Experimental Study on Mechanical Differences Between Prefabricated and Cast-In Situ Tunnel Linings Based on a Load-Structure Model

Abstract

With the accelerated development of urban underground spaces, prefabricated tunnel linings have become a research focus due to their advantages in construction efficiency and cost effectiveness. However, issues such as stress concentration at joints and insufficient overall stability hinder their broader application. This study investigates a cut-and-cover prefabricated tunnel project in the Chongqing High-Tech Zone through scale model tests and numerical simulations to systematically compare the mechanical behaviors of cast-in situ linings and three-segment prefabricated linings under surrounding rock loads. The experimental results show that the ultimate bearing capacity of the prefabricated lining is 15.3% lower than that of the cast-in situ lining, with asymmetric failure modes and cracks concentrated near joint regions. Numerical simulations further reveal the influence of joint stiffness on structural performance: when the joint stiffness is 30 MN·m/rad, the bending moment of the segmented lining decreases by 37.7% compared to the cast-in situ lining, while displacement increments remain controllable. By optimising joint pre-tightening forces and stiffness parameters, prefabricated linings can achieve stability comparable to cast-in situ structures while retaining construction efficiency. This research provides theoretical and technical references for the design and construction of open-cut prefabricated tunnel linings.

1. Introduction

With the rapid expansion of the population in large and medium-sized cities, traffic congestion and land resource constraints are becoming more and more prominent, and the development and utilisation of underground space on a global scale is gradually becoming the focus of attention of all countries. Tunnels built by traditional construction techniques are prone to quality problems such as lining voids, cracking, and falling blocks during operation, and the construction period is long, with a high consumption of manpower and material and financial resources in construction and maintenance. As a new type of tunnel construction technology, assembled tunnels, when prefabricated in the factory, can ensure the strength and geometric accuracy of concrete, and the site assembly is convenient, with a shorter construction cycle and higher economic benefits [1,2,3,4,5,6,7]. China’s underground engineering assembly tunnels are generally shield method tunnels and immersed tube tunnels, used for underground stations mostly, for arch tunnel research and the application of open excavation are less common.

For the assembled tunnel lining, most of the diseases appear in the joint position. Compared with the cast-in-place lining, the stability, force uniformity, and overall stiffness of the assembled lining are poor, and the reason is the design and production of the joint position. Some scholars [6,7] have found that the tongue-and-groove design of the joint increases the flexural stiffness of the joint, as well as the type of connector also having a more pronounced effect on the flexural stiffness of lining joints. A section of academics [8,9,10] have been working to improve the stiffness of assembled tunnel linings by optimising the materials used for the lining, and the mechanical behaviour of lining joints with these materials has been studied. Yang Xiuren’s research team [11,12,13] pioneered the construction of an underground station assembly construction technology system; their research adopts a 1:1 prototype test and refined numerical simulation parallel technical route, especially on the mortise and groove joint node force transfer mechanism for systematic demonstration. Professor Feng Kun’s team [14] carried out a pioneering study to systematically explain the stiffness degradation mechanism of large-diameter shield joints and the development of lining cracks through the establishment of the research framework of “theoretical analysis—scaled-down test—full-scale verification”. Qin Xin [15] improved the mechanical properties of joints by using high-ductility cementitious composites and applying them to assembled tunnel joints. Lin Zhi [16] explored the change rule of flexural performance of arch-shaped cut-and-cover tunnel joints under the joint action of different axial forces and bending moments through indoor tests. Yang Wensheng et al. [17] investigated the shear mechanical properties of assembled tubular joints in rectangular tunnels with large sections through experiments and obtained the relationship curves between shear force and longitudinal joint misalignment deformation in five stages. Hefny [18] studied the lining bending moment distribution law in depth by using Plaxis 2D finite element software, and the numerical analysis results showed that the way of arranging the joints and the number of joints had a determining effect on the distribution of internal forces in the structure, and this finding provided a basis for the optimisation of the lining design. Zhang Yujin [19] systematically analysed the segmentation and bearing characteristics of prefabricated assembled secondary lining in the composite lining of mine method tunnels and put forward the calculation model and design suggestions. It is shown that this method can not only significantly reduce the amount of reinforcement and connecting bolts, but also effectively improve the bending capacity of the pipe sheet. Guan Honghao [20] proposed a variety of cross-section forms and optimised assembly construction methods for the design and construction of shallow tunnel linings for high-speed railways. Zhao [21] and other scholars famously outlined the design selection, component preparation, construction assembly, and application of information technology in four parts of the railway tunnel prefabricated assembly construction technology system in the design of the key points, producing an objective analysis of the problems that still need to be researched and urgently need to be carried out for the promotion and application of this technology in the tunnel project to provide technical reference. Zhang Shenglong [22] and other scholars used a load-structure model to analyse the internal force characteristics of integral lining under different surrounding rock conditions. The lining structure was divided into eight prefabricated parts, and the finite element software was used to calculate the safety of the prefabricated structure, and the forces and deformations at the joints were analysed under different joint stiffness conditions.

At present, the research on open-arch assembled tunnels mainly focuses on the optimisation and enhancement of the joint section, with less research on the influence and change of the assembled lining as a whole. In this paper, based on a project of an open-arch assembled section of a tunnel in the Hi-Tech Zone of Chongqing Municipality, through the combination of a scaled-down test and numerical simulation, we investigate the force difference between fully cast lining and three-part assembled lining under the action of peripheral rock loading, and put forward the improvement measures for assembled lining to provide theoretical suggestions for the construction of three-part assembled tunnels, so that they can achieve the convenience of construction and the stability of the fully cast lining. The effect is as follows.

2. Load-Structure Indoor Experiment

2.1. Specimen Design

Considering the safety of the test and site limitations, the indoor scaling test adopts a scaling ratio of 1:20, and under the condition of meeting the purpose of this test, some locations in the actual project have been appropriately simplified, and the size of the lining model and monitoring points are shown in the following Figure 1 and Figure 2.

2.2. Material Parameters

According to the similarity theory method, and limited by test conditions, the primary goal of this study is to validate the effectiveness and scientific basis of numerical simulation through scaled-down testing. Considering only elastic similarity, and referencing the initial scaling ratio for tunnel lining materials in Luo Yunfei’s study [23], a cement mortar mix (cement:sand:water = 1:3.5:1.6) was used. For 100 mm × 100 mm × 100 mm non-standard specimens cured for seven days, the measured uniaxial compressive strength was 1.65 MPa and the modulus of elasticity was 1.78 GPa. While the elastic modulus (1.78 GPa) is very close to 1/20th of the typical modulus for C50 concrete used in the actual project (approximately 34.5 GPa/20 = 1.725 GPa, error < 10%), the compressive strength (1.65 MPa) shows a larger deviation from 1/20th of C50 strength (50 MPa/20 = 2.5 MPa, error ≈ 34%). Achieving perfect material similarity in scaled-down models faces significant technical challenges. At a finer scale, accurately replicating key parameters such as concrete aggregate gradation and steel reinforcement arrangement is difficult. This may lead to deviations in micromechanical responses, like crack propagation patterns, compared to the prototype structure. Although this non-exact similarity at the micro-scale might influence local damage evolution, its impact on the study of the overall structural mechanical behaviour is considered acceptable within engineering tolerances. This is because the primary similarity requirement (elastic similarity for global response) is largely met by the mortar’s modulus, and the focus is on global behaviour rather than localised failure mechanisms. Therefore, under the fundamental premise of meeting the basic requirements of similarity theory, using this mortar mix for tunnel lining model testing possesses sufficient theoretical justification and engineering applicability. Specific material properties and comparisons are detailed in

Table 1. Mechanical properties of materials.

Material Type	Compressive Strength (MPa)	Modulus of Elasticity (GPa)
C50 concrete	38.4	3.5
Similar material	1.65	1.78

.

2.3. Loading System

The test loading system adopts a bi-directional synchronous loading mechanism, in which the vertical uniform load is applied by rigid pads to simulate the vertical pressure of the surrounding rock, while the horizontal direction is accurately controlled by the symmetrically arranged hydraulic jacks on both sides of the specimen in conjunction with the high-strength transfer bar system to achieve the precise control of the lateral pressure; this is shown in Figure 3. When the specimen is installed, a laser positioner is used to precisely adjust the model to the geometric centre of the loading frame to ensure the accuracy of the load transfer path. When loading, by controlling the load increment of the top force transfer bar, the mechanical behaviour of the two lining structures in the progressive damage process is systematically observed and recorded, with emphasis on the comparative analysis of the characteristics of their damage modes and the differences in damage mechanisms.

2.4. Monitoring System

In order to comprehensively grasp the characteristics of the mechanical behaviour of the lining structure under loading, a multi-parameter simultaneous monitoring system was constructed in this study. The test system consists of three main measurement modules: the pressure sensor module is used to obtain the pressure distribution characteristics of the structural surface, the displacement gauge module is used to record the deformation development process of the joints, and the strain gage module is used to monitor the evolution law of the structural internal force. The data acquisition system adopts the DH3818Y static strain tester produced by Chengdu Donghua Testing Technology Co., Ltd. (Chengdu, China). which is equipped with a dual-channel data acquisition unit, and each channel can simultaneously collect test data from 24 measurement points. In terms of system configuration, a dual-machine cooperative working mode is adopted, in which one instrument is dedicated to collecting structural strain field data and the other one records pressure and displacement parameters synchronously. The test system supports a variety of wiring methods, such as full bridge, half bridge, and 1/4 bridge, which can realise the accurate measurement of static stress and strain.

3. Cast-In Situ Lining

Comparative analyses of the test results of fully cast-in-place tunnel lining structures throughout the process from loading to damage, mainly focusing on the damage process and changes in deformation and internal forces of the members.

3.1. Structural Failure Process and Deformation

In Figure 4, the vertical pressure in the gradual loading process reaches the target value and each time, there will be a short slow decline section; this is due to the structure in the force process resisting the pressure, so that the jacks rebound, which belongs to the permissible error range. We focus on the sudden decline in the mutation node and the final lining structure damage when the vertical load Fu reached 340 kPa (6.8 MPa in the simulation reality); this lining structure to the seventh loading occurred in the damage. The first mutation node appeared when the vertical load reached 0.6 Fu, and the first cracks appeared above the left arch footing, at the top of the arch, at the right arch girdle and at the superelevation arch of the structure, but they were very subtle. As the pressure increased, the cracks began to gradually expand and extend longitudinally. At the fifth loading, the second crack appeared below the left arch foot of the lining structure, and the expansion of the first crack at the superelevation arch and right arch waist was not obvious. When the vertical load reached 0.8 Fu, the second crack began to extend to the middle of the superelevation arch, and a triangle appeared at the superelevation arch, and cracks also appeared above the right arch foot, at which time the cracks in the top of the arch continued to expand and began to fall off the block. When the vertical load was close to Fu, no new cracks appeared in the lining structure, and the falling block phenomenon was serious; at this time, the maximum width of the crack above the left arch footing was 7 mm, and the maximum width of the crack below the left arch footing was 10 mm. When the structure was finally damaged, the whole lining structure was tilted to the left and lost its stability.

At the beginning of loading, the tunnel lining is in an elastic phase, and the springs in the force-transmitting rods and bearing platforms are only squeezed appropriately. Under the action of loading, tensile stresses are gradually generated on each mass point of the tunnel lining cross-section, but due to the non-homogeneity of the concrete material structure itself, the tensile stresses are not uniformly distributed on the concrete surface, and there are a large number of irregular stress concentration points. If there is no reinforcing mesh, the stress at these points will be the first to reach the tensile limit strength of concrete, and then enter the plastic state and produce plastic deformation. After the configuration of reinforcing steel mesh, the overall stiffness of the specimen is improved, and at the same time, the reinforcing steel mesh will share the tensile stress of the concrete and disperse the stress at the concentration points to the whole surface of the concrete, thus delaying the time for the concrete to enter the plastic state. The loading damage process is shown in the Figure 5 and

Table 2. Crack propagation patter.

Loading Stage	Crack Development Characteristics	Crack Width Range (mm)	Key Observations	Structural State
0.6 Fu	Initial cracking observed above left springing, crown, right haunch, and invert. Initial cracks formed at the following locations: above the left springing, the crown, the right haunch, and the invert.	<0.1 (Subtle)	No spalling observed	End of elastic stage
0.6–0.8 Fu	New cracking developed below left springing. Existing cracks propagated longitudinally. Cracks in the invert/right haunch remained stable.	0.1–0.5	Stress redistribution	Stable propagation stage
0.8 Fu	The crack below left springing propagated towards the mid-section of the invert. New cracking emerged above right springing. A triangular cracking zone formed within the invert.	0.5–3.0	Initiation of rockfall at the crown	Accelerated propagation stage
0.9 Fu	The crack above left springing developed into a through crack. The crack below left springing propagated through the invert to become a through crack.	3.0–7.0	Spalling area > 15%	Plastic failure stage
1.0 Fu	No new cracking was observed. Existing cracks widened significantly (rapidly).	Above left springing: 7.0 Below left springing: 10.0	Spalling area > 30% Structural inclination > 5° to the left	Ultimate limit state
Failure Stage	The crack network interconnected, forming a major failure path.	>10.0	Global tilting instability	Loss of load-bearing capacity

below.

After the lining structure was damaged, the whole structure was taken out for observation and research. The following conclusions can be summarised from the damage pattern of the structure: (1) the arch foot and the vault took the lead in damaging and forming through cracks, and the cracks were too large, leading to the phenomenon of falling blocks on the vault, and even the tendency of collapsing; (2) the development of the cracks was irregular, and the cracks under the left arch foot extended new cracks to the direction of the superelevation arch, and the triangular area appeared; (3) the location of the cracks, which basically appeared in the arch foot and the vault, indicated that the cracks were in these positions; (4) the left side of the lining structure was damaged more seriously, probably due to the deviation of the jack position, and finally shifted to the left leading to damage; this is shown in Figure 6.

3.2. Analysis of Results

In order to further study the deformation characteristics of the lining structure and make the damage deformation more specific, the data collected by the displacement meter is plotted as a displacement–deformation curve as shown in the following Figure 7, where the data is positive for sinking and negative for uplifting.

It can be learnt from the above displacement curve that the displacement change is more obvious in the first two loading steps, which is due to the fact that the spring on the transfer bar and bearing platform is undergoing extrusion, and the whole lining structure is sinking downwards. With the loading step, the displacement at the arch top and arch waist gradually increases and this is a stepwise growth. The displacement at the foot of the arch does not fluctuate much, but the overall trend is upward. It indicates that the lining structure is in the trend of overall sinking, up-and-down extrusion, and expansion towards the foot of the arch under the action of loading. After the fourth loading, the growth of displacement at the arch top becomes faster, exactly when it reaches 0.6 Fu, indicating that the lining structure starts to be damaged and the displacement increases. After the sixth loading, the displacement of each position changes suddenly, at this time for the lining structure damage. For the fully cast lining, a more pronounced displacement at the vault is evident, which is specific to the tunnel structure, especially after the fifth loading step. And at the beginning of the fifth loading step, the lining starts to break down to some extent, which leads to a significant increase in the displacement of the lining structure at various locations.

In summary, it can be clear that the reasons for the displacement change of the superstructure mainly contain two aspects: the first aspect is the application of the initial load, which makes the spring squeezed and leads to the sinking of the lining structure; the second aspect is the destruction of the weak point due to the increase in the load, which leads to the deformation. The main reason for the displacement of the substructure is the extrusion of the superstructure and the expansion of the structure in the direction of the footing.

The strains at various locations of the fully cast lining structure are shown in the following Figure 8, where the positive sign indicates tension, and the negative sign indicates compression.

From the analysis of the above figure, it can be seen that for the left arch footing, a large sudden change occurs at the third loading step, which indicates that cracking has occurred at the left arch footing at this point. As the load continues to be applied, the strain at the left arch foot continues to increase, which indicates that the left arch foot continues to be loaded and the lining structure continues to work until after the sixth loading step, when a sudden change to 0 occurs again, which indicates that the lining structure has been destroyed.

For the left arch waist, vault, and left superelevation arch, during the loading process, the strain changes at these locations were small, and between the fourth loading step and the sixth loading step, more stage-type back-and-forth fluctuations occurred, which indicated that, up to the fourth loading step, small cracks began to appear at these locations, and the lining structure continued to rebalance the internal forces in order to be able to continue to work so that the structure could continue to be stressed. Finally, until after the sixth loading step, the strains at these locations showed large abrupt changes, which indicated that the lining structure was in complete failure.

For the right girdle and right footing, there is a tendency for the strain to increase with each loading step, and after the fourth loading step, there is a step change. Eventually, after the sixth loading step, a final change of 0 is produced, indicating the damage of the tunnel lining structure.

For the right superelevation arch, after the fourth loading step, there is a stepwise decrease in strain, which may be due to the rupture of the right foot joint, resulting in a tendency of upward buckling at the right foot.

In summary, the tunnel lining structure shows a tendency to tilt to the left during load application, which may be due to a slight error in the load application position during the test. However, this does not affect the comparison with the strain change of the assembled lining structure in the later section.

4. Three-Segment Prefabricated Lining

The test results of the three-part tunnel lining structure from loading to destruction are compared and analysed mainly around the destruction process of the members and the changes in deformation and internal force.

4.1. Structural Failure Process and Deformation

The load behaviour of the three-part lining model with loading steps was similar to that of the fully cast type, but the ultimate load was lower than that of the fully cast type and the cracks appeared earlier than those of the fully cast lining, which indicates that the assembled structure was more susceptible to damage, even though it was connected by connectors. As can be seen from Figure 9 and Figure 10 above, the vertical load Fu at the time of final lining structure damage reached 288 kPa at the sixth loading step, and the first moment of large sudden change was near the left arch foot connection location of the structure when the vertical load reached 0.6 Fu. With the increase in the vertical load, cracks started to develop in the vault joints, the cracks in the left arch footing started to expand, and the joints in the right arch footing showed signs of larger fracture. When the vertical load reached 278 kPa, the joint at the right arch foot position of the lining structure was fractured, and there was a slight decrease in the force of each pressure sensor, but the lining structure still maintained its working condition. As the vertical load continued to be applied, the lining structure was finally damaged.

In terms of damage location, the arch and soffit regions, as the stress concentration zones of the structure, were the first to undergo damage, which was manifested by the formation and development of penetrating cracks. Among them, the arch region caused local spalling of concrete due to the continuous expansion of crack width, which in turn induced the overall instability of the structure.

From the crack expansion characteristics, the crack development path showed obvious regularity, and no random bifurcation phenomenon was observed. This feature is closely related to the structural characteristics of the assembled lining: under the pressure of the surrounding rock, relative displacement occurs on both sides of the structure, resulting in the formation of a significant stress concentration zone in the joint area, which ultimately leads to the rapid expansion of macro cracks and structural damage.

From the point of view of the damage mode, the structure shows obvious asymmetric damage characteristics. After analysis, this asymmetry mainly originates from the initial eccentricity of the loading system, which makes the left side of the lining suffer from a greater stress concentration effect, and ultimately leads to the destruction of the structure as a whole to the left overturning.

The above damage characteristics fully reveal the mechanical response law of the assembled lining structure under the action of load, which provides an important experimental basis for the design optimisation of similar structures.

4.2. Analysis of Results

In order to make the damage deformation more specific, the data collected by the displacement meter was plotted into a displacement–deformation curve, as shown in Figure 9, to further study the deformation characteristics of the lining structure. The displacement change curves of the assembled lining model at each position are shown in Figure 11.

It can be learnt from the displacement change curve in the above Figure 12 that the first loading makes the whole lining structure sink due to the compression of the spring. As the loading step proceeds, the displacement at the arch top and arch waist gradually increases, and there is a stepwise growth. The displacement at the foot of the arch floats less, but the overall trend is a stepwise increase. It indicates that the lining structure is in the trend of overall sinking, up-and-down extrusion, and expansion towards the foot of the arch under the action of load. After the fifth loading, the growth of displacement at the arch began to accelerate, at which time the load reached 0.6 Fu, indicating that the lining structure began to undergo damage and the displacement had increased. After the sixth loading, the displacement of each position changed suddenly, and the maximum displacement of the arch top reached 12.7 mm, indicating that the cracks of the lining structure expand suddenly, which means that the reinforcing mesh in the concrete has already fractured, and due to the anisotropic constraints, the lining structure is not damaged until the seventh loading, and the overall deformation trend corresponds basically to the experimental phenomenon.

From the analysis of the above figure, it can be seen that at the beginning of the loading step, the strain at each position does not start at 0. This is due to the fact that the preload is not applied at the joint position of the assembled lining structure, which makes it possible for the lining to start to be tightened at the beginning of the loading period, until it can be tightly fitted at each position, and then it starts to be loaded. As the load was applied, there is a step change in the lining locations.

For the assembled lining left arch foot, arch top, right arch waist, right arch foot, when the test process is carried out to the fourth loading step, began to appear a more obvious sudden change, which indicates that in these positions of the lining, more obvious cracking has appeared; when the load continues to be applied, the lining structure continues to be stressed; the position of the strain continues to increase until after the sixth loading step, when the lining structure of each position of the strain appears to be an obvious, sudden change to 0, and after that no change is shown, which indicates that the lining of each position has been closely fitted. After that, there is no change, which indicates the complete destruction of the lining structure.

Compared with the cast-in-place tunnel lining model, the strain at each position of the assembled lining is similar to that of the cast-in-place lining and can be regarded as three stages: a slow growth stage, a small sudden change stage, and an ultimate destruction stage, and the changes in the three stages are all in the form of a stepwise change. However, the assembled lining structure has the manifestation of shrinking first and then stressing at the beginning of loading, and the sudden change is also more obvious in the second stage. The final damage also occurs earlier than in the fully cast lining structure.

In summary, for the assembled tunnel lining, the pre-tensioning of the joint part is very important, and the pre-tensioning force applied to the joint position during the splicing can effectively prevent the assembled lining from entering the working state directly when it is subjected to the load and reduce the displacement of each position. From the analysis of the location of cracks, it can be seen that the cracks of the assembled lining structure generally appear around the joints, and the joints are more prone to damage, which is due to the joint position of the assembled lining structure; due to the reason of the connecting parts, it is easy for stress to concentrate, and the components do not have a rigid connection, so they are more likely to be displaced and damaged.

5. Load-Structure Model Finite Element Simulation

5.1. Model Parameters

In this paper, ABAQUS 2022 is used to establish the foot-scale model for the fully cast and assembled lining structures. In order to accurately analyse the force performance of different blocking methods under the same load and optimise the calculation process, a rotating pin unit (combin7) can be introduced into ANSYS 2022 to simulate the flexural stiffness of the joints. In ABAQUS, the computational model of prefabricated lining joints is achieved by introducing a hinge unit and setting the stiffness parameter in the contact properties to simulate the flexural stiffness of the joints in the bending state. The overall calculation adopts the load-structure model and selects the appropriate support structure and mechanical parameters based on the road tunnel design code and related standards. For the definition of some attributes of the finite element simulation, the approach of some scholars [19] in the local study of tunnel lining joints is borrowed. The tunnel lining is simulated using beam units, C50 concrete is selected for the assembled lining, and the Coulomb contact model is used between the precast blocks with the friction coefficient set to 0.4.

The stress–strain relationship curve of concrete material under a uniaxial compression condition (e.g., Figure 4.4) can be determined based on the compression curve defined by the stress–strain relationship curve of C50 concrete provided in the Design Code for Hydraulic Concrete Structures (NB/T 11011-2022) [24]. The material parameters of C50 concrete pipe sheet are shown in

Table 3. C50 concrete pipe sheet material parameters.

Density (kg/m3)	Modulus of Elasticity (N/m2)	Poisson’s Ratio	Shear Expansion Angle (°)
2500	3.45 × 1010	0.2	30

.

5.2. Comparative Analysis

For the three-part assembled lining structure, the stiffness of the joint position is adjusted to simulate the different connection forms adopted in the joint part, and the load-structure model is used to simulate the stress condition of the tunnel lining structure under the peripheral rock loading, in order to analyse the performance of the three-part assembled lining structure and the fully cast lining structure in terms of the stress performance of the various positions, and to put forward the stiffness of the joint position which is the most suitable for the three-part assembled lining structure to achieve the purpose of construction convenience and stability close to the purpose of the fully cast lining.

The joint position and stress cloud diagram of the three-part assembled lining structure are shown in Figure 13.

It can be seen from the above deformation cloud diagrams that under the three-part chunking scheme, the maximum stresses occurred at the arch waist with lateral displacements, smaller rotations occurred at the foot of the arch joints, and larger vertical displacements accompanied by larger rotations occurred at the vault joints. Comparing the three-part block condition with different joint stiffnesses and the whole lining condition under Class V perimeter rock loading, the calculated results of maximum axial force, maximum bending moment, maximum lateral displacement, and maximum vertical displacement of the structure are summarised in

Table 4. Comparison of lining calculation results.

Sports Event	Joint Stiffness (MN-m/rad)
	0	5	10	20	30	40	50	All-Cast
axial force (kN)	−1878.6	−1866.2	−1853.2	−1837.5	−1820.8	−1806.3	−1794.4	−1749.0
kyphosis rectangle (kN-m)	268.6	252.3	241.8	229.4	220.5	256.5	287.8	354.2
transverse displacement (mm)	7.83	7.41	6.94	6.55	6.38	6.19	6.03	5.28
vertical displacement (mm)	−21.82	−21.36	−20.81	−20.24	−19.72	−18.55	−18.28	−17.74

below.

Under the same loading conditions, according to the data in the table above, the axial force of the monolithic lining increased gradually with the decrease in the joint stiffness. When the joint stiffness decreases to zero, the axial force of the segmental lining reaches a maximum value of 1878.6 kN, which is an increase of 7.4% from the initial state.

Under the same loading conditions, the bending moment of the block lining showed a tendency of decreasing and then increasing with the decrease in the joint stiffness. When the joint stiffness is 30 MN-m/rad, the bending moment decreases to the minimum value of 220.5 kN-m, which is 37.7% lower than the initial state.

In terms of transverse displacement, the maximum transverse displacement of the split lining under the same loading condition increased significantly with the decrease in the joint stiffness. When the joint stiffness is zero, the transverse displacement reaches the maximum value of 7.83 mm, which is 48.3% larger than the initial state.

The trend of vertical displacement was similar to that of lateral displacement. Under the same loading condition, the maximum vertical displacement of the block lining increased with the decrease in joint stiffness. When the joint stiffness is zero, the vertical displacement reaches the maximum value of 21.82 mm, which is 23.0% larger than the initial state.

In summary, as the joint stiffness decreases, the overall axial force of the lining slightly increases, the bending moment first decreases and then increases, while the vertical and lateral displacements both increase significantly. When the trisection blocking method was used, the bending moment was significantly reduced despite the increase in the overall lining displacement. This indicates that the force state of the lining is more stable after the structure reaches equilibrium, thus improving the overall stability of the structure.

5.3. Safety Factor Analysis

To evaluate the impact of the aforementioned structural model on the overall stability of the tunnel, the safety factors of the tunnel cross-section were calculated. Five critical locations were selected: the crown, haunches, sidewalls, springings, and invert (see schematic diagram in Figure 14). The calculated safety factors for each component are summarised in

Table 5. Comparison of lining calculation results.

Location	Joint Stiffness (MN-m/rad)
	0	5	10	20	30	40	50	Monolithic Lining
Vault	35.1	34.2	33.0	31.9	30.8	29.8	28.6	25.4
Shoulder	19.6	18.9	18.3	17.9	17.6	17.4	17.2	14.6
Sidewall	8.6	8.9	9.2	9.4	9.6	10.2	10.8	11.1
Foot	12.1	12.0	12.0	11.9	11.8	11.6	11.6	10.5
Base	17.0	17.0	16.9	16.9	16.8	16.8	16.7	16.4

.

Under loading, the initial safety factor of the overall lining vault was 25.4. With the reduction in joint stiffness, the safety factor of the vault showed an increasing trend. When the joint stiffness decreased to zero, the safety factor increased to 35.1, representing a 27.6% increase from the initial value. The initial safety factor of the overall lining haunch was 14.6. During the reduction in joint stiffness, the safety factor of the haunch gradually increased. At zero joint stiffness, the safety factor reached 19.6, marking a 34.2% increase compared to the initial value. The initial safety factor of the overall lining sidewall was 11.1. As the joint stiffness decreased, the safety factor of the sidewall progressively declined. When the joint stiffness reached zero, the safety factor decreased to 6.8, reflecting a 22.5% reduction from the initial value. The initial safety factor of the overall lining arch foot was 10.5. With decreasing joint stiffness, the safety factor of the arch foot exhibited a slight increase. At zero joint stiffness, the safety factor reached 12.1, corresponding to a 15.2% increase from the initial value. The initial safety factor of the overall lining invert was 16.4. As the joint stiffness reduced, the safety factor of the invert experienced a minor increase. When the joint stiffness was reduced to zero, the safety factor attained 17.0, indicating a 3.7% increase relative to the initial value.

Based on the above analysis, under the three-block segmentation scheme, the safety factors of the tunnel vault, haunch, and arch foot significantly decrease with increasing bending stiffness, while the safety factor of the sidewall exhibits a moderate increase. Nevertheless, the safety factors for all sections remain significantly higher than the specified limits.

6. Conclusions

In this study, the difference in the mechanical response of fully cast and three-part assembled tunnel linings under peripheral rock loading is systematically investigated by combining scaled-down tests and numerical simulations, and optimisation recommendations are made. The main conclusions are as follows:

• Tests showed that the ultimate bearing capacity of the assembled lining (288 kPa) was 15.3 per cent lower than that of the cast-in-place lining (340 kPa), and that crack initiation and expansion were concentrated earlier in the joint area. The damage of the fully cast lining showed an overall tilt trend, while the assembled structure was damaged asymmetrically due to the lack of joint stiffness, with a maximum crack width of 12.7 mm and a significant increase in displacement.
• Numerical simulation results show that the joint stiffness has a significant role in regulating the mechanical properties of the block lining. When the joint stiffness is reduced from 50 MN-m/rad to 30 MN-m/rad, the structural bending moment is reduced by 37.7%, and the increase in transverse displacement is controlled within 6.38 mm, which indicates that the moderate reduction of the stiffness can improve the distribution of the internal force, but it is necessary to balance the demand for displacement control.
• In order to improve the stability of the assembled lining, it is recommended to apply preload to the joints during construction to eliminate the initial gap, and at the same time optimise the stiffness of the joints to the range of 20–30 MN-m/rad, so that the bending moment and displacement characteristics are close to those of the fully cast lining. In addition, it is necessary to strengthen the local reinforcement of the joints between the vault and the foot of the arch to inhibit crack expansion.
• The synergistic effect of surrounding rock and lining is not considered in this study, and the structural response under actual working conditions can be further analysed by a stratigraphic–structural model. At the same time, the influence of the material detail difference on the damage evolution in the scaled-down test needs to be verified by the prototype test. In the follow-up, further in-depth studies can be carried out on parameters such as fatigue damage and the durability of the lining.