Mohr-Coulomb Constitutive Model Research Articles

Probabilistic three-dimensional finite element analysis of geosynthetic-reinforced pile-supported embankments

The current study focuses on a probabilistic three-dimensional finite element analysis of geosynthetic-reinforced pile-supported embankments. The probabilistic analysis utilizes a finite element technique and was executed using Python scripting in Abaqus. A deterministic model is established for both unreinforced and geosynthetic-reinforced pile-supported embankments, employing a basic linear elastic perfectly plastic Mohr-Coulomb constitutive model. This numerical model adopted a simplified methodology that eliminates the need to simulate actual piles and subsoil. The results are validated across different embankment heights and mesh sizes. Based on results from Monte-Carlo simulations, we aimed to show how results can vary even by considering only one random variable. Probability density functions for various parameters, including pile efficacy, maximum differential settlement, and maximum strain in the reinforcement, are shown. The findings illustrate the ability of probabilistic approaches to predict the most likely occurrences for different governing parameters of geosynthetic-reinforced pile-supported embankments. They also highlight the potential of probabilistic approaches to expand further into a full-scale comprehensive study which can offer deeper insights into the stability of these embankments considering various sources of uncertainties.

Experimental and Numerical Study of Soil Strata for Underground Transportation System: A Case Study

In the current capital of Yemen, Sana’a, a time-efficient and economical transportation system is one of the greatest challenges to overcome the increasing urbanization for many years. Rapid transport systems use tunnel structures to reach the city's most inaccessible areas. Given the Gulf's geopolitical unrest, these structures could also serve as emergency shelters. Consequently, this research conducted an experimental soil exploration investigation in Sana'a, Yemen, to identify potential tunneling sites for the city's rapid transit system. The field exploration, in-situ, and laboratory soil testing at the four locations were performed with the collaboration of the Ministry of Public Works & Highways, Yemen. Further, to calculate the geotechnical parameters for tunnel design, numerical analysis has been carried out using the finite element package ABAQUS, and two-dimensional plane-strain numerical models of underground tunnel structure have been developed to conduct the parametric study in different soil types and boundary conditions under static loading. The material behavior of soil strata has been incorporated into the well-known Mohr-Coulomb constitutive model. The field investigation found that the geotechnical properties of the soil strata in Sana’a have a lot of variation. The numerical study shows that the maximum deformation in the concrete liner of the tunnel was observed at the crown of the tunnel. The ovalling effect in tunnel concrete liner was also seen in all the tunnel models, and the maximum ground settlement at sites 1, 2, 3, and 4 was estimated to be approximately 4, 25, 17, and 11 mm, respectively. Doi: 10.28991/CEJ-2024-010-01-03 Full Text: PDF

Investigation on Existing Tunnel Response to Piles Construction: A Numerical Study

Deep foundations are frequently built close to existing tunnels in the urban environment. Tunnels can only withstand very small movements. The construction of bored piles and/or the subsequent loading of the piles may result in unbearable movements or stresses that could result in cracking of the tunnel linings, which worries obstacles to the tunnel structure. This research presents an understanding of the interaction issue and investigates and evaluates various geometric factors that determine the effect of the construction of the pile on the existing tunnel. However, numerical modeling was established utilizing a modified Mohr-Coulomb constitutive model for the soil strata. Numerous factors have been examined, including different locations of the pile tip to the tunnel centerline as well as variable pile diameters and lengths. The numerical analysis results revealed that the bending moment decreases as the distance from the tunnel increases from 8 to 12 m and then remains constant, while the shear stress is not affected considerably. In addition, the shear stress and bending moment increase with pile diameter and length due to the increased confinement caused by the pile. The spacing has a considerable effect on the horizontal displacement with very little effect on the vertical displacement. Moreover, there is an increase in the shear force developed in the tunnel lining with pile diameter for different spacings between the tunnel and pile. This increase becomes smaller as the pile length increases. At small spacing between the pile and tunnel (8.3 m and 12.5 m), the bending moment in the tunnel lining decreases as the pile length increases. Doi: 10.28991/CEJ-SP2023-09-016 Full Text: PDF

Calibration Method and Material Constants of an Anisotropic, Linearly Elastic and Perfectly Plastic Mohr–Coulomb Constitutive Model for Opalinus Clay

AbstractNagra, the cooperative for developing and implementing a long-term radioactive waste depository in Switzerland, identified Opalinus Clay as the most suitable host rock for deep geological containment. This paper deals with those features of Opalinus Clay that are important for the design and construction of the underground structures. Consolidated drained (CD) and consolidated undrained (CU) triaxial compression tests on specimens from deep boreholes revealed that Opalinus Clay exhibits pronounced stiffness and strength anisotropy, dependency of stiffness on the initial confining pressure, slightly non-linear pre-failure stress–strain behaviour, and a drop in axial resistance after a certain amount of shearing. Within the scope of establishing a rigorous—yet practical—design approach for the repository tunnels and caverns, the simplest possible constitutive model capable of reproducing the main aspects of the Opalinus Clay behaviour is adopted. The non-associated linear elastic and perfectly plastic MC model is chosen as a starting point, on account of its wide use in tunnel engineering practice, its simplicity, and the clear physical meaning of its parameters. This paper presents a systematic and robust calibration method for an extended version of this model, which considers the pronounced strength and stiffness anisotropy of Opalinus Clay. The paper additionally provides the full suite of the equations that describe the model behaviour under triaxial CU or CD testing conditions and for any bedding orientation relative to the specimen axis. The equations are employed to determine ranges of material constants for two varieties of Opalinus Clay, based upon the results of 73 CU and CD tests. A thorough comparison between the model predictions and the experimental response is conducted, to demonstrate the versatility and limitations of the constitutive model and of the proposed calibration approach.

Probabilistic Evaluation of Geomechanical Risks in CO2 Storage: An Exploration of Caprock Integrity Metrics Using a Multilaminate Model

The probabilistic uncertainty assessment of geomechanical risk—specifically, caprock failure—attributable to CO2 injection, as presented in a simplified hypothetical geological model, was the focus of this study. Our approach amalgamates the implementation of a multilaminate model, the creation of a response surface model in conjunction with the Box–Behnken sampling design, the execution of associated numerical modeling experiments, and the utilization of Monte Carlo simulations. Probability distributions to encapsulate the inherent variability (elastic and mechanical properties of the caprock and reservoir) and uncertainty in prediction estimates (vertical displacement, total strain, and F value) were employed. Our findings reveal that the Young modulus of the caprock is a key factor controlling equivalent total strain but is insufficient as a stand-alone indicator of caprock integrity. It is confirmed that the caprock can accommodate significant deformation without failure, if it possesses a low Young’s modulus and high mechanical strength properties, such as the friction angle and uniaxial compressive strength. Similarly, vertical displacement was found to be an unreliable indicator for caprock integrity, as caprock failure can occur across a broad spectrum of vertical displacements, particularly when both the Young modulus and mechanical strength properties have wide ranges. This study introduces the F value as the most dependable indicator for caprock failure, although it is a theoretical attribute (the shortest distance between the Mohr circle and the nearest failure envelope used to measure the sensitivity to failure) and not physically measurable in the field. Deviatoric stress levels were found to vary based on stress regimes, with the maximum levels observed under extensive and compressive stress regimes. In conjunction with the use of the response surface method, this study demonstrates the efficacy of the multilaminate framework and the Mohr–Coulomb constitutive model in providing a simplified, yet effective, probabilistic model of the mechanical behavior of caprock failure, reducing mathematical and computational complexities.

Finite Element Analysis on Load-Settlement Behavior of Axially Loaded Pile on Sand

The analysis of geoengineering problems using various constitutive models necessitates substantial field and laboratory research, which entails a significant investment of time and money. As a result, the application of Finite Element Analysis in geoengineering projects is limited. This research focuses on numerically examining the behavior of a pile in a sandy soil layer. The study employs different relationships to estimate soil parameters from standard penetration tests and simple lab tests. These derived parameters, required for the Mohr-Coulomb & Hardening Soil constitutive model and the linear elastic model of the pile, are implemented in the PLAXIS 3D software. This software is used to simulate the settlement of the pile in sandy soil incorporating factors like mesh density and soil-pile interaction. The results of the study reveal that employing a finer mesh size leads to more precise results. Additionally, an interface strength of 67% proves to be more accurate for this study. Furthermore, the correlation introduced by Papadopoulos (1982) exhibits a close relation with field settlement values. In contrast, other correlations either overestimate or underestimate the results. Moreover, the study conclude that Mohr-Coulomb constitutive model satisfactorily predicts the behavior of the pile for the study area.

Research on Constitutive Model and Algorithm of High-Temperature-Load Coupling Damage Based on the Zienkiewicz–Pande Yield Criterion

The mechanical properties of rock can be weakened under the influence of high temperatures. To describe the mechanical behavior of rock under the action of high temperature more accurately, based on the Zienkiewicz–Pande yield criterion, the damage variable Dc which accounts for the coupling between high temperature and load is introduced. According to plastic potential theory and plastic flow law, the iterative incremental method for a high-temperature and load-coupled damage constitutive model in Flac3D is deduced in detail and compiled into the corresponding dynamic link library file (.dll file). By modifying the shape function to degenerate into the Mohr–Coulomb constitutive model, an elastic–plastic analysis of an ideal circular tunnel is performed, and a comparison is made between calculation results obtained from the built-in Mohr–Coulomb constitutive model in Flac3D, proving the correctness of the secondary development program. Finally, numerical simulations are conducted to study the effects of high-temperature damage using rock uniaxial compression tests, and the model’s validity is established by comparing it with previous experimental results.

Sustainable rural infrastructure: guidelines for roadside slope excavation

The construction of non-engineered, equipment-based rural roads in Nepal Himalaya is one of the predominant causes of landslides. The construction frequency of such roads has significantly increased over the past decade. However, the present guidelines governing slope excavation for these roads are not based on geotechnical characterizations of sites. The current study uses the limit equilibrium method with the Mohr–Coulomb constitutive model to determine safe cut heights and slopes for varying geometric and material parameters. GeoStudio Slope/W was used to model soil slopes with various gradients, and cuts with varying depths and slope angles were modeled to calculate the factor of safety (FoS) against shear failure for different geometric and material conditions. The results of the study were visualized in design charts with FoS as the dependent variable. The analysis highlights the importance of different parameters, i.e., excavation depth, excavation slope, and existing ground slope in the FoS, in addition to the slope-forming material. Furthermore, a field study was carried out to validate the model using the clustering approach. The results from the field are similar to those from the numerical model, although some additional site-specific parameters like vegetation cover and surface runoff conditions should be considered before selecting the cut slope. Finally, this study proposes that future road construction guidelines should consider terrain parameters, hydrology, and geotechnical site conditions to promote sustainable road infrastructure and reduce future disaster risks in the Himalayan region.

Damage constitutive model and mechanical properties of jointed rock mass under hydro-mechanical coupling

The damage evolution law and mechanical property weakening mechanism of jointed rock mass under hydro-mechanical coupling are important scientific problems in deep rock mass excavation. In this paper, the mineral composition of rock specimens was analyzed, and the distribution law of nuclear magnetic resonance T2 spectrum of granite under different axial stress was studied. Then the mechanical properties of jointed rock samples under triaxial stress and seepage pressure were studied. Based on the analysis of the stress field at the joint tip, the damage model of the jointed rock mass was obtained. Furthermore, the tensor of damage variables was analyzed, and the stress intensity factor under seepage pressure was calculated. The seepage pressure promotes the damage evolution process of jointed rock mass specimens and accelerates the strength failure of jointed rock mass specimens. The damage constitutive model of jointed rock mass under seepage pressure was established and verified. Based on the weakening law of seepage pressure, the developed hydro-mechanical coupling constitutive model was customized and imported into FLAC3D with the calculation function of the Mohr-Coulomb constitutive model as the compilation template. A three-dimensional numerical simulation model of underground rock mass engineering was established to analyze the stability of rock mass with different joint dip angles. For the surrounding rock with the dominant angle of 85° in the mine, its stability is poor, and the support needs to be strengthened.

Numerical Simulation of Curvature and Confining Pressure Effect on Progressive Failure of Surrounding Rock in Arch Tunnel with Straight Wall

Considering the influence of tensile plastic strain of intact rock on tensile strength and elastic modulus. The influence of arch curvature and height of the straight wall on the progressive failure of surrounding rock under different confining pressures are simulated based on the Mohr-Coulomb constitutive model and the nonlinear CWFS criterion of friction strengthening and cohesion weakening. The results show that when λ 1 = 0.2, the difference between vertical load and horizontal load is large, the buckling failure of rock burst and slab cracking is obvious, and the sectional curvature effect is obvious. When λ 3 = 0.5, the buckling failure of rock burst and slab cracking is very limited, the sectional curvature effect is reduced, and the confining pressure effect of rock burst and slab cracking is obvious. The shear yield localization of the surrounding rock is sensitive to sectional curvature, and the sectional curvature effect of shear failure under different lateral pressure coefficients is obvious. The numerical calculation results are consistent with the failure law of surrounding rock obtained from field and laboratory tests, which can provide a reference for tunnel excavation and support design.

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Finite Element Method (FEM) has been the state-of-the-art method in geotechnical analysis since it first formulated in the 40s. It capable to handle Multiphysics simulation, soil-structure and soil-water interaction, and time history analysis. Though powerful, the standard Lagrangian FEM suffers mesh distortion when handling large strain deformation problem. This mesh entanglement problem makes post-failure analysis is considerably challenging to model if not impossible to do using FEM. The Material Point Method (MPM) then later introduced to solve these large strain deformation problems. Adapted from the Particle in Cell (PIC) method, MPM is a hybrid method that combines Eularian and Lagrangian approach by utilizing moving material points which are moving over spatially fixed computational mesh. This approach enables MPM to calculate not only fluid mechanics such in PIC but also solid mechanics and its intermediatory states. To demonstrate the capability of MPM and its consistency with FEM in geotechnical analysis, this article presents a comparison of FEM and MPM analysis on a hypothetical slope using Mohr-Coulomb constitutive model. The simulation shows that both FEM and MPM analyses are consistent to each other especially in small strain scheme. However, in large strain deformation, MPM is still able to get convergent result while FEM is not. The MPM simulation is also able to animate post failure behavior clearly, calculate post-failure strains and stresses distribution, and present final geometry of the model.

Single piles under monotonic lateral loads-Full scale tests and numerical modelling

This paper aims to present the results of the analysis of full-scale lateral loading tests of a single pile driven into a bi-layered soil located in Plancoet (France). The pile was subjected to a monotonic sequence of loads, and the P-Y curves along the pile were derived and compared to those recommended by the current design methods. Displacement analysis was then undertaken by inputting these P-Y curves, as well as those currently recommended in the literature, into the software SPULL to predict the load-deflection curve. The calibration process was conducted by a 3D finite element model using Abaqus software based on the elastic-perfectly plastic Mohr–Coulomb constitutive model, and the surface-to-surface contact method was used to take into account the nonlinear response at the pile/soil interface. The determined soil elastic modulus was used to predict the pile deflections by using some usual elasticity-based methods, which led to good prediction of the small pile deflections.

Modeling of projectile penetrating fiber-reinforced concrete via the continuum discontinuum element method

In this paper, the projectile penetrating fiber-reinforced concrete (FRC) is modeled and simulated by the continuum discontinuum element method (CDEM) and a fiber-block interpolation coupling algorithm. The Mohr–Coulomb constitutive model is applied to the blocks to calculate the block forces, and the Mohr–Coulomb criterion and the maximum tensile criterion are applied to estimate the failure of contact surfaces. Numerical simulations of projectiles penetrating plain concrete and FRC with 1 to 3 vol% are performed. We verify the validity of the model by predicting the crack morphology and penetration depth for plain concrete and FRC, which are in agreement with experimental results. Detailed images of crack surfaces in the concrete blocks caused by projectile penetration are included. The effects of fiber content on crack width are analyzed. The results indicate that the normalized widths of the cracks approximately satisfy the Weibull distribution. Compared with plain concrete, the addition of fibers results in a reduction in both the expectation and variance of crack widths. However, the degree of reduction weakens as fiber content increased.

Numerical Analysis of an Explicit Smoothed Particle Finite Element Method on Shallow Vegetated Slope Stability with Different Root Architectures

Planting vegetation is an environmentally friendly method for reducing landslides. Current vegetated slope analysis fails to consider the influence of different root architectures, and the accuracy and effectiveness of the numerical simulations need to be improved. In this study, an explicit smoothed particle finite element method (eSPFEM) was used to evaluate slope stability under the influence of vegetation roots. The Mohr–Coulomb constitutive model was extended by incorporating apparent root cohesion into the shear strength of the soil. The slope factors of safety (FOS) of four root architectures (uniform, triangular, parabolic, and exponential) for various planting distances, root depths, slope angles, and planting locations were calculated using the shear strength reduction technique with a kinetic energy-based criterion. The results indicated that the higher the planting density, the stronger the reinforcement effect of the roots on the slope. With increasing root depth, the FOS value first decreased and then increased. The FOS value decreased with an increase in slope angle. Planting on the entire ground surface had the best improvement effect on the slope stability, followed by planting vegetation with a uniform root architecture in the upper slope region or planting vegetation with triangular or exponential root architecture on the slope’s toe. Our findings are expected to deepen our understanding of the contributions of different root architectures to vegetated slope protection and guide the selection of vegetation species and planting locations.

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.

Twin earth pressure balance tunnelling – monitoring and numerical study of an urban case

In recent decades, numerical calculations have often been used to optimise, from a technical and economical perspective, the design of underground works. Using these tools allows efficient and affordable designs to be obtained. Simulation of the tunnelling procedure when using a tunnel-boring machine and in urban areas is a complex soil–structure interaction problem. Here, a three-dimensional (3D) code using finite differences is used. The reference case of this study is Lyon metro line D project in France, where a non-symmetric load is present at the surface due to the presence of a retaining wall. An accurate on-site monitoring system was set up to assess ground movements during the mechanised excavation of twin tunnels. The collected data are used as a reference to show the validity and accuracy of the developed 3D model. Two constitutive models were used to simulate the soil behaviour: plastic hardening (PH) and linear elasticity with perfect plasticity (Mohr–Coulomb shear failure criterion). The Mohr–Coulomb constitutive model shows some drawbacks, which can be eliminated by using PH. The existence of a retaining wall induces a non-symmetric load condition; however, the settlement trough predicted by advanced numerical models shows good agreement with that obtained by monitoring data.

A Numerical Study of Ground Displacement and Stress Conditions of Small and Medium Circular Diaphragm Wall during Excavation

In the present study, a dimensional total-stress elasto-plastic FEM analysis was conducted, which was based on the Mohr-Coulomb constitutive model. The model was combined with a practical engineering case in order to investigate ground displacements and stress conditions during the installations of a medium-sized and a small-sized circular diaphragm wall, as well as the subsequent soil excavations within the walls. The distribution characteristics of the lateral radial displacements and stress conditions in the ground following the wall installations and excavations within the walls were investigated. Also, two different excavation methods, as well as three different soil depths for the walls, were considered. The distributions of the internal forces along the depth directions of the radial sections of the walls were also analyzed in this study. The analysis results showed that the slotting order had made the model nonaxisymmetric, which had further influenced the distribution characteristics of radial stress and displacements. It was found that the distributions of the horizontal radial displacements, along with the stress levels of the soil behind the walls, were only minimally affected by the excavations of the soil in the shaft. The internal force distribution of the wall radial section caused by the direct excavation method and the reverse excavation method is very small, that is, the wall bending moment generated by the reverse excavation process is larger, and the most obvious near the rock-socketed depth. The distribution pattern of the bending moment depth corresponding to different excavation construction methods is similar. Furthermore, the soil penetration depths of the walls were determined to have had little influence on the internal force distributions of the radial sections of the walls above the foundation pit. However, there was a greater influence observed on the internal force distributions of the radial sections of the walls below the foundation pit.

Effects of siltation and desiltation on the wave-induced stability of foundation trench of immersed tunnel

The evaluation of stability for the submarine artificial slope is important in the construction of offshore structures such as immersed tunnels and embedded pipelines. The siltation in marine dynamic environment is common, inevitable, but difficult to deal with. Cohesive sediment, or mud, is encountered in most water bodies throughout the world, and thus siltation inevitably occurs in the stage of underwater excavation for the offshore structure foundations. To this end, based on the temporal and spatial variations law of siltation observed from the trial trench in-situ test of Shenzhen-Zhongshan Link in China, a numerical study is carried out on the influences of siltation and desiltation on the stability of foundation trench slope under wave action. The waves are simulated by the Reynolds-Averaged Navier-Stokes (RANS) equations and then applied on the surface of seabed and trench slope. The pore pressure induced by the wave action is obtained by Darcy's law. The seabed is characterized by Mohr-Coulomb constitutive model and the factor of stability (FOS) of the slope is calculated using the strength reduction method. Three failure modes are assumed to analyze the stability of trench slope and to determine the most unstable mode. A sensitivity analysis is conducted on various key factors affecting the whole stability of the trench slope after siltation or desiltation, which is valuable for practical engineering design.

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.

Application of the Modified Mohr–Coulomb Yield Criterion in Seismic Numerical Simulation of Tunnels

To solve the classical problem that the Mohr–Coulomb yield criterion overestimates the tensile properties of geotechnical materials, a modified Mohr–Coulomb yield criterion that includes both maximum tensile stress theory and smooth processing was established herein. The modified Mohr–Coulomb constitutive model is developed using the user-defined material subroutine (UMAT) available in finite element software ABAQUS, and the modified Mohr–Coulomb yield criterion is applied to construct a numerical simulation of a shaking table model test. Compared with the measured data from the shaking table test, the accuracies of the classical Mohr–Coulomb yield criterion and the modified Mohr–Coulomb yield criterion are assessed. Compared to the shaking table test, the classical Mohr–Coulomb model has a relatively large average error (−6.98% in peak acceleration values, −8.47% in displacement values, −23.93% in axial forces), while the modified Mohr–Coulomb model has a smaller average error (+2.71% in peak accelerations value, +3.19% in displacements value, +7.56% in axial forces). The results of numerical simulation using the modified Mohr–Coulomb yield criterion are closer to the measured data.