# Predicting Ground Surface Settlements Induced by Deep Excavation under Embankment Surcharge Load in Flood Detention Zone

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## Abstract

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## 1. Introduction

## 2. Typical Surface Settlement Modes Induced by Excavation

_{ref}) and the foundation pit depth (i.e., h), the surface settlement curves under the maximum horizontal displacement (i.e., d) of different retaining walls are drawn by numerical integration, and the transverse distribution value of the surface settlement would be ultimately obtained by normalization processing.

## 3. Derivation of the Simplified Solution Method

#### 3.1. Solution Thought

_{I}(x) and S

_{II}(x) represent the settlement induced by adjacent excavation and embankment surcharge load, respectively.

_{m}represents the distance between maximum settlement point and the edge of foundation pit; and A

_{v}is the envelope area of surface settlement curve behind the wall and ω is empirical coefficient (i.e., 0.6–0.7 for a soft soil foundation pit).

#### 3.2. The Influence of Foundation Pit Excavation

_{v}and x

_{m}are important parameters directly related to the surface settlement curve. However, in many studies and engineering applications in the past, the selection of these two parameters was mostly determined by engineering experience, which may bring out major errors, even resulting in wrong results. Therefore, the determination of A

_{v}and x

_{m}should be carefully considered, and a simplified method will be performed in the following sections.

#### 3.2.1. Calculation of x_{m}

_{i}and h

_{i+}

_{1}is calculated by Equations (5) and (6), respectively. The relevant equation could be expressed as

_{i}and w

_{i+}

_{1}represent the ground settlement induced by segment i and segment i+1, respectively; d

_{i}and d

_{i+}

_{1}represent the retaining wall horizontal deformation of segment i and segment i+1, respectively; x

_{ref_i}and x

_{ref_i+}

_{1}represent the ground settlement range induced by segment i and segment i+1, respectively.

_{i}caused by the translation of any retaining wall segment in the foundation pit is obtained, which can be simplified as

_{ref_i}= mh

_{i}, x

_{ref_i+}

_{1}= mh

_{i+}

_{1}). Through the substitution of x

_{ref_i}and x

_{ref_i+}

_{1}into Equation (7), the final form of ∆w

_{i}can be simplified as

_{i}caused by the translation of each micro-section of the retaining wall can be superimposed and summed. As presented in Equation (9), the adjacent surface settlement formula under the horizontal deformation mode of any maintenance structure can be obtained.

_{m}, the maximum position of surface settlement, can be obtained by w in Equation (9), which is easily realized by programming.

#### 3.2.2. Calculation of A_{h}

_{v}) and the envelope area of the displacement curve of excavation retaining wall (i.e., A

_{h}) in the soft soil area, which can be expressed as

_{d}/h

_{1}(h

_{1}is the final excavation depth, and h

_{d}represents the wall embedment depth below the excavation bottom) is less than 0.5, β can be taken as 1.0–1.2; otherwise, it may be within the range of 0.8 to 1.0.

_{v}and A

_{h}, respectively.

_{h}), the displacement data of the calculated or measured points should be processed firstly to make it fit into a continuous smooth curve. In general, any function in a certain section can be approximated by polynomials. Therefore, assuming that the displacement point coordinates of the retaining wall calculated or measured along the depth direction of the foundation pit are (h, d), then the horizontal displacement fitting curve can be expressed as

_{i}represents the coefficient of the independent variable in the polynomial.

_{i}and d

_{i}represent the depth of the retaining wall and the corresponding horizontal displacement values acquired by calculating or measuring, respectively.

_{i}and d

_{i}into Equation (13), the values of the coefficients a

_{0}, a

_{1}and a

_{2}would be obtained. According to the vertex coordinates (0, a

_{0}) and extreme points (h

_{m}, d

_{m}) of the supporting structure, a

_{1}and a

_{2}can be finally derived as

#### 3.3. The Influence of Embankment Surcharge Load

_{x}. By assigning z to 0 in Equation (17), the expression for u (z) can be simplified to

_{0}L through integration, and u(z) can be finally derived as

_{II}(x)).

#### 3.4. Optimized Solution Procedure

## 4. Validation of the Simplified Analytical Method through Case Histories

#### 4.1. Case History 1

_{1}) at the CX2 section equals 25.9 mm, and the observed excavation basal displacement (i.e., d

_{3}) equals 124.5 mm. In this project, the displacement at the bottom of pit is the maximum displacement of retaining pile. It is a common way to predict the ground settlement around the foundation pit based on the calculated or measured displacement data of the retaining wall. The observed surface settlement data, the prediction formula in the literature [26], and proposed method in this paper are compared, and the surface settlement curves are, respectively, depicted in Figure 9b. According to the correlation between the influence degree and the influence scope of the foundation pit excavation, five observation points were set, respectively, located at 0 m, 5 m, 10 m, 20 m and 40 m from the edge of the foundation pit.

_{m}= 11 m. By utilizing numerical integration method, the envelope area of the retaining structure lateral deformation curve can be obtained: A

_{h}= 2314.5 m·mm, where β = 0.9, and ω = 0.65 according to experience. In the prediction formula [26], x

_{m}is defined as a parameter linearly related to the foundation pit depth based on engineering experience and geology conditions, and x

_{m}is set as 12.1 m in Case History 1, which equals to the excavation depth of 0.7 times. In addition, other parameters are consistent with the formula in this paper. The surface settlement curve can be obtained by substituting all parameters into Equations (15) and (16). As presented in Figure 9b, the method proposed in this paper performs well in approaching the observed results. Compared with the original settlement prediction formula, the simplified method used in this study is more accurate in fitting with the field monitoring values, especially the maximum settlement value, demonstrating the effectiveness of the proposed analytical method in this paper.

#### 4.2. Case History 2

_{1}= 0.14 mm. The maximum horizontal wall displacement occurred approximately at the excavation bottom, with a magnitude of d

_{2}= 55.71 mm. As depicted in Figure 10a, the displacement at the top of the wall was quite small, and the maximum horizontal displacement was located at the bottom of the foundation pit.

_{h}and A

_{v}are relatively close in the observed data, which is quite different from the conventional prediction formula. This may be caused by the vehicle dynamic load and material surcharge in the site. Due to the lack of available reference data, other parameters are obtained according to the literature [26]: A

_{h}= 1083.8 m·mm, β = 0.9, and w = 0.65. Moreover, the prediction formula proposed in this paper also draws on some parameters in the literature above, such as β and w, which improve the accuracy of surface subsidence results.

_{v}was 876.3 m·mm, while the method in the reference [26] predicted a value of 759.9 m·mm, with an error of 15.4%. This also causes the V

_{m}of this method to differ significantly from the actual observed value, at 13.7%. In the method presented in this paper, A

_{v}and V

_{m}have relatively small deviations from the field-measured values, which are 5.0% and 5.6%, respectively. Further investigation indicates that x

_{m}, a parameter closely related to surface settlement, was determined by engineering experience in the literature [26], whereas it was obtained by integral fitting in this paper. It is obvious that the prediction formula for the surface displacement field with skewed distribution behind the wall proposed in literature [26] is relatively simple. Up till now, most values of some parameters in the formula are obtained by engineering experience, which would increase the uncertainty of the prediction formula. In the proposed analytical method, the values of x

_{m}and A

_{h}are optimized to make the values of parameters more reasonable and the prediction results of surface settlement more accurate.

#### 4.3. Case History 3

_{h}) is 216.3 m·mm, and the empirical coefficient of the settlement envelope (i.e., β) is determined with 0.9 based on previous engineering experience. Therefore, the area of the surface settlement envelope curve (i.e., A

_{v}) outside the foundation pit is 194.7 m·mm. The value of x

_{m}can be obtained by superposition fitting of the micro-segment settlement curve calculated by Equation (8). In case history 3, the maximum settlement point calculated is 4.9 m away from the foundation pit. In addition, ω refers to the value of 0.65 in the reference [26]. By taking the above parameters into Equation (15) for calculation, the influence of foundation pit excavation on the surface settlement can be obtained. Furthermore, the influence of bank overloading can be easily obtained by the Boussinesq solution. Considering that the deformation of embankment pavement is the focus of attention, settlement observation points were set in the middle and both sides of the road.

## 5. Conclusions

- The ground overloading such as embankment overload has a certain influence on the surface settlement during the foundation pit excavation, which should be paid more attention to in the project. In this paper, the Boussinesq solution is applied to simplify the embankment load into the vertical concentrated force, and the ground settlement curve is easily calculated and fitted, which can well take into account the impact of ground overload.
- As for the surrounding surface settlement caused by foundation pit excavation, the value of x
_{m}is generally determined by engineering experience in the previous partial settlement prediction formula, which is an important factor leading to a large deviation between the measured value and the theoretical prediction value. This paper improves the determination of x_{m}by the method of combining calculus with curve fitting, and the predicted value obtained by this method comes close to the measured one. Accordingly, in the three cases, the deviation between the calculated value of v_{m}and the actual observation value is 4.6%, 5.5% and 3.4%, respectively. - Based on the classic prediction formula of surface subsidence skewness distribution, the simplified method in this paper draws on some empirical parameters, such as β and ω, which are derived from many engineering practices and have proved reliability among projects. However, the value range of these parameters is quite wide, and bring out many difficulties to determine the most reasonable parameter value in settlement prediction. As a result, it is necessary to make a more detailed division for the value range of empirical parameters in subsequent studies.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Settlement fissure induced by deep excavation: (

**a**) condition without surcharge load; (

**b**) condition under surcharge load.

**Figure 2.**Typical surface settlement modes under different types of retaining-wall deformation: (

**a**) translation mode; (

**b**) rotation around the wall base mode; (

**c**) rotation around the wall top mode; (

**d**) flexible parabola deformation mode.

**Figure 5.**Infinitesimal calculus diagram of surface settlement induced by the retaining wall horizontal deformation: (

**a**) equivalent calculation of surface settlement induced by arbitrary micro-section translation of retaining wall; (

**b**) equivalent calculation of surface settlement induced by displacement of arbitrary retaining wall.

**Figure 7.**Diagram of surface settlement induced by the retaining wall horizontal deformation: (

**a**) Boussinesq solution diagram; (

**b**) simplification of embankment surcharge load.

**Figure 10.**Validation based on the Case History 2 [26]: (

**a**) field monitoring of the retaining wall deformation; (

**b**) distribution of ground surface settlement under different methods.

**Figure 11.**Relative spatial position of the foundation pit and the embankment in the case History 3: (

**a**) relative plan layout of the steel cofferdam and the embankment; (

**b**) A-A′ cross-section profile.

**Figure 12.**Validation based on the Case History 3: (

**a**) field monitoring of the steel sheet pile deformation; (

**b**) distribution of ground surface settlement under different methods.

**Table 1.**Parameter values and results comparison of several methods in Case History 1 [25].

Methods | Key Parameter Values | Ground Settlement | ||||
---|---|---|---|---|---|---|

A_{h} | β | A_{v} | ω | x_{m} | v_{m} | |

Field monitoring [25] | 2295.8 m·mm | — | — | — | 10.3 m | 81.3 mm |

Prediction formula in literature [26] | 2256.9 m·mm | 0.9 | 2031.2 m·mm | 0.65 | 12.1 m | 63.4 mm |

Proposed method in this study | 2314.5 m·mm | 0.9 | 2083.0 m·mm | 0.65 | 11.2 m | 77.5 mm |

_{h}= envelope area of support structure displacement curve; A

_{v}= envelope area of ground settlement curve; β = proportionality coefficient related to insertion ratio (i.e., A

_{v}/A

_{h}); ω = empirical coefficients related to soil quality; x

_{m}= location of the maximum settlement point on the ground; v

_{m}= maximum surface settlement.

**Table 2.**Parameter values and results comparison of several methods in Case History 2 [26].

Methods | Key Parameter Values | Ground Settlement | ||||
---|---|---|---|---|---|---|

A_{h} | β | A_{v} | ω | x_{m} | v_{m} | |

Field monitoring [26] | 892.1 m·mm | — | 876.3 m·mm | — | 11.7 m | 43.1 mm |

Prediction formula in literature [26] | 1083.8 m·mm | 0.9 | 759.9 m·mm | 0.65 | 13.2 m | 37.2 mm |

Proposed method in this study | 925.0 m·mm | 0.9 | 832.5 m·mm | 0.65 | 10.9 m | 45.5 mm |

_{h}= envelope area of support structure displacement curve; A

_{v}= envelope area of ground settlement curve; β = proportionality coefficient related to insertion ratio (i.e., A

_{v}/A

_{h}); ω = empirical coefficients related to soil quality; x

_{m}= location of the maximum settlement point on the ground; v

_{m}= maximum surface settlement.

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## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Chen, S.; Ouyang, J.; Li, J.; Zhao, Y.; Lin, H.; Guo, P. Predicting Ground Surface Settlements Induced by Deep Excavation under Embankment Surcharge Load in Flood Detention Zone. *Water* **2022**, *14*, 3868.
https://doi.org/10.3390/w14233868

**AMA Style**

Wang Y, Chen S, Ouyang J, Li J, Zhao Y, Lin H, Guo P. Predicting Ground Surface Settlements Induced by Deep Excavation under Embankment Surcharge Load in Flood Detention Zone. *Water*. 2022; 14(23):3868.
https://doi.org/10.3390/w14233868

**Chicago/Turabian Style**

Wang, Yixian, Shi Chen, Jiye Ouyang, Jian Li, Yanlin Zhao, Hang Lin, and Panpan Guo. 2022. "Predicting Ground Surface Settlements Induced by Deep Excavation under Embankment Surcharge Load in Flood Detention Zone" *Water* 14, no. 23: 3868.
https://doi.org/10.3390/w14233868