# Influence of Shield Tunnel Oblique Penetration Construction on Existing Large-Span Masonry Structures

Authors: Dandan Zhang
Journal: Mathematical Problems in Engineering
 (2023)

---

## Abstract

When the shield tunnel obliquely penetrates the large-span masonry building, the ground deformation caused by shield construction may cause the risk of deformation and cracking of the existing masonry structure held above. Based on a shield tunnel obliquely penetrating a large-span masonry building in Zhengzhou, a three-dimensional finite element model of building-stratum-shield tunnel interaction was established by MIDAS-GTS, and the laws of settlement, deformation, and damage of the building were studied. Results show that when the first line (left line) of the tunnel is penetrated, the settlement groove along the horizontal direction of the building presents a “V” shape, while after the second line (right line) is penetrated, which changes from “V” shape to “W” shape, and the maximum settlement value of the building caused by the first line can account for about 2/3 of the total settlement value. The maximum tensile strain of both the building’s south and north walls occurs at the bottom of the wall within the range of the tunnel, which develops upward and gradually weakens. Influenced by the oblique crossing angle, the maximum positions of settlement and strain for the building’s front and rear walls are offset to some extent. With the masonry building’s stiffness increasing, the uneven settlement of buildings decreases linearly, and with the tunnel oblique crossing angle increasing, the uneven settlement increases exponentially, while with the tunnel buried depth increasing, the uneven settlement shows an exponential downward trend.


---

## Body

## 1. Introduction

The shield construction method has the advantages of small construction disturbance and a high safety coefficient and has become the preferred construction method for subway tunnels in cities [1–3]. With the decrease in urban space resources, tunnel construction under buildings has become a problem that must be paid attention to in shield construction [4–6]. In particular, there are still a large number of ancient masonry buildings in some cities. Due to their old age, the design standards and construction levels of these masonry buildings are relatively low, and their own stiffness has been significantly reduced due to years of weathering. Compared with reinforced concrete buildings, when shield tunnels pass under masonry buildings, the ground deformation caused by construction often has a greater impact on masonry buildings and even leads to cracking and damaging of buildings [7, 8]. Therefore, with the increasing emphasis on the protection of ancient architectural heritage at home and abroad, it is particularly important to carry out research on the impact of shield tunnel construction on masonry buildings.At present, some scholars have paid attention to the deformation and damage of adjacent buildings caused by tunnel construction. For example, Bilotta et al. [9] monitored the displacement of a historical church during the construction of Naples Metro Line 6 and analyzed the influence of the relative position of the tunnel, the building’s stiffness, and the building weight on the ground settlement. Acikgoz et al. [10] studied the settlement, deformation, and damage laws of buildings caused by shield tunnel side-crossing masonry buildings. Chen et al. [11] studied a subway shield tunnel orthogonally passing under a masonry structure building, and the tunneling-induced settlements and crack development of the building are obtained. Wang et al. [12] proposed a new method to assess the risk of shield tunnel excavation on nearby existing buildings and verified the reliability of the method. Zhang et al. [13] and Ma et al. [14] studied the impact of shield construction on building foundation and pile foundation based on monitoring data and analyzed the distribution characteristics and change rules of building settlement. Based on settlement monitoring data, Wang et al. [15] analyzed the effect of shield tunneling construction on the settlement of adjacent building foundations and analyzed the distribution of pore pressure in sandy soils with high water content as well as the distribution characteristics of soil displacement and plastic zone.The deformation and damage of buildings caused by shield tunnel construction are affected by many external conditions and construction parameters. Franziu et al. [16] studied the effect of building load on the ground and building deformation caused by tunnel excavation. Son and Cording [17] studied the influence of building shear stiffness on the ground settlement and evaluated the building damage caused by ground displacement due to tunnel excavation. Xu et al. [18] studied the influence mechanism of shield tunnel construction on building deformation through monitoring and analysis of different construction stages such as end reinforcement and shield tunneling. Dai et al. [19] studied the spatial deformation caused by the shield tunneling parallel to the building, found the laws of longitudinal deflection of buildings, soil deformation, and stress change caused by shield lateral penetration, and analyzed the effect of different building plane aspect ratios.With the rapid development of computer technology, numerical simulation methods are widely used in the design, construction, and evaluation of the impact of tunnels on adjacent buildings. Giardina et al. [20] studied the settlement and deformation of masonry buildings due to tunnel construction through the finite element method and proposed a semicoupled method to evaluate the damage of masonry structures caused by settlement. Burd et al. [21] proposed a simplified one-dimensional (1D) soil-foundation interaction model for assessing the risk of building damage caused by tunnel construction. Amorosi et al. [22] analyzed the deformation and damage mechanism of masonry structure caused by shallow buried tunnel based on the two-dimensional finite element model. Gong et al. [23] simulated the construction process of double-line shield tunnel passing through multilayer masonry structure by establishing a finite element model and studied the uneven settlement process and characteristics of the ground and buildings.At present, some research studies have been carried out on the buildings’ damage caused by the shield tunnel construction, but most of them are limited to the situations where the shields penetrate the buildings orthogonally or parallel to the sides. Compared with orthogonal and parallel side penetrations, the settlement and deformation mechanism of buildings caused by shield tunnel oblique penetration is more complex, and the influence mechanism of uneven settlement of buildings on its deformation and damage also needs to be further studied. In addition, the overall stiffness of large-span masonry buildings is small, and the settlement of buildings caused by shield tunnel construction is different from that of small-span buildings. At present, there is still a relatively lack of research on the impact of shield tunnels on large-span masonry buildings.In order to solve the abovementioned problems, based on a shield tunnel obliquely passing under a large-span masonry building in Zhengzhou, this paper establishes a three-dimensional finite element model of building-stratum-tunnel interaction and analyzes the settlement, deformation, and damage laws of the large-span masonry building, and the influence of the building’s stiffness, the tunnel’s oblique crossing angle, and the tunnel’s buried depth on the settlement of the masonry building is further studied. This study can provide a theoretical reference for the design and construction of the shield tunnel obliquely passing through the masonry building.


## 2. Project Overview

A two-line tunnel project of a subway in Zhengzhou adopts the shield method, as shown in Figure1(a). The left line of the tunnel is the first excavation section, and the right line of the tunnel is the latter excavation section, as shown in Figure 1(b). The axial distance of the two lines is 14.9 m, and the outer diameter of the EPB shield machine is 6.48 m, and the shell thickness of the shield machine is 0.3 mm. The tunnel segment is made of C30 reinforced concrete with an outer diameter of 6.2 m, a width of 1.5 m, a thickness of 0.35 m, and a buried depth of 10.4 m at the top of the tunnel. The shield machine obliquely passes through a 4-story masonry structure at an oblique angle of 102°. The length × width × height of the building is 54.9 m × 9.7 m × 14.3 m, and the wall thickness and the floor thickness are 340 mm and 120 mm, respectively. The building foundation is a strip foundation under the wall, with a width of 0.6 m and a buried depth of 1.1 m, and the distance between the bottom of the foundation and the top of the tunnel segment is 9.3 m. The building floor and foundation are made of C20 concrete, and the wall is made of MU7.5 brick and M5 mortar. In order to monitor the buildings settlement during the construction of shield tunnel, 14 monitoring points from A1 to A14 are set around the buildings, and the level gauge is used for settlement observation.Figure 1
Tunnel construction plan: (a) project site plan; (b) shield oblique crossing building plan.
(a)(b)The interval exploration boreholes are mainly arranged in the position of 3∼5 m outside the tunnel structure, the spacing of the exploration points is generally 10∼30 m, and the depth of the exploration boreholes enters about 15 m below the bottom of the structure. According to the field geological survey report, the soil layer condition of the shield tunnel crossing site is relatively flat. The soil layers from top to bottom are miscellaneous fill, silt, silty clay, and fine sand, and the physical and mechanical properties of the soil layers are mainly obtained by standard penetration test and pressure meter test, etc. The thickness of the soil layer and the main physical and mechanical properties of the soil are shown in Table1.Table 1
Soil layer thickness and mechanical parameters.
Soil layerLayer thickness (m)Severe (kN/m3)Elastic modulus (MPa)Poisson’s ratioInternal friction angle (°)Cohesive force (kPa)Miscellaneous fill1.515.55.60.351017Silt4.219.721.70.312218Silty clay13.519.232.30.281831Fine sand720.2520.25280


## 3. Establishment of Numerical Model

In order to reveal the deformation and damage mechanism of masonry buildings, a three-dimensional finite element model of building-strata-shield tunnel interaction is established by MIDAS-GTS. In order to reduce the influence of the boundary effect, the model size is taken as 110 m along the length of the building, 80 m along the tunnel excavation direction, 30 m in the vertical direction, and the left and right boundaries are 33 m from the edge of the building. When establishing the model, the soil layer, building wall, and building foundation all adopt 3D solid elements, and doors and window openings are set at the corresponding positions of the wall body, and 2D plate elements are adopted for the building floor, the shield machine, and the tunnel segment. Figure2 shows the established finite element model and its mesh division. The number of meshes of the established finite element model is 149003, and the number of nodes is 235450. The boundary conditions of the model are as follows: the ground surface is a free surface; the lateral displacement around the soil is limited to zero, and the vertical is free; all displacements at the bottom boundary are constrained.Figure 2
Finite element calculation model.In the finite element model, the M-C (Mohr−Coulomb) constitutive model is used to simulate the mechanical behavior of soils, and the physical and mechanical parameters are shown in Table1. Building wall, building foundation, building floor, shield machine, and tunnel segment are all regarded as elastic materials, and elastic constitutive models are adopted. The specific parameters of each element of the masonry building are obtained from literature [24], taking into account an aging discount of 20% for stiffness, and the model parameters are shown in Table 2.Table 2
Physical and mechanical parameters of masonry buildings and shield construction.
Structure typeUnit weight (kN/m3)Poisson’s ratioElastic modulusE (Gp)Constitutive modelBuildingFoundation230.2520.4Elastic modelFloor230.2520.4Wall200.21.9Shield tunnelShield machine250.2230Segment250.230When simulating the construction stage, the shield machine starts driving from 30 m in front of the building, and the excavation step of each step is 2 m. The specific construction process simulation steps are as follows: (1) we calculate the initial stress of the stratum and clear the stratum displacement; (2) we set masonry structure buildings and clear the displacement; (3) we passivate the tunnel excavation soil, activate the shield shell, support pressure and Jack thrust, and a support force of 200 kPa is applied at the excavation face to simulate the soil tank pressure of the shield machine, and a uniform compressive stress of 4 MPa is applied to the ring section of the shield tail segment to simulate the thrust of the Jack; (4) after the excavation of first three rings, we passivate the shield shell, activate the lining segment and grouting layer, and activate the grouting pressure, which acts on the corresponding segment in the form of 0.2 MPa surface load to prevent the soil from collapsing; (5) we repeat steps (3) to (4) until the tunnel excavation is completed.


## 4. Results and Discussion

### 4.1. Building Settlement

After the left and right lines of the shield tunnel pass through the building, respectively, the settlement values of monitoring points A1–A7 on the south wall and monitoring points A8–A14 on the north wall are shown in Figures3 and 4 respectively. According to the field measurement data, after the left line passes through the building, the maximum settlement point of the building south wall is A3, which can reach 11.42 mm, and the maximum settlement point of the north wall is A12, which can reach 12.31 mm. The maximum settlement points are located at the top of the tunnel and gradually decrease towards both sides of the building. At this time, the overall settlement of the building is relatively small, there are no cracks on the exterior of the building, and no plaster falls off. When the right line passes through the building, due to the superposition effect of the left line and right line tunnels, the settlement of the building increases significantly, and the influence range of the settlement curve expands significantly. At this time, the maximum settlement interval of the building occurs between the two lines. At this time, the maximum settlement point of the building south wall is still A3, and the maximum settlement is 16.98 mm, while the maximum settlement point of the north wall is A11, and the maximum settlement is 16.05 mm. Through on-site observation of the wall, it is found that there are local fine cracks and part of the plaster is falling off the wall of the building placed above the tunnel.Figure 3
Comparison between settlement of south wall and finite element model.Figure 4
Comparison between north wall settlement and finite element model.Comparing the finite element simulation results with the on-site measured data, it can be seen that the simulation results of the building settlement trend are basically consistent with the measured results. Simulation results and measured data are in good agreement, and the coefficient of determinationR2 can reach more than 0.9, which indicates the built model can simulate the building settlement caused by shield tunnel construction well. From the simulated settlement curve, it can be seen that the influence range of building settlement caused by shield tunnel construction can reach 4D (D is the tunnel diameter). After the left line of the tunnel is penetrated, the settlement curves of the north and south walls both show a “V” shape, while after the right line is penetrated, the settlement curve changes from a “V” shape to a “W” shape, indicating that the construction sequence is an important factor affecting the shape of the settlement.Overall, the building settlement caused by the tunnel on the leading line (left line) is larger than that of the trailing line (right line) after passing through the building, accounting for about 2/3 of the total settlement, which is mainly related to the stress redistribution caused by the leading line construction. In addition, different from the shield passing through the building orthogonally, when the shield passes through the building obliquely, the settlement of the wall before and after the building is significantly different. The maximum settlement of the south wall is slightly larger than that of the north wall, but the influence range of the maximum settlement interval of the north wall is relatively larger.


### 4.2. Main Tensile Strain Analysis and Damage Evaluation of the Wall

Based on the finite element simulation results, after the left and right lines of the shield tunnel pass through the building, the maximum principal tensile strain cloud diagrams of the north and south walls of the building are shown in Figures5–8, respectively. Boscardin and Cording [25] have studied a large number of engineering examples, showing that the damage grade of buildings is mainly determined by the maximum principal tensile strain and proposed the corresponding relationship between the damage grade of buildings and the maximum principal strain, as shown in Table 3. As can be seen from Table 3, the critical strain leading to cracking of masonry buildings is 0.05%.Figure 5
Principal strain cloud diagram of the south wall after the left line penetrates (observed from south to north).Figure 6
Principal strain cloud diagram of the north wall after the left line penetrates (observed from north to south).Figure 7
Principal strain cloud diagram of the south wall after the right line penetrates (observed from south to north).Figure 8
Principal strain cloud diagram of the north wall after the right line penetrates (observed from north to south).Table 3
Correspondence between maximum principal strain and damage grade.
Damage levelNegligible (%)Very slight (%)Slight (%)Medium (%)Serious (%)Maximum principal strain0∼0.050.05∼0.0750.075∼0.150.15∼0.3>0.3As can be seen from Figures5 and 6, after the left line of the shield tunnel passes through the building, the maximum principal strain of the north wall is 0.064%, while that of the south wall is 0.075%. The area where the wall may be damaged is trapezoidal, and the maximum principal tensile strain is mainly concentrated at the bottom of the wall in the tunnel area, developing towards the sides and top of the wall and gradually weakening. According to Table 3, at this time, the damage degree of the wall is “very slight” damage. After the right line of the shield tunnel passes through the building, the damage range of the south and north walls expands significantly, and the maximum value of the main tensile strain also increases significantly. At this time, the maximum value of the main tensile strain is mainly concentrated at the bottom of the wall in the tunnel range on the left and right lines. Similar to the left line, the principal strain expands from the bottom of the wall to both sides and the top and gradually weakens. At this time, the maximum principal strain of the north wall is 0.078%, the maximum principal strain of the south wall is 0.087%, and the damage degree of the wall is “slight” damage.Comparing the maximum principal strains of the south wall and the north wall, it can be seen that the strain of the south wall is relatively larger, which is mainly because the shield passes through the south wall first, and its construction disturbance is relatively greater. Section4.1 of this paper has shown that after the left and right lines of the shield tunnel are penetrated, the maximum settlement position of the building wall mainly occurs at the top of the tunnel and gradually decreases at both sides of the tunnel. This is consistent with the fact that the maximum strain of the wall in this section is mainly distributed at the top of the tunnel, which further proves that the wall damage of masonry buildings caused by shield construction is caused by the uneven settlement of the wall. In addition, due to the existence of door and window openings, the development of the principal strain on the wall is discontinuous, which makes the strain distribution in the wall more complicated, and local masonry cracking is more likely to occur due to stress concentration. In engineering practice, the monitoring of door and window openings at the bottom of the wall should be strengthened, and certain reinforcement measures should be taken if necessary.


### 4.3. Influence Analysis of Settlement of Masonry Buildings

Gong et al. [23] showed that the soil settlement tank shape and the building uneven settlement during the shield construction process are the main reasons for the damage of building. Based on finite element simulation, this paper takes the north wall of the abovementioned building as the research object and further studies the influence of the control parameters such as the stiffness of building, the tunnel’s oblique crossing angle, and the tunnel’s buried depth on the soil settlement tank depth and the building’s uneven settlement. The single factor analysis method is used in the analysis, and only the influence of a single variable on the simulation results is analyzed, and the remaining parameters are the same as above.


#### 4.3.1. Stiffness of Building

Due to the different building materials and construction techniques of masonry buildings and the differences in age, protection effect, and reinforcement degree of buildings, there are obvious differences in the stiffness for different masonry buildings. Based on the original elastic modulus of masonry building materials, the overall elastic modulus of the building is increased or discounted by 10% and 20%. The trend of the influence of the building stiffness on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel crossing is obtained, as shown in Figure9. As can be seen from the figure, as the building stiffness increases, the depth of the soil settlement tank and the uneven settlement of the building both gradually decrease, and both curves show a linear trend, and the R2 of the two reaches 0.995 and 0.988, respectively. It can be seen that when the stiffness of the building changes in the same range, the uneven settlement of the building changes more than the depth of the soil settlement tank. This is because the span of the masonry building in this study is large, the foundation is shallow, the overall antideformation ability of the building is poor, and the deformation of the building caused by the construction disturbance of the shield tunnel is more easily affected by the stiffness of the building. In conclusion, the deformation of the building is significantly affected by the overall stiffness of the building. When the building span is large and the foundation depth is shallow, the overall stiffness of the building is small, its resistance to deformation is weak, and it is more likely to flex in the longitudinal direction, resulting in damage to the building.Figure 9
Influence of building stiffness.


#### 4.3.2. Tunnel Oblique Crossing Angle

When the oblique angle between the shield tunnel and the building is different, the effect range of the tunnel construction disturbance on the building is different, which may lead to different degrees of settlement and deformation of the building. In this study, taking the orthogonal angle (90° included angle) between the building and the tunnel as the reference value, the tunnel is rotated clockwise by 15° (105° included angle), 30° (120° included angle), 45° (135° included angle), and 60° (150° included angle), respectively, and the influence trend of the tunnel’s oblique angle on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel passes through is obtained, as shown in Figure10. As can be seen from the figure, with the increase of the oblique angle between the tunnel and the building, the depth of the soil settlement tank and the uneven settlement of the building both increase exponentially. The R2 of the two reached 0.999 and 0.998, respectively. When the included angle between the tunnel and the building is 90°, the depth of the soil settlement tank and the uneven settlement of the building are the smallest, which are −16.2 mm and −1.62 mm, respectively. When the angle between the tunnel and the building is in the range of 90°∼120°, the increase of the soil settlement tank depth and the building uneven settlement are 0.18 mm and 1.08 mm, respectively, and the growth trend of the two is relatively gentle, while when the angle range is 120°∼150°, the increase of the two indicators reached 2.52 mm and 5.62 mm, respectively, and the change trend increased significantly. This is because when the included angle between the tunnel and the building is greater than 120°, the relative position of the building and the tunnel is closer to parallel, and most of the building foundation is located within the tunnel contour. At this time, the influence of the tunnel construction on the building is more obvious.Figure 10
Influence of tunnel oblique crossing angle.


#### 4.3.3. Tunnel Buried Depth

The design depth of the tunnel is set to 5 levels including 8 m, 9 m, 10 m, 11 m, and 12 m, and the influence trend of the tunnel’s buried depth on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel passes through is obtained, as shown in Figure11. As can be seen from the figure, with the increase of tunnel’s buried depth, the depth of soil settlement tank and the uneven settlement of buildings both decrease. The variation curve of the depth of the settling tank is approximately linear, while that of the building’s uneven settlement is approximately parabolic. R2 of the two reached 0.997 and 0.998, respectively. When the tunnel’s buried depth increased from 8 m to 10 m, the settlement tank’s depth and the building’s uneven settlement decreased from 19.67 mm and 2.03 mm to 16.20 mm and 1.62 mm, respectively. The settlement tank depth is significantly affected by the tunnel’s buried depth, but the variation trend of building’s uneven settlement is relatively gentle. When the tunnel’s buried depth increases from 10 m to 12 m, the settlement tank’s depth and the building’s uneven settlement decreased from 16.20 mm and 1.62 mm to 11.21 mm and 0.36 mm, respectively. At this time, the depth of the settlement tank and the building’s uneven settlement both decreased significantly with the increase of the tunnel’s buried depth, and the change trends of the two were relatively close. When the tunnel’s buried depth is shallow, the antideformation capability of the soil layer is weak, and the settlement of the soil layer is large. At this time, the stiffness of the masonry building plays a role, resulting in that the influence trend of the tunnel’s buried depth on the building’s uneven settlement is inconsistent with that of the soil settlement tank depth. When the tunnel is buried deeper, the settlement of the soil layer itself is small. At this time, the building’s uneven settlement is mainly affected by the deformation of the soil layer, and the change trends of the two are relatively close.Figure 11
Influence of tunnel buried depth.


## 4.1. Building Settlement

After the left and right lines of the shield tunnel pass through the building, respectively, the settlement values of monitoring points A1–A7 on the south wall and monitoring points A8–A14 on the north wall are shown in Figures3 and 4 respectively. According to the field measurement data, after the left line passes through the building, the maximum settlement point of the building south wall is A3, which can reach 11.42 mm, and the maximum settlement point of the north wall is A12, which can reach 12.31 mm. The maximum settlement points are located at the top of the tunnel and gradually decrease towards both sides of the building. At this time, the overall settlement of the building is relatively small, there are no cracks on the exterior of the building, and no plaster falls off. When the right line passes through the building, due to the superposition effect of the left line and right line tunnels, the settlement of the building increases significantly, and the influence range of the settlement curve expands significantly. At this time, the maximum settlement interval of the building occurs between the two lines. At this time, the maximum settlement point of the building south wall is still A3, and the maximum settlement is 16.98 mm, while the maximum settlement point of the north wall is A11, and the maximum settlement is 16.05 mm. Through on-site observation of the wall, it is found that there are local fine cracks and part of the plaster is falling off the wall of the building placed above the tunnel.Figure 3
Comparison between settlement of south wall and finite element model.Figure 4
Comparison between north wall settlement and finite element model.Comparing the finite element simulation results with the on-site measured data, it can be seen that the simulation results of the building settlement trend are basically consistent with the measured results. Simulation results and measured data are in good agreement, and the coefficient of determinationR2 can reach more than 0.9, which indicates the built model can simulate the building settlement caused by shield tunnel construction well. From the simulated settlement curve, it can be seen that the influence range of building settlement caused by shield tunnel construction can reach 4D (D is the tunnel diameter). After the left line of the tunnel is penetrated, the settlement curves of the north and south walls both show a “V” shape, while after the right line is penetrated, the settlement curve changes from a “V” shape to a “W” shape, indicating that the construction sequence is an important factor affecting the shape of the settlement.Overall, the building settlement caused by the tunnel on the leading line (left line) is larger than that of the trailing line (right line) after passing through the building, accounting for about 2/3 of the total settlement, which is mainly related to the stress redistribution caused by the leading line construction. In addition, different from the shield passing through the building orthogonally, when the shield passes through the building obliquely, the settlement of the wall before and after the building is significantly different. The maximum settlement of the south wall is slightly larger than that of the north wall, but the influence range of the maximum settlement interval of the north wall is relatively larger.


## 4.2. Main Tensile Strain Analysis and Damage Evaluation of the Wall

Based on the finite element simulation results, after the left and right lines of the shield tunnel pass through the building, the maximum principal tensile strain cloud diagrams of the north and south walls of the building are shown in Figures5–8, respectively. Boscardin and Cording [25] have studied a large number of engineering examples, showing that the damage grade of buildings is mainly determined by the maximum principal tensile strain and proposed the corresponding relationship between the damage grade of buildings and the maximum principal strain, as shown in Table 3. As can be seen from Table 3, the critical strain leading to cracking of masonry buildings is 0.05%.Figure 5
Principal strain cloud diagram of the south wall after the left line penetrates (observed from south to north).Figure 6
Principal strain cloud diagram of the north wall after the left line penetrates (observed from north to south).Figure 7
Principal strain cloud diagram of the south wall after the right line penetrates (observed from south to north).Figure 8
Principal strain cloud diagram of the north wall after the right line penetrates (observed from north to south).Table 3
Correspondence between maximum principal strain and damage grade.
Damage levelNegligible (%)Very slight (%)Slight (%)Medium (%)Serious (%)Maximum principal strain0∼0.050.05∼0.0750.075∼0.150.15∼0.3>0.3As can be seen from Figures5 and 6, after the left line of the shield tunnel passes through the building, the maximum principal strain of the north wall is 0.064%, while that of the south wall is 0.075%. The area where the wall may be damaged is trapezoidal, and the maximum principal tensile strain is mainly concentrated at the bottom of the wall in the tunnel area, developing towards the sides and top of the wall and gradually weakening. According to Table 3, at this time, the damage degree of the wall is “very slight” damage. After the right line of the shield tunnel passes through the building, the damage range of the south and north walls expands significantly, and the maximum value of the main tensile strain also increases significantly. At this time, the maximum value of the main tensile strain is mainly concentrated at the bottom of the wall in the tunnel range on the left and right lines. Similar to the left line, the principal strain expands from the bottom of the wall to both sides and the top and gradually weakens. At this time, the maximum principal strain of the north wall is 0.078%, the maximum principal strain of the south wall is 0.087%, and the damage degree of the wall is “slight” damage.Comparing the maximum principal strains of the south wall and the north wall, it can be seen that the strain of the south wall is relatively larger, which is mainly because the shield passes through the south wall first, and its construction disturbance is relatively greater. Section4.1 of this paper has shown that after the left and right lines of the shield tunnel are penetrated, the maximum settlement position of the building wall mainly occurs at the top of the tunnel and gradually decreases at both sides of the tunnel. This is consistent with the fact that the maximum strain of the wall in this section is mainly distributed at the top of the tunnel, which further proves that the wall damage of masonry buildings caused by shield construction is caused by the uneven settlement of the wall. In addition, due to the existence of door and window openings, the development of the principal strain on the wall is discontinuous, which makes the strain distribution in the wall more complicated, and local masonry cracking is more likely to occur due to stress concentration. In engineering practice, the monitoring of door and window openings at the bottom of the wall should be strengthened, and certain reinforcement measures should be taken if necessary.


## 4.3. Influence Analysis of Settlement of Masonry Buildings

Gong et al. [23] showed that the soil settlement tank shape and the building uneven settlement during the shield construction process are the main reasons for the damage of building. Based on finite element simulation, this paper takes the north wall of the abovementioned building as the research object and further studies the influence of the control parameters such as the stiffness of building, the tunnel’s oblique crossing angle, and the tunnel’s buried depth on the soil settlement tank depth and the building’s uneven settlement. The single factor analysis method is used in the analysis, and only the influence of a single variable on the simulation results is analyzed, and the remaining parameters are the same as above.


### 4.3.1. Stiffness of Building

Due to the different building materials and construction techniques of masonry buildings and the differences in age, protection effect, and reinforcement degree of buildings, there are obvious differences in the stiffness for different masonry buildings. Based on the original elastic modulus of masonry building materials, the overall elastic modulus of the building is increased or discounted by 10% and 20%. The trend of the influence of the building stiffness on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel crossing is obtained, as shown in Figure9. As can be seen from the figure, as the building stiffness increases, the depth of the soil settlement tank and the uneven settlement of the building both gradually decrease, and both curves show a linear trend, and the R2 of the two reaches 0.995 and 0.988, respectively. It can be seen that when the stiffness of the building changes in the same range, the uneven settlement of the building changes more than the depth of the soil settlement tank. This is because the span of the masonry building in this study is large, the foundation is shallow, the overall antideformation ability of the building is poor, and the deformation of the building caused by the construction disturbance of the shield tunnel is more easily affected by the stiffness of the building. In conclusion, the deformation of the building is significantly affected by the overall stiffness of the building. When the building span is large and the foundation depth is shallow, the overall stiffness of the building is small, its resistance to deformation is weak, and it is more likely to flex in the longitudinal direction, resulting in damage to the building.Figure 9
Influence of building stiffness.


### 4.3.2. Tunnel Oblique Crossing Angle

When the oblique angle between the shield tunnel and the building is different, the effect range of the tunnel construction disturbance on the building is different, which may lead to different degrees of settlement and deformation of the building. In this study, taking the orthogonal angle (90° included angle) between the building and the tunnel as the reference value, the tunnel is rotated clockwise by 15° (105° included angle), 30° (120° included angle), 45° (135° included angle), and 60° (150° included angle), respectively, and the influence trend of the tunnel’s oblique angle on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel passes through is obtained, as shown in Figure10. As can be seen from the figure, with the increase of the oblique angle between the tunnel and the building, the depth of the soil settlement tank and the uneven settlement of the building both increase exponentially. The R2 of the two reached 0.999 and 0.998, respectively. When the included angle between the tunnel and the building is 90°, the depth of the soil settlement tank and the uneven settlement of the building are the smallest, which are −16.2 mm and −1.62 mm, respectively. When the angle between the tunnel and the building is in the range of 90°∼120°, the increase of the soil settlement tank depth and the building uneven settlement are 0.18 mm and 1.08 mm, respectively, and the growth trend of the two is relatively gentle, while when the angle range is 120°∼150°, the increase of the two indicators reached 2.52 mm and 5.62 mm, respectively, and the change trend increased significantly. This is because when the included angle between the tunnel and the building is greater than 120°, the relative position of the building and the tunnel is closer to parallel, and most of the building foundation is located within the tunnel contour. At this time, the influence of the tunnel construction on the building is more obvious.Figure 10
Influence of tunnel oblique crossing angle.


### 4.3.3. Tunnel Buried Depth

The design depth of the tunnel is set to 5 levels including 8 m, 9 m, 10 m, 11 m, and 12 m, and the influence trend of the tunnel’s buried depth on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel passes through is obtained, as shown in Figure11. As can be seen from the figure, with the increase of tunnel’s buried depth, the depth of soil settlement tank and the uneven settlement of buildings both decrease. The variation curve of the depth of the settling tank is approximately linear, while that of the building’s uneven settlement is approximately parabolic. R2 of the two reached 0.997 and 0.998, respectively. When the tunnel’s buried depth increased from 8 m to 10 m, the settlement tank’s depth and the building’s uneven settlement decreased from 19.67 mm and 2.03 mm to 16.20 mm and 1.62 mm, respectively. The settlement tank depth is significantly affected by the tunnel’s buried depth, but the variation trend of building’s uneven settlement is relatively gentle. When the tunnel’s buried depth increases from 10 m to 12 m, the settlement tank’s depth and the building’s uneven settlement decreased from 16.20 mm and 1.62 mm to 11.21 mm and 0.36 mm, respectively. At this time, the depth of the settlement tank and the building’s uneven settlement both decreased significantly with the increase of the tunnel’s buried depth, and the change trends of the two were relatively close. When the tunnel’s buried depth is shallow, the antideformation capability of the soil layer is weak, and the settlement of the soil layer is large. At this time, the stiffness of the masonry building plays a role, resulting in that the influence trend of the tunnel’s buried depth on the building’s uneven settlement is inconsistent with that of the soil settlement tank depth. When the tunnel is buried deeper, the settlement of the soil layer itself is small. At this time, the building’s uneven settlement is mainly affected by the deformation of the soil layer, and the change trends of the two are relatively close.Figure 11
Influence of tunnel buried depth.


## 4.3.1. Stiffness of Building

Due to the different building materials and construction techniques of masonry buildings and the differences in age, protection effect, and reinforcement degree of buildings, there are obvious differences in the stiffness for different masonry buildings. Based on the original elastic modulus of masonry building materials, the overall elastic modulus of the building is increased or discounted by 10% and 20%. The trend of the influence of the building stiffness on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel crossing is obtained, as shown in Figure9. As can be seen from the figure, as the building stiffness increases, the depth of the soil settlement tank and the uneven settlement of the building both gradually decrease, and both curves show a linear trend, and the R2 of the two reaches 0.995 and 0.988, respectively. It can be seen that when the stiffness of the building changes in the same range, the uneven settlement of the building changes more than the depth of the soil settlement tank. This is because the span of the masonry building in this study is large, the foundation is shallow, the overall antideformation ability of the building is poor, and the deformation of the building caused by the construction disturbance of the shield tunnel is more easily affected by the stiffness of the building. In conclusion, the deformation of the building is significantly affected by the overall stiffness of the building. When the building span is large and the foundation depth is shallow, the overall stiffness of the building is small, its resistance to deformation is weak, and it is more likely to flex in the longitudinal direction, resulting in damage to the building.Figure 9
Influence of building stiffness.


## 4.3.2. Tunnel Oblique Crossing Angle

When the oblique angle between the shield tunnel and the building is different, the effect range of the tunnel construction disturbance on the building is different, which may lead to different degrees of settlement and deformation of the building. In this study, taking the orthogonal angle (90° included angle) between the building and the tunnel as the reference value, the tunnel is rotated clockwise by 15° (105° included angle), 30° (120° included angle), 45° (135° included angle), and 60° (150° included angle), respectively, and the influence trend of the tunnel’s oblique angle on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel passes through is obtained, as shown in Figure10. As can be seen from the figure, with the increase of the oblique angle between the tunnel and the building, the depth of the soil settlement tank and the uneven settlement of the building both increase exponentially. The R2 of the two reached 0.999 and 0.998, respectively. When the included angle between the tunnel and the building is 90°, the depth of the soil settlement tank and the uneven settlement of the building are the smallest, which are −16.2 mm and −1.62 mm, respectively. When the angle between the tunnel and the building is in the range of 90°∼120°, the increase of the soil settlement tank depth and the building uneven settlement are 0.18 mm and 1.08 mm, respectively, and the growth trend of the two is relatively gentle, while when the angle range is 120°∼150°, the increase of the two indicators reached 2.52 mm and 5.62 mm, respectively, and the change trend increased significantly. This is because when the included angle between the tunnel and the building is greater than 120°, the relative position of the building and the tunnel is closer to parallel, and most of the building foundation is located within the tunnel contour. At this time, the influence of the tunnel construction on the building is more obvious.Figure 10
Influence of tunnel oblique crossing angle.


## 4.3.3. Tunnel Buried Depth

The design depth of the tunnel is set to 5 levels including 8 m, 9 m, 10 m, 11 m, and 12 m, and the influence trend of the tunnel’s buried depth on the depth of the soil settlement tank and the uneven settlement of the building after the shield tunnel passes through is obtained, as shown in Figure11. As can be seen from the figure, with the increase of tunnel’s buried depth, the depth of soil settlement tank and the uneven settlement of buildings both decrease. The variation curve of the depth of the settling tank is approximately linear, while that of the building’s uneven settlement is approximately parabolic. R2 of the two reached 0.997 and 0.998, respectively. When the tunnel’s buried depth increased from 8 m to 10 m, the settlement tank’s depth and the building’s uneven settlement decreased from 19.67 mm and 2.03 mm to 16.20 mm and 1.62 mm, respectively. The settlement tank depth is significantly affected by the tunnel’s buried depth, but the variation trend of building’s uneven settlement is relatively gentle. When the tunnel’s buried depth increases from 10 m to 12 m, the settlement tank’s depth and the building’s uneven settlement decreased from 16.20 mm and 1.62 mm to 11.21 mm and 0.36 mm, respectively. At this time, the depth of the settlement tank and the building’s uneven settlement both decreased significantly with the increase of the tunnel’s buried depth, and the change trends of the two were relatively close. When the tunnel’s buried depth is shallow, the antideformation capability of the soil layer is weak, and the settlement of the soil layer is large. At this time, the stiffness of the masonry building plays a role, resulting in that the influence trend of the tunnel’s buried depth on the building’s uneven settlement is inconsistent with that of the soil settlement tank depth. When the tunnel is buried deeper, the settlement of the soil layer itself is small. At this time, the building’s uneven settlement is mainly affected by the deformation of the soil layer, and the change trends of the two are relatively close.Figure 11
Influence of tunnel buried depth.


## 5. Discussion

Compared with the reinforced concrete structures, the strength and stiffness of a large-span masonry building is much smaller. When disturbed by the shield tunnel construction, the masonry building is more prone to settlement deformation, resulting in cracks and even damage. Especially, when the shield tunnel passes through the masonry building obliquely, the damage degree and influence range of the masonry structure are relatively larger. When the shield tunnel passes through the masonry building obliquely, the masonry building’s stiffness, the tunnel’s oblique crossing angle, and the tunnel’s burial depth all have significant effects on the settlement deformation of the building. Among them, the settlement deformation shows a linear decreasing relationship with the masonry buildings’ stiffness, an exponential increasing relationship with the tunnel’s oblique crossing angle, and an exponential decreasing relationship with the tunnel’s buried depth. Therefore, when planning the shield tunnel, the key that protected masonry building should be avoided as much as possible. If not, the tunnel’s buried depth can be increased as much as possible (more than 10 m), or the angle of the tunnel crossing the large-span masonry building can be reduced (less than 120°). When the shield tunnel inevitably passes under the masonry building, the damage degree of the masonry building should be assessed in advance, and then the building should be properly reinforced to improve the overall stiffness of the building. There are some assumptions in this paper. In actual projects, the situations faced by masonry building are more complex, such as the masonry structures’ weathering degree, the complex environment around buildings, and the buildings’ reinforcement degree. However, in general, this study is still significant for the buildings’ protection where shield tunnels pass through masonry buildings.


## 6. Conclusion

In this article, based on the analysis of the measured data of a shield tunnel obliquely passing through a masonry building in Zhengzhou, a three-dimensional finite element model of building-stratum-tunnel interaction was established. The settlement, deformation, and damage laws of buildings are studied, and the following conclusions are drawn:(1)
After the leading line (left line) passes through the building, the settlement curve of the masonry building along the lateral direction is a “V” shape, while after the trailing line (right line) passes through, due to the superposition effect of tunnels’ left line and right line, the settlement range of the building expands, the maximum settlement amount increases significantly, and the settlement curve transforms into a “W” shape.(2)
After the left line passes through the building, the maximum main tensile strain of the south and north walls of the building is mainly distributed at the bottom of the wall in the tunnel area, while after the right line passes through, the maximum main tensile strain of the wall increases significantly, and the damage range expands significantly, and the main strain expands from the bottom of the wall to the sides and top and gradually weakens.(3)
The stiffness of building, the tunnel’s oblique crossing angle, and the tunnel’s buried depth all have certain influences on the soil deformation and the settlement of masonry buildings. As the stiffness of building or tunnel’s buried depth increases, the depth of the soil settlement tank and the uneven settlement of the building both decrease, while with the increase of the tunnel’s oblique crossing angle, the depth of the settlement tank and the building’s uneven settlement increase accordingly.To sum up, when the shield tunnel passes under the masonry building, if the ground conditions are poor and the tunnel’s buried depth is small, the oblique penetration angle of the tunnel should be reduced as much as possible. In addition, the deformation monitoring of the building wall should be strengthened to avoid cracking of the building due to excessive longitudinal deflection, and the building should be reinforced if necessary.



---

*Source: 7779168-2023-01-30.xml*