The variation in characteristic values of stress waves before and after passing through a material serves as a critical basis for evaluating its wave attenuation capacity. This can be characterized by the ratio of transmitted wave amplitude to the initial incident wave amplitude (i.e., transmission coefficient) in SHPB tests. However, due to the close correlation between the transmission coefficient and waveform parameters, it remains challenging to establish a quantitative characterization method for the transmission coefficient. Therefore, this study focuses on porous, irregular, and fragile calcareous sand as the research object. By combining physical experiments with numerical simulations, we investigate the influence of pulse width, platform duration, rising edge rate, falling edge rate, peak stress, and the central axis of symmetry on the transmission coefficient of calcareous sand. It is found that the transmission coefficient responds significantly to the coupling effects of the pulse width and the central axis of symmetry of the stress wave, the coupling effects of the platform section duration and the rising and falling edge rates, the coupling effects of the pulse width and the peak stress, as well as the coupling effects of the falling edge rate and the pulse width. Conversely, the response to the coupled effects of peak stress, rising edge rate, and falling edge rate is not pronounced. Owing to the difficulty in completely decoupling these waveform parameters, a prediction method is proposed for the transmission coefficient based on the gradient boosting algorithm, which effectively addresses multi-factor coupling issues. When the number of training samples reaches 91, the prediction accuracy exceeds 96%, which can effectively establish the mapping relationship between waveform parameters and transmission coefficients, providing a reference basis for the load design and calculation of protective engineering structures.

To study the wetting deformation characteristics of undisturbed loess under true triaxial force-water path, the true triaxial apparatus with rigid-flexible-flexible loading boundary was used to carry out the true triaxial single-line humidification test of undisturbed loess in Xi'an under different spherical stresses, intermediate principal stress parameters and stress ratios. The influence of true triaxial force-water path on the humidification deformation characteristics of undisturbed loess was comprehensively analyzed. The test results show that the relationship curve between the wetting volumetric (deviatoric) strain and the spherical stress presents a three-stage of slow-steep-slow. When the spherical stress is in the second stage, the wetting collapsibility of the soil is the largest, and a large wetting deformation can occur. At a certain stress ratio, the wetting volumetric strain gradually increases with the spherical stress, and the increase of the wetting volumetric strain decreases when the spherical stress exceeds 200 kPa. Finally, the variation law between the intermediate principal stress and each humidification strain is analyzed, and the calculation expression of loess collapsible deformation considering the intermediate principal stress is given according to the test results.

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.

The strength and deformation characteristics of rockfill materials are known to be closely related to their gradations. In order to predict the mechanical behavior of rockfill materials with different initial gradations, the influence of gradation on the mechanical properties of rockfill materials is first discussed within the framework of critical state constitutive theory. Subsequently, a method is proposed for rapidly predicting the initial and critical state void ratios for given gradations. Finally, by incorporating a state-dependent elastoplastic constitutive model, a prediction method for the gradation-related mechanical characteristics of rockfill materials is established. The results indicate that a good linear relationship exists between the minimum void ratio e_min and the critical state void ratio e_cs under low-stress conditions. Utilizing a particle packing algorithm, the critical state position of rockfill materials with specific gradations in the void ratio-pressure (e-p, e is the void ratio of the rockfill material in its current state, and p is the mean stress) space can be reliably predicted. Ultimately, this proposed prediction method facilitates the calibration of constitutive model parameters based on the test results of rockfill materials with known gradations, which subsequently allows for effective prediction of the mechanical behavior of other rockfill materials with different specified gradation profiles.

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 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 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.