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 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.