Study on Construction Response Characteristics of Large Cross-Section Tunnel Crossing Huge Karst Cave Backfill

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Introduction
In recent years, the number of tunnels built in karst landscapes has been increasing [1][2][3][4][5][6].Due to the complexity and diversity of karst landscapes, a large number of water and mud inrush hazards and collapses have occurred during the construction of karst tunnels, causing huge losses of economic [7][8][9][10][11][12][13][14][15][16][17][18].For example, the excavation face of the Chaoyang Tunnel encountered large karst caves, resulting in a water inrush disaster.A lining trolley was fushed out of the hole owing to the huge water pressure [19].Another typical case was Lingjiao Tunnel, which was known as the largest mudslide disaster in Chinese history [20,21].More than 40000 m 3 of mud and a 12 m deep collapse pit were generated on the surface above the tunnel.
At present, a lot of research has been carried out on the construction response characteristics of karst tunnels [22][23][24][25][26][27][28][29][30][31][32].Chen and Sha [33] studied the stability of the surrounding rock and the treatment structure during the Naqiu Tunnel excavation by means of feld tests and numerical simulation.Li et al. [34] analyzed the infuence of the size, volume, and location of karst caves on the displacement of diferent measuring points on the monitoring section through numerical simulation, and compared it with the situation without karst caves.Tus, a method for predicting the top of a hidden karst cave based on displacement monitoring during tunnel construction is proposed.Xu et al. [35] simplifed the geological conceptual model through PANDAS software, established a numerical model, and discussed the infuence of the location and size of the karst cave and the distance between the tunnel and the karst cave on the principal stress and displacement of the surrounding rock.Zheng et al. [36] took the tunnel crossing, the largest karst cave in the history of China, as an example, and put forward a series of disposal schemes.Te efectiveness of the scheme was verifed by the feld monitoring data, which laid a good foundation for the construction.Zhang et al. [37] established a three-dimensional numerical model to analyze the stress feld and displacement feld of surrounding rock after tunnel excavation around the karst cave, and revealed the variation law of the stress and displacement with tunnel excavation.Zhou et al. [38] used the three-dimensional fnite element software ANSYS to simulate the interaction between the karst cave treatment structure and tunnel excavation of the Baishugong Tunnel, and evaluated the reinforcement efect of the support structure.Li et al. [39] explored the development law of the surrounding rock stress feld and displacement feld under the condition of changing the excavation size of the tunnel and the development size of the karst cave by using the self-developed large-scale model test system, and revealed the process of karst cave disaster.
Te above studies show that most of the studies have focused on cavern solutions, and relatively few studies have been conducted on the construction response characteristics of huge cavern backflling [40][41][42][43][44][45][46][47][48][49][50][51].Although Chen et al. [52] studied the stress distribution and deformation of surrounding rock in their numerical simulation of a large karst cave in front of the Huaguoshan Tunnel.Li et al. [53] used the fnite diference method to conduct three-dimensional simulation calculations on the existence of a karst cave and the stress distribution, displacement characteristics, and plastic zone size of surrounding rock before and after grouting flling and reinforcement.Lin [54] studied the mechanical response of surrounding rock in the process of crossing the giant karst cave in front of the full section and based on this, selected and optimized the structure.However, there are few studies on the construction response characteristics of a superlarge cross-section tunnel crossing a giant karst cave.
Terefore, based on the construction of the YJS tunnel crossing the huge karst cave backfll, the numerical simulation method was used to analyze the law in the horizontal convergence of each step.Meanwhile, the stress feld distribution of the tunnel, the axial force of the transverse support, and the distribution characteristics of the plastic zone of the model were obtained.In view of the unstable stress and displacement of surrounding rock, a series of engineering countermeasures are proposed.Te reliability of the numerical modeling method was further verifed by site data.Tis study enriches the research status of a superlarge cross-section tunnel and a giant karst cave and has reference signifcance for the research and construction of similar projects.

Project Case
Te tunnel is located between Xingwen and Weixin on the Cheng-gui Railway line in China [55].Te tunnel area is in the terrain of the transition from the Sichuan Basin to the Yunnan-Guizhou Plateau, with steep mountains, gullies, and valleys, large relative height diferences, and strongly developed karst.Te tunnel is 25.21 m high, 19.52 m wide, with a cross-sectional area of 432 m 2 , a total tunnel length of 6306 m, and a maximum burial depth of 350 m.Te top of the tunnel is located near the roof of the hall, and section D3K279 + 855∼ + 960 crosses the cave hall.Te direction of the line mileage and the main axis of the cave intersect at a large angle of 80 °.Te relationship between the tunnel and the cave is shown in Figure 1.
Te cave is developed longitudinally for about 93 m along the line direction and laterally for about 230 m in the vertical line direction, roughly rectangular in shape [56,57].Te top of the cave is dome-shaped, and the vertical height of the hall varies from 50 to 120 m.Te bottom of the cave is flled with fll material, which is 30 to 90 m thick.Te surface soil is yellow clay, under which is the cave fll material in the form of crushed stones, gravelly soil, medium-coarse sand, and fne pebbles.Te cavern fll is dominated by crushed block stone soil, and according to the exploration, there are soft clay and other weak interlayers of 0-15 m thick distributed between them, with poor regularity.In addition, the accumulation is sloping from the top of the right side of the line to the bottom of the dark river, with a slope of 30-35 °, and the rock body where the cavern is located is limestone.Te construction plan is to excavate the backfll body after using slag and block backfll.A simplifed geological crosssection is shown in Figure 2.

Numerical Simulation
3.1.Numerical Model.Midas/GTS is a fnite element analysis software that organically combines the general fnite element analysis kernel with the specialized requirements of geotechnical tunnel structures.Compared with other engineering software, the software has many advantages in use, such as fast and intuitive 3D modeling, professional geotechnical analysis functions, fast and accurate automatic mesh generation, and intuitive analysis results.Te calculation and analysis results are relatively safe and favored by engineers.It has 15 kinds of intrinsic structure models and can customize the intrinsic structure models.Te analysis  Shock and Vibration functions available include construction phase analysis, static analysis, seepage analysis, dynamic analysis, and coupled seepage and stress analysis, covering almost all analysis functions in the tunneling feld.Te specifc modeling process is shown in Figure 3.
Te calculated dimensions of the model were L × W × H � 300 m × 85 m × 300 m.Te model range around the tunnel met 3-5 times the excavation section.Te geometric boundary shape of the giant cavern is very complex, and it is simplifed accordingly.Te flling soil in the cavern is mainly broken stone soil and soft clay, and the upper part of the cavern is backflled with rubble and spoil.Te calculation model is shown in Figure 4.
Te physical and mechanical parameters of the soil layers, backfll, support structure, reinforced soil layers, and the adopted intrinsic structure models are shown in Table 1.All materials are homogeneous, continuous, and isotropic.Limestone, crushed stone soil, soft clay, block stone, waste slag, the limestone, waste slag, and soft clay after reinforcement are simulated by a three-dimensional solid element, shotcrete is simulated by a slab element, and anchor rods and horizontal support are simulated by an embedded beam element.
Te actual depth of the cavern is about 350 m.According to the self-weight stress q � ch � 27 × 280 � 7560 kPa, a uniform load of 7560 kPa is applied to the upper part of the surrounding rock in the vertical direction of the model.In addition, the boundary conditions of the model are vertical restraint at the bottom and normal restraint around the perpendicular to the rock surface.Te initial stress states are the self-weight stress and the upper vertical uniform load.

Construction Stages Simulation.
Te sixth bench excavation construction method was adopted.Te whole construction process consists of six bench excavations and anchor shotcrete support as a cycle step.It mainly includes excavation, bolting and concreting support, lining construction, arch concrete backflling, horizontal support construction, grouting reinforcement at both sides and bottom, horizontal support removal, and other construction stages.Te construction process is shown in Table 2, and the important construction stages are shown in Figure 5.
Te release of the accumulated elastic energy of the soil is simulated by setting the load release factor to avoid the unbalanced internal forces due to excavation being loaded onto the excavation stages at once.Te excavation process is simulated by loading 40%, 30%, and 30% of the soil into diferent construction stages, gradually reducing the load by stages, and fnally completely releasing the soil.6, the displacement of the surrounding rock on the left side of the tunnel axis shows a trend of settlement, while the right side shows a trend of uplift.Tis is due to the fact the tunnel is located on the upper right side of the giant karst cave, resulting in the surrounding rock on the left side being flled with waste slag, block stone, crushed stone soil, soft clay, and other backfll.Compared with the limestone on the right side, its strength is low, its vertical settlement is large, and the tunnel is in a biased state.

Result Analysis
To further analyze its deformation law, a total of six measurement points at the arch waist on both sides of the three typical sections were selected for the study, and their displacement curves were made (Figures 7 and 8).It can be concluded that (1) the whole section of the frst step of the tunnel is excavated, resulting in a rapid increase in the displacement value at the arch waist.Te settlement of the left waist is 4.3 mm, and the uplift of the right side is 10.6 mm.However, if the bolt concrete support and grouting reinforcement measures are taken in time, the displacement can be well controlled.Te growth rate of displacement on the left and right sides of the arch waist is signifcantly reduced.( 2

Shock and Vibration
of the section at the measurement point is mainly caused by the excavation stage.Among them, about 92% of the total displacement at point 4 is caused by the excavation stage, and about 85% of the total displacement at points 5 and 6 is caused by the excavation stage.But with the application of horizontal support, the growth rate of displacement at waist gradually decreases, until the displacement value basically tends to stabilize and no longer grows after the application of grouting reinforcement to the backfll at the bottom of the tunnel.Te relative displacement of the left and right sides of the waist was basically maintained at about 29 mm.It shows that the construction of horizontal supports and bottom grouting reinforcement are efective means to control the large rate of deformation of the arch waist during large section excavation in the backfll of a giant karst cave.

Horizontal Convergence.
Figure 9 shows the construction steps-curve of cumulative horizontal convergence of section D3K279 + 916.It can be seen: ( 1) the horizontal convergence of the whole bench section increases rapidly in the excavation stage, and then it is in the slow growth stage    Shock and Vibration by the excavation.(4) Te maximum horizontal convergence of the frst stage before the construction stage of section S14 at 916 is about 6.2 mm, the maximum accumulated horizontal convergence of the fourth stage after the completion of construction is about 19.7 mm, followed by about 19.5 mm for the third stage.Terefore, more attention should be paid to the monitoring and control of the horizontal convergence at the frst stage in the early stage, and more attention should be paid to the monitoring and control of the horizontal convergence at the third and fourth stages in the later stage.Te minimum principal stresses in the initial stress state of the model and the stable state after construction are shown in Figure 11.It can be seen that ( 1) under the infuence of the uneven distribution of rock and soil in the huge cavern, the minimum principal stress at the bottom of the model is in the state of compressive stress.In the lower left corner of the model, the small angle corner below the cavern, and the right edge of the cavern, there is a concentration of the minimum principal stress, with the maximum values of 14 MPa, 26 MPa, and 11 MPa, respectively.Te minimum principal stresses in the surrounding rocks of the tunnel are all in the compressive stress state, with the right-hand side of the surrounding rocks being larger than the left-hand side, with a maximum value of around 2.7 MPa. (2) Under the infuence of oversized section tunnel excavation, only the minimum principal stress distribution in the surrounding rock around the tunnel changed signifcantly after construction was completed and stabilized.Te minimum principal stress near the left side arch waist and the right wall foot of the tunnel is concentrated, showing a state of tensile stress.Te stress concentration near the right arch waist and the left wall foot of the tunnel is in a state of compressive stress.Te maximum value of the minimum principal stress at the right wall foot of the tunnel is 0.1 MPa, and the maximum value of the minimum principal stress at the left arch waist is about 0.2 MPa.Te maximum value of the minimum principal stress of the right arch waist is about 7.3 MPa, and the maximum value of the maximum principal stress of the left wall footing is about 4.8 MPa.

Stress
From the above analysis, the principal stress values of the surrounding rock around the tunnel after the model is stable are shown in Table 3. "+" indicates that the principal stress is tensile stress, and "−" indicates that the principal stress is compressive stress.It can be seen from the table that the value of one principal stress at one place of the surrounding rock is always very small or even close to zero relative to the other principal stress.Terefore, the maximum principal stress can be used to express the tensile stress state of the surrounding rock around the tunnel, and the minimum principal stress can be used to express its compressive stress state.
In order to further analyze the variation law of the principal stress of surrounding rock with the tunnel construction, extract the principal stress at the left arch waist, right arch waist, left wall foot, and right wall foot, and draw a temporal curve (see Figure 12).It can be seen from the fgure that (1) during the whole construction process, the stress value at the right arch waist and wall foot is basically greater than that at the left arch waist and wall foot.Tis phenomenon is caused by the irregular shape of the giant karst cave and the complex distribution of rock and soil in it.Te principal stress values at the left arch waist and the right wall foot are in tensile stress throughout the process, and the stress values at the left wall foot and the right arch waist are in compressive stress throughout the process.( 2) With the construction of the tunnel, the principal stress values at the arch waist and the bottom of the wall increase as a whole.Due to the overall excavation of the frst step of the crosssection tunnel, the principal stress at the arch waist increases rapidly.After the frst step of anchor concrete support, arch concrete, and grouting reinforcement on both sides are completed, the principal stress value basically tends to be stable.After the excavation of the ffth step, the principal stress at the foot of the tunnel wall increases signifcantly.
With the excavation and support, the principal stress decreases gradually and fnally tends to be stable.Shock and Vibration layers of horizontal supports on each excavation section is shown in Figure 13.It can be seen from the fgure that the axial force distribution law of each cross-section of the twolayer cross support is basically the same, showing a pattern of "frst decreasing, maintaining stability, and then decreasing."Te axial force at the tunnel entrance is the largest, 270 kN for the frst layer and 216 kN for the second layer.Te axial force at the tunnel exit is the smallest, 148 kN for the frst layer and 75.8 kN for the second layer.Te axial force of the middle section decreases gradually with the increase in      excavation depth.Among them, the axial force of the 890-940 cross-section is basically the same.Te frst layer is about 210 kN, and the second layer is about 150 kN.Te axial force of the frst layer is generally greater than that of the second layer.

Horizontal Support Axial
In the case of oversized cross-sectional tunnels through giant caverns, the law of change of the cross supports during the construction process should not be ignored either.Take the horizontal support at the section with the maximum axial force of the frst and second foors as the research object, and draw the variation law of the axial force with the construction process, as shown in Figure 14.It can be seen that the variation law of the maximum axial force of the frst-foor horizontal support and the secondfoor horizontal support with the construction is basically the same.Firstly, the axial force increases rapidly when the horizontal support is just constructed.With the excavation of the corresponding bench to the completion of the excavation, the axial force value shows a trend where the growth rate gradually decreases and then tends to stabilize to reach the maximum axial force.Te maximum axial force of the frst layer is 270 kN, and the maximum axial force of the second layer is 216 kN.Te axial force of the horizontal support on the rigid construction increases rapidly, so more monitoring and prevention should be carried out.

Plastic Zone Analysis.
Te state of distribution of the plastic zone in the important construction stage of the tunnel is shown in Figure 15.Te red area in the fgure indicates that the rock and soil mass is in a plastic-bearing state.Although plastic deformation occurs, the strength of the rock and soil mass does not decrease.Te blue area indicates that the rock and soil mass are in a state of plastic loosening, and the strength decreases with plastic deformation.Te green area indicates that the soil mass is in a tensile plastic failure state, and the colorless area indicates that the rock mass is in an elastic state.
(1) During the stage of the initial stress, some of the fragmented broken stone soil and almost all of the soft clay soils in the lower strength giant cavern fll are in a plasticbearing state compared to the backfll and limestone.A few of the fragmentary broken stones are in the state of tensile plastic failure.Te limestone at the lower right of the giant karst cave, where the broken stone soil contacts the block stone, is in a plastic-bearing state due to the shape of the small angle corner karst cave, which is prone to stress concentration.(2) In the S2 construction stage, due to the whole section excavation of the frst step of the superlarge cross-section tunnel, although the corresponding bolting and concreting support was implemented in time, most of the rock mass in the plastic-bearing state in the initial stress state changed to plastic-loosening state.At the same time, both sides of the frst step of the tunnel change from an elastic to plastic-bearing state.After the S3 stage arch crown concrete and grouting reinforcement on both sides, the rock and soil mass in the plastic-bearing state on the left side of the frst step return to the elastic state, and the reinforcement efect is good.(3) After the excavation of the second bench in the S4 stage, the fll soil originally in the plastic-bearing area and the limestone at the small angle corner are all transformed into the plastic-loosening area.After the frst layer of horizontal support is applied at the S7 stage and the second layer of horizontal support is applied at the S11 stage, part of the flling area is restored from the plastic-loose state to the plastic-bearing state.It shows that the construction of transverse bracing has a certain stable efect on the excavation process of the superlarge cross-section tunnel passing through a giant karst cave.(4) It can be seen from the state of the plastic zone from the S4 stage to the S11 stage that the plastic-bearing zone is mainly distributed at the right edge of the tunnel section during tunnel excavation, which is mainly caused by the asymmetry of rock and soil mass on both sides of the tunnel caused by the giant karst cave.In addition, the plastic-bearing area gradually develops downward with the continuous excavation of the steps.Terefore, during the excavation of the tunnel, the surrounding rock state at the right waist, foot, wall, and wall foot of the tunnel should be monitored and prevented.(5) All the tunnels were excavated in the S29 stage, and the plastic zone in the flling area deteriorated to a certain extent, but the plastic state improved after grouting reinforcement at the bottom of the tunnel in the S30 stage.After the removal of the horizontal support in the S31 stage, almost all the rock and soil mass in the original plastic-bearing state have changed to the plasticloose state, but the tunnel as a whole is still in a stable state.
Terefore, although the state distribution of the plastic zone of the superlarge cross-section tunnel passing through the backfll of the giant cave is bad, it has been controlled to a certain extent after diferent reinforcement measures to ensure safe construction.Shock and Vibration vibrating-wire receiver, respectively [58][59][60][61].Trough the above monitoring items, the changes in displacement could be obtained.Due to the limited space, this article only shows the displacement results of monitoring sections (the most critical section has been chosen) [36,56,57].Te specifc section and its measuring point layout are shown in Figure 16.

Monitoring Data Analyses.
Te horizontal convergence monitoring data of section 916 during tunnel construction are presented in Figure 17.
It can be seen from the curve that (1) in the excavation and reinforcement stage of the frst bench, the horizontal convergence value at the frst bench is very small and basically remains unchanged.It shows that the anchor concrete support, vault concrete, and grouting reinforcement measures on both sides have a good control efect on the horizontal convergence caused by the overall excavation of the frst bench.(2) From the second step of section D3K279 + 916 to the completion of bottom slab construction, the horizontal convergence value of each step increases rapidly.After backflling the cavity behind the initial support, the growth of the horizontal convergence value of each step is restrained and tends to moderate.After the horizontal support is removed, the horizontal convergence value at the second step rebounds, but the horizontal convergence value at other steps does not increase.(3) During the whole construction process, the cumulative maximum value of horizontal convergence is about 17 mm, the numerical simulation result is about 19.7 mm, and the maximum error is 15.9%.Te temporal variation law of horizontal convergence is slow growth in the early stage, rapid growth of deformation during excavation, and stable deformation in the later stage.Tis is basically consistent with the numerical simulation results.
Te crown settlement monitoring data of sections 916∼956 were selected for comparative analysis, as shown in Figure 18.Te settlement curve of section D3K279 + 916∼956 fuctuates in the range of 80 days.After grouting and backflling, the fnal settlement is in a safe and stable range of between 0.4 mm and 13.5 mm.It took about three months for the accumulated crown settlement of the section to reach a stable state, and the fnal value was small.

Shock and Vibration
In order to further verify the accuracy of the numerical model, the crown settlement data for the key construction steps are extracted, as shown in Figure 19.Te numerical calculation results are in good agreement with the settlement trend of the site monitoring data, and the fnal settlement error is 8.6%.
In summary, considering the complexity of the actual project at the site and the limitations of the simulation software, the results of the numerical simulation can be approximated as having high reliability.Shock and Vibration

Conclusions and Prospects
In this paper, the distribution characteristics and variation rules of the displacement stress feld, horizontal support axial force, and plastic zone of surrounding rock and backfll body during the construction of a tunnel crossing a giant karst cave are analyzed.Te main conclusions are as follows: (1) During the excavation of the whole section of the frst stage, the horizontal convergence and arch waist displacement values increased sharply.Te deformation trend was efectively controlled after support and grouting, and the growth rate was reduced by 93%, and then remained stable.(2) Under the initial stress state, the maximum principal stress is mainly distributed in a "V" shape with the tunnel as the infection point, and the maximum value is 3.2 MPa in soft clay.Te maximum value of the minimum principal stress is about 26 MPa at the small angle corner below the karst cave.(3) Te stress is redistributed after the model is stable.
Stress concentration occurs in the area of the tunnel arch waist, and wall footing, which is easy to cause support damage.Te maximum compressive stresses are 7.3 MPa and 4.8 MPa, and the maximum tensile stresses are 3.8 MPa and 5.3 MPa, respectively, which should be monitored more during the construction process.It is recommended to take antibuckling measures to strengthen local fexural rigidity and reduce the internal force and stress concentration.Also, the construction of bolts follows closely.(4) Te change law of the axial force of the two layers of horizontal support is basically the same, showing a sharp increase and a gradually stable growth trend.Te axial force of the frst layer of horizontal support is larger than that of the second layer, 270 kN and 216 kN, respectively, and the axial force is the largest at the entrance of the tunnel.
(5) Te excavation disturbance of the tunnel leads to the deterioration of the rock and soil mass from the plastic-bearing state to the plastic-loose state.Te reinforcement means such as grouting reinforcement and horizontal support will restore the rock and soil mass from the plastic-loose state to the plastic-bearing state.Te plastic-bearing area is mainly distributed at the right edge of the tunnel section, and the plastic-bearing area gradually develops downward with the continuous excavation of the steps.(6) Te monitoring data show that the horizontal convergence and the crown settlement show a slow growth in the early stage and a rapid growth in deformation, and maintain a stable deformation trend.Te numerical results are in good agreement with the site monitoring data.Te average error of fnal settlement and peripheral convergence is 8.6% and 15.9%, respectively, which verifes the correctness of the numerical modeling method.
Te above study is only a preliminary one on the mechanical behavior and convergence deformation law of surrounding rock and the horizontal support of the YJS tunnel through the giant cavern.Te mechanical properties and internal force evolution law of the tunnel support structure can be explored subsequently, which verifes the feasibility of the tunnel design and construction plan.Meanwhile, model tests can be carried out on the settlement development of the backfll through indoor centrifugal tests to analyze the settlement development trend of the backfll and further verify the correctness of the numerical modeling method.

Figure 2 :
Figure 2: Location of the cavern in relation to the cross and longitudinal section of the tunnel.(a) Longitudinal section.(b) Cross-section.

Figure 9 :
Figure 9: Horizontal convergence of each step at 916 section.

Figure 10 :
Figure 10: Maximum principal stress distribution.(a) Initial stress state.(b) Stress state after model stabilization.

Figure 11 :
Figure 11: Minimum principal stress distribution.(a) Initial stress state.(b) Stress state after model stabilization.

Figure 12 :
Figure 12: Temporal plot of principal stress values.

5. 1 .Figure 13 :Figure 14 :
Figure 13: Distribution of fnal axial forces in two layers of horizontal supports at diferent sections.
when it is not excavated to the target section.When the target section is excavated, the convergence rate increases rapidly.After the bottom grouting reinforcement, the slow and stable deformation stage shall be restored.(2)Concrete in the arch and grouting reinforcement on both sides are efective in controlling the rapid growth of horizontal convergence caused by the excavation of the entire frst stage of an oversized section of the tunnel.(3) Te growth rate of horizontal convergence in the excavation stage of the tunnel gradually decreases with the application of horizontal support, indicating that horizontal support is efective in controlling the large rate of horizontal convergence caused

Table 2 :
Contents of the construction stage.

Table 3 :
Principal stress of surrounding rock after model stabilization.