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Planting vegetation is an environmentally friendly method for reducing landslides. Current vegetated slope analysis fails to consider the influence of different root architectures, and the accuracy and effectiveness of the numerical simulations need to be improved. In this study, an explicit smoothed particle finite element method (eSPFEM) was used to evaluate slope stability under the influence of vegetation roots. The Mohr–Coulomb constitutive model was extended by incorporating apparent root cohesion into the shear strength of the soil. The slope factors of safety (FOS) of four root architectures (uniform, triangular, parabolic, and exponential) for various planting distances, root depths, slope angles, and planting locations were calculated using the shear strength reduction technique with a kinetic energy-based criterion. The results indicated that the higher the planting density, the stronger the reinforcement effect of the roots on the slope. With increasing root depth, the FOS value first decreased and then increased. The FOS value decreased with an increase in slope angle. Planting on the entire ground surface had the best improvement effect on the slope stability, followed by planting vegetation with a uniform root architecture in the upper slope region or planting vegetation with triangular or exponential root architecture on the slope’s toe. Our findings are expected to deepen our understanding of the contributions of different root architectures to vegetated slope protection and guide the selection of vegetation species and planting locations.

Purpose Understanding the fluid flow through rock masses, which commonly consist of rock matrix and fractures, is a fundamental issue in many application areas of rock engineering. As the equivalent porous medium approach is the dominant approach for engineering applications, it is of great significance to estimate the equivalent permeability tensor of rock masses. This study aims to develop a novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses. Design/methodology/approach The radial point interpolation method (RPIM) and finite element method (FEM) are coupled to simulate the seepage flow in fractured porous rock masses. The rock matrix is modeled by the RPIM, and the fractures are modeled explicitly by the FEM. A procedure for numerical experiments is then designed to determinate the equivalent permeability tensor directly on the basis of Darcy’s law. Findings The coupled RPIM-FEM method is a reliable numerical method to analyze the seepage flow in fractured porous rock masses, which can consider simultaneously the influences of fractures and rock matrix. As the meshes of rock matrix and fracture network are generated separately without considering the topology relationship between them, the mesh generation process can be greatly facilitated. Using the proposed procedure for numerical experiments, which is designed directly on the basis of Darcy’s law, the representative elementary volume and equivalent permeability tensor of fractured porous rock masses can be identified conveniently. Originality/value A novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses is proposed. In the approach, the RPIM and FEM are coupled to simulate the seepage flow in fractured porous rock masses, and then a numerical experiment procedure directly based on Darcy’s law is introduced to estimate the equivalent permeability tensor.

In order to compensate for the shrinkage of geopolymer pastes uniformly, reactive MgO powders are evenly dispersed in the geopolymer. The deformation performance, mechanical properties, microstructure and components of geopolymer pastes with reactive MgO are characterized. The effects of the content and the activity of MgO are discussed. The results indicate that the chemical shrinkage, autogenous shrinkage and drying shrinkage decrease with the addition of reactive MgO. MgO reacted with water, and fine Mg(OH)2 crystals forms as a geopolymer paste. Mg(OH)2 produces uniform expansion, which refines the pore size of pastes and the compressive strength increases. The shrinkage of the geopolymer pastes is thus effectively compensated.