Cap Plasticity Research Articles

Obliquely incident seismic response of subway stations following urban soil internal erosion

Urban groundwater infiltration resulting from tropical storm rainfall can lead to internal soil erosion and ground subsidence. The long-term effects of these phenomena may result in uneven settlement of the subway system, posing risks to its safety and operational integrity. Suffusion poses a significant hazard to long-term subway operation. It is a type of soil internal erosion characterized by the migration of fine particles from the pore channels between coarse particles. This study focused on the performance degradation of different gap-graded sands caused by internal erosion, observed through triaxial compression tests. Using the cap plasticity model and considering mechanical parameters before and after soil erosion, a refined two-dimensional finite element model of a soil subway station structure based on ABAQUS was developed to analyze the deformation and damage pattern of the subway structure resulting from soil internal erosion and earthquake. The results of this study demonstrated that localized internal soil erosion significantly contributes to uneven settlement in subway stations, potentially compromising their seismic performance during oblique seismic excitations.

Classification of Multiaxial Behaviour of Fine-Grained Concrete for the Calibration of a Microplane Plasticity Model

Fine-grained high-strength concrete has already been tested extensively regarding its uniaxial strength. However, there is a lack of research on the multiaxial performance. In this contribution, some biaxial tests are investigated in order to compare the multiaxial load-bearing behaviour of fine-grained concretes with that of high-strength concretes with normal aggregate from the literature. The comparison pertains to the general biaxial load-bearing behaviour of concrete, the applicability of already existing fracture criteria and the extrapolation for the numerical investigation. This provides an insight into the applicability of existing data for the material characterisation of this fine-grained concrete and, in particular, to compensate for the lack of investigations on fine-grained concretes in general. It is shown, that the calibration of material models for fine-grained concretes based on literature results or normal-grained concrete with similar strength capacity is possible, as long as the uniaxial strength values and the modulus of elasticity are known. For the numerical simulation, a Microplane Drucker–Prager cap plasticity model is introduced and fitted in the first step to the biaxial compression tests. The model parameters are set into relation with the macroscopic quantities, gained from the observable behaviour of the concrete under uniaxial and biaxial compressive loading. It is shown that the model is able to capture the yielding and hardening effects of fine-grained high-strength concrete in different directions.

A multiscale framework for atomistic–continuum transition in nano-powder compaction process using a cap plasticity model

In this paper, a computational atomistic-continuum multiscale framework is presented for the simulation of the nano-powder compaction process using a cone-cap plasticity model. The atomistic representative volume element (RVE) comprises of nano-powder particles that is used to perform the molecular dynamics analysis in order to capture the mechanical behavior of nano-powder material. The periodic boundary condition is applied over the atomistic RVE to satisfy the inter-scale kinematic compatibility, and the stress tensor is derived according to the inter-scale energetic consistency principals from the nanoscale at each material point of the powder component. A multiscale framework is performed using the constitutive law of the coarse-scale domain enhanced by the molecular dynamics results of the fine-scale domain. The coarse-scale constitutive law is conformed to the cone-cap plasticity model as a robust and capable constitutive relation in modeling the powder compaction process, in which the cap plasticity parameters are determined using the data derived from the molecular dynamics simulations. The mechanical response of nano-powder particles within the RVE is obtained from the confining pressure test and true-triaxial test, where a sensitivity analysis is accomplished on the computed parameters of the cone-cap plasticity model. The enhanced cap plasticity model is then employed to simulate various industrial nano-powder components that illustrates the performance and efficiency of the proposed multiscale computational homogenization method.

A modified cap plasticity description coupled with a localizing gradient-enhanced approach for concrete failure modeling

The modeling of concrete has always been of great interest. In this work, a yield criterion with three surfaces is proposed to capture the plastic yielding behavior under different loading conditions, including uniaxial tension/compression, biaxial tension/compression and tension-compression. Material failure, characterized by the degradation and finally the complete loss of material integrity, can be modeled by the continuum damage approach. Within finite element methods, the nonlocal enhancement of integral-type or gradient-type is often required for the well-posedness of the partial differential equation system. In this work, a localizing gradient damage model has been adopted to obtain mesh-insensitive material responses, while ruling out the unphysical broadening of the damage zone often observed in constant length scale gradient damage models. Following a consistent derivation, the plasticity-damage coupled model has been implemented into an in-house finite element framework. Several representative and demonstrative examples serve to illustrate the capability of the proposed description in concrete modeling, followed by the conclusion, where some final insights are provided.

Effect of nonlinear soil−structure interaction and lateral stiffness on seismic performance of mid−rise RC building

In this study, the nonlinear soil-structure interaction (SSI) is considered to analyse the mid-rise structure's seismic performance with proportional lateral stiffness of columns in the orthogonal direction. The model's geometry is created using a finite element-based software package (ABAQUS). Cap plasticity and hysteretic models are used to mimic the nonlinear behaviour of soil and structural components, respectively. Truncated soil mass is incorporated using the spring and dashpot at the boundaries node with a MATLAB code for the dynamic analysis. The methodology validation is carried out on the shallow foundation under the cyclic loading and found in good agreement. Static pushover analysis of 4-storey, 8-storey mid-rise structures and 12-storey dual RC frame system is carried out to estimate the yielding displacement of the building structure at the roof level, which is further used in the incremental dynamic analysis (IDA) of the SSI and fixed base system. IDA is carried out for earthquake intensities ranging from 0.1g to 0.6g. IDA results are represented in terms of displacement ductility demand, normalised peak settlement, base shear, normalised peak foundation sliding and drift ratio. From the IDA analysis, the fragility assessment of the building is carried out for both the cases (fixed and SSI base). The present study concluded that lateral stiffness and SSI significantly affect the seismic performance of mid-rise buildings.

A hardening/softening viscoplastic model for large deformation of soil

AbstractA three‐invariant continuum cap plasticity model with viscoplastic features is developed for modeling the large deformation of soil. Multiple failure mechanisms including combined shear and compaction yielding and loss of strength under tension can be captured by this model. The shear yield surface of the model is formulated to be nonlinear and pressure‐dependent. The model also features a cap surface that governs inelastic compaction hardening. This cap is formulated as an explicit expression of porosity. The differences in triaxial compression and extension strength are also considered. A set of numerical examples are carried out, including triaxial compression and compression‐shear tests, in order to examine the model under confined loading conditions, and observe the formation of shear bands.

Effect of CPRF on nonlinear seismic response of an NPP structure considering raft-pile-soil-structure-interaction

A number of Nuclear Power Plants (NPPs) in India are coming up in soft soil condition particularly on alluvium in active seismic zone on Combined Piled-Raft Foundation (CPRF). So far, no study has been reported considering nonlinearity of soil for the NPP structures founded on CPRF considering earthquake loads.In the present study, the dynamic responses of raft, pile group and CPRF of a NPP are investigated by simulating the nonlinear finite element model. The effects of nonreflecting boundary condition, pile-soil-interaction by the embedded constraint, raft-pile interaction by the tie constraint and raft-soil-interaction by the penalty constraint, were considered. The material nonlinearity of soil was taken into account using an advanced constitutive model Drucker-Prager with cap plasticity. The geometrical nonlinearity is also considered using the concept of the contact surface. Thus, a complete 3D finite element numerical model of a nuclear structure considering raft-pile-soil-structure interaction (RPSSI) for nonlinear seismic analysis is developed. The validation is carried out by comparing the results from the present study with experimental and numerical results available in the literature. Nonlinear analyses of raft, pile group and CPRF in the time domain finite element formulation carried out and results are compared with that using the linear analysis.A comparison of two analyses shows that linear analysis underestimates the response of soil, piles and structure. The effect of type of boundary used in the analyses is significant. It was also observed that the response of NPP structure is significantly affected by the type of foundation used under the superstructure. The effect of SSI is examined with two major novelty i.e. (a) Effect of CPRF (b) Consideration of Nonlinearity of Soil. Effect of frequency of excitation and PGA of earthquake motion is examined. This study indicates the importance of CPRF over the raft foundation and pile group foundation for the design of nuclear power plants. Also, it examines the effects of nonlinearity on the response.

Simulation of highly nonlinear materials based on a stabilized non-ordinary state-based peridynamic model

Peridynamics (PD) is an effective method to solve discontinuity problems that involve cracking or crushing behaviors. In the non-ordinary state-based PD (NOSBPD), the so called zero-energy mode may cause inaccuracy particularly when the material is highly nonlinear. This paper proposed a novel stabilized NOSBPD modeling method to mitigate the inaccuracy and instability of NOSBPD solutions. A correction force for a PD point is defined as the difference between an internal force obtained by stress equilibrium equation and that obtained by the force states of the points within its horizon. The correction force is applied on the PD points to be corrected, e.g., that on the boundary of a PD model. Three examples are presented demonstrating the proposed method's effectiveness in static and dynamic analyses of both linear or highly nonlinear models, i.e., 3D cap plasticity concrete model and 2D multi-yield surface soil model. The predicted responses (e.g., displacements, stresses, strains at representative points) are analyzed and compared with those without force correction for both linear and highly nonlinear cases. The proposed method is demonstrated to be an effective method for mitigating the inaccuracy and instability of the NOSBPD solutions.

Phase-field implicit material point method with the convected particle domain interpolation for brittle–ductile failure transition in geomaterials involving finite deformation

A phase-field implicit material point method with the convected particle domain interpolation (PF-ICPDI) is proposed to model the brittle–ductile failure transition in pressure-sensitive geomaterials involving finite deformation. In this method, the phase-field fracture formulation relying on the microforce balance law and the second law of thermodynamics is adopted as a nonlocal damage function for the elastoplastic fracture analysis. A smooth two-yield-surface plasticity constitutive model is utilized to evaluate the brittle–ductile failure transition behavior of pressure-sensitive geomaterials. The coupling effect of phase-field fracture model and cap plasticity model is established by introducing an effective phase-field stress and splitting the total stored energy into elastic and plastic parts. The implicit material point method that can avoid severe mesh distortion and improve numerical stability is then developed to solve the quasi-static elastoplastic fracture finite deformation problem. Furthermore, the convected particle domain interpolation technique is adopted to eliminate numerical noises and improve computational accuracy while material points crossing cell boundaries in modeling the large deformation brittle–ductile failure transition process. The staggered incremental iterative scheme is carried out to solve the coupled discrete governing equations. The accuracy and capability of the proposed PF-ICPDI method are demonstrated through several representative numerical examples, as well as the effects of main material parameters on the phase-field brittle–ductile failure transition modeling of geomaterials are discussed.

Investigation of optimum compaction pattern in dynamic compaction operation using numerical simulation of adjacent impacts

ABSTRACT In this study, dynamic compaction in sandy soil has been simulated using a three-dimensional numerical model, considering a cap plasticity model and the large deformation effects. Two different approaches for modelling the tamper impact were considered. After simulation of impact at one point, three-dimensional modelling of two and three adjacent impacts was performed to investigate the effect of various parameters on the amount and extension of improvement in the overlap area. The results of analyses indicate that if the grid spacing in the first phase of dynamic compaction is considered equal to four times the tamper diameter and the impact energy of the second phase equal to or more than 85% of the first phase, the required improvement in the soil mass can be uniformly created until the desired depth.

Analysis of pore collapse and shear-enhanced compaction in hydrocarbon reservoirs using coupled poro-elastoplasticity and permeability

The withdrawal of fluid from a reservoir results in a decline of the fluid pressure followed by a consequent change in stress state in porous rocks. Stress change may cause irreversible deformation and compaction. Such compaction is generally the result of pore collapse and shear-enhanced compaction caused by changes at a microscopic level in the porous rocks. Pore collapse and shear-enhanced compaction are considered as potential problems during reservoir production and drilling operations. The purpose of this paper is to analyze the pore collapse and shear-enhanced compaction in hydrocarbon reservoirs using coupled poro-elastoplasticity and permeability. In this coupling, the poro-elastoplasticity analysis includes the linear component based on Biot’s theory and the nonlinear component based on a cap plasticity model. The fluid flow formulation is defined by Darcy’s law, including a nonlinear permeability model. The numerical approximation is implemented using continuous finite element approximations for rock deformation and mixed finite element approximation for pore pressure and flux. Several numerical simulations are performed to indicate the onset of pore collapse and shear-enhanced compaction and evaluate their effects on reservoir performance.

Estimation of the response of piled raft using nonlinear soil and interface model

ABSTRACT In this research paper, the complex interaction mechanism between different components of CPRF was simulated through 3D finite element analyses using the nonlinear interface and soil model for three case histories. The interface behaviour between concrete and soil was accounted using combined adhesion and friction model. The nonlinear soil behaviour was included using cap plasticity model, which has stress-dependant shear and compression yield surface, and captures the effect of stress history and stress path. The computed response parameters for the three case histories resulted in reasonably close agreement with the field measurements and led to significant improvement in the estimation of the load sharing of piles. The comparison of the results with the different methods showed that the stiffer interface results in a higher pile-raft coefficient and lesser settlement. The pile and soil stiffness found to vary with their position below the raft due to the different interactions.

Numerical Modeling of Lateral Dynamic Compaction on the Slope in Dry Sand

Dynamic compaction is a low-cost soil improvement method that is most commonly applied in sandy soils. Free fall compaction is not applicable to compact the soil in the slope, but it is possible to perform lateral dynamic compaction in the slope. In this method, the angle of impact of the tamper with the inclined surface is vertical. In this dynamic compaction method, the tamper is forced to move in a circular path by a cable with specific radius. In this study, ABACUS 6.14 software was used to simulate three-dimensional model of lateral dynamic compaction in the slope. The critical state model that used in numerical simulation is cap plasticity criteria. In this study, the effects of impact position, impact velocity and tamper weight on soil improvement for three different slope were investigated. The analysis focuses on crater depth and improvement region which are compared to the state of flat ground. It was found that on steep slopes to increase the tamper energy, the effect of increasing the impact velocity was greater than the effect of increasing the tamper mass to soil improvement. The crater depth due to lateral dynamic compaction is lower than the horizontal layer as well as the depth of soil improvement.

Experimental and numerical modelling of the mechanical behaviour of low-permeability sandstone considering hydromechanics

This paper proposed a novel approach, which combines an analytical model and a formula fitting function, to determine the hydromechanical relationships between the porosity and the permeability of low-permeability sandstone (LPS) that is further applied for the hydromechanical modelling. Then, several gas permeability experiments are conducted to measure the permeability and porosity of LPS under different confinement pressure. In conjunction with the Finite Element Method, the fracture propagation processes of LPS, which take physical triaxial experiments as reference experiments, are simulated by the considering hydromechanics. The results demonstrate that the absolute permeability is exponentially related to the porosity of LPS. Additionally, the porous media nonlinear elastic model and the modified Drucker–Prager cap plasticity model can accurately describe the deformation process of LPS. The simulation results correlate well with the experimental counterparts while being less scattered than the experimental data. This demonstrates the effectiveness of the proposed method in characterizing fracture properties of LPS considering hydromechanics.

Numerical modeling on thermoelastoplastic responses of Karamay oil sand reservoir upon steam circulation considering phase change of bitumen

Steam assisted gravity drainage technology has been widely applied to bitumen recovery in Karamay, northwest China. Steam circulation prior to production is designed to establish the thermal inter-well communication, aiming to create a desired initial steady steam chamber. Phenomenologically, the in situ immobile extremely viscous bitumen undergoes the change from solid to fluid state due to rheological fusion, and correspondingly the pay zone displays heated fusion and cold solid regions, within which thermal and mechanical properties differ considerably. To investigate these complex geomechanical responses, the heat transfer with phase change here was treated as a heat conduction with a moving boundary, and the modified Drucker-Prager model with cap plasticity was adopted to depict the mechanical behavior of oil sands. All models here used temperature-dependent constitutive parameters. This contribution coupled heat transfer, phase change and thermoelastoplastic deformation behaviors using a finite element code. A case study on SAGD well pairs using field operation parameters was conducted, and all reservoir information concerning temperature, phase change, deformation, stress and plastic zones were predicted. Temperature, deformation and stress along some typical paths at varying circulation periods were exhibited and discussed. The evolutions of phase change interfaces and plastic zones were provided. The changes of reservoir temperature as well as bitumen fluidity have significant impacts on the geomechanics, characterized by these interesting phenomena such as a maximum reservoir uplift occurring right above injection well, a high stress interference zone with shapes of arch or ellipse, and a plastic zone related to temperature distribution. This paper provides a coupled approach for the evaluation of reservoir thermoelastoplastic responses in steam circulation process, and it can also predict deformation change in permafrost and hydrate formation where transient heat transfer occurs incorporating phase change behavior.

Stand-alone lumbar cage subsidence: A biomechanical sensitivity study of cage design and placement.

Background and objectiveSpinal degeneration and instability are commonly treated with interbody fusion cages either alone or supplemented with posterior instrumentation with the aim to immobilise the segment and restore intervertebral height. The purpose of this work is to establish a tool which may help to understand the effects of intervertebral cage design and placement on the biomechanical response of a patient-specific model to help reducing post-surgical complications such as subsidence and segment instability. MethodsA 3D lumbar functional spinal unit (FSU) finite element model was created and a parametric model of an interbody cage was designed and introduced in the FSU. A Drucker–Prager Cap plasticity formulation was used to predict plastic strains and bone failure in the vertebrae. The effect of varying cage size, cross-sectional area, apparent stiffness and positioning was evaluated under 500 N preload followed by 7.5 Nm multidirectional rotation and the results were compared with the intact model. ResultsThe most influential cage parameters on the FSU were size, curvature congruence with the endplates and cage placement. Segmental stiffness was higher when increasing the cross-sectional cage area in all loading directions and when the cage was anteriorly placed in all directions but extension. In general, the facet joint forces were reduced by increasing segmental stiffness. However, these forces were higher than in the intact model in most of the cases due to the displacement of the instantaneous centre of rotation. The highest plastic deformations took place at the caudal vertebra under flexion and increased for cages with greater stiffness. Thus, wider cages and a more anteriorly placement would increase the volume of failed bone and, therefore, the risk of subsidence. ConclusionsCage geometry plays a crucial role in the success of lumbar surgery. General considerations such as larger cages may be applied as a guideline, but parameters such as curvature or cage placement should be determined for each specific patient. This model provides a proof-of-concept of a tool for the preoperative evaluation of lumbar surgical outcomes.

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part II: verification and numerical example

A fully implicit, fully coupled, and fully consistent finite element framework has been formulated in part I of this work for modeling reservoir compaction through linearizing coupled solid and flow field equations and constructing a local material integrator. In part II of this work, we focus on verification and performance analysis of our numerical formulation and computer implementation using several numerical examples. First, we design a cube problem in triaxial compression to verify our numerical formulation and computer code implementation especially for rock formation in compaction using cap plasticity models. The finite element prediction on stresses is compared with the analytical solution. The second problem we select is a strip footing problem popular in the geotechnical area where the evolution of soil consolidation degrees following the diffusion of pore pressure is the main interest. In this example, we demonstrate a good performance of the proposed numerical formulation on solving different shear and compaction-dominated deformation behaviors by varying the footing length. Importantly, an extremely sharp cap model based on real experimental data for Leda clays, a challenging cap model, is successfully applied in this footing problem. Our focus in this work is to model field reservoirs undergoing serious compaction. A reservoir with complex payzone geometries, multiple horizontal wells, and cap plasticity models with sharp cap surfaces has been successfully solved using our fully implicit formulation. The last example is to model a horizontal wellbore damage problem. Finally, the sensitivity of predicted subsidence to nonlinear flow model, cap hardening parameters, and Lode angles have been systemically investigated and documented in detail, which can provide a constructive guidance on how to successfully model field reservoir compaction problems with cap plasticity models.

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part I: theory and formulation

Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction.

Depletion-induced extreme plasticity across multiple horizontal wellbores in reservoirs with soft formations

Following depletion of oil and gas reservoirs with soft rocks, serious wellbore damage and a large amount of sand production result from the development of extremely large plastic deformation around wellbores. Evaluation on the development of plastic strain is crucial to wellbore instability analysis and sand production forecasting. Cap plasticity models have been developed to capture both shear and compaction failures for geomaterials. However, it has been a great challenge in accurately identifying extremely large plastic deformation around wellbores in reservoirs with soft formations using cap plasticity model coupled with fluid flow. To tackle this challenge, we have developed a fully implicit and fully coupled geomechanics and fluid flow finite element code where the Pelessone smooth cap plasticity model is consistently formulated for finite plastic deformation. In this work, with this robust and accurate computer code, we successfully investigate a detailed evolution of plastic strain up to its extreme condition around and across multiple horizontal wellbores following reservoir pore pressure drawdown.

Plasticity constitutive modeling of partially confined concrete with steel jacketing

Current research offers experimental and numerical investigation on concrete blocks with partial steel jackets, which endures axial compression. Experimental procedure provides the primary data for calibration of proposed model. Specimens have various steel jacketing ratios and the load is axial compression. The recorded data are strain components, elongation and the resisted force in experiment. A continuous cap plasticity surface expresses the non-uniform expansion and contraction of concrete beside an isotropic damage law that models the strength degradation using Abaqus® code. In presented mathematical model, the contraction and dilation of concrete is function of lateral pressure provided by steel jackets. The confining pressure is non-uniform due to discrete arrangement of steel ties in jacket and yielding of steel as concrete expands. Model provides parametric curves in order to design the confined-to-unconfined strength and ductility capacities of confined concrete. The presented numerical model is in close agreement with experimental results based on acquired results. We derive finally parametric curves for ductility and strength of confined concrete for various jacketing ratios.