental data on sandstones from the literature are compiled and integrated into this study. Prediction equations for the compressive strengths and young’s modulus of sandstone are established based on commonly available physical properties and known environmental conditions. The results show that the mean Uniaxial Compressive Strength (UCS) decreases as the porosity, water content, and mean grain size increase. Furthermore, a predictive empirical relationship for the triaxial compressive strength is established under different confinements and porosity. The relationship suggests that the mean peak compressive strength increases at a higher confinement and decreases at a higher porosity. The results and recommendations provide a useful framework for evaluating the strength and deformation of most sandstone.