Generalized Plasticity Model Research Articles

Modification of the Reloading Plastic Modulus in Generalized Plasticity Models for Soil by Introducing a New Equation for the Memory Parameter in Cyclic Loadings

Nowadays, with the widespread supply of very powerful laboratory and computer equipment, it is expected that the analyses conducted for geotechnical problems are carried out with very high precision. Precise analyses lead to better knowledge of structures’ behavior, which, in turn, reduces the costs related to uncertainty of materials’ behavior. A precise analysis necessitates a precise knowledge and definition of the behavior of the constituent materials, which itself requires applying an appropriate constitutive model to show the behavior of materials. Constitutive models used in the generalized plasticity framework are very powerful constitutive models for the simulation of sand behavior. However, the simulation of a cyclic behavior in these models, especially the simulation of the undrained cyclic behavior, is not well-recognized. In this study, in order to eliminate the weakness of generalized constitutive models under cyclic loading, a new equation is presented to substitute the so-called coefficient of the discrete memory factor to consider the loading history in such a way that the plastic modulus is modified during reloading and, as a result, more appropriate predictions of sand behavior are obtained. The performance accuracy of the proposed coefficient was evaluated in accordance with the experimental data. Finally, the results show that after using the modification of the loading history coefficient, predictions of the constitutive model are significantly improved.

Dynamic response of subsea tunnel in liquefiable layered seabed under combined earthquake and wave action

Liquefaction poses a potential threat to the safety of subsea tunnel during the earthquake. In the ocean environment, wave pressure is considered as a normal loading applied at the seabed surface. This study proposed a fully coupled dynamic effective stress finite element model for subsea tunnel in liquefiable layered seabed under combined earthquake and wave action. Biot u-p formulation integrated with a modified generalized plasticity model was adopted for liquefaction analyses of the seabed. The proposed model was validated through a wave flume model test in terms of excess pore water pressure (EPWP). The results showed that the tunnel – soil dynamic interaction significantly increased EPWP near the tunnel. Increasing the wave height significantly increased the liquefaction depth of the seabed; however, the wave loading can either suppress the displacement of the tunnel during the earthquake or increase the uplift of the tunnel during the subsequent wave loading. When investigating seismic response of subsea tunnels in liquefiable soils under combined earthquake and wave action, the ground motion was suggested to be input simultaneously with the wave pressure. This study also highlights the effect of the thickness of liquefiable layer and frequency content of earthquakes on dynamic responses of subsea tunnels.

Elastoplastic constitutive model of gravelly soil and its validation through numerical analysis of the Kobe Port Island liquefaction

The liquefaction of gravelly soil has been demonstrated in many earthquakes, but the constitutive model to predict its liquefaction behavior is limited. The dilatancy equation plays an important role in establishing elastoplastic models of geotechnical materials. Recognizing the unique dilatancy characteristics of gravelly soil, this study introduces an improved nonlinear dilatancy equation into the generalized plasticity model. Consequently, a unified elastoplastic constitutive model is proposed, aimed at accurately predicting both the monotonic and cyclic behaviors of saturated gravelly soil under diverse drainage conditions. A series of drained and undrained triaxial tests of gravelly soil under monotonic and cyclic loadings are carried out to validate the model performance. In addition, the model performance is also examined through monotonic and liquefaction tests of gravelly soil obtained from prior publications. Furthermore, the proposed model is implemented into the nonlinear finite element program GEODYNA and applied to the numerical simulation of the Kobe Port Island liquefaction to better validate the capabilities of the proposed model. From the comprehensive analysis of triaxial tests and numerical simulations, the proposed model performs well in predicting mechanical behavior of gravelly soil and can provide a powerful tool for seismic liquefaction analysis of gravelly soil sites.

A novel constitutive model for the concrete face slab of a CFRD and the numerical simulation of its seismic behavior

AbstractWith the rising demand for hydropower energy, China has built numerous concrete‐faced rockfill dams (CFRDs) with considerable heights. The potential failure pattern of the concrete face slab is the key to the safety of the anti‐seepage system. However, engineers commonly employ an elastic relationship to model the concrete face slab for simplicity, which induces inaccurate estimation of the face slab's stresses, especially under seismic conditions. On the other hand, the existing elastoplastic models for concrete often require complex derivation of the necessary formula and thus are difficult to apply to finite element (FE) analysis. Under the comprehensive action of the upstream water, supporting rockfill, and surrounding mountains, the damage mode of the quasibrittle concrete slab is not a tensile mode but a compressive shearing mode. Therefore, it is urgent to establish an elastoplastic model that is adapted to the actual working environment of the slab and easy to apply. To this end, a generalized plasticity model is developed within the phenomenology modeling concept, which is validated at both the experimental level and application level. The results indicate that three‐dimensional stress‒strain behaviors, such as the strength nonlinearity, prepeak dilatancy, and postpeak softening, can be effectively captured. In addition, the seismic characteristics of a 200‐m high CFRD are numerically investigated. The findings show that the slab's stress accumulation can be reflected during the earthquake and that the final stress distribution conforms to the field observations. The conclusions of this paper provide a reliable reference for the seismic resistance design of CFRDs.

A unified constitutive model for instantaneous elastic–plastic and time-dependent creep behaviour of gravelly soils under complex loading

The behaviours of gravelly soils under monotonic, cyclic and creep loading are generally simulated in separated processes with different models, which cannot describe the interactions between the instantaneous elastic–plastic and time-dependent creep behaviours under complex loading. To address the problem, an elastic–plastic–creep model framework for gravelly soils is described to present its basic components and the differences from the elastic–plastic model framework. Within this framework, a unified constitutive model for instantaneous elastic–plastic and time-dependent creep behaviour is proposed based on the widely used generalized plasticity model. In modelling the elastic–plastic behaviour, the plastic modulus in the original model is modified to capture the creep hardening by a unified hardening state parameter for monotonic, cyclic and creep loading. In modelling the creep behaviour, the creep strain rate independent of the time variable is presented to reflect the creep behaviours under the unloading–reloading path and its difference from that of virgin loading. The proposed model can be easily implemented into the computing program as the original model with only minor adjustments. The ability to simulate the time-dependent behaviour under multistage loading/reloading-creep, different strain rates, step changes in strain rate, and stress relaxation are proven with the experiments.

Response of soil–pile–superstructure–quay wall system to lateral displacement under horizontal and vertical earthquake excitations

The excess pore water pressure generated under the combined vertical and horizontal earthquake excitations is generally greater than that under the unidirectional excitation, which may further affect the dynamic response of soil-pile-superstructure-quay wall (SPSQ) system. This study conducted a coupled effective-stress analysis for the response of SPSQ system to liquefaction-induced lateral displacement under horizontal and vertical earthquake excitations. To accurately describe the lateral displacement behind the quay wall, the liquefaction behavior of soils was described by a modified generalized plasticity model with parameters properly determined from laboratory tests. The numerical model of the SPSQ system was validated against the previously reported centrifuge model tests. The results show that the earthquake excitation with abundant low-frequency component causes greater residual lateral displacements of pile cap (ux,RC) and quay wall (ux,RQ) than that with abundant high-frequency component. The ux,RC and ux,RQ tend to increase as the peak vertical acceleration increases for both vertical and inclined piles. Increasing the fixity of the quay wall significantly reduces the influence of vertical ground motion on the ux,RC and ux,RQ. The polarity reversal of the vertical ground motion also has a significant effect on the ux,RC and ux,RQ and should be considered in the analyses. In addition, the lateral displacement of liquefied ground causes an amount of rotation of the cap of the inclined pile, probably leading to the potential shear failure at the head of piles. Special consideration should be given to the earthquake-induced shear force at deeper location because the shear force could be significantly greater than that at the head of both inclined and vertical piles in certain cases.

An improved generalized plasticity model for rockfill materials and its experimental and numerical verification

PurposeThe stress–strain behaviors of rockfill materials in dams are significantly affected by the anisotropy and grain crushing. However, these factors are rarely considered in numerical simulations of high rockfill dams. This study intends to develop a reasonable and practical constitutive model for rockfill materials to overcome the above problems.Design/methodology/approachThe effects of anisotropy and grain crushing are comprehensively considered by the spatial position of the reference state line. After the improved generalized plasticity model for rockfill materials (referred to as the PZR model) is developed and verified by laboratory tests, it is used with the finite element method to simulate the stress–strain behaviors of the Nuozhadu high core rockfill dam.FindingsThe simulated results agree well with the laboratory tests data and the situ monitoring data, verifying the reliability and practicability of the developed PZR model.Originality/valueA new anisotropic state parameter is proposed to reflect the nonmonotonic variation in the strength as the major principal stress direction angle varies. This advantage is verified by the simulation of a set of conventional triaxial tests with different inclination angles of the compaction plane. 2) This is the first time that the elastoplastic model is verified by the situ monitoring data of high core rockfill dams. The numerical simulation results show that the PZR model can well reflect the stress–strain characteristics of rockfill materials in high core rockfill dams and is better than the traditional EB model.

Modeling the Mechanical Behavior of Methane Hydrate-Bearing Sand Using the Equivalent Granular Void Ratio

For the safe extraction of methane from hydrate reservoirs, modeling the mechanical behavior of the methane hydrate-bearing soil properly is crucial in order to enable designers to analysis hydrate-dissociation-induced geotechnical failures. Hydrate morphology is one of major factors affecting the mechanical behavior of soil containing hydrate. This paper presents a new constitutive model for methane hydrate-bearing sand (MHBS) using the equivalent granular void ratio as a state variable, which can quantify the effects of the pore-filling and load-bearing hydrate morphology under a unifying framework. The proposed model is a combination of generalized plasticity and an elastic damage model so as to take into account the observed frictional and bonding aspects of MHBS, respectively. By using the concept of state-dependent dilatancy, the equivalent granular void ratio is formulated and adopted in the generalized plasticity model. In addition, a nonlinear damage function is implemented to elucidate the degradation of hydrate bonds with respect to shearing. Compared with the basic generalized plasticity model for host sand, only three additional parameters are required to capture key mechanical behaviors of MHBS. By comparing the triaxial test results of MHBS synthesized from a range of host sands with a predicted behavior by the proposed model, it is demonstrated that the new model can satisfactorily capture the stress–strain and volumetric behavior of MHBS under different hydrate saturations, confining pressures, and void ratios.

Unified modeling behavior of rockfill materials along different loading stress paths

Rockfill materials used for dam construction show obvious stress path dependency during construction process. The constitutive model for rockfill materials are mainly established based on conventional triaxial test. This brings some deviation to the numerical calculation for earth rockfill dam engineering, and it is necessary to develop a constitutive model considering stress paths effect. In the framework of generalized plasticity, plastic modulus can be expressed as the function of dilatancy equation and tangent modulus, hence the influence of stress paths on model can be transfer to the dilatancy equation and tangent modulus. This leads to a new method to describe stress-strain response of rockfill under various loading stress paths. Based on the analysis of large-scale triaxial experiments of rockfill materials with various stress paths, we proposed new dilatancy equation and tangent modulus to better describe stress paths effect and corresponding modified generalized plasticity model is established. Through the prediction and comparison of three groups of rockfill materials triaxial tests, the model established in this paper can simulate behaviors of rockfill materials under various stress paths, using only a set of parameters.

Generalized plasticity model considering grain crushing and anisotropy for rockfill materials

Generalized plasticity model considering grain crushing and anisotropy for rockfill materials

Modified anisotropic generalized plasticity model for rockfills based on spatial mobilized plane

A modified anisotropic generalized plasticity model for rockfills is developed by improving the previous version. The improvements include a new anisotropic variable ω', a new anisotropic state parameter ξ', and a modified dilatancy equation. The ω' is constructed on the basis of the angle between the spatial mobilized plane and compaction plane and can degenerate to zero in the case of vertical compaction. The anisotropic state parameter ξ', which includes the effects of ω' and mean principal stress, can simulate the initial moduli changing with the direction angles of major principal stress under different confining pressures. The modification of the dilatancy equation including ξ' and correction term can reduce the overestimation of the volumetric contraction in the initial shear stage. To verify the modified model, triaxial tests for rockfill materials with different confining pressures and different direction angles are simulated and analyzed. The simulation results are in good agreement with the test values. Compared with the original model, the modified model is more effective in describing the mechanical properties of rockfill materials, especially in the initial shear stage, and more practical.

Three-dimensional refined analysis of seismic cracking and anti-seismic measures performance of concrete face slab in CFRDs

The concrete face slab is the primary anti-seepage component of concrete faced rockfill dams (CFRDs). Therefore, the seismic safety of the slab is an important issue. In this paper, the cohesive zone model and the explicit solution are expanded to conduct 3D seismic failure analysis of a CFRD. A combination of the generalized plasticity model of rockfill, state-dependent elasto-plastic model of soil-structure interfaces, a non-uniform wave input method and the scaled boundary finite element method is used to perform an elasto-plastic, cross-scale analysis of the seismic cracking evolution of concrete face slabs. The above combined method is used to investigate the cracking mechanism, cracking characteristics and potential anti-seismic measures. The results indicate that the cyclic deformation caused by the earthquake results in the formation of horizontal, connected cracks in the middle of the slab at 70–75% of the dam height. In addition, the plastic deformation of the rockfill leads to the formation of horizontal, unconnected cracks on both sides of the slab at 85% of the dam height. A comprehensive anti-seismic measure is proposed based on material property improvement and structural optimization, decreasing the maximum crack width and the total crack length by 21% and 89.9%, respectively.

A generalized plasticity model incorporating stress state, strain rate and temperature effects

Due to the difficulties in decoupling of the strain rate and stress state effects at high strain rates, very few constitutive models can account for the both effects simultaneously. Based on a novel method in the determination of the shear behaviors and constitutive modeling of materials (J. Mech. Phys. Solids 129 (2019): 184–204)), this work aims to propose a plasticity model that considers not only the stress state effect, but also the effects of strain, strain rate, and temperature on the flow stress. A series of experimental work has been conducted on the Ti-6Al-4V alloy to determine its plastic behaviors and micromechanism under different stress states (uni-axial tension, compression, and simple shear) over a large range of temperatures (93 K–1073 K) and strain rates (10−3 s − 1–6.5 × 103 s−1). Then a stress triaxiality and Lode parameter dependent plasticity model is proposed to describe the experimental results, with its performance compared systematically with the Johnson-Cook (JC) model. A much higher accuracy is shown by the present model in the characterization of the tension and compression tests. The applicability of this model is also checked by implementing it in the commercial finite element program ABAQUS/Explicit via the user material subroutine coded as VUMAT. Compared to the JC model, an obvious improvement is observed for the present model in the simulation results of both the stress waves and the flow stress curves.

Formulation and numerical implementation of a state parameter-based generalized plasticity model for mine tailings

Mine tailings are rock flour that is generally deposited in tailings dams. When deposited in a loose and saturated state, the tailings are prone to flow liquefaction. Simulating the onset of liquefaction and the post-liquefaction behavior of tailings has therefore become an essential aspect in geotechnical engineering of tailings dams. Several analysis procedures have been developed to address this problem, most of them employing the state parameter ψ as the key indicator of material behavior. The use of numerical deformation modelling for addressing the onset of flow liquefaction is increasingly practiced. Therefore, constitutive models, which are based on the state parameter and can simulate a wide range of stress paths, are demanded by the industry. This paper presents the formulation of an extension of a generalized plasticity model that is based on the state parameter and that simulates liquefaction within a critical state framework. As such, it is attractive for modelling loose tailings. The model is extended to the general 3D stress space and implemented by using an implicit integration scheme as a user model in Plaxis. This paper describes the set up and calibration of the model based on a set of laboratory tests on tailings and includes a numerical exercise proving the consistency and robustness of the formulation.

Liquefaction-induced settlement of the pile group under vertical and horizontal ground motions

End-bearing piles have been widely used to resist earthquake-induced settlement of buildings in sand deposits. However, the earthquake can generate the excess water pressure in saturated sand deposits and thus reduce both the friction resistance and end-bearing capacity of piles, further resulting in the pile settlement which may not be sustained by the superstructure. In this study, a fully coupled dynamic effective-stress finite element procedure is used to investigate the effects of the frequency content of input motion and the amplitude of both horizontal and vertical components of input motion on the settlement of the pile group in saturated sand deposits. A modified generalized plasticity model is employed to characterize the dynamic behavior of various density of sands. The effect of the soil permeability on the seismic response of the pile-soil system is investigated. The results indicate that the relatively distant earthquake cause more severe liquefaction at the sand deposit than the nearby earthquake and thus induces more settlement of the pile group under otherwise identical conditions. Moreover, the vertical ground motion could significantly increase the coseismic liquefaction-induced settlement of the pile group (ρE) and should be taken into account in engineering design. A simplified practical method based on the load-transfer methodology is proposed to estimate the ρE for the pile group with the cap above the ground.

Numerical simulation of the effect of moving loads on saturated subgrade soil

The substantial increase in excess pore pressure and plastic strain in subgrade soil due to faster and heavier trains is a major cause of track instability. Stresses that occur in track substructure during the passage of trains have not often been captured accurately due to insufficient rigour in dynamic analysis. This paper presents a numerical investigation into the plastic/dynamic characteristics of a saturated porous medium (capping and subgrade) subjected to moving axle loads. In this study, a detailed numerical analysis is described, whereby a coupled fluid-dynamic framework is developed for the saturated porous medium in conjunction with a generalized plasticity model, in order to examine the cyclic loading response of a soft subgrade soil. The constitutive model is calibrated by undrained cyclic triaxial testing carried out on a soft foundation soil retrieved from a coastal railroad site having a historical record of mud pumping. Kelvin elements are attached to the transmitting boundary to absorb wave energy and to prevent any back-propagation of waves into the saturated subgrade domain. This approach is then validated against a semi-analytical solution and wayside measurements. The results show that the stress path corresponding to the applied moving load exhibits a series of heart-shaped envelopes along which the deviator stress and mean effective stress gradually decrease with the successive loading cycles. The build-up of pore water pressure and the associated soil deformation (e.g. accumulated settlement) are exacerbated when the train speed approaches a critical velocity of the saturated subgrade. A relationship between the train speed, track settlement and drainage capacity of a sub-ballast (capping) layer is also established. As a practical guide, the influence of permeability of the capping layer is highlighted in relation to controlling track settlement for a given operational train speed.

Prediction and numerical simulation of the face‐slab extrusion damage of Dashixia concrete faced rock‐fill dam

AbstractOne of the core issues affecting the safety of high concrete faced rock‐fill dams (CFRDs) is the extrusion damage of the concrete face slabs. In this paper, the causes of the face‐slab extrusion damage under long‐term operational conditions are studied. It is found that not only the creep behavior of the dam materials but also the circulating water load in the reservoir is responsible for the uneven deformation of the dam that induces the extrusion damage of the face slabs. The possibility of the potential extrusion damage of the face slab of the Dashixia dam, which is now under construction in Xinjiang, China, is further predicted by means of a three‐dimensional finite element analysis (FEA). In the FEA, a unified generalized plasticity model that can reflect the volumetric contraction property during the unloading phase of coarse‐grained materials is adopted to overcome the shortcomings of previous studies where the effects of the circulating water load are neglected because of model limitations. Then, combined with an incremental creep model, the long‐term operational characteristics of the Dashixia dam are predicted and thoroughly discussed. Moreover, a submodel of the face slab is developed and introduced in the analysis to simulate the compressive stress along the thickness of the face slab. According to the results, it can be concluded that extrusion damage of the face slab of the Dashixia dam may occur under the current design conditions, and it is recommended to take some engineering measures to strengthen the slab.

Numerical modelling of the fluid–seabed-structure interactions considering the impact of principal stress axes rotations

The principal stresses that occur in soil below ground level often change direction due to engineering activities. A typical example would be the cyclic loading applied by waves and currents onto the foundation of offshore structures. Even though the principal stress rotations (PSR) are recognized as some kind of “loading” that is exerted onto seabed soil, it is ignored in most investigations into how soil around marine structures responds to ocean waves and currents. In response this paper will simulate the fluid-seabed-structure interactions (FSSI) while considering the impact of PSR. This simulation will utilize an integrated numerical model in which VARANS equations are used for the flow motion. A coupled fluid-dynamic framework and a generalized plasticity model will be developed for the saturated porous medium to examine the cyclic loading of seabed and the continuous rotation of principal stress orientations. It is predicted that the stress path in the τxz versus (σx′−σz′) plane around the structure will denote variations in deviator stress in conjunction with the rotations of the principal stress axis. The mechanical impact of PSR becomes most significant in the region beneath the breakwater and up to a depth of the half thickness of the seabed. Ignoring the PSR-induced deformation may lead to an underestimation of (p̄PSR−p̄no−PSR)∕γwd by 35% in this region.

Plastic damage analysis of pile foundation of nuclear power plants under beyond-design basis earthquake excitation

With the rapid development of nuclear industry in China, an increasing number of nuclear power plants (NPPs) are unavoidable to be constructed upon non-lithological foundations. Therefore, it is essential to optimize the current evaluation methods for non-lithological foundation reinforcement plans. By using the Octree discretization method combining with the scaled boundary polyhedron finite element method (SBFEM), a refined calculation model of a Generation III+ NPP is constructed. Due to the highly nonlinear dynamic characteristics of the system involved, this paper adopts a generalized plasticity model for the soil, a plastic damage model for the piles, and a nonlinear overburden layer-based seismic input method. Subsequently, large scale plastic damage analysis in detail to the NPPs under beyond-design basis earthquake inputs is performed. The results show that the pile foundation damage characteristics and distribution acquired from simulations agree well with the data from actual earthquake disasters. The most severe damage to the pile foundation occurred at the interface between the end of the pile and the base mat. The inclusion of plastic damage showed that the floor response spectra of the nuclear island experiences significant changes in three dimensions. Therefore, the effect of pile damage to the dynamic response of the power plants should be considered for strong earthquake excitation. The computational and analysis methods proposed in this paper can effectively reflect the dynamic nonlinear response of the nuclear power plants pile foundation-soil interaction.

Meshfree modeling of cyclic behavior of sands within large strain Generalized Plasticity Framework

Abstract In this publication the u - w finite strain formulation is enhanced with a Generalized Plasticity model for sands. The new model is numerically solved using an Optimal Transportation Meshfree approach that is best suited for numerical analysis at finite strains. This new model allows to capture the hydro-mechanical response under large deformations of a saturated sand like soils where acceleration of water with respect the solid skeleton is not negligible. To the authors’ knowledge, no attempt has been previously devoted to include in the u - w finite strain approach an elastoplastic behavior from the Generalized Plasticity theory. In order to assess the validity of the proposed model, four standard laboratory tests are numerically reproduced: i) an undrained triaxial test under monotonic loading, ii) a triaxial consolidation test under monotonic loading with drained boundary conditions, iii) an undrained cyclic triaxial test and iv) a drained cyclic triaxial test. The observed results are qualitatively correct and in agreement with numerical solutions previously obtained by other researchers and with related experimental data.