In the natural environment and engineering scenarios, there are not only bare unsaturated soils but also unsaturated soils covered by vegetation (i.e., unsaturated vegetated soils). For the unsaturated vegetated soil with a uniform root architecture, on the basis of considering the effects of roots on the hydrological properties, the linearized governing equations for one-dimensional transient seepage of water are acquired by some simplifying assumptions and variable substitution. The analytical solution for one-dimensional transient seepage of water in the unsaturated vegetated soil is obtained through the methods of separation of variable and series transformation. Subsequently, the computational results of this analytical solution have been compared with those of the existing analytical solution and the corresponding finite-difference solution to verify its reasonableness. Finally, a simple vegetated cover is taken as an example to analyze the influences of root-related parameters on its effectiveness in blocking rainwater infiltration. The results show that the cumulative leakage CQ_b at the bottom zone of a vegetated cover under the same rainfall scenario is smaller than that of a single cover without vegetation, and an increase in the rooted soil thickness l_g enhances the effectiveness of the vegetated cover in blocking rainwater leakage. The increase of the transpiration rate T_p significantly reduces the leakage rate at the bottom zone of the vegetated cover under the rainfall scenario, and the cumulative leakage CQ_b tends to decrease linearly with an increase in T_p. Compared with the extreme case where the root volume ratio R_v is zero and the effects of roots on the hydrological properties of soil are ignored, the effectiveness of the vegetated cover in blocking rainwater leakage is enhanced when the saturated permeability coefficient of the rooted soil decreases due to the value R_v, and conversely, it is weakened. Overall, this study could provide scientific guidance for engineering practices related to water infiltration in unsaturated vegetated soils.

Evaluating the compaction quality of rock-filled subgrades rapidly and accurately poses a pressing challenge in highway engineering. To address this, this study establishes a discrete element-finite difference coupling model to simulate the response of rock-filled subgrades under impact loading. The primary parameters of the model are calibrated using indoor large-scale triaxial tests, and the model's accuracy is verified through comparisons between calculated and field data. Furthermore, this study conducts an in-depth analysis of the dynamic response results of five commonly used gradations of rock-filled subgrades under varying degrees of compaction, discussing the influence of gradation fractal dimension and porosity on subgrade deformation response. The findings are as follows: (1) A good exponential relationship between subgrade porosity and resilient modulus is identified, and the concept of settlement ratio is introduced, with a linear relationship between settlement ratio and subgrade porosity being verified. It is suggested that both resilient modulus and settlement ratio should be used as control indicators when evaluating subgrade compaction quality. (2) A prediction function for subgrade resilient modulus considering fill gradation and porosity is obtained, revealing that particle gradation has a significant impact on resilient modulus. Specifically, as the gradation fractal dimension approaches 2.31, the resilient modulus increases more rapidly with decreasing porosity. (3) A settlement ratio of zero corresponds to the ideal compaction state of the subgrade. This study establishes a prediction model for the critical resilient modulus of the subgrade in its ideal state, considering fill gradation, and finds that the critical modulus first increases and then decreases with increasing fractal dimension D, reaching a maximum when D=2.34. These findings aim to provide new methods and theories for evaluating the compaction quality of rock-filled subgrades in engineering.

In order to investigate the influence of rock interface roughness on the characteristics of the charge induction signal during fault slip, the time-frequency characteristics of the multi-channel charge induction signal waveforms, the cumulative velocity of charge, the fractal dimension, and the primary and secondary frequency zones of the rock assemblage structure with different roughness during the slip process in the double-sided shear test under different vertical loads were investigated. The results show that: (1) The localized micro-rupture nucleation in the elastic deformation stage leads to multiple charge induction clusters with maximum values, which increase with the increase of interface roughness and vertical load, and then become dense and small-amplitude signals when entering into the start-slip stage. (2) With the increase of interface roughness and vertical load, the fluctuation of the accumulated charge velocity and fractal dimension are more obvious and highly correlated with the change of the waveform of the charge induction signal. In the elastic deformation stage, the accumulated charge velocity shows “slow increase in the main body and sudden increase in multiple points”, and each charge induction cluster is accompanied by the phenomenon of “first ascending and then descending” of the fractal dimension, with the main frequency area located in the low-frequency domain and the sub-main frequency area located in the high-frequency domain. In the start-slip stage, the accumulated charge velocity changes to an overall rapid increase and the fractal dimension fluctuates more obviously with the increase of fault interface roughness and vertical loading. During the start-slip stage, the charge accumulation rate changes to an overall rapid increase, and the fractal dimension is continuously downgraded, and the primary and secondary frequency regions show the phenomenon of “translational interchange”, with the primary frequency region shifted right to the high-frequency domain, and the secondary frequency region shifted left to the low-frequency domain, and the primary frequency of the charge signals at each slip stage falls into the frequency aliasing domain common to the whole process of slipping. (3) Comparing the time-frequency resolution and time-frequency focusing of the three time-frequency transform methods, wavelet transform, short-time Fourier transform and S transform, it is found that the wavelet transform performs the best in the low-frequency domain, the short-time Fourier transform the second, and the S transform the worst, while in the high-frequency domain, the S transform performs the best, the wavelet transform the second, and the short-time Fourier transform the worst. (4) Differences in charge signals of sensors at different locations during fault slip destabilization are mainly related to the aggregation of charges in specific regions caused by locally concentrated micro-ruptures before the start-slip phase, and are mainly caused by the change of misalignment of the relative positions between the slip surface and the sensors after the start-slip phase.

Based on the dynamic theory of elastic media, the horizontal vibration of end-bearing piles embedded in a transversely isotropic soil is studied via an analytical scheme. By introducing displacement potential functions, the governing equations of the soil are decoupled, and the general solutions for the displacement and stress fields around the pile are derived using the method of separation of variables. Applying the continuity conditions at the pile–soil interface, the horizontal complex impedance of the surrounding soil is incorporated into the motion equation of the pile, leading to analytical solutions for the displacement, rotation angle, bending moment, and shear force of the pile. In addition, explicit expressions for the horizontal, rocking, and coupled horizontal–rocking dynamic impedances at the pile head are derived. Comparison with existing theoretical solutions confirms the accuracy and reliability of the proposed method. Furthermore, the influence of soil anisotropy parameters on the horizontal vibration characteristics of the pile is systematically analyzed. The results indicate that the anisotropic modulus ratio has a significant impact on the dynamic impedance at the pile head, as well as on the distribution of horizontal displacement, rotation angle, bending moment, and shear force along the pile depth.

A widely distributed salinized silt in Northwest China exhibits the physical characteristics of both low-liquid-limit silt and saline soil, yet its long-term deformation behavior remains insufficiently understood. A series of uniaxial creep tests were conducted to investigate its creep properties under varying conditions of salt content, dry density, moisture content, and overburden stress. Test results indicate that, compared to salt-free soil, the creep rate of salinized silt accelerates significantly with increasing salt content, demonstrating more pronounced nonlinear creep characteristics. The final strain of the salt-washed soil was 10%, which increased to 14% at a salt content of 6.4%. To more accurately characterize the soil's creep behavior, the classical creep models were modified, leading to the proposal of two new models: an integer-order model and a fractional-order model. Comparative analysis between the experimental data and the improved models shows that both proposed models describe the actual deformation characteristics more accurately than the classical creep model. However, the integer-order model lacks refinement in describing the decay creep stage, whereas the fractional-order model demonstrates superior accuracy in capturing the detailed features of all creep stages and is therefore recommended for effectively predicting the creep behavior of salinized silt.

The energy development projects in western China require the construction of a large number of vertical shafts in weakly cemented gravel layers with poor stability. Anchor rod support is an important means of controlling the deformation of surrounding rock. However, most of the current theories on anchor reinforcement have overlooked the lagging support of anchor rods. Therefore, based on the spatial constraint effect of the working face, elastic-plastic theory, and the anchor rod stress uniform distribution method, this study proposes a semi-analytical calculation method for the deformation and stress of the surrounding rock of vertical shaft anchor bolts considering the lag support of anchor bolts. The correctness of this method was verified by finite element method. Based on the proposed semi analytical solution, the influence of anchor parameters was further explored. The research results show that the larger the lag distance of the anchor rod, the greater the deformation of the surrounding rock, and the smaller the surrounding rock pressure borne by the anchor rod and other supporting structures. When the lag distance x_gs of the anchor rod is less than 1.5r_A (r_A represents the excavation radius of the vertical shaft), the deformation u_r(r=r_A) and safety factor s of the surrounding rock change greatly. When the lag distance x_gs of the anchor rod is greater than 3.0r_A, the deformation u_r(r=r_A) and safety factor s of the surrounding rock remain basically unchanged. Increasing the diameter of the anchor rod improves the shear strength, but the impact gradually decreases. When the length of the anchor rod L is less than 1.0r_A, the deformation of the surrounding rock u_r(r=r_A) and the safety factor s change greatly. When the length of the anchor rod L is greater than 1.0r_A, the change is slow, so it is not recommended to excessively use long anchor rods. Research suggests that when selecting support parameters, consideration should be given to the support lag distance to ensure the stability of the surrounding rock. This study successfully applied this theory to the vertical shaft engineering of pressure pipelines, and the research results provide a solid theoretical basis for the design of anchor rod support for the surrounding rock of the vertical shaft.

The microbially induced calcite precipitation (MICP) technique can effectively enhance the mechanical properties of coral sand. To investigate the small-strain dynamic characteristics of MICP-treated coral sand, resonant column tests were conducted on specimens with varying biocementation cycles N_b and effective confining pressures and the development laws of dynamic shear modulus G and damping ratio λ were comparatively analyzed. The test results reveal that: at small strains, the dynamic shear modulus G increases significantly with both N_b and . The maximum dynamic shear modulus G_max exhibits a linear correlation with N_b and a power-law correlation with . A significant power-law relationship exists between G_max and unconfined compressive strength (q_ucs). As N_b increases, the reference strain γ₀ decreases gradually while the G/G_max-γ_d curves shift downward, indicating enhanced nonlinearity. Both minimum and maximum damping ratios increase, with the λ-γ_d curve moving upward and characterized by greater energy dissipation. In contrast, increasing produces opposite trends in both G/G_max-γ_d and λ-γ_d curves, exhibiting reduced nonlinearity and energy dissipation. Empirical relationships are established to quantify the nonlinear dynamic behavior and energy dissipation characteristics of MICP-treated coral sand. Scanning electron microscope (SEM) observations reveal that stiffness improvement primarily results from three mechanisms: contact cementation between sand grains, grain coating by calcite precipitates, and matrix supporting through pore filling.

Current research on rock freeze-thaw damage mainly focuses on uniform freeze-thaw tests. However, the situation of unidirectional freeze-thaw action is widely present in cold region engineering, and there is a lack of sufficient understanding of the evolution of mechanical properties and damage models under unidirectional freeze-thaw conditions. Therefore, this study selected sandstone as the research object and conducted unidirectional freeze-thaw cycle tests and uniaxial compression tests. The elastic modulus, uniaxial compressive strength, stress-strain curves, and failure modes under uniaxial compression were analyzed for sandstone samples parallel and perpendicular to the freeze-thaw direction after undergoing freeze-thaw cycles. The results indicate that, following unidirectional freeze-thaw action, the compressive strength of sandstone parallel to the freeze-thaw direction is greater than that perpendicular to it, while the elastic modulus parallel to the freeze-thaw direction is smaller than that in the perpendicular direction. Both the peak stress and strain in the parallel direction are higher than those in the perpendicular direction. In uniaxial compression tests, the failure mode of sandstone parallel to the freeze-thaw direction remains consistent with that of samples that have not undergone freeze-thaw action, exhibiting X-shaped shear failure, whereas the failure mode perpendicular to the freeze-thaw direction manifests as splitting along the loading direction. Under unidirectional freeze-thaw action, the mechanical properties of sandstone transition from isotropy to anisotropy. Based on the aforementioned experimental observations, an anisotropic coefficient for unidirectional freeze-thaw was introduced, and a damage model for sandstone under unidirectional freeze-thaw conditions was established. The model was subsequently validated using experimental data.

In rock-lined caverns with compressed air energy storage (CAES), the hoop tensile strength of rock is an important parameter for calculating the ultimate bearing capacity and long-term stability of the cavern. The existing methods for measuring the tensile strength of rock are direct tensile tests or indirect tensile tests, such as Brazilian splitting and point load bending tests, which cannot truly reflect the circumferential stress of rock under high internal air pressure. Based on this, a new measurement method is proposed. By injecting high-pressure air into the drilled rock sample, the rock burst pressure is obtained. Then a calculation formula for the rock tensile strength is proposed considering the rock pore stress. In the experiments, the inflation rate and the temperature are changed, and it is found that the rock burst pressure is negatively correlated with the inflation rate and positively correlated with the temperature. It is found that when the number of cycles is relatively small (n≤100), the rock burst pressure is positively correlated with the number of cycles. The results can guide the design and calculation of rock-lined caverns for CAES, which is conducive to the promotion and application of CAES technology and has important engineering application value.

The accumulation of excess pore water pressure (EPWP) under cyclic loading may induce partial or complete liquefaction of saturated coral sands, posing significant threats to the safety of structures and foundations. In numerical simulations and analyses, accurate prediction of EPWP development is essential, with the determination of threshold strain serving as a critical step. A novel method has been developed to determine the threshold strains (pore pressure threshold strain γ_tp, stiffness degradation threshold strain γ_td, and flow threshold strain γ_tf) for the EPWP generation and stiffness degradation in saturated coral sands under complex stress paths. This was achieved isotopically consolidated, undrained single-stage and multistage cyclic shear tests, including 90° jumps and continuous rotations of principal stress. The findings indicate that while γ_tp, γ_td, and γ_tf are relatively insensitive to the cyclic stress, they are significantly influenced by the initial relative density (D_r). Additionally, the gap between γ_tp and γ_td widens as D_r increases. Under varying cyclic loading conditions and initial physical states, γ_tf corresponds to the EPWP ratio of approximately 0.9, with a corresponding stiffness index of around 0.10. The proposed method for determining γ_tp, γ_td, and γ_tf can effectively reduce the number of required cyclic tests, making it suitable for use as input values in numerical calculations or analytical methods, and for characterizing soil behavior under stress and strain conditions.