Soil Constitutive Model Research Articles

Formulation and Implicit Numerical Integration of a Kinematic Hardening Model for Unsaturated Soils

ABSTRACTCurrently, our understanding of material‐scale deterioration resulting from meteorologically induced variations in pore water pressure and its significant impact on infrastructure slopes is limited. To bridge this knowledge gap, we have developed an extended kinematic hardening constitutive model for unsaturated soils that refines our understanding of weather‐driven deterioration mechanisms in heterogeneous clay soils. This model has the capability of predicting the irrecoverable degradation of strength and stiffness that has been shown to occur when soils undergo wetting and drying cycles. The model is equipped with a fully coupled and hysteretic water retention curve and a hysteretic loading–collapse curve and has the capability to predict the irrecoverable degradation of strength and stiffness that occurs during cyclic loading of soils. Here, we employ a fully implicit stress integration technique and give particular emphasis to deriving a consistent tangent operator, which includes the linearisation of the retention curve. The proposed algorithm is evaluated for efficiency and performance by simulating various stress and strain‐driven triaxial paths, and the accuracy of the integration technique is evaluated through the use of convergence curves.

Modelling the evolving critical state of crushable soils and parameter optimization with an improved genetic algorithm (AIS-RCGA)

The critical state line (CSL) plays an essential role in the constitutive modelling of granular soils. It serves as a reference line for the measurement of the state parameter. The critical state of crushable soils cannot accurately be determined from experimental data because of the ever-changing soil properties due to particle breakage. In this study, two new parameters eB and eb are introduced, which account for the final position and the evolution of CSL of crushable soils during shearing, respectively. To identify the optimal CSL-related parameters from experimental data, a hybrid genetic algorithm combining artificial immune system (AIS) and real-coded genetic algorithm (RCGA), namely AIS-RCGA is adopted. The fitness is defined to minimize the prediction error of both void ratio (or, pore water pressure) and deviatoric stress. We have refined the tuning methods for several hyperparameters of AIS-RCGA and proposed a novel method to assess the similarity of individuals within AIS-RCGA. Results show that the new method is more efficient in finding the global optimal for our problem. With optimized model parameters, the new constitutive model can accurately predict the response of crushable soil, outperforming other constitutive model reported in the literature.

Assessment of Free Energy Functions for Sand

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

Bearing Performance of a Helical Pile for Offshore Photovoltaic under Horizontal Cyclic Loading

For an offshore photovoltaic helical pile foundation, significant horizontal cyclic loading is imposed by wind and waves. To study a fixed offshore PV helical pile’s horizontal cyclic bearing performance, a numerical model of the helical pile under horizontal cyclic loading was established using an elastic–plastic boundary interface constitutive model of the clay soil. This model was compared with a monopile of the same diameter under similar conditions. The study examined the effects of horizontal cyclic loading amplitude, period, and vertical loads on the horizontal cyclic bearing performance. The results show that under horizontal monotonic loading, the bearing capacities of a helical pile and monopile in a serviceability limit state are quite similar. However, as the amplitude of horizontal cyclic loading increases, soil stiffness deteriorates significantly, leading to greater horizontal displacement accumulation for both types of piles. The helical pile’s bearing capacity under horizontal cyclic loadings is approximately 60% of that under monotonic loading. With shorter cyclic loading periods, horizontal displacement accumulates rapidly in the initial stage and stabilizes over a shorter duration. In contrast, longer cyclic loading periods lead to slower initial displacement accumulation, but the total accumulated displacement at stabilization is greater. When vertical loads are applied, the helical pile exhibits more stable horizontal cyclic bearing performance than the monopile.

Constitutive Damage Model for Rubber Fiber-Reinforced Expansive Soil under Freeze-Thaw Cycles.

To elucidate the degradation mechanism of expansive soil-rubber fiber (ESR) under freeze-thaw cycles, freeze-thaw cycle tests and consolidated undrained tests were conducted on the saturated ESR. The study quantified the elastic modulus and damage variables of ESR under different numbers of freeze-thaw cycles and confining pressure, and proposed a damage constitutive model for ESR. The primary findings indicate that: (1) The effective stress paths of ESR exhibit similarity across different numbers of freeze-thaw cycles, the critical stress ratio slightly decreased by 8.8%, while the normalized elastic modulus experienced a significant reduction, dropping to 42.1%. (2) When considering the damage threshold, the shear process of ESR can be divided into three stages: weak damage, damage development, and failure. As strain increases, the microdefects of ESR gradually develop, penetrating macroscopic cracks and converging to form the main rupture surface. Eventually, the damage value reaches 1. (3) Due to the effect of freeze-thaw cycles, initial damage exists for ESR, which is positively correlated with the number of freeze-thaw cycles. The rubber fibers act as tensile elements, and the ESR damage evolution curves intersect one after another, showing obvious plastic characteristics in the late stage of shear. (4) Confining pressure plays a role in limiting the development of ESR microcracks. The damage deterioration of ESR decreases with an increase in confining pressure, leading to an increase in ESR strength. (5) Through a comparison of the test curve and the theoretical curve, this study validates the rationality of the damage constitutive model of ESR under established freeze-thaw cycles. Furthermore, it accurately describes the nonlinear impact of freeze-thaw cycles and confining pressure on the ESR total damage.

Three-Dimensional Site Response Analysis of Clay Soil Considering the Effects of Soil Behavior and Type

To understand changes in bedrock motion at the ground surface, frequency effects, and spatial distribution within the soil, it is important to look at how a site responds to earthquakes. This is important for soil–structure interaction in structural and geotechnical earthquake engineering. This study deals with the effect of classifying clays according to shear wave velocity (stiff/medium/soft) and nonlinearity in behavior (linear/nonlinear) on the analysis of the site response. A 3D soil model with a combination of free fields and quiet boundaries and advanced constitutive models for soil to obtain accurate results was used to conduct this study. A strong TABAS earthquake was used to excite the compliant base of the model after converting the velocity record of TABAS to an equivalent surface traction force using a horizontal force–time history proportional to the velocity–time history. This study reveals that the site response analysis is affected by the type of clay soil and the soil material behavior, with soft clay soil causing higher PGV and PGV values in the linear case and lower values in the nonlinear case due to soil yielding, which causes soil response attenuation. This results in extremely conservative and expensive building designs when linear soil behavior is adopted. On the other hand, the applied earthquake exhibits greater attenuation at longer frequencies and greater amplification at mid and short frequencies. However, at frequencies near the applied earthquake frequency, neither attenuation nor amplification occurs. Furthermore, nonlinear soil behavior is crucial for soil evaluation and foundation design due to higher octahedral shear strain and settlement values, especially in softer soils, resulting from extensive plastic deformation.

Constitutive modelling in computational geomechanics – 61st Rankine lecture, British Geotechnical Association, 2023

Constitutive models are an essential part of computational modelling in geotechnics; they are at the heart of almost all theoretical predictions of geotechnical structures. How the stress–strain (and perhaps time) response of soil (and rock) is represented in these mathematical models is usually the key to successful prediction of the behaviour of geotechnical structures. However, the important details of these models, particularly the idealisations that are made, may be poorly or incompletely understood, or ignored, sometimes at significant cost to the unwary analyst. Indeed, the capabilities and the shortcomings of these models, especially the more advanced models, are not always easy to ascertain. In some cases, determination of the values of the input parameters is not straightforward. Consequently, it may be difficult to determine which model to select for a particular task. This paper explores some of the more important developments in the constitutive modelling of soils and addresses some of these issues of potential concern. The need for such models and the various attributes and capabilities that the commonly used models possess are reviewed. Also discussed is the issue of matching a particular model to the geotechnical problem at hand, which model attributes are required and why. The intention is to place emphasis on the physical basis of these models, rather than explore their mathematical complexity in detail. Some of the constitutive models encoded in the software packages used routinely in geotechnical practice are reviewed, and discussion is also provided on their specific limitations. Examples of practical applications, involving the solution of boundary and initial value problems, are described to illustrate both the advantages and some of the limitations of both commonly used and highly advanced constitutive models.

Constitutive relationship of soil in contact with mortar under continuous loading

Mortars will remain critical in future land wars due to their flexibility and versatility. When mortars are fired continuously, the contact soil is gradually compacted by the mortar base plate, and dynamic research into this process is the basis for innovative mortar design. However, the discontinuity and nonlinearity of soil contact absolutely necessitate the constitutive relationship of soil contact, which is difficult to study. Therefore, this study conducted experimental research and theoretical derivation to establish an accurate dynamic model of the mortar system. First, based on the nonlinear elastic–plastic theory and the stress–strain relationship of soil under cyclic loading, a theoretical analysis method for the constitutive relationship of contact soil under continuous loading was proposed. Second, an experimental and testing system was designed to simulate launch loads, and the stress–strain response of soil under continuous impact loads was obtained experimentally. Subsequently, based on theoretical analysis and experimental data, the stress–strain relationship during the gradual compaction of soil was established using the least squares method. Finally, a constitutive relationship model of the contact soil in the mortar system was established in ABAQUS using the VUMAT subroutine interface, and the calculated results were compared and analyzed with traditional calculation results. The results indicated that studying the constitutive relationship of mortar in contact with soil during continuous firing using this method can improve the accuracy of dynamically modeling mortar systems. Moreover, this study has practical value in the engineering design of mortar systems.

Practical considerations for numerical simulation of large-diameter monopiles for offshore wind turbines in overconsolidated sand: A case study of the VIBRO project in Cuxhaven, Germany

Monopiles are typically the preferred foundation for offshore wind turbines, which are becoming increasingly large. While 3D finite element modelling can aid the design process of monopile foundations, achieving reliable results requires precise constitutive soil models and input parameters derived from laboratory and field data, as well as careful consideration of soil sample preparation method. This study explores various soil preparation methods, including moist tamping, dry tamping, and air pluviation, along with two sample ratios (1 and 2) during triaxial tests. It uses an advanced soil model, the DeltaSand model, and a practical industry model, the Hardening Soil model with small strain (HSsmall). To evaluate model performance, the Vibro project performed in Cuxhaven, Germany, is used as a case study. Simulations using the DeltaSand model show good agreement with field data. The effects of soil preparation methods and sample ratios are more pronounced in HSsmall model simulations, in which better results are obtained when the model is calibrated using dry tamping data and a sample ratio of one.

Instability and deformation behaviors of root-reinforced soil under constant shear stress path

Climate change is becoming a greater global challenge, leading to more frequent and intense extreme weather events, which in turn increase mountain hazards like shallow landslides and soil erosion. Ecological slope protection using vegetation has gained in- creasing attention to mitigate natural disasters in recent years. While numerous studies have demonstrated the contribution of root systems to soil reinforcement, the comprehensive impact of roots on soil mechanical response under rainfall scenarios remains elusive. This study investigates the instability and deformation behaviors of root-reinforced soil through constant shear drained (CSD) tests. The role of root characteristics, including biomass, diameter, and length, in modulating the shear strength, instability and deformation behaviors of soils is investigated. The results indicate that the shear strength and stability of root-reinforced soil, as well as the inhibition effect of root on contractive deformation after the initiation of instability, increasing with greater root biomass and length and smaller root diameter. Moreover, due to the potential weak interfaces, fine or stiff long roots appear to increase the likelihood of volumetric dilation in root-reinforced soil at the later stage of unstable deformation. However, this dilatancy can be effectively resisted by increasing root planting density to form the root network. Furthermore, our experiments suggest that herbaceous vegetation with finer and longer roots is more effective in mitigating static liquefaction of soils induced by rainfall infiltration. This study helps develop a predictive constitutive model for root-reinforced soils and supports future bioengineering slope design.

The Influence of Pipeline-Backfill-Trench Interaction on Pipeline Response to Ice Gouging: A Numerical Investigation

Ice gouging is a destructive incident to subsea pipelines in Arctic regions. Trenching and backfilling is a cost-effective solution to physically protect the pipeline against ice gouging. Ice gouging imposes a complex combination of stresses and strains through the soil medium, the pipeline, and the interface. Remolded backfill materials with considerably less stiffness than native soil result in more complexity in soil failure mechanisms and pipe trajectories. However, this critical aspect is less explored in the literature on ice gouges. This paper investigated the influences of pipeline-backfill-trench interaction on the soil failure mechanisms and the pipeline responses by coupled Eulerian-Lagrangian (CEL) method. Two model configurations (shallowly buried and deeply buried pipeline) were set up to investigate the influence of trenching/backfilling, as well as pipe burial depth. Incorporation of the strain-rate dependency and strain-softening effects in the soil constitutive model involved the development of a user-defined subroutine and incremental update of the undrained shear strength within the Abaqus software. The research findings indicate that the conventional approach of assuming uniform seabed soil for trenched and backfilled pipelines may not accurately capture the pipeline behavior and soil failure mechanisms.

Enhancing Deep Excavation Optimization: Selection of an Appropriate Constitutive Model

To minimize the impact on nearby structures during deep excavations, choosing an appropriate soil constitutive model for analysis holds significant importance. This study aims to conduct a comparative analysis of various constitutive soil models—namely, the Mohr–Coulomb (MC) model, the hardening soil (HS) model, the hardening soil small strain (HSS) model, and the soft soil (SS) model—to identify the most suitable model for the lacustrine deposit. To implement these models, the soil’s index properties and mechanical behavior were evaluated from undisturbed soil samples. The numerical simulation and verification of these properties were carried out by comparing the laboratory test results with the outcome of the finite element method; the most suitable constitutive soil model for the soil was identified as the HSS model. Upon analyzing the wall deflection and ground settlement profiles obtained from respective constitutive models, it was observed that the HS and HSS models exhibit similar characteristics and are well-suited for analyzing typical lacustrine soil. In contrast, the MC and SS models yield overly optimistic results with lower wall deflection and ground settlement and fail to predict realistic soil behavior. As a result, this research highlights the significance of selecting the appropriate constitutive soil model and refining the parameters. This optimization process contributes significantly to the design of support systems, enhancing construction efficiency and ensuring overall safety in deep excavation projects.

Cyclic response of unsaturated weathered red mudstone: Experimental investigation and a cyclic model

The mechanical properties and constitutive model of unsaturated soils under cyclic loading are crucial for understanding the behavior of foundations and slopes subjected to dynamic motions such as earthquakes and traffic loading. In this study, multilevel strain-controlled cyclic simple shear tests of unsaturated weathered red mudstone (WRM) were conducted. The detailed investigation focused on cyclic responses, including shear stress-strain behavior and volume change, strain-dependent secant shear modulus and damping ratio, and stress–dilatancy behavior. This study revealed the significant influences of the degree of saturation and vertical stress on these responses, with the initial static shear stress mainly affecting the shear stress-strain behavior and volume changes at the initial loading stage. Based on the experimental observations, a cyclic constitutive model was proposed for unsaturated WRM. The model incorporates a slightly revised Davidenkov model and Masing criterion to generate shear stress-strain hysteresis loops with or without initial static shear stress. Additionally, a stress-dilatancy equation was included to capture the volume changes during cyclic loading. The proposed model was verified by comparing representative test data and calculation results, demonstrating the excellent performance of the proposed model in modeling the main features of unsaturated WRM under cyclic loading.

Numerical simulation of rainfall-induced deformations of embankments considering the coupled hydro-mechanical behavior of unsaturated soils

This paper presents numerical simulations of the deformation response of unsaturated embankments subjected to rainfall infiltration using a coupled hydro-mechanical constitutive model for unsaturated soils. The constitutive model accounts for the influence of degree of saturation on the stress–strain behavior and the influence of void ratio on the water retention behavior. The constitutive model was implemented in the finite difference program FLAC, calibrated using triaxial test data, and validated using measurements of wetting-induced deformations of embankment models from centrifuge tests. The validation demonstrates that the constitutive model can capture the coupled hydro-mechanical behavior of unsaturated soils under wetting conditions. Simulations of the hydro-mechanical response of unsaturated embankments subjected to rainfall infiltration indicate that the differential settlement across the top surface of the embankment between the centerline and shoulder increases significantly during rainfall infiltration, which could result in severe damage to overlying transportation infrastructure. As the rainfall infiltration increases, shear strains accumulate and form a potential failure surface at a shallow depth of approximately 2 m from the slope surface. Insights into the hydro-mechanical response of unsaturated embankments subjected to rainfall infiltration gained will be useful for considering climate change effects in design and construction of compacted embankments.

A Bayesian optimization-genetic algorithm-based approach for automatic parameter calibration of soil models: Application to clay and sand model

This paper develops a novel approach for automatic parameter calibration of soil constitutive models by combining Bayesian optimization (BO) and genetic algorithm (GA). The BO method enables locating the possible point over a large multi-parameter search domain quickly, by which the search domain is no longer required to be accurately pre-defined. Thereafter, the GA is employed to find the best solution within the BO-optimized search space. This calibration procedure can quickly give the best-matched model parameters for both sands and clays even with the same large search space. Taking a critical state-based soil model (Clay And Sand Model (CASM)) as an example, the superiority and capability of the proposed calibration method are examined by comparing experimental data with predicted results for both clays and sands. It is shown that the BO-GA-based approach can reduce errors by 46.4% for clays and 41.2% for sands compared with the conventional GA method and outperforms other traditional optimization algorithms. Eventually, the evolution process of BO and GA is visualized to better understand the principles of automatic parameter calibration, which is followed by model uncertainty analyses.

A Numerical Investigation on the Sinkage of the Deep-Sea Mining Vehicle Based on a Modified Constitutive Soil Model

Abstract The seabed soil of the polymetallic nodule mining area is relatively thin, soft, and fluid, which will produce large deformation under external disturbance. Its undrained shear strength is related to strain-rate and strain-softening effect. It is an important engineering safety problem for the deep-sea mining vehicle (DSMV) to travel in the soft seabed, and its sinkage is a vital index affecting the traction performance. It is necessary to study the sinkage performance of the DSMV under the characteristics of large soil deformation, but there are only few existing studies. This study established a numerical model of seabed soft soil with Tresca constitutive considering strain-rate and strain-softening effects. First, a numerical simulation study was carried out on the interaction between the DSMV track plate and the seabed soil, and the influence of track plate structures on the pressure–sinkage characteristic was obtained. Then, a simplified three-dimensional model of the “PIONEER-I” DSMV was established. Under the condition of wet weight and initial vertical velocity, the influence of different initial bottoming velocities, weight, and soil parameters on the sinkage of the DSMV was obtained. An empirical prediction model of the DSMV sinkage was established based on the energy method and numerical calculation results.

Performance of an advanced sand constitutive model in modelling soil and soil-structure interaction under seismic excitation

There is a growing number of available advanced soil constitutive models aimed at capturing soil cyclic behaviour and their subsequent use in seismic applications. Nevertheless, detailed validation studies of these soil constitutive models on benchmark experimental works including seismic soil-structure interaction are still rare. This work presents a short validation study of the seismic performance of an advanced elastoplastic sand constitutive model on a boundary value problem including kinematic and inertial soil-structure interaction. The results of the finite element numerical model for the free field and structural responses are compared with the experimental work on a group of piles analysed in a flexible soil container filled with dry sand and subjected to simplified seismic loading. In general, the comparisons show a satisfactory match between the results of the simulations and the experiments, with the exception of the numerical predictions of settlements. The computed results are discussed based on: i) the dominant stress-paths in soil; ii) parametric studies on the settlement evaluation; iii) the origin of the high frequency motion oscillations to simple sinusoidal input motions; all with respect to potential improvements in the formulation of the elastic behaviour of the constitutive model in the future.

Modeling the response of a shallow foundation using advanced soil constitutive models

Shallow foundations are a common type of foundation used for many significant structures. These foundations can be subjected to vertical loads, moments, and base shear, which induce stresses and strains in the supporting soil. Consequently, understanding soil behaviour is crucial in geotechnical engineering. This paper presents a numerical analysis of a shallow foundation using various soil behaviour laws, utilizing finite element methods implemented in Plaxis software. The primary objective of this study is to conduct numerical modeling of a foundation under a centered load. Specifically, it aims to compare the results obtained using different constitutive models, including the Mohr-Coulomb (MC) model, the Soft Soil model, and the modified Cam-Clay model. By employing these models, we aim to evaluate their effectiveness in predicting soil response under load and to identify the most accurate model for specific soil conditions. The comparative analysis provides insights into the advantages and limitations of each model, highlighting the importance of selecting appropriate soil behaviour laws for accurate geotechnical design. Furthermore, this study underscores the significance of advanced numerical tools in enhancing our understanding of soil-structure interaction and improving the reliability of foundation design. The findings contribute to the broader field of geotechnical engineering by offering guidance on the selection of constitutive models for various soil types and loading conditions, ultimately aiding in the design of safer and more efficient shallow foundations. This research also emphasizes the role of precise modeling in predicting settlement and bearing capacity, which are critical factors in the performance and longevity of shallow foundations. Overall, this study aims to improve foundation design practices significantly.

Prediction of retrogressive landslide in sensitive clays by incorporating a novel strain softening law into the Material Point Method

Sensitive clays, when subjected to large strains, exhibit a unique strain-softening behavior, transforming into a remolded liquid with remarkably low shear strength. When a slope fails, this behavior leads to the remolded clay moving away from its original position, triggering subsequent failures and catastrophic outcomes. To accurately predict such scenarios, it is crucial to incorporate realistic strain-softening characteristics into the constitutive soil model. This paper presents a novel yet practical strain-softening law developed by the authors that effectively captures the post-peak behavior of sensitive clays down to their remolded strength. The softening law is implemented in an elastoplastic Mohr-Coulomb model and incorporated into Anura3D, an open-source software that uses the Material Point Method to simulate large deformations. The constitutive model is calibrated by simulating the stress-strain behavior through direct shear tests conducted at three sensitive clay landslide locations. The accuracy of the overall numerical framework is assessed by predicting the post-failure movements of these landslides. Notably, two of the landslides, Sainte-Monique (1994) and Saint-Jude (2010), have previously been analyzed using other numerical tools, allowing for a comparative analysis with the method presented here. The third landslide, the Saint-Luc-de-Vincennes landslide, representing a composite flow slide and spread, has been numerically simulated for the first time. The post-failure behavior observed in the landslide events is compared with field observations and other numerical analyses. The results show that the MPM models with the proposed strain-softening law can reasonably predict post-failure retrogression and runout distance, which are crucial parameters for determining the risk of landslides in sensitive clays.

Optimal intensity measure for seismic performance assessment of shield tunnels in liquefiable and non-liquefiable soils

Relating the ground motion intensity measure (IM) and the structural engineering demand parameter is a crucial step in the performance-based earthquake engineering framework. This study investigates the selection of IM for development of probabilistic seismic demand model of urban shield tunnels subjected to earthquake ground motions in liquefiable and non-liquefiable soils. Nonlinear dynamic effective stress analyses are conducted to develop a database of the intensity measures and structural seismic responses exposed to ground shaking and soil liquefaction. Two advanced soil constitutive models (i.e., Pressure DependMultiYield03 and PressureIndependMultiYield for liquefiable and non-liquefiable soils, respectively) are employed to capture the nonlinear behavior. A suite of 23ground motion intensity measures is selected and assessed based on the evaluation criteria of correlation, efficiency, practicality and proficiency. Eventually, the multi-level fuzzy comprehensive evaluation method is employed to comprehensively consider the four evaluation criteria and establish the optimal ground motion IM suitable for probabilistic seismic demand analysis of shield tunnel structures. The obtained results show that the sustained maximum acceleration is the optimal IM for evaluating the structural seismic response, followed by the peak ground acceleration in both liquefiable and non-liquefiable soils. Peak pseudo velocity spectrum, displacement square integral and Housner spectral intensity are found to be not suitable for the probabilistic seismic demand analysis of shield tunnel structures.