Study on static characteristics of a novel prestress-reinforced railway subgrade

Abstract

Understanding the reinforcement effect of the newly developed prestressed reinforcement components (PRCs) (a system composed of prestressed steel bars (PSBs), protective sleeves, lateral pressure plates (LPPs), and anchoring elements) is technically significant for the rational design of prestressed subgrade. A three-dimensional finite element model was established and verified based on a novel static model test and utilized to systematically analyze the influence of prestress levels and reinforcement modes on the reinforcement effect of the subgrade. The results show that the PRCs provide additional confining pressure to the subgrade through the diffusion effect of the prestress, which can therefore effectively improve the service performance of the subgrade. Compared to the unreinforced conventional subgrades, the settlements of prestress-reinforced subgrades are reduced. The settlement attenuation rate (R_s) near the LPPs is larger than that at the subgrade center, and increasing the prestress positively contributes to the stability of the subgrade structure. In the multi-row reinforcement mode, the reinforcement effect of PRCs can extend from the reinforced area to the unreinforced area. In addition, as the horizontal distance from the LPPs increases, the additional confining pressure converted by the PSBs and LPPs gradually diminishes when spreading to the core load bearing area of the subgrade, resulting in a decrease in the R_s. Under the single-row reinforcement mode, PRCs can be strategically arranged according to the local areas where subgrade defects readily occurred or observed, to obtain the desired reinforcement effect. Moreover, excessive prestress should not be applied near the subgrade shoulder line to avoid the shear failure of the subgrade shoulder. PRCs can be flexibly used for preventing and treating various subgrade defects of newly constructed or existing railway lines, achieving targeted and classified prevention, and effectively improving the bearing performance and deformation resistance of the subgrade. The research results are instructive for further elucidating the prestress reinforcement effect of PRCs on railway subgrades.

Introduction

The high-speed passenger transport and heavy haul freight are the mainstream directions for the development of China’s railway industry, which also put forward higher requirements for the service performance of railways. In recent years, with increases in train axle loads, formation length, and operation speed, railway subgrades that meet current design and construction standards may still experience varying degrees of deterioration and damage (e.g., subgrade settlement, subgrade extrusion deformation, and, slope collapse) because of the insufficient soil confining pressure or a lack of lateral constraints on subgrade slopes [1, 2, 3, 4, 5, 6, 7–8].

For various types of subgrade defects, the commonly used improvement and treatment methods include subgrade replacement, jet-grouting columns, micro-piles, geogrids, grouting, etc. [9, 10, 11, 12, 13, 14–15]. Esmaeili and Khajehei [7] analyzed the performance of cement–soil mixing piles reinforced loose sandy subgrades using a scaled model test, revealing that the reinforcement structure significantly enhanced the bearing capacity and effectively reduced the settlement of the subgrade. Luo et al. [16] investigated the optimal replacement thickness for high-speed railway subgrades with the control objective to stabilize the subgrade cumulative deformation, and found that the required replacement thickness of the soft rock cutting bed displayed a nonlinear increasing trend with the decrease in rock strength. Alamshahi and Hataf [17] and Choudhary et al. [18] employed numerical simulations and model tests on geogrid-reinforced slopes, and the results demonstrated that adding geogrids effectively improved the slope stability. Bian et al. [19] conducted full-scale model tests and numerical analyses of ballastless track subgrade, and pointed out that grouting materials could effectively strengthen the degraded subgrade soil and reduce the vibration velocity of the track structure. Yang et al. [20] investigated the reinforcement effect of geocell chambers and analyzed the attenuation of dynamic response of the geocell chamber reinforced ground under moving loads. Chawla and Shahu [21] conducted monotonic and cyclic tests on reinforced track models and found that placing geosynthetics in the subgrade could control the development of cumulative deformation of the subgrade. Ding et al. [22] investigated the effect of geotextiles on the mud pumping phenomenon of a subgrade and found that geotextiles could reduce the pore water pressure and cumulative deformation of the subgrade.

The traditional reinforcement methods suffer from disadvantages of high workload, long construction period, high cost, and the tendency to affect or even interrupt the normal train operation. To save resources and protect the environment, Leng et al. [23] proposed a new type of prestressed reinforcement components (PRCs) (a system composed of prestressed steel bars (PSBs), protective sleeves, lateral pressure plates (LPPs), and anchoring elements) (see Fig. 1) that can strengthen the subgrade and treat subgrade defects by increasing soil confining pressure and providing lateral constraints without interrupting train operations. By tensioning prestressed steel bars, the pre-tension forces are converted into surface loads acting on the subgrade slope surface through the LPPs and diffused into the interior of the subgrade, promoting the prestressed reinforcement components and the subgrade work as an integrated system [24, 25]. This novel subgrade reinforcement technology can be used for both existing and newly constructed railway lines. The most prominent advantage is that the PRCs can be prefabricated and conveniently installed on the subgrade slopes, eliminating the need for large machinery and reducing machinery rental and labor cost, which therefore effectively shortens the reinforcement construction period and also avoids traffic suspension. This is extremely important for busy transportation lines and offers significant economic and social benefits. Preliminary comparisons have shown that the direct cost of using prestressed reinforcement components to strengthen subgrades is 20% to 50% less than conventional subgrade reinforcement methods (such as replacement, grouting, and utilization of geosynthetics) [26]. Besides, the PRCs do not require utilizing water or cement mortar during the construction process, and thereby can avoid softening or polluting the subgrade soil, and the prefabricated prestressed reinforcement components (e.g., steel bars and LPPs) are not easily corroded, with no adverse impact on the subgrade soil and groundwater during operation service. The PRCs are in line with the development trend of ‘green and environmentally friendly’ subgrade reinforcement technology by reducing harmful substances generated (e.g., effluents, emissions, and waste) during the subgrade reinforcement process. Additionally, during operation and maintenance, it is also convenient to supplement the lost prestress and replace the damaged PRCs, which provides long-term stable reinforcement effect and has the advantage of sustainable development. Compared to conventional subgrades, the novel prestressed subgrade has characteristics as shown in Fig. 2. Currently, existing studies regarding the prestressed subgrade mainly focus on the additional stress diffusion law and its distribution characteristics [24], the stability analysis methods of prestressed subgrade [25], the spacing design method for LPP layout [27], and analytical method for the prestress loss [28].

Fig. 1 [Images not available. See PDF.]

Schematic diagram of a new prestressed subgrade

Fig. 2 [Images not available. See PDF.]

Characteristics of the novel subgrade reinforcement structure. PRCs stands for the prestressed reinforcement components

Studying the static behavior of railway subgrades is crucial for their structural design and important for demonstrating their service performance, among which the subgrade settlement is a primary indicator and evaluation parameter in static tests. Li et al. [29] investigated the effect of fiber reinforcement on subgrade settlement under a static load of 100 kPa through model tests, discovering a 30.8% reduction in the total settlement of the fiber-reinforced subgrade compared to the unreinforcement model. Lee et al. [30] conducted full-scale subgrade static load model tests on subgrade structures with a thin layer of asphalt concrete and found that the asphalt concrete markedly mitigated the impact of train loads on the subgrade, thereby improving the service life of the track structure. Through field tests, Huang et al. [31] noted that the long-term settlement of the transition section between the frame culvert and subgrade filled with foam concrete is much less than that of an ordinary subgrade transition section. By performing scaled model tests and finite element analyses, Esmaeili et al. [11] found that placing geogrids inside the subgrade can effectively improve subgrade stability and reduce subgrade settlement. Huang et al. [32] conducted full-scale model tests, with results showing that compared to the traditional ballastless track subgrades, the use of foam concrete as subgrade filler can provide a better static stress diffusion effect, which is beneficial for the smooth operation of the railway line. Lu et al. [33] conducted field static load tests on a high-speed railway constructed on pile-grid composite foundation and found that the upper load is mainly borne by the piles. However, the previous studies on the static characteristics of railway subgrade are mostly limited to conventional or traditional subgrade reinforcement methods, research on the static performance of prestress-reinforced railway subgrades is less reported.

In this work, we established a three-dimensional (3D) finite element model (FEM) of the prestressed subgrade and completed its verification based on an independently developed static model test system. The model was then used for multi-condition simulation analyses. The simulation results demonstrated the influence of prestress level and reinforcement modes (i.e., unreinforcement, multi-row reinforcement, and single-row reinforcement) on the static characteristics of the subgrade. In addition, preventive and control measures for subgrade defects of existing and new lines are proposed to provide reference for the design of prestressed subgrade.

Static loading test for prestressed subgrade

To investigate the influence of PRCs (including PSBs, protective sleeves, LPPs, and anchoring elements) on the bearing and deformation performance of subgrade, Zhang et al. [34] performed a strip load plate test on a prestressed subgrade model. Figure 3 shows the layout of the model test. As depicted in Fig. 4, the prestressed subgrade model has specific dimensions as follows: the top width is 1.66 m, the bottom and foundation widths are 3.66 m, the longitudinal length is 2.70 m, and the slope ratio is 1:1.0. The subgrade consists of four layers from top to bottom, i.e., the subgrade bed surface layer (thickness: 0.12 m), the subgrade bed bottom layer (thickness: 0.38 m), the subgrade body layer (thickness: 0.50 m), and the foundation layer (thickness: 0.20 m). The surface and bottom layers of the subgrade bed were filled with Group A fine breccia soil, while the subgrade body and foundation layers were filled with Group B3 fine breccia soil with different gradations. The side length of the squire LPP is 0.28 m, and five rows by five columns of LPPs were arranged on each side of the subgrade slope. The subgrade model was filled in a ‘sandwich structure’ of unreinforced zone, prestress-reinforced zone, and unreinforced zone along the longitudinal direction. The length of the reinforced area is 1.40 m, and the length of the unreinforced zones on both sides is 0.65 m. (see Fig. 4b).

Fig. 3 [Images not available. See PDF.]

Layout of load plate test

Fig. 4 [Images not available. See PDF.]

Cross (longitudinal)-section size of prestressed subgrade (unit: cm): a cross-section layout; b longitudinal layout

Figure 5 displays the newly developed static loading system for the prestressed subgrade model, mainly composed of a hydraulic jack, reaction frames, datum beam, and dial gauges, enabling a control process of gradual loading, load stabilization, and step-by-step unloading. The track structure and train loads were applied according to the conversion soil-column method as outlined in the Chinese Code for Design of Heavy Haul Railway (TB 10625–2017) [35]. The covering width on the subgrade surface by extending the sleeper ends downward at an angle of 45° was designated as the width of loading area. According to the Buckingham Pi theorem [36, 37], the distribution width of the load on the subgrade surface was scaled to 0.74 m. An H-steel beam, measuring 0.74 m by 0.30 m (length by width), was utilized as the strip load plate. The strip load plate test was applied step-by-step with 10 graded loads, each with an increment of 50 kPa. This loading scheme refers to the general K₃₀ detection procedure of the subgrade structural layers, with the aim of ensuring the subgrade is within the elastic state and effectively comparing and evaluating the reinforcement effect of the prestressed structures. In the model test, dial gauges were used to measure the vertical deformation of the prestressed subgrade surface, and the specific locations are presented in Fig. 3. It is important to note that the dynamics and external environmental factors both affect the static performance of the new prestressed subgrade. Because of the limitations of test equipment, e.g., the lack of environmental simulation platforms in the laboratory, the current study conducted static load model tests, without considering the coupling effect of the aforementioned factors. In subsequent research, it is desirable to utilize dynamic loading devices and environmental simulation platforms to further explore the operational performance of the prestressed subgrade under different conditions.

Fig. 5 [Images not available. See PDF.]

Static loading system of prestressed subgrade

Numerical model of prestressed subgrade

Geometric dimensions and parameters of the model

Although the model test could reflect the static deformation behavior of the prestressed subgrade, the measurement points are generally limited to the outline of the subgrade. To further investigate the reinforcement effect of PRCs on the interior of the subgrade, a 3D FEM of the prestressed subgrade is established based on the developed static load model test system, using the ABAQUS finite element software. The present study analyzes the influence of prestress level and reinforcement modes (unreinforcement, multi-row reinforcement, and single-row reinforcement) on the static characteristics of the subgrade. The structural layers of the subgrade, including a subgrade bed surface layer, a subgrade bed bottom layer, a subgrade body layer, and a foundation layer, are all modeled using an elastoplastic constitutive model based on the Mohr Coulomb yield criterion. Since the model test does not lead to plastic behavior of the LPPs and PSBs, both are simulated using an elastic constitutive model. The deformation parameters (i.e., elastic modulus (E) and Poisson’s ratio (µ)) adopted for the prestressed subgrade fillers were determined by referring to the Code for Design of Concrete Structures (GB50010-2010) [38] and a large number of literature (e.g., Refs. [39, 40, 41, 42–43]) regarding the common range of deformation parameters for the Group A and B fillers in conjunction with the compaction quality, while the strength parameters (i.e., the cohesion (c) and internal friction angle (φ)) regarding the total stress condition were obtained using laboratory direct shear tests. The specific constitutive parameters are listed in Table 1. Furthermore, it should be noted that the fillers with optimum moisture contents (w_opt) were used to fill the subgrade model, which were 6.80%, 6.41%, and 7.17% for the subgrade bed layer, the subgrade body layer, and the foundation layer, respectively, resulting in a relatively low moisture condition that was far away from saturation for the subgrade model. For soil layers with moisture content well below saturation, numerical analyses can be performed under total stress conditions using total stress strength parameters obtained from laboratory direct shear tests. This approach aligns with the commonly used assumption when analyzing the static and dynamic performance of subgrades in existing studies [44, 45].

Table 1. Material properties of the prestressed subgrade model

Components	Elastic modulus E (MPa)	Poisson’s ratio µ	Density ρ (kg·m−3)	Cohesion c (kPa)	Frictional angle φ (°)
Lateral pressure plate	32,500	0.20	2,400	N/A	N/A
Prestressed steel bar	200,000	0.25	7,850	N/A	N/A
Subgrade bed surface layer	195	0.30	2,300	69	43
Subgrade bed bottom layer	195	0.30	2,300	69	43
Subgrade body	150	0.30	2,250	46	37
Foundation	135	0.30	2,175	41	32

Element types and boundary conditions

The LPPs and subgrade structural layers are meshed using eight-node linear brick reduced integration (C3D8R) elements, which can prevent unexpected element shear locking, making them appropriate for nonlinear analyses with adequate accuracy and widely employed in a number of similar numerical simulations implemented using ABAQUS [46, 47]. For the PSBs, 3D two-node truss (T3D2) elements are used (see Fig. 6) with a diameter of 12 mm. Considering the more pronounced deformation in the loading area, the mesh there was refined for enhancing the computation accuracy. In Fig. 6, the X-axis denotes the cross-sectional direction of the line, the Y-axis denotes the longitudinal direction, and the Z-axis denotes the vertical direction. The boundary conditions of the model are as follows: a fixed boundary is adopted at the model bottom, and the normal displacement of longitudinal and lateral surfaces of the model is constrained.

Fig. 6 [Images not available. See PDF.]

Finite element mesh for the prestressed subgrade

Prestress simulation method

In the prestressed subgrade model test, the outer sleeves separated the steel bars from the subgrade soil; it therefore can be considered that the steel bars were in an unbound mode with the soil. The ABAQUS can achieve free sliding between prestressed steel bars and subgrade soil by introducing virtual prestressed steel bars and setting local coordinate systems [48]. Furthermore, the bolt load method provided in ABAQUS is employed to simulate the tensioning and locking processes of the PSBs [49] because it can maintain a constant prestress level in the computing process while satisfying the compatibility deformations between steel bar and subgrade soil.

Notably, to avoid sliding of the LPPs along the subgrade slope during the application of prestress, the contact position between the LPPs and the slope surface is designed as ‘stepped’ shape (see Fig. 7), which is helpful for stably applying lateral constraints to the subgrade. In view of this, the contact relationship between the LPPs and the subgrade soil in the FEM is set to a ‘hard contact’ mode, and the tangential relationship is set to a ‘rough contact’ mode.

Fig. 7 [Images not available. See PDF.]

Prestressed reinforcement components (PRCs)

Calculation conditions for prestressed subgrade

The present study focuses on exploring the influence of prestress level and the LPP reinforcement position on the static characteristics of the subgrade (see Fig. 8). According to the Chinese Code for Design of Heavy Haul Railway (TB 10625–2017) [35], the uniformly distributed static load on the subgrade surface subjected to a heavy haul train with an axle load of T = 27 t is 68 kPa. Xu et al. [50] and Dong et al. [51] noted that when the distance between the LPPs and the shoulder line is less than twice the LPP width, the subgrade shoulder is prone to ‘upward arching shear failure.’ To avoid soil failure at the shoulder position, the prestress of the first row of PSBs is set as 50% of the other rows, as detailed in Table 2 for specific simulation conditions.

Fig. 8 [Images not available. See PDF.]

Schematic diagram of simulation calculation conditions

Table 2. Numerical simulation cases

No.	Reinforcement mode	Reinforcement position	Axle load T (t)	Prestress Pre (kPa)
C1	Unreinforcement subgrade	N/A	27	N/A
C2	Multi-row reinforcement mode	The first, second, third, fourth, and fifth rows		25, 50, 75, and 100
C3	Single-row reinforcement mode	Only the first row		25, 50, 75, and 100
C4	Single-row reinforcement mode	Only the second row		25, 50, 75, and 100
C5	Single-row reinforcement mode	Only the third row		25, 50, 75, and 100
C6	Single-row reinforcement mode	Only the fourth row		25, 50, 75, and 100
C7	Single-row reinforcement mode	Only the fifth row		25, 50, 75, and100

Model validation

To verify the reliability of the numerical model, the calculated settlement results at three test points (S1, S2, and S3, see Fig. 3) in the strip load plate test are compared with the measured results, as shown in Fig. 9, where the final load value acting on the strip load plate is 500 kPa. From the test data, it is evident that under two sets of prestressed conditions (P_re = 50 and 100 kPa), the settlement at the middle position (S2) of strip load plate was significantly greater than at the end positions (S1 and S3). Under the prestress level of 50 kPa, the settlements at the three points were 0.586 mm (S1), 0.847 mm (S2), and 0.593 mm (S3), respectively. In contrast, the settlements at each point under prestress of 100 kPa were 95.2% to 97.5% of those under prestress of 50 kPa. The settlement values had all decreased, indicating that the prestress reinforcement played a positive role in controlling the subgrade deformation and improving its deformation resistance. A comprehensive analysis of the numerical simulation and model test results indicates consistent trends and high numerical credibility, demonstrating the effectiveness of the numerical model herein.

Fig. 9 [Images not available. See PDF.]

Comparison of the results from the numerical simulation and scale model test

Analysis of the effect of prestress reinforcement effect

Lateral restraint of PRCs

The prestressed subgrade uses PSBs to pull the LPPs (with a side length of L) on both sides of the subgrade, converting the horizontal pre-tension force F of the PSB into a surface load q acting on the subgrade slope, transmitting the prestress to the interior of the subgrade, and amplifying the lateral pressure exerted on the soil [52]. As shown in Fig. 10, the mechanical model of the prestressed subgrade showcases how LPPs convert the concentrated pre-tension force into horizontal pressures, thereby facilitating the spread of additional stress within the subgrade.

Fig. 10 [Images not available. See PDF.]

Mechanical model schematic diagram of a prestress subgrade

Figure 11 presents the contour maps of lateral stress on the subgrade slope surface beneath the coverage area of a single LPP for prestress levels of 50 kPa and 100 kPa, showing that the applied pre-tension force F of the PSB has been converted into a surface pressure acting on the slope surface. Figure 12 shows the lateral displacement distribution on the slope surface just beneath the coverage area of a single LPP for prestress levels of 50 kPa and 100 kPa. It is found that applying prestress results in a ‘lateral contraction’ effect on the subgrade slope. Except the corners of the LPP, the lateral displacement in the middle area of the plate bottom is relatively uniform. Specifically, under the prestress level of 50 kPa, the lateral displacement measures 0.065 mm which increases to 0.130 mm when the prestress level is raised to 100 kPa. This indicates that the application of prestress can provide effective lateral constraints for the subgrade slope, thereby enhancing the service performance of the subgrade.

Fig. 11 [Images not available. See PDF.]

Contour maps of lateral stress on the subgrade slope surface beneath the coverage area of a single LPP: a prestress P_re = 50 kPa; b prestress P_re = 100 kPa

Fig. 12 [Images not available. See PDF.]

Lateral displacement on the subgrade slope surface beneath the coverage area of a single LPP: a prestress P_re = 50 kPa; b prestress P_re = 100 kPa

Analysis of the reinforcement effect with multi-row reinforcement mode

Figure 13 presents the variation curves of the lateral displacement along the subgrade slope direction at the longitudinal middle section (Y = 1.35 m) of the unreinforced and multi-row reinforced subgrades. Within the range of 0 to 0.26 m from the shoulder position along the slope direction, the unreinforced subgrade slope surface experiences ‘internal contraction deformation,’ with a maximum internal shrinkage deformation of 0.039 m at the shoulder position. As the distance from the shoulder increases, the inward shrinkage deformation gradually decreases, and the slope surface changes from ‘inward shrinkage deformation’ to ‘outward extrusion deformation’ at a distance of 0.26 m from the shoulder. This shift indicates that a conventional subgrade undergoes settlement under upper loads, subsequently causing lateral extrusion at the lower part of the subgrade slope, with a maximum extrusion deformation of 0.032 mm. In contrast, owing to the constraining effect of PRCs, the horizontal extrusion force within the subgrade under vertical static loads can be jointly borne by the subgrade, LPPs, and PSBs. The tensile resistance of the PSBs and the additional confinement provided by the LPPs enhance the lateral deformation resistance of the subgrade, resulting in an overall ‘internal contraction deformation’ of the subgrade slope (see Fig. 13). In addition, the amount of internal shrinkage deformation increases with the increase in prestress level. For instance, at a distance of 0.707 m away from the shoulder line, the internal contraction deformations measure 0.111, 0.239, 0.367, and 0.508 mm under prestress levels of 25, 50, 75, and 100 kPa, respectively.

Fig. 13 [Images not available. See PDF.]

Lateral displacement of subgrade slope surface (Y = 1.5 m)

In summary, the PRCs play a vital role of ‘active confinement,’ which can improve the overall service performance of the subgrade and mitigate the ‘external extrusion deformation’ of the subgrade slope through the diffusion effect of prestress. It is worth noting that even when no prestress is applied, due to the anchoring connection of the PSBs and LPPs, the LPPs pulling by the PSBs could act akin to a ‘passive retaining wall’ in case active sliding or slippage occurs in the subgrade soil, still providing good passive protection and effectively preventing the sliding damage of the subgrade.

Figure 14 illustrates the settlement distribution of the conventional subgrade surface under load. Figure 15 presents the settlement contour map at the longitudinal middle section (Y = 1.35 m) of the unreinforced subgrade model. It can be seen that the settlement of the subgrade surface along the cross-sectional direction exhibits a significant non-uniform distribution pattern, with the overall surface showing a concave distribution, and the maximum settlement value being 0.322 mm. The settlement values show a decreasing trend along the cross-section and subgrade depth directions. Considering the limited load application area, the present study takes the 0.74 m wide loading range (see Fig. 15) as the main load bearing area of the subgrade to further investigate the effect of prestress reinforcement.

Fig. 14 [Images not available. See PDF.]

Settlement distribution of conventional subgrade surface under load

Fig. 15 [Images not available. See PDF.]

Contour map of longitudinal middle section settlement of the line (Y = 1.35 m)

Figure 16 depicts the settlement curves of the main load bearing area of the subgrade under different prestress levels, demonstrating that the subgrade surface settlement under different conditions has a ‘U-shaped’ symmetrical distribution with generally consistent variation patterns. The maximum settlement occurs at the center of the subgrade surface, with values of 0.322 mm (conventional subgrade), 0.306 mm (P_re = 25 kPa), 0.294 mm (P_re = 50 kPa), 0.281 mm (P_re = 75 kPa), and 0.266 mm (P_re = 100 kPa). Compared to the conventional subgrade, the settlement of the prestressed subgrade is reduced, indicating that the PRCs can improve the deformation performance of the subgrade with a total settlement and uneven settlement reduction effect of the subgrade surface. Moreover, as the prestress increases, the settlement reduction effect becomes more pronounced, which can effectively alleviate the excessive subgrade settlement caused by transportation capacity expansion (e.g., increasing train axle load).

Fig. 16 [Images not available. See PDF.]

Settlement of subgrade surface under different prestress levels

To better evaluate the improvement effect of PRCs on the subgrade, a settlement attenuation rate (R_s) is introduced to quantitatively analyze the settlement reduction effect of the subgrade under different reinforcement conditions. The definition is as follows:

1

$$R_{\text{s}}=\frac{\left(S_{\text{c}}-S_{\text{p}}\right)}{S_{\text{c}}}\times 100\%,$$where S_c and S_p are the settlements of the conventional subgrade prestressed subgrade under static load, respectively.

Figure 17 shows the variation curves of the R_s of the subgrade surface under different prestress levels with multi-row reinforcement mode. The R_s curves exhibits a symmetrical distribution pattern with larger values at the ends and lower values in the middle, demonstrating that the reinforcement effect is more pronounced near the LPPs. Moreover, the R_s at the center positon increased from 4.79% to 17.44% when the prestress rose from 50 to 100 kPa, implying that increasing the prestress has a positive effect on maintaining the deformation stability of the subgrade.

Fig. 17 [Images not available. See PDF.]

Settlement attenuation rate (R_s) of subgrade surface under different prestress levels

To further explore the diffusion effect of prestress, contour lines of the R_s at the subgrade surface are plotted for both the reinforced and unreinforced areas, as presented in Fig. 18. The figure demonstrates that the R_s of the middle area reinforced by the prestress is greater than those of both sides, and the attenuation rate contour lines display an ‘unimodal’ distribution pattern along the longitudinal direction. Under different prestress levels, the maximum values of the R_s contour lines in the reinforced area are 7.12% (P_re = 25 kPa), 13.38% (P_re = 50 kPa), 19.53% (P_re = 75 kPa), and 27.33% (P_re = 100 kPa). In this study, an R_s of 15% is taken as the dividing line. As the prestress increases, the area covered by the contour lines with R_s values greater that 15% gradually expands, and this area almost crosses the whole subgrade surface when the prestress is increased to 100 kPa. The R_s contour lines can transition from the reinforced area to the unreinforced area, implying that the unreinforced area also benefits from the reinforcement of PRCs. These characteristics further demonstrate that increasing prestress can effectively improve the reinforcement range, and the additional stress provided by the PRCs can diffuse from the reinforcement area to the unreinforced area. In engineering design, by reasonably arranging the reinforcement areas, the amount and cost of reinforcement work can be optimized while maintaining a certain reinforcement effect.

Fig. 18 [Images not available. See PDF.]

Contour lines of subgrade surface settlement attenuation rate (R_s) under different prestress levels: aP_re = 25 kPa; bP_re = 50 kPa; cP_re = 75 kPa; dP_re = 100 kPa

The contour lines of the R_s at the longitudinal middle cross section (Y = 1.35 m) of the main load bearing area are presented in Fig. 19. It can be seen that at the same depth below the subgrade surface, the R_s exhibits a ‘convex single-peak’ curve distribution with higher values at both ends and lower values at the center, and the R_s gradually decreases along the depth direction. At the subgrade bed layer bottom, the R_s are 1.82%, 2.15%, 2.50%, and 4.70% for prestress levels of 25, 50, 75, and 100 kPa, respectively. The main reason for these relative small R_s values is that the horizontal distance of the main load bearing area to the subgrade slope surface increases with an increase in the subgrade depth. As a result, the additional confining stress provided by the PRCs gradually attenuates when it spreads to the main load bearing area (see Fig. 19) of the subgrade. To increase the reinforcement effect at the subgrade bed bottom, it is possible to appropriately increase the prestress value for existing subgrades. As for newly constructed subgrades, increasing the subgrade slope ratio can be an alternative measure to improve the reinforcement effect by reducing the horizontal distance between the main load bearing area and the subgrade slope surface (i.e., increasing the slope ratio of the reinforced subgrade).

Fig. 19 [Images not available. See PDF.]

Contour lines of subgrade settlement attenuation rate (R_s) in the main load bearing area (Y = 1.35 m) under different prestress levels: aP_re = 25 kPa; bP_re = 50 kPa; cP_re = 75 kPa; dP_re = 100 kPa

Influence of position of single-row PRCs

This section focuses on analyzing the differentiated reinforcement effect of different placement positions of the single-row PRCs (see Fig. 8). Figure 20 displays the vertical displacement curves of the subgrade surface under the single-row reinforcement mode with prestress levels of 50 kPa and 100 kPa. It is found that the application of prestress can result in uplift deformation of the subgrade surface. Notably, the first and second rows of PRCs are close to the subgrade shoulder. When applying prestress, the vertical deformation of the subgrade surface shows a significant ‘concave’ distribution feature. Specifically, when the prestress is applied only at the first row position, the subgrade surface displays downward settlement near the centerline, while uplift deformation occurs near the subgrade shoulder. The staggered deformation pattern of uplift deformation and downward settlement is likely to cause soil cracking or even damage. Therefore, excessive prestress should not be applied to the positions near the subgrade shoulder.

Fig. 20 [Images not available. See PDF.]

Vertical displacement of subgrade surface: a prestress P_re = 50 kPa; b prestress P_re = 100 kPa

Considering that the first and second rows of PRCs are close to the shoulder position, the following analyses focus solely on the reinforcement effect of the third, fourth, and fifth rows of PRCs under the single-row reinforcement mode. The settlement attenuation rate curves of the target reinforcement area (i.e., the main load bearing area) at different reinforcement positions under prestress levels of 25, 50, 75, and 100 kPa are shown in Fig. 21. It can be seen that the settlement attenuation rate of the subgrade surface near the LPPs is larger than that of the central load bearing position that is further away from the slope. Furthermore, with increasing the prestress, the curves generally shift upward. These characteristics are consistent with the observations in the multi-row reinforcement mode. The reinforcement effect in the single-row mode is ranked as 3rd row > 4th row > 5th row. Owing to the greater distance from the subgrade surface, the reinforcement effect of the 5th row PRCs on the target area is weaker compared to the 3rd and 4th rows of PRCs, while the difference in the reinforcement effect of the 3rd and 4th rows of PRCs is relatively small. According to Figs. 17 and 21, it can be found that the reinforcement effect on the subgrade surface under the multi-row reinforcement mode is much better than that under the single-row reinforcement mode, due to the ‘diffusion effect’ and ‘superposition effect’ of the prestress.

Fig. 21 [Images not available. See PDF.]

Settlement attenuation rate (R_s) at different reinforced positions: aP_re = 25 kPa; bP_re = 50 kPa; cP_re = 75 kPa; dP_re = 100 kPa

Figure 22 presents the contour lines of the settlement attenuation rate R_s of the subgrade surface under a prestress of 50 kPa, where the results show that for both the 3rd and 4th rows of PRCs in single-row reinforcement mode, the maximum R_s is around 5.5%. If taking the contour line with a R_s value of 5.0% as a benchmark, the enclosed area of the contour line moves downward as the placement position of the PRCs moves downward, indicating that the prestressed reinforcement area is significantly affected by the placement position of the PRCs. For sections with subgrade defects, strategically positioning PRCs in the target area may achieve a rational and effective reinforcement effect.

Fig. 22 [Images not available. See PDF.]

Contour lines of subgrade settlement attenuation rate (R_s) at different reinforced positions: a only the third row; b only the fourth row

Strategies for prevention and control of railway subgrade defects

Prevention of subgrade defects in existing railways

The present study investigated the reinforcement effect of the prestressed subgrade through finite element analyses, which further demonstrates the effectiveness and feasibility of using PRCs to reinforce railway subgrades. Taking a heavy haul railway in China as an example, in the construction stage, because of a lack of high-quality filling materials, the subgrade was filled with improved silt, and in some sections, gravel ballast layers was directly laid on the soil subgrade, which did not meet the current design standards and resulted in subgrade problems, such as large and uneven settlement of the subgrade, ballast collapse, and subgrade shoulder extrusion (see Fig. 23). If using the PRCs to reinforce the existing railway subgrades, it can break the restrictions of the maintenance ‘skylight time’ and avoid interruption of the train operation because the installations of the PRCs can be implemented on the subgrade slope. This has substantial economic and social significance for busy transportation lines. Moreover, the PRCs have the advantages of flexible installation and high construction efficiency as the components can be prefabricated in the factory and conveniently assembled on site.

Fig. 23 [Images not available. See PDF.]

Typical subgrade problems

Prevention of subgrade defects in new railway construction

Compared to existing subgrades, it is no need to drill holes to install PSBs in a newly constructed subgrade. The protective sleeves and PSBs can be arranged during the layered construction process of the subgrade. After the completion of subgrade filling, the steel bars are anchored and connected to the LPPs installed on both sides of the subgrade slope to form a prestressed subgrade structure.

As previously analyzed, the additional confining stress provided by the PRCs gradually attenuates as it diffuses to the interior of the subgrade (see Figs. 18 and 19). To shorten the prestress diffusion distance to the main load bearing area and effectively mobilize the reinforcement effect of the PRCs, the slope ratio of the newly constructed subgrade can be adjusted from 1:1.5 to 1:1.0 (or even 1:0.75) (see Fig. 24). Increasing the subgrade slope ratio is not only beneficial for achieving the desired reinforcement effect, but also can significantly diminish land occupation, earthwork filling, and the range of soft ground improvement below the subgrade, which is of great significance for the construction of railway subgrades in site restricted and facility intensive areas.

Fig. 24 [Images not available. See PDF.]

Increase the slope rate of the newly constructed subgrade

Conclusion

A novel prestressed railway subgrade reinforcement technique is introduced in this study. By establishing a 3D FEM of the prestressed subgrade and verifying it based on a scaled static load model test, the influence of the prestress level and reinforcement modes (unreinforcement, multi-row reinforcement, and single-row reinforcement) on the reinforcement effect of the subgrade was systematically analyzed. The main conclusions drawn from this study are as follows:

1. The PRCs, composing of LPPs, steel bars, and anchoring elements, play an ‘active confinement’ role and provide additional confining stress to limit the ‘extrusion deformation’ of the subgrade slope by applying prestress, thus enhancing the overall service performance of the subgrade.

2. The PRCs contribute a settlement reduction effect, which is more pronounced near the LPPs. At the subgrade surface center, the settlement attenuation rate R_s was 4.79% under a prestress level of 50 kPa, which would increase to 17.44% when the prestress rose to 100 kPa, indicating that increasing prestress can effectively mitigate excessive subgrade settlement caused by the expansion of transportation capacity.

3. The contour lines of the R_s at the subgrade surface could cover both the reinforced and unreinforced areas. In the main load bearing area, the R_s gradually diminishes as the depth from the subgrade surface increases. Effective reinforcement for the subgrade bed bottom may be achieved by increasing the prestress and subgrade slope ratio.

4. In the single-row reinforcement mode, the reinforcement effect of the middle two rows (i.e., the third and fourth rows) is better than that of the other three rows. The reinforcement area is affected by the placement position of the PRCs, and strategic reinforcement of the target area may be achieved by reasonably arranging the PRCs.

5. Applying PRCs to existing subgrades facilitates targeted and classified prevention and treatment of subgrade defects, without interrupting the normal train operation, which therefore has important economic and social significance. As for newly constructed subgrades, the prestress reinforcement effect can be improved by increasing the subgrade slope ratio, which is also helpful for reducing the land occupation, earthwork filling, and the soft ground improvement range below the subgrade base.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51978672 and 52308335), the Natural Science Funding of Hunan Province (Grant No. 2023JJ41054), the Natural Science Research Project of Anhui Educational Committee (Grant No. 2023AH051170).

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