Soil Constitutive Model Research Articles

Overconsolidated flysch-type clays. Engineering considerations for the Strait of Gibraltar tunnel project

The stress-strain behaviour of 85 overconsolidated clay samples from Campo de Gibraltar Flysch Through Domain (Algeciras Unit, South Spain) is presented and discussed. The samples were identified and classified following ASTM standards while their chemical and mineralogical composition were determined by chemical and X-ray techniques. Several samples were tested under triaxial as well as oedometric conditions. Given the results, a detailed comparison was made between different theoretical constitutive models and real testing data, using the finite-elements method. The comparison indicated a good fit between experimental data and those found with finite-elements modelling when the Hardening Soil constitutive model was used. This model showed a better fit than did the Modified Cam- Clay model (historically used for modelling clayey soils), although the latter fit proved better for lower strain values (<5%) than higher ones. These results clarify this intermediate material (hard soils – weak rocks) behaviour and will help in Strait of Gibraltar tunnel project design, as these materials are widely involved in this tunnel design.

State space model of undrained triaxial test data for Bayesian identification of constitutive model parameters

Soil constitutive model parameters can be identified from triaxial test data. The identification is frequently performed by fitting a constitutive model to triaxial test data from a purely statistical or probabilistic perspective based on an assumption that measurements are independent. This ignores the sequential attribute of triaxial test data and is, hence, not realistic. In this paper, a probabilistic state space model (SSM) is proposed for undrained triaxial test data analysis, with which the sequential data attribute is explicitly considered and a constitutive model (physics) is linked to the SSM model (statistics) in a natural way. Then, constitutive model parameters can be rigorously learned under a Bayesian framework based on the SSM without artificially augmenting them into hidden variables of SSM. Without loss of generality, the modified Cam Clay (MCC) model is taken as an example to develop the SSM and to demonstrate the proposed Bayesian framework, which is illustrated using simulated and real-life data. Results from the proposed Bayesian framework based on the SSM include not only the best estimates of MCC model parameters but also their posterior distributions for quantifying the identification uncertainty, based on which the identifiability of MCC model parameters is discussed and highlighted.

Shear failure investigation of unbound pavement layers under accelerated heavy aircraft loading: case study

ABSTRACT Airport pavements are designed to sustain aircraft-induced stresses while maintaining adequate serviceability. To enhance pavement design procedures, the Federal Aviation Administration (FAA) utilises the National Airport Pavement Test Facility (NAPTF) to perform full-scale tests of airfield pavements under representative tire loads. Due to higher tire loads and pressures, unbound layers may experience shear failure and excessive permanent deformation. In this study, a new methodology is proposed to estimate the shear strength parameters of unbound materials by extrapolating resilient modulus test data until failure by adopting the hyperbolic stress–strain constitutive soil model. Using those shear strength parameters of unbound pavement layers of the NAPTF Construction Cycle 3 (CC3), a comprehensive simulation was performed using a modified version of SuperPACK (Super Heavy Load Pavement Analysis PACKage), developed based on the Federal Highway Administration (FHWA) Analysis Methodology for superheavy load (SHL). Pavement behaviour and performance were investigated for four FAA flexible pavement configurations tested mainly to study the role of different subbase thicknesses. It was found that modified SuperPACK was able to reasonably predict the shear failure mechanism in the different unbound layers existing in CC3.

Numerical Evaluation of a Semi-Integral Bridge Abutment under Cyclic Thermal Movements

This paper presents a two-dimensional Finite Element (FE) simulation of the interaction between a semi-integral stub-type concrete bridge abutment and a granular backfill under cycles of temperature-induced lateral displacements. A numerical model was proposed utilizing an elastoplastic soil constitutive model considering the characteristics of a semi-integral bridge abutment located near the City of Palestine, Texas, USA. The numerical model was validated against data collected in the field from pressure cells installed on the soil side of the abutment of the semi-integral bridge. The long-term response of the backfill-abutment system representing a 50-year period was investigated numerically for annual cycles of expansion–contraction of the bridge. According to the results of the investigation, it is observed that annual cyclic lateral movements of the bridge abutment led to a rapid increase of lateral earth pressures upon the abutment wall. The locus of maximum lateral earth pressures occurred on the upper third of the abutment, which disagrees with the conventional earth pressure distributions often assumed in design guidelines for integral bridge abutments. The magnitude of the settlement trough that formed under annual cycles is deemed sufficient to negatively affect bridge performance soon after start of the bridge operation. Results predicted that cumulative shear strains prevailed in the region of the backfill soil far from the abutment wall. On the other hand, cumulative compressive volumetric strains (densification) dominated in the vicinity of the soil-abutment interface. While stabilization of lateral earth pressures on the soil-abutment interface was predicted to occur with the balance between both densification and shearing effects, settlements adjacent to the soil-abutment interface were predicted to persist as a consequence of the continued growth of cumulative shear strains (ratcheting) in the portion of the soil away from the abutment wall.

Study on triaxial test and constitutive prediction model of frozen silty clay

With the increasing demand for engineering construction in the seasonal frozen area and the background of the Belt and Road Initiative, the frozen soil constitutive model should be studied in depth. At present, the constitutive prediction model of frozen silty clay has many problems, such as complex formula, single model application and poor prediction ability. Random forest optimal model hyperparameter input was very difficult. Particle Swarm Optimization (PSO) was used to optimize the parameters of the number of neurons, dropout and batch_size in the Long-term and Short-Term Memory network (LSTM) structure. The optimization results were 61, 0.09 and 95 respectively. The results showed that the strength tended to be stable after 6,9,6,9 and 9 freeze-thaw cycles under initial moisture content = 25, 22.5, 20, 17.5, and 15%, respectively. After 18 freeze-thaw cycles, the strength decreased by 2.66%, 11.85%, 18.83%, 16.79, and 29.02%, respectively. The predicted values of frozen soil binary medium model (BM), random forest model (RF) and PSO-LSTM model were compared with the measured values under different working conditions, and good accuracy was obtained. The R2 of the PSO-LSTM model test set was trained to more than 98%, and RMSE, MAE and MAPE were also trained to the lowest under the same working conditions. The influencing factors of deviator stress of frozen silty clay were given in order from strong to weak: initial moisture content>strain>confining pressure>number of freeze-thaw cycles. The LSTM optimal combination input parameters were searched by PSO, and the parameter adjustment speed of the model for the data learning process of frozen silty clay was greatly increased, which was conducive to the promotion of other soil constitutive prediction models. A new constitutive prediction model of frozen silty clay was developed using PSO-LSTM algorithm. 15 working conditions had been verified, and the optimal model had high accuracy in the constitutive prediction of frozen silty clay, which provided a good reference for the application of frozen soil engineering in cold regions.

Deformation constitutive model of subgrade soil under intermittent cyclic loading

During the actual operation of subways, high-speed railway, and other infrastructure, subgrade soil will be subjected to periodic vibration and intermittent loading, i.e., intermittent cyclic load. To study the deformation characteristics of subgrade soil under intermittent cyclic loading, the Newtonian dashpot in the generalized Kelvin model is replaced by the fractional Abel dashpot, a fractional generalized Kelvin model is established. Then, a nonlinear viscoplastic body model considering damage is proposed, which is connected in series with the improved fractional generalized Kelvin model, and the deformation constitutive model of soil under intermittent cyclic loading is obtained. Finally, the effectiveness and applicability of the model are analyzed, and the model is compared with other constitutive models. The results show that the constitutive model established in the paper can reflect the combined effect of confining pressure, frequency, dynamic stress amplitude and other factors on the cumulative plastic strain of soil, and can well characterize the development law of three types of cumulative plastic strain curves of soil: stable, critical, and failure. The fitting parameters alpha and eta tend to decay and rise, respectively, with the increase in loading stage N, which reflects the rationality and accuracy of the model.

The Influence of Input Motion Scaling Strategies on Nonlinear Ground Response Analyses of Soft Soil Deposits

A key issue for the estimation of ground shaking is the proper selection of input motions at the seismic bedrock. At the same time, the effect of the input motion scaling strategy on structural response is typically studied disregarding the presence of the soil deposit. In this work, different soft soil deposits are selected by varying the shear wave velocity profiles and the depth to the seismic bedrock, modelling the soil behaviour through a nonlinear constitutive model implemented into a fully coupled FE code. Seven input motions are retrieved for several selection strategies in conjunction with two seismic intensity levels. Hence, more than 300 one-dimensional ground response analyses are performed. The results of the analysed cases, which are presented in terms of spectral response at ground surface and amplification factors, indicate that: (i) the use of an advanced elasto-plastic soil constitutive model accounts for nonlinear ground response effects, including higher site amplification in the mid-period range and deamplification of the peak ground accelerations; (ii) the different scaling strategies lead to comparable mean values of the amplification factors, and (iii) the variability of the amplification factors is significantly reduced when the scaling strategy seeks the compatibility with the target spectrum over a specified period range. The research will aid the prediction of local seismic site response over large areas, particularly in the absence of the fundamental period of a structure and facilitate its use in general recommendation for quantifying and reducing uncertainty.

Initial data for Hardening Soil model

Nowadays, civil engineering makes high demands on numeral modelling in geotechnical engineering, notably, to ensure reliability of a structure at minimum cost. Using of codes and standards supported with numerical calculations and soil constitutive models makes the design satisfying this requirement possible. But no matter how complex the model is its fidelity depends on input data. The article describes a method for determining the main characteristics of the Hardening Soil model (including calculating the power parameter m and reducing the deformation characteristics of the soil to the recommended value of the reference pressure). A comparison of two approaches was made: using a table of physical and mechanical characteristics; and the approach based on the analysis of the results of laboratory tests in accordance with the methodology given in the article and further verification of the obtained parameters. The result of the comparison was the complete inconsistency of the first approach for assigning the parameters of the nonlinear soil model and the need to refer to the test protocols was confirmed.

Swelling Prediction of Expansive Soil Using Numerical Method Analysis

Expansive soil is one of the factors that cause road damage in Indonesia. Its behavior is influenced by moisture content. At high moisture content, expansive clay has a very low bearing capacity and high swelling and shrinkage rate compared to other soil types. This soil expansion causes a heave force on the road pavement. When the force exceeds the strength of the pavement, the pavement will deform and break as the initial damage is created. Therefore, it is critical to investigate the effect of moisture content on the swelling-shrinkage behavior of expansive soil. In this study, soil expansion is numerically predicted using the finite element approach on ABAQUS compared to the laboratory expansion index test. The geometric shape and loading of the soil model are the same as the sample shape and loading of a laboratory expansion index test. The Mohr-Coulomb soil constitutive model with sorption is used to simulate water absorption in partially saturated soils. Coupled wetting liquid flow and porous medium stress analysis are used to simulate swelling and shrinkage. The simulation is divided into two types: geostatic, which simulates soil model loading, and coupled pore fluid, which simulates changes in water content. The simulation is then compared to the laboratory test for validation. The numerical analysis results show that the model's accuracy depends highly on the constitutive soil model, whereas the Mohr-Coulomb model shows a limitation in accuracy with the maximum swelling in the simulation is 21.704%, while the average maximum swelling in laboratory testing is 15.515%.

A small-strain soil constitutive model for initial stiffness evaluation of laterally loaded piles in drained marine sand

Three-Dimensional Finite-Element Method (3-D FEM) analyses were performed to investigate the initial stiffness of the laterally loaded piles in drained marine sand. A small-strain soil constitutive model developed based on Menq model was implemented in the 3-D FEM model to simulate the response of laterally-loaded piles in the sand over a range of small displacements. The model incorporated how the shear modulus for sand increased with the mean effective stress and decreased non-linearly with the increasing shear strain. The procedure of calibrating the model was proposed based on fitting the measurements from both laboratory tests and in-situ site investigation This soil constitutive model was implemented within a 3-D FEM analysis using an isotropic material with strain-induced anisotropy behavior in order to simulate the response of laterally-loaded piles under monotonic loading. A comparison of model predictions with laboratory and field test results indicated that this model had the promise to simulate the non-linear relationship between lateral load and pile-head deflection for mudline deflections ranging from less than 0.25-percent of the pile diameter.

Cyclic stress–dilatancy relations and plastic flow potentials for soils based on hypothesis of complementarity of stress–dilatancy conjugates

Soil, rocks and rock masses dilate or compact when sheared, i.e., distortion necessitates volume change. This coupling between distortional strains and volumetric strains, described by stress–dilatancy theories, endows soils with manifestation of peculiar characteristics when they are subjected to shear. Stress–dilatancy theories have become central in describing the mechanical energy dissipation mechanism and further establishing flow rules in constitutive modelling of soils. The classical stress–dilatancy theories, such as Taylor's and Rowe's, are endowed with simplicity and descriptive power, but they were developed for describing the dilatancy behaviour of soils subjected to loading in shear (mobilizing away from isotropic stress state) and needed to be extended for describing plastic dissipation and shear-induced volumetric changes when soils are subjected to cyclic shear. In this paper, hypothesis of complementarity of stress–dilatancy conjugates is proposed as a unifying hypothesis for deriving stress–dilatancy relations for both loading in shear and unloading in shear. Then, plastic potential functions are derived based on the resulting stress–dilatancy relations. In so doing, the resulting stress–dilatancy relations and plastic potential functions are rendered with a quality to be used for the modelling of deformation behavior of soils subjected to both monotonic and cyclic shearing. The theoretical framework is applied first for plane strain and axisymmetric stress–strain conditions; and then extended for the general stress condition considering the Lode angle dependency of the shear strength of soils, using the multilaminate framework and applying the Matsuoka–Nakai spatial mobilized plane.

Numerical simulations of displacement piles in a tropical soil

The behavior of pile foundations under axial loading is directly influenced by the effects that its installation process induces in the surrounding soil. Consequently, the consideration of these effects is essential for the correct numerical modeling of these geotechnical structures. In the present study, numerical simulations of driven cast-in-situ piles under axial loading have been carried out using finite element analysis. Three 3.5 m long piles with diameters ranging from 114.3 to 219.1 mm were analyzed. The pile installation effects have been considered indirectly by employing two distinct approaches, both based on the concepts of cylindrical cavity expansion. The behavior of the tropical soil profile is described with the Hardening Soil constitutive model. The load-displacement response and load distribution along the pile obtained with the numerical simulations have been analyzed and compared with in-situ load tests results. In the failure conditions, both approaches accurately predicted the bearing capacity of the piles, with an average error of only 2% compared to the measured values. The results in terms of load distribution over depth were also satisfactory. The difference between measured and numerical ultimate base resistance values ranged from 0% to 30%. The good agreement between the numerical and experimental results indicates that the proposed numerical approaches have been effective in simulating the piles installation process and reinforces the importance of considering the installation effects in the numerical modeling of these geotechnical structures. Both approaches can also be used to predict the bearing capacity of displacement piles.

A simple numerical simulation method for unsaturated stratum under the water environmental load

A simple numerical simulation method is proposed to investigate the mechanical response of the unsaturated stratum under the water environmental load. The proposed numerical simulation method applies the water environmental load to the unsaturated stratum as the load condition, and adopts the developed non-orthogonal elastoplastic constitutive model for unsaturated soil to describe the mechanical behaviors at the material scale. The mechanical response of unsaturated stratum is obtained by solving the discretized governing equation of the mechanical equilibrium. The proposed numerical simulation method is implemented based on the commercial finite element software ABAQUS. The effectiveness of the proposed method is verified through the element tests on the Botkin silt, the element tests on the Pearl clay, and a model test of the rising water level on a sand column. The numerical simulations of the rising and decreasing groundwater level in the unsaturated stratum are conducted. During the rising groundwater level, the non-collapsible stratum produces rebound deformation, the collapsible stratum below the groundwater level occurs rebound deformation, and the collapsible stratum above the groundwater level mainly produces settlement deformation. During the decreasing groundwater level, both the collapsible stratum and the non-collapsible stratum produce the settlement deformation.

Chemo-mechanical behaviour of non-expansive clays accounting for salinity effects

Changes in the chemistry of the pore fluid are known to have an impact on the hydro-mechanical behaviour of clays. Experimental evidence collected in recent decades has led to the formulation of constitutive chemo-mechanical models for expansive soils used in engineering practice for the containment of pollution, such as bentonite. Less attention has been paid to modelling the chemo-mechanical behaviour of non-expansive clays, which are less frequently used for geoenvironmental applications, but equally exposed to chemical changes. Key differences between the impact of salinity on the fabric of expansive and non-expansive clays are pointed out. At the macroscopic scale, an increase in salinity causes a translation of the normal compression line of non-expansive clays to higher void ratios, which in some cases is also accompanied by an increase in compressibility. The opposite occurs for expansive clays. Such experimental evidence provides the basis for a chemo-mechanical model formulated in the frame of elasto-plasticity with generalised hardening, whose yield surface expands with pore fluid concentration. The model is validated against experimental results, both original and from the literature. Simulation results compare very well with those of tests performed on reconstituted, compacted and intact samples.

Inspection of two sophisticated models for sand based on generalized plasticity: Monotonic loading and Monte Carlo analysis

AbstractThe generalized plasticity theory has evolved in the last decades and attracts the attention of different research groups, because of characteristics like the absence of an explicit flow surface formulation. This paper presents a detailed inspection of two sophisticated constitutive models for granular soils under monotonic loading: the Pastor‐Zienkiewicz‐Chan (P‐Z‐C) model[1] and the Manzanal‐Merodo‐Pastor (M‐M‐P) model.[2] Even though they are similar in mathematical framework, the P‐Z‐C model requires only eight parameters compared to the M‐M‐P model which requires 18 parameters to describe the material behavior under monotonic loading. Parameters of both models were calibrated based on the extensive experimental database available for monotonic triaxial tests performed on Karlsruhe fine sand by Wichtmann et al.[3] An objective discussion addressing the strengths and weaknesses of each model is presented. Finally, a procedure to identify the most relevant parameters that control different elements in the model like the stiffness, the evolution of dilatancy or the hardening variables is introduced, using the Monte Carlo Toolbox (MCAT) for simulations. Some interesting inferences could be obtained, like the conclusion that the MCAT is a helpful tool for identifying material parameters and their interaction, but it cannot replace the human factor, the experience and objective judgement of the modeller for the calibration of constitutive models.

On the Practical Use of Advanced Constitutive Laws in Finite Element Underground Structures Analysis

Abstract This article emphasizes the value of applying sophisticated constitutive soil models in numerical modeling as daily geotechnical practice. The capabilities of two different constitutive relations for the modeling of the second Heinenoord bored tunnel are compared. The hypoplastic model of Wolffersdorff for granular materials (Hypo) is a relatively simple model without recourse to yield surface or plastic potential based on rational mechanics, whereas the chosen elastoplastic model, the Hardening Soil Model (HSM) belongs to the non-associative plasticity with double hardening. A modification of the hypoplastic model with improved intergranular strain (IGS) was tested, leading to improve model behavior. Comparisons between numerical simulations and experimental values demonstrate the advantages of using the hypoplastic model with improved intergranular strain (IGS).

Simulation of compound anchor intrusion in dry sand by a hybrid FEM+SPH method

The intrusion of deformable compound anchors in dry sand is simulated by coupling the Finite Element Method (FEM) with Smoothed Particle Hydrodynamics (SPH). This novel approach can calculate granular flows at lower computational cost than SPH alone. The SPH and FEM domains interact through reaction forces calculated from balance equations and are assigned the same soil constitutive model (Drucker–Prager) and the same constitutive parameters (measured or calibrated). Experimental force–displacement curves are reproduced for penetration depths of 8 mm or more (respectively, 20 mm or more) for spike-shaped (respectively, fan-shaped) anchors with 1 to 6 blades. As the number of blades increases, simulations reveal that the granular flow under the anchor deviates from the vertical and that the horizontal granular flow transitions from orthoradial to radial. We interpret the strain field distribution as the result of soil arching, i.e., the transfer of stress from a yielding mass of soil onto adjoining stationary soil masses. Arching is fully active when the radial distance between blade end points is less than a critical length. In that case, the normal stress that acts on the compound anchor at a given depth reaches the normal stress that acts on a disk-shaped anchor of same radius. A single-blade anchor produces soil deformation and failure similar to Prandtl’s foundation sliding model. Multiblade anchors produce a complex failure mechanism that combines sliding and arching.

Soil-structure interaction of integral abutments

Integral abutment bridges (IABs) are pioneering structures that offer certain advantages over conventional bridges. The main difference is the ability of IABs to eliminate the necessity of utilizing bearings and expansion joints. This results in more economical construction and enhanced structural performance. However, the intricate soil-structure interactions of IABs under the influence of seasonal changes are not yet fully understood. This paper aims to improve the understanding of these innovative structures by utilizing comprehensive numerical models to investigate their geostructural performance under various conditions. The case study selected for this research was the Middlesex bridge in Vermont, USA. A full-scale monitoring program at this bridge measured and recorded the bridge acting pressures, deformations, and internal forces, making it possible to gain insight into the thermal response of such structures. For the numerical research, a comprehensive two-dimensional numerical model, developed by using the PLAXIS software, was verified against the available field measurements. Subsequently, parametric studies were conducted to investigate earth pressure and pile bending moment variations influenced by different model conditions. Key model parameters were varied, including the constitutive soil model, thermal loading, backfill stiffness, pile size and orientation, and span length. It was found that utilizing a linear constitutive soil model could lead to significant inaccuracies in the results. Increasing the backfill stiffness was seen to increase passive earth pressures and decrease pile bending moments. With smaller pile sections, oriented for weak-axis bending, pile bending moments decreased substantially and lateral earth pressures increased. Because dead load magnitudes were closely linked to span lengths, pile bending moments and backfill pressures increased when fewer and longer bridge spans were used.

Numerical modeling of a pile-supported wharf subjected to liquefaction-induced lateral ground deformations

Fully-coupled nonlinear dynamic analysis is increasingly used for assessing the seismic performance of pile-supported wharf structures subjected to liquefaction-induced lateral ground deformations. Several numerical challenges exist for analysis of this highly nonlinear soil-structure interaction, which require robust, yet practical, solutions that are validated with experimental data. This study presents a numerical model of a pile-supported wharf and evaluates the applicability of a soil constitutive model, and modeling assumptions and methods by using recorded data from a well-instrumented, large-scale centrifuge test. The objectives of this study include: (a) evaluating the performance of a recently developed pressure-dependent multi-yield surface constitutive soil model (PDMY03) to simulate the behavior of a liquefiable sand (b) assessing the effectiveness of a soil–pile interaction modeling approach in capturing the kinematic displacement demands on piles from a laterally spreading ground, and (c) evaluating the effectiveness and limitations of the 2D numerical model in approximating the 3D behavior of a wharf structure supported by multiple rows of piles, including the dynamic response of the centrifuge container. The implications of these assumptions and lessons learned from this study provide guidance for researcher modelers and practitioners for numerical modeling of similar soil–structure systems.

Sensitivity of the seismic response of bored pile embedded in cohesionless soil to the soil constitutive model

Sensitivity of the seismic response of bored pile embedded in cohesionless soil to the soil constitutive model