Constitutive Model For Clays Research Articles

Deformation-related earth pressure within grid wall-pattern foundation under adjacent surcharge

This study investigated the deformation-dependent earth pressure evolution on the periphery of the grid wall-pattern foundation fully embedded into soft ground. The numerical modelling was performed using the embedded Modified Cam Clay Constitutive model in the FLAC3D software platform and numerical results were validated using centrifuge results. The induced effective vertical and horizontal stresses acquired from the numerical modelling were used to compute the corresponding deformation-dependent earth pressure at different buffer zone distances and surcharge loading. Thereafter, the parameters that influence the determination of the lateral displacement, induced effective vertical stress and deformation-dependent earth pressure coefficient were investigated using machine learning and genetic programming was used to establish the physical equations that could be used to estimate parameters for similar problems. Moreover, for the deformation-dependent earth pressure to be within Rankine's active and passive earth pressure the buffer zone distance/depth ratio should be 10% of the grid wall-pattern foundation embedment into the ground. Furthermore, it was also discovered that the structure fully embedded into the ground under adjacent loading cannot only be designed based on Rankine's active and passive earth pressure investigation on the periphery but the evaluation should be done within the entire location of the grid wall foundation.

New Numerical Technique for the Inbuilt Modified Cam Clay Constitutive Model in FLAC3D

Fast Lagrangian Analysis of Continua (FLAC) is a powerful numerical platform for simulating the deformation and stability of geotechnical structures. Presently, it is documented that the embedded Modified Cam Clay constitutive model in the FLAC platform is deficient in solving geotechnical problems. This paper outlines the new calibration approach by determining the isotropic preconsolidation pressure multiplier based on the relationship between the total stress in the geotechnical problem and the reference pressure. The multiplier was used to establish the nominated maximum isotopic preconsolidation pressure and maximum referential consolidation ratio at the bottom of the soil layer. Subsequently, the maximum isotopic preconsolidation pressure was used to determine the bulk maximum. In addition, the developed approach was used to investigate the lateral displacement of the large grid wall foundation by deep mixing under the adjacent surcharge loading. The feasibility was validated using the centrifuge results. The coefficient of determination between lateral displacement from numerical and centrifuge modelling R2 was 0.95. The proposed numerical technique and calibration approach demonstrated that the embedded Modified Cam Clay model can be used to solve practical geotechnical problems.

A thermoplastic clay constitutive model with temperature dependent evolution of stress anisotropy

This paper presents a thermomechanical constitutive model that captures temperature dependent evolutions of preconsolidation stress and stress anisotropy in normally consolidated and lightly overconsolidated saturated clays. Following a non-associative flow rule, the model was formulated to account for the rate of evolution of stress anisotropy as a function of temperature. A temperature-dependent rotational hardening parameter was introduced and calibrated employing a simple optimization algorithm for four different clays. The developed model was further implemented in a finite element (FE) analysis software for use in boundary value problems. Success of such numerical implementation and predictive performance of the constitutive model was further verified through FE simulations of drained and undrained triaxial tests on saturated clays at reference and elevated temperature. FEA results obtained from these simulations agreed very well with test data reported in the literature.

CONSTITUTIVE MODELLING OF SANDS UNDER MONOTONIC LOADING

This paper presents the drained and undrained behavior of soils using a modified version of the original cam clay constitutive model. The strain hardening behavior of soils is one of the major challenges in geotechnical engineering. The constitutive equations are numerically integrated over fixed time steps to apply effective stress to the derived elastoplastic soil model. Convergence of solution is controlled by a constitutive relation, namely the associated flow rule. This study provides step by step Python and octave programs to solve for q"-" p by solving the associated non-linear system. The problem is formulated by assuming small strains in the elastic region and large strains in the plastic region. The transition from over-consolidated to normally consolidated states is predicted to be smooth by this elastoplastic model. The model is recognized and solved as a boundary value problem with only two effective stress variables namely q"-" p which is an approximation of three-dimensional invariants.

Effect of Aspect Ratio on Bearing Capacity of Footings in Structured Clay

This research analyzed the role of footing aspect ratio in influencing the limit bearing capacity and associated failure mechanism in saturated, structured clays. The effects of footing aspect ratio and footing–soil interface conditions on the extent of soil destructuration, during mobilization of limit load, were investigated using advanced finite-element analyses. These analyses employed a clay constitutive model that accounted for continuous load-induced evolutions of soil destructuration and stress-induced anisotropy. The soil destructuration process caused 30%–35% reduction in the limit bearing capacity of shallow foundations. Moreover, the proposed analysis-based shape factor for footings in structured clay suggests that the use of shape factors available in the literature would overpredict the limit bearing capacity for footings in clays prone to destructuration.

Dynamic stability assessment of reservoir colluvial landslide using a hypoplastic clay constitutive model considering the effects of drying-wetting cycles on the hydro-fluctuation belt

The hydro-fluctuation belt of reservoir landslides undergoes repeated drying-wetting (D–W) cycles due to the annual fluctuation of water level in the Three Gorges Reservoir Area. Mechanical properties of the hydro-fluctuation belt subjected to D-W cycles should be considered for the evolution of landslide stability affected by seasonal rainfall and periodic reservoir water fluctuations. In addition, a reliable constitutive model essential for evaluating landslide stability should be employed to describe the mechanical property of soil. In this study, taking the Tangjiao landslide as an example, a series of drained triaxial and oedometer tests were conducted to study the effects of D-W cycles on the shearing and compression behaviors of the sliding mass soil. Then, the time-varying parameters of a hypoplastic clay constitutive model were calibrated based on the soil experiments under different D-W cycles. Eventually, the hydro-mechanical coupled simulation analyses were performed to study long-term deformations of the landslide front part influenced by actual rainfall and reservoir water fluctuations. Moreover, the evolution of landslide stability was analyzed using the vector-sum method based on stress fields with different time steps. The test results show that the D-W cycle significantly affects the mechanical property of soil. The hypoplastic model predicts well the shearing and compression behaviors of soil under different D-W cycles. The numerical results indicate that the soil weakening in the hydro-fluctuation belt increases the deformation magnitude of the toe slope and gradually decreases the landslide stability. This study provides some references for the dynamic stability assessment and long-term hydro-mechanical simulation of reservoir landslides.

A Variable-Order Dynamic Constitutive Model for Clay Based on the Fractional Calculus

To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and the basic element model, a variable-order fractional dynamic model designed to predict accumulative strain of clay was exhibited. Firstly, the cyclic load was separated into static and alternating load in accordance with cyclic load characteristics, and the strain of clay under static and alternating load was analyzed. Then, on the basis of the variable-order Abel dashpot model, rheological theory and elastoplastic theory, the expressions of the rheological constitutive model and strain response were both obtained. Finally, in combination with the undrained dynamic triaxial testing of Zhan Jiang clay and Tian Jin soft clay, a series of analyses was carried out on the effectiveness and parameter sensitivity of the model when subjected to long-term cyclic loading. By comparing the dynamic constitutive model with pre-existing models, the superiority of the dynamic constitutive model is revealed. The results show that the dynamic constitutive model can characterize properly the deformation characteristics of clay under the action of long-term cyclic loading, especially in its accelerating stage. The parameter sensitivity of the model exhibits a growing trend with the increment of loading duration.

A 3D Elasto-plastic Constitutive Model for Clay Based on the Unified Hardening Model with Insights into the Coupling Effect of Small-Strain Stiffness and Over-Consolidation Ratio

A 3D Elasto-plastic Constitutive Model for Clay Based on the Unified Hardening Model with Insights into the Coupling Effect of Small-Strain Stiffness and Over-Consolidation Ratio

Settlement Analysis of Pipe Culvert Situated in Soft Clay Treated with Prefabricated Vertical Drains

Engineering structures built on soft and compressible soils are often subjected to a long‐lasting consolidation settlement. It is difficult to achieve an acceptable level of consolidation during the first few years/days of operation. Similarly, the culvert structure provided at station km 159 + 112 of the Awash‐Kombolcha‐Hara Gebeya Railway Project, Ethiopia, was situated along the route traversing soft clay ground of significant thickness. For the intention of reducing consolidation time and lessening the precarious impact of the postconstruction settlement, the soft clay ground was treated with preloading and prefabricated vertical drains. However, the culvert structure is currently undergoing consolidation settlement with varying magnitudes. The vertical deformation of the culvert site is monitored using settlement gauges installed at the site. Monitoring of the site continued for 120 days to track the extent of ground deformation at the culvert site. However, because of environmental and technical factors like calibration and alignment errors, the settlement instrument readings may be exposed to uncertainties, which may probably affect the safety of the culvert structure. Hence, the study is primarily aimed at evaluating the field deformation performance of the culvert structure for 120 days of the consolidation period through numerical analysis and comparing the result with the site settlement monitoring data. The critical effect of wick drain and some key parameters (fill thickness and wick drain spacing) were also scrutinized. Finite element‐based numerical modeling was conducted by using the 2D GeoStudio/SigmaW package, and the Modified Cam Clay Constitutive model was adopted. The conducted numerical analysis revealed that the finite element result has good agreement with the field settlement monitoring data with only 0.0305 m maximum deviation in which the numerical analysis result remained greater for majority of the consolidation time. It can also be inferred that granular fill thickness and wick drain spacing were the key parameters impacting the settlement of the culvert structure.

Thermal volume change of saturated clays: A fully coupled thermo-hydro-mechanical finite element implementation

The creep and consolidation behaviors of clays subjected to thermal cycles are of fundamental importance in the application of energy geostructures. This study aims to numerically investigate the physical mechanisms for the temperature-triggered volume change of saturated clays. A recently developed thermodynamic framework is used to derive the thermo-mechanical constitutive model for clays. Based on the model, a fully coupled thermo-hydro-mechanical (THM) finite element (FE) code is developed. Comparison with experimental observations shows that the proposed FE code can well reproduce the irreversible thermal contraction of normally consolidated and lightly overconsolidated clays, as well as the thermal expansion of heavily overconsolidated clays under drained heating. Simulations reveal that excess pore pressure may accumulate in clay samples under triaxial drained conditions due to low permeability and high heating rate, resulting in thermally induced primary consolidation. Results show that four major mechanisms contribute to the thermal volume change of clays: (i) the principle of thermal expansion, (ii) the decrease of effective stress due to the accumulation of excess pore pressure, (iii) the thermal creep, and (iv) the thermally induced primary consolidation. The former two mechanisms mainly contribute to the thermal expansion of heavily overconsolidated clays, whereas the latter two contribute to the noticeable thermal contraction of normally consolidated and lightly overconsolidated clays. Consideration of the four physical mechanisms is important for the settlement prediction of energy geostructures, especially in soft soils.

Formulation and implementation of a practical multi-surface soil plasticity model

This paper presents a new constitutive model for clay, for undrained monotonic and cyclic loading, that has been developed specifically for geotechnical design applications. The model employs a parallel Iwan approach, consisting of multiple elastic-perfectly-plastic micro models. Degradation of stiffness and strength during cyclic loading is incorporated using an empirical cyclic overlay method. The theoretical framework and calibration processes for the model are presented. An implementation of the model in a commercial finite element program is then described; this implementation is demonstrated via 3D finite element analyses of example offshore monopile foundations subjected to monotonic and cyclic lateral loading.

A constitutive model for clays and plastic silts in plane-strain earthquake engineering applications

A plasticity model for representing clays and plastic silts, as opposed to purely nonplastic silts or sand, in geotechnical earthquake engineering applications is presented. The PM4Silt model builds on the framework of the stress-ratio controlled, critical state based, bounding surface plasticity PM4Sand model, and is coded as a user defined material for use with the program FLAC. The model was developed to provide reasonable approximations of monotonic undrained shear strength, cyclic undrained shear strength, and shear modulus reduction and hysteretic damping responses. The model does not include a cap, and therefore is not suited for simulating consolidation or reconsolidation settlements (i.e., volumetric strains) or strength evolution with consolidation stress or seismic loading history. The primary input parameters are the undrained shear strength ratio (or undrained shear strength), the shear modulus coefficient, and the contraction rate parameter. All secondary input parameters are assigned default values based on a default calibration, but may be adjusted when calibrating against advanced laboratory test data or performing sensitivity studies. The calibration process is described and illustrated by calibrations for three different normally consolidated, fine-grained soils with plasticity indices ranging from 4 to 20. The model is shown to provide reasonable approximations of behaviors important to many earthquake-engineering applications and to be relatively easy to calibrate.

A new method of developing elastic-plastic-viscous constitutive model for clays

A new method is presented to develop the existing elastic-plastic constitutive model into an elastic-plastic-viscous one for clays. The actual loading process is divided into an instant process and a delayed process denoting the elastic-plastic strain and viscous strain, respectively. The elastic-plastic strain is determined by either an elastic-plastic model for overconsolidated clays or an improved model based on the elastic-plastic model for normally consolidated clays. In order to calculate viscous strain, a reference state line is defined based on the actual loading path. Combining the reference state line, an existing elastic-plastic model can be conveniently developed into an elastic-plastic-viscous model. Furthermore, using the proposed method, the modified cam clay model is extended into an elastic-plastic-viscous model. Comparisons with test results demonstrate that the extended model can capture the main time-dependent behaviours of clays, including creep, stress relaxation and strain rate effects.

Enhancing Constitutive Models for Soils: Adding the Capability to Model Nonlinear Small Strain in Shear

The deviatoric stress‐deviatoric strain relationship in soils is highly nonlinear, especially in the small strain range. However, the constitutive models which aim to replicate the small strain nonlinearity are often complex and rarely used in geotechnical engineering practice. The goal of this study is to offer a simple way for updating the existing constitutive models, widely used in geotechnical practice, to take into account the small strain shear modulus changes. The study uses an existing small strain relationship to derive a yield surface. When the yield surface is introduced to an existing soil model, it enhances the model with the nonlinear deviatoric stress‐deviatoric strain relationship in the small strain range. The paper also gives an example of such a model enhancement by combining the new yield surface with the Modified Cam Clay constitutive model. The validation simulations of the undrained triaxial tests on London Clay and Ham River sand with the upgraded constitutive models replicate the experiments clearly better than the base models, without any changes to existing model parameters and the core source code associated with the base model.

Evaluation of Hypoplastic Clay Model for Deep Excavation Modelling

AbstractThis paper presents an evaluation of the Hypoplastic Clay constitutive model for finite element analysis of deep excavations and displacements induced by excavations in the influence zone. A detailed description and formulation of the Hypoplastic Clay soil model is included. A parametric case study of a deep excavation executed in Pliocene clays is presented. FE analysis was performed using several soil models (Mohr-Coulomb, Modified Mohr-Coulomb, Drucker-Prager, Modified Cam-Clay, Hypoplastic Clay) and the results were compared to in-situ displacements measurements taken during construction. Final conclusions concerning the suitability of the Hypoplastic Clay model for deep excavation modelling in terms of accurate determination of horizontal displacements of the excavation wall, the uplift of the bottom of excavation, and, most importantly, vertical displacements of the terrain in the vicinity of the excavation are presented.

Three-Dimensional Numerical Analyses of Pile Response due to Braceded Excavation-Induced Lateral Soil Movement

Using the explicit finite difference code FLAC3D, the behavior of pile adjacent to braced excavation is investigated. The Modified-cam clay constitutive model was employed to model the non-linear stress-strain soil behavior, and the pile was assumed to have linear elastic behavior. The interface model incorporated in FLAC3D code was used to simulate the soil/pile contact, The built-in 'fish' language was used to calculate the data demanded. The pile response such as pile deflection, bending moment and lateral soil pressure were studied, and it is shown that the pile response is different from that caused by the excavations which are unstructted. In "standard" problem, the effect of different pile head constraints on the pile response was investigated, the effect of lateral displacement of the wall, distance from the excavation face, pile stiffness, pile length and axial load on the pile response are also investigated when the pile head is constrained from deflection. The research finding was compared with other published case history and reasonably good agreement was found between them.

ON IMPLEMENTATION AND PERFORMANCE OF AN ANISOTROPIC CONSTITUTIVE MODEL FOR CLAYS

Numerical implementation of an anisotropic constitutive model for clays (SANICLAY) is presented. Moreover, a case study in which a soil embankment is placed on a K0-consolidated over-consolidated clay is analyzed by conducting an elastoplastic fully-coupled finite element analysis. It is shown that anisotropy has significant impact on the ground settlement caused by the placement of soil embankment and on the pore pressure generation and dissipation within the foundation soil. The simulations using SANICLAY favorably compare with the field measurements of ground settlement and pore pressure. The drawbacks of the use of an isotropic elastoplastic model (Cam Clay) are also demonstrated.

A Strain-Rate Dependent Clay Constitutive Model with Parametric Sensitivity and Uncertainty Quantification

This paper presents a strain-rate dependent plastic constitutive model for clays. Based on the concepts of critical-state soil mechanics and bounding surface plasticity theory, the model reproduces the mechanical response of clays under triaxial and simple shear loading conditions. The model parameters are determined for Boston Blue Clay, London Clay and Kaolin Clay, and the performance of the model in simulating the mechanical response of these clays is demonstrated for low to medium strain rates. The sensitivity of each model parameter is checked by perturbing the calibrated values by ±20 %. Subsequently, a probabilistic analysis using Monte Carlo simulations is performed by treating the model parameters as random variables and the impact of the statistics of the parameters on the undrained shear strength is investigated.

Shaft Resistance of Drilled Shafts in Clay

Thecurrentstudyexaminesandquantifiesthelimitshaftresistanceofdrilledshaftsinstalledinclaythrough finite-elementanalyses that use an advanced two-surface-plasticity constitutive model for clay. The clay constitutive model used in this study reproduces the mechan- ical responseofclaysundermultiaxial loadingconditions,predictsbothdrainedandundrainedbehavioratsmallandlargestrains,andcaptures the drop in strength toward a residual value at very large shear strains. One-dimensional finite-element analyses are performed to simulate the essential stages of the installation and loading of drilled shafts in clay for different initial stresses, different overconsolidation ratios, and dif- ferent values of the difference between the critical-state and the minimum residual friction angles. On the basis of these simulations, equations for the shaft friction coefficient are proposed that can be used in the calculation of the shaft resistance of drilled shafts in clay. Predictions using theproposedequationscomparewellwiththedataderivedfromdifferent fieldpileloadtestsondrilledshafts.DOI:10.1061/(ASCE)GT.1943- 5606.0000803. © 2013 American Society of Civil Engineers. CE Database subject headings: Drilled shafts; Piles; Clays; Numerical models; Plasticity; Finite element method; Constitutive models. Author keywords: Drilled shaft; Nondisplacement piles; Shaft capacity; Clay; Numerical modeling and analysis; Two-surface plasticity.

Numerical Modeling of Nonhomogeneous Behavior of Structured Soils during Triaxial Tests

The nonhomogeneous behavior of structured soils during triaxial tests has been studied using a finite element model based on the Structured Cam Clay constitutive model with Biot-type consolidation. The effect of inhomogeneities caused by the end restraint is studied by simulating drained triaxial tests for samples with a height to diameter ratio of 2. It was discovered that with the increase in degree of soil structure with respect to the same soil at the reconstituted state, the inhomogeineities caused by the end restraint will increase. By loading the sample at different strain rates and assuming different hydraulic boundary conditions, inhomogeneities caused by partial drainage were investigated. It was found that if drainage is allowed from all faces of the specimen, fully drained tests can be carried out at strain rates about ten times higher than those required when the drainage is allowed only in the vertical direction at the top and bottom of the specimen, confirming the findings of previous studi...