# The Optimization of Shed-Tunnel Structure in the Confined Environment

Authors: Wu Yi; Huizhao Shao; Zhoutong Cui; Xiaohu Huang; Ying Zhou
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The design of shed-tunnel structure in the confined environment can help to avoid the safety of passing vehicles and pedestrians from being threatened by the impact of upper rockfall in highway, railway, and other rockfall disaster protection engineering. Due to the limitation of the space environment, it is necessary to optimize the shed-tunnel structure to provide enough space for passing vehicles and pedestrians. In this study, a case study was made on the passing shed tunnel of Badong Juebitianhe Revolutionary Education Base. First, the theoretical calculation of rockfall impact force was compared and optimized. Then, the optimization scheme of “column + anchor bolt + buffer layer” was proposed based on the commonly used shed-tunnel form and was verified by ABAQUS numerical simulation. The performance of the optimized shed-tunnel structure is greatly improved in terms of the space utilization rate of shed tunnel and the impact resistance of rockfall.


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## Body

## 1. Introduction

Confined environment refers to the environment with limited space. In the theory system of geological disaster prevention and control, confined environment is mainly manifested by high and steep slope in the inner side and gully cliff in the outer side of the mountain road with limited passage width. Under the impact of natural factors, the inner slope is prone to collapse and rockfall disaster, especially the high and steep rock slopes with sparse vegetation and developed rock fissures. Affected by rainfall and dead weight, such slops tend to form negative terrain such as local inverted ridge and cause rockfall disaster, which seriously affect road passage and vehicle and pedestrian safety.Shed-tunnel structure protection is commonly used for preventing dangerous rock collapse in such geological environments. New structural forms such as frame shed tunnel, skew joist shed tunnel, and all-steel shed tunnel are often adopted at tunnel entrances [1]. To a certain extent, the shed-tunnel structure solves the difficulties brought by bad geological problems to railway construction. Yang et al. [2] proposed a new type of flexible shed tunnel, which achieved buffer energy dissipation by flexible using the energy-dissipating structure formed by flexible metal mesh and spring struts to replace the sand-gravel cushion laid at the top of the traditional reinforced concrete shed tunnel. Jiang et al. [3] conducted a related study by establishing two simulation models of frame portal shed tunnel through the ANSYS/LS-DYNA finite element software. The research results show that the impact resistance of the shed tunnel can be improved to some extent by changing the structure roof angle. Based on the numerical simulation on the impact process of rockfall using a dynamic finite element, Wu et al. [4] obtained the dynamic and mechanical responses of the structure under different impact angles of rockfall and concluded that the deflection deformation of the roof plate and the roof beam of the shed tunnel presented a quadratic parabolic shape. According to the comparative analysis of experiments of ordinary support shed tunnel and energy dissipation support shed tunnel, Bertrand et al. [5] concluded that the energy dissipation support made of mild steel could improve the bearing performance of the shed tunnel. In addition, Delhomme et al. [6] replaced the sand-gravel cushion by adding structurally dissipating rock-sheds (SDR) at the support of concrete shed tunnel to absorb rockfall impact energy and studied its dynamic behavior by scale test. In addition, many scholars have conducted a lot of theoretical analyses on the numerical simulation of shed tunnel. For example, Labiouse et al. [7] summarized the empirical algorithm of rockfall impact force by combining it with the field rockfall impact test. Yang and Guan [8] studied the factors affecting the impact force by using a hammer impact buffer layer through an indoor model test and proposed relevant formulas for rockfall impact calculation. Pichler et al. [9] studied the impact characteristics of rockfall by using a numerical simulation method and combining it with the pipeline protection structure in sandy cobble stratum.The traditional shed tunnel can ensure the safety of management engineering in a confined environment, but it can not meet the requirements in terms of economic cost and impact resistance. Therefore, it is necessary to optimize the shed-tunnel structure. With the shed tunnel of Badong Juebitianhe Revolutionary Education Base, as an example, first of all, the rockfall impact theory calculation methods of confined environment were compared, and the traditional methods were optimized. Second, based on the optimal impact theory, the optimized shed-tunnel structure was put forward. Next, numerical simulation was conducted on the stress and displacement in the different parts (beams and columns) of the optimized shed tunnel through the ABAQUS software.


## 2. Comparison and Optimization of Theoretical Calculation of Rockfall Impact Force in a Confined Environment

Few people pass through a confined environment. Besides, there are mostly steep cliffs in the mountain area, resulting in a low safety index. The shed-tunnel structure mainly needs to bear the external load of the impact load of rockfall. Thus, the calculation of the impact force of rockfall can provide a basis for the practical engineering prevention and control.The existing impact force algorithms include the subgrade code method, tunnel manual method, Yang Qixin method, Japanese road authority method, Swiss method, Ye Qiqiao method, and Xiang Xin method. The following assumptions were made before comparing these methods:(1)
Rockfall was assumed to be a homogeneous sphere. Besides, both the fragmentation of rockfall and the splashing of buffer soil were ignored in the impact process.(2)
The rockfall height group setting is as follows: 15 m, 30 m, 45 m, 60 m, and 75 m.


### 2.1. Introduction to Existing Calculation Methods

The different calculation methods and formulas are summarized in Table1.Table 1
Different calculation methods and formulas.
Calculation methodCalculation formulaSubgrade code methodP=PZF=2yZ2tan445°+ϕ/2−1F, where Z=VRQ/2gγF×1/2tan445°+ϕ/2−1Tunnel manual methodp=Qv0/gtt=2h/cc=1−μ/1+μ1−2μ×E/ρYang Qixin methodp=ζmamaxa=2gh/tt=1/1000.097mg+2.2h+0.045/H+1.2Xiang Xin method [10]F=3.2377l×γ×Nγ1/3mgH2/3, Nγ=1.8Nq−1tanϕ, Nq=tan245°+ϕ/2extanϕ, Fmax=7.412l×γ×Nγ1/3mgH2/3Note. In the formula of the existing calculation method, P denotes the impact force of falling rock, (kN); P(Z) denotes the unit resistance of rockfall impact on the buffer layer (kPa); VR denotes the impact velocity (m/s) when rockfall contacts the buffer soil layer; Φ denotes the density of the layer (kN/m3); g denotes the acceleration of gravity (m/s2); and F denotes the cross-sectional area of the equivalent sphere of rockfall (m2).The following results were obtained according to the comparison of different calculation methods of impact force: with the increase of rockfall radius, the impact force calculated by all methods kept increasing trend. To be specific, the impact force calculated by the Xiang Xin method had the fastest increase and the largest calculated impact force, followed by the Japanese road authority method and the Swiss method; the impact force calculated by the tunnel manual method had the slowest increase and the least calculated impact force. With the increase of the height of free fall, however, the difference between the methods became larger and larger.


### 2.2. Comparison of Each Method with Simulation Results

According to the comparison and analysis of the impact force of rockfall with an equivalent radius of 0.2–0.5 m falling from a height of 20–100 m, it was concluded that the simulated values were close to those calculated by the Xiang Xin method and Japanese road authority method. The deviations between the simulated values and the values calculated by the above two methods were 1.9% and 20.62%, respectively, when the equivalent radius of rockfall was 0.2 m and the height of rockfall was 100 m. With the increase of rockfall mass and falling height, however, the simulated values gradually approached the values calculated by the Xiangxin method. The deviation between the simulated values and the values calculated by above two methods was −1.85% and 40.67%, respectively when the equivalent radius of rockfall was 0.5 m and the falling height was 100 m. The impact force calculated by the Xiangxin method was the closest to the simulated value, and the deviations were all within 10%. However, the amplification coefficient of the impact force in this method needed to be improved because of the large mass and height of rockfall in a confined environment.


### 2.3. Advantages and Disadvantages of Each Method

Among the above methods, the value obtained by the tunnel manual method was the minimum. The effect of gravity in the process of rockfall was not considered; the rockfall did not rebound after the regulated impact; the impact duration obtained by this method was too long. Hence, the values obtained were smaller. Some experiments proved that the impact duration of rockfall generally did not exceed 0.14 s. In fact, the value obtained by this method was the average value of the impact process, rather than the maximum impact force.Similarly, the value obtained by Yang Qixin was also the average value in the process of rockfall impact, rather than the maximum impact force. In addition, the effect of gravity in the process of rockfall was not considered, so the impact force calculated by this method was still smaller, being similar to the value obtained by the tunnel manual method.According to the functional principle, the value obtained by the subgrade code method was actually also the average impact force and was smaller. Its calculation result was close to that of Yang Qixin and could not reflect the changing relationship between rockfall and the thickness of buffer layer.As for the Japan Road community method and Switzerland method, the empirical formula was established based on a field test. The calculation result was the maximum impact, and it was more in line with the engineering practice. The value obtained by the Japan Road community method was larger. The two methods were different in terms of the selection of lame constant and deformation modulus, but they did not consider the effect of buffer layer thickness of rockfall impact.Based on the theory of energy conservation and foundation bearing capacity, the Xiang Xin method calculated the reaction force of buffer layer, so the impact force obtained was the maximum, being the calculated maximum value among the above methods. It was more consistent with the actual rockfall engineering of free-falling body, but it was highly sensitive to rockfall.Therefore, the Xiang Xin method was the most suitable for the calculation of rockfall impact force in a confined environment, and it is reasonable and feasible to optimize the shed-tunnel structure by using the Xiang Xin method as the calculation method of rockfall impact force in a confined environment.


## 2.1. Introduction to Existing Calculation Methods

The different calculation methods and formulas are summarized in Table1.Table 1
Different calculation methods and formulas.
Calculation methodCalculation formulaSubgrade code methodP=PZF=2yZ2tan445°+ϕ/2−1F, where Z=VRQ/2gγF×1/2tan445°+ϕ/2−1Tunnel manual methodp=Qv0/gtt=2h/cc=1−μ/1+μ1−2μ×E/ρYang Qixin methodp=ζmamaxa=2gh/tt=1/1000.097mg+2.2h+0.045/H+1.2Xiang Xin method [10]F=3.2377l×γ×Nγ1/3mgH2/3, Nγ=1.8Nq−1tanϕ, Nq=tan245°+ϕ/2extanϕ, Fmax=7.412l×γ×Nγ1/3mgH2/3Note. In the formula of the existing calculation method, P denotes the impact force of falling rock, (kN); P(Z) denotes the unit resistance of rockfall impact on the buffer layer (kPa); VR denotes the impact velocity (m/s) when rockfall contacts the buffer soil layer; Φ denotes the density of the layer (kN/m3); g denotes the acceleration of gravity (m/s2); and F denotes the cross-sectional area of the equivalent sphere of rockfall (m2).The following results were obtained according to the comparison of different calculation methods of impact force: with the increase of rockfall radius, the impact force calculated by all methods kept increasing trend. To be specific, the impact force calculated by the Xiang Xin method had the fastest increase and the largest calculated impact force, followed by the Japanese road authority method and the Swiss method; the impact force calculated by the tunnel manual method had the slowest increase and the least calculated impact force. With the increase of the height of free fall, however, the difference between the methods became larger and larger.


## 2.2. Comparison of Each Method with Simulation Results

According to the comparison and analysis of the impact force of rockfall with an equivalent radius of 0.2–0.5 m falling from a height of 20–100 m, it was concluded that the simulated values were close to those calculated by the Xiang Xin method and Japanese road authority method. The deviations between the simulated values and the values calculated by the above two methods were 1.9% and 20.62%, respectively, when the equivalent radius of rockfall was 0.2 m and the height of rockfall was 100 m. With the increase of rockfall mass and falling height, however, the simulated values gradually approached the values calculated by the Xiangxin method. The deviation between the simulated values and the values calculated by above two methods was −1.85% and 40.67%, respectively when the equivalent radius of rockfall was 0.5 m and the falling height was 100 m. The impact force calculated by the Xiangxin method was the closest to the simulated value, and the deviations were all within 10%. However, the amplification coefficient of the impact force in this method needed to be improved because of the large mass and height of rockfall in a confined environment.


## 2.3. Advantages and Disadvantages of Each Method

Among the above methods, the value obtained by the tunnel manual method was the minimum. The effect of gravity in the process of rockfall was not considered; the rockfall did not rebound after the regulated impact; the impact duration obtained by this method was too long. Hence, the values obtained were smaller. Some experiments proved that the impact duration of rockfall generally did not exceed 0.14 s. In fact, the value obtained by this method was the average value of the impact process, rather than the maximum impact force.Similarly, the value obtained by Yang Qixin was also the average value in the process of rockfall impact, rather than the maximum impact force. In addition, the effect of gravity in the process of rockfall was not considered, so the impact force calculated by this method was still smaller, being similar to the value obtained by the tunnel manual method.According to the functional principle, the value obtained by the subgrade code method was actually also the average impact force and was smaller. Its calculation result was close to that of Yang Qixin and could not reflect the changing relationship between rockfall and the thickness of buffer layer.As for the Japan Road community method and Switzerland method, the empirical formula was established based on a field test. The calculation result was the maximum impact, and it was more in line with the engineering practice. The value obtained by the Japan Road community method was larger. The two methods were different in terms of the selection of lame constant and deformation modulus, but they did not consider the effect of buffer layer thickness of rockfall impact.Based on the theory of energy conservation and foundation bearing capacity, the Xiang Xin method calculated the reaction force of buffer layer, so the impact force obtained was the maximum, being the calculated maximum value among the above methods. It was more consistent with the actual rockfall engineering of free-falling body, but it was highly sensitive to rockfall.Therefore, the Xiang Xin method was the most suitable for the calculation of rockfall impact force in a confined environment, and it is reasonable and feasible to optimize the shed-tunnel structure by using the Xiang Xin method as the calculation method of rockfall impact force in a confined environment.


## 3. The Design Optimization of Shed-Tunnel Structure Based on Optimization Impact Force Theory

### 3.1. Shed-Tunnel Structure Type

The design of shed tunnel needs to be considered for mountainous areas where most geological disasters occur, so the classification of shed tunnel in mountainous areas is of great significance [11]. Shed tunnel has various structure forms, which is mainly composed of five parts, namely, outer support structure, inner wall, roof, transverse connection at the bottom, and the outer foundation [12]. To be specific, the outer supporting structure is in the form of straight column, inclined column, cantilever, wall type, and arch beam; the inner wall is in the form of retaining wall and curved arch; the roof is in the form of flat plate and curved arch; the outer foundation structure is in the form of independent foundation, strip foundation, pile foundation, and underground continuous wall.


### 3.2. Optimization of Shed-Tunnel Structure

Shed tunnel can help to avoid endangering the lives of passing vehicles and pedestrians. Due to the limitation of the space environment, however, it is necessary to optimize the structure form of the shed tunnel. In the study, by comparing with the traditional shed-tunnel structure, the shed tunnel was optimized from the aspects of structure shape, connection mode of the shed tunnel and the rock mass, and the buffer layer material of the roof board to improve the utilization rate of space while satisfying the structural performance.Therefore, based on the comparison with the ordinary shed-tunnel structure described in Section3.1, the following optimization measures were proposed for shed-tunnel structure:(1)
Shed tunnel has more strict requirements for concrete material. Thus, the rock mass was replaced by shed-tunnel stress components; the original internal and external pillars as the main stress components were replaced by only lateral pillars. Besides, the inner pillars were removed and replaced by the slope rock mass and anchor bolt.(2)
According to the study of Luo Wenjun and Cao [13], the vibration isolation effect of the barrier filled with tire debris was optimal within the frequency band of 1–10 Hz and 15–25 Hz. Therefore, abandoned tires were used to provide the buffer energy dissipation effect of rockfall for the buffer soil layer of the shed tunnel.The optimized shed-tunnel structure model is shown in Figure 1.Figure1 shows a three-dimensional schematic diagram of an optimized shed-tunnel structure. In the figure, the main stressed components of the shed tunnel are the roof plate and column. The overall enhancement inside is achieved by embedding the shed-tunnel with the rock slope body by anchor rods.Figure 1
Three-dimensional schematic diagram of portal anchoring shed tunnel.The section drawings of shed-tunnel structure before and after optimization are shown in Figures2 and 3:Figure 2
Section of portal anchoring shed tunnel.Figure 3
Section of portal wall shed tunnel.The comparison of shed tunnel before and after optimization is listed in Table2.Table 2
Comparison of shed tunnel before and after optimization.
Contrast factorBefore optimizationAfter optimizationOptimization resultsAvailable volume of space5.05 m³6.313 m³Being improved by 25%Useable volume of concrete6.375 m³5.025 m³Economic returns increased significantlyPeak value of impact force on the roof5.7 N/mm22.8 N/mm2Being improved by 50%Note. The extension length of the shed tunnel is 1 m.


## 3.1. Shed-Tunnel Structure Type

The design of shed tunnel needs to be considered for mountainous areas where most geological disasters occur, so the classification of shed tunnel in mountainous areas is of great significance [11]. Shed tunnel has various structure forms, which is mainly composed of five parts, namely, outer support structure, inner wall, roof, transverse connection at the bottom, and the outer foundation [12]. To be specific, the outer supporting structure is in the form of straight column, inclined column, cantilever, wall type, and arch beam; the inner wall is in the form of retaining wall and curved arch; the roof is in the form of flat plate and curved arch; the outer foundation structure is in the form of independent foundation, strip foundation, pile foundation, and underground continuous wall.


## 3.2. Optimization of Shed-Tunnel Structure

Shed tunnel can help to avoid endangering the lives of passing vehicles and pedestrians. Due to the limitation of the space environment, however, it is necessary to optimize the structure form of the shed tunnel. In the study, by comparing with the traditional shed-tunnel structure, the shed tunnel was optimized from the aspects of structure shape, connection mode of the shed tunnel and the rock mass, and the buffer layer material of the roof board to improve the utilization rate of space while satisfying the structural performance.Therefore, based on the comparison with the ordinary shed-tunnel structure described in Section3.1, the following optimization measures were proposed for shed-tunnel structure:(1)
Shed tunnel has more strict requirements for concrete material. Thus, the rock mass was replaced by shed-tunnel stress components; the original internal and external pillars as the main stress components were replaced by only lateral pillars. Besides, the inner pillars were removed and replaced by the slope rock mass and anchor bolt.(2)
According to the study of Luo Wenjun and Cao [13], the vibration isolation effect of the barrier filled with tire debris was optimal within the frequency band of 1–10 Hz and 15–25 Hz. Therefore, abandoned tires were used to provide the buffer energy dissipation effect of rockfall for the buffer soil layer of the shed tunnel.The optimized shed-tunnel structure model is shown in Figure 1.Figure1 shows a three-dimensional schematic diagram of an optimized shed-tunnel structure. In the figure, the main stressed components of the shed tunnel are the roof plate and column. The overall enhancement inside is achieved by embedding the shed-tunnel with the rock slope body by anchor rods.Figure 1
Three-dimensional schematic diagram of portal anchoring shed tunnel.The section drawings of shed-tunnel structure before and after optimization are shown in Figures2 and 3:Figure 2
Section of portal anchoring shed tunnel.Figure 3
Section of portal wall shed tunnel.The comparison of shed tunnel before and after optimization is listed in Table2.Table 2
Comparison of shed tunnel before and after optimization.
Contrast factorBefore optimizationAfter optimizationOptimization resultsAvailable volume of space5.05 m³6.313 m³Being improved by 25%Useable volume of concrete6.375 m³5.025 m³Economic returns increased significantlyPeak value of impact force on the roof5.7 N/mm22.8 N/mm2Being improved by 50%Note. The extension length of the shed tunnel is 1 m.


## 4. Engineering Cases

In this study, the optimization scheme of the traditional shed tunnel was explained by taking the shed-tunnel design of the geological disaster spot of Juebitianhe in Juebitianhe an example. Juebitianhe Revolutionary Education Base is located in Qingtaiping Town and Shuibuya Town, Badong County. There are a certain number of disaster spots along the base. Any instability will affect the normal operation of irrigation canals, drinking water, and irrigation for tens of thousands of people in Badong and Changyang counties. Besides, it will affect the lives and property safety of more than 200 households below the canal. In addition, it will pose a serious threat to the life safety of students, party cadres, and tourists who come here to carry out party day activities.The destroying modes of the dangerous rock mass in the rocky slope were dominated by falling type and dumping type. Moreover, lithologic was hard limestone rock mass. Therefore, the ordinary shed-tunnel structure was optimized as follows: the inter side and rock mass were built-in into an organic whole through an anchoring bolt; as the contact of the shed-tunnel structure, the outer side held the stress passed to the pillar from the top of the shed tunnel through the pile foundation. The engineering geology section is shown in Figure4, and the elevation layout of the engineering is shown in Figure 5.Figure 4
Section of engineering geology.Figure 5
Elevation layout of the engineering.Stratigraphic lithology of Badong Juebitianhe Revolutionary Education Base is listed in Table3.Table 3
The stratigraphic lithology of Badong Juebitianhe revolutionary education base.
FormationDistribution location and material compositionQ4Quaternary colluvial deposits (Q4col + dl)It is distributed below the cliff Tianhe channel of the exploration route of Shuibuya Section of the exploration line, with an uneven thickness of generally 3–5 m. It is mainly composed of collapsed stones with diameters of generally 0.5–1 m and 1.8 m at most.Quaternary artificial accumulation layer (Q4ml)It is distributed below the precipitous Tianhe channel of the exploration route from Sanlicheng to Baishuoping Section. The main material composition is gravel soil, with the soil-rock ratio of 7 : 3, presenting a loose to slightly dense state, with a distribution thickness of 1–3 m.Quaternary landslide deposits (Q4del)It is distributed in the exploration route from Shuiliuping Section to Baishuoping Section, that is, the large landslide, which is composed of gravel soil, with the content of about 40%–50%; gravel components are limestone, with the diameter of generally 5 cm–30 cm and about 1 m at most; the soil has a high content of yellowish-brown clay particles. The accumulation layer has an average thickness of 4 m, and a total volume of about 3.2 × 104 m3.Bed rockLower triassic daye formation (T1d)The lithology of the stratum is a thin layer and medium-thick layer limestone, with the stratum occurrence of 135–240°∠4–15°, serious surface weathering, and local small-scale falling. Rock mass and slope form tangential slope and reverse slope structure.The mountain terrain in the Juebitianhe area has a large slope, generally reaching 60°–80°, and most of them are steep cliffs, which provide good space conditions for the formation of dangerous rock masses. The dangerous rock mass is composed of thin layer and middle layer of limestone with hard brittle lithology, which provides a material source for the formation of dangerous rock mass. The rock mass fractures are complexly developed and are dominated by steeply inclined fractures, and they can deform and expand under gravity unloading. Besides, the weathering of rock mass, the infiltration of fissure water, and the wedging of plant roots can quicken the collapse and deformation of dangerous rock mass. The space is limited in the construction process. The traditional shed tunnel was optimized by the optimization scheme proposed in this study. The optimized shed tunnel not only facilitated the construction but also took into account the requirements of the confined construction site under the actual environmental conditions.


### 4.1. Contrastive Analysis of Stress

The portal wall shed-tunnel structure was taken as an example before the optimization. The optimization model in this study used ABAQUS as simulation software, and the material constitutive model was mainly based on the actual optimization model. The physical parameters of the management project in Enshi, Hubei province, are calculated and simulated, as listed in Table4. The stress nephogram is shown in Figure 6.Table 4
Physical parameter values of materials.
Densityρ (kg/m³)Elasticity modulusE (Mpa)Poisson’s ratioμCohesionc (kPa)Friction angleφ (°)78502000000.32025250050000.241850350.352500300000.2Figure 6
Equivalent stress nephogram of portal wall shed-tunnel structure.The portal anchoring shed-tunnel structure is taken as an example after the optimization, with the stress nephogram, as shown in Figure7.Figure 7
Equivalent stress nephogram of portal anchoring shed-tunnel structure.Based on the comparison and analysis of Figures6 and 7, it was found that the external force on the joints between columns and beams of the portal wall shed tunnel was much greater than that of the portal anchoring shed tunnel.According to the equivalent stress nephogram, the unit stress curves of the key parts of the jack stringer of the shed tunnels could be obtained, as shown in Figures8 and 9.Figure 8
The unit stress curves of the key parts of the jack stringer of the portal wall shed tunnel.Figure 9
The unit stress curves of the key parts of the jack stringer of the portal anchoring shed tunnel.Based on the comparison and analysis of Figures8 and 9, it was found that the peak value of unit stress in the key position of the jack stringer of the anchoring shed tunnel and the unit stress value after the structure was stabilized were lower than the corresponding position of the wall shed tunnel.According to the equivalent stress nephogram, the unit stress curves of the key parts of the center pillars of the shed tunnels could be obtained, as shown in Figures10 and 11.Figure 10
The unit stress curves of the key parts of the center pillars of the portal wall shed tunnel.Figure 11
The unit stress curves of the key parts of the center pillars of the portal anchoring shed tunnel.As seen from the comparison and analysis of Figures10 and 11, the peak value of unit stress in the key position of the center pillars of the anchoring shed-tunnel and the unit stress value after the structure was stabilized were lower than those at the corresponding positions of wall shed-tunnel.In conclusion, the stress values of the key parts of the jack stringer and center pillars of the anchoring shed tunnel were smaller than those of the corresponding positions of the wall shed tunnel. Thus, the anchoring shed tunnel was more suitable in confined environment.


### 4.2. Comparative Analysis of Displacement

The displacement of portal shed tunnel was analyzed. The displacement nephograms of portal wall shed tunnel and portal anchoring shed tunnel were obtained, as shown in Figures12 and 13.Figure 12
The maximum displacement nephograms of portal wall shed-tunnel structure.Figure 13
The maximum displacement nephograms of portal anchoring shed-tunnel structure.The portal wall shed-tunnel structure was the shed-tunnel structure before optimization. Based on the analysis of the displacement variation of the maximum displacement nephograms of the portal wall shed-tunnel structure, it was found that the beam-column joints of the portal wall shed tunnel had obvious displacement variation under the action of the great external force. Based on the analysis of the maximum displacement nephograms of the portal anchoring shed-tunnel structure in Figure13, it was found that the beam-column joints of the optimized shed tunnel received relatively small external forces under the same position.The structure displacement first occurred at the center of the roof plate of the shed-tunnel just below the rockfall and the middle position of the jack stringer when the rockfall initially contacted with the cushion. With the gradual contact between rockfall and cushion, the displacement range gradually expanded to the jack stringer and the center pillar, and the maximum displacement of the roof extended to the inside. When the rockfall movement stopped and the structure tended to be stable, the maximum displacement occurred in the center pillar and the jack stringer. The displacement boundary was relatively clear, and the maximum displacement also occurred at the structure stress concentration.The diachronic curves of the maximum displacement of the jack stringer of the portal anchoring shed tunnel and portal wall shed tunnel are shown in Figure14.Figure 14
Diachronic curves of the maximum displacement of the jack stringer of the anchoring shed tunnel and wall shed tunnel.As shown in Figure14, the maximum displacement of the jack stringer of the wall shed tunnel was significantly greater than that of the anchoring shed tunnel. Based on the comparison of the maximum displacement values of representative units in the key parts of the structure, such as the jack stringer, roof plate, and interior stringer, it could be concluded that the anchoring shed tunnel was more suitable for a confined environment than the wall shed tunnel under the same conditions.


## 4.1. Contrastive Analysis of Stress

The portal wall shed-tunnel structure was taken as an example before the optimization. The optimization model in this study used ABAQUS as simulation software, and the material constitutive model was mainly based on the actual optimization model. The physical parameters of the management project in Enshi, Hubei province, are calculated and simulated, as listed in Table4. The stress nephogram is shown in Figure 6.Table 4
Physical parameter values of materials.
Densityρ (kg/m³)Elasticity modulusE (Mpa)Poisson’s ratioμCohesionc (kPa)Friction angleφ (°)78502000000.32025250050000.241850350.352500300000.2Figure 6
Equivalent stress nephogram of portal wall shed-tunnel structure.The portal anchoring shed-tunnel structure is taken as an example after the optimization, with the stress nephogram, as shown in Figure7.Figure 7
Equivalent stress nephogram of portal anchoring shed-tunnel structure.Based on the comparison and analysis of Figures6 and 7, it was found that the external force on the joints between columns and beams of the portal wall shed tunnel was much greater than that of the portal anchoring shed tunnel.According to the equivalent stress nephogram, the unit stress curves of the key parts of the jack stringer of the shed tunnels could be obtained, as shown in Figures8 and 9.Figure 8
The unit stress curves of the key parts of the jack stringer of the portal wall shed tunnel.Figure 9
The unit stress curves of the key parts of the jack stringer of the portal anchoring shed tunnel.Based on the comparison and analysis of Figures8 and 9, it was found that the peak value of unit stress in the key position of the jack stringer of the anchoring shed tunnel and the unit stress value after the structure was stabilized were lower than the corresponding position of the wall shed tunnel.According to the equivalent stress nephogram, the unit stress curves of the key parts of the center pillars of the shed tunnels could be obtained, as shown in Figures10 and 11.Figure 10
The unit stress curves of the key parts of the center pillars of the portal wall shed tunnel.Figure 11
The unit stress curves of the key parts of the center pillars of the portal anchoring shed tunnel.As seen from the comparison and analysis of Figures10 and 11, the peak value of unit stress in the key position of the center pillars of the anchoring shed-tunnel and the unit stress value after the structure was stabilized were lower than those at the corresponding positions of wall shed-tunnel.In conclusion, the stress values of the key parts of the jack stringer and center pillars of the anchoring shed tunnel were smaller than those of the corresponding positions of the wall shed tunnel. Thus, the anchoring shed tunnel was more suitable in confined environment.


## 4.2. Comparative Analysis of Displacement

The displacement of portal shed tunnel was analyzed. The displacement nephograms of portal wall shed tunnel and portal anchoring shed tunnel were obtained, as shown in Figures12 and 13.Figure 12
The maximum displacement nephograms of portal wall shed-tunnel structure.Figure 13
The maximum displacement nephograms of portal anchoring shed-tunnel structure.The portal wall shed-tunnel structure was the shed-tunnel structure before optimization. Based on the analysis of the displacement variation of the maximum displacement nephograms of the portal wall shed-tunnel structure, it was found that the beam-column joints of the portal wall shed tunnel had obvious displacement variation under the action of the great external force. Based on the analysis of the maximum displacement nephograms of the portal anchoring shed-tunnel structure in Figure13, it was found that the beam-column joints of the optimized shed tunnel received relatively small external forces under the same position.The structure displacement first occurred at the center of the roof plate of the shed-tunnel just below the rockfall and the middle position of the jack stringer when the rockfall initially contacted with the cushion. With the gradual contact between rockfall and cushion, the displacement range gradually expanded to the jack stringer and the center pillar, and the maximum displacement of the roof extended to the inside. When the rockfall movement stopped and the structure tended to be stable, the maximum displacement occurred in the center pillar and the jack stringer. The displacement boundary was relatively clear, and the maximum displacement also occurred at the structure stress concentration.The diachronic curves of the maximum displacement of the jack stringer of the portal anchoring shed tunnel and portal wall shed tunnel are shown in Figure14.Figure 14
Diachronic curves of the maximum displacement of the jack stringer of the anchoring shed tunnel and wall shed tunnel.As shown in Figure14, the maximum displacement of the jack stringer of the wall shed tunnel was significantly greater than that of the anchoring shed tunnel. Based on the comparison of the maximum displacement values of representative units in the key parts of the structure, such as the jack stringer, roof plate, and interior stringer, it could be concluded that the anchoring shed tunnel was more suitable for a confined environment than the wall shed tunnel under the same conditions.


## 5. Conclusion

In this study, the optimization of shed-tunnel structure in a confined environment is studied, and the following conclusions are drawn:(1)
Through comparative analysis of traditional impact force calculation methods, the Xiang Xin method is most suitable for the calculation of rockfall impact force in a confined environment.(2)
The optimization of the shed tunnel increases the space utilization rate, reduces the cost, and greatly improves the impact resistance of rockfall. The results provide a reference for similar shed-tunnel management.(3)
The shed-tunnel design still can be further optimized for Juebitianhe geological disaster site in Enshi. If there are difficulties in the actual construction process, then the potential safety threats in the construction process still exist. Because the main force falls on the column, high requirements are proposed for the concrete used by the column. In the later stage, the model can also optimize the shed-tunnel structure by changing the bending moment, shear force, and energy.



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*Source: 3874783-2022-08-05.xml*