Bounding Surface Plasticity Model Research Articles

Assessment of Free Energy Functions for Sand

ABSTRACTThe advantages of constitutive models in energy‐conservation frameworks have been widely addressed in the literature. A key component is choosing an appropriate energy potential to derive the hyperelastic constitutive equations. This article investigates the advantages and limitations of different energy potentials found in the literature based on mathematical conditions to guarantee numerical stability, such as the desired order of homogeneity, positive and non‐singular stiffness within the application range, and equivalent Poisson's ratio from a constitutive modelling standpoint. Potentials meeting the aforementioned criteria are employed to simulate the response envelopes of Karlsruhe fine sand (KFS). Moreover, the performance of the potentials, in conjunction with plasticity theories, is examined. To achieve this, the hyperelastic constitutive equations have been coupled with the bounding surface plasticity model of Dafalias and Manzari to reproduce the soil response in a hyperelastic–plastic frame. Finally, one of the potentials is modified, whereas recommendations for incorporating other appropriate free energy functions into different soil constitutive models are presented. Furthermore, 100 closed elastic strain cycles have been simulated with the bounding surface plasticity model of Dafalias and Manzari considering the original hypoelastic stiffness and hyperelastic–plastic constitutive equations. Using the hypoelastic framework in the simulation led to stress accumulation after 100 closed elastic strain loops, while a reversible response was predicted using the hyperelastic stiffness tensor.

3D FE simulation of PISA monopile field tests at Dunkirk using SANISAND-MS

This paper presents an investigation into the suitability of the SANISAND-MS model for the three-dimensional finite-element (3D FE) simulation of cyclic monopile behaviour in sandy soils. In addition to previous work on the subject, the primary focus of this study is to further assess the model's capability to reproduce the accumulation of permanent deflection/tilt under cyclic lateral load histories. To this end, experimental data from the PISA field campaign are employed, particularly those emerged from the medium-scale cyclic tests conducted at the Dunkirk site in France. The methodology adopted herein involves calibrating the SANISAND-MS model's parameters to align with 3D FE simulation of a selected monotonic pile test reported by the PISA team using a bounding surface plasticity model partly similar to SANISAND-MS. Subsequently, the soil parameters governing SANISAND-MS’ ratcheting response are calibrated using only minimal information from published PISA field data. While representing the first attempt to simulate the reference data set using a fully ‘implicit’ 3D FE approach, this paper offers novel insights into calibrating and using advanced cyclic models for monopile analysis and design – particularly, with regard to the quantitative influence of pile installation effects and sand's microstructural evolution under drained cyclic loading.

A Hyperelastic Bounding Surface Plasticity Model for Unsaturated Granular Soils

A Hyperelastic Bounding Surface Plasticity Model for Unsaturated Granular Soils

Constitutive modeling of anisotropic small-strain stiffness behavior of Shanghai soft clay

Small strain stiffness plays an important role in determining the deformation of geotechnical engineering in soft soils. To model the anisotropic small strain stiffness behavior of soft clay, an enhancement to the bounding surface plasticity model is proposed. This enhancement involves incorporating the anisotropy in soil stiffness at very small strains and its non-linear degradation. Small strains are considered via cross-anisotropy elasticity, while the concept of intergranular strain is used to reflect the non-linear degradation of stiffness with strains and the effect of recent stress history. Using the proposed model, the triaxial test results on K0 consolidated Shanghai clay specimens are simulated to investigate the model’s performance. In the simulation, three typical shear stress paths are adopted. The comparison of the model simulations against experimental evidence is discussed, where the effects of anisotropy in initial soil stiffness and stress-induced anisotropy on the variation of small-strain stiffness, pore pressure, and shear-volume coupling response are highlighted.

BOUNDING SURFACE COUPLED FINITE ELEMENT CONSOLIDATION ANALYSIS OF NORMALLY AND OVERCONSOLIDATED CLAYS

The radial mapping version of the bounding surface plasticity model is implemented in a computer program to predict the response of cohesive soils. The eight-noded isoparametric element and Biot’s theory are used in this study for analyzing soil consolidation problems. The model has been used in the analysis for two classes of problems. The first involves the comparison of model predictions with the results of laboratory tests in compression and extension for normally and overconsolidated clays. The second class involves using the model to predict the results of one- and two-dimensional finite element problems of soil consolidation. The comparisons with experiments demonstrate that the model, through its simplicity, can describe realistically the soil response under different monotonic loading conditions at any overconsolidation ratio. The comparison between the bounding surface plasticity model with the classical modified Cam clay model shows considerably different rates and magnitudes of settlement, and different pore pressure behavior during the consolidation process.

A viscoplastic constitutive model for plastic silts and clays for static slope stability applications

A viscoplastic model for representing plastic silts and clays in geotechnical static slope stability applications is presented. The PM4SiltR model builds on the stress ratio-controlled, critical state-based, bounding surface plasticity model PM4Silt and is coded as a dynamic link library for use in the finite difference program FLAC 8.1. PM4SiltR incorporates strain rate-dependent shear strength, stress relaxation, and creep using a consistency approach combined with an internal strain rate and auto-decay process. The model does not include a cap, and as such cannot simulate strain rate-dependent consolidation under increasing overburden stress. Six parameters control the viscous response for PM4SiltR while the parameters controlling the nonviscous components of the response are the same as for PM4Silt. Single element simulations are presented to illustrate the influence of viscoplasticity on the constitutive response in direct simple shear loading and undrained creep. Single element responses are shown to be consistent with observed experimental results. Simulations of a hypothetical tailings dam constructed using the upstream method are performed to illustrate use of PM4SiltR at field scale. Results of field scale simulations show PM4SiltR can model undrained creep and progressive failure leading to delayed slope instability after relatively minor changes in loading conditions at field scale.

Implementation of an advanced bounding surface constitutive model in OpenSees

The dynamic behaviour of saturated coarse-grained soils has recently received wide attention because of its impact on the seismic performance of geotechnical and structural systems. This is due to the peculiarities of their cyclic response (e.g., liquefaction, ratcheting and volumetric-deviatoric coupling). Consequently, the seismic risk mitigation of the built environment requires efficient predictive models applicable in design and assessment. To this end, several constitutive models have been developed for a realistic description of the cyclic soil behaviour. From this perspective, this paper describes the implementation and testing of the bounding surface plasticity model developed by Papadimitriou and Bouckovalas (2002) in OpenSees as a means for advanced assessment of soil-structure systems. The implemented model includes essential features of the cyclic soil response. Moreover, a modified fabric tensor evolution equation is introduced for improving the response and numerical stability in boundary value problems, at the cost of an extra model constant. The workflow concerning the integration of the model into OpenSees is presented, followed by instructions about its use in boundary value problems. A comprehensive verification of the model response is discussed. The numerical simulations demonstrated the robustness of the implemented code in capturing soil behaviour from small to large strain levels.

The pullout capacity of OMNI-Max anchors in sand

As the latest development and benchmark of a gravity installed anchor (GIA), the OMNI-Max anchor stands as a cutting-edge achievement and benchmark, finding increasingly widespread use within mooring systems due to its exceptional operational performance and adaptability. Notably, while investigations into the pullout capacity of OMNI-Max anchors have been conducted extensively in clay, the relevant studies are seldom observed in sand. Actually, the mechanical properties of sand are quite different from those of clay, and sand is also widely distributed in seabed soil. Full knowledge of OMNI-Max anchors not only in clay but also in sand is necessary to a wider application of the anchors. In the present work, the large deformation finite element (LDFE) method is adopted combined with the coupled Eulerian-Lagrangian (CEL) technique to study the end-bearing characteristics of the OMNI-Max anchor in sand seabeds. A bounding-surface plasticity model is taken as the constitutive model to capture the characteristics of sand. Through investigation and analysis, OMNI-Max anchors are closely related to the anchor embedment depth, the soil relative density, the anchor orientation, the loading angle and the bearing area, so the working conditions related to these five factors are designed and calculated. An explicit expression of the end-bearing capacity factor is finally derived to provide a simple and fast tool of evaluating the pullout capacity of the anchor in sand under multiple factors. Validation cases and orthogonal tests have confirmed the effectiveness and applicability of the explicit expression.

Comparison of a tailings material and a natural sand in seismic site response analyses

This article investigates the seismic response of a tailings sand material in the context of site response analysis. The computed response is contrasted with that obtained for an equivalent deposit consisting of a well-characterised natural sand. Initially, the fundamental properties of both materials are used to interpret and compare their behaviour in the framework of Critical State Soil Mechanics (CSSM). Subsequently, both materials' monotonic and cyclic responses are calibrated for an advanced bounding surface plasticity model. Finally, the impact of different calibration approaches is examined through site response analyses under a strong motion. This process identifies fundamental differences between the two geo-materials, impacting the single elements simulations, especially the accuracy of undrained cyclic triaxial tests. The site response analyses examined herein show the impact of the calibrations adopted for both materials in terms of acceleration response spectra, displacements, and excess of pore water pressures (PWP). Although a relatively deep phreatic surface is adopted, the cyclic resistance and permeability of both materials plays a dominant role in the site response characteristics, controlling the excess PWP generation and hence the non-linear behaviour in the soil deposit. Finally, parametric studies are also conducted to explore the impact of permeability of the sands in the site response.

Bounding Surface Plasticity Model for Clay under Cyclic Loading Conditions Considering Fabric Anisotropy

Bounding Surface Plasticity Model for Clay under Cyclic Loading Conditions Considering Fabric Anisotropy

A bounding surface plasticity model for methane hydrate-bearing sediments in deep seabed

This study proposes a new constitutive model to simulate the mechanical behavior of methane hydrate-bearing sediments, by modifying the SANISAND-C model originally designed for sands with low cement content. To capture the distinctive cementation effect of methane hydrate (MH), modifications are made to the state parameter and bonding degradation law of the SANISAND-C model. In addition, the initial bonding strength of MH is not only determined by MH saturation but also by a condition parameter that depends on temperature, pore pressure, and salinity. The densification effect caused by MH pore-filling and grain-coating is captured by replacing the original void ratio in the elastic and plastic moduli of the SANISAND-C model with a reduced void ratio. The model is verified through a comparison of its predictions not only with experimental data but also through discrete element method simulations that cover a wide range of loading paths including drained and undrained true triaxial tests. The model successfully captures the stiffness, strength and dilatancy enhancements induced by MH, as well as the temperature, pore pressure, and salinity-dependent behavior of sediment. Additionally, the model developed can account for different hydrate occurrence habits by adjusting a single parameter related to bonding strength.

Bounding surface plasticity model modification for ratcheting of metals

The Bounding Surface (BS) plasticity model for metals is modified according to the proposition introduced in the works of Burlet and Cailletaud (1986) and Delobelle (1993) for the kinematic hardening of a classical Armstrong/Frederick (AF) model, called the BCD modification from the initials of the foregoing authors. The BCD modification was introduced in the relative kinematic hardening between Yield Surface (YS) and BS, unlike its introduction in the absolute and single kinematic hardening of YS for an AF model, hence, achieving two objectives: first, maintaining the inherent feature of BS for decoupling plastic modulus and direction of kinematic hardening, and, second, allowing a flexibility as to the relative kinematic hardening direction without altering the value of the plastic modulus, a property of BCD modification. In addition, the introduced BCD modification for the BS is significantly modified itself, by introducing a properly varying modification parameter instead of the fixed one used in the original works. This simple feature of the novel BCD modification provides a dramatically improved capability to simulate multiaxial ratcheting (MR), because it affects directly the changing flow rule direction, due to the relative kinematic hardening, during complex multiaxial loading, without sacrificing accurate simulations under uniaxial ratcheting (UR) since the plastic modulus is not affected. An additional significant contribution to successful UR simulations is provided by the free-to-choose kinematic hardening of the BS, since the BCD modification is applied only to the relative kinematic hardening between BS and YS. The new model, named SANIMETAL-BCD, is shown to yield superior or equal simulations of UR and very complex MR experimental data for three Carbon Steel specimens, in comparison with other models, within a much simpler constitutive framework. Shortcomings and future necessary improvements are discussed in details.

A discrete-based multi-scale modeling approach for the propagation of seismic waves in soils

A three-dimensional multi-scale discrete–continuum model (Finite Volume Method × Discrete Element Method, FVM × DEM) is developed for a discrete-based description of the mechanical behavior of granular soils in boundary value problems (BVPs). In such a scheme, the constitutive response of the material is derived through direct DEM computations on a representative volume element attached to each mesh element. The developed multi-scale approach includes the inertial effect in the stress homogenization formulation and serves to study the mechanism of propagation of seismic waves, in comparison with a more classical BVP simulation that adopts an advanced bounding surface plasticity model “P2PSand”. We start with a detailed and fair calibration and validation of these two models against laboratory tests for Toyoura sand under monotonic and cyclic loading. Then, the performance of the two approaches is compared for the case of a seismic wave loading passing through a saturated soil column with different relative densities, revealing several differences between the results of the two models.

On the influence of cyclic preloadings on the liquefaction resistance of sands: A numerical study

Soil deposits may be subjected to preloading episodes due to different factors such as previous earthquakes, excavations, refilling, compaction, construction of overlying structures, storms under onshore/offshore conditions, among many others. It is well-known that preloading episodes remarkably influence the subsequent soil mechanical behavior and liquefaction resistance. In order to accurately describe the influence of cyclic preloadings, advanced constitutive models which are able to realistically reproduce the soil mechanical behavior are necessary. In this work, a numerical study was carried out to investigate the influence of cyclic preloadings on the liquefaction resistance of sands. The numerical analyses were performed considering three advanced and well established constitutive models, namely: the hypoplastic model for sands by Von Wolffersdorf (1996) with the Intergranular Strain extension by Niemunis and Herle (1997), the same hypoplastic model for sands extended with Intergranular Strain Anisotropy by Fuentes et al. (2020), and the bounding surface plasticity model Sanisand by Dafalias and Manzari (2004). The simulations were performed based on the experimental databases on Zbraslav sand by Duque et al. (2023a,b). Remarks about the model capabilities and limitations on tests with different types of cyclic preloadings and their repercussion on boundary value simulations are given at the end.

An anisotropic egg-shaped bounding surface model for saturated soft clay

An anisotropic egg-shaped bounding surface plasticity model (AESBS model) is proposed to describe cyclic and monotonic behaviors of saturated clays. The model is based on an innovative egg-shaped bounding surface, which not only eliminates the singularity present in most plasticity models and facilitates numerical calculation but also can be degenerated into various configurations. Moreover, to improve its representation when considering the initial consolidated state, an anisotropic tensor is incorporated into the bounding surface. Furthermore, a novel generalized isotropic hardening rule that combines isotropic and kinematic hardening is applied. It regards reversal stress points as homological mapping centers, hence leading to discrete and movable mapping centers. Notably, the elastic zone concept is employed to produce a more realistic performance of nonlinearity during cyclic loading. These modifications formulate the novel model that can be utilized to enhance the ability in predicting the behavior of saturated clays. To improve the convergence of the model, an implicit integration scheme is used to solved the constitutive relationship through some nonlinear algebraic equations. The comparison of simulation results and published experimental data from one-way undrained cyclic and monotonic triaxial tests for saturated clays demonstrates the efficiency of this model under different consolidated conditions.

Roles of pre- and post-liquefaction stages in dynamic system response of liquefiable sand retained by a sheet-pile wall

This study examines the dynamic system response of a liquefiable deposit retained by a sheet-pile wall, with emphasis on the roles of pre- and post-liquefaction stages of soil response. A recently developed constitutive model, SANISAND-MSf, is utilized to simulate the pre- and post-liquefaction cyclic response of sands. The model is a stress-ratio controlled, critical state compatible, bounding surface plasticity model, which incorporates the concepts of memory surface and semifluidized state. The model’s performance is validated using a combination of cyclic simple shear tests and dynamic centrifuge tests from the LEAP-2020 project. A sensitivity analysis is then conducted by varying the base input motion intensity and duration. The results reveal that the amplitude of equivalent uniform base acceleration in pre-liquefaction correlates well with the timing of liquefaction triggering, and the cumulative absolute velocity of the base acceleration during the post-liquefaction stage correlates well with the post-liquefaction displacements. The study highlights the importance of accurately simulating response in the pre-liquefaction stage for the extent and timing of occurrence of liquefaction, which regulates the remaining intensity and duration of shaking, and in turn, affects the post-liquefaction permanent deformations at the system level.

Modelling unsaturated silty tailings and the conditions required for static liquefaction

The potential for static liquefaction of tailings is a major focus in the design and operation of tailings storage facilities. This research models the behaviour of unsaturated tailings, with a variety of degrees of saturation, addressing the propensity for static liquefaction during monotonic loading. Unsaturated triaxial tests, including constant suction conditions and constant water–air mass conditions, were performed. A bounding surface plasticity model was used to simulate the results. The constant mass condition is relevant to undrained closed-system loading, which may prevail during fast deformation after the tailings becomes unstable, when the air and water in the pore space remain locked inside the tailings. Boyle's law and hydraulic hysteresis were accounted for to model the changes of pore air and water pressures, and suction, with the change in tailings volume. Good agreement was achieved between test results and model simulations. Additional simulations to mimic rising water tables under constant total stress states in the field, situations that may trigger instabilities, are also shown. Results are added to charts which relate peak and post-liquefaction strengths, as well as collapse lines, to measures of initial state, for unsaturated conditions, which may be of use in practice.

Implicit Algorithm of the SBSP-R Model for Predicting the Non-Unique Critical State of Soils

The non-unique critical state represents the distance between the critical state line (CSL) and the isotropic consolidation line (ICL) that significantly varies with stress paths and particle size distribution of soils. A structural bounding surface plasticity model with spacing ratio r (SBSP-R model) was implemented using an explicit algorithm. However, the explicit algorithm did not well capture the non-unique critical state of soils with a large spacing ratio r, which prevented the soil mechanics research on non-unique critical state via finite element analysis. To overcome the limitation, the implicit algorithm of the SBSP-R model is formulated, and it mainly includes elastic prediction and plastic correction. The plastic correction is realized using the Newton–Simpson scheme with a controlling equation set related to consistency condition, plastic flow, hardening parameter, structural bounding surface, plastic modulus, and mapping rule. Case studies indicate that the implicit algorithm of the SBSP-R model is right and stable in predicting non-unique critical states. Comparisons between predicted and tested results indicate that the implicit algorithm of the SBSP-R model not only captures the critical state, stress-strain, and stress paths of various soils but also shows higher computational accuracy and efficiency compared with the previous explicit algorithm. These results indicate that the formulated implicit algorithm of the SBSP-R model is an alternative approach to the previous explicit algorithm.

Constitutive modelling of instabilities and strengths of an unsaturated tailings

Instabilities mostly happen in fully saturated and loose non-cohesive geomaterials like sands or silts or tailings, but it is also possible in unsaturated geomaterials. When unsaturated they can experience a reduction in effective stress and strain soften during water (and air) undrained loading, attaining a very low residual strength. This study focuses on modelling the conditions required to cause instability in unsaturated silty tailings, giving particular consideration to the presence of air and the way it alters the ability for volume change when it remains trapped inside the tailings. A gold tailings is used to calibrate the UNSW boundingsurface plasticity model. The effect of air, including the volumetric change caused by air compression, the alteration of air pressure, the contribution of suction to the effective stress, and suction hardening, are explored. Collapse lines (sometimes referred to as instability lines or flow liquefaction lines which represent boundaries between stable and potentially unstable stress states) in the 𝑞𝑞 − 𝑝𝑝′ plane are explored. The undrained shear strength ratios and slopes of the collapse lines are compared to those of other tailings andsands when unsaturated.

Numerical and analytical investigation on inclined plate anchors in sand

The paper investigates the ultimate capacity of inclined plate anchors in sand through a series of finite element (FE) analyses. The FE simulations adopted a sophisticated bounding surface plasticity model that accounts for stress and density dependent behaviour, thus portraying a realistic estimate of the shear stresses and shear strains within the failure mechanism. The simulations considered a strip anchor with different plate widths, plate inclination angles and shallow embedment ratios in dense sand. The FE results show good agreement with previously reported experimental data. A limit equilibrium solution is subsequently proposed to predict capacity of inclined strip anchors in sand, based on mathematical expressions of the FE simulated normal and shear stresses along mobilised failure planes. The limit equilibrium solution is shown to produce satisfactory agreement with results from a large database of inclined plate anchors.