Mohr-Coulomb models

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. 

Linearly elastic-perfectly plastic Mohr-Coulomb model was used to model the preliminary fill, the sand cushion, and the RSW backfill. 

To obtain the proper initial geostatic stress state of the slope, static calculation is required before the dynamic analysis (Itasca Consulting Group, 1999). Two procedures are followed in the static calculation (a) set relevant mechanical parameters and take elastic model as material constitutive model, and then make the slope model balanced in gravity field (b) take Mohr-Coulomb model as the material constitutive model (Yan et al., 2011) and reset cohesion and tensile strength to their initial value, and then rebalance the model. This is just the slope model on which the dynamic load will be applied. The contour plot of initial vertical geostatic stresses in the slope (Figure 3) reflects the vertical stress state in which no dynamic load is applied on the slope. 

An element of soil in the ground would be expected to have in situ stress such as point Kq. From this point, the simplest elastic-Mohr-Coulomb model gives the vertical stress path KqA for undrained behaviour. Because the strength is limited by the effective stress angle of shearing resistance [Pg.39]

It should be noted that since the time of Nicoll Highway Plaxis have altered the advice given in their manual about modelling undrained behaviour. However, their use of the term Method A is different from that used in the Nicoll Highway inquiry. Plaxis include within this term the use of more advanced nonlinear models of soil behaviour, which may give better predictions of undrained stress paths. In the Nicoll Highway inquiry these were termed Method D , and Method A was used only to refer to elastic-Mohr Coulomb models. 

The properties adopted for finite element analysis are shown in Table 1, in which RS indicates residual soil and LST indicates limestone. Elastic-Mohr-Coulomb models were used for all the work described here. Further comments on the permeabilities shown in Table 1 are given below. 

It was noted above that Table 1 does not mention dilation, a difficult topic that many geotechnical engineers prefer to ignore. For Mohr-Coulomb models, Plaxis and SAFE allow angles of dilation it to be specified by the user with default values of zero and a limit to the total amount of accumulated dilation. For its default value, CRISP assumes normality, treating the yield surface as a plastic potential, which, for a Mohr-Coulomb model, implies it = cp. This is shown in Figure 19 by the vector of plastic strain increments (5yP) for the plane strain case. All the CRISP analyses reported here use it = shear strains become very large as shear failure occurs. 

For basic calculations, the FEM is not often used for settlement analysis. The use of Terzaghi s formula is often more straightforward. When using the FEM, the simple Mohr-Coulomb model (hnear elastic-plastie) should not be used for a reliable prediction of the deformations. 

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. 

Each block is modeled as linear, isotropic, homogeneous and elastic medium and subdivided with a mesh of constant-strain triangle finite-difference elements. Key factors affecting the hydraulic behaviour of fractures such as opening, closure, sliding and dilation of fractures are modeled by an elasto-perfectly plastic constitutive model of a fracture. A step-wise non-linear normal stress-normal closure relationship is adopted with a linear Mohr-Coulomb failure for shear (Figure 3). 

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. 

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

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). 

Finn (1966) presented an analysis of the earthquake stability of an infinite cohesive slope shown in Figure 11.22. This analysis used a Bingham model incorporated in a Mohr-Coulomb failure criteria. Based on this analysis the minimum acceleration coefficient ky to cause yielding of the slope in a c-( ) material is given by the following equation ... 

In the following example we illustrate the first type of use of the second thermodynamic principle discussed in Section 6, namely, by verifying a constitutive model of EPS geofoam a posteriori for thermodynamic consistency. This model was developed by the authors (Wong and Leo, 2006) based on experimental results from a series of standard "drained" tiiaxial tests. It initially adopted the Mohr-Coulomb yield function used widely in soil mechanics but upon further testing with a true triaxial apparatus (Leo et al., 2008), a Drucker-Prager type yield function was subsequently preferred. This is written as ... 

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. 

The constitutive model of rock masses is Mohr-Coulomb criteria and the commercial numerical software (FLAC3D) is used. The mechanical parameters of rock masses are selected through back analysis of excavation process, and compared the simulated results and monitoring data of surrounding rock mass displacement. 

In this limit analysis of pile foundation, the ANSYS software was used. The finite element model was 1/4 body. The strength criterion of pile body material was linear elastic model, and the criterion of soils was Mohr-Coulomb equivalent area circle criterion. The mechanics characteristic of pile-soil interface was simulated by contact element. The contact surface behavior on the side of pile was the form of Rough. The contact surface behavior on pile toe was the form of No separation. 

Mohr-coulomb constitutive model is adopted in numerical calculation, calculation parameters are as shown in Table 2, strength reduction method is adopted to simulate collapse, namely for non collapsible soil, its parameters shall remain unchanged in calculation for collapsible soil, the parameters before immersion given in Table 2 are adopted to calculate initial stress and then it shall be used in conjunction with parameters after immersion ... 

Model materials the rock and soil mass in the slope is divided into two layers (Figure 2), and the relevant physical and mechanical parameters are listed in Table 1. The parameters are inverted from the drilling data, geophysical data and microtremor in situ testing result of the slope site, so as to guarantee the accuracy of numerical simulation. Mohr-Coulomb plastic model built in the software... 

Numerical analyses, most often using finite elements, are now more or less routine in ground engineering. Analyses of even simple problems often use numerical models that are more sophisticated than purely elastic and Mohr-Coulomb. Most importantly analyses should be validated by comparison with hand calculations and laboratory tests, by close examination of stress and strain paths in selected locations and other means. Validation of numerical analyses requires common sense, deep understanding of fundamental soil mechanics and ground behaviour but not necessarily high-level mathematics. 

The soft clays were modelled using effective stress parameters, assuming linear elastie behaviour bounded by a Mohr-Coulomb envelope t/s = sin

shear stress/normal stress diagram for plane strain, in which the Mohr-Coulomb envelope is marked, together with a typical effective stress path for undrained behaviour of a normally consolidated clay. This path reaches failure at point F on the Mohr-Coulomb envelope with undrained strength c . 

The elastic-plastic constitutive model for triaxial simulations is introduced to illustrate the Mohr-Coulomb strength criterion and dilatancy. Figure 11 shows the soil model for the simulation of a displaeement-controlled drained triaxial test, where total stresses from the previous isotropic compression are taken as initial conditions. A vertical displacement... 

---