Bounding Surface Model Research Articles

Dynamic response of OWT tripod pile foundation in clay considering scour

Tripod-supported offshore wind turbine (OWT) foundation must withstand wind, wave, and seismic loads. In addition, it may be threatened by scouring during its service life, which could affect its bearing capacity and the overall OWT dynamic response. This study develops a three-dimensional numerical model of OWT tripod pile foundation to investigate scour effects. The numerical model incorporates a simplified single bounding surface model to simulate the dynamic stress–strain response of clay soil. The results revealed that scouring can reduce the first-order natural frequency of tripod pile-OWT system; however, the reduction usually does not lead to resonance within the 1P frequency range. Nonetheless, as the scour depth increases under wind and wave loads, the horizontal displacement of the wind turbine structure increases monotonously; however, its peak acceleration increases initially then decreases slightly as the scour depth continues to increase. Under seismic loading only, the OWT response exhibits complex evolution pattern as the scour depth increases. On the other hand, the foundation horizontal displacement and rotation angle increase significantly under combined wind-wave-seismic loads when the scouring depth reaches three times the pile diameter. Finally, the scouring depth has a relatively small impact on the foundation vertical displacement.

A bounding surface model for anisotropic and structured soils under saturated and unsaturated conditions

Sedimentary soils usually have an anisotropic structure, and they are generally unsaturated, especially at shallow depths. Existing models for anisotropic and structured soils mainly focus on saturated conditions, while the unsaturation effects are not considered. In this study, a bounding surface model for anisotropic and structured soils under both saturated and unsaturated conditions is developed. The model incorporates the anisotropy and structure effects on the mechanical behaviour (e.g., the loading collapse (LC) bounding surface) and considers the structure degradation and anisotropy evolution. Furthermore, based on experimental results in the literature, the increase in water retention capacity with an increasing degree of anisotropy is incorporated by a new anisotropy and void ratio-dependent soil water retention equation. The proposed hydro-mechanical model is validated against extensive experimental data. Comparisons between experimental and calculated results show that the behaviour of anisotropic and structured soils under both saturated and unsaturated conditions can be well captured.

A unified thermo-mechanical bounding surface model for saturated clay and sand

To accurately predict soil thermal effects is of great importance for simulations of complex boundary value problems such as the energy foundations and nuclear waste disposal. Existing thermo-mechanical constitutive models only account for clay, and cannot simulate the sand’s behaviour under thermo-mechanical conditions. In this study, a unified thermo-mechanical bounding surface (UTMBS) model is proposed for saturated clay and sand. Based on the thermal effects on the isotropic compression line, the model proposes a new unified thermal softening relationship and a plastic modulus for clay and sand, with the thermal cyclic behaviour replicated by a memory surface. The unified model considers the thermal effects on the critical state line and the shape of the bounding surface, accounting for both drained and undrained shearing of clay and sand at different temperatures. In addition, the non-linear elasticity relationship represents the hysteresis loops of the stress–strain relationship in the mechanical cycles. The performance of the proposed model is evaluated against existing experimental results for clay and sand in terms of their thermal cyclic behaviour, drained/undrained triaxial compression, and mechanical cyclic behaviour at different temperatures. It is evident that the UTMBS model is able to simulate various thermo-mechanical behaviours of clay and sand.

A numerical method for calculating the long-term settlement of three-dimensional subgrade under numerous traffic loads

Settlement problems caused by various traffic loads significantly impact infrastructure sustainability. Accurately predicting the long-term settlement of subgrade is crucial for improving infrastructure resilience. This study determined the element strain of soil using an explicit strain model, based on the bounding surface model and associated flow rules. Using the method of generalized shear strain equivalent, a cyclic cumulative factor is proposed for determining the magnitude of cumulative strain increment. The direction of plastic strain increment was determined using the bounding surface model combined with associated flow rules. A cumulative strain calculation method integrating the bounding surface and explicit strain models under general stress states was established. This computational method, combined with equivalent finite elements, can be used for calculating the long-term settlement of three-dimensional subgrade under numerous cyclic loads at general stress states through a user-defined subroutine provided by the commercial finite element modeling (FEM) software. The reliability of the method was verified through unit tests.

Constitutive modeling structural behaviors of Shanghai deep clay

The rapid development of underground engineering requires a comprehensive understanding of deep soils. Existing study about the deformation and strength behaviors of Shanghai clay is mostly focused on shallow soft clay (generally within 30 m depth), while counterpart for deep clay is needed. This work investigates the physical properties and mechanical behaviors of Shanghai deep clay (block samples of layer (8) obtained at a depth of around 50 m), via conducting a series laboratory tests including physical property tests, onedimensional consolidation tests and undrained triaxial compression tests, performing constitutive modelling. The results show: (1) Shanghai layer (8) clay can be classified as a low-plasticity silty clay, and the void ratio measured in the laboratory of the block samples is larger than remoulded samples; (2) The clay is a normally consolidated clay, and the block samples show greater compressibility and stronger initial structure; (3) The block samples show contraction behaviors in the undrained triaxial compression tests; (4) The structural behaviors is well captured by structural bounding surface model.

An elastoplastic model with egg-shaped yield surface for coastal soft clay

A novel elastoplastic constitutive model with an egg-shaped yield surface (ESE model) is proposed herein to elucidate the strength-deformation characteristics of marine soft clay. One of the key improvements offered by this model is its ability to address the singularity associated with plastic strain increments at yield surface corners—a limitation commonly encountered in traditional elastoplastic models. Additionally, the proposed model demonstrates flexibility, as it can transform into various forms under different conditions. Subsequently, to evaluate the efficacy of this egg-shaped elastoplastic model, numerical simulations are performed within the finite element software ABAQUS using an implicit integration algorithm through the user material subroutine interface (UMAT). The simulations encompass standard triaxial consolidation tests involving saturated soft clay sourced from the Itsukaichi marine clay as well as two types of saturated kaolin clays. The outcomes derived from these simulations by the ESE model are compared with both empirical data and numerical simulations originating from the widely employed Modified Cam-Clay (MCC) model. The simulations of the ESE model for three conventional triaxial tests on clay demonstrate superior concordance with experimental measurements in comparison to the MCC model. This underscores the efficacy of the proposed ESE model in predicting the strength and deformation characteristics manifested by coastal soft clays under undrained conditions. Finally, the predictions for deformation in an adjacent tunnel according to the ESE model closely align with experimental measurements and prior to the simulations conducted using the MCC model and advanced models such as the bounding surface model and the unified model, thereby affirming its practical utility in engineering applications.

A Bounding Surface Model for Cemented Soil at Small and Large Strains

A Bounding Surface Model for Cemented Soil at Small and Large Strains

A bounding surface model of methane hydrate-bearing carbonate sand-silt mixtures

The geological environment of marine methane hydrate-bearing sediments (MHBS) is highly complex. Mastering the mechanical behavior of MHBS is crucial for analyzing geomechanical hazards and evaluating its stability. The marine sediment in the South China Sea (SCS) contains a significant amount of porous foraminifera shells, which serve as the primary storage space for natural gas hydrates and differ significantly from other sea areas. In the laboratory, porous carbonate sand (CS) and cohesion-less silt were utilized to prepare host sand of methane hydrate. In this paper, based on the analysis of experimental data, a bounding surface model was proposed to describe the mechanical behavior of artificial MHBS. The effect of methane hydrates on the elastic strain, normal consolidation and critical state of host sand is discussed, and corresponding equations for the model parameters are established, taking into consideration the cementing mechanism of hydrates. These equations are defined as functions of hydrate saturation, carbonate sand content (CSC), and initial void ratio. The increase in hydrate saturation significantly reduces the compressibility of the host sand and improves its strength. The proposed model is applied to predict the results of isotropic consolidation and drained triaxial tests on MHBS, demonstrating satisfactory performance.

Optimised calibration algorithm of a bounding surface model for coarse-grained soils

Optimised calibration algorithm of a bounding surface model for coarse-grained soils

Performance evaluation of the Generalized Bounding Surface Model in the simulation of Cajicá clay subjected to monotonic loading

Different constitutive models, based on principles of mechanics and experimental evidence, have been developed over several decades to represent and predict the stress-strain behavior of soils subjected to various loading conditions. The Generalized Bounding Surface Model (GBSM) is one of them and is defined as a fully three-dimensional elastoplastic constitutive model for saturated cohesive soils that employ the bounding surface plasticity in conjunction with a nonassociative flow rule and a soil microfabric-inspired rotational hardening rule. The GBSM has been successfully validated on numerous laboratory reconstituted soils, but not on natural or undisturbed soil samples. Hence, in this paper the predictive capabilities of the GBSM are evaluated in the simulation of the monotonic behavior of an undisturbed cohesive soil called “Cajicá clay” from the high plain of Bogotá in Colombia. In the first instance, an isotropic consolidation test and a set of axisymmetric triaxial compression and extension tests are conducted using an automated triaxial equipment, to experimentally describe the response of the undisturbed soil. From experimental data, the parameters associated with the GBSM model are calibrated to finally evaluate its capabilities in the simulation of a cohesive natural soil. A comparison between experimental data and numerical simulations is presented to show both performance and advantages of the GBSM model.

A thermal state‐dependent bounding surface model for volume change of clay

AbstractThermally induced volumetric strain of clay is crucial for geotechnical applications involving thermal loading. The volumetric response of clay shows a ratcheting pattern during thermal cycles until reaching a thermal stabilized state. It is also affected by the stress history of soil, including over‐consolidation ratio (OCR) and recent stress history (RSH). This paper introduces a new bounding surface model to capture effects of OCR and RSH on thermo‐mechanical behaviour of soil. A thermal state parameter is proposed to characterize the effects of stress history and thermal history. Based on the new thermal state parameter, the commonly recognised thermal softening mechanism is modified and incorporated with a bounding surface. The newly proposed model, with only 10 parameters, can provide an elegant approach to predict the volumetric response under thermal cycles coupled with different stress histories well.

Fractional order viscoplastic modeling of anisotropically overconsolidated clays with modified isotach viscosity

Current overstress typed elastic viscoplastic models fall short in describing some time-dependent mechanical behaviors of anisotropically overconsolidated clays comprehensively. This paper presents a rigorous fractional order anisotropic elastic viscoplastic two-surface model for such clays, based on the principles of fractional consistency viscoplasticity and bounding or subloading surface theory. First, a three-dimensional formulation of isotach viscosity is proposed and integrated into two rate-dependent surfaces, i.e., the loading surface and yield surface. Then, by incorporating the stress-fractional operator of the rate-dependent loading surface into isotropic, progressive, and rotational hardening rules, the incremental form of stress-strain-time model with a fractional order viscoplastic flow rule is developed by meeting the consistency condition on the loading surface. Accordingly, the proposed model cannot only maintain the predictive capabilities of a classic bounding surface model but also describe the general features of the time-dependent behavior under various stress conditions. Validation and versatility of the proposed fractional order elastic viscoplastic model are successfully evaluated against constant strain-rate and stress relaxation tests on anisotropically overconsolidated resedimented Boston Blue clay.

Numerical investigation on lateral monotonic and cyclic responses of scoured rigid monopile based on an integrated bounding surface model

Offshore wind turbines (OWTs) are affected by wind, wave, and current during their service life, which lead to the substructures undergoing combined effects of complex lateral loads and local scour. This phenomenon poses a significant challenge to the bearing capacity and cyclic responses of the widely used rigid monopiles for OWTs. This study develops three-dimensional numerical model to investigate the behavior of a rigid monopile subjected to lateral monotonic and cyclic loads, considering the stress history alteration induced by local scour. The hysteresis and plasticity accumulation of soils are captured by a bounding surface model. An accurate and concise semi-implicit stress integration scheme is creatively proposed to effectively incorporate this advanced constitutive model into the finite element (FE) software. The numerical model is verified by comparing FE results with centrifuge test results. Subsequently, the key factors such as cumulative deformation characteristics and bending moments distribution are investigated under different scour and cyclic loading conditions. The results indicate that with the facilitation of proposed semi-implicit scheme, the bounding surface model is capable of capturing the deformation pattern and cumulative deformation behavior of laterally loaded rigid monopile, and the cyclic responses of the monopile are significantly affected by the local scour.

Comparison and analysis of four advanced bounding surface models

The accuracy of the constitutive model affects the precision of the finite element analysis. Four advanced sand constitutive models—the DM04 model, the SANISAND-MS model with memory surface (MS), the SANISAND-Sf model with semi-fluidized state (Sf), and the SANISAND-MSf model with both memory surface and semi-fluidized state—are examined in this article based on a comparison of simulation and experiment results of element tests. First, four constitutive models are implemented in OpenSees, and the constitutive models are calibrated based on the cyclic loading experiments of Karlsruhe fine sand. After that, the advantages and disadvantages of four constitutive models under different test conditions are analyzed. Finally, the finite element model of the LEAP-UCD-2017 (Liquefaction Experiments and Analysis Project, University of California Davis, 2017) centrifuge test is established to evaluate the performance of the four constitutive models for solving boundary value problems. It is found that the SANISAND-MSf model can well reproduce the undrained cyclic properties.

Dynamic analysis of tripod pile foundation in clays for offshore wind turbines

Tripod pile foundation is pursued as an efficient foundation system for offshore wind turbines (OWTs) installed in deeper waters (20–50m). In this application, the foundations would be subjected to dynamic loads including due to wind, waves, and earthquakes. This paper presents a numerical method for analyzing the dynamic responses of tripod pile foundation installed in clay based on a simplified bounding surface model to capture the clay stiffness degradation. Their behaviors under lateral monotonic, cyclic and seismic loads were investigated, and their bearing mechanism was analyzed. The results revealed that the loading direction significantly affects the ultimate bearing capacity of tripod pile foundation as the foundation capacity results from either a Pile A in tension and a Pile B in compression or vice versa. The evolution of axial force, bending moment and lateral displacement profiles of the Pile A and Pile B with the number of cycles exhibit different characteristics under lateral one-way and two-way cyclic loading. The foundation experiences cumulative rotation angles toward the Pile A side under seismic load due to the lower vertical bearing capacity of the Pile A compared to the Pile B. The tower top experiences the maximum lateral displacement and rotation angle, and the top of tripod support experiences the maximum bending moment. These findings should be considered in the design of OWT tripod pile foundations.

Development of 1D bounding surface model for lattice spring model on predicting rock failure under cyclic loading

A sound interpretation of the deformation and failure of rock material subjected to cyclic loadings is of great importance when predicting the long-term stability of rock structures. The bounding surface model is generally utilized to depict the mechanical behaviour of rock subjected to cyclic loadings. In this work, a simplified 1D bounding surface model is developed into a 4D lattice spring model (4D-LSM) to predict rock failure under cyclic loading. To better represent the nonlinear behaviour of rock material, a microcrack model is also introduced in the simplified 1D bounding surface model, together with a macro strength criterion and a cohesive zone model to represent the failure process of the rock. GPU-based parallel computing is realized to accelerate the time-consuming numerical simulation. The numerical results indicate that the proposed model reproduces the deformation and failure process of rock material under different cyclic loading paths. Moreover, the fatigue life of the rock under different conditions is predicted, including different stress levels, confining stresses, and preexisting macro joints. These numerical results reveal that the simplified 1D bounding surface model not only satisfactorily describes the mechanical response of rock under cyclic loading (like in classical continuum-based constitutive models) but also shares the advantage of the discrete-based numerical model in modelling the fracture and failure processes of rock under cyclic loading. This approach could also be used in other discrete numerical models, such as the discrete element model (DEM).

SANISAND-H: A sand bounding surface model for high pressures

This paper presents a new bounding surface constitutive model for sand, named SANISAND-H, capable of predicting the shear and volumetric behavior of the material under extra-high range of pressures, in addition to normal pressures. The model is an extension of the SANISAND08 model (Taiebat and Dafalias, 2008) with a closed cone-type yield surface that obeys rotational and isotropic hardening. The critical state line and the limiting isotropic compression curve of the SANISAND08 model are modified to accommodate a wide range of pressures. A new constitutive ingredient is the definition of a reference compression curve that serves as bounding surface for establishing the isotropic hardening rule of the yield surface. The kinematic hardening rule and stress-dilatancy relationship of the SANISAND08 model are significantly modified, to better capture the response of sands under high pressure. The value of the back stress ratio at the initiation of a new loading process is re-introduced, ensuring a smooth elastic-plastic transition necessary for accurate simulation of the response under loading reversals. The SANISAND-H model simulations are in very good agreement with test data for Toyoura and Cambria sands under various drained and undrained monotonic stress loading paths in a wide range of densities and pressures.

A bounding surface model for gassy clay

Gassy clay can be frequently encountered in the seabed. Gassy clay is a composite material with a saturated soil matrix and discrete gas bubbles. The soil behaviour is significantly affected by the interaction between the soil matrix and gas bubbles. Existing constitutive models have all focused on the response of normally consolidated clay. These models cannot give reasonable prediction of pore water pressure evolution for overconsolidated clay in shear. This can cause poor prediction of overconsolidated gassy clay behaviour because pore water pressure has a significant influence on soil-gas interaction. A new bounding surface model for gassy clay is proposed to model the elastoplastic behaviour of this soil. The gas cavities are assumed to have a detrimental effect on the plastic modulus and shear strength as they affect the integrity of the soil structure. Bubble flooding can occur within the soil, which makes the saturated soil matrix partially drained under a globally undrained condition, leading to higher stiffness and shear strength of gassy clay. The model has been validated by the undrained triaxial compression tests on gassy Malaysian Kaolin and Speciwhite Kaolin clay. Effect of the total stress path on undrained gassy clay behaviour has been analysed.

Impact of hyper-elasticity on cyclic sand modelling: A numerical study based on SANISAND-MS

Accurate simulation of foundation response subjected to repeated loading require reliable sand constitutive models to reproduce realistic sand cyclic behaviour. Many elastoplastic constitutive models adopted the hypoelasticity law, which results in physically inaccurate strain accumulation prediction of soil when subjected to elastic cyclic loading. To address this issue, the existing elastoplastic bounding surface model SANISAND-MS has been upgraded with a hyperelastic formulation that is derived from the Helmholtz free energy function. The complete form of the derived nonlinear elasticity functions enhanced by stress induced anisotropy is presented in this work. The calibration of the upgraded SANISAND-MS is briefly discussed. It is demonstrated that the hyperelastic formulation with volumetric-deviatoric coupling: (1) guarantees no accumulation of elastic strain upon elastic cyclic loading, and (2) captures the stress-induced anisotropy of sand under reverse loading. This upgraded SANISAND-MS model with a physical adaptation and thermodynamically consistent elasticity law can predict strain accumulation accurately and is physically appropriate. Moreover, the upgraded SANISAND-MS is suitable for simulating problems with high-cyclic loads and is able to be used in boundary value problem simulations in areas including offshore engineering and railway engineering.

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.