The strain softening model of rock damage under compression and tension

Deformation and failure of brittle material under compression are different from those under tension. The differences are characteristic for the brittle material such as rock, concrete and others. At present, few constitutive models for rock can reflect the differences. A damage-induced softening model for rock constitutive relations is presented based on statistical strength theory, continuum damage mechanics and elastic mechanics. The model can consider properties of rock mechanics such as strain softening, difference in strength between compression and tension, non-liner stress-strain relation, compressive hardening, brittleness and so on. The model is well-adapted, simple and practical as it is flexible and has only 7 parameters which can be easily obtained from uniaxial test under compression and tension. Under triaxial compression, uniaxial compression and uniaxial tension, the stress-strain relations obtained from the presented model are compared with those obtained from laboratory tests. The comparisons show that the differences between results obtained respectively from the presented model and laboratory tests are small. The presented model is rational

Static and Dynamic Discrete Element Modelling of Slender Coal Pillars

Highwall mining is a mining method used in surface coal operations that involves driving a series of parallel entries into the exposed coal seam at the highwall face under an unsupported roof leaving behind a series of long, but very slender coal pillars. Highwall mining often occurs simultaneously with production blasting taking place in other areas of the mine. Although no failures of highwall pillars have been attributed to nearby blasting, numerical modelling presents an inexpensive means of investigating the possible effects of strong ground motion on the stability of these pillars. This thesis documents the development of a discrete element rock mass model and its application to the simulation of both static and fully dynamic highwall pillar simulations. The approach is geared toward parameter analysis and mechanism identification rather than exact prediction. Some conclusions are made regarding the potential effects of blast vibration on highwall coal pillars and general excavations in rock. The limitations of the modelling approach are discussed and suggestions for future research are proposed

Hydro-mechanical coupled behavior of brittle rocks: laboratory experiments and numerical simulations

‘Coupled process’ implies that one process affects the initiation and progress of the others and vice versa. The deformation and damage behaviors of rock under loading process change the fluid flow field within it, and lead to altering in permeable characteristics; on the other side inner fluid flow leads to altering in pore pressure and effective stress of rock matrix and flow by influencing stress strain behavior of rock. Therefore, responses of rock to natural or man-made perturbations cannot be predicted with confidence by considering each process independently. As far as hydro-mechanical behavior of rock is concerned, the researchers have always been making efforts to develop the model which can represent the permeable characteristics as well as stress-strain behaviors during the entire damage process. A brittle low porous granite was chosen as the study object in this thesis, the aim is to establish a corresponding constitutive law including the relation between permeability evolution and mechanical deformation as well as the rock failure behavior under hydro-mechanical coupled conditions based on own hydro-mechanical coupled lab tests. The main research works of this thesis are as follows: 1. The fluid flow and mechanical theoretical models have been reviewed and the theoretical methods to solve hydro-mechanical coupled problems of porous medium such as flow equations, elasto-plastic constitutive law, and Biot coupled control equations have been summarized. 2. A series of laboratory tests have been conducted on the granite from Erzgebirge–Vogtland region within the Saxothuringian segment of Central Europe, including: permeability measurements, ultrasonic wave speed measurements, Brazilian tests, uniaxial and triaxial compression tests. A hydro-mechanical coupled testing system has been designed and used to conduct drained, undrained triaxial compression tests and permeability evolution measurements during complete loading process. A set of physical and mechanical parameters were obtained. 3. Based on analyzing the complete stress-strain curves obtained from triaxial compression tests and Hoek-Brown failure criterion, a modified elemental elasto-plastic constitutive law was developed which can represent strength degradation and volume dilation considering the influence of confining pressure. 4. The mechanism of HM-coupled behavior according to the Biot theory of elastic porous medium is summarized. A trilinear evolution rule for Biot’s coefficient based on the laboratory observations was deduced to eliminate the error in predicting rock strength caused by constant Biot’s coefficient. 5. The permeability evolution of low porous rock during the failure process was described based on literature data and own measurements, a general rule for the permeability evolution was developed for the laboratory scale, a strong linear relation between permeability and volumetrical strain was observed and a linear function was extracted to predict permeability evolution during loading process based on own measurements. 6. By combining modified constitutive law, the trilinear Biot’s coefficient evolution model and the linear relationship between permeability and volumetrical strain, a fully hydro-mechanical coupled numerical simulation scheme was developed and implemented in FLAC3D. A series of numerical simulations of triaxial compression test considering the hydro-mechanical coupling were performed with FLAC3D. And a good agreement was found between the numerical simulation results and the laboratory measurements under 20 MPa confining pressure and 10 MPa fluid pressure, the feasibility of this fully hydro-mechanical coupled model was proven

Tensile fracture mechanism of masonry wallettes parallel to bed joints: A stochastic discontinuum analysis

Nonhomogeneous material characteristics of masonry lead to complex fracture mechanisms, which require substantial analysis regarding the influence of masonry constituents. In this context, this study presents a discontinuum modeling strategy, based on the discrete element method, developed to investigate the tensile fracture mechanism of masonry wallettes parallel to the bed joints considering the inherent variation in the material properties. The applied numerical approach utilizes polyhedral blocks to represent masonry and integrate the equations of motion explicitly to compute nodal velocities for each block in the system. The mechanical interaction between the adjacent blocks is computed at the active contact points, where the contact stresses are calculated and updated based on the implemented contact constitutive models. In this research, different fracture mechanisms of masonry wallettes under tension are explored developing at the unit–mortar interface and/or within the units. The contact properties are determined based on certain statistical variations. Emphasis is given to the influence of the material properties on the fracture mechanism and capacity of the masonry assemblages. The results of the analysis reveal and quantify the importance of the contact properties for unit and unit–mortar interfaces (e.g., tensile strength, cohesion, and friction coefficient) in terms of capacity and corresponding fracture mechanism for masonry wallettes.This research received no external funding

Evaluating the effect of scale and heterogeneity on the mechanical behaviour of rock blocks

Rock block strength is a significant factor controlling the rock mass behaviour and the rock-support interactions in fractured rock masses. Especially when the design relies on discontinuum analysis, the adopted block properties are a dominant driver influencing the results. A series of 2D UDEC grain-based models were performed on samples of different sizes and qualities to simulate the results of lab- and block-scale experiments. The effect of pre-existing defects was simulated either in a smeared sense by adjusting the grain micro-properties or by explicitly modelling micro-Discrete Fracture Networks (DFN) that were previously generated within FracMan. Relationships that link the rock block strength with its volume and in-situ heterogeneity were proposed for the estimation of scaled Mohr–Coulomb and Hoek–Brown parameters. The UCS of blocks was expressed as a function of scale, defect intensity, persistence and strength. The quantified scale/condition dependant reduction of block strength was then linked with a block-scale Geological Strength Index parameter named micro GSI (mGSI). Special focus was also given on the selection of appropriate constitutive relationships and discontinuum modelling techniques when simulating tunnel-scale problems. For continuum blocks in-between DFNs the traditional Hoek–Brown approach does not capture realistic behaviours and the modified Damage-Initiation and Spalling-Limit approach is needed to predict the expected damage near the excavation boundaries. When blocks are simulated as a packing of grain elements, considerably reduced damage, stress relaxation and deformation is predicted as the Voronoi skeleton creates a well-interlocked structure that clamps the pre-existing joints. The research highlights that the estimation of representative block properties is of equivalent importance with the selection of appropriate modelling approaches

Chemically induced compaction bands: Triggering conditions and band thickness

International audienceDuring compaction band formation various mechanisms can be involved at different scales. Mechanical and chemical degradation of the solid skeleton and grain damage are important factors that may trigger instabilities in the form of compaction bands. Here we explore the conditions of compaction band formation in quartz- and carbonate-based geomaterials by considering the effect of chemical dissolution and grain breakage. As the stresses/deformations evolve, the grains of the material break leading to an increase of their specific surface. Consequently, their dissolution is accelerated and chemical softening is triggered. By accounting for (a) the mass diffusion of the system, (b) a macroscopic failure criterion with dissolution softening and (c) the reaction kinetics at the micro level, a model is proposed and the conditions for compaction instabilities are investigated. Distinguishing the micro-scale (grain level) from the macro-level (Representative Elementary Volume) and considering the heterogeneous microstructure of the REV it is possible to discuss the thickness and periodicity of compaction bands. Two case studies are investigated. The first one concerns a sandstone rock reservoir which is water flooded and the second one a carbonate rock in which CO2 is injected for storage. It is shown that compaction band instabilities are possible in both cases

Geometric Effect of Asperities on Shear Mechanism of Rock Joints

Three-dimensional tracking of changes of asperities is one of the most important ways to illustrate shear mechanism of rock joints during testing. In this paper, the changes of the role of asperities during different stages of shearing are described by using a new methodology for the characterization of the asperities. The basis of the proposed method is the examination of the three-dimensional roughness of joint surfaces scanned before and after shear testing. By defining a concept named ‘tiny window’, the geometric model of the joint surfaces is reconstructed. Tiny windows are expressed as a function of the x and y coordinates, the height (z coordinate), and the angle of a small area of the surface. Constant normal load (CNL) direct shear tests were conducted on replica joints and, by using the proposed method, the distribution and size of contact and damaged areas were identified. Image analysis of the surfaces was used to verify the results of the proposed method. The results indicated that the proposed method is suitable for determining the size and distribution of the contact and damaged areas at any shearing stage. The geometric properties of the tiny windows in the pre-peak, peak, post-peak softening, and residual shearing stages were investigated based on their angle and height. It was found that tiny windows that face the shear direction, especially the steepest ones, have a primary role in shearing. However, due to degradation of asperities at higher normal stresses and shear displacements, some of the tiny windows that do not initially face the shear direction also come in contact. It was also observed that tiny windows with different heights participate in the shearing process, not just the highest ones. Total contact area of the joint surfaces was considered as summation of just-in-contact areas and damaged areas. The results of the proposed method indicated that considering differences between just-in-contact areas and damaged areas provide useful insights into understanding the shear mechanism of rock joints.Hydro-Québec (FONCER-INFRA Grant