Mathematical Problems in Rock Mechanics and Rock Engineering

With increasing requirements for energy, resources and space, rock engineering projects are being constructed more often and are operated in large-scale environments with complex geology. Meanwhile, rock failures and rock instabilities occur more frequently, and severely threaten the safety and stability of rock engineering projects. It is well-recognized that rock has multi-scale structures and involves multi-scale fracture processes. Meanwhile, rocks are commonly subjected simultaneously to complex static stress and strong dynamic disturbance, providing a hotbed for the occurrence of rock failures. In addition, there are many multi-physics coupling processes in a rock mass. It is still difficult to understand these rock mechanics and characterize rock behavior during complex stress conditions, multi-physics processes, and multi-scale changes. Therefore, our understanding of rock mechanics and the prevention and control of failure and instability in rock engineering needs to be furthered. The primary aim of this Special Issue “Mathematical Problems in Rock Mechanics and Rock Engineering” is to bring together original research discussing innovative efforts regarding in situ observations, laboratory experiments and theoretical, numerical, and big-data-based methods to overcome the mathematical problems related to rock mechanics and rock engineering. It includes 12 manuscripts that illustrate the valuable efforts for addressing mathematical problems in rock mechanics and rock engineering

Mechanical Behavior of Shale Rock under Uniaxial Cyclic Loading and Unloading Condition

In order to investigate the mechanical behavior of shale rock under cyclic loading and unloading condition, two kinds of incremental cyclic loading tests were conducted. Based on the result of the short-term uniaxial incremental cyclic loading test, the permanent residual strain, modulus, and damage evolution were analyzed firstly. Results showed that the relationship between the residual strains and the cycle number can be expressed by an exponential function. The deformation modulus E50 and elastic modulus ES first increased and then decreased with the peak stress under the loading condition, and both of them increased approximately linearly with the peak stress under the unloading condition. On the basis of the energy dissipation, the damage variables showed an exponential increasing with the strain at peak stress. The creep behavior of the shale rock was also analyzed. Results showed that there are obvious instantaneous strain, decay creep, and steady creep under each stress level and the specimen appears the accelerated creep stage under the 4th stress of 51.16 MPa. Based on the characteristics of the Burgers creep model, a viscoelastic-plastic creep model was proposed through viscoplastic mechanics, which agrees very well with the experimental results and can better describe the creep behavior of shale rock better than the Burgers creep model. Results can provide some mechanics reference evidence for shale gas development

Mining Safety and Sustainability I

Safety and sustainability are becoming ever bigger challenges for the mining industry with the increasing depth of mining. It is of great significance to reduce the disaster risk of mining accidents, enhance the safety of mining operations, and improve the efficiency and sustainability of development of mineral resource. This book provides a platform to present new research and recent advances in the safety and sustainability of mining. More specifically, Mining Safety and Sustainability presents recent theoretical and experimental studies with a focus on safety mining, green mining, intelligent mining and mines, sustainable development, risk management of mines, ecological restoration of mines, mining methods and technologies, and damage monitoring and prediction. It will be further helpful to provide theoretical support and technical support for guiding the normative, green, safe, and sustainable development of the mining industry

Study of the Dynamic Failure Characteristics of Anisotropic Shales Under Impact Brazilian Splitting

The mechanical behaviors of shales with transversely isotropic characteristics under dynamic loading have great significance for structural instability in geotechnical engineering. To understand the effect of transverse isotropy on the deformability and tensile strength of shales subjected to dynamic loading, a group of impact Brazilian tests were carried out on shale specimens via a split Hopkinson pressure bar (SHPB) testing system. High-speed digital image correlation technology was applied to monitor the fracture process. The experimental results demonstrate that the failure strength has considerable anisotropy as the bedding angle of the embedded layers changes. Moreover, the tensile strength of shales with vertical bedding is usually higher than that of shales with parallel bedding. The observed failure mode is mainly the interaction between tensile and/ or shear fractures, and with increasing loading rate, layer-activated fractures tend to occur. Furthermore, five typical fail ure patterns of transversely isotropic shales characterized by different mechanisms under dynamic Brazilian testing were found. The shales were sensitive to the strain rate when the deformation and fracture response under dynamic loading were assessed. In addition, the modified Nova‒Zaninetti criterion that considers the strain rate effect was proposed according to the Brazilian splitting data and dynamic coordinate system. The established criterion not only properly represents the law of dynamic strength but also provides a new understanding of the effect of strain rate on strength. It has proven to be effective for predicting the dynamic strength characteristics of shales.China Postdoctoral Science Foundation, 2023TQ0025, Xianhui Feng, National Natural Science Foundation of China, 41941018, Chun’an Tan

Biologically Induced Cementation for Soil Stabilisation

Soil bio-cementation via microbially induced calcite precipitation (MICP) process generates calcite in the soil matrix through ureolysis by bacteria. This research has successfully produced effective calcite crystals; relatively larger in size than previously reported ones, and are rhombohedral in shape that favours the strategic spots of soil pore throats for precipitation. These effective calcite crystals bind sand grains together, resulting in an increase in both the strength and stiffness of the otherwise uncemented soil

Comparison of machine learning and statistical approaches to estimate rock tensile strength

Tensile strength is very important in drilling operations. The main objective of this study was to assess petrography, physical, and mechanical properties and predict the Brazilian tensile strength of sedimentary rocks by leveraging key parameters such as Schmidt hardness, compressional wave velocity, density, and porosity. A diverse array of predictive models was employed, encompassing simple regression, multivariate linear and nonlinear regression, backpropagation artificial neural network, gaussian process regression, classification and regression tree, K-nearest neighbor, random forest, and support vector regression. Based on thin section analysis and X-ray diffraction, the samples were identified. The sandstone samples were meticulously categorized into two distinct groups: arenite and litharenite. Additionally, the limestone samples were stratified into the categories of packstone to mudstone based on texture. The highest failure mode frequency of the samples under the Brazilian tensile strength test was identified as central fracturing. Upon meticulous examination, it was discerned that compressional wave velocity exerted the most substantial influence on Brazilian tensile strength estimates, while density exhibited the least impact. Comparing the outcomes derived from the diverse modeling techniques, it was unequivocally established that the support vector regression model showcased the highest level of performance for forecasting Brazilian tensile strength. This was evidenced by the remarkable coefficient of determination of 0.99 along with an impressively low root mean square error of 0.03

The Performance of Two Alkoxysilane Consolidants on Three Berea Sandstones Through Controlled Environmental Stress Cycling

This thesis contributes to the body of knowledge about the performance of sandstone consolidants in North America. A sandstone consolidant in use in Europe was tested alongside a consolidant in use in North America. Based on laboratory testing of sample stone treated with the two consolidants, this thesis analyzes the performance of the consolidants in comparison to one another. Establishing the important performance characteristics of a successful sandstone consolidant and identifying the characteristics of the three Berea sandstones, and the two consolidants being tested, allows for an analytical performance of these materials. Controlled environmental stress cycling in the laboratory exposed the consolidated stone to conditions approximating those in the field. Comparing the maximum biaxial flexural strength of the stone samples, showed that the two consolidants show comparable performance, in consolidating each of the three sandstones

Deviatoric stress-strain curve construction with strain-softening account via the damage-modified Duncan-Chang, arctangent and informer models: a comparative analysis

Engineering construction in cold regions cannot be separated from permafrost research. This study aimed to determine the mechanical properties and changing laws of artificially frozen clay through triaxial tests. Two models have been established: a physical model based on the tradi-tional phenomenological constitutive theory and a deep learning model based on the data-driven constitutive theory, taking into account the softening phenomenon. The accuracy and applica-bility of the models were verified, followed by a comparative analysis. The results of the analysis are as follows. The Duncan-Chang model can describe the characteristics of the hardening-type deviatoric stress-strain curve, but it cannot describe the characteristics of the softening-type de-viatoric stress-strain curve. The Modified Duncan-Chang (MDC) model fails to accurately de-scribe the characteristics of a smooth deviatoric stress-strain curve. The Strain-Damage Modified Duncan-Chang (SD-MDC) model exhibits a good fit in both the ascending and descending seg-ments of the curve, but it lacks effectiveness in the convergence segment of the S-shaped sof-tening curve. For this reason, this paper has chosen the arctangent function to establish a Strain-Damage Modified arctangent constitutive model (SD-MAM). This model accurately re-flects the stress evolution process of different types of frozen soils. Additionally, the Informer time series prediction algorithm was utilized to develop the Informer permafrost deviatoric stress prediction model which achieved an R2 value above 99%. In comparison to the SD-MAM model, the Informer model demonstrates higher precision, does not rely on assumptions, is cost-effective, and has a wide range of applications. However, it lacks physical meaning, and interpretability, and requires further discussion regarding the reliability of the results. This study offers valuable insights into the development and application of constitutive models for frozen soils