This paper presents a method to create rubber clumps without significant volume loss within the framework of the discrete-element method (DEM), enhancing the understanding of particle-scale stress transmission and small strain behavior of sand-rubber mixtures. Extensive calibrations were conducted, including the compressive response of individual pure rubber clumps, the small strain stiffness and the shear behavior of pure rubber specimens. These calibrations aimed to accurately capture the key characteristics of rubber materials, including their deformability. The calibrated model was then used to study the mechanics of sand-rubber mixtures. The simulation data indicated a higher coordination number for rubber clumps, a result of their greater deformability and significant sensitivity to stress levels in comparison with sand grains. The research has further demonstrated that the proportion of the overall stress transferred by the rubber remained below its volumetric content, highlighting its significant sensitivity to stress and density levels, which are characteristics not significant in sand particles. Additionally, the small strain stiffness values of sand-rubber mixtures decrease with increasing rubber contents, reflecting the negligible contributions of rubber materials on small-strain stiffness. This observation supports the validity of refined state variables that exclude rubber materials when characterizing the small-strain behavior of sand-rubber mixtures. While this research is fundamental, the data presented herein can be useful to engineers working on embedding waste materials such as granular rubber in engineered fill.

The Discrete Element Method (DEM) has been widely used to study the macro-micro behaviour of granular materials at large strains (>1%). However, investigations over a wider strain range are lacking. This study conducts DEM triaxial tests on specimens with different particle physical properties to examine their influence on macro-micro behaviour from small strains (below 1 %) to large strains. Small-strain behaviour is characterised by the maximum shear modulus, elastic range and stiffness degradation rate. Large-strain behaviour is analysed through the peak stress ratio, critical state stress ratio and void ratio. Then, the micro-mechanisms underlying these results are examined using the Stress-Force-Fabric (SFF) relationship, which links the (macro) stress ratio and (micro) anisotropy source. This study is the first to apply the SFF relationship to small strain behaviour. Results reveal the qualitative relationship between particle physical properties and macro-behaviour at different strains: increasing particle Young's modulus enhances the maximum shear modulus but accelerates stiffness degradation; increasing shearing and rolling friction significantly reduces the stiffness degradation at small strains and enhances strength and dilation at large strains. This study also highlights the limitation of the Hertz contact model in capturing both small-strain and large-strain behaviour quantitatively using a single set of parameters. Hence, modellers should calibrate model parameters based on whether their focus is on large-strain or small-strain behaviour. For micro-behaviour, the relative importance of anisotropy sources depends on strain level rather than particle physical properties. At small strains, the mechanical anisotropy source (both normal and tangential forces) primarily controls stiffness and its degradation. At large strains, material strength is influenced by both mechanical and geometrical anisotropy sources, with anisotropy from the normal force being the most significant, followed by contact normal, tangential forces, and branch vector.

The behavior of soft soils distributed in coastal areas usually exhibits obvious time-dependent behavior after loading. To reasonably describe the stress-strain relationship of soft soils, this paper establishes a viscoelastic-viscoplastic small-strain constitutive model based on the component model and the hardening soil model with small-strain stiffness (HSS model). First, the Perzyna's viscoplastic flow rule and the modified Hardin-Drnevich model are introduced to derive a one-dimensional incremental Nishihara constitutive equation. Next, the flexibility coefficient matrix is utilized to extend the one-dimensional model to three-dimensional conditions. Then, by combining the HSS elastoplastic theory with the component model, the viscoelastic-viscoplastic small-strain constitutive model is subsequently established. To implement the proposed model for numerical analysis, the corresponding UMAT subroutine is developed using Fortran. After comparing the results of numerical simulations with those of existing literature, the reliability of the constitutive model and the program written in this paper is verified. Finally, numerical examples are designed to further analyze the effects of small-strain parameters and viscoelastic-viscoplastic parameters on the time-dependent behavior of soft soils.

This paper aims to investigate the wave-induced evolution of small-strain stiffness and its effects on seismic wave propagation. To this end, an advanced numerical framework based on the dynamic porous media theory was developed, in which the Iwan multi-surface constitutive model was adopted to model the soil behavior during cyclic loading. Moreover, the numerical framework integrates key parameters such as ocean wave characteristics and depth-dependence seabed conditions to model the intricate interactions between waves and the seabed. Following model verification via analytical solutions and previous experimental data, comprehensive parameter studies are conducted, from which the effects of different wave conditions and seabed properties on the dynamic response of the seabed were obtained, revealing the wave-induced small- strain stiffness spatial and temporal variation. Subsequently, simulations of geophysical monitoring instants are conducted, assessing the impact of evolving small-strain stiffness on seismic wave propagation. The findings highlight the implications of stiffness changes on seismic wave propagation characteristics. The study provides valuable insights into the challenges and opportunities associated with interpreting geophysical data in dynamic submarine environments, offering implications for subsurface characterization and monitoring applications.

Comprehensive investigations have been conducted to study the structure and overconsolidation of upper Shanghai clays, i.e. Layers 2-6 clays, typically located at depths of 30-40 m. However, limited information is available on their anisotropy, and even less is known about the correlation between structure, overconsolidation, and anisotropy. In this study, the undrained anisotropy characteristics of shear strength and small-strain shear stiffness in upper Shanghai Layers 2-6 clays were thoroughly assessed using a series of K0-consolidated undrained triaxial compression (TC) and triaxial extension (TE) tests (K0 is the coefficient of lateral earth pressure at rest). The effective stress paths, shear strength, and small-strain shear stiffness from the undrained TC and TE tests demonstrate the anisotropic behaviors in upper Shanghai clays. Analyses of data from upper Shanghai clays and other clays worldwide indicate that the shear strength anisotropy ratio (Ks) converges at 0.8 as the overconsolidation ratio (OCR) and plasticity index (Ip) increase, while the small-strain shear stiffness anisotropy ratio (Re) converges at 1.0. The influence of OCR on Ks and Re is more pronounced than that of Ip and sensitivity (St). Nevertheless, no clear correlation between Ks and Re is observed in upper Shanghai clays. (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/).

In this paper, the resonant column tests were utilized to examine the small-strain stiffness and attenuation of clay-gravel mixture (CGM) under various effective consolidation pressures and freeze-thaw cycles, on the basis of investigating the electrical resistivity variation trend of CGM samples undergoing various freeze-thaw cycles. It is shown that the resistivity of CGM tends to stabilize when the freeze-thaw cycles (N) reach 9, and, thus, the samples after 0, 3, 6, 9, and 12 cycles were selected for resonance column testing. The results show that, once N > 9, the decay in dynamic shear modulus demonstrates a weakened association with Nand the stiffness degradation effect of freezing-thawing would be weakened and inhibited by high effective consolidation stress. Additionally, a mathematical model was constructed to predict the maximum dynamic shear modulus (Gmax) in the basis of freeze-thaw cycles and effective consolidation stress. Microscopic analysis results suggest that the freeze-thaw effect on CGM lies in the development of soil aggregates and porosity variation within the fine-grained soil. Compared to gravel soils and frozen soil, the cementation of matrix soil and the effect of blocky structure are considered as fundamental reasons for the improved small-strain stiffness and reduced vulnerability to freeze-thaw cycles of CGM.

In geotechnical engineering, the small-strain shear modulus and its attenuation characteristics are pivotal for analyzing and evaluating soil vibration responses to various engineering construction projects. This study conducts the resonant column test on undisturbed fissured clay samples, exploring the impacts of fissure inclination and confining pressure on the shear modulus in small-strain range. Results indicated that the shear modulus and its attenuation behavior in undisturbed fissured clay are substantially affected by both the fissure inclination angle and the confining pressure. With constant confining pressure, the shear modulus increases as the fissure inclination angle grows, reaching its maximum value at a fissure angle of 90 degrees. In addition, as the confining pressure rises, there is a notable increase in the shear modulus and a corresponding reduction in the decay rate. Through the threshold strain, the elastic deformation of the specimen increases as the fissure inclination angle increases, and the confining pressure increases the ability of the fissured soil to deform at small strains elastically. Based on the acquired data, this research analyzes the relationship between the fitting parameters A and N and the fissure angle in the context of the Harding-Drnevich formula. Consequently, a mathematical model based on the fissure inclination angle and the effective confining stress was established to predict the maximum dynamic shear modulus (Gmax) and decay attributes of undisturbed fissured clay. Additionally, the study offers a comparative analysis of the maximum shear modulus and its attenuation features in clay with varied degrees of fissure development. The stiffness anisotropy is related to the orientation of particles and the normalized decay rate of the fissured clay has a certain relationship with the fissure density.

Lateritic clay has distinct properties from other clays due to its high sesquioxide content. Its stiffness characteristics have not been well understood, especially when the soil is unsaturated and anisotropic. This study investigated the stiffness characteristics of compacted lateritic clay through suction -controlled triaxial compression tests equipped with local strain measurements. Both vertically and horizontally cut specimens were tested to determine the evolution of stiffness anisotropy during shearing. Three suctions (0, 10, and 150 kPa) and two confining pressures (50 and 200 kPa) were considered. When strains are relatively small (e.g., less than 0.2%), the secant Young's modulus E sec of vertical specimens is consistently higher than that of horizontal specimens at all suctions and stresses due to the inherent anisotropic structure. The degree of anisotropy increases with increasing suction since suction enhances the stiffness more significantly in vertical specimens than in horizontal specimens. This behaviour may be due to an enhanced force chain in the vertical direction during shearing. As strains increase, the degradation of E sec normalized by the maximum Young's modulus E 0 is almost independent of suction and anisotropy. Lateritic clay has a higher degradation rate than other clays with a similar plasticity index because of its aggregated microstructure.

Constitutive models that are able to accurately predict cyclic soil behaviour are crucial for finite element design of offshore foundation or railway embankments. Basic hypoplastic models introduce the history of loading in state variables such as the stress and void ratio and are therefore incapable of describing small-strain stiffness and cyclic loading. In this work, clay hypoplasticity is extended with a modified intergranular strain proposed by Duque et al. [3]. The new model is compared to the one coupled previously with ISA based on unconventional as well as complex cyclic loading paths. Abilities and limitations of the models are addressed: (i) showing that both models predict a reduction in strain accumulation with an increasing number of cycles. (ii) For both models pronounced over- and undershooting effects can occur for certain cyclic loading paths and certain parameters. Despite the consensus in the literature, the results show that a yield surface in the (intergranular) strain space is not sufficient to ban these effects. Furthermore, the models' predictive capabilities are verified with simulations of monotonic and cyclic tests of Lower Rhine clay.

For the characterization of soil stiffness anisotropy at small strains and the calculation of soil elastic constants derived from the cross-anisotropic model, it is important to obtain stress wave phase velocities of soils in both principal and oblique directions. This study developed an original eight-prismatic shape apparatus equipped with disk-shaped shear plates to measure shear (S-) wave phase velocities (V-phase) in multiple directions, and four granular materials of various shapes were tested by this apparatus under isotropic confinement. Experimental results confirm the capability of the new apparatus and reveal that both S-wave propagation and oscillation directions are sensitive to soil inner fabric, i.e., V-s changes with the variation of either S-wave propagation or oscillation direction. Based on the experimental observations, it is suggested to keep the same S-wave oscillation direction when measuring V-s in multiple propagation directions so that the corresponding shape of the S-wave surface (polar plots of V-s in arbitrary propagation directions) is more precise to reflect the small-strain stiffness anisotropy of soils.