This paper presents a rigorous, semi-analytical solution for the drained cylindrical cavity expansion in transversely isotropic sand. The constitutive model used for the sand is the SANISAND-F model, which is developed within the anisotropic critical state theory framework that can account for the essential fabric anisotropy of soils. By introducing an auxiliary variable, the governing equations of the cylindrical expansion problem are transformed into a system of ten first-order ordinary differential equations. Three of these correspond to the stress components, three are associated with the kinematic hardening tensor, three describe the fabric tensor, and the last one represents the specific volume. The solution is validated through comparison with finite element analysis, using Toyoura sand as the reference material. Parametric analyses and discussion on the impact of initial void ratio, initial mean stress level, at-rest earth pressure coefficient and initial fabric anisotropy intensity are presented. The results demonstrate that the fabric anisotropy of sand significantly influences the distribution of stress components and void ratio around the cavity. When fabric anisotropy is considered, the solution predicts lower values of radial, circumferential and vertical stresses near the cavity wall compared to those obtained without considering fabric anisotropy. The proposed solution is expected to enhance the accuracy of cavity expansion predictions in sand, which will have significant practical applications, including interpreting pressuremeter tests, predicting effects of driven pile installation, and improving the understanding of sand mechanics under complex loading scenarios.

In geotechnical engineering, the development of efficient and accurate constitutive models for granular soils is crucial. The micromechanical models have gained much attention for their capacity to account for particle-scale interactions and fabric anisotropy, while requiring far less computational resources compared to discrete element method. Various micromechanical models have been proposed in the literature, but none of them have been conclusively shown to agree with the critical state theory given theoretical proof, despite the authors described that their models approximately reach the critical state. This paper modifies the previous CHY micromechanical model that is compatible with the critical state theory based on the assumption that the microscopic force-dilatancy relationship should align with the macroscopic stress-dilatancy relationship. Moreover, under the framework of the CHY model, the fabric anisotropy can be easily considered and the anisotropic critical state can be achieved with the introduction of the fabric evolution law. The model is calibrated using drained and undrained triaxial experiments and the results show that the model reliably replicates the mechanical behaviors of granular materials under both drained and undrained conditions. The compatibility of the model with the critical state theory is verified at both macroscopic and microscopic scales.

Anisotropic soils exhibit complex mechanical behaviours under various loadsing conditions, e.g., reversible dilatancy, three-dimensional failure strength, fabric anisotropy, small-strain stiffness, cyclic mobility, making it difficult to comprehensively capture these characteristics within a single constitutive model. Failure to capture anisotropic soil behavious may result in poor predictions in geotechnical engineering. Hence, to provide a unified prediction for the mechanical responses of anisotropic sand and clay under both monotonic and cyclic loading conditions, a fabric-based anisotropic constitutive model, i.e., the CASM-CF, is developed within the framework of the standard Clay and Sand Model (CASM) in this paper. Effects of small-strain stiffness and anisotropic elasticity are incorporated into the stiffness matrix to capture the stiffness variation over a wide strain range and reversible dilation. The fabric tensor defined by particle orientation and its evolution law are integrated into the CASM-CF model through the Anisotropic Transformed Stress (ATS) method. The plastic modulus is modified by considering cyclic loading history and stress reverse to better predict the mechanical responses of soils when subjected to cyclic loadings. The newly proposed model is employed to predict the mechanical behaviours of clay and sand under various strain scales and stress paths, including monotonic, cyclic, proportional, and non-proportional loading conditions, in the literature. Conclusions can be drawn that the model performs satisfactorily under various stress paths, and it has the potential to be used in the analysis of practical geotechnical applications of wide range.

Predictive modeling of dielectric heating in porous foods is challenging due to their nature as multiphase materials. To explore the relationship between the topological structure of multiphase foods and the accuracy of dielectric mixture models, the degree of anisotropy of two cooked rice samples with 26 and 32 % porosity was determined, and their dielectric properties were estimated using the Lichtenecker (LK), Landau-LifshitzLooyenga (LLL), and Complex Refractive Index Mixture (CRIM) equations. These properties were used in a predictive finite-element model for reheating an apparent homogeneous rice sample on a flatbed microwave (MW) for 120 s. The results were compared with experimental data and a validated two-element model. Unlike LK and LLL equations, the CRIM equation predicted heat accumulation towards the edges of the container at the two values of porosity ratio evaluated, in accordance with the experimental results and the isotropic nature of the sample. The simulated temperature distributions suggest that the three evaluated equations could predict the MW heating behavior of rice to some extent, but that in order to obtain more accurate results, it could be useful to obtain an empirical topology-related parameter specific for this sample. These results can provide insight on the relationship between the topology of the porous structure in the sample and the adequacy of different dielectric mixture models.

Granular materials usually copossess inherent and stress-induced anisotropy that significantly influences their mechanical behaviors. This paper presents a series of true-triaxial tests on aeolian sands to consider the inherent and stress-induced anisotropy in terms of soil deposition angles and intermediate principal stress coefficients, respectively. These results show that the deposition angle primarily affected the elastic-plastic stage under axisymmetric conditions. Otherwise, the deposition angle affects all deformation processes after the elastic stage when the intermediate principal stress coefficient changes. Moreover, the critical state is not unique but depends on the combined effect of the deposition angle and the intermediate principal stress coefficient, which indicates that the strength, stress-strain response, and dilatancy behavior of sands are affected by both inherent and stress-induced anisotropy.

The stress state and density of soil have been considered as the key factors to determine the liquefaction resistance. However, the results of seismic liquefaction case histories, laboratory tests and centrifuge model tests show that the fabric characteristics also influence liquefaction resistance, even more significantly than the contributions of stress state and density. In this study, anisotropic specimens with different consolidation histories were prepared using the 3D Discrete Element Method (DEM) to investigate the influence of fabric characteristics on the mechanical behavior of granular materials and the underlying mechanisms. The simulations revealed that under monotonic shear conditions, horizontally anisotropic specimens exhibited strain hardening and dilatancy characteristics, as well as higher peak strength. Under cyclic shear condition, the normalized liquefaction resistance of the specimens showed a strong linear relationship with the degree of anisotropy, independent of confining pressures and density. Microscopic results indicate that the fabric arrangement aligned with the loading direction leads to the evolution of the mechanical coordination number and average contact force in a manner favorable to resisting loads, which is the underlying mechanism influencing macroscopic mechanical properties. Additionally, the evolution patterns of contact normal magnitude and angle in anisotropic granular materials under cyclic loading conditions were also analyzed. The results of this study provided a new perspective on the macroscopic mechanical properties and the evolution of the microstructure of granular soils under anisotropic conditions.

Macro- and micromechanical interactions between the geogrid and granular aggregates considering particle shape effects are essential for the performance of reinforced soil structures under cyclic normal loading (CNL). Crushed limestone and spherical granular media were mixed to obtain samples with different overall regularities (OR = 0.707, 0.774, 0.841, 0.908, and 0.975). Direct shear tests under CNL were conducted at various overall regularities, normal loading frequencies, and waveforms. Consistent with experiment tests, a discrete-element method (DEM) simulation was performed, incorporating authentic particle shapes obtained through three-dimensional (3D) scanning technology. The results showed that the macroscopic interface shear strength and volume change decreased with an increase in the overall regularity and normal loading frequency. The interface shear strength and deformation under the square waveform are bound to be higher than that under other waveforms. The coordination number, porosity, and fabric anisotropy were used to explain the macroscopic interface shear behavior in relation to the overall regularity. A higher coordination number and stronger contact force were observed with a decrease in the overall regularity. As the overall regularity decreased, the interface integrity and stability became stronger, with the result that the reinforced soil structure can withstand a larger principal stress deflection. Through experimental and DEM analyses, the underlying explanation for the effect of particle shape on the mechanical interaction of reinforced soil was revealed.

Transversely isotropic rocks (TIRs) are widespread in geological formations, and understanding their mechanical behavior is crucial for geotechnical and geoengineering applications. This study presents the development of a novel analog material that reproduces the directional mechanical properties of TIRs. The material is composed of quartz sand, mica flakes, and gelatin in adjustable proportions, allowing control over strength and stiffness anisotropy. Uniaxial compressive strength (UCS) and direct shear tests were conducted to evaluate mechanical responses across different anisotropy angles. Results show that the analog material replicates key features of natural TIRs, including directional variations in strength and fracture modes. In UCS tests, the anisotropy angle (beta) governs the transition between tensile and shear failure. In direct shear tests, the orientation angle (alpha) significantly affects shear strength. Higher gelatin concentrations increase cohesion and Young's modulus without changing the internal friction angle, while mica content reduces overall strength and stiffness. Comparisons with published data on sedimentary and metamorphic rocks confirm the mechanical representativeness of the material. Its simplicity, tunability, and reproducibility make it a useful tool for scaled physical modeling of anisotropic rock behavior in the laboratory. This approach supports the experimental investigation of deformation and failure mechanisms in layered rock masses under controlled conditions.

For many solids, irreversible deformation is often accompanied by changes in the internal structure, impacting the reversible responses, a phenomenon termed elasto-plastic coupling. This coupling has been observed experimentally in various geomaterials, including clayey and sandy soils, as well as hard and soft rocks. Fabric anisotropy, which characterizes the internal structure, is a distinct feature of soils and significantly influences both reversible and irreversible behaviors. In this study, we adopted a coupling formulation based on the framework of anisotropic critical state theory (ACST) to describe the anisotropic elasto-plastic coupling response of soils. The formulation incorporates a deviatoric fabric tensor F, which consistently quantifies the internal structure of soils in both reversible and irreversible range, into a hyperelastic formulation and a plastic model, respectively. A novel evolution rule of F, defined based on the current stress ratio and plastic strain, is proposed, where the direction gradually aligns with the loading direction and the norm achieves different asymptotic values depending on the applied loading paths. This allows for the representation of evolved anisotropy effects on elasticity, dilatancy and strength simultaneously, providing a natural description of elasto-plastic coupling. Within this coupling framework, any anisotropic model within ACST can serve as the plastic platform for developing the elasto-plastic coupling models with anisotropic hyperelasticity. Herein, a bounding surface plastic model is utilized for illustration. The proposed model's performance is demonstrated by especially comparing simulated results to test data on evolving elastic stiffness ratios and overall elastoplastic responses under varying monotonic and cyclic loading conditions.

Three simplified models for the analytic determination of the dynamic response of a crossanisotropic poroelastic half-plane to a load moving with constant speed on its surface are presented and compared against the corresponding exact model. The method of analysis of the exact and approximate models uses complex Fourier series to expand the load and the displacement responses along the horizontal direction of the steady-state motion and thus reduces the partial differential equations of the problem to ordinary ones, which are easily solved. The three simplified models are characterized by reasonable simplifying assumptions, which reduce the complexity of the exact model and facilitate the solution. In the first simplified model all the terms of the equations of motion associated with fluid acceleration are neglected. In the second simplified model, solid displacements are assumed to be equal to the corresponding fluid ones, while the third simplified model is the second one corrected with respect to the fluid pressure at the free boundary (top) layer. All three simplified models are compared with respect to their accuracy against the exact model and the appropriate range of values of the various significant parameters of the problem, like porosity, permeability, anisotropy indices, or load speed, for obtaining approximate solutions as close to the exact solution as possible is thoroughly discussed.