Experimental Investigation on the Mechanical Properties of Vault Void Lining in Highway Tunnels and Steel Plate Strengthening

: In the present study, large-scale specimens based on the tunnel prototype were prepared and static load tests were carried out to investigate the damage caused by lining voids. Based on the strengthening scheme of the tunnel, the strengthened specimens were prepared to explore the strengthening effect on the strengthening structure. The strengthening structure is made of a steel plate ﬁxed with chemical anchor bolts and two-component epoxy adhesive. By analyzing the failure mode, structural deformation, and the relationship between load and strain, the damage caused by vault void with various void heights was analyzed and the obtained results were veriﬁed through the experiment. Moreover, the enhancement of the bearing capacity and stiffness of the structure strengthened by surface bonding steel was studied. The obtained results show that the damage caused by the lining void mainly occurs at the void boundary. The damage appears as multiple longitudinal cracks. The crack starts from the lower surface and develops radially. Using chemical anchor bolts and two-component epoxy adhesive to bond the steel plate on the lining surface, the damage can be reduced, and the bearing capacity of the structure can be improved effectively when the void height is a quarter of the second lining thickness, the number of cracks is reduced from 14 to 5 after steel plate strengthening, and the length of the longest crack is reduced from 13.2 cm to 8.3 cm, reduced by 37.12%. The steel plate strengthening also reduces the strain of the lower steel bar at the void boundary from 1130.58 µε to 555.12 µε , and the strain decreases by 50.89%. The experimental results show that the position where the void has the greatest impact on the lining is at the void boundary. Therefore, when steel plates are used to strengthen the void lining, the void boundary should be emphasized, which makes the strengthening more accurate and saves the cost of treatment.


Introduction
With the rapid development of highways in China, the construction of highway tunnels has accelerated in the past few years.By the end of 2018, 17,738 highway tunnels with a total length of 17,236.1 km had been constructed in China, which is 1509 tunnels and 1951.0 km more than those in 2017 [1].The rapid tunnel construction is accompanied by some engineering challenges [2,3].The vault void in the secondary lining is a common problem in this regard [4].
In the tunnels constructed by the New Austrian Tunnelling Method (NATM), the secondary lining is constructed by pouring concrete in sealed steel formwork on-site so that the concrete accumulates from arch foot to vault.Accordingly, lining voids appear in the vault once problems such as residual gas in the vault formwork, poor concrete fluidity, and over-dense steel mesh occur.It is worth noting that the secondary lining in the void area is separated from the primary support [5], which is not affected by the surrounding rock pressure transmitted by the initial support.This separation directly affects the force state of the secondary lining [6].Under this circumstance, stress concentration occurs near the edge of voids, thereby increasing the adverse tensile stress.It can seriously affect the safety of the lining structure and if not treated in time [7,8], it may result in serious accidents and even lining collapse [9].
Reviewing the literature indicates that numerous investigations have been carried out on the lining void problems.In this regard, Yasuda et al. [10] presented two-dimensional elastic solutions for a deep circular tunnel with a void behind the lining and under far-field static loading.Accordingly, they analyzed the influence of lining voids on the structure under different loads.However, the boundary conditions of underground structures are generally complex.Consequently, it is an enormous challenge to obtain accurate analytical solutions in practical engineering.In order to resolve this shortcoming, numerical simulations have been widely applied in tunnel engineering.Then, different parameters, including size, boundary, and load conditions of the tunnel can be studied.Consequently, these numerical methods have attracted many scholars in engineering fields.Meguid and Dang [11] evaluated the effect of erosion voids developing in the close vicinity of existing tunnels on the circumferential stresses in the lining.A series of simplified void geometries were defined beside and under the lining.Elastic-plastic finite element analyses were performed to study the influence of those voids on the thrust forces and bending moments in the lining.Wang et al. [12] studied the void effect of different sizes, locations, and depths through elastic-plastic finite element analysis.Moreover, different parameters such as lining flexibility, in situ stress, and tunnel shape were also considered.Min et al. [13] designed the model experiment and established a model to study the cracking mechanism of the arch roof lining with voids, and reproduce a three-dimensional response for an asymmetric multi-arch tunnel structure caused by voids.
Although these studies are helpful to understand the influence of the voids on the lining structure, there are still some limitations.For example, the stress variation along the thickness direction of the lining is not considered in these methods.Moreover, there is no accurate understanding of the void caused by the insufficient thickness of the lining.Therefore, it is of great significance to study the circumferential stress characteristics and failure modes of the void region.
Studies show that structure strengthening is an effective treatment for the vault void problem.Currently, structure strengthening methods can be mainly divided into three categories, including pasting a high-strength fiber layer [14,15], sticking a steel plate [16][17][18][19][20], and constructing an umbrella arch [21,22].In an operating highway tunnel with a void problem, numerous auxiliary facilities such as lighting and fans are installed near the vault, limiting the available space margin for the strengthened structure.In these cases, sticking a steel plate on the lining surface has unique advantages in the treatment of voids in the vault.
With an increase in the traffic volume, the demand for large section tunnels is gradually increasing [23].Studies show that large cross-section tunnels are subjected to greater surrounding rock pressure.Accordingly, the secondary lining in these tunnels is generally thicker, thereby increasing the risk of void problems during the concrete pouring process.
In the present study, the highway tunnel is considered the research object, and it is studied from the following three aspects: (i) A model experiment was carried out to study the stress characteristics and the failure modes of the vault lining with different thickness voids.(ii) A mechanical model is established based on the experiment.Then the model is analyzed and verified through experimental results.(iii) The strengthening effect of the steel plate on the void lining is studied by making steel plate strengthening models.
In the second chapter of this paper, the details of the experimental device and specimen will be introduced.Then, in the third chapter, the void lining and strengthened lining will be analyzed from the perspective of damage, stress and deformation according to the experiment results.In addition, a simplified mechanical model will be established in the fourth chapter to calculate and verify the rules obtained from the experiment.

Prototype
Figure 1 shows that the studied tunnel is a bi-directional and four-lane highway tunnel, which can be categorized as a large section tunnel in the form of a three-centered arch.The detection of the tunnel lining shows that there are several voids behind the secondary lining.Moreover, the steel plate strengthening scheme was designed and installed to prevent lining cracks or falling blocks.Figure 2 shows the installation site of the strengthened steel plate.
In the second chapter of this paper, the details of the experimental device and sp men will be introduced.Then, in the third chapter, the void lining and strengthened lin will be analyzed from the perspective of damage, stress and deformation according to experiment results.In addition, a simplified mechanical model will be established in fourth chapter to calculate and verify the rules obtained from the experiment.

Prototype
Figure 1 shows that the studied tunnel is a bi-directional and four-lane highway t nel, which can be categorized as a large section tunnel in the form of a three-centered a The detection of the tunnel lining shows that there are several voids behind the second lining.Moreover, the steel plate strengthening scheme was designed and installed to vent lining cracks or falling blocks.Figure 2 shows the installation site of the strengthe steel plate.fourth chapter to calculate and verify the rules obtained from the experiment.

Prototype
Figure 1 shows that the studied tunnel is a bi-directional and four-lane highway tunnel, which can be categorized as a large section tunnel in the form of a three-centered arch.The detection of the tunnel lining shows that there are several voids behind the secondary lining.Moreover, the steel plate strengthening scheme was designed and installed to prevent lining cracks or falling blocks.Figure 2 shows the installation site of the strengthened steel plate.

Specimen Design Scheme
The established specimens consist of the arch crown section with a scale of 1:2.The concrete strength grade was C30.Moreover, the HRB335 rebar was used as the main strengthening, and a plain bar was used as the stirrups.In Figure 3, R (R = 4285 mm) and

Specimen Design Scheme
The established specimens consist of the arch crown section with a scale of 1:2.The concrete strength grade was C30.Moreover, the HRB335 rebar was used as the main strengthening, and a plain bar was used as the stirrups.In Figure 3, R (R = 4285 mm) and L (L = 3000 mm) denote the radius and length of the specimen, respectively.Moreover, D (D = 300 mm) and H (H = 200 mm) are the width and height of the cross-section of the specimen, respectively.It was assumed that there is a void of height h at the vault of each specimen.Details of the specimens are shown in Table 1.

Specimen Design Scheme
The established specimens consist of the arch crown section with a scale of 1:2.The concrete strength grade was C30.Moreover, the HRB335 rebar was used as the main strengthening, and a plain bar was used as the stirrups.In Figure 3, R (R = 4285 mm) and L (L = 3000 mm) denote the radius and length of the specimen, respectively.Moreover, D (D = 300 mm) and H (H = 200 mm) are the width and height of the cross-section of the specimen, respectively.It was assumed that there is a void of height h at the vault of each specimen.Details of the specimens are shown in Table 1.In the present study, two specimens are made for each working condition as a control group.The first specimen is not strengthened, while the second one is strengthened by a steel plate.The strengthening structure adopts the same scheme as the site, and the scale is also reduced.Meanwhile, a Q235 steel plate with a thickness of 5 mm was used as the  In the present study, two specimens are made for each working condition as a control group.The first specimen is not strengthened, while the second one is strengthened by a steel plate.The strengthening structure adopts the same scheme as the site, and the scale is also reduced.Meanwhile, a Q235 steel plate with a thickness of 5 mm was used as the sticking plate.M12 anchor bolts and a two-component epoxy resin adhesive were used in the adhesive layer.Figure 4 shows the arrangement of anchor bolts.

Loading Device
In the present study, a 500 kN symmetrical servo actuator with double output rods

Loading Device
In the present study, a 500 kN symmetrical servo actuator with double output rods was used to apply the desired load to the specimen.Figure 5 shows that the linkage loading method is adapted in both actuators.The arc distribution beam was designed to evenly distribute the load to the non-void part of the external surface.The load on the secondary lining vault caused by the initial support is simulated to make the model stress in line with the actual situation.The model is connected to the base by rigid support.To avoid the local damage to the concrete caused by the inclined sliding of the model in contact with the support, a 10 mm thick rubber layer is installed at the contact point between the support and the specimen to make the contact surface of the model and the support more tightly.

Loading Device
In the present study, a 500 kN symmetrical servo actuator with double output rod was used to apply the desired load to the specimen.Figure 5 shows that the linkage load ing method is adapted in both actuators.The arc distribution beam was designed t evenly distribute the load to the non-void part of the external surface.The load on th secondary lining vault caused by the initial support is simulated to make the model stres in line with the actual situation.The model is connected to the base by rigid support.T avoid the local damage to the concrete caused by the inclined sliding of the model in con tact with the support, a 10 mm thick rubber layer is installed at the contact point betwee the support and the specimen to make the contact surface of the model and the suppor more tightly.

Measurement Configuration and Scheme
During the loading process, the following indicators were measured: (a) model strain; (b) vertical displacement; (c) angle variation; (d) cracking process.For the unstrengthened specimen, strains on the bottom surface of the concrete, lateral void boundary, and the steel bar were measured.Moreover, strains of the strengthened steel plate, lateral void boundary, and steel bar were measured for the strengthened specimen during the experiment.
In order to measure the concrete strain, the bottom surface strain gauge and lateral strain gauge are utilized.Figure 7a illustrates the location of four strain gauges at the void boundary on the lateral surface.It is observed that seven strain gauges were installed on the transverse centerline of the bottom surface.These gauges were located at the mid-span, void boundary on both sides, midpoint between the void boundary on both sides and the mid-span, and the midpoint of the lining without void on both sides.

Crack Mode of Specimens
Figure 8 illustrates the distribution of cracks under various working conditions.It is observed that the concrete structure is mainly damaged near the void boundary.Moreover, some cracks appear near the support.However, these cracks mainly originate from uneven contact between the support and the model.Based on the Saint-Venant principle [24], the force near the support only affects the local stress distribution near the support and had almost no effect on the stress in the void area.Accordingly, the load-induced structural damage mainly appears near the void boundary.Under the existing bearing conditions, there is a negative correlation between the void height and the degree of damage.
For unstrengthened specimens, the crack development can be mainly divided into two stages.In the first stage, cracks appear at the boundary of the gap on the bottom surface.In this stage, cracks gradually extend as the applied load increases.When the crack further propagates and reaches the steel bar, the crack propagation suspends.Then, the crack enters the second stage as the applied load further increases.Furthermore, original cracks in the cracked area grow, and new cracks appear on the lower surface.At this time, oblique cracks begin to appear at the specimen support.
In the strengthened specimens, the number of cracks is significantly reduced and the length of cracks is significantly shortened after steel plate strengthening.When the void height is H/4, compared with the unstrengthened specimen, the number of cracks in the specimen strengthened by steel plate is reduced from 14 to 9, and the length of the longest crack is reduced from 13.2 cm to 8.3 cm.When the void height is H/3, the number of cracks is reduced from 10 to 1, and the length of the longest crack is reduced from 13.9 cm to 3.7 cm.When the void height is H/2, the number of cracks is reduced from eight to six, and the length of the longest crack is reduced from 12.3 cm to 6.3 cm.When the void height is Figure 7b shows the measured strain for the steel plate and the steel bars.Six strain gauges were installed on the upper and lower main bars on the same side.In addition, 11 strain gauges were installed on the surface of the steel plate.
Moreover, Figure 7 indicates that seven displacement gauges and seven inclination sensors were installed on the bottom surface of the specimen to detect deformations.The displacement meters were installed next to the concrete strain gauges on the bottom surface at different points, including the middle of the span, void boundaries, midpoint of the midspan and void boundary, and midpoint between the mid-span and the model boundary.

Experimental Result
3.1.Failure Mode 3.1.1.Crack Mode of Specimens Figure 8 illustrates the distribution of cracks under various working conditions.It is observed that the concrete structure is mainly damaged near the void boundary.Moreover, some cracks appear near the support.However, these cracks mainly originate from uneven contact between the support and the model.Based on the Saint-Venant principle [24], the force near the support only affects the local stress distribution near the support and had almost no effect on the stress in the void area.Accordingly, the load-induced structural damage mainly appears near the void boundary.Under the existing bearing conditions, there is a negative correlation between the void height and the degree of damage.

Crack Mode of an Adhesive Layer
In the strengthened specimens, the adhesive layer at some positions is damaged due to excessive stress on the lower surface of the concrete.The failure forms of the adhesive layer at different positions are different.Figure 9a refers to the shear failure with inclined cracks in the adhesive layer, which mainly occurs near the two rows of anchor bolts at the void boundary.Figure 9b refers to the separation failure with the adhesive layer pulling away from the concrete surface, which mainly occurs near the mid-span.

Deformation of the Bottom Surface
Figure 10 shows bottom surface deformation and fracture distribution under four void conditions, including the vertical displacement, and rotation angle for unstrengthened and strengthened specimens.It can be seen that the cracks of the standard lining are mainly distributed symmetrically along the middle of the span, while the cracks of the void lining are mainly distributed at the void boundary.In the unstrengthened specimens, seven measuring points on the bottom surface reflect the relative deformations of the void and boundary area.When the void height is H/4, the vault settlement is the largest, which For unstrengthened specimens, the crack development can be mainly divided into two stages.In the first stage, cracks appear at the boundary of the gap on the bottom surface.In this stage, cracks gradually extend as the applied load increases.When the crack further propagates and reaches the steel bar, the crack propagation suspends.Then, the crack enters the second stage as the applied load further increases.Furthermore, original cracks in the cracked area grow, and new cracks appear on the lower surface.At this time, oblique cracks begin to appear at the specimen support.
In the strengthened specimens, the number of cracks is significantly reduced and the length of cracks is significantly shortened after steel plate strengthening.When the void height is H/4, compared with the unstrengthened specimen, the number of cracks in the specimen strengthened by steel plate is reduced from 14 to 9, and the length of the longest crack is reduced from 13.2 cm to 8.3 cm.When the void height is H/3, the number of cracks is reduced from 10 to 1, and the length of the longest crack is reduced from 13.9 cm to 3.7 cm.When the void height is H/2, the number of cracks is reduced from eight to six, and the length of the longest crack is reduced from 12.3 cm to 6.3 cm.When the void height is 2H/3, there is no obvious crack on the lower surface of the steel plate strengthened specimen after loading.The experimental results show that steel plate strengthening can effectively reduce the damage caused by lining voids.

Crack Mode of an Adhesive Layer
In the strengthened specimens, the adhesive layer at some positions is damaged due to excessive stress on the lower surface of the concrete.The failure forms of the adhesive layer at different positions are different.Figure 9a refers to the shear failure with inclined cracks in the adhesive layer, which mainly occurs near the two rows of anchor bolts at the void boundary.Figure 9b refers to the separation failure with the adhesive layer pulling away from the concrete surface, which mainly occurs near the mid-span.

Deformation of the Bottom Surface
Figure 10 shows bottom surface deformation and fracture distribution under four void conditions, including the vertical displacement, and rotation angle for unstrengthened and strengthened specimens.It can be seen that the cracks of the standard lining are mainly distributed symmetrically along the middle of the span, while the cracks of the void lining are mainly distributed at the void boundary.In the unstrengthened specimens, seven measuring points on the bottom surface reflect the relative deformations of the void and boundary area.When the void height is H/4, the vault settlement is the largest, which is 4.74 mm.However, as the void height increases, the relative settlement of the vault gradually decreases.When the void height is 2H/3, the vault has a relative upward bulge, and the uplift value reaches 1.41 mm.In the strengthened specimens, the steel plates in the strengthened specimens are bonded to the concrete through the adhesive layer.During the loading process, the adhesive layer is damaged and the steel plate is separated from the concrete.Consequently, there is a certain deviation between the steel plate settlement and the specimen settlement.

Crack Mode of an Adhesive Layer
In the strengthened specimens, the adhesive layer at some positions is damaged due to excessive stress on the lower surface of the concrete.The failure forms of the adhesive layer at different positions are different.Figure 9a refers to the shear failure with inclined cracks in the adhesive layer, which mainly occurs near the two rows of anchor bolts at the void boundary.Figure 9b refers to the separation failure with the adhesive layer pulling away from the concrete surface, which mainly occurs near the mid-span.

Deformation of the Bottom Surface
Figure 10 shows bottom surface deformation and fracture distribution under four void conditions, including the vertical displacement, and rotation angle for unstrengthened and strengthened specimens.It can be seen that the cracks of the standard lining are mainly distributed symmetrically along the middle of the span, while the cracks of the void lining are mainly distributed at the void boundary.In the unstrengthened specimens, seven measuring points on the bottom surface reflect the relative deformations of the void and boundary area.When the void height is H/4, the vault settlement is the largest, which

Lateral Strain of the Void Boundary
Figure 11 shows the lateral strain at the void boundary on both sides of each specimen.The numbers 1-4 are concrete measuring points on the side of the void boundary in Figure 7a, numbered from bottom to top.It is observed that the lower side of the void boundary is under tension, while the upper side is under compression.With the increase in the applied load, the tensile and compressive strains increase gradually so that some tensile strain gauges are damaged, indicating crack propagation.A comparison of the obtained results for unstrengthened specimens indicates that the tensile strain of the bottom surface decreases as the void range increases.This is consistent with the crack propagation at the bottom surface in the experiment.Meanwhile, comparing the strengthened and unstrengthened specimens indicates that variations of the tensile stress near the bottom surface of the strengthened specimen are small, while the tension on the upper surface increases and the neutral axis of the cross-section of the sample moves down, demonstrating that the strengthened steel plate effectively reduces the generation of adverse tensile stress and plays an important role in the strengthening.

Strain of Steel Bars
Figure 12 shows the strain diagram of steel bars under various working conditions.The letters a-f represent 6 measuring points at different positions on the reinforcement in Figure 7b, numbered from left to right.Generally, when the lower steel bars are under tension, the upper one is under compression, and the stress of the steel bars at the void boundary is greater than that at the mid-span.In the unstrengthened specimen, the tensile strength of the lower layer of the void boundary decreases as the void range increases.This is consistent with the crack propagation on the bottom surface of the specimen.In the strengthened specimens, the tensile force of the lower steel bars is effectively restrained due to the strengthening effect of the steel plate.
gradually decreases.When the void height is 2H/3, the vault has a relative upward bulge, and the uplift value reaches 1.41 mm.In the strengthened specimens, the steel plates in the strengthened specimens are bonded to the concrete through the adhesive layer.During the loading process, the adhesive layer is damaged and the steel plate is separated from the concrete.Consequently, there is a certain deviation between the steel plate settlement and the specimen settlement.

Strain of Steel Plate
Figure 13 depicts the strain diagram of steel plates under various working conditions.The numbers 1-11 represent 11 measuring points at different positions on the steel plate in Figure 7a, numbered from left to right.The strain of the steel plate generally increases with the increase in the load.However, due to the damage to the adhesive, the strain of the steel plate decreases at some points.When the void height h = H/4, the strain at 5, 6, and 7 points decreases.These points are located within the void range and there are no anchor bolts.As the load increases, the adhesive is gradually destroyed, and the tensile stress of the steel plate is gradually reduced.When the void height h = H/3, the strain at points 3, 4, 5, and 6 decreases.There are anchor bolts at points 3, 4, and 5.When the adhesive layer fails, the anchor bolt bears the tensile stress.However, the tensile stress gradually decreased due to the lack of anchor bolts at point 6.When the void height h = H/2, the tensile stress of the steel plate is significantly reduced, and the strain gauge at point 4 is damaged.When the void height is h = 2H/3, the steel plate does not receive excessive tension.It is only in tension at the initial stage of loading.The steel plate is gradually turned into a compressive state with the load increases.

Strain of Steel Plate
Figure 13 depicts the strain diagram of steel plates under various working conditions.The numbers 1-11 represent 11 measuring points at different positions on the steel plate in Figure 7a, numbered from left to right.The strain of the steel plate generally increases with the increase in the load.However, due to the damage to the adhesive, the strain of the steel plate decreases at some points.When the void height h = H/4, the strain at 5, 6, and 7 points decreases.These points are located within the void range and there are no anchor bolts.As the load increases, the adhesive is gradually destroyed, and the tensile stress of the steel plate is gradually reduced.When the void height h = H/3, the strain at points 3, 4, 5, and 6 decreases.There are anchor bolts at points 3, 4, and 5.When the adhesive layer fails, the anchor bolt bears the tensile stress.However, the tensile stress gradually decreased due to the lack of anchor bolts at point 6.When the void height h = H/2, the tensile stress of the steel plate is significantly reduced, and the strain gauge at point 4 is damaged.When the void height is h = 2H/3, the steel plate does not receive excessive tension.It is only in tension at the initial stage of loading.The steel plate is gradually turned into a compressive state with the load increases.

Simplified Model Calculation
An analysis of the obtained results indicates that the most serious damage area is located near the void boundary.To verify the cracking position of the specimen, the elastic center method is used to calculate the internal force of the specimen.As shown in Figure

Simplified Model Calculation
An analysis of the obtained results indicates that the most serious damage area is located near the void boundary.To verify the cracking position of the specimen, the elastic center method is used to calculate the internal force of the specimen.As shown in Figure 14, the coordinate system is established and the model is simplified to a hinged arch.Since the symmetrical structure bears symmetrical force, there is no shear force, (i.e., X3 = 0), and only two forces X1 and X2 should be calculated.The governing equations can be expressed as: The term δ12 is the auxiliary coefficient and can be obtained from Equation (2).
When the structure is individually subjected to the forces X1 = 1, X2 = 1, X3 = 1, we can obtain: Introducing Equation (3) into Equation ( 2) with δ12 = δ21 = 0 results in the following expression: (1) where ys is the length of the rigid arm and can be calculated as follows: Since the symmetrical structure bears symmetrical force, there is no shear force, (i.e., X 3 = 0), and only two forces X 1 and X 2 should be calculated.The governing equations can be expressed as: The term δ 12 is the auxiliary coefficient and can be obtained from Equation (2).
When the structure is individually subjected to the forces X 1 = 1, X 2 = 1, X 3 = 1, we can obtain: Introducing Equation (3) into Equation ( 2) with δ 12 = δ 21 = 0 results in the following expression: where y s is the length of the rigid arm and can be calculated as follows: For an arch structure, the curvature has little impact on the deformation.Therefore, the displacement of the straight bar can be used to solve the coefficient and free term.
where E donates the modulus of elasticity; I is the moment of inertia of the section; A is the cross-sectional area; ϕ represents the central angle between the radius of the calculated point and the Y-axis; y k is the ordinate of point k; M P is the bending moment generated by the external load at the point.X 1 and X 2 can be calculated from Equation (1).The section height of the voided section model is defined as follows: where h denotes the height of the vault void, and H 1 and H 2 are the radius of the outer and inner contours, respectively.Since the height of the cross-section changes in the void area, voided and unvoided sections are separately integrated during the calculation.The bending moment at point K is the sum of the bending moments generated by the forces and moments at this point.This can be mathematically expressed in the form below: where y s is the length of the rigid wall; M KP is the bending moment produced by the external load on the half structure.Since the external load does not cause a bending moment at the void boundary, M KP can be set to 0. In order to analyze the distribution of the cracks in the void lining under external loads, the void height is interpolated based on the experimental conditions.Figure 15 shows the bending moment diagram of the specimen under the void conditions.It is observed that the bending moment in the void area is positive, indicating that the bottom surface in this area is under tension.Moreover, the bending moment reaches its maximum near the void boundary.Therefore, cracking always starts from the void boundary.Figure 16 shows the axial force diagram of the semi-structure.It is found that the axial force is low and almost constant within the void range of the same height, while it gradually increases from the void boundary to the support section.The axial force of the structure appears as an inflection point due to the void, and the inflection points all occur at the void boundary.
In order to determine the location of the first crack, the stress superposition method was used to superimpose the surface stress caused by the axial force and the bending moment at the lower edge of the section.
Figure 17 shows the lower surface stress under various working conditions.It can be seen from the figure that the bottom surface is under tension in the void range, and the maximum tensile stress of the bottom surface appears near the void boundary.This is consistent with the observed cracked area in the experiment.It is worth noting that the maximum value of normal stress does not just appear at the void boundary but the outside of the boundary.In order to determine the location of the first crack, the stress superposition method was used to superimpose the surface stress caused by the axial force and the bending moment at the lower edge of the section.
Figure 17 shows the lower surface stress under various working conditions.It can be seen from the figure that the bottom surface is under tension in the void range, and the maximum tensile stress of the bottom surface appears near the void boundary.This is consistent with the observed cracked area in the experiment.It is worth noting that the maximum value of normal stress does not just appear at the void boundary but the outside of the boundary.In order to determine the location of the first crack, the stress superposition method was used to superimpose the surface stress caused by the axial force and the bending moment at the lower edge of the section.
Figure 17 shows the lower surface stress under various working conditions.It can be seen from the figure that the bottom surface is under tension in the void range, and the maximum tensile stress of the bottom surface appears near the void boundary.This is consistent with the observed cracked area in the experiment.It is worth noting that the maximum value of normal stress does not just appear at the void boundary but the outside of the boundary.

Conclusions
In the present study, a large-scale model static loading experiment was carried out to explore the failure mode of the arch lining with roof voids.Based on the on-site strength-

Conclusions
In the present study, a large-scale model static loading experiment was carried out to explore the failure mode of the arch lining with roof voids.Based on the on-site strengthening scheme, appropriate steel plate strengthened void specimens were made to study the strengthening effect of the steel plate with a chemical anchor bolt and epoxy adhesive.Then, calculations were carried out and verified through experiments.Nine specimens were analyzed and accordingly, the following conclusions were obtained: (1) The damage caused by vault void is mainly tensile damage and is mainly concentrated in the void boundary.This damage develops radially from the bottom surface upward.With the increase in the void range, the subsidence of the midspan relative to the void boundary gradually decreases.That is, there is a relative uplift in the middle of the span.The deformation changes from 4.74 mm downward in void height H/4 to 1.41 mm upward in void height 2H/3.(2) Compared with the unstrengthened specimens, the strengthened ones have fewer and shorter cracks under the same applied load.It is inferred that the steel plate strengthening with chemical anchor bolts and the epoxy adhesive has significantly reduced the void-induced damages.For instance, when the void height is H/4, the number of cracks after steel plate strengthening is reduced from 14 to 9, and the maximum crack length is shortened from 13.2 cm to 8.3 cm, which is a decrease of 37.12%.In addition, the steel plate strengthening also reduces the strain of the lower steel bar at the void boundary from 1130.58 µε to 555.12 µε, and the strain decreases by 50.89%.When the void range is small, the whole steel plate is under tension.However, when the void range increases, the tensile force of the strengthened steel plate decreases gradually, and the compression area appears.(3) With the increase in load, the failure of the adhesive layer can be divided into two forms.At the void boundary, the adhesive layer has inclined cracks and gradually loses its function.However, due to the presence of chemical anchors here, the steel plate stress is maintained.Because there is no chemical anchor bolt in the mid-span, the stress of the steel plate decreases gradually with the expansion of the damage range of the adhesive layer.(4) A simplified calculation model is established.Considering the influence of section change on eccentricity, the bending moment, axial force, and lower surface stress of the model are obtained by integration.The results show that the voids increase the bending moment at the void boundary, reduce the axial force, and cause large tensile stress at the void boundary.The calculated results are in good agreement with the experiment.
Although the void lining is analyzed through experiments, this experimental specimen is based on local specimens, and the experimental results may be affected by the size effect.Subsequently, we may carry out the whole lining model experiment and use the numerical model to verify the results in future studies.

Figure 1 .Figure 1 .
Figure 1.Transverse section and strengthening scheme of the studied tunnel.

Figure 1 .Figure 2 .
Figure 1.Transverse section and strengthening scheme of the studied tunnel.

Figure 2 .
Figure 2. Installation of the steel plate.(a) Hoisting steel plate; (b) drilling; (c) installation of anchor bolts and adhesive layer; (d) final installed plate.

Figure 2 .
Figure 2. Installation of the steel plate.(a) Hoisting steel plate; (b) drilling; (c) installation of anchor bolts and adhesive layer; (d) final installed plate.

Figure 3 .
Figure 3. Installation of the steel plate.

Figure 3 .
Figure 3. Installation of the steel plate.
Appl.Sci.2022, 12, x FOR PEER REVIEW 5 of 20 sticking plate.M12 anchor bolts and a two-component epoxy resin adhesive were used in the adhesive layer.Figure4shows the arrangement of anchor bolts.

Figure 5 .
Figure 5. Layout of the loading system.

Figure 6
Figure 6 illustrates the configuration of the loading device.It should be indicated tha several loading processes were carried out before the experiment until the displacemen

Figure 5 .
Figure 5. Layout of the loading system.

Figure 6 Figure 6 .
Figure 6  illustrates the configuration of the loading device.It should be indicated that several loading processes were carried out before the experiment until the displacement meter becomes stable.The whole loading was performed in 10 stages of 1 min, where a load of 50 kN was added at each stage.In the two adjacent loading steps, a one-minute interval was maintained.Appl.Sci.2022, 12, x FOR PEER REVIEW 6 of 20

Figure 6 .
Figure 6.Configuration of the loading system.(a) Front of experimental equipment; (b) Back of experimental equipment.

Figure 7 .
Figure 7. Measurement scheme.(a) Measurement scheme of the concrete; (b) Measurement scheme of the reinforcement.

Figure 7 .
Figure 7. Measurement scheme.(a) Measurement scheme of the concrete; (b) Measurement scheme of the reinforcement.

Figure 9 .
Figure 9. Failure modes of the adhesive layer.(a) Shear failure; (b) Separation failure of the bonding interface.

Figure 9 .
Figure 9. Failure modes of the adhesive layer.(a) Shear failure; (b) Separation failure of the bonding interface.

Figure 9 .
Figure 9. Failure modes of the adhesive layer.(a) Shear failure; (b) Separation failure of the bonding interface.

Table 1 .
Details of the specimens.

Table 1 .
Details of the specimens.