Nonlinear Mohr-Coulomb Failure Criterion Research Articles

Calculation Method for Active Non-limit Earth Pressure of Cohesive Soil on a Rigid Wall Based on the Nonlinear Mohr–Coulomb Failure Criterion

Calculation Method for Active Non-limit Earth Pressure of Cohesive Soil on a Rigid Wall Based on the Nonlinear Mohr–Coulomb Failure Criterion

Seismic Bearing Capacity of Strip Footing with Nonlinear Mohr–Coulomb Failure Criterion

Many published studies on seismic conditions have focused on a pseudostatic method with a linear Mohr–Coulomb failure criterion. However, the pseudostatic method ignores the influence of time and spatial variables on seismic accelerations, and almost all soils have nonlinear strength properties rather than linear properties. Herein, a new approach was established for calculating the seismic bearing capacity that considers a linear distribution of the seismic coefficients. A nonsymmetrical failure mechanism and the nonlinear Mohr–Coulomb failure criterion were used to describe the collapse process and soil properties. A layerwise summation method was developed to calculate the work rates because the pseudodynamic method depicts the variation in seismic acceleration as well as the time and spatial variables. In this work, a first application for calculating the seismic bearing capacity of soil foundations with nonlinear strength properties was conducted using the kinematic approach of limit analysis. Based on the numerical results and discussions, the key conclusions were as follows: (1) the reliability of this approach was verified by making exact comparisons with theoretical results and lab data; (2) in general, nonlinear solutions were more conservative than linear solutions; and (3) a high value of initial cohesion c0 resulted in an increase in the seismic bearing capacity qlim, and qlim decreased when the ratio of tensile strength σt to initial cohesion c0 or the value of nonlinear parameter m increased for a given value of initial cohesion c0.

Three-Dimensional Upper Bound Limit Analysis of Tunnel Stability with an Extended Collapse Mechanism

A three-dimensional collapse mechanism that can consider a combined collapse of the tunnel roof and the side walls is proposed in this work. The three-dimensional upper bound support pressure is formulated with the power balance principal in the upper bound theorem. The nonlinear Mohr-Coulomb failure criterion is used to replace the commonly used linear MohrCoulomb failure criterion. The method has been validated by a series of examples, in which the three-dimensional collapse mechanism and support pressures are in a good agreement with the numerical results and solutions found in the literatures. Furthermore, sensitivity analyses of the geotechnical and geometrical parameters on the support pressure are conducted and the collapsing range is measured. The results show that a higher value of nonlinear failure coefficient, tensile strength, initial cohesion and tangential internal friction angle can increase tunnel stability, while tunnel stability is threatened by a higher value of burial depth, unit weight, tunnel width and height. The predicted collapse range increases noticeably with the increase of the nonlinear coefficient. This study is of great significance for predicting the three-dimensional safety support pressure and collapse mechanism of tunnel.

Study on stability of reinforced soil slope based on upper limit method

Based on the nonlinear Mohr-Coulomb failure criterion, the upper bound method of limit analysis is used to investigate slope stability by introducing new strength parameters ct and φt. It is assumed that the potential weak zone in the soil layer is a straight line, so the straight line fracture surface is used to study the non-reinforced soil and reinforced soil in this study, and the expression of the stability coefficient Ns of the non-reinforced soil slope is derived. In addition, the calculation equations of the safety factor F, the ultimate slope height H, and the ultimate slope height H of the reinforced soil slope are also derived. The CVX toolbox developed by Stanford University and a MATLAB program developed by the authors are used for illustrations, and good results are obtained. The relationship between the nonlinear parameter m and the limit slope height H, the included angle θ, the new strength parameter φt, the slope stability coefficient Ns, the relationship between the slope angle β and the safety factor F, and the relationship between different reinforcement tensile strength Kt and the limit slope height H are summarized.

Active lateral earth pressure of geosynthetic-reinforced retaining walls with inherently anisotropic frictional backfills subjected to strip footing loading

In this paper, a detailed numerical study is conducted to evaluate the lateral earth pressure acting on geosynthetic-reinforced retaining walls with an anisotropic granular backfill subjected to strip footing loadings. To this end, the well-established lower bound theory of limit analysis coupled with the robust second order cone programming (SOCP) and the finite element discretization method is exploited and implemented in the stability analysis of reinforced retaining structures. For the finite element limit analysis, a number of constraints associated with the lower-bound axioms are satisfied, including element equilibrium, discontinuity equilibrium, boundary conditions and the yield criterion enforcement. By adopting second-order cone programming (SOCP) optimization, the nonlinear Mohr-coulomb failure criterion is simulated using three nodal auxiliary variables defined as functions of nodal stresses generated at each point. In addition, the primal-dual interior-point algorithm is adopted to gain the optimal solution for the unknown stress variables in the SOCP optimization problem. Accordingly, the contribution of soil inherent anisotropy to the influence ofa number of parameters on the lateral earth pressure is thoroughly examined. It was observed that as the anisotropy ratio increases (the horizontal friction angle decreases) and the number of reinforcement layers decreases, the coefficient of active earth pressure increases in all cases of geosynthetic-reinforced retaining structure. Decreasing the number of reinforcement layers in the retained backfill will be translated into an equivalent softened material; hence, increasing the active earth pressure coefficient. In addition, the increase in the anisotropy ratio leads to the overall decrease in the shear strength of the backfill soil, causing the retaining structure to reach the limit state earlier at smaller displacements, thus giving rise to the increase in the coefficient of active lateral earth pressure. The rate of increase in the coefficient of active earth pressure with anisotropy ratio grows with the increase in the foundation width and load intensity and the decrease in the foundation-wall distance.

Active Stability Analysis of 3D Shallow Tunnel Face with Longitudinally Inclined Ground Surface Based on Nonlinear Mohr–Coulomb Failure Criterion

Abstract The longitudinally inclined (the tunnel excavation direction) ground surface often appearing at the shallow tunnel entrance and exit zone threatens and reduces the tunnel face stability. H...

Analysis of tunnel face stability with non-linear failure criterion under the pore water pressure

In this work, the stability of a shield tunnel face under pore water pressures is examined by combining the non-linear Mohr-Coulomb failure criterion in the framework of the kinematic approach of limit analysis. The non-linear Mohr-Coulomb failure criterion represented by the tangent technique in combination of the pore water pressure distribution calculated by the mesh dividing optimization technology are incorporated into the 3D rotational failure mechanism to assess the critical support pressure of a tunnel face for the first time. Based on the proposed method, parametric studies are performed by giving design charts to study the effect of model parameters on the calculated critical support pressure. In these charts, comparisons with results from the linear Mohr-Coulomb failure criterion are used to verify the proposed method. Finally, the influence of the non-linear coefficient on the feature of the 3D rotational failure mechanism is presented.

Face stability analysis for a shield-driven tunnel with non-linear yield criterion

The aim of this work was to investigate the face stability of a tunnel driven by a pressurised shield for cases of collapse failure and blow-out failure based on the kinematic approach of limit analysis. For the analyses, the soil material was assumed to follow the non-linear Mohr–Coulomb failure criterion. Advanced rotational failure mechanisms were applied to the face stability analysis. The numerical results, optimised using Matlab, were close to the existing solutions, proving that this approach is reliable. The influences of two parameters (the tunnel buried depth C and the initial cohesion co) on the critical support pressures and the shapes of the failure mechanisms for collapse failure and blow-out failure were investigated. The results of the collapse failure and blow-out failure showed that the critical support pressures and the shapes of failure mechanisms were significantly influenced by these parameters and the non-linear failure criterion should be considered in practice to improve the accuracy of the critical support pressures.

A limit analysis of the ultimate pullout capacity of a shallow horizontal strip anchor plate embedded in slope

Aiming at calculating the ultimate pullout capacity of a shallow horizontal strip anchor plate embedded in complicated topographical regions, e.g., mountainous areas, a kinematic admissible velocity field of the curved failure mechanism is constructed for the shallow horizontal strip anchor plate embedded in slope, based on the upper bound limit analysis theorem, the nonlinear Mohr-Coulomb failure criterion as well as the associated flow rules. The ultimate pullout force and failure mechanism are deduced using the variation minimum principle. Influences of the inclination angle and embedded depth on the ultimate pullout force are discussed in detail. The results show that the ultimate pullout force of the anchor plate decreases with the increasing inclination angle and the failure planes of the above ground are no longer symmetrical with an obvious shifting to the down side of the slope. Along with the increasing embedded depth, the ultimate pullout force of the anchor plate increases with a larger failure scope of the above ground. The inclination angle has a greater impact on the ultimate pullout force of the anchor plate with a smaller embedded depth. This effect should be taken into account for reasonably characterizing the ultimate bearing feature of a shallow horizontal strip anchor plate embedded in slope.

Seismic stability of 3D soil slope reinforced by geosynthetic with nonlinear failure criterion

This work conducts a seismic stability of a three-dimensional (3D) geosynthetic-reinforced slope in soils following the linear and nonlinear Mohr-Coulomb failure criterion. Three categories of reinforcement distribution patterns and four kinds of clays are considered. Within the framework of limit analysis and the generalized tangent technique, expressions of required reinforcement strength and the stability factor under different distribution patterns are derived from the energy balance equations. Comparisons are conducted to verify the validity of new expressions. Parametric analysis is conducted to explore the impacts of seismic force, soil strength nonlinearity, 3D character of slope and reinforcement strength on slope stability. It is found from the results that the downwardly-strong triangular (DTD) distribution pattern is the most effective choice for slope reinforcement, while the upwardly-strong triangular (UTD) pattern is the worst. One should intensify the density of reinforcement layers at the bottom of the slope to achieve a better slope stability condition. Besides, soil strength nonlinearity and seismic forces both have non-negligible negative effects on slope stability.

Variation analysis of ultimate pullout capacity of shallow horizontal strip anchor plate with 2-layer overlying soil based on nonlinear M-C failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and an associated flow rule, a kinematic admissible velocity field of failure mechanism of the 2-layer soil above a shallow horizontal strip anchor plate is constructed. The ultimate pull-out force and its corresponding failure mechanism through the upper bound limit analysis according to a variation principle are deduced. When the 2-layer overlying soil is degraded into single-layer soil, the model of ultimate pullout force could also be degraded into the model of single-layer soil. And the comparison between results of single-layer soil variation method and those calculated by rigid limit analysis method proves the correctness of our method. Based on that, the influence of changes of geotechnical parameters on ultimate pullout forces and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are analyzed. The results show that the ultimate pull-out force and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are affected by the nonlinear geotechnical parameters greatly. Thus, it is very important to obtain the accurate geotechnical parameters of 2-layer soil for the evaluation of the ultimate pullout capacity of the anchor plate.

Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules, the three-dimensional (3-D) axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity (UPC) is determined. A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory. By using difference principle, the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained. The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied. The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor, surface overload, initial cohesion, geomaterial density and friction angle increase. The failure surface is similar to a symmetrical spatial funnel, and its shape is mainly determined by dimensionless parameter m; the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density. As the dimensionless parameter m=2.0, the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution. In addition, the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.

Three-dimensional limit analysis of seismic stability of tunnel faces with quasi-static method

Based on the existing research results, a three-dimensional failure mechanism of tunnel face was constructed. The dynamic seismic effect was taken into account on the basis of quasi-static method, and the nonlinear Mohr-Coulomb failure criterion was introduced into the limit analysis by using the tangent technique. The collapse pressure along with the failure scope of tunnel face was obtained through nonlinear limit analysis. Results show that nonlinear coefficient and initial cohesion have a significant impact on the collapse pressure and failure zone. However, horizontal seismic coefficient and vertical seismic proportional coefficient merely affect the collapse pressure and the location of failure surface. And their influences on the volume and height of failure mechanism are not obvious. By virtue of reliability theory, the influences of horizontal and vertical seismic forces on supporting pressure were discussed. Meanwhile, safety factors and supporting pressures with respect to 3 different safety levels are also obtained, which may provide references to seismic design of tunnels.

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem. The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule. The multipoint tangent (multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion. A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique, and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming. The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule, which demonstrates the rationality of the presented method. Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique. The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis. The combined effect of nonlinearity and dilation on slope stability was analyzed, and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

Effect of the vertical earthquake component on permanent seismic displacement of soil slopes based on the nonlinear Mohr–Coulomb failure criterion

In the present study, a model is developed to calculate the upper bound of the seismic displacement of a slope based on the sliding rigid block model. In this model, it is assumed that the geotechnical materials satisfy the nonlinear Mohr–Coulomb (M–C) failure criterion, and the instantaneous shear strength parameters are introduced by the “external tangent method”. A sequential quadratic program, based on the nonlinear iteration procedure, is also employed to obtain the optimal solution for the objective function. Using the upper bound method and the Newmark sliding rigid block model, the effect of the vertical earthquake component on the permanent displacement of slopes is studied under the following two conditions: (1) It is assumed that the vertical acceleration is in phase with the horizontal acceleration; (2) Actual vertical ground motion records are used (i.e., the vertical and horizontal accelerations are mutually independent). The results show that the nonlinear parameter m significantly affects the permanent displacement of slopes, and that the effect of the vertical earthquake component on permanent displacement cannot be ignored. The impact of the vertical earthquake component on slope stability will be overestimated if the vertical acceleration is in phase with the horizontal acceleration.

Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion

Based on nonlinear Mohr-Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr-Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr-Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5 to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels, appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.

Ice rubble behaviour and strength: Part II. Modelling

Part I of this paper reviews ice rubble testing methods and the interpretation of test results. The present Part II elaborates on the modelling of ice rubble behaviour and strength. A pseudo-discrete continuum model is presented as a tool to study ice rubble behaviour (2D) in the primary failure mode that is associated with breakage of the initial skeleton. A non-linear Mohr–Coulomb failure criterion is proposed to describe the secondary failure mode of ice rubble.

Analysis of Behavior of Sand Surrounding Pile Tips

A finite-element approach is presented to predict the behavior of dense sand surrounding the pile tip in a fairly large stress range, from low stress levels to very high ones, where particle breakage occurs. The approach is based on a constitutive model for sand, which is characterized by critical-state–type yield surfaces and by a nonlinear Mohr-Coulomb failure criterion, the latter being defined on the basis of constant-volume shear strength and of dilatancy. In addition, the concept of constant relative breakage surfaces, which represent families of curves characterized by constant amounts of particle crushing, is introduced. It is shown that the model, applied to the analysis of the behavior of the tip of nondisplacement piles in sand, can be used to visualize and to predict the distribution of strength, dilatancy, and grain breakage in the soil surrounding the pile base.