Abstract
The Metro Jet System (MJS), widely utilized for reinforcing weak foundations, relies critically on the mechanical properties of its piles to ensure effective soil stabilization. Unlike laboratory-scale tests that often overlook real-world constraints and soil heterogeneity, this study conducted full-scale field experiments to replicate in-situ MJS pile formation. Core samples extracted post-construction were analyzed to evaluate the effects of cement content, radial non-uniformity, and surrounding soil characteristics on compressive strength, stress-strain behavior, and failure modes. Complementing the experiments, discrete element numerical simulations were employed to microscopically validate the mechanisms underlying macroscopic observations. The research findings indicate that the stress-strain relationship of the pile specimens exhibits strain-softening behavior, and post-peak brittleness of the specimens increases with higher cement content. The mechanical properties of the pile body specimens are significantly influenced by cement content and distance from the pile center, with less correlation to the strength of the surrounding strata. Higher cement content, shorter distance from the pile center, and increased strength are observed to be interrelated. Numerical simulation results show that as cement content increases, the rate of reduction in the coordination number of the specimens decreases. In the early stages of numerical experiments, the rate of increase in the number of cracks becomes progressively lower. A numerical model considering cement content for the mechanical properties of the piles was established, demonstrating good predictability for pile compressive strength. These results underscore the necessity of full-scale testing for reliable in-situ performance assessment and provide actionable insights for optimizing MJS pile design in geotechnical engineering.
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Introduction
The rapid expansion of urban underground space development has led to the widespread adoption of underground engineering projects, particularly tunnels. However, this progress is accompanied by escalating challenges in reinforcing weak geological strata1. High-pressure jet grouting, a technique that stabilizes soft soil foundations by injecting and mixing cement slurry with in-situ soil2, has been extensively utilized in applications such as soft soil rehabilitation, foundation sealing for deep excavations, and grout support for tunnel boring machine launch/reception zones, as well as joint sealing in underground diaphragm walls to prevent leakage2,3,4,5. Nevertheless, this method faces issues such as not being environmentally friendly, hindered slurry discharge, and uneven mixing of cement during the grouting process, leading to strength discrepancies between the upper and lower portions of the piles6,7. The MJS addresses these challenges by employing a porous pipe method and front-end positive suction device to facilitate active sludge discharge and pressure monitoring8. Reducing ground pressure and sludge discharge ensures the expansion of the pile diameter9. Consequently, its piling effectiveness surpasses that of traditional high-pressure piling. Therefore, this technology is widely applied in reinforcing weak geological layers in underground structures such as tunnels, and foundation pits10. It is found that the MJS pile has a better reinforcement effect and can effectively reduce the settlement of the foundation or building11,12. Furthermore, MJS technology has limited influence on the surrounding buildings and soil, and can effectively control the stress concentration release induced by shield tunnel construction1,11,13. Therefore, the safety of tunnel engineering can be greatly improved.
The Metro Jet System (MJS) is highly effective in safeguarding adjacent structures from construction-induced disturbances, such as those arising from deep foundation pit excavations14. However, achieving precise control over MJS pile strength and length remains a critical challenge in practical applications15. To ensure quality, post-construction assessments must rigorously evaluate both the mechanical properties and geometric characteristics of the cement-soil columns. Quality control for jet grouting columns primarily involves two methods: controlling the compressive strength and geometric dimensions of the concrete column. Scholars have conducted extensive research to determine the strength and operating mechanisms of the piles under different conditions16,17. In laboratory conditions, the impact of additives, cement types, and curing time on pile strength has been investigated using uniaxial compression tests18. On the other hand, the method of jet grouting also has a certain impact on the diameter and strength of the columns. The initial moisture content in clay areas and technical parameters of jet grouting, such as grout volume and pressure, drilling speed, rotation speed, and time intervals per step, influence the geometric shape of the pile15,16,19. It is found that with increasing injection pressure and volume, the uniaxial compressive strength exhibits logarithmic growth20. The results also show that the increase of lifting speed significantly reduces the uniaxial compressive strength, but slightly reduces the column diameter21. FHWA-HRT-13–046pointed out that strength under full-scale conditions is generally lower than the strength produced under laboratory conditions. Simulating actual construction conditions and accounting for common unknown factors in the laboratory is impractical. Although laboratory studies are valuable for identifying microstructural parameters influencing pile strength, this aspect is not the focus of this paper. To ensure quality control over the geometric shape and mechanical characteristics of jet-grouted columns, research must be based on full-scale construction to fully simulate construction conditions22,23. This is because the strata are not entirely uniform under actual conditions, making it impossible to estimate the actual diameter and comprehensive testing must be conducted to validate these assumptions. This underscores the necessity of conducting full-scale experimental research in the field of geotechnical engineering. However, comprehensive research in this regard has not been sufficiently extensive to date.
Simultaneously, experimental methods suffer from drawbacks such as high resource consumption and significant time costs. In contrast, numerical simulation can visually depict the entire process of sample failure, providing an intuitive means to analyze the mechanical properties and failure mechanisms of the research object from a microscopic perspective. Therefore, it has gained widespread application among scholars in recent years24. Discrete elements can be macrodispersed into grids or particles for the two major types of natural materials, rock mass and soil mass, which can truly reflect the rock and soil morphology, so many scholars have applied them to the damage analysis of soil mass, concrete and other materials25,26.
Discrete element software has been widely adopted to simulate fracture propagation, damage evolution, and heterogeneous mechanical behavior in cementitious materials, which share similarities with MJS piles in terms of composite microstructure and localized failure mechanisms. Some scholars also utilized the Particle Flow Code (PFC) software to numerically simulate experiments on flood embankment materials and structures to investigate the microscopic mechanisms of flood embankment instability27. On this basis, considering the coupling action of soil and water, a numerical method combining PFC with computation fluid dynamics is developed to simulate the seepage failure of soil levels28. Hou et al. proposed a multi-scale DEM-MD (molecular dynamics) framework to simulate crack propagation in cementitious materials under tensile loading, demonstrating that DEM effectively captures both macroscopic stress-strain responses and microscopic crack initiation29. Wang et al. coupled FLAC (a continuum-based code) with PFC to analyze damage evolution in jointed rock masses, highlighting DEM’s ability to bridge continuum and discrete behaviors in hybrid materials30. Kong et al. developed an improved fluid-solid coupled DEM model to study crack propagation in high-brittle cement mortar under combined hydraulic and shear stresses, proving DEM’s adaptability to simulate continuum-like failure in cement-based systems31. These studies confirm that DEM, when combined with appropriate bonding models (e.g., parallel bonds), can effectively simulate quasi-continuum materials by representing cohesive interactions between particles.
The Erqi Square business district exemplifies a high-risk urban construction scenario, where the foundation pit excavation for the upper tunnel of Zhengzhou Metro Line 1 is situated adjacent to two operational subway lines and heritage landmarks. Such proximity necessitates stringent control over soil deformation to safeguard existing infrastructure, making MJS technology indispensable for ground reinforcement. However, discrepancies persist between laboratory-derived mechanical properties and field performance of MJS piles, particularly at engineering scales. Critical knowledge gaps remain regarding the effects of cement content, radial anisotropy, and stratigraphic variability on pile integrity under real-world conditions. To address these limitations, this study integrates full-scale field tests with discrete element numerical modeling. Quantifying the influence of cement content, soil layer characteristics, and radial non-uniformity on compressive strength and failure modes. Additionally, a discrete element numerical model of the piles is established to further explore the mechanical characteristics of the piles. By bridging laboratory-field disparities and elucidating multi-scale mechanical behaviors, this work provides actionable insights for optimizing MJS pile design in spatially constrained urban environments.
Materials and methods
Soil
The Erqi Square Tunnel Project, located in Zhengzhou City, Henan Province, China, involves excavation in close proximity to Metro Line 1, necessitating the use of the Metro Jet System (MJS) for soil reinforcement to mitigate disturbance risks to the adjacent subway infrastructure. Geological exploration revealed a stratified subsurface profile dominated by silty soil and silty clay, with distinct mechanical and physical properties across layers. A small amount of miscellaneous fill is found at the top of the soil layers, primarily consisting of artificially piled silty soil, bricks, and construction debris, with a mixed composition and loose structure. The distribution of soil layers is distinct, with significant variations in the mechanical properties of each layer. According to the results of geotechnical tests, the strength of the silty soil ranges between 50 and 80 kPa, categorizing it as moderately strong silty soil, while the strength of the silty clay can reach 123.1 kPa, indicating relatively high strength. Both silty soil and silty clay contain 30–50% fine particles (clay/silt fraction) and display low porosity (< 0.75), classifying them as dense, compression-resistant soils. Detailed physical and mechanical properties are summarized in Tables 1 and 2, respectively.
MJS process
The MJS construction workflow comprises the following sequential steps:
(1) Pile Positioning and Depth Marking. The pile center is precisely located using GPS or laser alignment tools, followed by depth line markings to ensure vertical accuracy.
(2) Equipment Installation and Calibration. The MJS rig is assembled on-site, and the drill rod is advanced to the design depth (20 m in this study). Zero calibration and system debugging are performed to validate sensor accuracy and grouting parameter synchronization.
(3) Swing Jetting Operation. A swing jetting technique is employed, with a step interval of 25 mm and a jetting duration of 76 s per step. The nozzle is lifted at a controlled speed of 50 m/min while maintaining a jetting pressure of 40 MPa, ensuring uniform slurry penetration and radial pile expansion.
(4) Pile Formation. The process achieves a target pile diameter of 2 m, with cement-soil mixing optimized to minimize radial strength variability.
Experiment design
After the completion of pile formation, the GXY-1 type drilling machine is employed for core sampling of the MIS pile, as illustrated in Fig. 1. Subsequently, the core sample is cut into cylindrical specimens with a height and diameter of 65 mm, as shown in Fig. 2. Following the processing, the specimen surface is smooth, dry, and exhibits a regular shape, facilitating optimal conditions for experimentation.
Sampling process of pile test.
Samples.
Research has indicated that slurry properties and jetting pressure are crucial factors influencing the effectiveness of the MJS piling process16,20,32,33. Additionally, due to significant differences in the mechanical properties of different soil layers within the site, a single pile located at various depths may exhibit variations in mechanical performance. In summary, this paper separately investigates the impact of cement ratio, soil layer characteristics, and pile anisotropy on the mechanical properties of the piles. The specific sampling parameters are outlined below.
(1) To investigate the influence of cement content on the strength of the piles, four different cement ratios, namely 25%, 30%, 35%, and 40%, were selected. The sampling locations were at the center of the piles in the 2 m deep soil layer (① miscellaneous fill), with five samples taken for each ratio. The sampling information is presented in Table 3.
(2) To study the anisotropy of the piles, samples were taken at distances of 1 m, 0.5 m, and at the center of the pile. The depth was 2 m, the cement ratio was 40%, and five samples were taken for each group. The sampling schematic is illustrated in Fig. 3 (a), and specific parameters are outlined in Table 3.
Sampling diagram.
(3) To investigate the influence of the mechanical properties of soil layers on the strength of the piles, samples were taken at depths of 6 m (② silty soil), 9 m (③ silty soil), and 12 m (④ silty clay) from the periphery of the same pile. Five samples were taken for each group. The sampling schematic is illustrated in Fig. 3 (b), and specific parameters are outlined in Table 3.
Uniaxial compression tests
The specimens were subjected to uniaxial compression tests using an MTS hydraulic testing machine. Uniaxial compression tests were conducted with a displacement loading method, setting the rate at 0.5 mm/min, until the specimens failed.
Experimental results and analysis
Stress-strain curves
Figure 4illustrates the stress-strain relationships of MJS pile specimens under varying cement ratios. All curves exhibit distinct strain-softening behavior, characterized by post-peak stress degradation and increasing brittleness at higher cement contents. The curves can be categorized into four sequential stages34:
Stress-strain curves of samples with different cement content.
Compaction Stage: The initial loading phase displays an upward concave curve due to the closure of pre-existing microcracks under axial compression. Higher cement ratios shorten this stage, indicating fewer initial defects in the cement-soil matrix.
Elastic Stage: A linear stress-strain relationship emerges as internal pores stabilize into compacted configurations. Strain progresses uniformly with minimal crack nucleation.
Yielding Stage: Beyond the elastic limit, localized plastic deformation initiates crack propagation. The curve slope decreases progressively, culminating in peak stress as cracks extend radially.
Post-Peak Stage: The internal fracture surface of the specimen rapidly expands, intensifying the expansion of the pile core. Absolute strain volume in crack development sharply increases. Axial stress begins to decline, and the pile’s load-bearing capacity rapidly decreases, entering a residual stage with a certain residual strength, and exhibiting strong brittle failure characteristics. The graphical representation indicates variations in pile strength and ultimate strain under different ratios, while the curve characteristics remain similar.
Moreover, from Fig. 4, it is evident that the cement ratio significantly influences the deformation characteristics after reaching the peak stress point. With an increase in the cement content of the pile, the rate of descent gradually intensifies. Analysis suggests that this is attributed to the higher cement content, leading to increased brittleness in the specimen. Consequently, the expansion speed of cracks accelerates, resulting in a rapid escalation of the pile’s failure velocity.
Influence of cement content on physical characteristics of piles
Based on the stress-strain curves, the elastic modulus for each set of specimens was calculated, as illustrated in Fig. 5. The results indicate a significant impact of cement content on the elastic modulus of the pile. With the increase in cement content, the elastic modulus of the pile shows an upward trend. In comparison to the 25% group, the elastic modulus for the other groups increased by 112.85%, 125.12%, and 172.07%, respectively. This suggests that within the range of 25–40%, an increase in cement content effectively enhances the elastic modulus of the pile. The reason is that in the cement structure, its microstructure affects the macroscopic mechanical properties, and the interface fracture at the microscopic level is the weakest link, which mainly controls the curvature in the stress-strain relationship35. With the increase of cement content, the water-cement ratio decreases, the porosity of the structure decreases, the microstructure becomes denser, and micro-cracks are less likely to appear, so the elastic modulus is higher. This is also consistent with existing literature36,37.
Physical characteristics of pile and cement content.
The relationship between the elastic modulus of the pile and cement content was fitted using a linear function, as shown in Eq. (2).
Where E represents the elastic modulus (GPa), and x represents the cement content (%). Among them, the value range of x is about 25–40%.
The variation curve of compressive strength with cement content is shown in Fig. 5. Analysis reveals that specimens with cement contents of 30%, 35%, and 40% exhibit an unconfined compressive strength increase of 37.35%, 89.83%, 127.42%, respectively, compared to the 25% group. As the cement content increases, the unconfined compressive strength of the specimens steadily rises. This is attributed to the higher cement content leading to the production of more hydration products such as calcium silicate hydrate, resulting in increased strength38.
Influence of surrounding soil on physical characteristics of pile
As the MJS principle relies on high pressure to mix the subsurface soil with the slurry, the physical and mechanical properties of the soil layer as well as its compatibility with cement may affect the mechanical properties of the pile. In this experiment, core samples were taken at representative locations of 6 m, 9 m, and 12 m along the pile, corresponding to soil layers ② (silty soil), ③ (silty soil), and ④ (silty clay), respectively. The analysis aims to understand the impact of different soil layers on the strength of the pile. The test results in the figures are the average of 5 samples, and the variability of the data results is shown through the error bar.
The experimental data in Fig. 6reveals minimal differences in pile strength at various depths, within the range of 2–8%. According to the geological survey results, the soil layers at 6 m, 9 m, and 12 m are identified as ② silty soil, ③ silty soil, and ④ siliceous clay, respectively, with strengths of 58.3 kPa, 78.2 kPa, and 123.1 kPa. The strength differences between these layers range from 40 to 60%. Therefore, there is no strong correlation between soil strength and pile strength. Surprisingly, the pile made from the soil layer at 6 m, despite having the lowest soil strength, exhibits higher strength than the pile at 9 m. This observation suggests that MJS pile strength is primarily influenced by cement strength, given that cement strength is significantly higher than soil strength, and the correlation with soil properties is limited32. This is because the high injection pressure used by MJS in the process of pile formation far exceeds the strength of the soil mass, resulting in the soil mass being destroyed into a granular shape, the original position being replaced by cement, and the cement is mixed with the cement to form a consolidated body of cement and soil particles. The cement is hydrated to form a dense structure that encloses some of the soil particles. The higher the cement content, the more hydration products of the specimen, the denser the microstructure, and the higher the strength. Therefore, soil does not affect the performance of the pile itself.
Strength of samples at different depths.
Influence of non-uniformity of pile strength distribution
To investigate the non-uniformity of the pile, samples were taken at the pile center, 0.5 m from the center, and at the outer periphery. These samples were analyzed to assess the distribution of pile strength. The samples were obtained from MJS piles with a diameter of 2 m and a cement content of 40%. The corresponding peak strength is depicted in Fig. 7.
Strength of test pile at different positions.
This indicates that even with fixed parameters during MJS construction, it is challenging to ensure uniform material properties throughout the pile body. This is due to the attenuation of injection pressure and limitations on slurry diffusion. The injection pressure decreases with the distance from the nozzle, leading to varying degrees of slurry mixing at different distances. Additionally, under high pressure, cement slurry tends to distribute more within the pile and less on the outer side, resulting in significantly lower strength at the outer periphery of the pile compared to the center. Therefore, in designing the strength of the pile body, it is crucial to fully consider the strength of the peripheral pile body to avoid situations of insufficient strength during actual use.
Failure characteristics of pile
The test results indicate that the pile body mainly undergoes three types of failure modes under uniaxial compression: (1) Penetrating tensile failure; (2) Shear-tensile failure; and (3) Sliding failure along structural planes.
Failure characteristics of the sample.
As shown in Fig. 8, the penetrating tensile failure exhibits a clear crack surface with a smooth failure section. This indicates that, under the primary compressive stress, the pile body generates tensile stress perpendicular to the primary compressive stress, leading to lateral expansion deformation. When the lateral expansion deformation reaches the limit, cracks develop parallel to the primary compressive stress direction, failing. This demonstrates distinct brittle material characteristics. Shear-tensile failure occurs when the shear force on the inclined section first reaches the ultimate bearing capacity of the pile body. With the gradual increase in test pressure, cracks appear at the inclined crack location parallel to the primary compressive stress, manifesting as a tensile failure. Due to the increased pressure, the peripheral region of the pile body experiences crushing, leading to a rapid failure process with apparent brittle characteristics. Structural sliding failure along the structural planes results in a rough and uneven failure surface. This indicates that when the shear stress on the structural planes exceeds the shear resistance capacity, the structural planes slide and detach, causing failure. Moreover, due to the high pressure at this point, the pile body is often simultaneously crushed, with stresses exceeding the bearing capacity in all directions. Consequently, irregular cracks emerge, and the entire process exhibits strong brittle failure characteristics. In summary, MJS piles belong to brittle materials, and the test results predominantly demonstrate tensile and shear failures, given the significantly higher compressive strength compared to tensile strength.
It is found that the loading failure of the specimen has obvious stage characteristics. In the compaction stage, the strain gradually increases and the original microscopic cracks inside the specimen gradually close, but the specimen still maintains a complete structure. As the loading continued, cracks appeared on the surface of the specimen, and the stress-strain curves showed oscillatory jumps. When the stress peak point is exceeded, multiple cracks appear and the stress-strain curve decreases rapidly, showing obvious brittle failure characteristics. At the same time, the higher the cement content, the shorter the compaction stage, the stronger the brittleness of the pile, and then the crack expansion speed is intensified, resulting in a sharp increase in the failure speed of the pile. Therefore, under the premise of ensuring the strength of the pile, it is necessary to control the cement content to prevent the tensile shear failure of the MJS pile. During the post-peak stage, rapid fracture surface expansion significantly influences the mechanical behavior of the pile core. As axial stress declines (Fig. 4), penetrating tensile cracks propagate parallel to the loading direction (Fig. 8), relieving lateral confinement and redistributing stress to localized zones. This process reduces the effective cross-sectional area of the core, limiting its capacity for uniform expansion. Specimens with higher cement content (e.g., 40%) exhibited accelerated crack growth and abrupt stress drops, leading to brittle core fragmentation. In contrast, moderate cement ratios (30–35%) retained partial residual strength due to slower crack propagation, enabling limited core expansion even after initial failure. This highlights the trade-off between cement-induced strength and ductility in controlling post-peak behavior.
Numerical simulation
Considering the high cost, long duration, and non-repeatability of in-situ experiments, the paper employs numerical simulation to analyze the failure mechanisms and factors’ impact on the specimen from a microscopic perspective. Compared to finite element software, the Particle Flow Code (PFC) software can better reflect the dispersion, fragmentation, and other deformation characteristics of the research object. Therefore, PFC software is used to analyze the uniaxial compression failure process of the pile body. The PFC software model consists of 2D disks, 3D spheres, and walls, where these particles occupy a certain space. Each particle moves independently and follows Newton’s second law as the governing principle for particle motion. Different contact constitutive models are utilized to describe the interactions between different discrete elements. The contact constitutive model not only reflects the interaction mechanism between contacting particles but also determines the evolution of forces and moments at the contact point over time. Therefore, defining the contact constitutive model between particles and walls enables the simulation of the material’s force-induced failure process.
The establishment of the numerical model
The numerical experiments were conducted using the Particle Flow Code (PFC) 2D discrete element software. The numerical model consists of soil particles and grout particles, with linear contact between soil particles. The MJS pile is modeled as a bonded granular system using the parallel bond model (PBM), which replicates the cohesive behavior of cement-soil composites. This approach aligns with DEM applications in cementitious materials29,30, where particle-scale bonding captures both continuum-like strength and discrete fracture mechanisms. Table 4 provides the basic parameters of the numerical model. The dimensions of the numerical model for the uniaxial compression test are a diameter of 65 mm and a height of 65 mm. Soil particles are simulated using 2D disk models, with particle radii following a uniform distribution, generating an initial porosity of 0.15 for the soil sample.
The model boundaries and their loading environment were simulated using the “wall” command. Four walls (top, bottom, left, and right) were generated to enclose a rectangular area of 65 mm × 65 mm. Discrete element particles representing soil and cement were randomly distributed within the enclosed area. The model was then balanced under its self-weight. Subsequently, initial microscopic parameters were assigned to the constitutive model. The walls on the left and right sides of the model were removed, and the axial loading function was simulated using the top and bottom walls. The top and bottom walls were gradually moved toward each other under the software’s servo mechanism, applying pressure to the specimen. The test was considered complete when the stress value dropped to 70% of the peak stress, indicating specimen failure.
Parameter calibration
Unlike conventional finite element software, PFC cannot directly determine the cross-sectional properties of the model material. Before performing discrete element numerical simulations using PFC software, it is essential to calibrate microscopic parameters for the model to ensure that the assigned mechanical parameters effectively reflect the macroscopic mechanical characteristics of the pile.
The calibration is typically done using a trial-and-error method. Initially, input the initial basic parameters of the particles and contact constitutive model parameters. Apply the gravitational field and cycle the model to a stable state. Conduct numerical experiments of uniaxial compression on the created model. Compare and analyze the stress-strain curves obtained from numerical simulations with those from laboratory experiments. Observe linear features of the curves, changes in slope, elastic modulus, peak strength, and other characteristics. If the results of the two experiments quantitatively match, it indicates that the input microscopic parameters align with the macroscopic mechanical properties of the pile. Bond parameters were calibrated to reflect the composite nature of MJS piles, ensuring macroscopic alignment with experimental results. Similar methodologies have been validated for cement-based materials39,40. The calibrated contact parameters are shown in Table 5.
To simulate different cement contents (25–40%), the ratio of grout particles to soil particles was adjusted proportionally. For example, a 40% cement content model contained 40% grout particles by volume. The parallel bond model parameters (Table 5) were then scaled to reflect the enhanced bonding strength and stiffness associated with higher cement ratios, ensuring alignment with experimental stress-strain relationships. The compressive strength of the pile from experiments and numerical simulations is presented. Based on this, the error between the numerical simulation results and experimental compressive strength is calculated, and it can be observed that the error is controlled within 15%. This validates the effectiveness of the numerical simulation, indicating that the simulation results can reflect the mechanical characteristics of the pile.
Results and discussion
Compressive strength simulation results
To investigate the influence of cement content on compressive strength, the same method was applied to simulate the failure process of 11 groups of pile bodies with different cement contents. The obtained compressive strength data is shown in Fig. 9. A linear function was used to fit the simulated compressive strength against the cement content, and the results are shown in Eq. (2).
Compressive strength and cement content.
Where, σ represents the unconfined compressive strength (MPa), and x represents the cement content (%). Among them, the value range of x is about 25–40%.
The high correlation between numerical simulation results and experimental results from Fig. 9 demonstrates that numerical simulation can predict the mechanical characteristics of the pile.
Porosity
The porosity can indirectly reflect the compactness of the pile, thereby indirectly indicating the stress and deformation of the pile particles. The porosity distribution maps after loading for each specimen were extracted in PFC, as shown in Fig. 10.
Porosity distribution after loading.
The initial porosity of the specimens was 0.15, and after loading, the extreme porosities for the four groups of specimens reached 0.33, 0.36, 0.48, and 0.6, respectively. In addition, all four groups of specimens exhibited large porosity distributions, but the low-content groups (25% and 30%) had larger distribution areas, while the high-content groups (35% and 40%) still had relatively smaller overall distributions. Bands penetrating the pile appeared in these regions with large porosities. This indicates that after uniaxial compression, some particles experienced significant movement, leading to the formation of penetrating cracks inside the pile, and the specimens subsequently underwent failure. This is consistent with the failure modes discussed in Sect. 3.4.
Stress distribution
PFC software allows for the measurement of stress field data for discrete element particles by setting up measurement circles. The axial stress distribution maps after loading were plotted, as shown in Fig. 11. Stress values were assigned to crack locations based on the interpolation calculation principles.
Axial stress distribution after loading (Pa).
It can be observed that the stress in the specimens is primarily compressive. The phenomenon of stress concentration often occurs in the internal regions of the pile, roughly presenting as vertically banded shapes. The stress values in the pile are lower on both sides and gradually increase in the internal regions. The areas with lower stress values generally correspond to regions with larger porosities.
The maximum compressive stress values for the four groups of specimens increase with the higher cement content. The maximum compressive stress that the material can withstand increases with the higher cement content, indicating a gradual enhancement of the pile’s bearing capacity. This observation indirectly suggests that the numerical model can realistically reflect the mechanical properties of the pile.
Failure characteristics
To further investigate the failure state of the pile material, images of the specimens at the point of failure were extracted from the software and compared with the experimental failure patterns in the laboratory, as shown in Fig. 12. There is a widespread occurrence of particle spalling at the edges of each specimen. Additionally, microcracks are present inside the pile, gradually accumulating and eventually penetrating the entire pile. Some regions in the numerical experiment did not completely match the experimental failure patterns in the laboratory. This discrepancy is attributed to the “clamping” effect on the specimen ends by the testing machine during the loading process in the laboratory experiment, which influences the strength and failure characteristics of the specimen. This effect was not replicated in the numerical experiment.
Sample failure characteristics.
With the increase in cement content, the speed of specimen failure at the end has increased, corresponding to the characteristic of an increased descent rate in the stress-strain curve. At the same time, the decrease in peak strain results in an earlier onset of failure. The material exhibits more brittle characteristics. The failure mode in the uniaxial compression test of the specimens mainly manifests as splitting failure.
Coordination number
In PFC, the average contact number of model particles is referred to as coordination number, which indicates both the compactness of model particles and reflects the material strength and stiffness characteristics of the model.
Coordination number and time step.
During the simulated loading process, the coordination number of the pile constantly changes. The curves depicting the variation of coordination numbers with time steps for each group of specimens are shown in Fig. 13. As the loading time progresses, the coordination number of the pile first decreases slowly and then suddenly drops significantly. For the pile with 40% cement content, the initial coordination number is approximately 4.18. After a slow decrease to around 4.15, the coordination number experiences a “cliff-like” drop, indicating the occurrence of pile failure. Moreover, it can be observed from the graph that in the initial stage of loading, the higher the cement content, the slower the decrease in the coordination number of the pile. This suggests that with an increase in cement content, the load-bearing capacity of the specimen gradually strengthens. In addition, it can be observed that the coordination numbers for the other three groups are all greater than that of the 25% group. Specifically, the coordination number of the 35% cement content specimen is smaller than that of the 30% group. The reason is that during the loading process, the pile of the 35% group accumulates micro-cracks continuously, coincidentally forming a through crack and leading to premature failure. This results in insufficient overall loading on this specimen.
The coordination number characterizes the amount of contact between particles and therefore has a certain relationship with the porosity of the material. By comprehensive comparison of Figs. 10 and 13, it can be found that when the cement content is higher, the porosity of the specimen is lower, the number of contacts between particles is higher, and the coordination number is higher. When bearing loads, the lower the porosity, the higher the strength of the specimen, the stronger its resistance to failure and deformation, the less likely micro-cracks are to appear inside, and the more difficult the contact between particles is to be destroyed, so the higher its coordination number. It can also be found from the comparison of Fig. 14 that the higher the cement content, the lower the porosity, the denser the structure, and the more prone to brittle failure, resulting in penetrating cracks. After the destruction, the residual block can still maintain integrity, and the porosity is still low, so its coordination number is still high.
Crack number and time step.
Fracture number
During the loading process, cracks accumulate continuously. The number of cracks can indirectly reflect the damage characteristics of the specimen under load. Therefore, the curves depicting the number of cracks over time steps and after loading are presented in Fig. 14, respectively. It can be observed that the pile with 25% cement content develops cracks rapidly in the early stages of compression and reaches the maximum crack value earlier, leading to the failure of the pile. The piles with 30% and 35% cement content exhibit similar crack development rates. In contrast, the specimen with 40% cement content has the slowest crack development rate. As the cement content increases, the crack development in the early stages of loading becomes slower, indicating that increasing cement content contributes to enhancing the load-bearing capacity of the pile and delaying the occurrence and development of cracks.
The rapid increase in crack numbers during the post-peak stage (Fig. 14) correlates with destabilization of the pile core. As fractures coalesce into penetrating surfaces, porosity localizes in weakened zones (Fig. 10), redirecting energy from uniform core expansion to localized failure. This phenomenon is further validated by coordination number trends (Fig. 13), where abrupt particle contact loss coincides with core fragmentation. These results emphasize that post-peak crack dynamics dominate the structural integrity of the pile core, necessitating careful cement content optimization to balance strength and ductility.
Conclusion
This study investigates the mechanical properties of Metro Jet System (MJS) piles through full-scale experiments and numerical simulations, focusing on the influence of cement content, pile non-uniformity, and surrounding soil characteristics. The key findings and innovations are summarized as follows:
(1) The stress-strain relationship of MJS piles exhibits strain-softening behavior. Higher cement content increases post-peak brittleness, leading to more abrupt failure due to the presence of micro-defects.
(2)Compressive strength and elastic modulus increase with cement content, as more hydration products enhance pile density and strength. The study confirms that pile strength is primarily governed by cement content rather than surrounding soil strength.
(3) MJS piles exhibit significant radial non-uniformity. Strength is highest at the pile core and decreases outward, due to the outward diffusion of cement slurry under high grouting pressure. This highlights the need to account for strength variations in engineering design.
(4) Discrete element simulations reveal that higher cement content reduces initial coordination number loss, slows crack development, and increases peak axial stress. An empirical formula for compressive strength prediction is proposed and validated against experimental results.
(5) Uniformity in MJS piles is achievable through a combination of optimized jetting parameters, controlled cement ratios, real-time monitoring, and rigorous post-construction verification. While radial non-uniformity remains inherent due to pressure attenuation, our findings emphasize that centralizing high-cement zones and adjusting grouting protocols can significantly enhance homogeneity. Future work will integrate machine learning for dynamic parameter optimization during construction.
Data availability
Data will be made available by the corresponding author on request.
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Chunting Lu: Methodology, Investigation, Data Curation, Writing-Original Draft. Baoli Wei: Funding Acquisition, Methodology, Supervision Conceptualization. Zhijun Zhou: Review and Editing.
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Lu, C., Wei, B. & Zhou, Z. Research on the influencing factors of the mechanical properties of metro jet system by full-scale test. Sci Rep 15, 18228 (2025). https://doi.org/10.1038/s41598-025-00190-4
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DOI: https://doi.org/10.1038/s41598-025-00190-4
