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Article

Numerical Study of Dig Sequence Effects during Large-Scale Excavation

by
Danli Li
1,
Ying Chen
1,*,
Bing Dai
1,
Zhengyi Wang
2 and
Hao Liang
2
1
School of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, China
2
China Railway 11 Bureau Group Co., Ltd., Wuhan 430061, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(20), 11342; https://doi.org/10.3390/app132011342
Submission received: 9 September 2023 / Revised: 10 October 2023 / Accepted: 10 October 2023 / Published: 16 October 2023
(This article belongs to the Section Civil Engineering)
Browse Figures
Versions Notes

Abstract

:
The appropriate excavation sequence can improve the overall stability of a foundation pit. In this study, eight schemes were created using FLAC3D to examine the impact of the excavation sequence on a foundation pit by analyzing a deep foundation pit in Nanjing, which had an irregular large rectangle shape. The results show that different excavation sequence schemes and different phases of the foundation pit can change the displacement values and the horizontal displacement type. The min–max normalization method was used to score the schemes in terms of six parameters and confirm the best excavation sequence scheme. In addition, the irregular shape of the foundation pit also leads to local differences in the stability of a foundation pit; the wide end is only slightly longer than the narrow end, but its displacement is significantly higher than that of the narrow end, so attention should be paid to reinforcing the weak parts when carrying out the support. This study can inform the selection of the excavation sequence for actual construction processes.

1. Introduction

Metro construction can be an efficient way to relieve the transportation stresses that are produced by fast-expanding cities and growing populations. To address the ever-increasing traffic pressure, the construction of metro stations needs to address challenges in different features related to construction depth (large excavation depth), construction scale (large scale), proximity (close to important buildings), and difficult conditions (complex geological environment and working conditions) [1,2,3]. These factors further lead to long-duration construction and high construction risk during the foundation pit excavation process. If the foundation pit collapses, it will cause large economic losses and casualties. At present, foundation pit excavation methods can be mainly divided into two categories: unprotected [4] and protected excavation [5]. Due to the increasing difficulty of metro foundation pit construction, support is necessary to ensure the safety of the project. Therefore, more and more metro support excavation methods and theories have been proposed, namely, the open cut method [6] and the undercutting method [7]; the common support structures include composite soil nailing walls [8], pile row supports [9], diaphragm walls (DWs) [10], artificial freezing [11], prestressed fish-belly beam supports [12], trench-belly beam supports [13], soil mixing walls [14], and center island excavation [15]. DWs have received extensive research interest and have been widely applied because they may significantly lower the likelihood of safety mishaps during deep foundation pit projects, making it the most significant and crucial support structure in foundation pit construction.
Chen et al. [16] designed a test model incorporating a scalable internal support system and investigated the coordination of deformation characteristics between the internal support system, the ground-connected wall, and the soil behind the wall. Qiao et al. [17] conducted a measurement analysis of a long and narrow deep foundation pit in a deep soft ground layer in Guangzhou, China, using a ground-connected wall with internal support as the enclosure system; they elucidated the traits of the enclosure system of long and narrow deep foundation pits in soft ground. Feng et al. [18] numerically simulated a symmetrical foundation pit in Suzhou, China, using finite element software to investigate the deformation mechanism of the enclosing structure and the surrounding soil during the excavation of a soft soil foundation pit. They performed sensitivity analysis and finally verified the reliability of the model using field-measured data. Ma et al. [19] proposed a method of using isolation piles and diaphragm walls for joint support to protect buildings near a foundation pit; they used numerical simulation software to analyze the deformation law of a building adjacent to the foundation pit under the combined support throughout the excavation process, as well as the deformation characteristics of the isolation pile diaphragm wall. Zhou et al. [20] proposed a Bayesian-network-based deflection risk analysis model for underground diaphragm walls, which more accurately accounts for the dynamic characteristics of hydrogeological design updates and the construction variables during construction progress based on subway construction site data. The proposed method was compared with traditional methods such as fault tree analysis. Yang et al. [21] combined many excavation examples in the soft soil area in Suzhou, China, and investigated the excavation performance indices of diaphragm walls such as uplift and lateral deformation, the vertical deformation of the ground surface, the vertical deformation of the surrounding buildings, and earth pressure. Wang et al. [22] used infrared thermography for the detection of potential leakages in underground diaphragm walls in foundation pits and investigated the infrared radiation characteristics of the leaking and potentially leaking parts of underground diaphragm walls through indoor simulation tests and on-site inspection methods. Zeng et al. [23,24] conducted similar modeling tests to simulate the precipitation process to investigate the mechanism of pit deformation caused by pre-excavation precipitation. Through numerical simulations and experiments, You et al. [25] carried out a study on the appropriate thickness of the piezometric head of an upper pressurized aquifer, where the base of the pit was located to avoid the problem of uplift at the base of the pit. He et al. [26] simulated the mechanical properties of a pile support structure under different combinations of excavation depths, support pile burial depths, and excavation widths, and they investigated the performance of the support structure under different excavation sizes with the help of finite element software.
In summary, many researchers have focused on the theoretical and technological aspects of safety control in the deep foundation pit excavation process, but so far, few studies have been conducted on the effect of foundation pit excavation sequence on the stability of DW structures, even though it is a critical factor. Additionally, with the complexity of urban construction, the foundation pit may have an irregular shape; currently, the deformation law for foundation pits with irregular shapes under different excavation methods is different from the deformation law of foundation pits with regular shapes. Taking the deep foundation pit of a metro project in Nanjing, China, as an example, we utilized a 3D fast Lagrangian analysis code (FLAC3D) to study the stability of both the deep foundation pit, shaped as an irregular large rectangle, and the DW structure under various excavation schemes to provide a reference for the excavation sequence of similar projects in the future.

2. Project Overview

The foundation pit in Nanjing that was considered in this study is an interval air shaft of two metro stations, which is arranged in the northwest–southeast direction. The geomorphology has the characteristics of a mudflat beach along the Yangtze River, and the terrain gently slopes toward the Yangtze River basin. The design level of the pit was Grade 1, and the service life of the temporary components of the enclosure structure was two years. It had a three-column, four-span, underground five-story frame structure with half-submissive and half-retrograde construction. The enclosure structure included a 1.5 m thick DW and a 0.8 m thick plain wall, the structural column was a Φ900 mm round steel pipe concrete column, the pile foundation included φ2500 bored piles, the temporary columns of the upper support system of the foundation pit were 740 × 740 lattice columns, the foundation of lattice columns comprised φ1500 bored piles, and the tops of the piles were embedded in the main structure by 100 mm. The project scale was 148.1 m × (33.4~36.4 m) × 44 m (length × width × height), of which the wide end was the big shield starting working shaft, with a 36.4 m width, and the narrow end was the small shield starting working shaft, with a33.4 m width. Figure 1 shows a schematic of the study area. Figure 2 illustrates the parameters of the foundation pit support structure and the main geological layer.

3. Modeling and Scheme Design

Numerical simulation technology has become a significant tool for addressing difficult engineering difficulties given the increasing complexity of engineering and the continued progress of computational science [27,28,29]. It can be used to effectively overcome the drawbacks of theoretical analysis and similar simulation tests. FLAC3D is a numerical analysis code developed based on the theory of continuous media and the explicit finite difference method, which is widely applied in the field of geotechnical engineering and is particularly suitable for the development of complex multiple conditions, large deformations, nonlinear material behaviors, and instability damage [30,31,32]. Therefore, in this study, we used FLAC3D (6.0) to conduct the related research.
The DW structure is constructed first while the foundation pit is being constructed, and, once it is complete, excavation of the foundation pit starts. Before the foundation pit is excavated, the front and back of the DW are subjected to static earth pressure with equal values, so they are kept in equilibrium. Foundation pit excavation leads to a change in the stress state of the DW: the DW outside face (away from the foundation pit face) starts to be subjected to active earth pressure, and the DW inside face starts to be subjected to passive earth pressure [33], as shown in Figure 3.

3.1. Modeling

The depth of the foundation pit was 44 m, which was planned to be excavated in five layers, and the specific excavation depth of each layer is shown in Figure 4. The first excavation layer was 5.6 m, the second excavation layer was 5.4 m, the third excavation layer was 7.0 m, the fourth excavation layer was 8.2 m, and the fifth excavation layer was 17.8 m. The DW, which was 64.5 m long and 1.5 m thick, was made of HRB400 reinforcing bars cast into C30 concrete. The common parameters of the concrete and steel reinforcing materials show that the C30 concrete typically has a density of about 2400 kg/m3, Poisson’s ratio of about 0.2, and elasticity modulus of between 28 and 35 GPa (there may be minor variations in the literature). HRB400 steel reinforcement has an elasticity modulus of about 200 GPa, a Poisson’s ratio of about 0.3, and a density of about 7850 kg/m3. Therefore, the modulus of elasticity of a wall made of C30 concrete with HRB400 reinforcing bars, when properly designed and constructed, is in the range of 32 to 40 GPa, Poisson’s ratio in the range of 0.2 to 0.3, and density in the range of 2.6 to 2.8 t/m3. It should be noted that these values are also affected by the actual site environment, construction form, quality standards, and other factors, and then change. The WD parameters in this study are shown in Table 1.
Using Rhino (7.0) and Griddle (2.0), a foundation pit excavation mode that was 500 m × 200 m × 100 m (long × wide × high) was created, which had a total of 238,431 zones and 164,512 gridpoints (Figure 5). According to Saint Venant’s principle [34], the dimension of the model does not affect the results of the excavation of the foundation pit in this case. The soil was modeled as a zone structural element with the Mohr–Coulomb [35,36] model commonly used in geotechnical simulation, and the DW was a shell structural element. The boundary conditions of the model were set: the top was a free interface without constraints, the sides were constrained by velocity in the horizontal direction, and the bottom was a fixed boundary, which constrained the velocity in the horizontal and vertical directions at the same time. Considering the self-gravity stress, the gravity acceleration was taken as 10 m/s2. In addition, this study focused on the influence of the excavation sequence on the foundation pit and WD, so some parts were simplified, such as the construction process of the WD; the foundation pit precipitation and the beam support were neglected. Likewise, the lateral pressure coefficients of the different soil layers ranged from 0.2 to 0.6, and 0.25 was taken here for simplification and evenly distributed on the side of the model. Details are shown in Figure 6.

3.2. Scheme Design

Differences in the excavation sequence of the foundation pit may affect the redistribution result of geostress, which in turn affects the stability of the foundation pit and its supporting structure. To explore the mechanisms of the impact of the excavation sequence on foundation pit stability, according to the area division of the foundation pit excavation (Figure 5), the excavation scheme shown in Table 2 was designed. In this study, the area to be excavated from 1-① to 5-⑧ was divided into forty groups, and 500 steps were calculated for each completed excavation. Subject to the constraints of the construction factors, at most two groups were excavated at the same time, and only 500 steps were calculated total for the two groups simultaneously excavated.

4. Simulation Results and Analysis

The displacement of a foundation pit caused by excavation is the crucial factor reflecting construction stability. Figure 7 shows the displacement results. Differences in the excavation sequence significantly affect the displacement results and displacement distribution characteristics of a foundation pit. For the total displacement (the cumulative value of the displacements in six directions), the E scheme (1454.4 mm) is only 67.5% of that the A scheme (2155.3 mm), and there are differences in the distribution features of the displacements for the different excavation schemes. For example, in the X-direction displacement, in scheme A, the excavation starts from the wide end of the foundation pit, and the wide end is in proximity for a long period, so its displacement is significantly larger than that of the narrow end; in scheme B, the excavation occurs in the opposite order, so the displacement of the narrow end is significantly larger than that of the wide end. Likewise, in both the Y direction and Z direction, the displacement of the lower wall (in the top view, the wide end is the left side, and the narrow end is the right side; the lower wall is the lower side in this view, and the upper wall is the same) is slightly larger than that of the upper wall, and the range of displacements of the lower wall is larger than that of the upper wall, which is closer to the narrow end. In addition, Y-direction displacement > Z-direction displacement > X-direction displacement.
The horizontal displacement of the foundation pit directly reflects the stability of the project. Figure 8 records the horizontal displacement results of four locations of the foundation pit under different excavation schemes. At the center of the wide end of the foundation pit (Figure 8a), the horizontal displacements for all excavation schemes are the “Compound type”. At the center of the narrow end of the foundation pit (Figure 8b), the horizontal displacements of the scheme F all are the “Compound type”, while the horizontal displacements of other excavation schemes all are “Contradictory type Ⅰ”. At the center of the lower wall of the foundation pit (Figure 8c), the horizontal displacements of the schemes A and B all are “Compound type Ⅰ”, while the horizontal displacements of other excavation schemes all are “Concave type Ⅰ”. At the center of the upper wall of the foundation pit (Figure 8d), the horizontal displacements of the scheme F all are the “Compound type”, while the horizontal displacements of other excavation sequence schemes all are “Concave type”. Likewise, the horizontal displacements at the top of the wide end of the foundation pit are generally larger than at the narrow end (34.8%, 48.8%, 56.1%, 59.5%, 41.9%, 313.6%, 61%, and 64.1% larger at the wide end than at the narrow end, from A to B, respectively), and the degree of inhomogeneity is greater at the wide end.
Figure 9 depicts the evolution of the settlement displacement at the four monitoring points (at the point directly above the history profile in Figure 8) as the excavation proceeds. Due to the differences in the excavation scenarios, A and B require twice the number of steps to complete the excavation process, and they therefore produce slightly more settlement than the other schemes.
The plastic zone in FLAC3D is the area where the material experiences plastic deformation after its elastic limit is exceeded. By analyzing the plastic zone, we can determine the shape, scale, and type of the plastic deformation region of the model during the numeration process [37,38]. After the excavation of the foundation pit, the DW, as the most important supporting structure, plays a decisive role in guaranteeing the stability of the foundation pit, so it is of significance to analyze the DW after excavation following different excavation sequence schemes. In addition, studying the nodal velocity, maximum principal stresses, and moment in the model can also give a reference for the analysis of the results, minimizing mistakes that may occur from analyzing too few elements. These data can be found in Appendix A.

5. Discussion

Metro foundation pit construction scale and difficulty have increased as a result of complicated construction environments and increased traffic demand. During foundation pit scale growth, the shape is no longer “regular”. These changes make the stability of the foundation pit increasingly difficult to control, and previous engineering experience is often insufficient to predict the displacement changes and stress transform caused by excavation. Therefore, it is crucial to conduct specific studies for specific engineering situations.
The excavation sequence is an important factor affecting stability during the foundation pit excavation process. You et al. [39] analyzed the coupling effect between the foundation pit during the whole excavation process and the support construction of a complex foundation pit group, and they investigated the deformation characteristics of the support structure of the foundation pit group under different construction sequence schemes. Su et al. [40] investigated the effect of the construction sequence on the force characteristics of the anchored anchors and the pile structure, and they gave construction excavation and support recommendations. These studies have expanded the knowledge of the effects of the excavation sequence on foundation pit stability, but most of them have focused on the effect of the excavation sequence in different foundation pit areas rather than the construction sequence of each excavation layer. The metro foundation pit in Nanjing, with a length of more than 150 m and a width of only about 40 m, has an aspect ratio of 3.75, an excavation depth of 44 m, and an “irregular” situation of one end being wide and another end being narrow, so this pit is categorized as an “irregular large-scale rectangle deep foundation pit”. As such, the construction design is challenging, and the construction sequence is complicated (see Figure 10 for the construction site). This study focused on the impact of the excavation sequence of each excavation layer on the stability of the foundation pit in order to guarantee the project’s safety and effectiveness.

5.1. Determination of the Optimal Excavation Scheme

To objectively judge the advantages and disadvantages of different excavation sequence schemes, we defined the foundation pit excavation safety coefficient Kes for comprehensive evaluation. Kes consists of the displacement of the foundation pit, K1; the time required for construction, K2; the deformation rate of the foundation pit, K3; the volume of the plastic zone of the foundation pit, K4; the maximum principal stress for DW, K5; and the maximum moment at DW monitoring point, K6. The specific composition of each factor is shown in Table 3. The weight of each factor was 0.5, 0.1, 0.1, 0.1, 0.1, and 0.1, respectively. Subsequently, all the results were processed via min–max normalization [41]. The specific formula is shown in Equation (1), and the results were obtained as shown in Table 4.
X n e w = X − X m i n X m a x − X m i n
where X n e w is the normalized value, X m a x is the maximum value of the sample data, and X m i n is the minimum value of the sample data.
From the above results, it can be seen that schemes C and E have significant advantages, and E is the optimal scheme.

5.2. Process Stability of the Optimal Excavation Scheme

In this section, the E scheme is taken as an example to further explore the process stability of the optimal excavation scheme.
Figure 11 shows the horizontal displacement monitoring curves of the foundation pit after each layer of excavation. The displacements caused by the first three layers of excavation are relatively tiny, and the results of the four “history profiles” show that the horizontal displacement type are the “Cantilever type” when the excavation depth is shallow (but there is some bending at the wide and narrow ends of the foundation pit). The horizontal displacement changes after each layer of excavation, especially after the fourth layer. After the excavation of the fourth layer, the horizontal displacement at the wide and narrow ends of the foundation pit is obviously “Contradictory type Ⅱ”. For the soil of the lower and upper walls, the horizontal displacement after the excavation of the fourth layer is the “Compound type”, while after the excavation of the fifth layer, the type changes to the “Cantilever type”, but the wide end of the foundation pit remains “Contradictory type II”. In addition, the maximum horizontal displacement at the wide end of the DW is 2.22 times that at the narrow end of the DW, and the lower end of the DW is 1.13 times that of the upper end of the DW. Therefore, even though the wide end of the DW is only 3 m wider than the narrow end of the DW, it still has a significant impact on the displacement results.
Foundation pit excavation leads to a change in the values of horizontal displacement, which is consistent with the findings in the literature [39,42], but the results do not show that the excavation completion of different excavation layers leads to a change in the horizontal deformation pattern. Similarly, the horizontal displacements at different locations of the foundation pit are not consistent. Therefore, according to the different deformation characteristics of different areas of foundation pit, it is very important to design a supporting scheme that is adapted to local conditions.

6. Conclusions

In this study, the effect of excavation sequence on the stability of irregular large-scale rectangular deep foundation pit was investigated through numerical simulation, the optimal excavation sequence scheme was determined, and the main conclusions were obtained as follows:
(1)
Different excavation sequences can significantly affect the stability of a foundation pit, for the displacement, in which the maximum cumulative value of the displacement under scheme E is only 67.5% of that under scheme A. In addition, the excavation sequence and excavation phases lead to a change in the type of horizontal displacement of the foundation pit.
(2)
We defined a foundation pit excavation safety coefficient Kes, which comprises six factors that were scored using the min–max normalization method, and we obtained the optimal excavation sequence scheme, i.e., scheme E: “Excavate from the two ends of the foundation pit to the center at the same time, and then after completing the excavation of the first layer, then excavate from the center of the next layer to the two ends”.
(3)
Irregular-shaped foundation pits can also lead to local differences in the foundation pit’s stability; for example, in scheme E, the maximum displacement of the wide end reaches 221% of that the narrow end, but the length of the wide end is only 108.9% of that of the narrow end. Therefore, attention should paid to the reinforcement of weak areas when implementing supports.

Author Contributions

Conceptualization, D.L., Y.C., B.D., Z.W. and H.L.; methodology, D.L. and Y.C.; software, D.L.; validation, Y.C.; formal analysis, B.D.; investigation, D.L.; resources, Y.C. and Z.W.; data curation, Z.W.; writing—original draft preparation, D.L.; writing—review and editing, D.L. and Y.C.; visualization, B.D.; supervision, Z.W. and H.L.; project administration, Y.C. and H.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (52004130), the Provincial Natural Science Foundation of Hunan (2022JJ40601, 2022JJ40373), the China Postdoctoral Science Foundation (2021M693799), and the Postgraduate Scientific Research Innovation Project of Hunan Province (QL20220213).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Appendix A.1. Deformation Pattern of DW

Because changes in stress will lead the DW to produce deformation, researchers have analyzed and generalized the deformation of DWs using on-site monitoring, numerical simulation, and theoretical analysis, and they have divided the deformation types into six categories [43,44], as shown in Figure A1.
Applsci 13 11342 g0a1
Figure A1. Deformation patterns of DWs.
Figure A1. Deformation patterns of DWs.
Applsci 13 11342 g0a1

Appendix A.2. Data from Other Simulation Results

Applsci 13 11342 g0a2
Figure A2. Displacement of contour plots in the XYZ direction after foundation pit excavation completed.
Figure A2. Displacement of contour plots in the XYZ direction after foundation pit excavation completed.
Applsci 13 11342 g0a2
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Figure A3. Results of velocity analyses.
Figure A3. Results of velocity analyses.
Applsci 13 11342 g0a3
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Figure A4. Plastic zone distribution.
Figure A4. Plastic zone distribution.
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Figure A5. Plastic zone volume.
Figure A5. Plastic zone volume.
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Figure A6. Shell (DW) maximum principal stress. (a) Contour cloud diagram; (b) statistical results.
Figure A6. Shell (DW) maximum principal stress. (a) Contour cloud diagram; (b) statistical results.
Applsci 13 11342 g0a6
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Figure A7. Shell (DW) moment monitoring (position: center of front wall −64.5 m).
Figure A7. Shell (DW) moment monitoring (position: center of front wall −64.5 m).
Applsci 13 11342 g0a7

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Applsci 13 11342 g001
Figure 1. Schematic of the study area.
Figure 1. Schematic of the study area.
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Figure 2. Support structure and main geological layer parameters.
Figure 2. Support structure and main geological layer parameters.
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Figure 3. Schematic of soil pressure evolution before and after foundation pit excavation.
Figure 3. Schematic of soil pressure evolution before and after foundation pit excavation.
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Figure 4. Schematic of pit excavation sequence numbering.
Figure 4. Schematic of pit excavation sequence numbering.
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Figure 5. Numerical model of foundation pit excavation.
Figure 5. Numerical model of foundation pit excavation.
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Figure 6. Model boundary conditions and geostress simplification. (a) Model boundary conditions. (b) Modeled ground stress values schematic. (c) Theoretical lateral stress factor schematic.
Figure 6. Model boundary conditions and geostress simplification. (a) Model boundary conditions. (b) Modeled ground stress values schematic. (c) Theoretical lateral stress factor schematic.
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Figure 7. Result of displacement in the XYZ directions.
Figure 7. Result of displacement in the XYZ directions.
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Applsci 13 11342 g008aApplsci 13 11342 g008b
Figure 8. Horizontal displacement monitoring. (a) History profile 1. (b) History profile 2. (c) History profile 3. (d) History profile 4.
Figure 8. Horizontal displacement monitoring. (a) History profile 1. (b) History profile 2. (c) History profile 3. (d) History profile 4.
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Figure 9. Settlement displacement monitoring. (a) History point 1. (b) History point 2. (c) History point 3. (d) History point 4.
Figure 9. Settlement displacement monitoring. (a) History point 1. (b) History point 2. (c) History point 3. (d) History point 4.
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Figure 10. Foundation pit construction site.
Figure 10. Foundation pit construction site.
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Applsci 13 11342 g011aApplsci 13 11342 g011b
Figure 11. Horizontal displacement of the pit after each layer of excavation for scheme E. (a) History profile 1. (b) History profile 2. (c) History point 3. (d) History profile 4.
Figure 11. Horizontal displacement of the pit after each layer of excavation for scheme E. (a) History profile 1. (b) History profile 2. (c) History point 3. (d) History profile 4.
Applsci 13 11342 g011aApplsci 13 11342 g011b
Table 1. Parameters of the DW.
Table 1. Parameters of the DW.
Value TypeThicknesses (m)Elasticity Modulus (GPa)Poisson’s RatioDensity (t/m3)
actual value1.5350.252.5
simulated value1.51000.22.5
Table 2. Foundation pit excavation design program *.
Table 2. Foundation pit excavation design program *.
SchemePresentation Total
Steps
A1-①→1-②→1-③→1-④→1-⑤→1-⑥→1-⑦→1-⑧→
2-①→2-②→2-③→2-④→2-⑤→2-⑥→2-⑦→2-⑧→
3-①→3-②→3-③→3-④→3-⑤→3-⑥→3-⑦→3-⑧→
4-①→4-②→4-③→4-④→4-⑤→4-⑥→4-⑦→4-⑧→
5-①→5-②→5-③→5-④→5-⑤→5-⑥→5-⑦→5-⑧→		Applsci 13 11342 i00120,000
B1-⑧→1-⑦→1-⑥→1-⑤→1-④→1-③→1-②→1-①→
2-⑧→2-⑦→2-⑥→2-⑤→2-④→2-③→2-②→2-①→
3-⑧→3-⑦→3-⑥→3-⑤→3-④→3-③→3-②→3-①→
4-⑧→4-⑦→4-⑥→4-⑤→4-④→4-③→4-②→4-①→
5-⑧→5-⑦→5-⑥→5-⑤→5-④→5-③→5-②→5-①→		Applsci 13 11342 i00220,000
C1-①, 1-⑧→1-②, 1-⑦→1-③, 1-⑥→1-④, 1-⑤→
2-①, 2-⑧→2-②, 2-⑦→2-③, 2-⑥→2-④, 2-⑤→
3-①, 3-⑧→3-②, 3-⑦→3-③, 3-⑥→3-④, 3-⑤→
4-①, 4-⑧→4-②, 4-⑦→4-③, 4-⑥→4-④, 4-⑤→
5-①, 5-⑧→5-②, 5-⑦→5-③, 5-⑥→5-④, 5-⑤→		Applsci 13 11342 i00310,000
D1-④, 1-⑤→1-③, 1-⑥→1-②, 1-⑦→1-①, 1-⑧→
2-④, 2-⑤→2-③, 2-⑥→2-②, 2-⑦→2-①, 2-⑧→
3-④, 3-⑤→3-③, 3-⑥→3-②, 3-⑦→3-①, 3-⑧→
4-④, 4-⑤→4-③, 4-⑥→4-②, 4-⑦→4-①, 4-⑧→
5-④, 5-⑤→5-③, 5-⑥→5-②, 5-⑦→5-①, 5-⑧→		Applsci 13 11342 i00410,000
E1-①, 1-⑧→1-②, 1-⑦→1-③, 1-⑥→1-④, 1-⑤→
2-④, 2-⑤→2-③, 2-⑥→2-②, 2-⑦→2-①, 2-⑧→
3-①, 3-⑧→3-②, 3-⑦→3-③, 3-⑥→3-④, 3-⑤→
4-④, 4-⑤→4-③, 4-⑥→4-②, 4-⑦→4-①, 4-⑧→
5-①, 5-⑧→5-②, 5-⑦→5-③, 5-⑥→5-④, 5-⑤→		Applsci 13 11342 i00510,000
F1-④, 1-⑤→1-③, 1-⑥→1-②, 1-⑦→1-①, 1-⑧→
2-①, 2-⑧→2-②, 2-⑦→2-③, 2-⑥→2-④, 2-⑤→
3-④, 3-⑤→3-③, 3-⑥→3-②, 3-⑦→3-①, 3-⑧→
4-①, 4-⑧→4-②, 4-⑦→4-③, 4-⑥→4-④, 4-⑤→
5-④, 5-⑤→5-③, 5-⑥→5-②, 5-⑦→5-①, 5-⑧→		Applsci 13 11342 i00610,000
G1-①, 1-③→1-⑤, 1-⑦→1-②, 1-④→1-⑥, 1-⑧→
2-①, 2-③→2-⑤, 2-⑦→2-②, 2-④→2-⑥, 2-⑧→
3-①, 3-③→3-⑤, 3-⑦→3-②, 3-④→3-⑥, 3-⑧→
4-①, 4-③→4-⑤, 4-⑦→4-②, 4-④→4-⑥, 4-⑧→
5-①, 5-③→5-⑤, 5-⑦→5-②, 5-④→5-⑥, 5-⑧→		Applsci 13 11342 i00710,000
H1-②, 1-④→1-⑥, 1-⑧→1-①, 1-③→1-⑤, 1-⑦→
2-①, 2-③→2-⑤, 2-⑦→2-②, 2-④→2-⑥, 2-⑧→
3-①, 3-③→3-⑤, 3-⑦→3-②, 3-④→3-⑥, 3-⑧→
4-①, 4-③→4-⑤, 4-⑦→4-②, 4-④→4-⑥, 4-⑧→
5-①, 5-③→5-⑤, 5-⑦→5-②, 5-④→5-⑥, 5-⑧→		Applsci 13 11342 i00810,000
* Table 2 should be used in conjunction with Figure 5 to understand the division of the foundation pit excavation groups and the design of the excavation sequence.
Table 3. Components of the foundation pit excavation safety coefficient Kes.
Table 3. Components of the foundation pit excavation safety coefficient Kes.
Compositional FactorWeightNote
Foundation pit
excavation safety
factor (Kes)		Displacement of the
foundation pit (K1)		0.5The displacement maxima in 6 directions XYZ in the model, maximum settlements at 4 monitoring points, maximum horizontal displacements on 4 survey lines
Time required for
construction (K2)		0.1The total steps required to complete pit excavation
Deformation rate of
the foundation pit (K3)		0.1The maximum deformation rate in the model
The volume of the plastic zone
of the foundation pit (K4)		0.1The “shear-now”, “shear-past”, “tensile-now”, and “tensile-past” volumes in the modeled plasticity region
Maximum principal
stress for DW (K5)		0.1Maximum principal in the shell structure stress
Maximum moment at
DW monitoring point (K6)		0.1Maximum moment of the monitoring points in the shell structure
Table 4. Normalization results for the constituents of Kes.
Table 4. Normalization results for the constituents of Kes.
Compositional FactorsABCDEFGHWeight
K1X-10.080.000.500.970.350.841.000.980.5
X-20.530.860.240.870.000.600.471.00
Y-10.690.600.140.930.000.530.901.00
Y-21.000.960.060.410.220.000.220.24
Z-10.951.000.010.340.240.000.300.30
Z-20.650.250.160.590.000.490.771.00
S-11.000.970.000.410.090.060.180.23
S-20.661.000.100.400.000.450.220.27
S-30.000.310.271.000.120.990.340.29
S-40.991.000.160.520.000.370.430.41
H-10.520.520.351.000.100.820.260.00
H-20.951.000.080.450.000.290.320.31
H-31.000.320.100.170.000.220.130.14
H-40.401.000.150.120.050.190.010.00
K21.001.000.000.000.000.000.000.000.1
K31.000.850.000.400.110.030.200.230.1
K4S-n0.771.000.000.360.140.020.240.290.1
S-p1.000.520.120.270.000.370.110.18
T-n0.060.120.010.030.001.000.010.43
T-p1.000.880.340.580.460.000.460.47
K50.781.000.050.340.270.000.260.300.1
K61.000.900.020.590.000.410.360.400.1
Total value0.790.790.100.460.090.290.300.351.0
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Li, D.; Chen, Y.; Dai, B.; Wang, Z.; Liang, H. Numerical Study of Dig Sequence Effects during Large-Scale Excavation. Appl. Sci. 2023, 13, 11342. https://doi.org/10.3390/app132011342

AMA Style

Li D, Chen Y, Dai B, Wang Z, Liang H. Numerical Study of Dig Sequence Effects during Large-Scale Excavation. Applied Sciences. 2023; 13(20):11342. https://doi.org/10.3390/app132011342

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Li, Danli, Ying Chen, Bing Dai, Zhengyi Wang, and Hao Liang. 2023. "Numerical Study of Dig Sequence Effects during Large-Scale Excavation" Applied Sciences 13, no. 20: 11342. https://doi.org/10.3390/app132011342

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