Roots can mechanically reinforce soils against landslides, but the impact of their typically random and complex distribution on this reinforcement is not well understood. Here, using a modelling approach based on homogenization theory, we aim to assess the effect of the randomness and complexity of root spatial distribution in soils on the mechanical properties of the soil-root composite and the resulting reinforcement. To do this, we modeled the soil-root composite as a three-dimensional (3D) soil column through which parallel roots penetrate vertically. The unit cell (UC) of the soil-root composites with a nonuniform root distribution was created based on the characteristics of root diameter distributions of Elymus dahuricus measured in the field, and the equivalent elastic modulus and strength parameters of the composites were calculated. The accuracy of the homogenization method was verified by direct shear tests with undisturbed soil-root samples. The results showed that the UC model of the soil-root composites could effectively predict its equivalent elastic parameters. A parametric analysis using the proposed homogenization model showed that roots can mobilize significant soil portions to resist deformation by increasing both the number and complexity of root distributions, even at the same root volume ratio. This makes the stress distribution in the soil more uniform and improves the shear strength of the soil-root composites. The presence of Elymus dahuricus roots significantly improved the shear strength of the soil-root composites, primarily due to an increase in cohesion of 23%. This study presents a new perspective on the development of a constitutive model for soil-root composites and highlights its potential value for engineering applications that use roots to reinforce soils.

Sandy cobble soil is a composite made of soil matrix and cobbles, and the estimation of its shear strength always requires expensive large-scale experiments. The strength of the sandy cobble soil exhibits macroscopic anisotropy with respect to the direction of the major stress due to the observed dominant distribution of the cobble dip angle. In the present paper, a numerical homogenization procedure for anisotropic strength identification of the sandy cobble soils is established, which can take into account the influencing factors of the size, shape, and inclination of the cobbles and the mesoscopic strength of the soil-rock interface. To consider the condition of plain strain, the particle size distribution of the cross of the stratum is derived based on the fractal theory and the transformation method of Walraven. The mesostructure of the sandy cobble soils is randomly produced using ellipses to model the cross of the cobbles. An iterative procedure is utilized to represent the major stress orientation-dependent macroscopic strengths. The results are validated against the data from indoor experiments and global mesoscopic computations. It is shown that the macroscopic strength of the sandy cobble mixtures can be accurately determined and the iterative multiscale limit analysis method is reliable and efficient. Parameter analysis is finally conducted to discuss the effect of the mesoscopic properties on the macroscopic strength.

In cold regions, the frozen soil-rock mixture (FSRM) is subjected to cyclic loading coupled with freeze-thaw cycles due to seismic loading and ambient temperature changes. In this study, in order to investigate the dynamic mechanical response of FSRM, a series of cyclic cryo-triaxial tests were performed at a temperature of -10 degrees C on FRSM with different coarse-grained contents under different loading conditions after freeze-thaw cycles. The experimental results show that the coarse-grained contents and freeze-thaw cycles have a significant influence on the deformation properties of FSRM under cyclic loading. Correspondingly, a novel binary-medium-based multiscale constitutive model is firstly proposed to describe the dynamic elastoplastic deformation of FSRM based on the coupling theoretical framework of breakage mechanics for geomaterials and homogenization theory. Considering the multiscale heterogeneities, ice-cementation differences, and the breakage process of FSRM under external loading, the relationship between the microscale compositions, the mesoscale deformation mechanism (including cementation breakage and frictional sliding), and the macroscopic mechanical response of the frozen soil is first established by two steps of homogenization on the proposed model. Meanwhile, a mixed hardening rule that combines the isotropic hardening rule and kinematic hardening is employed to properly evaluate the cyclic plastic behavior of FSRM. Finally, comparisons between the predicted results and experimental results show that the proposed multiscale model can simultaneously capture the main feature of stress-strain (nonlinearity, hysteresis, and plastic strain accumulation) and volumetric strain (contraction and dilatancy) of the studied material under cyclic loading.

In light of its complicated makeup and fluctuating states of ice and salt crystals, it is challenging to forecast the strength of sodium sulfate saline sand. To examine the strength and deformation properties of sodium sulfate saline sand with various salt levels, many indoor triaxial shear tests were conducted at -2 degrees C, -5 degrees C, -8 degrees C, and 25 degrees C. The strength of sodium sulfate saline sand was found to be affected by temperature and the salt content, and the probable corresponding processes were then demonstrated. The introduction of the linear comparison composite (LCC) approach and homogenization theory led to the development of an upscaling strength model for sodium sulfate sand. Each phase's mechanical characteristics and the interactions between different components were taken into consideration. The triaxial tests of both unfrozen and frozen saline sand served as a basis for the developed strength prediction model's validation. It is believed that the findings of this study would shed light on how saline sand gains its strength from macroscopic and mesoscopic viewpoints.

The current study adopts a micromechanical approach to explore the nature of stress transmission in wet granular materials. First, we derive the discrete form of the capillary stress tensor obtained from homogenization to show the virial nature of capillarity through the application of point -wise capillary forces in Discrete Element Modeling (DEM). Furthermore, the non -spherical character of the capillary stress tensor is highlighted through a series of DEM triaxial simulations. Contrary to common thinking, the capillary stress tensor has indeed both mean and deviatoric components due to the underlying micromechanical aspects. Relevant key dimensionless parameters are identified to evaluate the relative magnitude of the capillary stress to the externally applied and contact (intergranular) stresses, thus determining the specific conditions under which the contribution of the deviatoric part becomes considerable. In addition, a DEM simulation of a simple shear test is performed to confirm the anisotropy (non -sphericity) of capillary stress tensor. Finally, the effective nature of the contact stress in the sense of Terzaghi for the constitutive behavior of wet granular materials is investigated via a DEM stress probing analysis. Results suggest that a single contact stress variable - germane to an effective stress - cannot relate to strain for the constitutive law in triphasic condition.

The complex mechanical and damage mechanisms of rocks are intricately tied to their diverse mineral compositions and the formation of pores and cracks under external loads. Numerous rock tests reveal a complex interplay between the closure of porous defects and the propagation of induced cracks, presenting challenges in accurately representing their mechanical properties, especially under true triaxial stress conditions. This paper proposes a conceptualization of rock at the mesoscopic level as a two-phase composite, consisting of a bonded medium matrix and frictional medium inclusions. The bonded medium is characterized as a mesoscopic elastic material, encompassing various minerals surrounding porous defects. Its mechanical properties are determined using the mixed multi-inclusion method. Transformation of the bonded medium into the frictional medium occurs through crack extension, with its elastoplastic properties defined by the Drucker-Prager yield criterion, accounting for hardening, softening, and extension. Mori-Tanaka and Eshelby's equivalent inclusion methods are applied to the bonded and frictional media, respectively. The macroscopic mechanical properties of the rock are derived from these mesoscopic media. Consequently, a True Triaxial Macro-Mesoscopic (TTMM) constitutive model is developed. This model effectively captures the competitive effect and accurately describes the stress-deformation characteristics of granite. Utilizing the TTMM model, the strains resulting from porous defect closure and induced crack extension are differentiated, enabling quantitative determination of the associated damage evolution. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V.

Cemented granular materials play an important role in both natural and engineered structures, as they are able to resist traction forces. However, modeling the mechanical behavior of such materials is still challenging, and most of existing constitutive models follow phenomenological approaches that unavoidably disregard the microstructural mechanisms taking place on the bonded grains scale. This paper presents a multiscale approach applicable to any kind of granular materials with solid bonds between particles. Inspired from the H-model, this approach allows simulating the behavior of cemented materials along various loading paths, by describing the elementary mechanisms taking place between bonded grains. In particular, the effect of local bond failure process on the macroscopic response of the whole specimen is investigated according to the bond strength characteristics.

Permeability is a fundamental property of porous media. It quantifies the ease with which a fluid can flow under the effect of a pressure gradient in a network of connected pores. Porous materials can be natural, such as soil and rocks, or synthetic, such as a densified network of fibres or open-cell foams. The measurement of permeability is difficult and time-consuming in heterogeneous and anisotropic porous media; thus, a numerical approach based on the calculation of the tensor components on a 3D image of the material can be very advantageous. For this type of microstructure, it is important to perform calculations on large samples using boundary conditions that do not suppress the transverse flows that occur when flow is forced out of the principal directions. Since these are not necessarily known in complex media, the permeability determination method must not introduce bias by generating non-physical flows. A new finite element-based method proposed in this study allows us to solve very high-dimensional flow problems while limiting the biases associated with boundary conditions and the small size of the numerical samples addressed. This method includes a new boundary condition, full permeability tensor identification based on the multiscale homogenization approach, and an optimized solver to handle flow problems with a large number of degrees of freedom. The method is first validated against academic test cases and against the results of a recent permeability benchmark exercise. The results underline the suitability of the proposed approach for heterogeneous and anisotropic microstructures.

Chemical reactions occur in geotechnical, biological and synthetic porous media. Swelling and shrinkage phenomena can be observed in clays, shales and gels, when they are in close contact with water. In petroleum engineering, wellbore-stability problems are caused by swelling or shrinking of the wellbore. Thus, it is significant to model the Chemo-Hydro-Mechanical (CHM) processes in porous media that include different physical and geometrical heterogeneities. In this paper, a multiscale computational homogenization approach is developed for the analysis of CHM problems. In this manner, the first-order homogenization technique is adopted for the two-scale formulation. The heterogeneities are assumed in the microscale level and a homogeneous domain is considered for the macroscale level, where the constitutive behavior is derived from the microscopic level. The governing equations and constitutive equations of the CHM processes are presented in the coupled manner. The primary variables are taken as the displacement, pore pressure, and solute concentration fields. Moreover, the transient terms are included in the microscale level to increase the accuracy of computations. Consequently, a generalized form of Hill-Mandel principle of macro-homogeneity is defined between the two scales. Appropriate microscopic boundary conditions, i.e. the linear and periodic boundary conditions, are employed to satisfy the averaging constraints. Finally, the accuracy and efficiency of the proposed computational multiscale method are illustrated through several numerical examples.

Volatile abundances in lunar mantle are critical factors to consider for constraining the model of Moon formation. Recently, the earlier understanding of a dry Moon has shifted to a fairly wet Moon due to the detection of measurable amount of H2O in lunar volcanic glass beads, mineral grains, and olivine-hosted melt inclusions. The ongoing debate on a dry or wet Moon requires further studies on lunar melt inclusions to obtain a broader understanding of volatile abundances in the lunar mantle. One important uncertainty for lunar melt inclusion studies, however, is whether the homogenization of melt inclusions would cause volatile loss. In this study, a series of homogenization experiments were conducted on olivine-hosted melt inclusions from the sample 74220 to evaluate the possible loss of volatiles during homogenization of lunar melt inclusions. Our results suggest that significant loss of H2O could occur even during minutes of homogenization, while F, Cl and S in the inclusions remain unaffected. We model the trend of H2O loss in homogenized melt inclusions by a diffusive hydrogen loss model. The model can reconcile the observed experimental data well, with a best-fit H diffusivity in accordance with diffusion data explained by the slow mechanism for hydrogen diffusion in olivine. Surprisingly, no significant effect for the low oxygen fugacity on the Moon is observed on the diffusive loss of hydrogen during homogenization of lunar melt inclusions under reducing conditions. Our experimental and modeling results show that diffusive H loss is negligible for melt inclusions of >25 mu m radius. As our results mitigate the concern of H2O loss during homogenization for crystalline lunar melt inclusions, we found that H2O/Ce ratios in melt inclusions from different lunar samples vary with degree of crystallization. Such a variation is more likely due to H2O loss on the lunar surface, while heterogeneity in their lunar mantle source is also a possibility, A similar size-dependence trend of H2O concentrations was also observed in natural unheated melt inclusions in 742204 By comparing the trend of diffusive H loss in the natural MIs and in our homogenized MIs, the cooling rate for 74220 was estimated to be similar to 1 degrees C/s or slower. (C) 2017 Elsevier B.V. All rights reserved.