Strain-softening Mohr Coulomb Research Articles

Similarity Solutions for Spherical Cavity Expansion in Strain-Softening Soils and its Application in Cone Penetration Test

The cavity expansion theory is commonly employed to predict the grouting pressure and cone penetration resistance. However, existing theoretical solutions for cohesive-frictional soils with dilation fail to simultaneously consider both the elastic deformation in the plastic zone and strain-softening behaviour of soils. To address this limitation, a similarity solution was derived for the expansion of spherical cavities from a zero initial radius with an initial confining pressure in strain-softening Mohr–Coulomb materials. The results demonstrate good agreement with previous theories, predicting an ultimate pressure higher than that obtained by neglecting elastic deformation in the plastic zone but lower than that calculated by neglecting softening characteristics. Moreover, several influential factors affecting the radius of the plastic zone and ultimate pressure were meticulously examined. On-site cone penetration test data and the theoretical results showed notable agreement. This indicates that the proposed solution exhibits a better conformance with the field data than do the previous solutions.

Progressive Failure Analysis of Soil Slope with Strain Softening Behavior Based on Peridynamics

In this study, the nonlocal, nonordinary state-based peridynamics (NOSBPD) is introduced as a novel regularization technique to study the strain localization and progressive failure of soil slopes due to strain softening behavior. The NOSBPD formulations are introduced first, and then the strain-softening Mohr–Coulomb model is incorporated into the nonlocal framework. The implicit formulations of the nonlinear NOSBPD model under the plane strain condition combined with the energy dissipation-based arc-length method to avoid the limitations of the force and displacement control in the nonlinear analysis are given. Numerical examples, including the plane strain biaxial experiments and slope models, validate the effectiveness of the proposed method in terms of alleviating mesh sensitivity. The results show that this nonlocal method can remove the mesh dependence, and the localized shear band is related to the nonlocal parameter δ. The proposed method involves being able to capture strength mobilization in different parts of the sliding surface during the progressive failure process of the soil slope. It can avoid the dilemma that the peak strength is too dangerous and the residual strength is too conservative due to the rigid body assumption in the limit equilibrium method.

Numerical modelling of laterally loaded piles driven in low-to-medium density fractured chalk

Chalk’s sensitive, variable nature poses difficulties for foundation designers. It can present as weak rock and yet be de-structured to very weak putty by dynamic or high-pressure loading. The development of multiple offshore wind farms at north European chalk sites led to the recent ALPACA Joint Industry Programme, which undertook intensive material characterisation and large-scale field testing at St Nicholas at Wade (SNW), Kent, UK to capture and better understand the behaviour of piles driven in fractured low-to-medium density chalk. Noting that lateral loading response is a vital design concern for monopile and jacket supported structures, this paper focuses on 3D Finite Element (FE) modelling of ALPACA’s monotonic lateral loading field tests on open-ended driven tubular steel piles. The brittle chalk is modelled with a strain-softening Mohr-Coulomb model combined with nonlocal regularisation, calibrated meticulously against the ALPACA characterisation dataset. A second, simpler modelling approach, adopting a perfectly-plastic Mohr-Coulomb model, is also explored as a simplified practical alternative. Both approaches can match field lateral capacity and bending moment distributions, after taking due account of pile installation and chalk fracturing effects. The analyses indicate how robust, accurate and cost-effective lateral loading design may be approached for low-to-medium density fractured chalks.

A simple method to reduce mesh dependency in modelling landslides involving brittle soils

This paper focuses on the numerical simulation of the deformation processes occurring in the slopes when soils with strain-softening behaviour are involved. In these circumstances, a progressive failure may occur with the consequent motion of the unstable soil mass in the post-failure stage. This problem can be only solved using advanced numerical techniques capable also of accounting for the occurrence of large deformations. However, the solution is generally mesh dependent and may be affected by lack of convergence. In this study, the material point method is employed to simulate the occurrence of large deformations, in conjunction with a strain-softening Mohr–Coulomb constitutive model, in which the shear strength parameters are reduced as a function of the accumulated deviatoric plastic strain, and a model parameter controlling the rate of strength decrease. To evaluate this parameter and to reduce the effects of the mesh dependency on the numerical solution, a novel procedure based on the results of direct shear tests is presented. This methodology is completely analytical and requires few parameters with a clear physical meaning and of simple experimental determination. Some simulations are performed to assess the reliability of the proposed procedure.

Analysis of an excavation-induced landslide in stiff clay using the material point method

The results of an analysis concerning a landslide occurred in Calabria (Southern Italy) in 2014 are presented. This landslide was triggered by some excavations carried out at the slope toe to allow the construction of a power plant. Failure developed mainly within a thick layer of stiff clay that experienced a pronounced strain-softening behaviour during the laboratory tests. The landslide involved some gabion walls and a sheet-pile wall, which were severely damaged. The paper focuses on the triggering mechanism of the landslide and on its evolution after the slope failure (run-out process). To simulate the occurred deformation processes, the material point method (MPM) is used along with a strain-softening Mohr–Coulomb constitutive model in which the soil strength reduces with increasing deviatoric plastic strain. In this connection, an analytical and simple to use methodology is proposed to reduce the mesh influence on the numerical results. The study shows that a progressive failure occurred in the slope owing to the excavations. Location of the failure surface, displacement magnitude and final configuration of the landslide body resulting from the numerical simulation are in good agreement with the observed ones. Some kinematical aspects of the landslide are also discussed.

Simulating retrogressive slope failure using two different smoothed particle finite element methods: A comparative study

Various smoothed particle finite element methods (SPFEMs) have been developed to simulate large deformation problems, but their efficiency and accuracy in simulating progressive landslides in sensitive clays have remained unclear. In this study, a series of numerical analyses are carried out to investigate the development of retrogressive landslides by two SPFEMs (an edge-based strain smoothing PFEM, ESPFEM, and a node-based strain smoothing PFEM, NSPFEM) in view of their outstanding performance in large deformation analysis. A strain-softening Mohr–Coulomb (MC) model is adopted to simulate the behaviour of sensitive clays during landslide, assuming a Poisson's ratio of 0.49 to ensure undrained conditions. The influence of mesh density on the development of retrogressive failure is evaluated for two SPFEMs. Numerical analyses of three mesh sizes (0.2 m, 0.15 m and 0.12 m) are carried out sequentially, with all results demonstrating that (1) the spread retrogressive landslides with horsts and grabens can be achieved by both SPFEMs with the adopted soil model, (2) run-out and retrogression distances decrease as mesh density increases for both methods, (3) retrogressive collapse occurs earlier for ESPFEM but is delayed for NSPFEM with increased mesh density, (4) NSPFEM allows faster calculations and reduces mesh dependency problems when compared with ESPFEM and (5) the increase of shape factor can accelerate retrogressive evolution of landslides. Finally, a real landslide in sensitive clay at Sainte-Monique, Quebec, is simulated to demonstrate ESPFEM's computational efficiency and accuracy.

Ground Reaction Curve for Deep Circular Tunnels in Strain-Softening Mohr–Coulomb Rock Masses Considering the Damaged Zone

Abstract The drill and blast method is one of the most widely used techniques for excavation of tunnels in rock masses. The most worrying issue in this method is unfavorable damage induced by blast...

Numerical simulation of a free fall penetrometer deployment using the material point method

Free Fall Penetrometer (FFP) testing consist of a torpedo-shaped body freefalling into a soil target. The use of this type of device is becoming popular for the characterization of shallow sediments in near-shore and off-shore environments because it is a fast, versatile, and non-expensive test capable of recording acceleration and pore pressures. In recent years, the data analysis advanced considerably, but the soil behavior during fast penetration is still uncertain. Hence, there is a need to develop numerical models capable of simulating this process to improve its understanding. This paper proposes a numerical framework to simulate the deployment of an FFP device in dry sands using the Material Point Method (MPM). A moving mesh technique is used to ensure the accurate geometry of the FFP device throughout the calculation, and the soil-FFP interaction is modelled with a frictional contact algorithm. Moreover, a rigid body algorithm is proposed to model the FFP device, which enhances the performance of the computation and reduces its computational cost. The sand is simulated by using two constitutive models, a non-associate Mohr-Coulomb (MC) and a Strain-Softening Mohr-Coulomb (SSMC) that reduces, exponentially, the strength parameters with the accumulated plastic deviatoric deformation (Yerro et al., 2016). Variable dilatancy, which reduces as a function of the plastic strain, is also taken into account, and the strain-rate effects have been evaluated in terms of peak friction angle. In general, the behavior predicted by the MPM simulations is consistent with the experimental test. The results indicate that the soil stiffness has a big impact on the deceleration time-history and the development of a failure mechanism, but less influence on the magnitude of the peak deceleration and the penetration depth; the soil dilatancy reduces the FFP rebound, and the FFP-soil contact friction angle and the peak friction angle are highly linked to the peak deceleration.

Numerical Investigation on Roadside Backfill Area Roof Failure Mechanism Subjected to Roadside Backfill Body: A Case Study

In retained gob-side entry (RGE) of coal mining, the immediate roof above roadside backfill area (RBA) plays a key part in transferring the main roof load downward and transferring the roadside backfill body (RBB) resistance upon the main roof upward. Numerical investigation was performed to evaluate the stress distribution, deformation characteristics, and plastic zone distribution of the immediate roof above RBA based on a field case of RGE in a Chinese colliery. The double-yield model for gob, strain-softening Mohr–Coulomb model for RBB and strain-softening Mohr–Coulomb model for the roof above RBA were proposed to improve the reliability of the 3D global numerical model in FLAC3D. The numerical results of the calibrated global numerical model indicate that the vertical stress of the immediate roof above RBA shows a V-shaped distribution when the RBB width is less than 2.4 m. The horizontal stress of the immediate roof above RBA reaches the maximum when the RBB width is 2.0 m. The vertical displacement and horizontal displacement of the immediate roof above RBA positively are associated with the RBB width. In addition, the tensile failure area of the immediate roof above RBA, and the ratio of the tensile failure depth of the immediate roof above RBA to the tensile failure depth of the road-in immediate roof increases with the increase of the RBB width while the tensile failure depth of the immediate roof above RBA decreases. The proposed modeling procedure can be repeated in RGE to evaluate surrounding rock stability with different geological and engineering conditions.

A block particle coupled model and its application to landslides

ABSTRACT To simulate the progressive failure of slope, a block particle coupled model is introduced. Particle oriented cell mapping (POCM) algorithm is used to enhance the search efficiency, and particle-point, particle-edge, particle-face contact detecting method is adopted to establish contact pair between particles and blocks precisely. Strain softening Mohr Coulomb model with tensile cutoff is adopted for blocks, and brittle Mohr Coulomb model is used for particles. The particle-block replacement approach is used to describe the fracture and fragmentation process of continuum media. Once the cohesion or tensile strength of one block reaches zero, the block will be deleted, and particles are generated at the same place with all information inherited from the deleted block. Some numerical cases related to landslides demonstrate the precision and rationality of the coupled model.

Response Analysis of the Free Field under Fault Movements

A quasistatic simulation of highly nonlinear problems under fault movements was carried out using the EXPLICIT module of ABAQUS. Combined with the secondary development program of the software, the application of the strain softening Mohr–Coulomb model in the simulation was realized. Free field‐fault systems were simulated with two types of fault types (normal and reverse faults), four fault dip angles (45°, 60°, 75°, and 90°), and two kinds of soil (sand and clay). Moreover, the rupture laws and sensitivities of the sand and clay were studied with different soil thicknesses and different fault dip angles in the free field. The results show that the width of the ground zone with obvious deformation, which represents the point of the fault outcrop, the critical displacement of the fault, and the rupture characteristics of the overlying soil are closely related to the fault type and soil parameters. The critical displacement of the reverse fault is larger than that of the normal fault. The width of the ground zone with obvious deformation varies from 0.65 to 1.3 and does not exhibit a regular relationship with the type of soil. Compared with a normal fault, the rupture of a reverse fault is not prone to exposure at the surface.

Internal Progressive Failure in Deep-Seated Landslides

Except for simple sliding motions, the stability of a slope does not depend only on the resistance of the basal failure surface. It is affected by the internal distortion of the moving mass, which plays an important role on the stability and post-failure behaviour of a landslide. The paper examines the stability conditions and the post-failure behaviour of a compound landslide whose geometry is inspired by one of the representative cross-sections of Vajont landslide. The brittleness of the mobilized rock mass was described by a strain-softening Mohr–Coulomb model, whose parameters were derived from previous contributions. The analysis was performed by means of a MPM computer code, which is capable of modelling the whole instability procedure in a unified calculation. The gravity action has been applied to initialize the stress state. This step mobilizes part of the strength along a shearing band located just above the kink of the basal surface, leading to the formation a kinematically admissible mechanism. The overall instability is triggered by an increase of water level. The increase of pore water pressures reduces the effective stresses within the slope and it leads to a progressive failure mechanism developing along an internal shearing band which controls the stability of the compound slope. The effect of the basal shearing resistance has been analysed during the post-failure stage. If no shearing strength is considered (as predicted by a thermal pressurization analysis), the model predicts a response similar to actual observations, namely a maximum sliding velocity of 25 m/s and a run-out close to 500 m.

Progressive failure of Aznalcóllar dam using the material point method

The material point method, which combines features of finite-element and particle discretisation methods, has been extended to solve coupled flow-deformation problems in granular media. The method is applied to simulate the construction and failure of the Aznalcóllar dam. The brittle foundation clay is characterised by means of a strain-softening Mohr–Coulomb elasto-plastic model. The rupture process of the foundation is associated with a progressive failure mechanism. The model predicts the development of a localised shearing band that initiates at the toe of the dam at some intermediate stage of construction, and propagates downstream and upstream. The shape and position of the failure surface reproduce actual field observations.

A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass

A simple numerical procedure for calculating the distribution of stresses and radial displacements around a circular tunnel excavated in a strain-softening Mohr–Coulomb or generalized Hoek–Brown rock mass is proposed. The problem is considered as axisymmetric, i.e. the initial stress state is assumed to be hydrostatic and the rock mass is said to be isotropic. By invoking the finite difference approximation of the equilibrium and compatibility equations, the increments of stresses and strains for each ring, starting from the outmost one for which boundary conditions are known a priori, are calculated in a successive manner. In the proposed approach, the potential plastic zone is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium equation. For the strain-softening behavior, it is assumed that all the strength parameters are a linear function of deviatoric plastic strain. Several illustrative examples are given to demonstrate the performance of the proposed method. For the brittle–plastic case, the results show a very good agreement with the closed-form solution. For strain-softening cases, the predictions by the proposed method are also in good agreement with the known rigorous numerical solutions. It is shown that the approximate solution converges to the exact solution when the increment of stress for each ring becomes smaller. The influence of the strength parameter ‘a’, appearing in the generalized Hoek–Brown criterion, on the elasto-plastic solutions is examined through the establishment of ground reaction curves and the discussion for the locations of the plastic radii.

Fracture initiation, growth and effect on stress field: a numerical investigation

A numerical investigation was made of the relationships between fracture initiation, growth, stress field and boundary conditions. Two-dimensional plane strain continuum models were used in which fractures appeared as zones of strain localization developed through application of a strain softening Mohr–Coulomb constitutive model. R and R′ fractures developed first, followed by Y fractures at larger strains. The models showed that equal development of conjugate R and R′ fractures is easily changed to favor one or the other set by minor variations in model initial conditions. Strength loss in fractures caused stress field rotations in regions bounded by fractures, altering the orientation of subsequent fractures. The amount and sense of stress field rotation is dependent on the strength loss during displacement on the fractures, the orientation of fractures, and on the boundary conditions. Y oriented fractures could be explained on the basis of a Mohr–Coulomb failure criterion provided that stress field rotation is accounted for. Monitoring of fracture slip activity showed that, under conditions of constant boundary velocity, slip was discontinuous in time, alternating on fractures throughout the model.