The red bedded mudstone, known for its expansive and water-sensitive nature, poses a long-term potential threat to the construction and post-construction deformation control of regional highways and high-speed railroads. In this study, an in-situ water infiltration response characteristics test was conducted on slightly-expansive mudstone foundations using a red mudstone road cut in Lanzhou, Gansu Province. The test aimed to analyze the spatial and temporal evolution of swelling deformation volume, swelling force, and volumetric water content of the mudstone foundations, as well as to compare the differences between laboratory tests and in-situ tests. The results reveal that the water infiltration forms in the red mudstone foundation include fissure flow and pore flow. The distribution of water in the rock mass exhibits significant spatial and temporal heterogeneity, with rock mass fissures promoting seepage and expansion. During the infiltration process, the water absorption and expansion of the mudstone exhibit significant time dependence. The expansion amount and expansion force of the in-situ foundation experience stages of rapid increase, slow growth, and eventually fail to converge. After reaching the infiltration peak, the surface of the mudstone gradually softens or even turns into mud, leading to a decrease in the bearing capacity of foundation. Additionally, through the analysis of macroscopic expansion time history variation characteristics and microscopic pore structure distribution laws of indoor and in-situ mudstone, it is found that laboratory tests provide limited characterization of the water infiltration response characteristics of in-situ soil.

This study investigates the influence of fracture geometry and interaction mechanisms on the mechanical behavior of coal under static loading conditions. The digital image correlation method is used as a full-field observation technique, and uniaxial compression tests are conducted on three-crack samples of raw coal prefabricated at different positions using an MTS816 rock servo testing machine. The mechanical properties, crack evolution, and failure characteristics of multi-fractured coal under different position distribution conditions are studied by combining particle flow simulations. Based on the fracture mechanics theory, the influence and applicability of T stress on the multi-fracture tip of coal are discussed. The results show that as the fractures transition from parallel collinear distribution to parallel overlapping distribution, the macroscopic strength of coal samples gradually increases. The distribution form of the fracture affects the pressure state of the coal body, where widely spaced fractures create independent stress weak zones that expand and coalesce as stress increases. Conversely, when fractures tend to overlap, stress concentration areas and weak areas form a unified force system that influences each other. When multiple fractures are collinear or offset distributed, shear stress dominates the fracture surface, and the driving mode supplemented by tensile stress leads to tensile-shear composite failure of coal samples. However, when fractures tend to overlap, shear stress on the fracture surface converts to tensile stress in the rock bridge area, resulting in tensile failure dominated by tensile stress. When considering the influence of T stress, the theoretical prediction value of the crack angle containing three T stress components (T_x, T_y and T_xy) is found to be more suitable for studying crack growth angle of multiple fracture tips of finite plate subjected to compression shear stress.

The strata in urban backfill areas mostly exist in the form of loose soil-rock mixture, with high structural porosity, low strength, and poor engineering performance. They are sensitive to dynamic loads such as tunnel construction disturbance and subway train operation. The hysteretic curve can reflect the deformation, stiffness and energy dissipation of soil under dynamic load. It is of great significance to study the hysteretic curve of soil-rock mixture for the construction and operation safety of subway in backfill area. Using KTLDYN servo-controlled dynamic triaxial test system, the cyclic load test on soil-rock mixture samples in backfill area was carried out by means of cyclic loading. The effects of stone content (P), water content (ω ), consolidation stress ratio (k_c) and loading frequency (f) on the morphological characteristics (including adjacent center spacing (d), long axis slope (k), enclosing area (S) and degree of non-closure (ε_p)) and backbone curves of hysteretic curves are investigated. The results show that the typical hysteretic curves of soil-rock mixture are in long fusiform shape on the whole, with pointed lobes at both ends. With the increase in vibration level, d, S and ε_p increase nonlinearly, while k decreases logarithmically. For the same vibration level, d and ε_p decrease with the increases of P, k_c and f, and first decrease and then increase with the increase of ω . k increases with the increases of P, k_c and f, and increases first and then decreases with the increase of ω. S is positively correlated with P, increasing first and then decreasing with the increase of ω , and decreasing with the increases of k_c and f. The dynamic stress and slope of backbone curve increase with the increases of P, k_c and f when the dynamic stress variation is the same, and they first increase and then decrease with the increase of ω .

The dynamic property of rock is a crucial internal factor which influences the seismic stability of a rock slope. Cyclic loading induced by an earthquake can lead to rock damage, deterioration in rock performance, and a decrease in slope stability. To investigate the dynamic damage characteristics of rock in-depth, this study examines Permian limestone samples obtained from a rock slope. Uniaxial cyclic loading and unloading tests, combined with microscopic and mesoscopic analyses, are conducted to study the damage features and evolution rules of rock specimens. The effects of different loading conditions on the microscopic and mesoscopic damage of rock specimens are analyzed, and the correlation between macroscopic, microscopic and mesoscopic parameters is investigated. The results reveal that rock damage is progressive, primarily characterized by the generation, propagation, and connection of micropores, followed by a slight increase in macropores, which are present in smaller quantities. Compared to cyclic loading with a variable upper limit stress, loading with a variable lower limit stress promotes greater connectivity of micropores and the formation of macropores, resulting in a larger microfissure area in the rock specimen and a decrease in the average elastic modulus. Under loading with a variable upper limit stress, low stress amplitudes have a more significant degradation effect on the internal structure of the rock compared to uniaxial compression. Conversely, high stress amplitudes may compact the internal pores of the rock, leading to relatively low porosity and weakened deterioration effects. By considering the evolution trends of different microscopic damage variables, a steady crack development phase is observed, with the corresponding upper limit stress range being 0.4−0.6 times the static peak strength(σ_f), and the lower limit stress range being 0.3−0.5 times the static peak strength. These research findings enhance our understanding of the dynamic characteristics of rock at the micro- and meso-levels. They also provide theoretical explanations for the dynamic behavior of rock slopes and the initiation process of disasters under seismic conditions.

Due to the fixed negative charges in the skeleton of expansive soil, there are exchangeable cations between the layers that balance the negative charges in expansive soil. That makes the soil exhibit strong expansion and shrinkage properties. The research results show that the expansion and shrinkage of expansive soil will be affected by the chemical composition of the pore solution. In this paper, based on the strong expansive soil in Guangxi, a series of tests are carried out to investigate the soil-water retention curve (SWRC) and the soil shrinkage curve (SSC) for the soil saturated with solutions of different NaCl concentrations. To address this issue, the concept of intergranular stress is introduced, which takes into account the effects of osmosis, capillary, and adsorption. The results show that pore saline solution affects the SWRC through osmotic suction, with a lesser effect on matric suction. The shrinkage deformation of soil samples during the drying process is controlled by intergranular stress, similar to the phenomenon of pressure-induced consolidation. The majority of shrinkage occurs during the capillary stage, exhibiting elastoplastic deformation; less shrinkage occurs during the adsorption stage, which is characterized by elastic deformation. A cutoff point on the compression curve is identified to distinguish between the regimes of capillarity and adsorption, consistent with the independently measured SWRCs at different compactness. The intergranular stress is shown to better describe the chemo-mechanical behavior of expansive soil, particularly at low water content.

In order to study the dynamic deformation characteristics of rubber-clay mixtures, resonance column tests were conducted on mixtures with different rubber contents, rubber particle sizes, and confining pressures. The development patterns of dynamic shear modulus G and damping ratio λ were analyzed. A calculation method for skeleton void ratio e_sk expressing the contact state of mixtures was proposed based on the binary medium model. Furthermore, the maximum dynamic shear modulus G_max of mixtures was evaluated based on skeleton void ratio e_sk. The results show that adding rubber particles leads to a decrease in G and increase in λ. As the rubber content increases, G decreases and λ increases. Additionally, G increases and λ decreases with increasing confining pressure. Moreover, G increases and λ decreases with increasing rubber particle diameter. With an increase in rubber content, the skeleton void ratio e_sk increases and G_max decreases. At the same rubber dosage, as the rubber particle size increases, e_sk increases and G_max rises. Based on Hardin’s formula, a characterization model of G_max considering rubber content and rubber particle size is proposed using skeleton void ratio e_sk. The model exhibits good accuracy and can serve as a basis for evaluating G_max of rubber-clay mixtures.

Fiber-reinforcing technology involves adding discrete and tension-resistant fibers into soils to improve the mechanical properties of the soils. This study investigates the static liquefaction responses of the fibre-reinforced sand in loose states by performing the undrained triaxial compression tests. The feasibility of varied excess pore pressure ratios for assessing the liquefaction of fibre-reinforced sand also has been discussed. The test results reveal that the loose sand without reinforcement is highly susceptible to static liquefaction under undrained triaxial compression, while the inclusion of fibers prevents the development of static liquefaction in the sand samples. The presence of fibers significantly alters the effective stress path experienced by the sand skeleton and thereby influencing its liquefaction response. The conventionally defined excess pore pressure ratio (r_u) based on the principle of effective stress may provide incorrect indications of liquefaction in fiber-reinforced sand. To address this, the study introduces the newly defined effective excess pore pressure ratio (r′_u) and the skeleton excess pore pressure ratio (r* u), which offer improved indications of liquefaction in reinforced sand. By invoking a constitutive framework based on the rule of mixture, the stress contributions of fibers are quantified. The skeleton excess pore pressure ratio takes into account stress contributions of the fibers and reveals how the external load is shared among the fibers, sand skeleton and the pore water. When r* u= 1 is attained, the effective mean stress carried by the sand skeleton drops to zero, resulting in liquefaction of the fiber-reinforced sand.

A three-dimensional rough structural surface characterization was carried out based on the Weierstrass-Mandelbrot (W-M) fractal function. The effects of typical W-M geometric parameters on the three-dimensional surface morphology were discussed. The two-dimensional and three-dimensional W-M geometric parameters corresponding to typical Barton JRC curves were analyzed and provided. Experimental fracture seepage tests on specimens with different fractal parameters and fracture aperture were conducted using a self-designed fracture seepage system based on 3D printing technology. The test results showed that the fluid flow exhibited obvious nonlinearity with increasing hydraulic gradient and roughness. The coefficients of A and B in the Forchheimer equation increased with increasing fracture roughness and decreased with increasing fracture aperture. Meanwhile, the critical Reynolds coefficient tended to decrease as the roughness increased, indicating a tendency towards non-Darcy flow. The analysis of fluid flow patterns revealed that the flow velocity of the smooth structure surface of the model was relatively uniform. The flow field of the rough surface was complex showing several high and low flow velocity regions along the rough surfaces. The research results provide reliable analytical methods and models for the study of fracture seepage characteristics.

To investigate the dynamic propagation process of the fracturing crack across the coal-rock interface, similar materials were used to prepare coal-rock combined specimens. Three-point bending tests and true triaxial hydraulic fracturing tests were carried out. By the digital speckle technology and the acoustic emission (AE) technology, the dynamic propagation characteristics of the fracturing crack were captured. The fracture pattern and its influencing factors were analyzed. The results show that in the three-point bending test, the crack can penetrate into the coal seam directly from the roof without changing direction at the interface. The peak stress required for the specimen fracturing is reduced while increasing the prefabricated crack length. In the true triaxial hydraulic fracturing test, due to the strong plasticity of the coal seam, the crack height and length in the roof are both larger than those in the coal seam, and the proportion of acoustic emission events in the roof is also higher than that in the coal seam. When the crack propagates across layers, increasing the distance between the horizontal well and the top surface of the coal seam will lead to the extension of the crack propagation time. Increasing the injection rate of the fracturing fluid can increase the penetration depth of the crack into the coal seam, but it is easy to cause the crack height to be out of control and the reduction of crack length. The fracturing method with variable injection rates was proposed. In the initial stage, the fracturing fluid injection with a large rate promotes the crack propagation across layers, and then the injection rate is reduced to promote the lateral propagation of the crack in the roof and coal seam. There is a competitive propagation phenomenon among cracks when multiple cracks are initiated synchronously, and part of the cracks can not propagate across layers. The research results can provide support for mastering the propagation characteristics of the crack across the coal-rock interface and optimizing the hydraulic fracturing parameters.

To effectively address the issue of ground vibration induced by the rail transit, a locally resonant metamaterial surface wave barrier (LRMB) vibration isolation method was developed based on the concept of acoustic metamaterials, and the structure model was constructed using concrete and rubber pad. According to the theory of elastic dynamics in semi-infinite space, an analytical calculation formula for LRMB bandgap was derived, and the influences of rubber pad and concrete on LRMB bandgap characteristics was analyzed. The vibration isolation performance of LRMB was further analyzed based on the measured ground vibration induced by the rail transit. The results show that the generation of LRMB surface band gap is mainly related to its vertical vibration, and the band gap calculation method for LRMB assuming vertical vibration mode is accurate. Increasing the thickness of the rubber pads decreases the starting frequency of the bandgap and increases its width. Conversely, increasing the width of the rubber pads increases the starting frequency of the bandgap and decreases its width. Additionally, increasing the mass of the concrete decreases the starting frequency of the LRMB bandgap and increases its width. The vibration isolation efficiency can be improved by increasing the number of primitive cells and the vibration isolation coefficient with 4−6 cells reach 20−25 dB. Using Jinan Rail Transit Line 1 project as an example, the ground vibration attenuation can reach 70%−80% after using LRMB, validating its strong vibration isolation performance.

In the cold region, frost heave damage in water conveyance channels constructed on expansive soil poses a significant threat to project sustainability. This study aims to investigate the evolution and physical mechanisms of frost heave inhibition by soilbags for expansive soils with varying water contents and dry densities. Standard calibration tests for sample preparation and frost heave deformation tests were conducted on expansive soils with and without soilbag constraints. The test results demonstrate a direct correlation between the compaction height of the sample and its dry density, enabling precise control of the dry density by adjusting the compaction height. Regardless of the presence of soilbag constraints, the relationship between frost heave deformation and time can be divided into three stages: cold shrinkage, rapid freezing and freezing stability. The frost heave of the expansive soil was significantly reduced under the restraint of the bag for samples with the same initial state, indicating that the soilbag can effectively inhibit the frost heave of the expansive soil. Moreover, as water content and dry density increased, the frost heave rate of the samples exhibited a significant increase. The frost heave inhibition rate of the soilbag increased significantly with the increase of dry density, but it did not increase notably with increasing water content. The intrinsic mechanism of soilbag inhibiting frost heave of expansive soil is revealed using the theory of segregation potential and the principle of reinforcement constraint. A conceptual model of the skeleton structure of frozen expansive soil under the influence of soilbag constraints is proposed, based on the pore diameter distribution curve obtained through mercury intrusion porosimetry. This model better explains the variations in the evolution of frost heave inhibition rates of soilbags under different water contents and dry densities.

Both weights and buried depth can influence the allowable hydraulic gradient of soil, but these effects have not been quantified. Quantification of these influences is the key to determine the allowable hydraulic gradient and to evaluate seepage safety. In this study, the axial stress was adopted to simulate the effects of weights and buried depth. A list of seepage tests under different axial stresses was performed on soil ③-1 of Luding Hydropower Station, and the influences of weights and buried depth on the critical hydraulic gradient were quantified. The results indicate that the critical hydraulic gradients of the upper and middle envelopes of particle size distribution linearly increase with the increase in axial stress, while that of the lower envelope is not influenced by the axial stress. The influences of weights and buried depth on the allowable hydraulic gradient were quantified based on the experimental results, and a formula describing the variation of the allowable hydraulic gradient with axial stress was proposed, and then a method determining the allowable hydraulic gradient which can consider the influences of weights and buried depth was established, and it can provide a reference for the similar project.

Due to the fact that the lining of the secondary tunnel overlaps on the arch waist of the lining of the front tunnel, the stress situation of the surrounding rock and lining is complex. Therefore, it is of important engineering significance to carry out stress and displacement analysis of the surrounding rock and lining. This study proposes a calculation method for stress and deformation analysis of the surrounding rock and lining in a double-arch tunnel without a middle drift, considering the deep burial conditions and the presence of the lining. The method utilizes the complex variable function theory and Schwarz alternating method. In the case of a double-arch tunnel without a middle drift, where the two tunnels intersect, the Cauchy integral method is employed to solve the problem. The boundary integral condition for the contact between the lining of a single tunnel and the surrounding rock is transformed into the subtraction between the complete boundary integral and the intersectional boundary integral when only a single tunnel exists. A similar treatment is applied to the calculation of the “additional surface force” in the Schwarz alternating method. Finally, the calculation method of intersectional boundary stress and displacement is given. A numerical example is provided to demonstrate the feasibility and accuracy of the method by comparing the analytical results with numerical simulation results.

Energy piles, as innovative energy underground structure, serve the dual purpose of shallow extracting geothermal energy while bearing the upper building load. There are few studies on the thermomechanical properties of energy piles under combined horizontal and vertical loads. The temperature change of pile body under combined horizontal and vertical loads will result in variations in pile bending moment, horizontal and vertical displacement, etc. This paper investigated the deformation characteristics of energy piles under combined vertical and horizontal loads through model tests with 10 heating-cooling cycles applied to the piles. The results showed that the heating-cooling cycles under combined load led to further increase in the pile bending moment, particularly affecting the middle section of the pile, with the maximum increase in pile bending moment reaching 117%. Additionally, the heating-cooling cycles caused cumulative displacement at the top of the pile. The vertical displacement of the test pile increased by 0.201 mm, and the increase in horizontal displacement due to the thermal cycles reached 1.46% D (D is the diameter of the pile). Simultaneously, the heating-cooling cycles induced a forward tilt of the pile, with the tilt angle reached 1.88×10⁻³ rad after 10 heating-cooling cycles and gradually increasing with the number of thermal cycles. Moreover, the soil pressure in front of the pile decreased during heating, while increased during cooling.

The incremental method based on the beam finite element method is commonly used for calculating foundation pit enclosure structures. However, there is a lack of research on the dynamic decrease of soil spring stiffness in the passive zone during excavation, which leads to soil resistance softening. This paper introduces two stiffness variation coefficients to quantify the dynamic change of soil spring parameters in the passive zone and establishes an incremental method for calculating foundation pit enclosure structures based on this process. For nonlinear foundation models, a refined incremental method is proposed for numerical calculations. Three basic soil spring models (linear elastic, ideal elastic-perfectly plastic, and hyperbolic) are used to obtain the softening p-y curves in the passive zone. A comparison of these models shows that the variation curve of the equivalent horizontal resistance coefficient obtained using the hyperbolic soil spring model aligns better with actual observations. An engineering example demonstrates that the calculation results based on the hyperbolic soil spring model correspond better to measured wall displacements at different excavation stages. Parameter analysis highlights the significant influence of the stiffness variation coefficient related to the ultimate resistance p_u of the soil in the passive zone. Therefore, when using the proposed method, careful attention should be given to calculating the ultimate resistance p_u and the influence of excavation on it in the passive area should be considered.

This paper presents an analytical theoretical model for air-boosted vacuum preloading, focusing on the influence of air injection on soil consolidation. A simplified force model based on the equivalence of air-boosted pressure is proposed, and a new parameter called the “horizontal permeability coefficient increase parameter h” is introduced to account for changes in soil permeability due to gas injection. Based on Barron equal vertical strain assumption and linear Darcy’s law, the governing equation and consolidation analytical solution for air-boosted vacuum preloading are derived, considering factors such as radial and vertical seepage, prefabricated vertical drain smear effect, well resistance, and surcharge. Additionally, the theoretical formula for the equivalent air-boosted pressure p(t) is derived using elastic mechanics methods. Specific analytical solutions are provided for two cases: instantaneous air-boosted and linear air-boosted. An engineering case study is used to verify the rationality of the analytical solution and the mechanical equivalence method. Through the analysis of consolidation behavior, the following conclusions are drawn: the air injection boosting method increases the negative pore water pressure in the soil, facilitating faster drainage and consolidation; the “η ” parameter significantly affects the consolidation rate, and considering changes in the horizontal permeability coefficient during gas injection improves the accuracy of the analysis model; well resistance slows down the consolidation rate, and while pore pressure can dissipate completely during radial and vertical seepage, it may not dissipate completely during radial seepage alone.

Karst geological hazards pose a significant challenge for the urban construction and underground space development and utilization in the Guangdong-Hong Kong-Macao Greater Bay Area, especially in Guangzhou and Shenzhen. Karst exploration generally involves identifying and assessing caves through a combination of drilling and geophysical information. In recent years, the cross-hole computed tomography (CT) geophysical method has been widely used in karst exploration in the Greater Bay Area due to its ease of operation and strong ability to obtain geological information. However, the accuracy of this method in identifying caves still needs to be quantitatively evaluated. This paper collected a large amount of data on karst drilling and exploration, and the accuracy of cross-hole CT karst identification was statistically analyzed using the model factor method. The results showed that this method could accurately detect the buried depth of the cave roof, floor and height, with an average error less than 5%. The predictive accuracy of the buried depths of the cave roof and floor has very low variability, only 5%, while the predictive accuracy of the cave height has medium variability, exceeding 35%. The accuracy stability of the cross-hole CT karst identification method is satisfactory and not affected by the factors such as CT method type, cave filling condition, emission and reception point distance, drilling type, cave roof thickness, drilling distance, and verification hole distance. This paper also conducted a simple correction of the current cross-hole CT method, which increased the average accuracy of the model by 4% and reduced the variability by 3% without increasing the computational complexity. Finally, the analysis confirmed that the model factors for predicting cave height follow a Weibull distribution. The research results can provide theoretical support for karst cave exploration and risk assessment in karst areas

The geomechanical parameters for a particular site exhibit inherent uncertainties due to geological processes, and probabilistic back analysis incorporating field observation data can effectively reduce these uncertainties. Although the BUS (Bayesian Updating with Subset simulation) method can transform the high-dimensional probabilistic back analysis problem with the equality site information into an equivalent structural reliability problem, the value of the constructed likelihood function can become extremely small or even lower than the computer floating-point operation accuracy as the field observation data increase, which might seriously affect the computational efficiency and accuracy of probabilistic back analysis. To this end, this paper proposes an improved BUS method based on the parallel system reliability analysis. Starting from the Cholesky decomposition-based midpoint method, the total failure domain with a low acceptance rate is decomposed into several sub-failure domains with a high acceptance rate so as to avoid the “curse of dimensionality” arising from the integration of a large amount of field observation data, and to achieve accurate back analysis of the geomechanical parameters of slopes. Finally, the effectiveness of the proposed method is validated through a case study of an undrained saturated clay slope. The results show that the proposed method can integrate a large number of borehole data and the observation information of slope service state for efficient probabilistic back analysis of geomechanical parameters and slope reliability evaluation with reasonable accuracy. The proposed method provides an effective tool for high-dimensional probabilistic back analysis of spatially variable soil parameters and slope reliability evaluation.

With exploiting of the urban underground space, the problem of anti-floating foundation becomes prominent in the soft soil areas. Bored and precast piles are widely used due to their environmental friendliness, but drilling process typically reduces the shaft resistance. Thus a constrained grouting pile is proposed. In order to accurately evaluate the uplift capacity of steel pipe pile with constrained grouting, the failure mechanism is analyzed, and the logarithmic spiral curve is adopted to fit the local slip surface. The simplified calculation formula is derived, and its effectiveness is verified by a classic case study. Based on the design concept of orthogonal experiment, the influencing factors of uplift capacity are compared. The results show that the diameter of pile and the strength of pile-soil interface control the uplift capacity. Field test on the steel pipe pile with constrained grouting is carried out. The test shows that the uplift capacity of the pile is increased by 70%. It is more accurate and safer to use the theoretical formula proposed to calculate the uplift capacity of foundation pile. The research results provide reference for the uplift capacity design of the constrained grouting piles.

During tunnel excavation, the digital drilling process monitoring (DPM) system can quickly obtain rock strength parameters in real time, and guide on-site excavation and support operations in a timely manner. In order to obtain the surrounding rock strength in front of the tunnel face in real time, this study carried out the in situ digital drilling tests based on the digital drilling process monitoring (DPM) system mounted on the pneumatic percussion rotary drilling rig. Through the real-time monitoring, recording and analysis of the drilling parameters such as propulsion pressure, rotary pressure, impact pressure and drill pipe displacement in the whole drilling process, the characteristics of the drilling parameters in different drilling processes are obtained. On this basis, each drilling process is identified, and the drilling parameters of the pure drilling process are separated by using the DPM time series analysis method. The results show that the drilling depth of the pure drilling process changes linearly with the drilling time. The variation of working pressure of the drilling rig with the drilling time is relatively constant, and it has limited influence on the rate of penetration in different rate-of-penetration sections. Meanwhile, the rate of penetration decreases with the increase in rock strength, and an exponential relationship model between rock strength and rate of penetration is established to guide engineering practice.

This study focuses on addressing the issues associated with the “end-suspended pile” structure in deep foundation pits within soil-rock composite strata by implementing an enclosure structure called “micro-steel tube pile internally connected into concrete pile”. The structure is analyzed considering the “knot effect” between the micro steel pipe pile and the rock, as well as the similar mechanical characteristics between excavated rocks and cracked concrete. The structure is modeled as a stepped variable section pile (beam), consisting of an upper concrete pile and a lower equivalent cracked beam without stirrups. The micro steel pipes serve as axial reinforcements for the equivalent beam, while the rocks represent the cracked concrete of the equivalent beam. The reduction in lateral stiffness is used to quantitatively assess the impact of section reduction and rock mass fractures. An elastic subgrade method based on lateral stiffness reduction is employed, taking into account the dowel action of axial reinforcement to calculate the shear bearing capacity of the equivalent beam. The analysis of a case study demonstrates that the lateral stiffness reduction coefficient β  ranges from 0.85 to 0.12, the bending moment of the upper concrete pile increases by 55.8%, the bending moment of the lower equivalent beam decreases by 48.7%, the shear force of the upper concrete pile decreases by 13.6%, the shear force of the lower equivalent beam decreases by 22.0%, and the horizontal displacement of the concrete pile top increases by 39.5%. Comparing this structure with the “end-suspended pile” structure, it is observed that the horizontal displacement and vertical settlement of the concrete pile top do not significantly increase. The final horizontal displacement and vertical settlement of the concrete pile top are only 43% and 69%, respectively, compared to the “end-suspended pile” structure. The measured horizontal displacement at the concrete pile top is 5.5 mm, which is only 35% of the calculated results, suggesting that the lateral stiffness reduction coefficient can be appropriately adjusted. This study provides valuable insights for the design and protection of deep foundation pits in soil-rock composite strata.

This study focuses on investigating the steady seepage characteristics of fracture network with free surface. A visual two-dimensional fracture network seepage test device was designed to conduct a series of fracture network seepage tests by adjusting the upstream and downstream heads of the fracture network model, and recording the height of free surface head and seepage flow. Additionally, a two-dimensional fracture network numerical model with equal proportions was established using the Darcy interface of the finite element software COMSOL Multiphysics. The test conditions were reproduced in the numerical simulation and compared with the test results. The findings demonstrate that the test results are basically consistent with the simulation results, which verifies the effectiveness of the test results and the accuracy of the numerical simulation. The results show that the main factors affecting the change of free surface are the height of upstream and downstream heads and the height difference between them. A larger seepage hydraulic gradient leads to a faster drop in the position of the free surface. Under the same hydraulic condition of seepage hydraulic gradient, higher the upstream and downstream water heads result in higher the free surface water heads and steeper falling curve of free surface. Notably, if the upstream and downstream water head heights are not at similar levels, their influence on the position of the free surface differs greatly. The basic laws of free surface change align with Dupuit formula. The hydraulic gradient of steady seepage is linearly correlated with the average flow rate only when the flow rate is small, while with increasing hydraulic gradient, the relationship becomes noticeably nonlinear.

Smoothed particle hydrodynamics (SPH) is a Lagrangian meshless method, which has remarkable advantages in numerical analysis of solids with extremely large deformation. The present paper deals with SPH simulation of large solid deformation involving frictional contact interface. A new pure smoothed particle PTVD (point-to-volume discrete) contact algorithm is developed based on the FPM (finite particle method) particle interpolation, which is an alternative SPH formulation for improving the interpolation accuracy near boundaries. The PTVD contact algorithm transforms equivalently the interface contact force into the external interactive forces between particles near the contact interface. To be specific, the particles modelling either body in contact are grouped as master particles and slave particles with respect to the feature of the contact interface. For each slave particle near the contact point, the relative position is determined according to the amount of master particles contained in the influence domain of that particle, and the normal contact force is then calculated considering the contact stiffness. The shear contact force is determined considering the relative shear velocity between two particle groups within the influence domain and the friction of the interface. The proposed PTVD contact algorithm highlights the nonlocal characteristics of the SPH methods and avoids the complex algorithm for identifying and accurately describing the interface. Following the verification through the classic contact and friction examples, the PTVD algorithm is applied to the SPH analysis of quasi-static collapse of cohesionless granular soil and projectile penetration into soft soil. The results demonstrate the effectiveness and applicability of the proposed contact algorithm in SPH modelling of frictional contact problems.

This study analyzes the dynamic impedances of pile group foundations in unsaturated ground using a numerical approach that couples the boundary element method (BEM) and finite element method (FEM). The governing equations for the pile element are derived using beam equations, establishing a numerical model of the pile group using FEM. The governing equations for the unsaturated ground in the BEM are derived using the weighted residual method and Laplacian transform, based on the governing equations of the unsaturated poroviscoelastic medium. The fundamental Green solutions for the unsaturated medium are obtained using the properties of the adjoint matrix. The coupled numerical model, comprising the BEM model for the unsaturated ground and the FEM model for the pile group foundation, is obtained from force balance conditions and displacement compatibility at the interfaces between the piles and soil. The study investigates the effects of soil saturation degree, pile length, pile spacing, pile number, and ground properties on the dynamic impedances of group piles. The research findings indicate that an increase in saturation degree reduces the stiffness of the pile group foundation and the damping coefficient at low frequencies. Additionally, both an increase in saturation degree and an increase in pile number enhance the interaction between the pile and soil. The presence of an underlying bedrock in layered ground increases the pile-soil interaction and significantly influences the horizontal impedance of pile group.

In order to simulate the deformation characteristic and motion forms of rock mass, a three-dimensional deformable spheropolyhedral discrete element method is presented, by combining the spheropolyhedral discrete element method (DEM) and the finite element method (FEM). This method effectively captures the irregular characteristics of the block, simplifies contact detection, and provides accurate representations of block deformation. The contact detection object is simplified from individual contact pair to the entire element during tangential contact force calculation, which significantly improves the computational efficiency. In order to analyze the deformation characteristics of the block, the finite element mesh is divided inside the discrete element of the block, with the outermost mesh defined as the minimum contact element. Contact forces are translated to equivalent nodal contact forces using the direct average method. Nonlinear finite element methods accurately simulate element deformation, overcoming the rigid body assumption of spheropolyhedra. Five numerical examples are simulated to verify the accuracy of the proposed method in capturing the deformation, motion morphology and mechanical characteristics of the element.

Simulating suffusion involves computing both the seepage flow of pore water in soil and the transport of fine particles with pore water flow. Since the conventional finite element method (FEM) exhibits instability when used to solve the pure transport equations, a staggered method that employs FEM to solve the seepage equation and the finite volume method (FVM) for the particle transport equation is proposed. As conventional FEM cannot provide a locally conservative velocity field that satisfies the input requirement of FVM, an algorithm, based on the global re-balance of the element residual fluxes, is employed to correct the flow velocity at element boundaries. With this algorithm, the local conservation of the flow velocity computed by FEM at the element boundary is achieved. This enables FVM to solve the particle transport equation on the same FEM mesh, facilitating the convenient integration of FVM with existing FEM codes. Case studies demonstrate that the proposed local conservation algorithm and the staggered method exhibit high computational efficiency and acceptable accuracy, offering a straightforward and practical approach to simulating suffusion problems.

Ramming settlement is a crucial indicator for evaluating the quality of dynamic compaction foundation reinforcement. At present, it mainly relies on manual monitoring, which seriously affects the efficiency of dynamic compaction construction, and safety cannot be guaranteed. To address these issues, this study proposes a non-contact measurement method using monocular photogrammetry to accurately measure ramming settlement. The method begins by analyzing and scientifically defining the suitable definition of ramming settlement for monocular visual monitoring. Next, based on the fundamental principles of visual imaging, a numerical equation is developed to measure the three-dimensional attitude of the rammer. This is achieved by leveraging the rotation invariance of the rammer to identify geometric feature points and solve for their three-dimensional coordinates. Finally, the proposed method is then tested on the construction site, and the algorithm is optimized using the conditional adjustment method. The experimental and engineering application results demonstrate that this method offers high precision, fast processing speed, and robustness. It can effectively automate the calculation of ramming settlement, a key parameter for monitoring the quality of dynamic compaction. This research provides a new direction and means for advancing the current automatic monitoring technology of dynamic compaction.