Investigation on performance of steel strut servo system braced deep excavation adjacent to existing buildings: a case study

Abstract

In response to increasingly stringent safety and construction environmental impact requirements for urban underground engineering, this study investigates the performance of a steel strut servo system braced deep excavation adjacent to existing buildings, using a subway station project as a case study. A three-dimensional finite element model is established to analyze the behavior of the steel strut servo system during deep excavation, focusing on the deformation characteristics of soil and structural members, as well as the factors influencing the system’s performance. The findings indicate a strong correlation between the deformation of soil and structural members and the excavation depth, with greater deformation observed at deeper depths. When excavation is completed, the maximum and minimum vertical displacement of soil mass are 24.3 and − 5.8 mm, respectively. The maximum total displacement of buildings A and B is 3.86 and 3.82 mm, respectively. The servo system can inhibit the displacement of diaphragm wall to some extent. The maximum values of the servo area and other areas are 25.21 and 40.4 mm, respectively. The axial force of the strut is mainly pressure, with a maximum value of − 2,883.4 kN. The horizontal displacement of diaphragm wall is sensitive to the change of servo system position and servo axial force value. The deformation control effect is best when all steel struts are controlled by servo system. When the servo system is set with 2 struts, the maximum value decreases as the position of the servo system moves down. In addition, the maximum displacement decreases with the increase of the servo axis force value. This research provides valuable insights for the design optimization and construction control of similar projects.

Introduction

In recent years, with the continuous development of the economy and the improvement of people’s living standards, more and more people choose to live, work and travel in big cities¹. The continuous increase in the population of big cities will bring many problems. For example: traffic congestion, inconvenient travel, expensive parking, and difficulty in parking². It is evident that the contradiction between the increase in population and the limited space is becoming increasingly prominent³. The emergence of these problems not only affects the healthy development of cities but also hinders the improvement of people’s sense of happiness⁴. Effective development and utilization of underground space can help alleviate the contradiction of insufficient living space in big cities⁵. At present, underground space is regarded as an important resource for urban development⁶. The Chinese government attaches great importance to the development and utilization of urban underground space⁷. Furthermore, with the continuous increase in the depth of urban underground space development, subways have become an important demand for the sustainable development of many large cities⁸. At present, there are nearly 50 cities with subways in China⁹, such as Beijing¹⁰, Shanghai¹¹, Hangzhou¹² and other cities. The subway has improved travel efficiency¹³ and can effectively relieve the pressure on ground traffic¹⁴. It is well known that subway stations are an important part of the subway system¹⁵. Obviously, the construction of subway stations inevitably requires the excavation of deep foundation pits¹⁶. The excavation project of deep foundation pits for subways belongs to the development and utilization of underground space. Some scholars have conducted research on related issues¹⁷. The existing research contents mainly include two aspects. One is the response problem of the foundation pit support structure and the surrounding soil during excavation¹⁸. The other one is the deformation control of the foundation pit support structure and the surrounding soil¹⁹.

In terms of the response of foundation pit supporting structure and surrounding soil mass during excavation, the existing research methods mainly include numerical simulation, on-site monitoring, theoretical analysis, and model test²⁰. In terms of numerical simulation, Wang et al.²¹ simulated the strut structure of deep excavation engineering of subway stations, the results showed that the maximum horizontal displacement of the retaining wall occurred at the upper part of about 1/3 of the depth of deep excavation. Cui et al.²² studied the evolution law of strut structure during deep excavation construction. The results show that the inner deep excavation will have a great influence on the deformation of the strut structure. Meanwhile, Qi et al.²³ analyzed the deformation of the deep excavation and its surrounding environment from different angles. Besides, Liu et al.²⁴ studied the deformation characteristics of soil–cement mixing wall and soils around deep excavation. The results show that the maximum lateral displacement of mixing wall and the maximum surface settlement increase with the increase of excavation depth. Similarly, Paramour et al.²⁵ studied the influence of different construction methods on land settlement. The results show that different construction methods have different effects on ground deformation. Wang et al.²⁶ studied the influence of different embankment heights on the earthen arch effect of embankments. Hu et al.²⁷ carried out the modeling and prediction of settlement during shield tunnel excavation. Long et al.²⁸ studied the mechanical behavior of reinforcing bars in concrete under different loads. In terms of field monitoring, the research results of Pan et al.²⁹ showed that the horizontal displacement of tunnel caused by deep soil mixing is the largest. Ren et al.³⁰ studied the influence of deep excavation on the deformation characteristics of strut structures. Meanwhile, Niu et al.³¹ showed that the reverse fault would increase the deformation of retaining piles. Tavallaie et al.³² believed that one of the effective construction methods for shallow-buried subway stations is to adopt diaphragm wall. Similarly, Ran et al.³³ and Tang et al.³⁴ analyzed the influence of construction on the deformation of existing subway structures.

On the theoretical analysis side, Zhang et al.³⁵ studied the stress and deformation rules of the retaining structure near subway stations. Li et al.³⁶ established the differential equation of beams on elastic foundation and derived the calculation formula of tunnel deformation. Meanwhile, Li et al.³⁷ designed a prediction method of building inclination around deep excavation based on mathematical model. Similarly, Mu et al.³⁸ revealed the influence mechanism of deep excavation excavation on shield tunnel. Wang et al.³⁹ conducted a study on the earth arch effect of embankments. Wu et al.⁴⁰ conducted a study on the sensitivity of arch section parameters. Meng et al.⁴¹ proposed an analytical method that simultaneously considers the influence of excavation and dewatering on tunnels. Besides, Zhang et al.⁴² proposed a tunnel displacement prediction method with time effect. Furthermore, Zheng et al.⁴³ conducted a study on the structural response of tunnels during the excavation process. On the model test side, Zhang et al.⁴⁴ studied the influence of different structural plane inclination angles on the stability control effect of deep excavation. Gu et al.⁴⁵ analyzed the influence of tides on the deformation of coastal sandy deep excavation from multiple perspectives. Besides, Cao et al.⁴⁶ conducted an experimental study on deep excavation in seasonal frozen soil area. The study found that the soil retaining structure deformation fluctuates according to the temperature. Moreover, Feng et al.⁴⁷ studied the influence of vertical load on the deformation of cutoff wall. Wei et al.⁴⁸ conducted a study on the influence of excavation on the internal forces and deformation of adjacent tunnels. In addition, the experimental results of Wang et al.⁴⁹ show that the increase in the dosage of sulphoaluminate cement significantly improves the mechanical properties of rock-like materials. Furthermore, Yao et al.⁵⁰ conducted test studies on variables such as concrete strength and short beam length. Zhang et al.⁵¹ conducted a study on the feasibility of applying the interval seismic strategy to the seismic resistance and vibration reduction of high-rise structures.

In addition, in the aspect of deformation control of foundation pit supporting structure and surrounding soil mass, some scholars have carried out research on the related problems of support servo system. For instance, Di et al.⁵² conducted a comparative analysis of the deformation control effects between servo steel supports and ordinary steel supports. Nangulama et al.^53,54 verified the servo deformation control capability of deep foundation pit engineering. Besides, Wang et al.⁵⁵ conducted research on a new type of servo concrete support system. Wei et al.⁵⁶ studied the influence of servo steel supports on underground continuous walls. Li et al.⁵⁷ proposed a simple method for calculating the wall deflection caused by excavation. Moreover, Wang et al.⁵⁸ proposed a calculation method to understand the law of axial force loss of adjacent supports caused by servo support loading.

To sum up, the development and utilization of underground space related issues are increasingly concerned by scholars, and has already obtained relatively rich results. Obviously, these studies have a certain positive significance for the exploitation and utilization of underground space. It significantly enhances urban carrying capacity, disaster resilience, and robustness, reduces carbon emissions, and promotes harmonious coexistence between humans and nature⁵⁹. However, the excavation of deep foundation pits can cause variations in the displacement and stress fields of surrounding soils, which hence induces adverse effects on adjacent structures⁶⁰. Conventional deep excavation support systems have fixed length of struts, which can lead to a significant discrepancy between deformations of actual and designed diaphragm wall systems. As a result, failure of support system is likely to occur during the deep excavation⁶¹. As a novel type of supporting system, servo steel struts have been employed frequently in deep excavations adjacent to important infrastructures⁶².

It is worth noting that the subway station has the function of entering and leaving the station and transferring¹³, as a result, many people gather at subway stations every day. Therefore, it is very important to ensure the safety of subway stations. In addition, many subway stations are located in central areas of cities, where important buildings may be located nearby. In view of this, during the construction of subway stations, it is necessary not only to ensure the safety of the foundation pit construction process, but also to ensure the safety and stability of adjacent buildings¹⁴. Furthermore, in the design and construction of subway stations, the interaction between adjacent structures should be taken into consideration¹⁵. Therefore, it is necessary to study the control and protection of deep excavation engineering and surrounding environment. Moreover, the problem of axial force loss is common in traditional steel struts, this makes the ordinary enclosure structure difficult to meet some high deformation requirements of the project⁶¹. As a new strut system, steel strut axial force servo system is gradually applied in many fields, such as tunnels near the subway and deep excavations with complex surrounding environment⁶³. Although some scholars have carried out research on the control of steel strut axial force servo system. However, the research related to the application of servo system in deep excavation is still in its infancy. And there is relatively little experience for reference⁵⁵. At the moment, the design and application of servo struts are mainly based on engineers’ previous experience⁶⁵. The effectiveness of servo struts in controlling excavation induced wall deflection and ground settlement is still not fully understood⁶⁴. Furthermore, given their high cost, servo steel struts typically are used only in specific sections of foundation pits in which nearby buildings are sensitive to excavation-induced deformation. Servo steel strut adjustments affect the mechanical behaviors of adjacent ordinary-steel-strut-supported areas. However, the plane strain assumption is used in current designs, ignoring this influence⁶⁶. Therefore, it is necessary to conduct a systematic study on the construction mechanical behavior of the steel support servo system for the deep foundation pit of the metro in adjacent buildings.

In view of this, based on the above research results, this paper conducts relevant research on the construction mechanics behavior of the steel support servo system of a metro deep foundation pit project in Hangzhou as the background. The research content mainly includes four parts: Firstly, a 3D finite element model is established using MIDAS/GTS NX software and numerical calculations are carried out. Secondly, the reliability of the model is verified by comparing the numerical calculation results with the measured results. Thirdly, conduct research on the construction mechanics behavior of the steel support servo system for deep foundation pits of the subway. And finally, the influencing factors of the steel support servo system were studied. The research conclusion has certain reference significance for the design and construction of similar projects.

Project overview

The research object of this paper is the deep excavation project of subway station. The project is located in Hangzhou City. The surrounding environment of subway stations is complicated, which brings severe challenges to construction technology and environmental safety. Furthermore, the length, width and depth of the standard section of the subway station are 180, 20 and 26 m, respectively. Moreover, the length, width, and depth of the end well are 26, 28, and 26 m, respectively. To be clear, the deep excavation is constructed by open excavation method. Besides, the enclosure structure is mainly composed of diaphragm wall and struts. The material of the diaphragm wall is reinforced concrete. Moreover, the thickness and total depth are 0.8 and 32 m, respectively. The embedment depth is 6 m. In addition, there are 6 struts. The first is reinforced concrete strut, and the other five are steel struts. The longitudinal and horizontal spacing of the strut of the standard section are 4 and 5 m, respectively. Besides, the longitudinal and horizontal spacing of the strut in the end well are 4 and 7 m, respectively. Moreover, the simplified soil layer are 7 layers. From top to bottom are: ①miscellaneous fill, ②silty clay, ③muddy clay, ④clay, ⑤fully weathered tuff, ⑥highly weathered tuff, and ⑦moderately weathered tuff. Figure 1 presents the cross-section of the standard section of the subway station. Meanwhile, the specific content of soil layer parameters is depicted in Table 1. Furthermore, the relevant parameters of strut structure are summarized in Table 2.

Fig. 1

Section of the standard section of the subway station.

Table 1 Parameters of the soil layer.

Table 2 Parameters of strut structure.

It is worth noting that there are two normally used buildings near the subway station project. They are named Building A and B, respectively. The foundations of both buildings are piles. Furthermore, the length and diameter of the pile are respectively 30 and 600 mm. The upper part of the building is reinforced concrete frame structure. Moreover, the height and total number of each floor are 4 and 6 m, respectively. It should be noted that, the closest distance between buildings A and B and the metro station are 16 and 20 m, respectively. In order to ensure the normal use of the building during the construction process, the project adopts steel support servo system in some areas.

Related studies have shown that the deformation of the diaphragm wall has obvious spatial effects during excavation: the middle area of the long side will produce the largest deformation^36,38,40. This means that, the middle part of the long side of the diaphragm wall is the most dangerous area. Besides, the deformation in the most dangerous area is closely related to the deformation of adjacent soil, and there is a positive correlation between them⁵⁷. While the building is located on the soil near the deep excavation, the soil deformation will also cause the building deformation^58,59. Obviously, when the deformation is too large, the building may produce uneven settlement and cracks⁶⁰. This will affect the safety performance and normal use of the building. Due to ensure the safety performance and normal use of the building, it is necessary to take relevant measures for the design and construction of deep excavation.

In view of this, according to the principle of the most unfavorable, the project adopts the steel strut servo system in the middle area of the long side of the deep excavation. Figure 2 shows the working diagram of the servo system. It should be noted that the steel support shaft force servo system is mainly composed of ultrasonic rangefinder, strut head, oil cylinder, and steel strut (See Fig. 2 for details). The specific working principle is as follows: Firstly, the servo system measures the compression deformation of the steel support in real time through the displacement sensor. Secondly, it uses the preset program to convert the deformation of the steel support into the axial force of the steel support and compares it with the axial force range set in the system. When the measured supporting axial force exceeds the preset axial force range, the system issues an instruction to retract the jack, thereby reducing the supporting axial force of the steel. Conversely, the system issues instructions to extend the jack, thereby increasing the axial force of the steel support.The steel supporting shaft force servo system actively controls the deformation of the enclosure structure by constantly adjusting the supporting shaft force in real time, so that the deep foundation pit project can meet the requirements of deformation control^63,64,65. Obviously, the traditional struts are only installed at the corresponding positions of the foundation pit as part of the supporting structure and do not have the function of adjusting the axial force according to the actual situation. Therefore, traditional struts have some deficiencies in actively controlling the deformation of foundation pits^67,68,69.

Fig. 2

Schematic diagram of the servo system.

Moreover, the area plan of the servo system setup is shown in Fig. 3. To be clear, the setting of the servo system covers all the steel struts where the plane area is located. Meanwhile, the servo axial force added to all steel struts in the servo system area is 2,000 kN.

Fig. 3

Area plan of servo system.

Model building and numerical calculation

Basic assumptions

Firstly, the impact of groundwater is not considered. Secondly, the soil layer is continuously and evenly distributed. Thirdly, each excavation is carried out as a whole by layers. And finally, other assumptions are consistent with reference 67.

Calculation model

In this study, the 3D finite element model was established by MIDAS GTS NX software (version 2022). The length (X), width (Y) and height (Z) of the model are 472 m, 268 m and 120 m, respectively. The numerical model is shown in Fig. 4. Besides, the number of units and nodes in the model are 245,303 and 187,461, respectively. The model coordinate system and boundary conditions are consistent with reference 20. Furthermore, the constitutive relationship and element type of structural components are consistent with reference 67.

Fig. 4

Numerical model.

Arrangement of monitoring points

Diaphragm wall is one of the most critical structural components in deep excavation engineering^67,68,69,70. The steel support servo system installed in this project is connected to the diaphragm wall.Obviously, the servo system will have a certain influence on the deformation and stress of diaphragm wall. In view of this, the deformation and force of the diaphragm wall are crucial to the response problem of the steel strut servo system. As a matter of fact, many monitoring points are set up in the actual construction process. This study selected representative locations as monitoring points. The specific location of the monitoring point is described in Fig. 5. Apparently, there are six monitoring points of the diaphragm wall in this study. The names of the monitoring points are: (A-A), (B-B), (C-C), (D-D), (E-E), and (F-F). Where, (A-A) and (B-B) are located in the middle of the servo system layout area. Besides, both (C-C) and (D-D) are located at the end of the standard segment. Meanwhile, both (E-E) and (F-F) are located in the middle of the end well. In addition, in order to facilitate the study, the diaphragm wall is divided into four parts and numbered. The serial numbers are: diaphragm wall 1, 2, 3, and 4. The specific number content and location are illustrated in Fig. 5.

Fig. 5

Schematic diagram of monitoring points of diaphragm wall.

It should be noted that in this study, the axial force of the strut of concrete was monitored using a vibrating wire type concrete strain gauge (model: ZXQC-160, manufacturer: Beijing Haifuda Technology Co., LTD.). The horizontal displacement of the underground continuous wall is monitored by a inclinometer (model: BXS16-CX-06A, manufactured by Beijing Beixin Chuangzhan Automation Technology Co., LTD.). To ensure the accuracy and reliability of the monitoring results, the main measures taken in this study are as follows: (1) Select monitoring instruments that match the engineering requirements and have them calibrated by a third-party institution before use. In addition, regular re-inspections should be conducted during construction (once a month), and the calibration records should be archived for future reference. (2) Standardize the installation and protection of monitoring instruments. On the one hand, when pre-embedding the inclinometer tubes in the underground continuous wall for inclinometer tube installation, ensure that the verticality deviation of the tube body is ≤ 1°. Ensure that the joint is tightly sealed and backfill with sand and gravel to prevent voids. In addition, the inclinometer tube opening is covered for protection to prevent construction machinery from colliding with it or foreign objects from entering. On the other hand, when installing the vibrating wire strain gauge, it should be welded and fixed to the steel cage, with the axis line consistent with the force direction to avoid eccentricity. In addition, the cables are protected by PVC pipes to prevent breakage during concrete pouring or electromagnetic interference. (3) Data Collection and Processing: Collection frequency. Excavation stage: Collect once every 1 to 2 days. Excavate to a critical depth (such as 50%, 80%), and increase the frequency to 1 to 2 times a day after rainfall or when data is abnormal. In addition, obvious outliers (such as sensor power failure and human misoperation data) are eliminated during data processing.

Simulated construction

The construction process of this study consists of 18 parts. The details are summarized in Table 3. It should be noted that the completion of excavation refers to “Step 13”.

Table 3 Main construction steps.

Comparative of simulation and field measurements

Figure 6 illustrates the comparison between simulated values and monitored values. Figure 6a clearly shows the horizontal displacement comparison diagram of the monitoring point (A-A) at the completion of excavation. Obviously, the results of both methods show similar changes. The rule of change is the shape of “convex belly”. In terms of maximum value, the monitoring and simulation values are 26.6 mm and 25.2 mm, respectively. The maximum value occurs at the position 4 m above the excavation face. Obviously, the field monitoring results were relatively larger, with a 5.5% difference between the two methods. Besides, Fig. 6b is the comparison of the maximum axial force of strut 1. Obviously, the results of both methods show similar changes. The change rule is “first rapid increase, then slow increase, and then slow decrease”. Obviously, in terms of maximum values, the monitoring and simulation values are − 2,569 and − 2,412 kN, respectively. The maximum values are displayed in Step 9. Apparently, field monitoring results were relatively larger, with a difference of 6.5% between the two methods. It can be seen that the numerical simulation results are in good agreement with the monitoring results. It is demonstrated that the reliability of the numerical model established in this paper is verified. Moreover, the displacement values are less than the standard requirements, and the deep excavation is in a safe state.

Fig. 6

Comparison of simulated and monitored values: (a) horizontal displacement comparison diagram of (A-A); (b) maximum axial force comparison diagram of strut 1.

At the same time, it can be found that the results of field monitoring are larger. The reason may be that the numerical simulation cannot fully consider the complexity of the actual construction conditions, which leads to a certain difference between the simulation results and the actual deformation. For example, material loads and vehicle loads that may occur near deep excavation. However, these factors are not fully taken into account in the numerical simulation. The emergence of these situations may lead to the on-site monitoring data is too large^71,72. To sum up, the established model has a certain reliability. On the basis of this model, the construction mechanical behavior of steel strut servo system for subway deep excavation can be studied.

Numerical result

The main objects of this study are: soil, buildings, diaphragm walls, and struts. Besides, the main contents of the research are: the overall vertical displacement, the total displacement of the building, the displacement of the diaphragm wall, the axial force of the strut, and the analysis of the influencing factors of the servo system.

Overall vertical displacement

Figure 7 is the overall vertical displacement cloud image. Obviously, different construction steps, vertical displacement is also different. In step 1, the maximum and minimum values are 1.7 and − 0.63 mm, respectively. In step 2, the maximum and minimum values are 3.65 and − 1.21 mm, respectively. Moreover, in step 13, the maximum and minimum values are 24.3 and − 5.8 mm, respectively. Obviously, the displacement has positive and negative values. This shows that the vertical deformation of soil mass in the construction process is relatively complicated. The deformation has both uplift and subsidence.

Fig. 7

Overall vertical displacement cloud image: (a) step 1; (b) step 3; (c) step 5; (d) step 7; (e) step 8; (f) step 9; (g) step 10; (h) step 11; (i) step 13.

It can be observed that the largest uplift appears in the area near the long side of the deep excavation. The maximum settlement occurs in the middle area of the long side of the deep excavation. And there is a certain distance from the deep excavation. Meanwhile, the subsidence area with the increase of excavation depth has a growing trend. This also shows that the impact of deep excavation on the surrounding environment has a spatial effect. That is to say, the closer to the middle of the deep excavation, the greater the impact. This conclusion is consistent with that of reference 67. This also verifies the reliability of the model established in this study.

The cause of the largest uplift is that the soil mass is excavated and the free surface is formed in the lower soil mass. The upper constraint of the bottom soil is reduced, so the rebound effect of the bottom of the pit is produced. Meanwhile, at the bottom of the pit, there is a bulge and deformation. In addition, the diaphragm wall at the bottom of the deep excavation is connected. The rebound at the bottom of the pit causes the vertical displacement of the diaphragm wall. The movement of the diaphragm wall will also cause the vertical deformation of the surrounding soil closely connected with it. Furthermore, the phenomenon that the largest uplift occurs in the area near the long side of the deep excavation is shown.

It should be noted that the reason for the maximum settlement is also related to the rebound effect of the bottom of the pit. The soil at the bottom of the pit moves upward, and the lower soil connected to the soil at the bottom of the pit also moves upward. This causes the soil near the bottom of the pit to move vertically down and then show settlement. Apparently, it is important to note that the maximum settlement does not occur in the area where the building is located. This may be due to the use of pile foundations for the foundation of the building in this study. As a matter of fact, the length and diameter of the pile are 30 and 0.6 m, respectively. Moreover, the upper structure is reinforced concrete frame structure. That is to say, the overall performance of the building is relatively good.

Figure 8 is a comparison chart of the overall vertical displacement. Figure 8a is the comparison chart of the maximum values. Obviously, during the construction process, the maximum displacement as a whole shows a trend of “increasing slowly at first and then rapidly”. The maximum value occurred when the excavation was completed, with a value of 24.3 mm. By comparison, it can be found that the increase in displacement in the two stages of steps 12 and 13 is relatively large, both being 2.8 mm. Figure 8b is the comparison chart of the minimum values. Obviously, during the construction process, the minimum displacement as a whole shows a trend of “constantly increasing”. The maximum settlement value occurred when the excavation was completed, with a value of − 5.8 mm. By comparison, it can be found that the displacement increase in step 13 is the largest, which is 0.8 mm.

Fig. 8

Displacement comparison diagram: (a) maximum value; (b) minimum value.

To sum up, the overall vertical displacement is the greatest when the excavation is completed. Steps 12 and 13 have the greatest influence on the overall vertical displacement. Therefore, during the design and construction processes, it is necessary to pay close attention to the design and construction of these two stages and enhance monitoring. When necessary, measures can be taken (such as improving the excavation method or enhancing the rigidity of the supporting structure, and so on³⁴.) to reduce the adverse impact of excavation on the overall vertical displacement.

Total displacement of buildings

Figure 9 is the total displacement cloud image of building A. Obviously, the total displacement is different for different construction steps. Specifically: in step 1, the maximum and minimum values are 0.56 and 0.25 mm respectively. In step 2, they are 1.21 and 0.55 mm, respectively. At step 13, they are 3.86 and 0.74 mm, respectively. Although the values of the total displacement are positive, the values are not the same, which indicates that the building has uneven forces and deformation. Obviously, excavation has adverse effect on the building. It can be found that the maximum displacement occurs in the middle of the side of the building near the deep excavation. However, the minimum displacement mainly appears at the corner of the side of the building away from the deep excavation. This also indicates that the construction of the deep excavation has a spatial effect on the surrounding environment. That is to say, the closer to the middle of the deep excavation, the greater the impact will be. This conclusion is consistent with that of reference 67. This also verifies the reliability of the model established in this study.

Fig. 9

Total displacement cloud map of building A: (a) step 1; (b) step 2; (c) step 4; (d) step 7; (e) step 10; (f) step 13.

The reason for the maximum displacement is that the soil is excavated by the construction, and the free surface is generated in the lower soil. Therefore, the bottom of the pit has a rebound effect, which is manifested as the bottom uplift. In addition, the bottom of the deep excavation is connected to the diaphragm wall. The rebound of pit floor causes the vertical displacement of diaphragm wall resistance. The movement of the diaphragm wall will also cause the vertical deformation of the surrounding soil closely connected with it, and then the phenomenon that the largest uplift occurs in the area near the long side of the deep excavation. However, building A is close to the side of the deep excavation and closely connected to the middle of the long side of the deep excavation. So it shows the largest total displacement. In addition, the main reason for the occurrence of minimum displacement is that the influence of uplift on surrounding soil caused by construction decreases with the increase of distance⁶⁷. Moreover, the corner of the building is a relatively solid part of the building, and the integrity is stronger. Therefore, this region generates the smallest displacement value.

Figure 10 is the total displacement cloud image of building B. Obviously, the vertical displacement is different with different construction steps. Specifically: in step 1, the maximum and minimum values are 0.42 and 0.11 mm respectively. In step 2, they are 0.92 and 0.24 mm, respectively. At step 13, they are 3.82 and 1.74 mm, respectively. Although the values of the total displacement are positive, the values are not the same. Which indicates that the building has uneven forces and deformation. Obviously, the maximum displacement occurs at the end of the building near the middle of the deep excavation. The minimum displacement mainly occurs at the end of the building away from the middle area of the deep excavation. This also indicates that the excavation of the deep excavation has a spatial effect on the surrounding environment. Obviously, the closer to the middle of the deep excavation, the greater the impact will be. This conclusion is consistent with the conclusion in reference 67. This also verifies the reliability of the model established in this study. The reason for the maximum displacement is that the soil is excavated by the construction, and the free surface is generated in the lower soil. Therefore, the bottom of the pit has a rebound effect, which is manifested as the bottom uplift. In addition, the deep excavation bottom diaphragm wall connected. The rebound of pit floor causes the vertical displacement of diaphragm wall resistance. And then, the movement of the diaphragm wall will also cause the vertical deformation of the surrounding soil closely connected with it. Furthermore, the phenomenon that the largest uplift occurs in the middle area of the long side of the deep excavation is shown. Building B is close to the middle part of the deep excavation and is closely connected to the middle part of the long side of the deep excavation, so the total displacement is the largest. In addition, the main reason for the occurrence of minimum displacement is that the influence of heave on surrounding soil caused by construction decreases with the increase of distance. Consequently, this region generates the smallest displacement value.

Fig. 10

Total displacement cloud map of building B: (a) step 1; (b) step 2; (c) step 4; (d) step 7; (e) step 10; (f) step 13.

Therefore, in the design and construction, it is necessary to pay attention to the impact of the deep excavation on the adjacent buildings. On the one hand, it is necessary to strengthen the monitoring of the building. On the other hand, it is important to strengthen the monitoring of the central position of the deep excavation near the building side.

Figure 11 shows the comparison diagram of the maximum displacement of buildings. Figure 11a is A comparison chart of the maximum displacement of Building A. Obviously, during the construction process, the maximum displacement as a whole shows a trend of “first increasing rapidly, then increasing slowly, then increasing rapidly again, and finally increasing slowly”. It can be seen that the maximum value occurs when the excavation is completed, and the value is 3.86 mm. By comparison, it can be found that in steps 1, 2, and 4, the maximum increase amounts are relatively large, which are 0.56, 0.66, and 0.51 mm respectively. Figure 11b is a comparison chart of the maximum displacement of Building B. Obviously, during the construction process, the maximum displacement as a whole shows a trend of “increasing rapidly at first and then slowly”. It can be seen that the maximum value occurs when the excavation is completed, and the value is 3.82 mm. By comparison, it can be found that in steps 1, 2, and 4, the maximum increase amounts are relatively large, which are 0.56, 0.92, and 0.43 mm respectively. The maximum values all occur when the excavation is completed, which indicates that the excavation depth has a significant impact on adjacent buildings. Furthermore, the increase in displacement in steps 2 and 4 are relatively large. This might be because soil was excavated in these stages but no struts were added, which in turn led to a greater impact on adjacent buildings.

Fig. 11

Displacement comparison diagram: (a) building A; (b) building B.

To sum up, the total displacement of the building is the greatest when the excavation is completed. Steps 1, 2, and 4 have the greatest impact on the overall displacement of the building. Therefore, during the design and construction process, it is necessary to pay close attention to these stages of design and construction and enhance monitoring. When necessary, measures can be taken (such as reducing the depth of each excavation, increasing the thickness of underground continuous walls, and so on³⁴.) to minimize the adverse effects of foundation pit excavation on buildings.

Displacement of diaphragm wall

Figure 12 shows the horizontal displacement cloud image of diaphragm walls 1 and 2. Obviously, in different construction steps, the displacement is different. For diaphragm wall 1, the maximum values of steps 1, 2 and 13 are 2.9, 6.1, and 30.9 mm, respectively. For diaphragm wall 2, the maximum values of steps 1, 2 and 13 are − 2.7, − 5.8, and − 30.6 mm, respectively. Apparently, the location of the maximum value varies in different steps. For the first two steps, the maximum value occurs in the middle of the diaphragm wall. This is mainly because there is no servo axial force in the first two construction steps, which shows the same characteristics as other similar excavation results³¹. On the contrary, the location where the maximum appears at the other steps changes. It appears outside the servo system area. This is mainly because these stages add servo axial force to the strut, and the servo axial force has a certain influence on the deformation of the diaphragm wall. Therefore, it is necessary to systematically study the construction mechanics behavior of steel strut servo system in deep excavation of subway.

Fig. 12

Displacement cloud diagram of diaphragm wall 1 and 2 in Y direction: (a) step 1; (b) step 2; (c) step 4; (d) step 7; (e) step 10; (f) step 13.

Meanwhile, the maximum horizontal displacement of the diaphragm wall meets the minimum required by the current relevant regulations³¹. This shows that the strut structure design and excavation method in this study have certain reliability. It is worth noting that the horizontal displacement of diaphragm wall 1 and 2 is different. This may be due to the different positions of the buildings on both sides of the deep excavation. Therefore, the location of the building may have a certain impact on the excavation results.

In order to display the horizontal displacement change of the diaphragm wall more intuitively. The calculated results were extracted and the curve was drawn. It should be noted that this study selected representative monitoring points (The specific distribution of monitoring points is depicted in Fig. 5).

Figure 13 presents the displacement comparison diagram of the monitoring point (A-A). Figure 13a illustrates the displacement comparison curve of monitoring point (A-A). Obviously, at different stages, the horizontal displacement curves show the characteristics of “convex belly”. On the whole, the maximum displacement shows a trend of “increasing”. The location of the maximum value decreases with excavation. Apparently, when the excavation is completed, the maximum displacement occurs at the position 4 m above the excavation face. It is worth noting that the displacement of the same position does not increase with the increase of the depth of excavation. Specifically, in the first two construction steps, the displacement of the same position increases with the increase of the excavation depth. In contrast, in other steps, the displacement of the same position does not increase with the increase of the depth of excavation. This phenomenon shows different response characteristics from deep excavation without servo system⁴⁴. This is mainly because, although the strut is added in the first two steps, the servo axial force is not added. In other steps, the monitoring point (A-A) is in the servo system setup area. The servo axial force is applied to other struts in this area, so it may have a certain influence on the deformation of the diaphragm wall. In addition, it can also be seen that the position of the steel strut servo system has a significant effect on the deformation of the diaphragm wall. It shows the characteristics of restraining the deformation of diaphragm wall to the interior of deep excavation. Obviously, this inhibition has a more obvious effect on the deformation of the diaphragm wall above the setting point of the steel strut servo system. On the contrary, the influence on the deformation of the diaphragm wall below the setting point of the strut servo system is relatively small. This also shows that the setting of the steel strut servo system has a certain role in controlling the deformation of the deep excavation.

Fig. 13

Displacement comparison diagram of the monitoring point: (a) (A-A); (b) Maximum value.

Figure 13b is the comparison diagram of the maximum displacement of the monitoring point (A-A). Obviously, the maximum value generally shows the law of “fluctuation change, continue to increase”. Obviously, the maximum displacement is 25.21 mm when excavation was completed. By comparison, it can be found that at steps 3, 5, 7, 9, and 11, the maximum increase in displacement is relatively small, which are 2.06, 1.4, 0.64, − 0.27, and − 0.45 mm respectively. This is mainly due to the addition of steel struts in these steps, and the addition of servo axial force. Apparently, the steel strut servo system can inhibit the maximum displacement of diaphragm wall. In contrast, in other stages, the increase in the maximum displacement is relatively large.

Figure 14 illustrates the displacement comparison diagram of the monitoring point (B-B). Figure 14a presents the displacement comparison curve of the monitoring point (B-B). Obviously, during the construction process, the displacement curve also presents the characteristics of “convex belly”. The maximum value is also “increasing” in general. The location of the maximum value decreases with excavation. When the excavation is completed, the maximum displacement occurs at the position 4 m above the excavation face. It is worth noting that the horizontal displacement of the same position does not increase with the increase of the depth of excavation. Specifically, in the first two construction steps, the horizontal displacement of the same position increases with the increase of the excavation depth. However, in other steps, the horizontal displacement of the same position does not increase with the increase of the depth of excavation. This phenomenon shows different response characteristics from deep excavation without servo system⁶⁷. The reason is the same as the monitoring point (A-A).

Fig. 14

Displacement comparison diagram of the monitoring point: (a) (B-B); (b) maximum value.

Figure 14b indicates the comparison of the maximum displacement of the monitoring point (B-B). Obviously, the maximum value also shows the law of “fluctuating change and increasing” in general. Obviously, the displacement was the greatest when the excavation was completed, with a value of − 23.17 mm. By comparison, it can be found that the maximum displacement increases at steps 3, 5, 7, 9, and 11 were relatively small, which were 2.01, 1.43, 0.62, − 0.3, and − 0.58 mm, respectively. The reason is the same as the monitoring point (A-A).

Figure 15 presents the displacement comparison diagram of the monitoring point (C-C). Figure 15a illustrates the displacement comparison curve of the monitoring point (C-C). Obviously, at different construction stages, the horizontal displacement curves show the characteristics of “convex belly”. The maximum displacement showed a trend of “increasing”. The location of the maximum value decreases with excavation. When the excavation is completed, the maximum displacement is 4 m above the excavation face. It is worth noting that the horizontal displacement of the same position increases with the increase of the excavation depth. This phenomenon shows different response characteristics from the deep excavation with servo system²⁰. This may be because the monitoring point (C-C) is not in the servo setting area, so the horizontal displacement is relatively less affected by the servo setting. In other words, the restraining effect of the servo system on the deformation of the diaphragm wall mainly plays a role in the servo area. Therefore, it is very important to choose the servo area reasonably.

Fig. 15

Displacement comparison diagram of the monitoring point: (a) (C-C); (b) Maximum value.

Figure 15b presents the comparison of the maximum displacement of the monitoring point (C-C). Obviously, the maximum value in general shows the law of “increasing”. Obviously, the displacement was the greatest when the excavation was completed, with a value of 30.14 mm. By comparison, it can be found that at steps 3, 5, 7, 9, and 11, the maximum increase in displacement is relatively small, which are 2.71, 2.07, 1.64, 1.69, and 1.5 mm respectively. The reason is the same as the monitoring point (A-A).

Figure 16 presents the displacement comparison diagram of the monitoring point (D-D). Figure 16a illustrates the displacement comparison curve of the monitoring point (D-D). Obviously, at different stages, the displacement curve shows the characteristics of “convex belly”. The maximum displacement showed a trend of “increasing”. The location of the maximum value decreases with excavation. When the excavation is completed, the maximum displacement occurs at the position 4 m above the excavation face. It is worth noting that the horizontal displacement of the same position increases with the increase of the excavation depth. The reason is the same as the monitoring point (C-C).

Fig. 16

Displacement comparison diagram of the monitoring point: (a) (D-D); (b) maximum value.

Figure 16b presents the comparison of the maximum displacement of the monitoring point (D-D). It is clear that the maximum value in general shows a “constantly increasing” law. It can be seen that the displacement is the largest when the excavation is completed, with a value of 30.69 mm. By comparison, it can be found that at steps 3, 5, 7, 9, and 11, the maximum increase in displacement is relatively small, which are 2.75, 2.07, 1.62, 1.68, and 1.53 mm respectively. The reason is the same as the monitoring point (C-C).

Figure 17 shows the displacement cloud image of diaphragm wall 3 in the Y direction. Obviously, the displacement cloud diagrams are different at different steps. In step 1, the maximum value is 2.32 mm. Subsequently, in step 2, the maximum value is 4.82 mm. Moreover, in step 13, the maximum value is 40.4 mm. The location of the maximum value decreases continuously with excavation.

Fig. 17

Displacement cloud diagram of diaphragm wall 3 in Y direction: (a) step 1; (b) step 2; (c) step 4; (d) step 7; (e) step 10; (f) step 13.

Figure 18 presents the displacement comparison diagram of the monitoring point (E-E). Figure 18a indicates the displacement comparison curve of the monitoring point (E-E). Obviously, in different construction stages, the displacement curve shows the characteristics of “convex belly”. The maximum displacement showed a trend of “increasing”. Besides, the location of the maximum value decreases with excavation. When the excavation is completed, the maximum displacement occurs at the position 6 m above the excavation face of the deep excavation. It is worth noting that the horizontal displacement of the same position increases with the increase of the excavation depth. This phenomenon shows different response characteristics from the deep excavation with servo system (see Fig. 12 for details). The reason is the same as the monitoring point (C-C).

Fig. 18

Displacement comparison diagram of the monitoring point: (a) (E-E); (b) maximum value.

Figure 18b shows the comparison of the maximum displacement of the monitoring point (E-E). It is clear that the maximum value in general shows a “constantly increasing” law. It can be seen that the displacement is the largest when the excavation is completed, with a value of 40.4 mm. By comparison, it can be found that at steps 3, 5, 7, 9, and 11, the maximum increase in displacement is relatively small, which are 2.5, 2.15, 3, 4, and 3.4 mm respectively. The reason is the same as the monitoring point (C-C).

Figure 19 presents the displacement cloud image of diaphragm wall 3 in the X direction. Obviously, the displacement is different for different steps. In step 1, the maximum value is 1.97 mm. And then, in step 2, the maximum value is 4.2 mm. Moreover, in step 13, the maximum value is 25.4 mm. The location of the maximum value decreases continuously with excavation.

Fig. 19

Displacement cloud diagram of diaphragm wall 3 in X direction: (a) step 1; (b) step 2; (c) step 4; (d) step 7; (e) step 10; (f) step 13.

Figure 20 shows the displacement comparison diagram of the monitoring point (F-F). Figure 20a presents the displacement comparison curve of the monitoring point (F-F). Obviously, in different construction stages, the displacement curve presents the characteristics of “convexity”. The maximum displacement showed a trend of “increasing”. Besides, the location of the maximum value decreases with excavation. When the excavation is completed, the maximum displacement occurs at the position 4 m above the excavation face. It is worth noting that the horizontal displacement of the same position increases with the increase of the excavation depth. This phenomenon shows different response characteristics from the deep excavation with servo system (see Fig. 12 for details). The reason is the same as the monitoring point (C-C).

Fig. 20

Displacement comparison diagram of the monitoring point: (a) (F-F); (b) maximum value.

Figure 20b presents the comparison of the maximum displacement of the monitoring point (F-F). It is clear that the maximum value in general shows a “constantly increasing” law. It can be seen that the displacement is the largest when the excavation is completed, with a value of 25.4 mm. By comparison, it can be found that at steps 3, 5, 7, 9, and 11, the maximum increase in displacement is relatively small, which are 2.25, 1.84, 1.4, 1.7, and 1.4 mm respectively. The reason is the same as the monitoring point (C-C).

Figure 21 shows the displacement comparison diagram of all monitoring points at the completion of excavation. It should be noted that in order to facilitate the study, the displacement results of the monitoring point (B-B) are treated as absolute value. Figure 21a shows the comparison of displacement curves. Obviously, the displacement curves of different monitoring points show the characteristics of “convex belly” when the excavation is completed. It can be seen that the maximum displacement is also different for different positions of the monitoring points. This shows that the construction mechanical behavior of steel strut servo system in subway deep excavation has certain spatial effects. The maximum values from (A-A) to (F-F) are respectively: 25, 23, 30, 31, 40, and 25 mm. Obviously, the maximum displacement of the monitoring points (A-A) and (B-B) is relatively small. The maximum displacement of other monitoring points is relatively large. It is worth noting that the maximum value does not occur in the same place. The locations where the maximum values of the monitoring points (A-A) and (B-B) appear are all 4 m above the excavation surface. However, the others occur at a position 6 m above the excavation face. This shows that the setting of the servo system also has a certain influence on the position of the maximum displacement when the excavation is completed. The setting of the servo system makes the position of the maximum displacement of the diaphragm wall in the servo area move downward. Figure 21b shows the comparison plot of the maximum values. Obviously, the maximum displacement values at different monitoring points are different. The displacement of the monitoring point (E-E) is the largest, with a value of 40.37 mm. The displacement of the monitoring point (B-B) is the smallest, with a value of 23.17 mm. This might be because the monitoring point (E-E) is not in the axial force servo area, while the monitoring point (B-B) is in the axial force servo area. This also indicates that the servo system has a certain constraining effect on the deformation of the supporting structure.

Fig. 21

Displacement comparison diagram of the monitoring point: (a) displacement curve; (b) maximum value.

In summary, the maximum displacement of diaphragm wall is greatly affected by excavation. The displacement tends to increase with the increase of excavation depth. The steel strut servo system can inhibit the maximum displacement of diaphragm wall. In addition, the setting of the servo system makes the position of the maximum displacement of the diaphragm wall in the servo area move downward. Therefore, in the design and construction process of deep excavation, it is necessary to pay attention to the design, construction and monitoring of the servo system.

Strut axial forces

Figure 22 presents the cloud image of strut axial force. Obviously, the construction stage is different, the axial force is also different. In terms of maximum axial force, in step 1, the value is − 419.4 kN. Subsequently, in step 2, the value is − 928.2 kN. The maximum value is found at the end of the first strut. Moreover, When the excavation is completed, the value is − 2,883.4 kN, which appears at the end of the 6th strut. In terms of minimum axial force, In step 1, the value is − 79.3 kN. Besides, in step 2, the value is − 192.5 kN. When the excavation is completed, the value is 630.6 kN, which appears in the middle of the first strut. It should be noted that the maximum axial force value is negative. This shows that the main axial force of the strut is pressure. By comparison, it can be seen that the maximum axial force mainly appears in the strut at the end of the deep excavation. This is mainly because the central strut is located in the axial force servo area. Servo axis forces are added to the strut of the servo zone. Therefore, it shows that the axial force of the middle strut is relatively small, and the axial force of the end strut is relatively large. This also reflects that the strut at the end of the deep excavation is a weak point prone to compression failure.

Fig. 22

Cloud image of strut axial force: (a) step 1; (b) step 2; (c) step 3; (d) step 4; (e) step 5; (f) step 7; (g) step 9; (h) step 11; (i) step 13.

Figure 23 shows the comparison diagram of axial forces. It can be seen from Fig. 23a that the maximum value shows a trend of "increasing first, then decreasing, and increasing again". The maximum value appears in step 13, with a value of − 2,883.4 kN. It can be seen from Fig. 23b that the minimum value of the axial force shows a trend of “fluctuating first and then remaining stable”. The minimum value appears in step 3, with a value of 852.9 kN. That is to say, throughout the entire foundation pit construction process, the support bears the greatest pressure when the excavation is completed. The support bears the greatest tensile force in step 3.

Fig. 23

Axial force comparison diagram: (a) maximum value; (b) minimum value.

Table 4 shows the changes in the supporting axial force. Obviously, the variation of axial force varies at different construction stages. In terms of the maximum value, at step 2, the increase in axial force is the largest, which is 848 kN. This might be because the soil has been excavated at this stage, and the earth pressure around the foundation pit has increased. However, no new strut was added, thus resulting in a relatively rapid increase in axial force. In terms of the minimum value, the increase in axial force in step 3 is the largest, which is 1,046 kN. This might be due to the fact that during step 3, the strut was added and the servo axial force was also added, which led to the greatest change in the strut axial force at this stage.

Table 4 Axial force value change table.

In conclusion, when the excavation is completed, the maximum axial force value of the strut is the greatest. The increase in axial force is the greatest in steps 2 and 3. Therefore, it is necessary to attach importance to the design and construction of struts in these stages.

Figure 24 shows the comparison diagram of the axial force of the first strut. It can be known from Fig. 24a that the maximum value shows a trend of “increasing first and then decreasing”. The maximum value occurs in step 9, with a value of − 2412 kN. It can be known from Fig. 24b that the minimum value of the axial force shows a trend of “fluctuating first and then remaining stable”. The minimum value occurs in step 10, which is 377 kN. That is to say, during the entire foundation pit construction process, support 1 bears the greatest pressure at step 9. Support 1 bears the greatest tensile force at step 10.

Fig. 24

Comparison of axial forces of strut 1: (a) maximum value; (b) minimum value.

Table 5 shows the changes in the axial force of the first strut. Obviously, the variation of axial force varies at different construction stages. In terms of the maximum value, at step 2, the increase in axial force is the largest, which is 509 kN. This might be because the soil has been excavated at this stage, and the earth pressure around the foundation pit has increased. However, no new strut was added, which led to a relatively rapid increase in the axial force of the strut 1. In terms of the minimum value, the increase in axial force in step 3 is the largest, which is 384 kN. This might be due to the fact that during step 3, the strut was added and the servo axial force was also added, which in turn led to the greatest change in the axial force of the strut 1 at this stage. It can be seen that the Settings of the servo system will have a certain impact on the supporting axial force in the non-servo area.

Table 5 Axial force value change table (Strut 1).

To sum up, at step 9, the axial force value of the first strut is the greatest. The increase in axial force is the greatest in steps 2 and 3. Therefore, it is necessary to attach importance to the design and construction of the strut 1 in these several stages.

Figure 25 shows the axial force diagram of the second strut. It can be known from Fig. 25a that the maximum value of the axial force shows a trend of “constantly increasing”. The maximum value appears in step 13 and is − 1962 kN. It can be known from Fig. 25b that the minimum value of the axial force shows a trend of “fluctuating first and then remaining stable”. The minimum value appears in step 3, with a value of 853 kN. That is to say, during the entire foundation pit construction process, support 2 bears the greatest pressure at step 13. Support 2 bears the greatest tensile force in step 3.

Fig. 25

Comparison of axial forces of strut 2: (a) maximum value; (b) minimum value.

Table 6 shows the changes in the axial force of the second strut. Obviously, the variation of axial force varies at different construction stages. In terms of the maximum value, at step 4, the increase in axial force is the largest, which is 458 kN. This might be because the soil has been excavated at this stage, and the earth pressure around the foundation pit has increased. However, no new strut was added, which led to a relatively rapid increase in the axial force of the strut 2. In terms of the minimum value, the increase in axial force in step 3 is the largest, which is 853 kN. This might be due to the fact that during step 3, the strut was added and the servo axial force was also added, which in turn led to the greatest change in the axial force of the strut 2 at this stage. It can be seen that the Settings of the servo system will have a certain impact on the supporting axial force of the servo area.

Table 6 Axial force value change table (Strut 2).

To sum up, when the excavation is completed, the axial force value of the second strut is the greatest. The increase in axial force is the greatest in steps 3 and 4. Therefore, it is necessary to attach importance to the design and construction of the strut 2 in these several stages.

Figure 26 shows the axial force diagram of the third support. It can be known from Fig. 26a that the maximum value of the axial force shows a trend of “increasing rapidly first and then slowly”. The maximum value occurs in step 13, which is − 2,584 kN. It can be known from Fig. 26b that the minimum value of the axial force shows a trend of “fluctuating first and then remaining stable”. The minimum value appears in step 5 and is 782 kN. That is to say, during the entire foundation pit construction process, support 3 bears the greatest pressure at step 13. Support 3 bears the greatest tensile force at step 5.

Fig. 26

Comparison of axial forces of strut 3: (a) maximum value; (b) minimum value.

Table 7 shows the change table of axial force of inner support 3. Obviously, the variation of axial force varies at different construction stages. In terms of the maximum value, at step 6, the increase in axial force is the largest, which is 679 kN. This might be because the soil has been excavated at this stage, and the earth pressure around the foundation pit has increased. However, no new strut was added, which led to a relatively rapid increase in the axial force of the strut 3. In terms of the minimum value, the increase in axial force in step 5 is the largest, which is 782 kN. This might be due to the fact that during step 5, the strut was added and the servo axial force was also added. This further leads to the greatest change in the axial force of support 3 within this stage. It can be seen that the Settings of the servo system will have a certain impact on the supporting axial force of the servo area. Furthermore, it is worth noting that the reduction in axial force in step 6 is also relatively large, at − 628 kN. This might be because the soil has been excavated at this stage, and the pressure on the strut will increase. However, support 3 has added servo axial force, so it is manifested as a decrease in the axial force value.

Table 7 Axial force value change table (Strut 3).

To sum up, when the excavation is completed, the axial force of the third strut is at its maximum. The increase in axial force is the greatest in steps 5 and 6. Therefore, it is necessary to attach importance to the design and construction of the strut 3 in these several stages.

Figure 27 shows the axial force diagram of the fourth support. It can be known from Fig. 27a that the maximum value of the axial force shows a trend of “constantly increasing”. The maximum value occurs in step 13, which is − 2,689 kN. Obviously, the increase in steps 7 and 8 is relatively large. The increase amounts were 734 kN and 857 kN respectively. It can be known from Fig. 27b that the minimum value of the axial force shows a trend of “first increasing rapidly, then fluctuating and changing, and then continuously decreasing”. Specifically, the minimum value occurs in step 7, with a value of 611 kN. Obviously, at step 7, the increase in the minimum axial force is relatively large, with an increase of 611 kN. The reason for the largest increase is the same as that in Table 7.

Fig. 27

Comparison of axial forces of strut 4: (a) maximum value; (b) minimum value.

To sum up, when the excavation is completed, the axial force of the fourth strut is at its maximum. The increase in axial force is the greatest at steps 7 and 8. Therefore, it is necessary to attach importance to the design and construction of the strut 4 in these several stages.

Figure 28 shows the axial force diagram of the fifth support.It can be seen from Fig. 28a that the maximum axial force shows an “increasing” trend. The maximum value appears in step 13, with a value of − 2,531 kN. Obviously, at step 10, the increase was relatively the largest, with the increases being 2,272 kN respectively.As can be seen from Fig. 28b, the minimum value of axial force shows a trend of “rapid increase at first, followed by fluctuation change”. The maximum value occurs in step 9, with a value of − 884 kN. Obviously, at step 9, the increase was relatively the largest, with the increase amounts being 884 kN respectively. The reason for the largest increase is the same as that in Table 7.

Fig. 28

Comparison of axial forces of strut 5: (a) maximum value; (b) minimum value.

To sum up, when the excavation is completed, the axial force of the fifth strut is at its maximum. The increase in axial force is the greatest at steps 9 and 10. Therefore, it is necessary to attach importance to the design and construction of the strut 5 in these stages.

Figure 29 shows the axial force diagram of the sixth strut.It can be seen from Fig. 29a that the maximum axial force shows a trend of “increasing”. The maximum value occurs in step 13, which is − 2,883 kN. Obviously, at steps 12 and 13, the increase in axial force was relatively large, and the increase was close to 950 kN. According to Fig. 29b, the minimum axial force showed a trend of “first increasing, then decreasing, and then increasing”. The minimum value appears in step 13 and is − 1,447 kN. Obviously, at steps 12 and 13, the increase in axial force was relatively large, and the increase was close to 900 kN. The reason for the largest increase is the same as that in Table 7.

Fig. 29

Comparison of axial forces of strut 6: (a) maximum value; (b) minimum value.

To sum up, when the excavation is completed, the axial force of the sixth strut is at its maximum. The increase in axial force is the greatest at steps 12 and 13. Therefore, it is necessary to attach importance to the design and construction of the strut 6 in these several stages.

Influence analysis of servo system position

The different position of servo system may have a certain influence on the mechanical behavior of subway deep excavation construction. Therefore, the influence analysis of servo system position is helpful to clarify the influence law of servo system position on the mechanical behavior of subway deep excavation construction. It is helpful to guide the design and construction of subway deep excavation servo system scientifically. In this study, based on the above model, the influence analysis of the servo system position on the deformation of the diaphragm wall is carried out. The position of the servo system is mainly divided into 6 kinds of situations. Specifically: (1) struts 2, 3, 4, 5, and 6; (2) struts 2 and 3; (3) struts 3 and 4; (4) struts 4 and 5; (5) struts 5 and 6; (6) struts 2 and 6. All other conditions are consistent with the numerical model established in the above study.

Figure 30 illustrates the displacement cloud image when the servo system position changes. Obviously, when the servo system position is different, the displacement cloud map is also different. Specifically, when located at struts 2 and 3, the maximum value is 30.65 mm. Besides, when located at struts 3 and 4, the maximum value is 30.97 mm. Furthermore, when located at struts 4 and 5, the maximum value is 30.99 mm. Subsequently, when located at struts 5 and 6, the maximum is 31 mm. It can be seen that the maximum value shows an increasing trend as the position of the servo system decreases.

Fig. 30

Displacement cloud image of servo system position change: (a) 2,3; (b) 3,4; (c) 4,5; (d) 5,6.

Figure 31 illustrates the comparison of horizontal displacement curves of the monitoring point (A-A). Obviously, the horizontal displacement of the diaphragm wall is also different with the location of the servo system. This shows that the position of servo system has a certain influence on the horizontal displacement of diaphragm wall. In general, when the position of the servo system is different, all the displacement curves show the change law of “convex belly” shape. The maximum value occurs at the position 4 m above the excavation face. This shows that the position of the maximum value is not sensitive to the servo system position change. Specifically, when set at struts 2, 3, 4, 5, and 6, the maximum value is 25 mm. Besides, when set at struts 2 and 3, the value is 30 mm. In addition, when set at struts 3 and 4, the value is 29 mm. Moreover, when set at struts 4 and 5, the value is 28 mm. Furthermore, when set at struts 5 and 6, the value is 27 mm. Besides, when set at struts 2 and 6, the value is 28 mm. It can be found that the maximum displacement value is minimum when set at struts 2, 3, 4, 5, and 6. Obviously, when all steel struts are set with servo system, the deformation control effect of diaphragm wall is the best. Apparently, it can also be found that when the servo system is set with 2 struts, the maximum displacement decreases gradually with the downward movement of the setting position. Obviously, when set at struts 2 and 3, the maximum displacement value is maximum. On the contrary, when set at struts 5 and 6, the value is minimum. Therefore, when the servo system is set up with 2 struts, the position of the strut is set as close to the excavation face as possible.

Fig. 31

Comparison of horizontal displacement curves of monitoring point (A-A): (a) horizontal displacement curve; (b) maximum value.

Influence analysis of servo axis force value

The different servo axial force may have a certain influence on the mechanical behavior of deep excavation construction. Therefore, the influence analysis of servo axial force is helpful to clarify the influence law of servo axial force on the mechanical behavior of deep excavation construction. In this study, based on the above model, the influence of servo axial force on the deformation of diaphragm wall is analyzed by changing the servo axial force. And the servo axial force is mainly divided into five situations. Specifically: (1) 1,000 kN, (2) 1,500 kN, (3) 2,000 kN, (4) 2,500 kN, (5) 3,000 kN. All other conditions are consistent with the numerical model established in the above study. It should be noted that the servo system in this study is set on struts 2, 3, 4, 5, and 6 at the same time.

Figure 32 shows the displacement cloud image when the servo axial force changes. Obviously, when the servo axial force is different, the displacement is also different. Specifically, When the servo axial forces are 1,000 kN, 1,500 kN, 2,500 kN, and 3,000 kN, the maximum displacements are 30.96, 30.92, 30.86, and 30.83 mm respectively. Obviously, the maximum value of displacement shows a decreasing trend with the increase of the servo axis force.

Fig. 32

Displacement cloud diagram for different servo axis forces: (a) 1,000 kN; (b) 1,500 kN; (c) 2,500 kN; (d) 3,000 kN.

Figure 33 presents the horizontal displacement comparison of the monitoring point (A-A). Figure 33a presents the comparison of horizontal displacement curves. Obviously, the horizontal displacement of the diaphragm wall is different with different servo axis forces. This shows that the servo axial force has a certain influence on the horizontal displacement of the diaphragm wall. In general, when the servo axis force is different, all displacement curves show the change law of “convex belly” shape. The maximum displacement occurs at the position 4 m above the excavation face. This shows that the position of the maximum displacement is not sensitive to the change of the servo axial force value. Specifically, When the servo axial forces are 1,000 kN, 1,500 kN, 2000 kN, 2,500 kN, and 3,000 kN, the maximum displacements are 28, 27, 25, 24, and 22 mm respectively. It can be found that when the servo axial force is 3,000 kN, the maximum displacement value is minimum. On the contrary, when the servo axial force is 1000 kN, the maximum displacement value maximum. Obviously, when the servo axial force is 3,000 kN, the deformation control effect of the diaphragm wall is the best. At the same time, the comparison can also find that the maximum value of displacement decreases gradually with the increase of the servo axis force.

Fig. 33

Comparison of horizontal displacement of monitoring point (A-A): (a) horizontal displacement curve comparison diagram; (b) horizontal displacement fitting curve diagram.

Figure 33b presents the fitting curve of horizontal displacement. Apparently, the maximum horizontal displacement presents a nonlinear correlation with the servo axial force value. The maximum horizontal displacement decreases with the increase of servo axial force value. It can also be seen that in this study, the fitting equation between the maximum horizontal displacement and the servo axial force value is: y = (125.9 ± 19.8)*x^{(−0.2±0.02)}. Where y represents the maximum horizontal displacement. x stands for servo axial force value. In addition, R² = 0.97006. The value of R² is close to 1. This indicates that the fitting effect is good^71,72.

Discussion

In this paper, the construction mechanical behavior of steel strut servo system for subway deep excavation is studied. The results show that the steel strut servo system has a certain inhibitory effect on the diaphragm wall displacement. The horizontal displacement of diaphragm wall is sensitive to the position of servo system and servo axial force. Obviously, the reasonable setting of servo system is conducive to the safety of urban underground engineering and the control of its environmental impact during construction. The research results will play a positive role in the design optimization and construction guidance of similar engineering structures. However, the research results also show that when the servo system is set at 2 struts, the maximum horizontal displacement of the diaphragm wall gradually decreases with the moving down of the position. The maximum value is minimum when the servo system is set at struts 5 and 6. This indicates that the servo system set at struts 5 and 6 has a better control effect on the deformation of the deep excavation. Therefore, it is necessary to discuss the relevant content of the diaphragm wall displacement when the servo system is set at struts 5 and 6. In this discussion, the horizontal displacements of the monitoring points (A-A) and (B-B) located in the area where the servo system is located are selected as the research objects.

Figure 34 presents the displacement comparison curve. Figure 34a shows the displacement comparison curve of control points (A-A). Obviously, the displacement of the first eight excavation stages and the last two excavation stages increases with the excavation depth of the deep excavation. Regarding the maximum values, at steps 1, 2,8,12 and 13, the values were 2.9, 6.1, 21, 25, and 27.3 mm respectively. And the maximum increase is relatively large in all these stages. It is worth noting that the displacement at steps 9 and 11 are 20.7 and 23 mm, respectively. However, the displacement of step 10 is 23.3 mm. Obviously, although the displacement increases with the excavation depth, but compared to the previous period, the increase is negative. This is mainly because these two stages not only add steel strut, but also add servo axial force. This shows that the servo system plays an active role in controlling the deformation of deep excavation.

Fig. 34

Displacement comparison curve: (a) (A-A); (b) (B-B).

Figure 34b shows the displacement comparison curve of control points (B-B). Apparently, the displacement of the first eight excavation stages and the last two excavation stages increases with the excavation depth. For the maximum value, in step 1, the value is 2.5 mm. In step 2, the value is 5.3 mm. In step 8, the value is 19.3 mm. In step 12, the value is 22.3 mm. In step 13, the value is 24.8 mm. The maximum increase is larger in these stages. It is worth noting that the displacement at steps 9 and 11 is 19 and 20.9 mm, respectively. The displacement of step 10 is 21 mm. Obviously, although the displacement increases with the excavation depth. But compared to the previous period, the increase is negative. The reason is consistent with the rule presented by the (A-A) displacement comparison curve.

To sum up, when the servo system is set at struts 5 and 6, the displacement at steps 9 and 11 is reduced compared with the previous stage. On the contrary, the displacement of the other stages is increasing compared to the previous stage. Therefore, in similar projects, it is necessary to focus on the design of servo system position.

The main shortcomings of this study are as follows: (1) It does not consider the possible influence of surrounding pipelines, vehicles and rainfall weather. (2) There is no comparative analysis of the impact of changes in floor height and distance. (3) The number of influencing factors to be considered is small. The thickness, elastic modulus, insertion ratio and strut spacing of the envelope were not studied. (4) The characteristics of strut axis force and underground diaphragm wall displacement with time under the control of servo system have not been studied. (5) The adjacent buildings’ influence on deformation and load redistribution are not thoroughly analyzed, include discussion or modeling of these effects.

Future research directions are as follows: (1) More comprehensive consideration of the surrounding environment of subway station deep excavation engineering. The possible pipeline, rainy weather and vehicle load around the deep excavation engineering of subway station are included in the future research. (2) On the basis of this study, the influence of changes in floor height and distance will be compared and analyzed. (3) Enrich influencing factors. The influencing factors such as thickness, elastic modulus, insertion ratio and strut spacing change of diaphragm wall will be studied. (4) The characteristics of the strut axis force and the diaphragm wall displacement with time under the control of the servo system are further studied. (5) Future studies will be carried out in the direction of adjacent buildings’ influence on deformation and load redistribution, include discussion and modeling of these effects.

Conclusions

In this paper, a combined method of numerical simulation and on-site monitoring is adopted to conduct relevant research on the construction mechanics behavior of the steel support servo system for deep excavation of metro. The main findings are summarized as follows:

• 1. Based on modified Mohr Coulomb constitutive model, MIDAS/GTS is used to numerically simulate deep excavation engineering of subway station. The simulation results agree well with the measured data. During the construction process, the displacement of structural members and soil is small, and the adjacent buildings tend to be safe. It is feasible to adopt the measure of “steel strut + servo system” to the construction of deep excavation project of subway station.

• 2. When the excavation is completed, the maximum and minimum vertical displacement of the soil mass are 24.3 and − 5.8 mm, respectively. The maximum uplift occurred in the area adjacent to the long edge of the deep excavation. Besides, the maximum settlement occurs in the middle area of the long side of the deep excavation, and there is a certain distance from the deep excavation. The maximum total displacement of buildings A and B is 3.86 and 3.82 mm, respectively. For building A, the maximum value occurs in the middle of the side of the building near the deep excavation. Besides, for building B, the maximum value occurs at the end of the area near the middle of the deep excavation.

• 3. The horizontal displacement curves of the diaphragm wall all show the characteristics of “convex belly”. The steel strut servo system plays a certain role in restraining the maximum displacement. The effect of inhibition on the deformation above the setting point of the servo system is more obvious. When the excavation is completed, the maximum value of the servo zone is 25.21 mm, which appears at a position 4 m above the excavation face. In other areas, the maximum value is 40.4 mm, which occurs at the position of 6 m above the excavation face. The axial force of the strut is mainly pressure. The maximum value is − 2,883.4 kN, which occurs at the end of the 6th strut.

• 4. The maximum displacement of the diaphragm wall is sensitive to the change of the position of the servo system. When the excavation is completed, the deformation control effect is the best when the servo system is used for all steel struts. And the maximum value is the smallest, which is 25 mm. When the servo system is set on 2 struts, the maximum value gradually decreases as the servo system moves down. When set at struts 2 and 3, the maximum value is maximum, and the value is 30 mm. On the contrary, when set at struts 5 and 6, the maximum value is minimum, with a value of 27 mm. The shape and maximum position of the horizontal displacement curve are not sensitive to the position of the servo system. When the position is different, the displacement curves all show the change rule of “convex belly” shape. The maximum value occurs at the position 4 m above the excavation face.

• 5. The maximum displacement of diaphragm wall is sensitive to the change of servo axial force. The maximum value decreases gradually with the increase of servo axial force. When the excavation is completed, the maximum value is 22 mm when the servo axial force is 3,000 kN. On the contrary, when the servo axis force is 1,000 kN, the maximum value is the largest and the value is 28 mm. The shape of horizontal displacement curve and the maximum position are not sensitive to the axial force of servo system. When the axial force is different, the displacement curves all show the change rule of “convex belly” shape. The maximum value occurs at the position 4 m above the excavation face.