Different clay grains affect the structural strength of loess through the cementation of skeletal particles. This study investigates both clay-clay grains and quartz-clay grains. Clay-clay grains mixed loess (CM-L) and quartz-clay grains loess (Q-L) samples were prepared, and their unsaturated shear properties analyzed. X-ray diffractometry (XRD) analysis was conducted to determine the types and proportions of clay grains. Ball mill grinding and laser particle size analysis were employed to ensure comparable sizes of clay grains, while mercury intrusion porosimetry (MIP) tests confirmed similar pore characteristics. Scanning electron microscope (SEM) and unsaturated triaxial consolidation and drainage tests explored the impact of different clay grains on loess shear characteristics, assessing both microscopic and macroscopic performance. The results indicate that CM-L loess exhibits higher cohesion and a lower internal friction angle at the same matric suction level. The cohesion and internal friction angle of both CM-L and Q-L loess exhibit a linear relationship within the range of 50-200 kPa matrix suction. The cohesive force ranges for CM-L and Q-L loess are 60.31-80.07 kPa and 43.01-69.60 kPa, respectively, while the ranges for internal friction angles are 19.95 degrees-19.59 degrees and 25.91 degrees-25.06 degrees, respectively. Compared to Q-L loess, CM-L loess exhibits an average difference in cohesion of 23.18 kPa and in internal friction angle of -5.72 degrees. The microscopic variation in shear strength can be attributed to the "fish scale-like" interlocking state between clay-clay grains and the "tower-like" scattering arrangement of quartz-clay grains. In conclusion, the effect of different clay-grain types on the shear strength of loess varies significantly. The present study elucidates the relationship between the influence of different clay grains on the mechanical properties of loess and their microscopic structural characteristics, thereby providing crucial data for investigating the microscopic effects on the structural strength of loess.

Irregular topographies are widely distributed in nature, particularly in mountainous areas. The cliff on the canyon top forming over long periods of geological evolution significantly influences the amplification or reduction of ground motion. In this study adopting the wave function expansion method, a comprehensive analytical solution is formulated to address the scattering issue under shear horizontal (SH) waves induced by a shallow asymmetrical V-shaped canyon with cliffs. In general, employing the appropriate Graf's addition formula, wave function expressions in different polar coordinate systems can be unified. According to continuity conditions of stress and displacement on the auxiliary boundary, the region-matching technique (RMT) has also been adopted to determine the unknown coefficients in the algebraic equation. Further, by comparing the results obtained in this study with those from previous studies, the correctness and applicability of the proposed theoretical model and analytical solution have been verified. A significant finding indicates that the maximum difference in peak displacement under a canyon with cliffs (d1/a = 0.4) can reach 1.81 times that without cliffs (d1/a = 0). Meanwhile, the asymmetric effect in this study is mainly concentrated on the ground motion of the canyon inner surface (-1 <= x/a <= 1), as opposed to a symmetrical V-shaped canyon with cliffs and an asymmetrical V-shaped canyon without cliffs. The proposed analytical solution not only enriches the category of well-known canyon problems related to SH-waves scattering, but also can serve as a reference for numerical verification and engineering practice.

Vegetation is natural and environment-friendly material for slope reinforcement. To simple and effective analysis of vegetated slopes, a new method is proposed to consider the tensile strength cutting criterion (C–F criterion) of unsaturated root–soil composites. The proposed method incorporates the hydrological and mechanical effects of vegetation roots. A 1D stability model is developed to calculate the safety factors of vegetated slopes under steady transpiration state. Parametric studies are performed to investigate the effects of shrub root depth, slope angle, rainfall intensity, transpiration rate, and tensile strength on pore-water pressure (uw) and slope safety factors (Fs). uw and Fs are calculated using both the C–F criterion and the Fredlund strength criterion. The results demonstrate that Fs and uw decreases with increasing slope angle and rainfall intensity. Slope angle and rainfall intensity of vegetated slopes has a negative impacts on the slope stability. Moreover, Fs increases with increasing tensile strength. Furthermore, the transpiration rate and root depth increases, Fs and uw increases. Root depth, tensile strength, and transpiration rate are adverse for slope stability. Increasing slope angle and rainfall have detrimental effects on slope stability. Shallow slopes are more sensitive to rainfall than deep slopes. Fs for vegetated slopes with tensile strength cut-off are reduced compared to those based on the Fredlund strength equation. The C–F criterion is best suited for evaluating the shallow slope stability. Overall, the proposed method is a simple and practical approach to assess the vegetated slopes stability.

Vegetation plays an important role in improving slope stability. It is crucial to develop simple and effective methods for assessing the stability of vegetated slopes. Based on upper bound limit analysis, a method was proposed to analyse the stability of a two-dimensional vegetated slope with uniform root architectures under steady transpiration state. The effects of water absorption and reinforcement by vegetation roots on slope stability were considered using this method. Parametric studies were performed to investigate the effects of the soil type, root depth, plant transpiration rate, root tensile strength, slope angle and internal friction angle on slope stability. Several generic stability plots were provided. The results showed that roots significantly improved soil cohesion but slightly affected the internal friction angle. Root systems could provide additional soil cohesion. Horizontally and vertically distributed roots imposed the best mechanical reinforcement effect on the soil. The shear strength increases by 1.78 times. Compared with that of plain soils, the critical state line (CSL) of the root-soil composite moved upwards. The soil type strongly influences the pore water pressure. With increasing plant transpiration rate, root tensile strength and root depth, vegetated slope stability can increase by 58 %. The slope stability decreases by 50 % with increasing slope angle. The stability number (Ns) decreases with increasing internal friction angle. The effects of water absorption and reinforcement by roots on slope stability decrease with increasing desaturation coefficient and saturated permeability coefficient. Compared with that of loess and sand slopes, the reinforcement effect of vegetation roots is more significant for the stability of clay slopes.

To investigate the influence of plant roots on the mechanical properties of root-soil composite,triaxial tests were conducted on root-soil composite with varying root content.The mechanical properties dependent on root content and nonlinear failure criterion of the root-soil composite were analyzed.Results demonstrate that roots en-hance the shear strength of the soil by providing tensile strength.Roots primarily impact the cohesion of the rooted soil,while slightly affect the internal friction angle of the root-soil composite.At a root content of 0.36％,the cohe-sion increased by 64.91％.The principal stress difference increases rapidly at the initial stage of strain,but such change slows down when the axial strain is greater than 2％.The specimen failure is characterized by dilative shear and the formation of longitudinal cracks.Increasing the confining pressure weakens the dilative shear effect of the root-soil composite.The initial tangent modulus increases with increasing confining pressure and root content.The maximum and minimum failure stress ratio of the root-soil composite is 0.99 and 0.63,respectively.The nonlinear strength failure criterion reflects the failure characteristics of the root-soil composite with varying root content.The failure envelope is nonlinear at low confining pressure and linear at high confining pressure,with the critical stress correlated to the confining pressure.

Developing analytical solutions for water flow in partially saturated soil slopes is a significant issue in practical engineering. In this study, an analytical solution to rainfall seepage into vegetated unsaturated soil slopes considering hydro-mechanical coupling is proposed using Green's function. The proposed analytical solution is compared with the solution of finite element method. Combined with the limit equilibrium method, the proposed analytical solution is used to assess the slope stability. Parametric studies are performed to investigate the effects of slope angle, rain intensity, suction-based elastic modulus, and transpiration rate on pressure head and factor of safety for slopes. The results show that the pressure head and factor of safety (Fs) decrease with the increase of slope angle or rain intensity. As the transpiration rate increases, the pressure head and Fs increases. The smaller the absolute value of the suction-based elastic modulus, the more obvious the effect of hydro-mechanical coupling on Fs. Additionally, the vegetated slope stability varies more greatly than that of bare slopes due to the hydro-mechanical coupling effect. The proposed analytical solution is simple in form and has few input parameters, which can be used as a simple and effective method for analyzing rainfall infiltration in vegetated slopes.

The Green–Ampt (GA) model is widely applied in practice because of its simplicity and relatively few parameters. However, the GA model and its modifications are mostly only suitable for uniform rainfall, and rarely account for the effect of water uptake by vegetation roots. In this study, a modified GA model that accounts for both roots and moisture redistribution is proposed to assess slope stability. Compared with the numerical solution, the modified GA model slightly overestimates the wetting front depth and underestimates the moisture content of surface soil. The hydrological and mechanical effects of vegetation roots on slope stability are also incorporated in the proposed model. Parametric analyses are performed to investigate the effects of parameters including rainfall intensity on the safety factor (Fs). The results show that the wetting front depth decreases/increases with the increase of slope angle/rainfall intensity, and Fs of the slope decreases with the increase of slope angle and rainfall intensity. The safety factor of the slope is negatively correlated with rainfall duration and initial moisture content. Exponential and triangular roots have more significant effect on reinforcing shallow soils than uniform roots. The safety factor of the shrub-covered slope is 1.45 times that of the bare slope. The proposed method has the advantages of simplicity and few parameters.

A modified Gauss-Seidel iterative method (MP(m)-GS) with multistep preconditioner is developed to solve partial differential equations of rainfall infiltration. The finite difference method (FDM) is applied to numerical discretization. Furthermore, a system of linear equations is solved using an iterative scheme. For some unfavorable numerical conditions, such as large initial conditions, classical Picard iterative method usually has low accuracy and computational efficiency. Conventional linear iterative methods have a slower convergence rate, such as Gauss-Seidel (GS) and Jacobi iterative methods, particularly for small discrete space step size. Thus, MP(m)-GS is developed to simulate rainfall infiltration into unsaturated soils. The analytical solutions are employed to verify the proposed methods. The results indicate that the MP(m)-GS has higher computational efficiency and accuracy than the improved Picard methods. Compared with the conventional linear iterative methods GS and SOR, MP (m)-GS also demonstrates faster convergence rate and higher computation efficiency. The results show nice applications in modeling rainfall infiltration in unsaturated soils.

Abstract Rockburst is a common geological hazard in underground mining and excavating, constituting a serious threat to the safety of workers and equipment. Rockburst liability prediction is of crucial significance to the prevention of rockburst hazards. Multi-criteria decision-making approach is an effective tool to predict rockbursts. In this paper, five empirical factors (strength-stress ratio, Russenes criterion, brittleness index, strain energy storage index, and integrity index) were used to construct the standard of rockburst liability. A novel analytic hierarchy process (AHP) was proposed to determine the weight of these factors, and then a cloud model was established for rockburst liability prediction on this basis. In the new AHP, the random errors induced by the pairwise comparison matrices of decision-makers were corrected according to the Bayesian theories. Nine cases from engineering projects in China were collected to validate the proposed model for rockburst liability prediction, and the prediction results were consistent with the field status. The quantitative index (Euclidean distance) indicates that the novel analytic hierarchy process has better performance than the original analytic hierarchy process in the weight calculation of factors; the new proposed cloud model is also superior to the original cloud model and the technique for order preference by similarity to an ideal solution model in the prediction of rockburst liability.