On-Site Construction and Experimental Study of Prefabricated High-Strength Thin Concrete Segment Liners for the Reinforcement of Underground Box Culverts

Abstract

Conventional trenchless pipeline rehabilitation technologies are primarily designed for circular pipelines, with limited applicability to box culvert structures. Even when adapted, these methods often lead to significant reductions in the effective cross-sectional area and fail to enhance the structural load-bearing capacity due to geometric incompatibilities. To overcome these limitations, this study proposes a novel construction approach that employs prefabricated high-strength thin concrete segment liners for the reinforcement of underground box culverts. The feasibility of this method was validated through full-scale (1:1) experimental construction in a purpose-built test culvert, demonstrating rapid and efficient installation. A static stacking load test was subsequently conducted on the reinforced upper section of the culvert. Results indicate that the proposed reinforcement method effectively restores structural integrity and satisfies load-bearing and serviceability requirements, even after removal of the original roof slab. Additionally, a finite element analysis was performed to simulate the stacking load test conditions. The simulation revealed that variations in the mechanical properties of the grout between the existing structure and the new lining had minimal impact on the internal force distribution and deformation behavior of the prefabricated segments. The top segment consistently exhibited semi-rigid fixation behavior. This study offers a promising strategy for the rehabilitation of urban underground box culverts, achieving structural performance recovery while minimizing traffic disruption and enhancing construction efficiency.

1. Introduction

With the rapid advancement of urbanization, underground structures have become increasingly prevalent in civil engineering projects. Among these, municipal underground pipelines—constructed earlier than many modern standards—often preceded the development of normative design codes. After nearly half a century of service, these pipelines have experienced varying degrees of structural deterioration due to aging, environmental influences, and inadequate maintenance [1]. Many pipelines show signs of deformation and damage after 20 to 30 years of operation, posing significant risks to urban infrastructure.

Concrete box culverts are widely used in municipal underground pipe networks due to their minimal excavation requirements, ease of installation, simple cross-sectional geometry, and high spatial utilization. These culverts serve multiple purposes, including flood drainage, stormwater and sewage conveyance [2], large-capacity water storage, utility tunnels for electricity, telecommunications, heating, and gas, as well as underground pedestrian walkways and tundra passages. However, the rectangular geometry of box culverts results in non-uniform stress distribution, making them more prone to degradation under long-term loading compared to circular pipelines [3]. This is especially problematic for older culverts built with low design fortification standards and without adequate seismic protection measures, leading to accelerated structural deterioration and increasing threats to surface-level transportation safety [4].

Traditionally, the reinforcement of underground box culverts involves excavation along the road axis [5], followed by direct structural strengthening or retrofitting. In some cases, the load path is modified using cast-in-place slabs and newly installed bored piles to redistribute vertical loads away from aging culverts [6]. While effective, these interventions significantly disrupt road traffic and urban functionality [7]. In contrast, trenchless rehabilitation technologies offer clear advantages: low cost, minimal disruption to surroundings, faster implementation, and improved construction safety.

Trenchless technologies for pipeline rehabilitation have been widely applied for over 40 years and are considered mature [8]. Common methods include the sliplining method [9,10], traditional lining [11,12], cured-in-place pipe (CIPP) [13,14], spiral wound liners [15], and pipe bursting techniques [16,17]. While their mechanisms differ, these methods generally focus on reinforcing the inner surface of damaged pipelines—largely evolved from solutions for circular pipes. In terms of scope, they range from localized reinforcement to full structural lining. Cement-mortar lining, for example, has been used since the early 1900s for the rehabilitation of riveted steel pipes [18,19,20], and spray-applied cement mortar is now a mature repair method for underground pipelines [21]. Hsu et al. [22] validated CIPP through composite joint testing and showed it could restore hoop strength. Azoor and Benjamin [23] demonstrated that polymer spray-lined pipes maintained working pressure under load. Shou et al. [24] applied numerical modeling to explore the mechanical performance of pipelines repaired by CIPP and found it effective in reducing stress concentration. Allouche et al. [13] reported excellent long-term results in a pilot study evaluating CIPP liners after up to 25 years of service.

Among the newer approaches, the 3S (Simple See-through Segment) modular rehabilitation method, developed in Japan, has shown promise for square-section box culvert rehabilitation. While this method has been successfully applied in multiple countries, it still has limitations. Most existing trenchless methods—including CIPP, spraying, and spiral lining—were designed for circular pipes and remain semi-structural when applied to rectangular culverts. They often reduce the effective flow cross-section and cannot adequately restore structural load-bearing capacity. Therefore, it is of great importance to develop a new and efficient structural repair technology and verify its reliability and feasibility.

The Finite Element Method (FEM) has become a cornerstone in analyzing complex underground structures due to its ability to model irregular geometries, material nonlinearity, and soil-structure interactions. This review synthesizes recent advancements in FEM applications for underground box culverts, focusing on structural behavior analysis and progressive extension to reinforcement strategies. Wang et al. [25] employed 3D nonlinear FEM to simulate shield tunneling beneath railway box culverts, revealing deformation patterns and stress concentration zones. Their model accurately predicted culvert displacement and provided mitigation measures. Barros et al. [26] integrated FEMIX 4.0 to model SFRC box culverts, demonstrating enhanced load-bearing capacity and energy dissipation under static/dynamic loads. The interface elements between soil and concrete were pivotal in simulating realistic behavior. Barros et al. [27] proposed a Mohr-Coulomb-based interface model within FEMIX, enabling tensionless stress transfer simulations. This allowed partial replacement of traditional rebars with SFRC, reducing reinforcement by 95%. The same study by Barros et al. [27] validated that FEM-driven optimization could cut reinforcement from 118.5 kg/m³ to 5.1 kg/m³ while maintaining safety, revolutionizing cost-effective culvert retrofitting. Feng and Gray (2018) [28] utilized FEM to simulate fracture behaviors in wellbore strengthening (analogous to culverts). Their damage model predicted delamination under variable-mode loading, informing repair strategies for cracked culverts. Marinkovic and Zehn (2019) [29] surveyed model-order reduction techniques for real-time FEM, crucial for monitoring rehabilitated culverts under live loads.

In this paper, a construction method based on prefabricated high-strength thin-walled concrete segments for lining reinforcement inside box culverts is proposed to address the limitations of existing trenchless rehabilitation technologies for box culvert structures. First, referring to a practical engineering project, the construction process is validated using a full-scale 1:1 underground box culvert mock-up. Following successful installation, a graded stacking load test is conducted on the upper part of the reinforced overall structure to investigate the deformation characteristics and the interaction behavior at the interface between the new lining and the original structure. These observations provide valuable guidance for optimizing reinforcement design. Finally, a finite element simulation of the stacking load test is performed to analyze the mechanical response during the experimental process and to explore key factors influencing reinforcement effectiveness. The approach draws inspiration from recent research on composite structural behavior, such as the axial bearing capacity improvements observed in concrete-filled steel tubular columns with internal prestressing [30] and the influence of interfacial bonding and structural parameters on the load transfer mechanisms in reinforced CFST columns [31], providing theoretical support for the proposed reinforcement method.

2. Reinforcement Method and Segment Fabrication

2.1. Reinforcement Method

Traditional trenchless pipeline rehabilitation technologies exhibit limited applicability to large-section or non-circular conduits, particularly requiring cast-in-place operations that prolong construction timelines while yielding suboptimal cost-effectiveness. Consequently, the emerging paradigm for box culvert reinforcement prioritizes non-excavation technologies characterized by three critical performance metrics: (1) cross-sectional adaptability, (2) structural enhancement efficiency, and (3) accelerated construction execution.

Based on prefabricated assembly principles, this study proposes a rapid reinforcement method utilizing segmented liners for trenchless rehabilitation of box culverts. The prefabricated high-strength thin concrete segments must be transportable through maintenance manholes and subsequently assembled in situ. The reinforcement schematic is illustrated in Figure 1. The structural design of these segments addresses three primary requirements:

• Trenchless constructability: Segment dimensions must permit passage through existing maintenance manholes and enable assembly within the box culvert.
• Structural compatibility: Segments adopt the original structure’s square cross-section and incorporate grouting holes to ensure reliable composite action with the host culvert.
• Stability under soil pressure: Despite constraints imposed by the original structure and connectors, assembled segments maintain structural stability through circumferential interlocking via L-shaped splices (Figure 1).

2.2. Segment Design and Manufacturing

Box culverts are categorized into three primary structural systems: frame structures, rigid frame structures, and simply supported structures. Frame structures represent the most common configuration, characterized by rigid connections between the top slab, bottom slab, and sidewalls. This system provides comparatively high overall rigidity and favorable adaptability, making it suitable for applications with moderate foundation-bearing capacity requirements. In contrast, rigid frame structures typically omit the bottom slab, featuring rigid connections between the top slab and sidewalls. The sidewalls are rigidly consolidated with foundations, which may comprise pile foundations or enlarged spread footings. Simply supported structures encompass variants such as cover-plate culverts, where the top slab and sidewalls lack rigid connections. A bottom slab may be present but functions solely as backfill support; its consolidation with sidewalls depends on site-specific conditions.

The assembled precast concrete liner system exhibits complex stress distributions under the constraints of the original culvert’s embedment, as illustrated in Figure 1. Its structural behavior precludes straightforward classification into the aforementioned categories. To simplify the design process, this study idealizes segment joints as two connection types in reinforcement calculations: pinned connections and rigid connections. Structural analysis determines the maximum internal forces for both connection types, which are subsequently used for reinforcement design. A load-bearing capacity calculation model for the typical concrete box culvert cross-section was established as shown in Equations (1) and (2). Given the critical waterproofing requirements for underground structures, crack width control was verified in accordance with Equations (3)–(5).

$$N={\alpha }_1{f}_{c}bx-f_y{A}_s$$

(1)

$$M={\alpha }_1{f}_{c}bx(h-{\alpha }_s-x/2)-N(h/2-{{\alpha }_s}^{\prime }+e_a)$$

(2)

where M is bending moment at the calculated points (N·m); N is axial force at the calculated point (N); α₁ is the ratio of equivalent rectangular stress in the equivalent compressed concrete to the compressive strength of concrete, f_c is compressive strength of concrete (MPa); b is width of concrete section (mm); h is height of concrete section (mm); x is the calculated height of the concrete’s equivalent compressed zone; f_y is tensile strength of the reinforcement; α_s is thickness of concrete cover; α_s′ is distance from the center of tensile reinforcement to the surface of the concrete; e_a is artificially defined eccentricity error of axial force.

$${\rho }_{te}=2A_s/bh$$

(3)

$$\psi =1.1-0.65f_{tk}/{\alpha }_2{\rho }_{te}{\sigma }_{sq}$$

(4)

$$w=1.8\psi {\displaystyle \frac{{\mathit{\sigma }}_{sq}}{E_s(1.5c+0.11d/{\rho }_{te})(1+{\alpha }_1)\nu }}$$

(5)

where ρ_te is reinforcement ratio; A_s is area of reinforcement; ψ is stress unevenness factor of tension steel in the cracking zone; f_tk is standard value of tensile strength of reinforcement; α₂ is a coefficient, and 1.0 can be used here; σ_sq is actual tensile stress of reinforcement; w is maximum value of crack width; E_S is reinforcement modulus of elasticity; C is clear cover thickness of concrete; d is equivalent diameter of tension reinforcement; α₁ is a coefficient, and 0 can be chosen here; v is characteristic factor for tension reinforcement, and taken as 0.7 here.

3. Construction Method and On-Site Construction

3.1. Construction Method

This section details the construction sequence, emphasizing critical procedures including segment transportation, assembly, and composite reinforcement. Where high groundwater levels are encountered, dewatering measures are recommended. Operational functions of the pipeline section must be suspended during pre-construction preparations.

Construction method selection depends on site-specific box culvert conditions, including internal dimensions and accessibility. Internal clearances dictate segment weight limitations and assembly space, directly influencing construction efficiency. Two methods are proposed based on segment placement approaches: pull-in installation (Figure 2) and manual in situ assembly.

Pull-in installation (Figure 2): Prefabricated concrete segments are lowered through maintenance shafts into the box culvert and assembled to form an internal liner. Longitudinal continuity is achieved via post-tensioned steel strands, followed by grout injection into the annular space between the original structure and new liner. Construction proceeded sequentially as follows:

• Condition assessment of the existing culvert
• Sediment removal and interior profiling
• Guide rail installation
• Segment hoisting
• Manual assembly beneath maintenance shafts
• Segment pull-in along the culvert axis
• Post-tensioning of longitudinal strands
• Grout injection and backfilling.

Manual in situ construction: Workers hoist prefabricated concrete segments through maintenance shafts and transport them to reinforcement positions using mechanical aids. Following preliminary assembly, connectors are secured to ensure longitudinal continuity, with subsequent grout injection into the interstructural void. The construction sequence comprises:

• Condition assessment of the existing culvert
• Sediment dredging and interior profiling
• Segment hoisting
• Mechanical transport within the culvert
• In situ manual assembly
• Grout injection and backfilling

Spatial constraints in small-to-medium box culverts impede worker mobility, reducing construction efficiency. For larger culverts permitting human access, segment weight often exceeds feasible handling limits, compromising longitudinal joint integrity in pull-in installations. Under such conditions, manual in situ construction provides a more viable alternative.

3.2. On-Site Construction

The testing site is an open area next to a materials warehouse belonging to Beijing Urban Drainage Group Co., Ltd. located in Changping District, Beijing. A full-scale 5m-long masonry drainage box culvert has been constructed manually. The top cover of the square ditch has a maintenance manhole (inspection well), the size of which is determined based on the actual situation.

The specific implementation method of trenchless reinforcement construction involves lifting and installing prefabricated segments for reinforcement in the full-scale masonry square ditch that was built manually. Then, grouting is carried out between the segments and the original walls through the grout hole that has been reserved on the segments. The upper part is subjected to a design bearing capacity verification heap load test after the reinforcement treatment meets the requirements.

Since it is currently winter, meeting the necessary strength requirements in a short amount of time after grouting treatment is proving to be difficult. In addition, the construction process is complex, and the structure becomes difficult to excavate after the testing is completed. Therefore, for this test, artificial sand filling is being used to fill the gap between the segments and the original wall. However, during the stacking test stage, it is challenging to manually set up instruments and observe the testing phenomenon by going down through the well. This method also poses potential safety hazards. Consequently, once the prefabricated structure is completed, one end of the pipeline is dug up to allow personnel access. The on-site tests are divided into two parts: prefabricated segment assembly construction implementation and the loading test. The ditch’s internal dimensions are W × H = 2000 × 1800 mm, and the maintenance manhole’s pore diameter is 700 mm.

In this experiment, the drainage box culvert was manually built temporarily, so there was no need for the original box culvert investigation, dredging, and trimming. Therefore, the main construction process for assembling the prefabricated concrete segments in the original box culvert included segment hoisting, transportation, and in-pipe assembly.

3.2.1. Hoisting and Transportation

To hoist and transport the prefabricated concrete segments, a crane with an 8-ton capacity was used for vertical transportation through the maintenance manhole. For horizontal transportation in the box culvert, a self-made mobile forklift was used. The hoisting and transportation process followed these steps:

• Install special hoisting connection rings in the segment’s hoisting holes and connect the hook;
• Lift the segment vertically and align the lower end with the maintenance manhole (shown in Figure 3);
• Assist in adjusting the position in the box culvert and lower the segment to the manhole’s bottom, manually adjusting the direction and position (Figure 3);
• Secure the segment’s lower end to the mobile forklift and move the forklift horizontally while simultaneously lowering the segment until it lands steadily on the forklift;
• Manually push the mobile forklift to move the segment to the reinforced position.

3.2.2. Assembly In-Pipe

This process was primarily used to assess the feasibility of assembling prefabricated concrete segments in the box culvert. After passing the transportation test, the segments were installed in the box culvert ring by ring (Figure 3). A detailed illustration of a splicing joint is shown in Figure 4. The single-ring assembly mainly involves the following steps:

• Use the mobile forklift to transport and position the bottom segment, side segment, and top segment vertically in sequence.
• Install waterproof rubber gaskets (Figure 4) and connectors to complete the single-ring assembly.
• After splicing a single-ring, tighten the connecting nuts, and check the size and quality of the splicing joint.
• Install a sealing rubber gasket on the longitudinal splicing socket after passing the quality check, and then bond it with structural glue or waterproof resin.
• Tighten the longitudinal connection, and then tighten the splicing nuts in the single-ring again.
• Fill the gap between the two-layer structures with grout and compact it.

It is worth noting that the assembly process should be carried out in strict accordance with the construction drawing and the assembly sequence to ensure the accuracy and quality of the assembly. Any problems found during the assembly process should be resolved in a timely manner to avoid affecting the construction progress and quality.

4. Stacking Load Test

The material and geometric parameters of the prefabricated segments employed in this experimental study are detailed in Figure 5 and

Table 1. Material parameters.

Component	Segment Material		Mechanical Properties Measured by the Test
			Elastic Modulus (MPa)		Tensile/Compressive Strength (MPa)
	C60 Concrete	HRB500 Rebar	C60 Concrete	HRB500 Rebar	C60 Concrete	HRB500 Rebar
Top/bottom segment	The entirety	Diameter 8 mm, double row arrangement, 9 pieces per 400 mm	3.61 × 104	2.05 × 105	67.86	495
Side segment	/	Diameter 8 mm, double row arrangement, 6 pieces per 400 mm

. This study focused on quantifying the bearing capacity [32] and characterizing failure mechanisms of the segments when constrained by the original box culvert structure, replicating actual field conditions.

Prolonged service typically induces structural degradation in existing culverts, with roof slab deterioration posing particularly critical safety implications. Consequently, this experiment adopted the design rationale that the original roof slab would be relieved of overburden loads following reinforcement. During load testing, the existing roof slab was physically removed to validate this assumption.

After removing the upper cover plate, the stacking loading experiment was conducted directly above the reinforced prefabricated segment roof (Figure 6). To minimize excavation and transportation, it was decided to cover the load with 1m of soil to simulate the soil’s diffusion effect on the upper load. In this pipe section, there were 13 prefabricated rings for reinforcement, and the stacking plate was 2.2 m × 2.3 m in size, positioned above the central five rings.

4.1. Sensorss and Loading Protocols

The data acquisition system integrates three core components: resistance strain gauges or displacement transducers, a strain data acquisition unit, and a computerized monitoring interface. Strain gauges interface with the acquisition unit via shielded twisted-pair cabling, while Ethernet protocol facilitates communication between the acquisition unit and computer. Figure 7 details the sensor topology, noting that the depicted configuration represents composite instrumentation distributed across multiple rings rather than a single ring. Strategic measurement points target three critical regions:

• Rebar strain: Reinforcement locations prone to preferential yielding [33] (typically main longitudinal bars at maximum moment regions).
• Mid-span displacement: Zones exhibiting peak relative displacement (crown, invert, and springlines of segments).
• Concrete strain: Tensile-critical regions at crown intrados where initial cracking typically initiates.

The test assembly comprised 13 precast segments with a total length of 5.2 m (0.4 m × 13) (Figure 8). To precisely locate loading points, segments were numbered sequentially from the entrance inward. Outer zone: Segments 4→3→2→1→0 (0–2.0 m from entrance); Central zone: Segments 4→3→2→1→0 (2.0–4.0 m from entrance); Inner zone: Three segments uniformly labeled 0-0-0 (4.0–5.2 m from entrance). Primary loading zones targeted Outer Segment 0 and Central Segments 4→1.

The loading capacity of the structure was determined based on the design value of the bearing capacity of buried rectangular pipes under 2 m overburden, as specified in Chinese ‘Specification for structural design of buried rectangular pipes in water supply and drainage works (CECS 145: 2002)’ [34]. The loading was simplified to four levels (Figure 9), with the first level being a 1.8-ton per square meter load (equivalent to a one-meter covering soil depth) after placing the stacking plate, followed by 3.6 tons per square meter and 5.5 tons per square meter for the subsequent levels. The segments were inspected for damage after each level of loading.

4.2. Observations

During the heap loading process under 1m soil overburden, no structural anomalies were detected and the concrete intrados remained uncracked (Figure 10a). At 1.8 ton/m² surcharge load (equivalent to 9-ton point load), the sidewalls and invert segments exhibited negligible deformation. However, a 3cm-long hairline crack initiated at the crown intrados adjacent to the longitudinal joint (Figure 10b). Joint integrity was maintained without concrete crushing, spalling, or distress indications. When loaded to 3.6 ton/m² (18-ton equivalent), multiple fine cracks propagated near the crown mid-span, with maximum lengths reaching 12cm (Figure 10c). At the target 5.5 ton/m² load (28-ton equivalent), full-depth cracks developed at the crown mid-span exhibiting 0.10mm maximum crack width (Figure 10d).

This damage pattern stems from construction constraints: During field implementation, the significantly stiffer existing sidewalls (relative to the precast segments) imparted rigid boundary conditions. This restrained lateral displacement of side segments, preventing their engagement in earth pressure resistance. Concurrently, the original sidewalls shielded the longitudinal joints from flexural moment transfer. Consequently, the side segments and joints functioned as compression struts during testing, explaining their minimal damage despite crown cracking.

4.3. Data Analysis

In light of the experimental observations, the data analysis should prioritize the key positions on the top plate. Specifically, the changes in the data from the four displacement meters located in the mid-span of the central pipe ring under the loading plate should be examined. As shown in Figure 11, several trends can be observed: (1) the mid-span deflection of the bottom segment remained at zero due to the displacement coordination effect of the concrete cushion; (2) the displacement of the lateral segment was negative, indicating that the reinforced segments on both sides actively bore the load after outward displacement due to the limiting effect of the original structure’s side walls on the soil on both sides. This finding aligns with the hysteretic stress characteristics of the reinforced structure in an actual project; (3) the top segment’s mid-span experienced the largest displacement, with a deflection of 4.675 mm, which meets the specification requirement of L/200 = 10 mm; and (4) the displacement of the segments on both sides primarily occurred during the first loading stage, with little change in subsequent stages. However, at approximately t = 102 min of loading time, the displacement of the left and top segments showed a sudden small change simultaneously, indicating that the filler between the tested segment and the original structure had changed to some extent. This could be a result of the filler being squeezed out of the sides or insufficient filling. This phenomenon further underscores the importance of fillers in jointly exerting the structural bearing capacity of old and new structures.

To determine the stress characteristics and the actual role of each segment in the single-ring structure under static load, the strain data of the rebar on the middle third ring segment were analyzed. Figure 12 illustrates the positions of the strain gauges (S1–S16) attached to the single-ring prefabricated segment. Notably, strain gauges S5 and S6 were affixed to different transverse main rebars at the same location. S5 (S15) was positioned at the center of the top segment, while S6 (S16) was near the longitudinal splicing joint (the socket in the assembly of tongue and socket). Moreover, S1, S8, S10, and S11 were positioned at the weak point of the splicing joint, which is prone to tearing, and S3 (S13) was located in the middle of the enlarged armpit.

Figure 13 shows the strain data of the top segment’s rebar, which are affected by the loading process that involves hoisting heavy objects and causes significant environmental disruption. The curves exhibit non-smooth changes during the test. By analyzing the curve of S1, it is evident that the splicing joint’s weak area gradually changes from compression to tension, indicating that the outside of the joint opened while the inside closed, thereby enhancing the structure’s waterproofing. Similarly, the armpit was also in a safe state of compression, as observed from the curve of S3. The curves of S2 and S4 essentially overlap, suggesting that the bending moment did not significantly vary after the transmission of the corner nodes. This is because the side wall did not exert any force on the corner nodes on both sides of the top segment, consistent with the phenomenon where lateral earth pressure is applied to the original structural wall. Comparing curves S5 and S6, it is noticeable that the rebar’s deformation near the socket of the longitudinal joint is larger than that of the rebar at the center position, indicating that the socket contracts inward, thereby strengthening the joint’s waterproofing and demonstrating the effectiveness of this type of longitudinal splicing. The maximum strain of the rebar, which is 843, indicates an elastic stage for the structure and excess bearing capacity. Since the graded loading was strictly performed according to the load of 1m deep covering soil each time, the rebar strain is depicted as a straight line in Figure 14, indicating that the structure was still in the elastic stage and safe and reliable under working conditions.

The strain data of the rebar on the bottom segment (Figure 15) reveal that the strains of the four measuring points near the armpit are relatively small, similar to those on the top segment, indicating that the sections near the armpit of the bottom segment are in a state of small eccentric compression. When comparing S13 and S3, S13 has a much smaller value than S3, indicating that the bending moment at the armpit of the bottom segment is very small. This suggests that the internal force of the top segment under the upper load is difficult to transmit to the bottom segment due to the restraint of the side wall. Therefore, the bottom segment is equivalent to a beam placed on an elastic foundation and subjected to concentrated loads at both ends. This is different from the general assumption that it receives a uniform load reaction force and should be taken into account in the structural simplification calculation. The strain values of S15 and S16 are fairly evident, with S16 being greater than S15 at the same time, which is consistent with the results of S5 and S6. This phenomenon is caused by the asymmetry of the structure in the longitudinal direction. As shown in Figure 14, due to the existence of sockets, the bending stiffness at the position of the reinforcement strain gauge S6 and S16 is less than that at the position of the reinforcement strain gauge S5 and S15. Therefore, the socket has a tendency to shrink inward, which is conducive to longitudinal connection and waterproofing with adjacent sockets. It is worth noting that the strain on the bottom segment is less than that on the top segment, which should be taken into account in the design to avoid overly conservative results.

Figure 16 displays the rebar strain data of the side segment. Rebar strain gauges S8-4 and S7-4 were located in the middle of the 4th ring segment, S8-3 and S7-3 in the middle of the 3rd ring segment, and S8-2 and S7-2 in the middle of the 2nd ring segment. From the first loading to the second loading, almost all strain changes indicate that the state of the measurement points shifts from compression to tension, demonstrating that the prefabricated segments for reinforcement interact with the original structure and start to work collaboratively. This means that the original structure imposes lateral restraints and loads on the prefabricated segments. However, from the second loading to the third loading, the strain changes mentioned above are no longer obvious or even reversed, indicating that the original structure significantly constrains the prefabricated segments for reinforcement and limits their deformation. Moreover, the strain values of the steel bars on the side segment are generally small, indicating that the side segment is in a state of small eccentric compression and is not prone to damage.

5. Finite Element Simulation

A finite element simulation was conducted to verify and further investigate the deformation characteristics and reinforcement mechanism of the structure during the reinforcement process. In addition, the choice of grouting material used for filling between the old and new structures during the reinforcement construction process may have a significant impact on the reinforcement effect of the structure. Therefore, a two-dimensional finite element model will be established below, and the necessary parameter analysis will be conducted.

5.1. Model Dimensions and Material Parameters

A finite element model was created based on the stacking loading test mentioned earlier. In Figure 17, the width of the soil model is 10 m, and the depth is 7 m. The original structure’s side walls have a thickness of 300 mm. The bottom cushion has a thickness of 200 mm, and the grouting layer between the old and new structures is 20 mm thick.

The materials listed in Table 1 were used to reinforce the concrete segments. The Mohr-Coulomb model is used for soil, the CDP model is used for concrete, and the double-polygonal constitutive model is used for reinforcing steel.

5.2. Element Types Mesh and Interaction

The assembly and mesh of the model built in ABAQUS 6.21-1 are shown in Figure 17. The soil, original structure, grouting material and prefabricated segments are all CPE4R plane strain units, and the steel trusses are T2D2 TRUSS units.

Surface-to-surface contact is used between the soil mass and the original structure, the original structure and the prefabricated segment, the prefabricated segment and the grouting layer, and the interior of the prefabricated segment. In Surface-to-surface contact, the normal behavior is set to “hard contact”; for the tangential friction coefficient, it is taken as 0.8 between the concrete structure and the grout layer, and 0.4 between the existing structure and the soil.

Mesh Sensitivity Analysis

Mesh sensitivity analysis is used to evaluate the impact of meshing on computational accuracy and efficiency, with the core goal of obtaining mesh-independent solutions (mesh-independent solutions). Methods include step-by-step refinement of the mesh until the key results do not change, and verification of reliability by comparing experimental data or high-precision literature results.

The meshing was divided into four groups according to the fineness, and the meshing in Figure 17 was recorded as the control group SL-1, and the number of grids in each group increased or decreased geometrically compared with the composition of the control.

In order to speed up the calculation and save time, only the first step (see Section 5.3 for the specific calculation content of the first step) is calculated, and the results of the maximum vertical displacement of the soil are compared for grid sensitivity analysis.

Table 2. Calculation results.

Group	Number of Grids	The Quality of the Mesh	Vertical Displacement/mm	Error/%	Calculation Time/min
SL-0	3948	0.68	6.954	6.05	8
SL-1	5152	0.87	7.402	/	12
SL-2	19634	0.93	7.516	1.54	37
SL-3	30158	0.95	7.509	1.45	56

shows the meshing data and calculation results. The quality of the mesh is calculated according to Equation (6). The calculation results show that further refining the grid based on the control group will not result in significant changes to the calculation results, with a relative difference of about 1.5%. However, the computational time cost will increase substantially. Although the rough grid has a shorter computation time, it has a relatively larger error. Therefore, it is feasible and more economical to continue using the grid defined in the control group (Figure 17) for subsequent analysis.

$$Q=l-{\displaystyle \frac{S}{M}}$$

(6)

where M is the mean of the Jacobian ratios and S is the standard deviation of the Jacobian ratios, both of which can be queried in the software tool.

5.3. Simulation Process and Results

The simulation is divided into two steps, the first step of which is to simulate the order of Geostatic, soil excavation, structural installation, and rebalancing under self-weight. Among them, the Geostatic verifies the correctness of the soil model and parameters through the lateral pressure coefficient of the soil. In the second step, a uniform load is applied directly above the model based on the maximum load of the stacking experiment above.

The grouting material’s effect on the reinforcement effect and the internal force distribution of the prefabricated segment is studied by changing the material parameters of the grouting material. The grouting material’s elastic modulus is set to E_s1 = 3.6 × 10⁴ MPa, E_s2 = 2.0 × 10⁴ MPa, and E_s3 = 1.0 × 10⁴ MPa, which are recorded as working conditions S1, S2, and S3 respectively. Among these conditions, S1 is the control group, with an elastic modulus consistent with the C60 concrete used in the field test.

After the soil excavation, original structure installation, and self-weight balance are completed in the first step, uniform pressure is directly applied to the upper surface of the prefabricated segment as the second loading process. Based on the aforementioned field test, the uniform pressure value is 0.07305 MPa.

Figure 18 displays the distribution of vertical displacement of the model under various working conditions. During the first step of soil excavation (Step-0), it is evident that the soil under the middle excavation section and the installed original structure experience relative upward displacement in relation to the surrounding soil. Therefore, the subsequent structural deformation analysis should prioritize relative displacement after loading. In the second loading step (Step-1), a design load of 73.05 kN/m² is applied above the structure, causing the original structure and reinforced segment to sink into the surrounding soil as a whole. As a result, the relative displacement between the top and bottom segments should be the main focus of displacement analysis for prefabricated segments.

The results are presented in

Table 3. Calculation results of the FE model.

Working Condition	Stress Nephogram	Sm (MPa)			Deformation Nephogram	U2′ (mm)
		Sm,max	Sm,top	Sm,suprt
S1		399.5	261.5	204.2		7.93
S2		350.0	263.2	207.9		7.91
S3		329.6	266.0	202.8		8.06

, where U₂′ represents the relative displacement at the midspan of the top and bottom segments, S_m represents the Mises stress, S_m,top represents the Mises stress of the rebar at mid-span of the top segment, S_m,suprt represents the Mises stress of the rebar at the supports at both ends of the top segment, and S_m,max represents the maximum value of the Mises stress. The results show that the reduction in the elastic modulus of the grouting material does not significantly affect the strain of the rebars on the key sections of the reinforced segment, with the maximum change not exceeding 2%. Therefore, the material properties of the grouting material have little effect on the reinforcement effect of the prefabricated segment structure. In addition, the relative displacement change between the top and bottom segments is not visible, with a value of approximately 7.9 mm~8.1 mm. Based on these findings, it can be concluded that the choice of grouting material has no significant impact on the deformation characteristics, internal force distribution, or static bearing performance of the prefabricated reinforcement segments. Therefore, the simulation results can be used for further analysis and comparison with the field test results.

The stress contour map of the concrete in the prefabricated segment presented in Table 3 indicates that the load on the upper surface of the structure is primarily borne by the soil below the structure’s bottom, resulting in higher stress at the soil bottom compared to the stress on both sides. Furthermore, the stress on the concrete of the top segment is higher, and its distribution characteristics are similar to those of beams fixed at both ends under uniform load. The strain value of the rebar at mid-span (average 1286 με) is approximately 1.28 times the strain value of the rebar at the support (average value 1000 με), indicating that the top segment is semi-rigid-fixed. These results are consistent with the findings obtained from the field test, highlighting the importance of closely integrating the top segment and the original structure during reinforcement construction.

6. Conclusions

This paper proposes a trenchless reinforcement method for underground box culverts using precast segments, enabling rapid construction without excavation. To verify efficacy, a full-scale masonry drainage box culvert was constructed for field validation. Subsequent static bearing capacity verification was implemented via heap loading tests at the reinforcement site. The test design excluded the original roof slab’s load-bearing contribution, aligning with observed severe deterioration in actual structures. The existing sidewalls’ effective three-dimensional restraint prevented structural yielding under design loads, demonstrating the method’s safety, reliability, and significant enhancement of original structural performance. Finite element simulations exhibited high consistency with field measurements. Key contributions are summarized as follows:

• The trenchless rapid reinforcement method proposed in this paper can quickly repair the old box culvert without affecting the road traffic, and the construction feasibility and applicability have been verified, which has a very large economic effect.
• The structural form of the prefabricated segments proposed in this paper has reasonable design and excellent bearing capacity, and is conducive to waterproof and anti-corrosion in both transverse and longitudinal splicing.
• In this paper, the internal force distribution characteristics of reinforced segments are explored, and it provides a theoretical basis for the calculation of internal forces and reinforcement design of control sections.
• The simulation work in this paper shows that in the case of small thickness of the grouting layer, due to the greater stiffness and strong constraints of the original structure, the selection of grouting material has little influence on the internal force distribution and deformation of the structure, so it points out the way for further analysis of the thickness of the grouting layer and the stiffness of the original structure.