Nonlinear Elastoplastic Constitutive Model Research Articles

Finite Difference Dynamic Stability and Liquefaction Analysis of Esphordi Mine Tailings Dam Implementing Non-Linear Elasto-Plastic Constitutive Model

Finite Difference Dynamic Stability and Liquefaction Analysis of Esphordi Mine Tailings Dam Implementing Non-Linear Elasto-Plastic Constitutive Model

Investigating the elastoplasticity of an Australian soft rock based on laboratory test results

For the stability and deformation analysis of open-cut mines using numerical methods, one critical step is to identify and simulate the elastoplasticity of geomaterials comprising the open-cut batters. The Victorian Brown Coal (VBC) in Australia is a non-textbook geotechnical material with a hardening feature in compression leading to brittle failure while showing a sharp post-peak softening behaviour. In order to study different aspects of elastoplasticity including the hardening and post-peak softening behaviour of the VBC, a series of laboratory tests including one-dimensional oedometer and triaxial tests were carried out on undisturbed VBC specimens taken from 30 m to 50 m below the ground level in one of the largest VBC open-cut mines in Victoria. By post-processing of the triaxial and oedometer test results, a yielding phenomenon was identified at the boundary between the fully elastic and elastoplastic domains. The magnitude of the material stiffness in the elastic domain was found to be independent of the confining pressure in triaxial tests while governed by the chemical bonding of the coal particles. The post-yield behaviour, however, was a frictional hardening and ruled by the magnitude of the confining pressure leading to a failure envelope sensitive to the organic content of the material. In this paper, a unified failure envelope is defined for the VBC using the Hvorslev-type normalisation process. Furthermore, a nonlinear elastoplastic constitutive model was examined to describe the elastoplasticity of VBC in triaxial condition, which led to a good agreement between the experimental and numerical modelling results.

Seismic response of underground structures under undrained loading with excess pore pressures accumulation

The seismic response of tunnels under undrained loading with excess pore pressures accumulation is poorly understood. Two-dimensional dynamic numerical analyses are conducted to assess the seismic response of deep circular tunnels located far from the seismic source under undrained loading conditions. For comparison purposes, analyses under drained loading are also performed. It is assumed that the liner remains elastic and that plane strain conditions apply. A cyclic nonlinear elastoplastic constitutive model is used to simulate the nonlinear behavior of the ground and excess pore pressures accumulation with cycles of loading.It is found that the tunnel’s response is determined by the loading of the liner, or by the distortions of the cross section, depending on the flexibility ratio (F). For stiff structures, with F⩽2, important thrust (axial) forces and bending moments are produced in the liner, with larger magnitudes for the undrained case, while the distortions of the cross section are small. When the tunnel becomes more flexible, i.e., F increases, the loading on the liner decreases, but the distortions of the cross section become important. For very flexible structures, with F⩾10, performance is largely determined by the distortions of the cross section, while the thrust forces and bending moments are almost negligible. Such distortions are larger for drained loading than for undrained loading early during the earthquake; however, the distortions drastically increase with the increase of excess pore pressures and can be even larger for undrained than for drained loading, late during the earthquake.

Nonlinear Dynamic Analysis Adopting Effective Stress Approach of an Embankment Involving Liquefaction Potential

Stability of an embankment under earthquake loads is challenging in the process of analysis and design. Some embankment design consist of saturated granular material that is potential to liquefaction. Earthquake loads to the embankment under this conditions is one of major cause of embankment failure. Seismic performance involving stress-deformations and excess-pore-water pressure was evaluated in this paper. The evaluation adopts effective stress approach with non-linear elasto-plastic constitutive model. Numerical simulations through parametric studies were performed to estimate minimum density and embankment height efficiently to tolerate lateral displacements due to liquefaction. A number of parametric analyses were performed to investigate the relationships among relative densities of sand, ground accelerations, embankment height to excess-pore-pressure and lateral displacement of the embankment. The liquefaction analysis is conducted numerically using a finite difference method FLAC Dynamic 2D software adopting Finn-Byrne constitutive model.

Compressive strain rate dependence and constitutive modeling of closed-cell aluminum foams with various relative densities

The dynamic compressive behavior of closed-cell aluminum foams with different relative densities at a wide range of strain rates up to 4000 s−1 was investigated using a 37-mm Split Hopkinson Pressure Bar (SHPB) apparatus. The 30-mm-diameter specimens with two thicknesses (i.e., 6 and 10 mm) and three nominal relative densities (i.e., 0.11, 0.16, and 0.21) were fabricated. The influences of strain rate, relative density, specimen thickness on the mechanical properties of aluminum foams (e.g., stress–strain relationship, collapse stress, plateau stress, densification strain, and energy absorption) were examined. The results indicate that the collapse stress, plateau stress, and densification strain of the aluminum foams with three relative densities exhibit obvious strain rate sensitivity. The collapse stress and plateau stress have a stronger density sensitivity and relatively weaker strain rate sensitivity. The specimen thickness has a very slight influence on the specimen strength at a lower strain rate (600 s−1), but this leads to a greater influence at a higher strain rate (2000 s−1). The energy absorption capacity of the closed-cell aluminum foams increases with increased relative density and strain rate in both quasi-static and dynamic compression. Finally, a multiparameter nonlinear elasto-plastic constitutive model was proposed to describe the typical three-stage features of stress–strain response in aluminum foams. There was acceptable agreement between theoretical predictions and experimental results.

Numerical simulation of the deformation response of geosynthetic reinforced soil mini-piers

This paper presents a numerical investigation of the deformation response of geosynthetic reinforced soil (GRS) mini-piers under service load conditions. The backfill soil was characterized using a nonlinear elasto-plastic constitutive model that incorporates a hyperbolic stress-strain relationship and the Mohr-Coulomb failure criterion. The geotextile reinforcement was characterized using linearly elastic elements with orthotropic stiffness. Various interfaces were included to simulate the interaction between different components. The three-dimensional numerical model was validated using experimental data from GRS mini-pier loading tests, including average settlements and maximum lateral facing displacements. Simulation results from a parametric study indicate that backfill soil friction angle, backfill soil cohesion, reinforcement vertical spacing, and reinforcement stiffness have the most significant effects on settlements and lateral facing displacements for GRS mini-piers under service load conditions.

Numerical study on maximum reinforcement tensile forces in geosynthetic reinforced soil bridge abutments

This paper presents a numerical study of maximum reinforcement tensile forces for geosynthetic reinforced soil (GRS) bridge abutments. The backfill soil was characterized using a nonlinear elasto-plastic constitutive model that incorporates a hyperbolic stress-strain relationship with strain softening behavior and the Mohr-Coulomb failure criterion. The geogrid reinforcement was characterized using a hyperbolic load-strain-time constitutive model. The GRS bridge abutments were numerically constructed in stages, including soil compaction effects, and then loaded in stages to the service load condition (i.e., applied vertical stress = 200 kPa) and finally to the failure condition (i.e., vertical strain = 5%). A parametric study was conducted to investigate the effects of geogrid reinforcement, backfill soil, and abutment geometry on reinforcement tensile forces at the service load condition and failure condition. Results indicate that reinforcement vertical spacing and backfill soil friction angle have the most significant effects on magnitudes of maximum tensile forces at the service load condition. The locus of maximum tensile forces at the failure condition was found to be Y-shaped. Geogrid reinforcement parameters have little effect on the Y-shaped locus of the maximum tensile forces when no secondary reinforcement layers are included, backfill soil shear strength parameters have moderate effects, and abutment geometry parameters have significant effects.

Numerical Simulation of Deformation and Failure Behavior of Geosynthetic Reinforced Soil Bridge Abutments

This paper presents a numerical investigation of the deformation and failure behavior of geosynthetic reinforced soil (GRS) bridge abutments. The backfill soil was characterized using a nonlinear elastoplastic constitutive model that incorporates a hyperbolic stress–strain relationship with strain-softening behavior and the Mohr–Coulomb failure criterion. The geogrid reinforcement was characterized using a hyperbolic load–strain–time model. The abutments were numerically constructed in stages, including soil compaction effects, and then monotonically loaded in stages to failure. Simulation results indicate that a nonlinear reinforcement model is needed to characterize deformation behavior for high applied stress conditions. A parametric study was conducted to investigate the effects of reinforcement, backfill soil, and abutment geometry on abutment deformation and failure behavior. Results indicate that reinforcement vertical spacing, reinforcement stiffness, backfill soil friction angle, and lower GRS wall height are the most significant parameters. The shape of the failure surface is controlled primarily by abutment geometry and can be approximated as bilinear.

Seismic analysis of landfill considering the effect of GM-GCL interface within liner

Geomembrane (GM) and geosynthetic clay liner (GCL) are extensively used in liner system which are placed beneath the landfill to isolate waste material from the surrounding environment but the geosynthetics can also be the weak interface, so analysis of seismic response and permanent deformation of landfill should be performed considering the influence of liner interface reasonably. In this study, a displacement-softening nonlinear elastoplastic constitutive model is established to describe the dynamic friction behavior of GM-GCL interface under various normal stress conditions and is validated against experimental results of cyclic shear tests and shaking table tests. Two-dimensional time-domain dynamic finite element analyses of typical above ground landfill incorporating the newly proposed dynamic interface friction model are conducted to provide an insight into the dynamic response and slip displacement along the GM-GCL interface. Neglecting the nonlinear elastoplasticity and displacement-softening property of the geosynthetic interface generally induces significant errors. The liner layer should be designed with full attention to restrict the seismic response and permanent deformation caused by earthquake. Extreme caution is required when using simplified dynamic analysis methods for seismic design or assessment of landfill.

A constitutive model considering friction property of geomaterials and stability analysis of borehole

The strength and deformation properties of geomaterials are essential to estimating the cracking behavior of rock, especially for deep exploration of conventional and unconventional hydrocarbon resources. Because the geomaterials encountered in hydrocarbon exploration are generally granular friction materials formed from deposition or cementation of granular materials in natural conditions, they sustain loads by means of intergranular friction, which forms the main source of their shear strength. Therefore, the deformation and failure of friction material is governed by the friction law. A mechanical element of the friction material is modelled based on the concept that the internal friction exists in both the elastic state and the plastic state. By assuming that the friction coefficient is proportional to the strain, the friction stress is computed, and then the corresponding nonlinear elasto-plastic constitutive model of the friction material is established. Based on analysis of the internal friction effect of rock during macroscopic shear deformation, the mechanical mechanism of geomaterials' friction strength enhancement is explained. The nonlinear elasto-plastic constitutive model was used to compute the fracture and failure of a tunnel and a deep borehole. The results show that the model is effective for estimating the mechanical response of important geotechnical problems, such as the analysis of cracked rock-mass strength, forecasting crack closure, and borehole wall collapse.

Three dimensional Finite Element modeling of seismic soil–structure interaction in soft soil

Earthquakes in regions underlain by soft clay have amply demonstrated the detrimental effects of soil–structure interaction (SSI) in such settings. This paper describes a new three dimensional Finite Element model utilizing linear elastic single degree of freedom (SDOF) structure and a nonlinear elasto-plastic constitutive model for soil behavior in order to capture the nonlinear foundation–soil coupled response under seismic loadings. Results from an experimental SSI centrifuge test were used to verify the reliability of the numerical model followed by parametric studies to evaluate performance of linear elastic structures underlain by soft saturated clay. The results of parametric study demonstrate that rigid slender (tall) structures are highly susceptible to the SSI effects including alteration of natural frequency, foundation rocking and excessive base shear demand. Structure–foundation stiffness and aspect ratios were found to be crucial parameters controlling coupled foundation–structure performance in flexible-base structures. Furthermore, frequency content of input motion, site response and structure must be taken into account to avoid occurrence of resonance problem.

Elasto-plastic constitutive model of aluminum alloy foam subjected to impact loading

A multi-parameter nonlinear elasto-plastic constitutive model which can fully capture the three typical features of stress-strain response, linearity, plasticity-like stress plateau and densification phases was developed. The functional expression of each parameter was determined using uniaxial compression tests for aluminum alloy foams. The parameters of the model can be systematically varied to describe the effect of relative density which may be responsible for the changes in yield stress and hardening-like or softening-like behavior at various strain rates. A comparison between model predictions and experimental results of the aluminum alloy foams was provided to validate the model. It was proved to be useful in the selection of the optimal-density and energy absorption foam for a specific application at impact events.

Computational Isotropic-Workhardening Rate-Independent Elastoplasticity

A novel formulation for elastoplasticity has been recently proposed by Liu and Hong. These authors have explored the internal symmetry of the constitutive model for perfect plasticity to ensure that the consistency condition is satisfied at each time step. Moreover, for perfect plasticity, they have converted the usual nonlinear elastoplastic constitutive model into a linear system of ordinary differential equations in redefined variables. The present paper is concerned with general isotropic workhardening. With the present formulation, it is still possible to satisfy the elastoplastic consistency condition at every time step, without the need for iterations even for nonlinear workhardening. The resulting system of ordinary differential equations, however, is, in general, nonlinear. Different strategies for obtaining numerical solutions of these equations are proposed in this paper, one of them based on group theory. Numerical solutions from the different schemes, for a simple illustrative example, are presented in the paper.