Mohr-Coulomb criterion

A more sophisticated model can be built from the Drucker-Prager s cone by introducing a dependence on the Lode s angle /I, in order to match more closely the Mohr-Coulomb criterion. It consists of a smoothed Mohr-Coulomb plasticity surface. The formulation based on the idea of Van Eekelen (1980) is used. It can be written in a very similar way to the Drucker-Prager s criterion ... 

The Mohr-Coulomb criterion is used to represent the shear failure of coal. In the modelling studies, after yielding has occurred, the total strain is assumed to consist of three components the elastic, plastic and damage components. 

According to the Mohr-Coulomb Criterion and Terzaghi s effective stress principle, the maximum equilibrium pore pressure can be derived as... 

This step is carried out in several stages, the first being to fit the macroscopic elastic parameters (Young s modulus and Poisson s ratio), followed by fitting the parameters of plastic behaviour (cohesion and friction angle for the Mohr-Coulomb criterion used in the present paper). 

FLAG has several built-in material behavior models. The failure of rock material is assumed to follow the Mohr-Coulomb criterion as illustrated in Fig. 4 which is used for materials that yield when... 

The calculation model of two-dimensional model, considering the angle of coal seam, set up as shown in Figure 1 and trapezoidal model, a total of 2800 mesh, 5858 nodes. The stress boundary condition, the model surface applied uniform vertical compressive stress, the model under the surface of the vertical displacement fixed. The calculation of the model using Mohr—coulomb criterion is used as a rock mass failure criterion (Qian et al. 1991, Li et al. 2000). 

The Mohr-Coulomb criterion is regarded as coal yield condition. 

Lund, A. C. and Schuh, C. A. (2004) The Mohr-Coulomb criterion for unit shear processes in metallic glasses, Intermetallics, 12, 1159-1165. 

The scalar quantities and p are given by (in order to make Drucker-Prager circle coincide with the outer apices of the Mohr-Coulomb criterion in the deviatoric plane (Owen and Hinton 1986))... 

The relations between failure deviatoric stress Oj O3 and plastic strain Ep under different confining pressures are shown in Figure 8, which shows that under constant confining pressure, failure stress decreases with accumulation of Ep. Mohr-Coulomb criterion is used as failure criterion. 

The geotechnical material was shear failure mainly, and it was adapted to Mohr-Coulomb criterion. Its shear strength was determined by the cohesion (c) and internal friction angle ( ). The limit condition might be reached by decreased the shear strength of material in SRM. It was expressed as follows ... 

It is therefore common to assume that the state variables that describe the rapid deformation response of granular materials would border on the parameters that describe the behavior of fluids and Coulomb type dissipation of energy (static). In view of the above it is common to find that the theories governing granular flow are formulated around the assumption of a continuum similar in some regard to viscous fluids however, the equilibrium states of the theories are not states of hydrostatic pressure, as would be in the case of fluids, but are rather states that are specified by the Mohr-Coulomb criterion (Cowin, 1974). The advantage of continuum formulations over alternative particulate (stochastic) formulations is that use of continuum is more capable of generating predictive results. Mathematically one... 

The yield stress of a material is a measured stress level that separates the elastic and inelastic behavior of the material. The magnitude of the yield stress is generally obtained from the results of a uniaxial test. However, the stresses in a structure are usually multiaxial. A measurement of yielding for the multiaxial state of stress is called the yield criterion. For example, the Mohr-Coulomb criterion, the Buyukozturk criterion, and the Drucker-Prager criterion are common yield criteria for concrete, and the von Mises criterion is the widely used yield criterion for steel. 

Mohr-Coulomb Failure Criterion and Coulomb Powders... 

The most common failure criterion for granular materials is the Mohr-Coulomb failure criterion. Mohr introduced his theory for rupture in materials in 1910. According to his theory, the material fails along a plane only when a critical combination of normal and shear stresses exists on the failure plane. This critical combination, known as the Mohr-Coulomb failure criterion, is given by... 

The Mohr-Coulomb failure criterion can be recognized as an upper bound for the stress combination on any plane in the material. Consider points A, B, and C in Fig. 8.4. Point A represents a state of stresses on a plane along which failure will not occur. On the other hand, failure will occur along a plane if the state of stresses on that plane plots a point on the failure envelope, like point B. The state of stresses represented by point C cannot exist since it lies above the failure envelope. Since the Mohr-Coulomb failure envelope characterizes the state of stresses under which the material starts to slide, it is usually referred to as the yield locus, YL. 

So far, we understand that the flowability of powders depends on their failure stresses from the Mohr-Coulomb failure criterion. Therefore, analyses of powder flows... 

Eq. (8.24), and the modified Mohr-Coulomb yield (or failure) criterion, Eq. (8.27). It should be noted that other yield criteria, such as the von Mises criterion, are used to model the flow of bulk solids in hoppers, and more conditions may need to be imposed, such as the Levy flow rule, in order to close the system of equations [Cleaver and Nedderman, 1993],... 

For these calculations, three different material models were investigated a linear elastic, an elasto-brittle, and elasto-plastic ubiquitous joint model. The ubiquitous joint, elasto-plastic model, is defined by a two-dimensional yield criterion, composed of two Mohr-Coulomb criteria, along two predefined directions characterised by their normal vectors ni and n2. 

This model is based on the mean features of the Mohr-Coulomb model and is expressed with stress invariants [Maleki (1999)] instead of principal stresses. Until plasticity is reached, a linear elastic behaviour is assumed. It is fully described by the drained elastic bulk and shear moduli. The yield surface of the perfectly plastic model is given by equation 7. Function 7i(0) is chosen so that the shape of the criterion in the principal stress space is close to the Lade criterion. 

LaRC 03 failure criterion The LaRC 03 failure criterion [12] consists of a family of six criteria. It is an extension of the Puck [11] and Hashin [13] failure criteria. Like the Puck criterion, it focuses on the fiacture plane that is determined by maximizing the Mohr—Coulomb stresses. In the LaRC 03 criterion, failure due to matrix compression is the result of local interaction of shear stresses on a fracture plane. This perspective comes from soil mechanics situafions where the compression strength is different than the tension strength. It is parficularly useful in cases where, on a certain plane in the material, there are both normal and shear stresses acting. The interaction line that... 

The failure envelope /(CTi (J3) = 0 is defined from point to i by the Mohr-Coulomb failure criterion /, = 0 with... 

Figure 4. Mohr-Coulomb failure criterion (FLAC3D...

The model calculation adopts the criterion of Mohr-Coulomb, and this yield criterion can be expressed as ... 

In accordance with the field sampling and rock mechanics test results, the rocks presented clear plastic deformation characteristics at different confining pressure conditions. In this paper, Mohr— Coulomb yield criterion was used to determine the... 

The idea of plastic yielding is also applied to granular materials, such as soils and powders. In this case, the shear stress required for deformation depends on the packing density, and the particle shape and surfaee characteristics. The shear resistance is commonly described by the Mohr-Coulomb yield criterion, i.e.. 

For a uniaxial compression test, determine the plane on which the maximum shear stress will occur for a material that obeys the Mohr-Coulomb yield criterion. Suggest an approach for measuring the material parameters (d>, Tq) in the Mohr-Coulomb yield criterion. (Hint construct the Mohr s circle (see Fig. 2.23) for various values of the normal stress.)... 

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