Mohr—Coulomb failure criterion

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... 

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...

Assumptions of the model (a) plane stress state, (b) The surrounding rocks are uniform and elastic isotropic materials, (c) the fault is assumed as contact element with no thickness., and (d) Mohr-Coulomb failure criterion is chosen for rocks. 

The Geogrid was modeled as linearly elastic-perfectly plastic material with Mohr-Coulomb failure criterion. The axial stiffness (J) and the tensile strength (T) were needed in the program and taken J = 620 kN/m and T = 70 kN/m, respectively. The interaction coefficient between the geogrid and cohesive backfill was taken 0.7. 

In this instance, it seems difficult for students to grasp plastic soil behaviour. The Mohr-Coulomb failure criterion, when looked at superficially, makes most students perceive the soil crumbles immediately after reaching the shear strength. When dilatancy is included, it is, thus, more difficult for them to foresee what is occurring within the soil. 

The limit equilibrium methods forming the framework of slope stability/instability analysis generally accept the Mohr-Coulomb failure criterion, which can be expressed in terms of effective or total stresses. The Mohr-Coulomb shear strength in terms of effective stresses is as follows ... 

According to the Mohr-Coulomb failure criterion (Scholz 2002 Zoback 2007), shear stress on an activated fault must exceed critical value t, which is calculated from cohesion C, fault friction li and effective normal stress cr ... 

Earthquake Mechanisms and Stress Field, Fig. 6 Mohr-Coulomb failure criterion. The red area shows all possible orientations of fault planes which satisfy the Mohr-Coulomb failure criterion. The blue dot with shear and normal stresses Xc and Oc denotes the principal fault plane which is optimally oriented with respect to stress, and C denotes the cohesion... 

If the Mohr-Coulomb failure criterion is satisfied (red area in Fig. 6), the fault becomes unstable and an earthquake occurs along this fault. The higher the shear stress difference. At = t, the higher the instability of the fault and the higher the susceptibility of the fault to be activated. A fault most susceptible to failure is called the principal fault (Vavrycuk 2011a) being defined by the point in which the Mohr-Coulomb failure criterion touches the Mohr s circle diagram (blue point in Fig. 6)... 

Fig. 12 Example of data used in numerical tests of stress inversions. The plots show 200 noise-free focal mechanisms selected to satisfy the Mohr-Coulomb failure criterion. Left/right plots - dataset with a full/ reduced variety of focal mechanisms, (a, b) Mohr s circle diagrams, (c, d) P/T axes and (e, f) corresponding nodal lines. The P axes are marked by the red circles and T axes by the blue crosses in (c) and (d). The tti,

Numerical tests performed with sets of 25-250 focal mechanisms are presented. The stress tensor is fixed for all datasets. The focal mechanisms are selected to satisfy the Mohr-Coulomb failure criterion (see Fig. 12a, b) and subsequently they are used for the calculation of moment tensors. The moment tensors were contaminated by uniform noise ranging from 0 to 50 % of the norm of the moment tensor (calculated as the maximum of absolute values of the moment tensor eigenvalues). The noisy moment tensors were decomposed back into strikes, dips and rakes of noisy focal mechanisms inverted for stress. The deviation between the true and noisy fault normals and slips attained values from 0° to 25°... 

Strength parameters (adhesion and friction angle) can be obtained as described in a traditional geotechnical manner using an adapted form of the Mohr—Coulomb failure criterion (Eq. [15.1]) ... 

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