Constitutive models of sands play an essential role in analysing the foundation responses to cyclic loads, such as seismic, traffic and wave loads. In general, sands exhibit distinctly different mechanical behaviours under monotonic, regular and irregular cyclic loads. To describe these complex mechanical behaviours of sands, it is necessary to establish appropriate constitutive models. This study first analyses the features of hysteretic stressstrain relation of sands in some detail. It is found that there exists a largest hysteretic loop when sands are sufficiently sheared in two opposite directions, and the shear stiffness at a stress-reversal point primarily depends on the degree of stiffness degradation in the last loading or unloading process. Secondly, a stress-reversal method is proposed to effectively reproduce these features. This method provides a new formulation of the hysteretic stress-strain curves, and employs a newly defined scalar quantity, called the small strain stiffness factor, to determine the shear stiffness at an arbitrary stress-reversal state. Thirdly, within the frameworks of elastoplastic theory and the critical state soil mechanics, an elastoplastic stress-reversal surface model is developed for sands. For a monotonic loading process, a double-parameter hardening rule is proposed to account for the coupled compression-shear hardening mechanism. For a cyclic loading process, a new kinematic hardening rule of the loading surface is elaborately designed in stress space, which can be conveniently incorporated with the stressreversal method. Finally, the stress-reversal surface model is used to simulate some laboratory triaxial tests on two sands, including monotonic loading tests along conventional and special stress paths, as well as drained cyclic tests with regular and irregular shearing amplitudes. A more systematic comparison between the model simulations and relevant test data validates the rationality and capability of the model, demonstrating its distinctive performance under irregular cyclic loading condition.

The overconsolidation ratio (OCR) is a critical factor in determining the mechanical behaviour of overconsolidated clays. On the basis of the three requirements for the peak strength line, a continuous and smooth peak strength line is constructed from the perspective of the peak stress ratio, and then a new yield function for overconsolidated clays is developed. The developed yield function in the stress space is characterized by an elliptical curve. The evolution of the developed yield function in the stress space is captured by a new hardening parameter, which is constructed by integrating the proposed peak strength surface with the subloading surface concept. By combining the developed yield function with the non-orthogonal plastic flow rule, a non-orthogonal elastoplastic constitutive model of overconsolidated clays is established to consider the influence of the OCR on strength and deformation. The proposed model requires seven material parameters, all of which have a clear physical meaning and can be easily determined via conventional laboratory tests. Three typical stress paths are employed to demonstrate the essential features of the proposed model. The effectiveness of the proposed model is confirmed by comparing the experimental data with corresponding model predictions.

Accurately describing the solid-like and fluid-like behaviors of granular media is crucial in geotechnical engineering. While the unified frictional-collisional model, integrating rate-independent frictional and ratedependent collisional stresses, is widely used for solid-fluid phase transitions, an effective model is still under investigation, and comprehensive analyses are lacking. This study addresses these gaps by developing an enhanced elastoplasticity-based frictional-collisional model. The frictional stress is modeled using a critical-statebased elastoplasticity approach, and the collisional stress is formulated through an enhanced kinetic theory incorporating particle stiffness. Subsequently, comprehensive element simulations are conducted to explore the effects of concentration, particle stiffness, and strain rate paths on the model. The proposed model's effectiveness is also validated against experimental data. Finally, a detailed comparison with the typical mu(I) rheology model and a state-equation-based phase transition model is conducted. Our analyses show that the developed model effectively captures strain rate path and particle stiffness through the collisional stress component, while concentration-dependent characteristics are captured through both frictional and collisional stress components. Through comparative analyses, we also found that both the state-equation-based and elastoplasticity-based models depict solid-like behavior and replicate the rheology of granular media in a fluid-like state, similar to the mu(I) model. However, they differ in implementing critical state theory: the state-equation-based model acts as a partial-range phase transition model, describing stress evolution from the critical state to the fluid-like state, while the proposed elastoplasticity-based model serves as a full-range phase transition model, covering stress evolution from the initial to the fluid-like state.

Accurate continuum modelling of granular flows is essential for predicting geohazards such as flow-like landslides and debris flows. Achieving such precision necessitates both a robust constitutive model for granular media and a numerical solver capable of handling large deformations. In this work, a novel unified phase transition constitutive model for granular media is proposed that follows a generalized Maxwell framework. The stress is divided into an elastoplastic part and a viscous part. The former utilizes a critical-state-based elastoplasticity model, while the latter employs a strain acceleration-based mu(I) rheology model. Key characteristics such as nonlinear elasticity, nonlinear plastic hardening, stress dilatancy, and critical state concept are incorporated into the elastoplasticity model, and the non-Newtonian mu(I) rheology model considers strain rate and strain acceleration (i.e., a higher-order derivative of strain) to capture changes in accelerated and decelerated flow conditions. A series of element tests is simulated using the proposed unified phase transition model, demonstrating that the novel theory effectively describes the transition of granular media from solid-like to fluid-like states in a unified manner. The proposed unified model is then implemented within the material point method (MPM) framework to simulate 2D and 3D granular flows. The results show remarkable consistency with results from experiments and other numerical methods, demonstrating the model's accuracy in capturing solid-like behaviour during inception and deposition, as well as liquid-like behaviour during propagation.

Damping plays a crucial role in the design of offshore wind turbine (OWT) monopile foundations. The soil damping of the monopile-soil system (MSS) represents the energy dissipation mechanism arising from the interaction between the pile and the soil. It is typically derived by back-calculating from the overall damping measured in the entire OWT structure. However, few studies have independently examined the soil damping in MSS, and the impact of key parameters such as pile diameter, pile embedded depth, cyclic load amplitude, and load eccentricity on the variation of soil damping in MSS remains unclear. This paper introduces an elastoplastic-damage constitutive model for the numerical simulation of the damping ratio variation in seabed soil and MSS. The model is implemented in ABAQUS software and validated against cyclic triaxial tests on stiff clay soil. On this basis, a three-dimensional finite element sensitivity study was conducted to elucidate the effect of these key parameters on the MSS damping ratio. The results of the study reveal that the MSS damping ratio exhibits a nonlinear and asymmetric trend as the loading cycles increase. The MSS damping ratio decreases with increasing pile diameter and embedded depth but increases with increasing lateral cyclic load amplitude and load eccentricity from the mudline.

Sand cushions for passive protection structures could reduce the damage that is induced by rockfall impact. Therefore, evaluation of the peak impact force generated by rockfall on the sand cushion is significant to the design of passive protection structures. This study aims to estimate the peak impact force using the elastoplastic linear strengthening model when a rockfall hits the sand cushion. Impact tests were conducted to study the effect of rockfall mass, impact velocity, and cushion thickness on the rockfall impact force. The experimental results indicate that the decreasing rockfall mass, impact velocity, and increasing cushion thickness could decrease the impact force of rockfalls. The sensitivity analysis results show that the main factor that influences the peak impact force is impact velocity, followed by rockfall mass and cushion thickness. In addition, the calculation method for the peak impact force and penetration depth of rockfall was proposed by the elastoplastic linear strengthening model. The impact force-deformation curves of this model were provided and discussed. The relationship between the strengthening coefficient and influencing factors was established. In addition, the simulation results indicate that the elastoplastic linear strengthening model showed good reliability when estimating the impact force compared with the five classical models. The strengthening coefficient of other cushion materials needs to be calibrated.

The majority of existing effective stress-based constitutive models approach thermal effects through the temperature dependency of surface tension and its effects on the soil-water retention curve (SWRC) and effective stress. Experimental tests and theoretical studies, however, suggest that the temperature effect on surface tension alone is not sufficient to properly explain thermal-induced changes in the effective stress and SWRC. This study focuses on the temperature-dependent elastoplastic behavior of low plasticity unsaturated soils by developing a set of constitutive-level relations that incorporate temperature-dependent SWRC and effective stress models. These models account for the effect of temperature on the enthalpy, contact angle, and surface tension. The application of the presented constitutive relations was demonstrated and validated for low plasticity soils, specifically incorporating temperature effects into the hardening modulus, specific volume change, yield stress of the modified Cam-Clay model, and stress-strain relationships. The proposed relationships are incorporated in any effective stress-based constitutive model for modeling temperature dependency of elastoplastic response in low plasticity unsaturated soils. Employing these relationships can enhance the numerical simulation of low plasticity unsaturated soils under thermo-mechanical or other coupled processes involving temperature-dependent conditions.

Frozen mixed soils are widely distributed in the strata and slopes of permafrost regions. This paper aims to study the strength criterion and elastoplastic constitutive model for frozen mixed soils from micro to macro scales. Based on the knowledge of mathematical set theory and limit analysis theory, the support function of frozen soils matrix is derived. The concept of local equivalent strain is proposed to solve the problem of nonuniform deformation caused by rigid inclusions in frozen mixed soils. According to the nonlinear homogenization theory and the Mori-Tanaka method in micromechanics, the strength criterion of frozen mixed soils is established, which can consider coarse particle contents. By introducing the concepts of equivalent yield stress and equivalent plastic deformation, the elastoplastic constitutive model is proposed by the associated flow rule, which can also consider the influence of coarse particle contents. Finally, using the data in the literature, the proposed strength criterion and elastoplastic constitutive model for frozen mixed soil are verified, respectively. The effects of coarse particle contents on the mechanical properties of frozen mixed soils are discussed.

Due to the development of plastic strains, the strain path within the meridian plane deviates from the reference line corresponding to elastic state. Similarly, under true triaxial stress conditions, the strain path within the deviatoric plane deviates from the reference line corresponding to the constant Lode angle. This deviation is attributed to the plastic shear strain associated with the Lode angle. To account for these phenomena, a novel three-dimensional elastoplastic constitutive model incorporating Lode angle is proposed to characterize the deformation behavior of sandstone. The yield and potential functions within this model incorporate parameters that vary with the plastic internal variable, enabling the evolution of the yield and plastic potential surfaces in both the meridian and deviatoric planes. The comparison between experimental data and the analytic solution derived from the constitutive model validates its reliability and accuracy. To examine the differences between yield surface and plastic potential surface, a comparison between the associated and non-associated flow rules is conducted. The results indicate that the associated flow rule tends to overestimate the dilatancy of sandstone. Furthermore, the role of Lode angle dependence in the potential function is explored, highlighting its importance in accurately describing the rock's deformation.

Numerical challenges, incorporating non-uniqueness, non-convexity, undefined gradients, and high curvature, of the positive level sets of yield function F > 0 are encountered in stress integration when utilizing the return-mapping algorithm family. These phenomena are illustrated by an assessment of four typical yield functions: modified spatially mobilized plane criterion, Lade criterion, Bigoni-Piccolroaz criterion, and micromechanics-based upscaled Drucker-Prager criterion. One remedy to these issues, named the Hop-to-Hug (H2H) algorithm, is proposed via a convexification enhancement upon the classical cutting-plane algorithm (CPA). The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point. Furthermore, a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform. Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence. All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation, in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).