Linear Mohr Coulomb Criterion Research Articles

Crack propagation from 3-d surface fractures in pmma and marble specimens under uniaxial compression

To understand deeply the fracture mechanism of brittle rock material, the rock specimen containing combined flaws (two square holes and one pre-existing fissure) with seven different fissure angles is carried out the numerical simulation by RFPA2D. Numerically simulated results show a good agreement with the experimental results. The crack coalescence behavior of specimen containing combined flaws under uniaxial compression is summarized, which is closely dependent to fissure angle. The stable propagation of original cracks does not lead to a larger AE event, but the coalescence of new cracks causes a larger AE event. The peak strength of specimen containing combined flaws increases with the confining pressure. According to the linear Mohr–Coulomb criterion, the cohesion and internal friction angle of specimen containing combined flaws are obtained, which is found to take on a distinct nonlinear relation with the fissure angle. The accumulated AE events decreases as the confining pressure increases from 0 to 30 MPa, which results mainly from the restraining of higher confining pressures on the initiation and propagation of tensile cracks at the fissure tips and nearby double squares.

Yield and deformation of an assembly of disks subjected to a deviatoric stress loading

The deformation of an assembly of particles is examined using a discrete element method (DEM) numerical model. The particles are modeled as random-sized, rough, inelastic, circular two-dimensional disks. The simulations keep track of the displacements, velocities and contact forces of each particle in order to examine the local rearrangements of the particles during the deformation and to determine the bulk stress states. The behavior of cohesive materials can be examined by introducing tensile forces between particles. The tests are done by applying constant confining pressures on two parallel flexible boundaries and a constant displacement rate on the two other flat frictionless walls. During the loading, the axial stress on the moving walls reaches a peak value and afterwards remains essentially constant for large strains. Stress–strain curves are obtained for a large range of confining pressures. They show that the yield envelopes follow the linear Mohr–Coulomb criterion. The global angle of friction is determined for a large range of particle–particle friction angles and particle size distributions. It was found that the global friction angle φ cv increased with interparticle friction angle φ i for φ i<6°; for larger values of φ i, the global friction angle is essentially constant. As the spread in the particle size distribution increased, the magnitude of the internal angle of friction was found to increase for a given interparticle friction angle.

Ground Response of Circular Tunnel in Poorly Consolidated Rock

To study the surface-closure curve of a circular tunnel in poorly consolidated rocks, closed-form solutions for stresses and displacement near a circular opening subjected to a uniformly distributed external stress and internal pressure are obtained. An elastoplastic model incorporating the nonlinear Hoek-Brown criterion is used, as most poorly consolidated geomaterials display a nonlinear correlation for the strength curve. Because most existing closed-form solutions as such were obtained with a linear Mohr-Coulomb criterion, the proposed solution is compared to those results by the linear criterion to evaluate the possible effect of the linear assumption. It is concluded that the calculated results by the linear Mohr-Coulomb criterion may overestimate the surface closure in low normal stress, but underestimate the opening closure under high normal stress. For the nonlinear case, a comparison is also made between the results by using the associated flow rule for plastic deformation and by a nonassociated flow rule. It is shown, by comparing the calculated results with an experimental result, that a nonassociated flow rule should be used in general. It is suggested that a nonlinear yield criterion be used with a nonassociated flow rule to achieve an appropriate prediction for the opening surface-closure curve.

The effect of a nonlinear Mohr–Coulomb criterion on borehole stresses and damage-zone estimate

To investigate the possible error introduced by the assumption of a linear Mohr–Coulomb criterion on the stress distribution near a circular opening, a numerical approach is used to calculate both the damage-zone radius and the stresses near a circular opening. A general solution procedure for the stress calculation under a uniform far-field loading is presented and a closed-form solution for the near-opening stresses is given for a cohesionless medium. Based on the numerical results calculated, it is concluded that the linear assumption is acceptable for a strong rock with an unconfined compressive strength that is of similar magnitude to the far-field stress. However, the tangential stress calculated with this linear assumption may be overestimated, but the damage zone may be underestimated in weaker rock or soil such as an oil sand formation. Key words : Mohr–Coulomb criterion, circular opening, nonlinearity, oil sands, Gauss–Legendre method.

The Mechanical Behavior of Uncased Wellbores Situated in Elastic/Plastic Media Under Hydrostatic Stress

Abstract Analytical consideration is given to the elastic/perfectly plastic behavior of uncased wellbores that are situated in rock formations subjected to hydrostatic states of field stress. Plane strain is assumed, and the rock is supposed to be Plane strain is assumed, and the rock is supposed to be incompressible and to obey the linear Mohr-Coulomb criterion of plastic yield. Using elasticity and plasticity theories, equations are developed to plasticity theories, equations are developed to permit calculation of the wellbore pressure required permit calculation of the wellbore pressure required to prevent plastic yielding of an uncased wellbore wall and of the magnitude of the wall deformation if plastic yielding does occur. The state of induced stress corresponding to the development of a plastic annulus of circular shape around the wellbore is obtained. From analytical results, plastic instability and collapse of a wellbore are discussed. In general, the calculations for the pressures required to prevent plastic yielding and potential instability of wellbores plastic yielding and potential instability of wellbores are quantitatively reasonable. Introduction The mechanical behavior of an uncased wellbore situated at depth in a highly deformable rock medium is an important topic. In the usual drilling situation, the mud column exerts a fluid pressure on the wall of the wellbore, while the undisturbed rock formation is subjected to an interstitial-fluid pore pressure and a natural state of field stress. As a consequence of the fluid pressures and the natural field stress, the state of induced stress in the rock formation immediately adjacent to the wellbore may be of sufficient magnitude to cause plastic yielding of rock. If deformation results in a noticeable contraction of the wellbore, the motion of the drill bit may be restricted, or the emplacement of the casing after drilling ceases may be hampered. If the deformation results in a large expansion of the wellbore, the rock formation may fracture and result in lost circulation. Ideally, knowing the range of drilling mud weights that could be utilized for particular depth-rock formation combinations particular depth-rock formation combinations without causing plastic deformation of the wellbore wall would represent an important contribution to drilling technology. The deformational behavior of underground openings has been of considerable interest to the mining industry. Fenner, Labasse and Morrison and Coates have obtained analytical solutions for the states of stress around vertical- and horizontal-cylindrical openings situated in elastic/perfectly plastic, cohensionless media that obey the Coulomb failure criterion. The analyses are generally extended to consider the influence of concrete or steel liners in the openings. Pasley and Coates have considered analytically the state of stress induced by the flow or interstitial pore fluid into a wellbore for the case in which pore fluid into a wellbore for the case in which the field stress is uniform and the rock obeys the Mohr-Coulomb failure criterion. The rock strength required to prevent the initiation of plastic failure is related to the formation pore pressure and the extent of plugging around the wellbore. The wellbore deformation problem is very complex in that the deformations are usually nonlinear and time-dependent, and the virgin field stresses are nonuniform. We considered the deformations to be large, but not time-dependent, and assumed the natural field stress to be of a hydrostatic nature. The rock is taken to be isotropic and homogeneous and to obey the linear Mohr-Coulomb criterion at yield. In the rock formation adjacent to the wellbore, the deformation parallel to the wellbore axis is assumed to be negligible as compared to the radial deformation of the wellbore wall. Under these assumptions, it is possible to determine the range of mud weights required to prevent the initiation of plastic yielding at the wellbore wall and to obtain a reasonable estimate of the magnitude of the wall deformation should yielding occur, as well as the extent of the plastic region around the wellbore. By utilizing the results of these considerations, the potential instability of a wellbore, involving collapse, can be discussed with some degree of competence.