Decreasing the rockburst potential in longwall mining of burst-prone coal seams has been a longstanding challenge for geotechnical engineering worldwide. One of the effective approaches is drilling of relief boreholes in front of the coal seam face from the airways. This work presents a novel approach based on the integral rockburst factor (KIrb) taking account of the length of the dynamic abutment stress influence zone and the ratio of the vertical stress to the remote field virgin stress. The geotechnical conditions of seam 3 of the Alardinskaya mine (Kuznetsky basin, Russia) are taken as a study site. An approach of the finite-difference continuum damage mechanics is employed to describe the processes of deformation and fracture of coal and host rocks using an in-house software. The results indicate that the abutment stress maximum shifts deep into the seam after drilling and that the stress distribution along the coal seam horizon is a superposition of the solutions similar to those of the elastoplastic Kirsch problem. The results also indicate that the curves of KIrb dependence on spacing between the boreholes and their diameter are nonlinear and non-monotonic functions, which allows for optimizing of the drilling technology.

This work presents a new finite-difference continuum damage mechanics approach for assessment of threshold stresses based on the mechanical response of a representative volume element of a sandy-cement rock-like material. An original experimental study allows validating the mathematical model. A new modification of the damage accumulation kinetic equation is proposed. Several approaches based on acoustic emission, instantaneous Poisson's ratio and reversal point method are employed to determine the threshold stresses. Relying on the numerical modeling of deformation and failure of model samples, the threshold stresses and the deformation stages are determined. The model predicts the crack initiation stress threshold with less than 10% error. The model prediction of the crack damage stress threshold corresponds to the upper boundary of the experimental range. The model predicts the peak stress threshold with less than 0.2% error in comparison with the average experimental peak stress. The results of numerical modeling are shown to correlate well with the available experimental and literature data and sufficiently complement them.

The phenomenon of the strain-rate sensitivity of metallic materials has been a topic of interest since the first mechanical tests at different strain rates were performed. The problem of its theoretical description appeared simultaneously. Despite the significant number of studies covering this issue, it is necessary to rule out a few drawbacks of previously reported models, which is the goal of this work. Herein, an extension of the elastic–viscoplastic model to a generalized state of stress is proposed while aiming to describe the strain rate sensitivity of Armco-iron samples that were pulled in tension within the framework of the finite-difference method. A mathematical model was formulated using equivalent stress and strain, which alleviated the complexity of the relaxation-type constitutive equations. The critical shear stress (CSS) function describes S-type instability with a single equation. The plastic strain rate was calculated based on the well-known Orowan equation, which is related to dislocation dynamics. In addition, the model took the material’s microstructure into account based on the design of a representative volume element (RVE) using the step-by-step packing (SSP) method. The results of the modeling were compared with the available experimental data and were found to satisfactorily correlate with them. The results suggest that the misfit error between the model and experimental data did not exceed 10% in the range of strain rates under study, which is a reliable outcome.

Based on the recently reported experimental data, the Taylor (parabolic) strain hardening stage of mild steels corresponds to the emergence of nearly equidistantly located stationary maxima and minima of localized plastic deformation. The latter suggests that some regions of the material are subjected to stronger plastic deformation than others. From the Hall–Petch equation, it is well-known that the yield stress is composed of two constituents – the contribution to the flow stress from the basal slip planes and the contribution due to the influence of grain boundaries. However, it is still unclear which contribution is more significant. In this article, a microstructure-based finite-difference analysis is employed to provide a deeper insight into the emerging features in the parabolic hardening stage of low-carbon polycrystalline steel plastic flow. The step-by-step packing method is used to design a representative volume element (RVE) at mesoscale. The contributions from basal slip planes and grain boundaries, respectively, are considered separately. The modeling results better correlate with experimental findings when the hardening stage of the up-down-up constitutive equation is provided for by the change in the ky parameter of the Hall–Petch equation in the course of plastic flow development.

In this work, the computational study of Luders phenomenon is addressed. The material for investigation is low-carbon steel demonstrating the yield point phenomenon when pulled in tension. Modeling of samples loading is carried out in the framework of three-dimensional finite-difference method. Judging by the literature review, there is a lack of papers thoroughly addressing the curves of dependences of Luders elongation and front propagation velocity on parameters of up-down-up constitutive equation. This work fills this gap. It is shown that the difference between the true upper and lower yield stresses, and strain hardening factor have a strong impact on the duration of the yield plateau stage and ratio of front propagation velocity vf to loading velocity vl. The results of computational study complement the experimental data presented in available literature.

The design of new composite ceramic materials based on zirconium carbide is one of the effective methods of controlling the inherent brittleness of materials. A key physical parameter characterizing the ability of a material to resist crack growth is fracture toughness. A numerical method for estimating this parameter for heteromodulus ZrC ceramic materials under uniaxial compression is presented. It is shown that an introduction of low-modulus (in comparison with the matrix) particles delays the fracture and reduces the integral brittleness of the material due to the implementation of additional fracture mechanisms. It is demonstrated that, based on the mechanical response of the mesovolume of the material with an explicit consideration of the microstructure under uniaxial compression, it is possible to estimate the fracture toughness in a satisfactory agreement with the experimental data.

Longwall mining is one of the most widespread methods globally. During the preliminary development of the working, the coal seam is sectioned into panels divided by protective pillars. The pillars are necessary for maintaining the service life of underground mines, a highly productive stope, and personnel safety. In this work, we apply the finite-difference continuum damage mechanics approach to modeling the stress–strain evolution of the rock mass during the extraction of two adjacent longwall panels of an inclined seam. A new modification of the damage accumulation kinetic equation is proposed. The numerical-modeling approach accounts for an explicit number of numerous factors affecting the rock mass behavior. These factors are gravity forces, lithology, tectonic stresses, natural discontinuities, geotechnical, and mining parameters. When the model parameters are calibrated against the in situ observations, the results of the numerical-modeling approach provide a reliable basis for a pillar stability assessment. We build a structural model of a rock mass containing an underground working based on a simplified stratigraphy of the Kondomsky deposit, Kuznetsk coal basin, Russia. Based on the results of the numerical modeling, the stability of a pillar is analyzed. A new numerical technique extending the classical approach to the stability analysis is proposed and verified against the field data.

Despite extensive research, the question - what makes the fronts of plastic strain (e.g. Luders bands) propagate or remain still has not been solved yet. Therefore, the problem is acute for modern solid mechanics and physics. In this paper, an analysis of low-carbon steel plastic flow is carried out both numerically and experimentally. A microstructure-based finite-difference analysis is employed to provide a deeper insight into the emerging features of plastic flow. Low-carbon polycrystalline steel is chosen as the basic material for this investigation. A hand controlled iterative procedure based on the step-by-step packing method is utilized to design a representative volume element (RVE) of the low-carbon steel under study. The designed model represents a cluster of grains randomly distributed within the computational domain according to a certain law and randomly oriented with respect to the global coordinate system based on the results of EBSD study. A number of earlier reported models of plastic flow are combined and modified to study the yield plateau stage of the model samples. The mathematical model parameters are accurately calibrated against the experimental data using quite simple methods. The results of modeling satisfactorily meet the available experimental data and sufficiently complement them in terms of reproducing some regularities of plastic flow observed both at micro-and macrolevel. Relying on the numerical modeling data the conditions at the front of the Luders bands are discussed, which shed light on a possible mechanism of propagation.

Based on the results of a numerical experiment, the patterns of stress-strain state distribution of inhomogeneous rock massif in the vicinity of a worked-out area and development working, protected by a coal pillar, were revealed.

Numerical modeling of fault zone evolution and related seismicity can provide an insight into the process of large earthquake occurrences in a complicated fault system. In this paper, we develop a three-dimensional finite-difference numerical model of stress-strain evolution in and around the Chuya and Kurai depressions of Gorny Altai, Russia, to understand the fault zone evolution and the observed distribution of earthquakes in the region. Unlike in previous studies, the process of seismo-tectonic deformations of this region is addressed in a three-dimensional formulation with an improved model of rock massif behavior. A new geometrical model is designed, which is based on the seismotectonic, paleoseismological studies, and high-resolution Space-Radar-Topography-Mission data. The mathematical model applied here represents a set of partial differential equations, which are based on the fundamental conservation laws and constitutive equations for elastic and inelastic deformations. The initial stress state of the model is due to the action of gravity forces. The model is activated by assigning different displacement fields at the model boundaries – strike-slip and GPS-based displacements. The modeling results illustrate the stages of fault zone development and are in satisfactory agreement with the field observations in the case of GPS-based boundary conditions, which has not been modeled yet. Modeled seismic process is associated with the development of a fault zone resulting from the loss of strength in the subsurface points where the inelastic strain exceeds a certain threshold. The areas of high-degree of inelastic strain localization and the modeled fault zone represent an en-echelon system of dextral strike slips and various types of shear bands. The modeled seismic process obeys the Gutenberg-Richter (frequency-magnitude) law. The number of earthquakes in the attenuation part of the rock massif fracture process follows the Omori (aftershock decay) law.

In this paper, an analysis of the linear work hardening stage of plastic flow of low-carbon steel is carried out numerically. Unlike the yield plateau stage of plastic flow, much less attention is given to late stages of plastic flow, e.g. linear work hardening or parabolic work hardening. Late stages of plastic flow are interesting from the point of revealing the underlying mechanisms of fracture site formation. The non-uniform distribution of plastic strain is analyzed in both yield plateau and linear work hardening stages. Plastic strain localization features on the linear hardening stage are discussed based on the kinetic diagrams. A microstructure-based finite-difference analysis is employed. It is shown that maximums of plastic strain distribution stop their motion once the linear hardening stage is entered.

The processes of deformation and fracture of porous sandstones are studied by a 3D finite-difference analysis coupled with a continuous damage mechanics approach. The statistics of more than 100 samples is analyzed. The structure of the pore space is considered explicitly with an assumption of spherical pores distributed in the computational domain. The sample represents a dual-phase material while other structural features are disregarded. In contrast to numerous works, the piecewise linear function based on the Drucker-Prager criterion is used as the yield/damage envelope. The modification is related to different slopes for positive and negative semispaces of a stress space similar to the two-dimensional Haigh-Westergaard space. This allows for a more flexible validation of the model parameters against the experimental data. The method applied is based on an explicit dynamic formulation. Coupled with MPI algorithm, it allows using more than 20 million mesh elements and yields a sufficiently more smooth description of phase boundaries. The scalar damage parameter, which controls the features of damage accumulation and degradation of strength, is also modified. Special attention is paid to the stages of deformation of the samples, which are matched with the points of the complete stress-strain curve. Based on the results of numerical modelling, the threshold stresses of crack initiation σci, damage σcd, and peak σp are evaluated for samples with different porosities. The resulting values of the threshold stresses at different sample porosities and their failure patterns are in a satisfactory agreement with the experimental data and complement them.

A ZrO2 - 3.0mol%Y2O3 double-cantilever specimen with a chevron notch is manufactured to study the material toughening during a stable crack advancement. The shape of the resulting crack does not allow using the techniques currently available for the evaluation of the energy release rate. A recent publication reporting an experimental study of the deformation and fracture of the double-cantilever specimen subjected to wedging up to failure, in a contradiction with a typical brittle behavior of this material, has revealed a large nonlinear section in the loading diagram. In the present work, an FEM simulation-based approach is used to simulate the processes of deformation and fracture, and an interpretation of the experimental findings is provided. The Drucker-Prager yield criterion, modified for the purpose of this study, is employed as a part of the non-linear model, which reduces overcomplications in the constitutive response. All model parameters are validated against the experimental data obtained or those reported by other authors. The first law of thermodynamics is used for evaluation of the dissipated energy related to inelastic strain accumulation and crack propagation. The fracture toughness value obtained in numerical simulation is K-IC approximate to 5.45 MPa.m((1/2)). The results of numerical simulation are in a satisfactory agreement with our experimental data and in a good agreement with the other available data. An important finding for the engineering applications is that the fracture surface roughness has to be taken into account in evaluating the fracture toughness. Otherwise, the K-IC values would be overestimated because the real crack surface area is larger than its planar projection. For the material considered, the overestimation of K-IC is in the range of 8-10%.