Modified Cam Clay Model Research Articles

A Cam Clay constitutive relation for semi-analytical elasto-plastic modeling of wheel-soil interaction for fast applications

In this paper, a semi-analytical elasto-plastic (SAEP) model is proposed to simulate wheel motion on soft soil using a Modified Cam Clay (MCC) constitutive model. The focus is on enhancing computational efficiency by integrating the MCC model into the framework. The MCC-based model outperforms the Drucker-Prager with Cap hardening (DPC)-based model in terms of reduced computation time, stability, and convergence. Simulations with a 30% slip ratio show a significant reduction in solution time compared to the DPC-based model. For slip ratios of 50% and 90%, the computation time decreases even further. Overall, the MCC-based model demonstrates over 100 times reduction in the solution time compared to the DPC-based model, particularly with high slip ratios. Indeed, the DPC-based model was found to be highly sensitive to high values of slip ratios, whereas the MCC-based model is not. In comparison with existing methods in the literature, the proposed formulation is superior in terms of significantly reduced solution time and improved numerical stability, making it ideal for advanced applications where fast solutions are crucial.

APD: An automated parameter determination system based on in-situ tests

In-situ testing has numerous applications in geotechnical engineering. The interpretation of in-situ test results includes soil stratification and determination of soil parameters. This paper presents an automated parameter determination framework that aims to determine constitutive model parameters based on in-situ tests. The ongoing research project relies on a graph-based approach for determining the parameters. The framework has two main attributes: transparency and adaptability. Transparency is achieved by illustrating how a certain parameter was computed. Adaptability is ensured by allowing users to incorporate their expertise into the framework. The system currently determines parameters based on three main workflows that utilize the results of cone penetration tests, dilatometer tests, and shear wave velocity measurements. This study employs the three main workflows to determine soil parameters for one of the Norwegian GeoTest Sites. Additionally, the connection between the parameter determination system and finite element analysis is discussed, where the parameters for the Modified Cam Clay model are evaluated. The framework is valuable in the early stages of projects, providing detailed soil information when soil data is limited. Ongoing research aims to assess the accuracy of the derived soil and constitutive model parameters and to expand the system’s capabilities by including additional in-situ tests.

Rate effects of cylindrical cavity expansion in fine-grained soil

Soil responds to cavity expansion is inherently rate-dependent, especially in the case of fine-grained soils. To better understand such rate effects, self-boring pressuremeter tests were conducted on Kunming peaty soil within a strain rate range of 0.1%/min to 5.0%/min. The results showed a clear dependence of cavity pressure and excess pore pressure (EPP) on strain rates—both increased with higher rates for a given radial displacement. In light of the experimental results, three cases of cylindrical cavity expansion were investigated using the finite element method and analytical method, partially drained expansion in Modified Cam-Clay (MCC) soil, and undrained and partially drained expansion in elastoviscoplastic (EVP) soil. The EVP behavior was and modeled using the MCC model and the overstress viscoplastic theory. The results indicated that over the strain rate range of 0.0001%/min and 50%/min, the rate response of cavity pressure for the case of partially drained expansion in MCC soil (permeability coefficient ranging from 5×10-6 m/s to 2.5×10-11 m/s) is not obvious, while the EPP response during undrained expansion in EVP soil shows rate-independent. Only the partially drained solution for cavity expansion in EVP soil captured the rate-sensitive responses of both cavity pressure and EPP, confirmed by the pressuremeter tests on the Kunming peaty soil, Saint-Herblain clay, and Burswood clay. This suggests that the rate effect results from a combination of drainage-related and time-dependent soil behavior. Parametric studies further demonstrated that both viscous behavior and the overconsolidation ratio significantly influence cylindrical cavity expansion response, and the drainage conditions during expansion can be assessed using a nondimensional velocity.

Cylindrical cavity expansion-contraction solutions in undrained MCC soils with the auxiliary variable approach

Cylindrical cavity exhibits non-self-similarity during contraction process following expansion. Previous studies solve this problem with total strain approach and simple constitutive models, but the approach is not applicable when using an advanced constitutive model. This paper presents a semi-analytical solution for a cylindrical cavity undergoing expansion-contraction in undrained soils with auxiliary variable approach, incorporating the Modified Cam-Clay (MCC) model. The stress states around the cavity are formed by the superposition of initial and superimposed stress states. By treating superimposed effective stresses as self-similar, a semi-analytical solution is derived for solving the cavity expansion-contraction problem. The elastoplastic stress-strain relationship is formulated as a set of first-order differential equations, which can be solved as an initial value problem though Runge-Kutta (RK) method. Then the stress distribution around the cavity during expansion-contraction process can be determined. To validate the proposed approach, a series of well-conduced self-boring pressuremeter (SBP) tests are used to verify the proposed approach, which shows good agreements. Additionally, a FEM simulation incorporating the MCC model is performed, and the simulation results are presented to carry out parametric studies on soil parameters. A significant influence on the range of the plastic and reverse plastic zones is shown for overconsolidation ratio, while the in-situ coefficient of the earth pressure only quantitatively affects the stress distribution.

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.

Application of Dimension Extending Technique to Unified Hardening Model

This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm.

Determining Saturated Clay Parameters Using CPT and the Modified Cam Clay Model: Overconsolidation Ratio and Effective Friction Angle

Determining Saturated Clay Parameters Using CPT and the Modified Cam Clay Model: Overconsolidation Ratio and Effective Friction Angle

A neural network approach for the reliability analysis on failure of shallow foundations on cohesive soils

A collection of feed forward neural networks (FNN) for estimating the limit pressure load and the according displacements at limit state of a footing settlement is presented. The training procedure is through supervised learning with error loss function the mean squared error norm. The input dataset is originated from Monte Carlo simulations for a variety of loadings and stochastic uncertainty of the material of the clayey soil domain. The material yield function is the Modified Cam Clay model. The accuracy of the FNN’s is in terms of relative error no more than 10-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-5}$$\\end{document} and this applies to all output variables. Furthermore, the epochs of the training of the FNN’s required for construction are found to be small in amount, in the order of magnitude of 90,000, leading to an alleviated data cost and computational expense. The input uncertainty of Karhunen Loeve random field sum appears to provide the most detrimental values for the displacement field of the soil domain. The most unfavorable situation for the displacement field result to limit displacements in the order of magnitude of 0.05 m, that may result to structural collapse if they appear to the founded structure. These series can provide an easy and reliable estimation for the failure of shallow foundation and therefore it can be a useful implement for geotechnical engineering analysis and design.

Numerical modelling of multiple excavations in an ultra-deep foundation using an enhanced distinct lattice spring model with modified cam clay model

The control of foundation deformation has garnered significant attention. This study focuses on understanding the deformation induced by excavation activities in real foundation construction scenarios. To accurately model the complex geomechanical responses, an enhanced Distinct Lattice Spring Model (DLSM) was developed. The Modified Cam Clay (MCC) model is employed to represent the nonlinear behaviour of the soil. Integration with one-dimensional structure elements is implemented to model support structures and their interactions with the soil. The birth–death particle method is utilized to simulate the excavation process of the foundation. To improve computational efficiency, a CPU-GPU heterogeneous parallel technique is employed. The enhanced DLSM produces consistent results with the finite element method when calculating foundation-bearing capacity and demonstrates relatively close results compared to finite difference methods when analyzing the stability of foundation slopes under different parameters. Finally, a three-dimensional numerical model is established using the proposed DLSM to simulate the deformation of the foundation caused by the excavations. The entire simulation task is divided into twelve stages, involving in-situ stress, a diaphragm wall, ten supporting structures, and ten excavations. A comparative analysis between the MCC model and the ZP (Zienkiewicz-Pande) model is conducted. The findings indicate that the calculation results of the two are consistent in the early stages of excavation, while those calculated by the MCC in the later stages are relatively small. Sensitivity analysis of the MCC parameters using orthogonal analysis reveals that the porosity of the soil has the greatest impact on the deformation of the foundation pit, followed by the slope of the swelling line, while the slope of the critical state line has a minimal impact. This work provides an alternative high-performance tool for engineering-scale deformation analysis of geotechnical underground excavation.

Predictive abilities of constitutive models for clay under monotonic and cyclic loading: element tests and centrifuge experiments

A critical investigation of three constitutive models for clay by means of analyses of a sophisticated laboratory testing program and of centrifuge tests on monopiles in clay subjected to (cyclic) lateral loading is presented. Constitutive models of varying complexity, namely the basic Modified Cam Clay model, the hypoplastic model with Intergranular Strain (known as Clay hypoplasticity model) and the more recently proposed anisotropic visco-ISA model, are considered. From the simulations of the centrifuge tests with monotonic loading it is concluded that all three constitutive models give satisfactory results if a proper calibration of constitutive model parameters and proper initialisation of state variables is ensured. In the case of cyclic loading, the AVISA model is found to perform superior to the hypoplastic model with Intergranular Strain.

Implementation of modified cam–clay model using closest point projection method under Cartesian coordinate system

The modified Cam–Clay model is an elastoplastic soil model that holds a prominent position in civil engineering for its precise depiction of varied soil behaviors. Despite extensive examination of its numerical processes, the predominant focus on stress integration algorithms within the triaxial stress space presents challenges for individuals less acquainted with geotechnical science. In response to this, the present study derived the stress integration equations for the modified Cam–Clay model within the Cartesian coordinate system employing the closest point projection method. Subsequently, a finite element program was developed incorporating the derived integration process. This study computed and compared the consolidation processes under both drained and undrained conditions for cubic soil samples with various over-consolidation ratios using the developed program, ABAQUS, and analytical formulas. The findings demonstrate that equations integrated within the Cartesian coordinate system offer ease of understanding and programming. The feasibility, accuracy, and stability of the closest point projection method have been validated. Comparative analysis of soil samples across various over-consolidation ratios indicated a reduction in failure stress with an increase in over-consolidation ratio, indicating a higher propensity for failure under undrained conditions than under the drained conditions.

Modified cam clay bounding surface hyper-viscoplastic model

Clays exhibit complex mechanical behaviour with significant viscous, nonlinear, and hysteric characteristics, beyond the prediction capacity of the well-known modified cam clay (MCC) model. This paper extends the MCC model to address these important limitations. The proposed family of models is constructed entirely within the hyperplasticity framework deduced from thermodynamic extremal principles. More specifically, the previously developed MCC hyper-viscoplastic model based on the isotache concept is extended to incorporate multiple internal variables and to capture recent loading history, hysteresis, and smooth response of the material. This is achieved by defining an inelastic free energy and an element that implements a bounding surface within hyperplasticity, resulting in pressure dependency in both reversible and irreversible processes with a unique critical state envelope, and only eight material parameters with a readily measurable viscous parameter. A kinematic hardening in the logistic differential form in stress space is derived that enables the proposed model to function effectively across a wide range of stresses. Based on this kinematic hardening rule, the current stress state acts as an asymptotic attractor for the back/shift stresses whose evolution rates are proportional to their current state.

Geotechnical analysis involving strain localization of overconsolidated soils based on unified hardening model with hardening variable updated by a composite scheme

AbstractStrain localization simulation of overconsolidated soils with high overconsolidation ratio (OCR) has been a long‐standing challenge. Some critical state soil models, including the modified Cam‐clay (MCC) model, have been widely applied, but they may not predict the shear dilatancy of overconsolidated soils well in some cases. Hence, the unified hardening (UH) model, which may be viewed as a generalized version of the MCC model, is implemented. It has been recognized, nonetheless, that without resorting to the regularization mechanism, the standard finite element method (FEM) or the second‐order cone programming optimized finite element method (FEM‐SOCP) often experiences instability or interruption of calculating the hardening‐softening responses of overconsolidated soils. To resolve the aforementioned difficulty, the UH model is developed and implemented in the framework of FEM‐SOCP based on the micropolar continuum (mpcFEM‐SOCP) to predict strain localizations of overconsolidated soils. Furthermore, to obviate non‐convexity of mpcFEM‐SOCP induced by material softening, an effective composite update scheme of hardening variable pc, which refers to the implicit variable (IV) scheme for the hardening stage and then refers to the explicit variable (EV) scheme for the softening stage, is proposed. Based on one biaxial compression problem and one rigid strip footing problem, numerical analyses disclose that by applying mpcFEM‐SOCP in conjunction with the composite update scheme of pc, the UH model of micropolar continuum can effectively predict the strain localization behavior of overconsolidated soil during its failure stage, and the stable hardening‐softening responses of overconsolidated soils can be readily attained.

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.

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.

Modelling of the elastoplastic behaviour of the bio-cemented soils using an extended Modified Cam Clay model

An elastoplastic constitutive model based on the Modified Cam Clay (MCC) model is developed to describe the mechanical behaviour of soils cemented via microbially induced calcite precipitation (MICP). It considers the increase of the elastic stiffness, the change of the yield surface due to MICP cementation and the degradation of calcium carbonate bonds during shearing. Specifically, to capture the typical contraction-dilation transition in MICP soils, the original volumetric hardening rule in the MCC model is modified to a combined deviatoric and volumetric hardening rule. The model could reproduce a series of drained triaxial tests on MICP-treated soils with different calcium carbonate contents. Further, we carry out a parametric study and observe numerical instability in some cases. In combination with an analytical analysis, our numerical modelling has identified the benefits and limitations of using MCC-based models in the simulation of MICP-cemented soils, leading to suggestions for further model development.

Thermo-hydro-mechanical coupled model of unsaturated frozen soil considering frost heave and thaw settlement

Frost heave and thaw settlement of subgrade is the most typical engineering disease in permafrost regions, which seriously threatens the safe construction and operation of transportation infrastructure. On the basis of the Modified Cam Clay model, a thermoelastoplastic constitutive model of unsaturated frozen soil is proposed. This model can effectively describe two key issues of the mechanical behavior of frozen soils, that is, soil hardening caused by temperature reduction and volume compression during thawing. The proposed constitutive model is realized in the established thermo-hydro-mechanical (THM) coupled mathematical model, and the reliability of the coupled model is verified by comparing with the experimental results. In addition, the proposed THM framework is applied to describe the long-term freezing and thawing behavior of typical railway subgrade sections in the permafrost region of western China. The results show that water-heat transfer and deformation frequently occur on the subgrade surface as the seasons change. Moreover, the variation of thaw settlement is greater than that of frost heave, which seriously threatens the operation safety of railways in permafrost regions.

Proposition of new yield criterion for green sand mold and its experimental validation by FEM stress analysis of triaxial compression test

Prediction of the deformation during shape casting by FEM (finite element method) thermal stress analysis has been desired. For such prediction, validated constitutive models are essential for both the casting alloy and the mold. In this paper, two fatal defects in the modified Cam-Clay (MCC) model, which has conventionally been employed for a green sand mold, are clarified. The aim of this paper is to concurrently resolve these defects by a new yield criterion. The defects were those that cause an unreal distinct yielding and dilatancy peak on the stress-strain curve, which was clarified by comparing the true stress-strain curves obtained in the experiment and the FEM stress analysis of a triaxial compression test. A device capable of measuring the true stress during vertical compression was newly developed for the triaxial experiment. These defects inevitably led the MCC model to overestimate the mold strength by approximately 200% of the experimental value. This paper provides a new yield criterion, which employs an additional yield surface with the Drucker-Prager inherent surface, to rectify these defects of the MCC model. As a result of the stress analysis of the triaxial test with the new criterion, the smooth stress-strain curve with neither a peak nor a distinct yielding was reproduced. The calculated compressive stress traced the experimental value with less than a 15% error. Therefore, the new criterion should remarkably improve the accuracy of calculating the mold strength in the FEM thermal stress analyses during casting when compared to the MCC model.

Numerical Simulation of a Barge Impact on Bridges with Different Configurations of Pile Group Foundations

Three-dimensional finite element dynamic analyses were conducted to evaluate the effect of barge impact of different speeds on the lateral performance of three pile group (PG) configurations (vertical, battered, mixed) in terms of peak lateral displacement, peak shear force, lateral stiffness of PGs, and contribution of piles and pier columns to the total resisting force. The concrete material was modeled using the Concrete Damaged Plasticity model. The clay behavior was described using the Modified Cam Clay model; while the sand was modeled using the Drucker Prager model. The results showed that the vertical PG had the lowest lateral stiffness; while the battered and mixed PGs had closely larger stiffness, which allowed the development of larger impact force and pile cap displacement in vertical PG as compared to other PGs. The results of shear force showed that the foundation contributed up to 82% of the total lateral force in battered and mixed PGs. The results also showed that in vertical PG, the first row had slightly higher percentage of lateral force compared to other rows; while in battered PG, the load percentage was evenly distributed between rows. A contrast performance was observed for mixed PG. The results of bending moment (BM) showed that the piles in vertical PG had notably higher BM than the piles in other PGs due to larger pile cap displacement. In all PGs, the piles in the edge column had higher BM ratio, with the leading row (L) had the highest BM ratio (69–72%) in all PGs.

Lateral deformation of high-speed railway foundation induced by adjacent embankment construction in soft soils: Numerical and field study

The excessive displacement of an existing high-speed railway foundation due to the adjacent construction of a railway composite foundation significantly threatens the railway operation safety. In the typical soft soil region of Southeast China, a series of in-situ tests are carried out in this paper to investigate the layered settlement of newly constructed embankment and lateral displacement of an existing high-speed railway foundation induced by the new embankment. A two-dimensional (2D) finite element (FE) model is built to investigate the displacement of stratums and the modified Cam-clay (MCC) model is adopted to pursue the mechanical properties of the silt. Combining the genetic algorithm (GA), a back analysis framework was developed to determine the optimized input parameters of MCC model for silt layer. The results indicate that the displacement of the existing high-speed railway foundation induced by the adjacent construction of a railway embankment decreases with depth and horizontal distance from the newly constructed embankment toe. A hysteresis phenomenon is found in the foundation settlement data during the loading procedure of the embankment. Moreover, the optimized parameters for silt layer (i.e., λ = 0.361, M = 0.828, e0 = 1.347 and k = 0.826 × 10-8m/s) have the potential for the engineer application in the soft soil region.