Study on Settlement of Self-Compacting Solidified Soil in Foundation Pit Backfilling Based on GA-BP Neural Network Model

Abstract

In order to predict the settlement of self-compacting solidified soil in foundation pit backfilling, finite element software is used to study the influence of soil properties and the surrounding structural properties of the foundation pit on the settlement of backfilled self-compacting solidified soil based on a foundation pit project in the city of Nanjing. The degree of influence of various factors influencing settlement is considered, a grey relational grade analysis is conducted, and input layer parameters of the neural network are determined based on the results of the grey relational grade analysis. Based on the GA-BP neural network model, the settlement of soil is predicted using numerical simulation results. The results reveal that the settlement and structural disturbance of self-compacting solidified soil after backfilling are smaller than those of fine silty sand; self-compacting solidified soil significantly improves the engineering performance of excavated soil. In the grey relational grade analysis, the six influencing factors that have high correlation with soil settlement can be used as input layer parameters for the neural network model. Among them, the correlation degree between elastic modulus and soil settlement is the highest, reaching 0.8402. The correlation degrees of the remaining five influencing factors are above 0.5, and the values are close. The GA-BP neural network can improve the overfitting situation of a BP neural network trapped in local optima, with R² reaching 0.9999 and RMSE only 0.0018 mm, achieving high-precision prediction of settlement of self-compacting solidified soil.

1. Introduction

In recent years, the development of underground space in China has been rapid, and the excavation depth and scope of foundation pit engineering have become increasingly large. Foundation pit backfilling engineering faces the problem of uneven settlement of the upper structure, cracking, and deformation of the retaining structure after natural soil backfilling [1,2,3,4]. For natural soil, the method of adding solidification agents into soil can be used to mix and form a new kind of material called self-compacting solidified soil, which improves its performance [5,6]. In order to study the impact of properties of backfill solidified soil materials and the surrounding environment on the quality of foundation pit backfilling, some scholars have carried out relevant numerical simulation work [7,8]. Liu [9] used finite element numerical simulation to analyze the effect on site vibration of replacing backfill soil with remolded soil. The effects on free site vibration of wave velocity and thickness of backfill soil, as well as the size of the foundation pit, were analyzed; Feng [10] used the numerical simulation to investigate the dynamic response of backfill sand foundations. Zhang [11] conducted a finite element numerical simulation on backfill soil in mountainous slope areas, exploring the influence of backfill soil strength on the deformation of retaining walls. Jie [12] studied the foundation settlement problem of high-fill engineering in collapsible loess areas and, using numerical simulation, explored the soil settlement law under different environmental factors.

Now, the combination of neural network models and numerical calculations effectively improves computational efficiency with the increasing application of artificial intelligence technology [13,14,15]. Compared to the numerical calculation models, the neural network models compensate for the shortcomings of low computational efficiency and high resource consumption in numerical calculation models by learning from a certain amount of data [16,17]. Li [18] established the MEC-BP neural network model based on finite element numerical simulation results to achieve accurate inversion of horizontal displacement. Zhong [19] analyzed the factors affecting the horizontal displacement of foundation pit support and established the RS-MIV-ELM neural network model to achieve high precision and efficient prediction of maximum horizontal displacement. At the same time, accurate prediction of surface settlement around the foundation pit is achieved based on the highly correlated parameter SFLA-GRNN model of foundation pit settlement [20]. Xu [21] established the LTSM model for predicting landslide displacement due to rainfall infiltration, with which the high-precision prediction of landslide displacement is achieved. Based on the studies by the above scholars in various fields, it can be concluded that compared to numerical calculation models, neural network models significantly improve computational efficiency and accuracy [22,23]. It is of great significance to propose neural network models in practical engineering.

A large number of scholars have conducted research on the backfill effect of different soil properties and have proposed high-precision neural network models for certain projects. However, study of self-compacting solidified soil backfill in narrow areas using a corresponding high-precision neural network model is absent. Therefore, this paper focuses on researching the settlement of self-compacting solidified soil. From the perspective of soil settlement and disturbance to the diaphragm wall, the backfilling effect of excavation waste soil and self-compacting solidified soil is analyzed, and the influencing factors of soil settlement and horizontal displacement of the diaphragm wall are considered. Grey relational grade analysis is used to study the correlation degree of various influencing factors on soil settlement, and the neural network input layer parameters are selected. BP and GA-BP neural network models are established to test the data regression accuracy of the established model, and an efficient and accurate prediction model is explored.

2. Numerical Simulation of Foundation Pit Backfilling

2.1. Project Overview

After the excavation of a certain foundation pit project in Nanjing, a two-story basement will be built with a pit with a width of 1 m and depth of 10.2 m. According to the survey report, the soil mass of the foundation pit site from top to bottom is plain fill, silty sand, silty clay, and fine silty sand; it has high compressibility and low shear strength. The soil mass directly used for foundation pit backfilling after foundation pit excavation will have excessive settlement, which will affect the quality of foundation pit backfilling. Figure 1 shows the soil parameters of the foundation pit site. A large amount of fine silty sand is distributed from 6.8 m to 46.6 m underground, and the fine silty sand has certain differences in properties due to differences in composition such as content of quartz, mica, and silt. In order to fully utilize the soil abandoned during excavation of the foundation pit, a new type of soil called self-compacting solidified soil is developed using the ④-2 layers of fine silty sand mixed with a cement curing agent. It is used for backfilling of the foundation pit in this project.

2.2. Numerical Analysis Model

The ④-2 layers of fine silty sand in the site mixed with the cement curing agent are used for geotechnical tests, including the direct shear test, compression test, and the compression test. Considering that the actual numerical simulation needs to convert the compression modulus, Formula (1) [24] is used to convert. The parameters of ④-2 layers of fine silty sand and self-compacting solidified soil are finally determined as shown in

Table 1. Numerical simulation of backfill soil parameters.

Kind of Soil	Cohesion/kPa	Internal Friction Angle/°	Elastic Modulus/MPa
④-2 Fine silty sand	4.8	32.5	92.1
Self-compacting solidified soil	200	36	700

:

$$E=\alpha E_s$$

(1)

In the formula, $E$ is the elastic modulus; $E_s$ is the compressive modulus measured in the laboratory test; and $\alpha$ is the empirical conversion coefficient between the elastic modulus and compressive modulus, and it is taken as 8.2 in this paper.

To explore the settlement changes of self-compacting solidified soil in foundation pit backfilling, a full-scale model of the foundation pit is established using ABAQUS and is based on the actual situation of the foundation pit. The Mohr–Coulomb constitutive model is used for the backfill soil, and the linear elastic model is used for both the basement and the connecting wall. At the same time, the interaction between structures and soil in the numerical model also needs to be taken into account; this is achieved using the penalty function in ABAQUS tangential action, and the value of the penalty is set to 0.5577. The numerical analysis model of the foundation pit is shown in Figure 2.

The numerical simulation parameters of the basement and the diaphragm wall are shown in

Table 2. Material parameters of backfill soil surrounding structure.

Structure Name	Weight (kN·m−3)	Poisson Ratio	Elastic Modulus (GPa)
Two-story basement	2500	0.25	33
Diaphragm wall	2500	0.2	25
Plain concrete bottom plate	3000	0.18	20

.

2.3. Comparative Analysis of Backfilling with Fine Silty Sand and Self-Compacting Solidified Soil

Figure 3a shows that when using fine silty sand and self-compacting solidified soil for foundation pit backfilling, the settlement of self-compacting solidified soil backfill is only one eleventh of that of fine silty sand. The negative direction of the horizontal displacement on the right side of the diaphragm wall indicates the negative direction of the X axis; the negative value means that the backfilling of the soil will disturb the diaphragm wall toward the left side. Figure 3b shows that when self-compacting solidified soil is used for backfilling as a whole, it produces less horizontal displacement, which means less disturbance to the structure. In summary, compared to fine silty sand, the self-compacting solidified soil has smaller settlement and horizontal displacement in the backfill soil of the foundation pit, so the backfill effect is good.

2.4. Analysis of Settlement Influencing Factors

The factors affecting the settlement of soil after backfilling are mainly the parameters of soil and the surrounding environment of backfill soil. During the process of foundation pit backfilling, the interaction between the diaphragm wall and the soil is complex, so it is difficult to determine the settlement of the soil and the displacement of the diaphragm wall. The settlement formula and diaphragm wall displacement formula obtained by scholars in their research are extracted from the literature to reasonably select the influencing factors. Dong [25] proposed that in the relatively stable state of deformation, the soil structure undergoes deformation or even failure through loading. From the perspective of deformation results, it can be considered that the settlement of the soil is actually equivalent to applying the equivalent load q to the soil. Under the action of the equivalent load q, the settlement of the soil at depth z with time t and thickness z is:

$$s(z, t)=\frac{q}{E_s}[z-\frac{8H}{{\pi }^2}(1-cos\frac{m\pi z}{2H})e^{-\frac{{\pi }^2{C}_{v}t}{4H^2}}]$$

(2)

In the formula, $s(z, t)$ is the settlement of the soil at depth z and time t, m is a positive odd number, z is the depth, H is the equivalent thickness of the soil layer, q is the equivalent load that causes soil settlement, $E_s$ is the compressive modulus, $C_v$ is the consolidation coefficient, and t is the time.

Zhang [26] proposed the following formula for calculating the horizontal displacement of the diaphragm wall at the horizontal depths i and j under the n working condition when the soil changes under different working conditions in foundation pit engineering:

$$U_{n_{ij}}=K_{ij}\sum _{a=1}^n{U}_{a1}(2-\frac{K_{ha}}{K_{ha-1}})$$

(3)

In the formula, $U_{n_{ij}}$ is the horizontal displacement of the diaphragm wall at the horizontal depth i and depth j under the n working condition, $U_{a1}$ is the deformation increment of condition a without considering the spatiotemporal effect, $K_{ha}$ is the equivalent horizontal resistance coefficient of working condition a, and $K_{ha-1}$ is the equivalent horizontal resistance coefficient for condition a − 1.

Yan [27] used the elastic foundation beam method, where the unit width of the diaphragm wall is simplified as the elastic beam, the soil inside the pit is simplified as the soil spring, and the soil outside the pit is simplified as soil and water pressure. The horizontal displacement formula of the diaphragm wall under the unit width is obtained as follows. The model in this paper does not consider support, and the denominator can be simplified as $K+K_s$:

$$U=\frac{P}{K+K_s+K_m}$$

(4)

In the formula, U represents the deformation of the diaphragm wall, P represents the earth pressure behind the diaphragm wall, K represents the stiffness of the diaphragm wall, $K_s$ is the support stiffness, and $K_m$ is the stiffness of the soil spring.

During the backfilling process of the foundation pit soil, the settlement time of the soil is the same as the horizontal displacement of the diaphragm wall, and time factors are not considered. According to Formula (2), the direct factors affecting soil settlement are $E_s$ and $C_v$, in the ABAQUS numerical simulation; the study is conducted using the elastic modulus, and the compression modulus and elastic modulus are converted as mentioned earlier. According to Formula (3), it can be observed that the displacement of the diaphragm wall is influenced by the equivalent horizontal resistance coefficient of different excavation backfill conditions, and the equivalent horizontal resistance coefficient is the resistance capacity of the soil to the horizontal displacement of the foundation structure. The internal parameters such as cohesion, internal friction angle, and elastic modulus of the soil are important influencing factors. According to Formula (4), it can be inferred that the stiffness of the diaphragm wall is the important factor to consider, and it is achieved through the elastic modulus in ABAQUS. Combining Formulas (3) and (4), it can be concluded that the horizontal interaction between the soil and the diaphragm wall also needs to be considered. The Poisson ratio of the diaphragm wall is considered in ABAQUS to reflect the deformation capacity of the diaphragm wall in the horizontal direction.

To sum up, the soil parameters can be considered using the influence of cohesion, internal friction angle, and compression modulus of soil. The environment surrounding the soil can be considered using the influence of the elastic modulus, shear modulus of the left diaphragm wall, and the elastic modulus of the plain concrete bottom plate. The shear modulus of the diaphragm wall can be indirectly realized using the Poisson ratio. The influencing factors and working conditions of this experiment are shown in

Table 3. Analysis of influencing factors and working conditions.

Working Condition	${\mathit{E}}_{\mathit{s}\mathit{o}\mathit{i}\mathit{l}}$ (MPa)	${\mathit{c}}_{\mathit{s}\mathit{o}\mathit{i}\mathit{l}}$ (kPa)	${\mathit{\phi }}_{\mathit{s}\mathit{o}\mathit{i}\mathit{l}}$ (°)	${\mathit{E}}_{\mathit{d}\mathit{w}}$ (GPa)	${\mathit{\mu }}_{\mathit{d}\mathit{w}}$	${\mathit{E}}_{\mathit{p}\mathit{c}}$ (GPa)
1	200	200	36	25	0.2	20
2	700
3	1200
4	700	100	36	25	0.2	20
5		200
6		300
7	700	200	33	25	0.2	20
8			36
9			39
10	700	200	36	20	0.2	20
11				25
12				30
13	700	200	36	25	0.15	20
14					0.2
15					0.25
16	700	200	36	25	0.2	15
17						20
18						25

.

To make the tables and figures more concise, abbreviations are used to refer to various parameters. $E_{soil}$ refers to the elastic modulus of backfill soil, $c_{soil}$ refers to the cohesion of backfill soil, ${\phi }_{soil}$ refers to the internal friction angle of backfill soil, $E_{dw}$ refers to the elastic modulus of the diaphragm wall, ${\mu }_{dw}$ refers to the Poisson ratio of the diaphragm wall, and $E_{pc}$ refers to the elastic modulus of the plain concrete bottom plate.

The results of numerical simulation indicate that the properties of backfill soil and the surrounding structural properties have a certain degree of impact on soil settlement, and the settlement of backfill soil is generated by the self-weight of the backfill soil and the disturbance of the surrounding structure.

Figure 4 shows that when $E_{soil}$ increases from 200 MPa to 1200 MPa, the backfill soil has stronger resistance to deformation, and the horizontal deformation of the diaphragm wall gradually decreases. As $c_{soil}$ and ${\phi }_{soil}$ increase, the horizontal displacement of the diaphragm wall also gradually decreases, and the influence of cohesion on the horizontal displacement of the diaphragm wall is relatively small. As $E_{dw}$ gradually increases, its stiffness increases, and its resistance to deformation becomes stronger, with the horizontal displacement of the diaphragm wall gradually decreasing. With the increase in ${\mu }_{dw}$, the horizontal displacement of diaphragm wall changes little. As $E_{pc}$ increases, the deformation of the plain concrete bottom plate under the action of the upper soil decreases, and the horizontal deformation of the diaphragm wall also decreases.

It can be seen from Figure 5 that the settlement of soil gradually decreases with the increase in $E_{soil}$, $c_{soil}$, ${\phi }_{soil}$, and $E_{pc}$, and it increases with the increase in $E_{dw}$ and ${\mu }_{dw}$ after backfilling. As $E_{soil}$ gradually increases, the settlement of soil becomes smaller. When $E_{soil}$ increases from 200 MPa to 700 MPa, the decrease in soil settlement is significantly greater than the decrease in soil settlement when $E_{soil}$ increases from 700 MPa to 1200 MPa. As ${\phi }_{soil}$ increases, the friction between soil particles increases, and the resistance to deformation is stronger, resulting in a decrease in soil settlement. As $c_{soil}$ increases, the structural stability of the soil increases, and the soil settlement gradually decreases. When $c_{soil}$ increases from 200 kPa to 300 kPa, the decrease in soil settlement is smaller than when $c_{soil}$ increases from 100 kPa to 200 kPa. As $E_{pc}$ gradually increases, the vertical displacement of the plain concrete bottom plate at the bottom of the soil decreases, resulting in the corresponding decrease in soil settlement. Before backfilling the soil, the diaphragm wall completely resists the compression effect of the remaining soil, and when $E_{dw}$ increases, its stiffness gradually increases. The horizontal displacement of the diaphragm wall caused by the compression effect of the remaining soil decreases, which means its ability to resist the remaining soil is stronger, and the backfill soil is less compressed by the diaphragm wall. With the gradual increase in ${\mu }_{dw}$, the lateral deformation capacity of the diaphragm wall increases. With the increase in ${\mu }_{dw}$, the horizontal displacement of the diaphragm wall in the negative direction of the X axis gradually increases, and the backfill area is less squeezed. The variation in pattern of backfill soil affected by the influencing factors above is shown in Figure 5.

2.5. Grey Relational Grade Analysis

In order to fully understand the influence of properties of self-compacting solidified soil and parameters of the surrounding structure on soil settlement after foundation pit backfilling, a numerical simulation experiment with six factors and three levels (a total of 36 = 729 groups) is conducted, and the neural network database is. Due to the large experimental volume, there is no repeated arrangement and combination between the parameters. To improve computational efficiency, the parameters of material in the inp file of ABAQUS are modified to achieve the secondary development of automatic batch calculation. Based on the previous analysis, it can be seen that the settlement of self-compacting solidified soil is affected by the elastic modulus, cohesion, and internal friction angle of the self-compacting solidified soil; the elastic modulus of the diaphragm wall; the Poisson ratio; and the elastic modulus of the plain concrete bottom plate. The grey relational grade analysis is conducted using the MATLAB platform to understand the correlation levels of various influencing factors. The formulas [28] for the grey relational grade analysis using the MATLAB platform are as follows:

$$∆=\left|X_i-Y_i\left(j\right)\right|$$

(5)

$$A_{ij}=\frac{{∆}_{min}+{\rho ∆}_{max}}{{∆}_{ij}+{\rho ∆}_{max}}$$

(6)

$$R_j=1/m\sum _{i=1}^m{\mathrm{A}}_{\mathrm{i}\mathrm{j}}$$

(7)

In the formula, $∆$ is the difference coefficient matrix; $X_i$ is the column matrix, where $X_i$ is the i-th row element of the X matrix; $Y_i\left(j\right)$ is the i-th element of the j-th influencing factor; $A_{ij}$ is the correlation coefficient matrix; ${∆}_{min}$ is the minimum value of the difference coefficient matrix; ${∆}_{max}$ is the maximum value of the difference coefficient matrix; ${∆}_{ij}$ is the element in the i-th row and j-th column of the difference coefficient matrix; and $\rho$ is the resolution coefficient, with a value range from 0 to 1, and the value in this paper is 0.5.

$$\begin{array}{c}{X}_i=\left[\begin{array}{c}0.0077\\ 0.4844\\ 0.9763\\ 0.0074\\ \dots \\ 0.0646\end{array}\right]\\ Y_i\left(j\right)=\left[\begin{array}{ccc}0.0077& \cdots & 0.0077\\ 0.0156& \cdots & 0.4844\\ 0.0237& \cdots & 0.9763\\ 0.0074& \cdots & 0.0074\\ ⋮& \ddots & ⋮\\ 0.9354& \cdots & 0.0646\end{array}\right]\\ A_{ij}=\left[\begin{array}{ccc}0.9848& \cdots & 0.9848\\ 0.9698& \cdots & 0.5079\\ 0.9547& \cdots & 0.3387\\ 0.9855& \cdots & 0.9855\\ ⋮& \ddots & ⋮\\ 0.9354& \cdots & 0.0646\end{array}\right]\end{array}$$

In this paper, $Y_i\left(j\right)$ is the 729 × 6 matrix composed of normalized input variables for each influencing factor, and $X_i$ is the sequence of maximum settlement values of the corresponding backfill soil. The settlement of each row in $X_i$ is the normalized output value corresponding to each row of variables in $Y_i\left(j\right)$. $Y_i\left(j\right)$ reads from left to right, and each column represents the elastic modulus, internal friction angle, cohesion of self-compacting solidified soil, elastic modulus, Poisson ratio of diaphragm wall, and elastic modulus of the plain concrete bottom plate. The correlation coefficient matrix $A_{ij}$ is obtained from grey relational grade analysis of various influencing factors and settlement of self-compacting solidified soil, and it calculates the mean of all values in column j to obtain the grey relational grade of the influencing factor. Finally, the grey correlation matrix is obtained as R = [0.8402 0.5906 0.5912 0.589 0.5918 0.5936]. It can be seen that the influencing factors considered in this numerical simulation have high correlation with the settlement of self-compacting solidified soil, with selection of reasonable influencing factors, and the six influencing factors above can all be used as input layer parameters for the neural network. Among them, $E_{soil}$ has the greatest impact on the settlement, with $E_{pc}$, ${\mu }_{dw}$, $c_{soil}$, ${\phi }_{soil}$, and $E_{dw}$ following. Figure 6 shows the correlation between the parameters selected for numerical simulation and the settlement of self-compacting solidified soil in foundation pit backfilling.

3. GA-BP Neural Network Model

3.1. BP Neural Network

The BP (back propagation) neural network is the learning algorithm that uses forward transmission of information and reverse transmission of errors. The network structure consists of the input layer, the hidden layer, and the output layer. Data is propagated layer by layer from the input layer through the hidden layer, and each layer is connected by weights. When training the grid weights, the network connection weights are corrected layer by layer from the output layer in the direction of reducing errors, so that the output results approach the target value and ultimately reduce the error.

To avoid the problem of weight polarization during the neural network iteration process caused by order-of-magnitude differences in data, it is necessary to normalize all data and convert them to the same scale. In this experiment, the uniform scale of experimental data to the range of [0, 1] is chosen.

In the formula, x is the original data, $y$ is the normalized data, and $\mathit{max}\left(x\right)$ and $min\left(x\right)$ represent the maximum and minimum values in the original data, respectively.

$$y=\frac{x-min\left(x\right)}{\mathit{max}\left(x\right)-\mathit{min}\left(x\right)}$$

(8)

Since $E_{soil}$, $c_{soil}$, ${\phi }_{soil}$, $E_{dw}$, ${\mu }_{dw}$, and $E_{pc}$ in this numerical simulation test are all highly related to the settlement of backfill soil, it is determined that the above six variables are selected as the input layer for this neural network model. When the number of hidden layers in the neural network is one, it can demonstrate excellent data regression performance. The number of nodes under the single hidden layer has a significant impact on data regression. In this paper, the number of hidden layer nodes in neurons is determined to be eight by combining empirical Formula (9) [29] and a trial-and-error method.

$$N=\sqrt{m+n}+a$$

(9)

In the formula, N is the number of hidden layer nodes, m is the number of input layers, n is the number of output layers, and a is a constant between 1 and 10.

The neural network modeling scheme is shown in Figure 7.

3.2. GA-BP Neural Network

When a BP neural network performs data regression calculation, it needs to constantly adjust the weights and biases between neurons to optimize the performance of the neural network. The weights and biases between neurons are random, so this operation method easily falls into the local optimal solution, resulting in overfitting of neural network prediction results. The GA-BP neural network is the method that utilizes a genetic algorithm to optimize the initial weights and biases of the BP neural network. The initial values of weights and biases are encoded, and the training error obtained via BP neural network is used as the fitness value of the genetic algorithm. The optimal fitness value is obtained through operations such as chromosome cross mutation, and the network weights and biases of the optimal individuals are selected for training to achieve optimal prediction performance. In the neural network training, the root mean square error is selected as the fitness function. The specific optimization method of the GA-BP neural network is shown in Figure 8.

The relevant parameters of the GA-BP neural network are shown in

Table 4. Parameters of GA-BP neural network model.

Learning Rate	Learning Error	Max Iterations	Generations	Population Size	Selection Probability	Cross Probability	Mutation Probability
0.01	1 × 10−6	1000	50	100	0.09	0.75	0.2

.

3.3. Evaluation Indicators of the Neural Network Model

Based on the 729 groups of data obtained from numerical simulation, data were divided into the training set and the testing set. Among them, the data of 81 groups at the internal friction angle of 39° when the elastic modulus of self-compacting solidified soil is 1200 MPa are used as the testing set. The remaining 648 groups of data are used as the neural network training set. The specific division plan for the training and testing sets of the neural network is shown in

Table 5. Partition scheme for neural network training set and testing set.

Group	Parameters and Values						Number of Groups
	${\mathit{E}}_{\mathit{s}\mathit{o}\mathit{i}\mathit{l}}$ (MPa)	${\mathit{\phi }}_{\mathit{s}\mathit{o}\mathit{i}\mathit{l}}$ (°)	${\mathit{c}}_{\mathit{s}\mathit{o}\mathit{i}\mathit{l}}$ (kPa)	${\mathit{E}}_{\mathit{d}\mathit{w}}$ (GPa)	${\mathit{\mu }}_{\mathit{d}\mathit{w}}$	${\mathit{E}}_{\mathit{p}\mathit{c}}$ (GPa)
Training set	200, 700	33, 36, 39	100, 200, 300	25, 30, 35	0.2, 0.25, 0.3	15, 20, 25	648
	1200	33, 36
Testing set	1200	39					81

.

For the neural network model established in this paper, the mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R²) are selected as the prediction performance evaluation indicators of the model between the predicted value and the true value of the training set or test set. The MSE is usually used as the target error in the neural network training process. The RMSE reflects the degree of deviation of the predicted value from the true value. The MAE reflects the overall deviation of the predicted data in the set, while R² reflects the degree of regression of the model data. The formula expressions for MSE, RMSE, MAE, and R² are as follows [30,31]:

$$MSE=\frac{\sum _{i=1}^n{(A_i-T_i)}^2}{n}$$

(10)

$$RMSE=\sqrt{\frac{\sum _{i=1}^n{(A_i-T_i)}^2}{n}}$$

(11)

$$MAE=\frac{\sum _{i=1}^n\left|A_i-T_i\right|}{n}$$

(12)

$$R^2=1-\frac{\sum _{i=1}^n{(A_i-T_i)}^2}{\sum _{i=1}^n{(T_i-\overline{T})}^2}$$

(13)

In the formula, A is the predicted settlement value of self-compacting solidified soil using the neural network model, n is the number of predicted points, T is the settlement value calculated by numerical simulation, and $\overline{T}$ is the mean value of the settlement value calculated via numerical simulation.

4. Regression Analysis of GA-BP Neural Network Model Data

After the data preprocessing is completed, the data is substituted into the neural network model with determined parameters for data regression analysis. According to the MSE-iterations curve during the training process, the BP neural network and GA-BP neural network can converge quickly after repeated calculations and iterations of the prediction model. This can be seen in Figure 9. The BP neural network completes six rounds of cross validation in the 224th iteration, and the optimal validation error is 1.1613 × 10⁻⁶. The GA-BP neural network completes six rounds of cross validation in the 87th iteration with continuous optimization of weights and biases, and it achieves the optimal validation error of 1.4222 × 10⁻⁶ in the 81st iteration. Therefore, the GA-BP neural network continuously optimizes weights and biases, which can effectively improve the efficiency of the algorithm.

The settlement prediction results of the training set are shown in Figure 10a. It can be seen from the figure that the training accuracy of the BP neural network model and the GA-BP neural network model are both high, so the prediction effect of the training set data can match well with the measured values. According to Figure 10c, the point with the highest absolute error in the training set appears in the BP neural network with the absolute error of all points controlled within 0.3%, and the vast majority of points are located below 0.2%. The statistical results show that the MAE of the BP neural network is 0.12%, the RMSE is 0.0016 mm, and the R² is 0.9999. The MAE of the GA-BP neural network is 0.14%, the RMSE is 0.0018 mm, and the R² is 0.9999.

The trained BP neural network and GA-BP neural network are used to predict the testing set samples, and the prediction results are shown in Figure 10b,d. It can be seen that when the BP neural network has the perfect training effect on the training set, the prediction effect on the testing set is not ideal. In Figure 10b, there is a whole section of data that deviates from the true value. In Figure 10d, it can be seen that the predicted value deviates from the true value, and its MAE is also large. It can be seen that the BP neural network cannot achieve comprehensive learning of the training set data, and there is a certain degree of deviation in the prediction performance of the testing set. Overall, the BP neural network only achieves local optima, leading to overfitting. The GA-BP neural network method introduces genetic algorithm mutation operations and mutation probabilities into the algorithm, it enriches population diversity, improves global search ability and prediction accuracy, and effectively solves the problem of neural networks falling into the local optima of the model. According to the statistical results,

Table 6. Comparative analysis of regression results based on BP and GA-BP neural network data.

Number	Type of Neural Network	Training Set			Testing Set
		RMSE (mm)	MAE	R2	RMSE (mm)	MAE	R2
1	BP	0.0016	0.12%	0.9999	0.0035	0.36%	0.9674
2	GA-BP	0.0018	0.14%	0.9999	0.0018	0.14%	0.9910

shows that the MAE is 0.26%, the RMSE is 0.0035 mm, and the R² is 0.9674 for the BP neural network. The R² is 0.9910, the RMSE is 0.0018 mm, and the MAE is 0.14% for the GA-BP neural network. The prediction effect of the GA-BP is better than that of the BP neural network. Compared to the BP neural network, the weight and bias of the GA-BP neural network are more reasonable.

5. Discussion

This paper mainly conducts research using two aspects: numerical simulation and genetic algorithm improvement of the neural network model. From the numerical simulation results, it can be seen that the settlement and structural disturbance of self-compacting solidified soil are relatively small compared to engineering waste soil, and self-compacting solidified soil has good engineering application performance. In practical projects, the self-compacting solidified soil is mainly composed of engineered waste soil and a certain amount of curing agent. After maintenance of self-compacting solidified soil, its index of strength and effect of backfilling are better than those of engineered waste soil, and it can greatly improve the quality of foundation pit backfilling, solving the problem of difficult compaction of soil backfilling and difficulty in purchasing high-quality backfill materials. The waste materials can be fully used, the engineering costs can be saved, and sustainable development can be promoted. This paper combines numerical simulation with neural networks to achieve high-precision prediction of soil settlement in foundation pit backfilling. In practical engineering, settlement results can be quickly obtained by inputting the structural and soil properties of the backfill area into the neural network model, eliminating complex processes such as finite element model parameter adjustment and model modification.

Based on this paper, some prospects can be proposed. Firstly, the finite element software ABAQUS 2020 is selected as the calculation software for this numerical simulation due to its rich soil material models, fine mesh division, and excellent secondary development and post-processing modules. In addition to ABAQUS, professional geotechnical engineering foundation pit simulation finite element software such as Plaxis can also be considered, since it also has rich soil models. The discrete element software can also be used for numerical simulation of foundation pit backfilling, because it can more fully consider the interaction between soil particles. Compared to other finite element and discrete element software, the team is more familiar with the secondary development of ABAQUS, so it can significantly improve the computational efficiency of numerical simulation. In the future, research will be conducted on different software in the field of foundation pit backfilling. Secondly, multiple optimization methods for neural networks can be selected for comprehensive comparison. This paper selects the genetic algorithm to optimize the BP neural network. The optimized GA-BP has excellent data prediction ability. In addition to the genetic algorithm, the particle swarm optimization algorithm, ant colony optimization algorithms, and the support vector machine algorithm can also be used to optimize the BP neural network method. Further research on the above methods can be carried out in the future. Finally, based on the data obtained from the numerical simulation, this paper launches research on the data prediction effect of the neural network method. If there are on-site soil settlement and diaphragm wall deformation monitoring data for calibration, the numerical simulation results and neural network prediction results will be more accurate.

6. Conclusions

A numerical model for foundation pit backfilling is established based on a certain foundation pit backfilling project in Nanjing. The effects of soil properties and surrounding structural properties are considered. Through secondary development batch submission calculations, the grey relational grade between influencing factors and settlement of self-compacting solidified soil is discussed. Based on the results of numerical simulation and grey relational grade analysis, the GA-BP neural network-based self-compacting solidified soil settlement prediction model is proposed. The conclusions are as follows:

(1)

The self-compacting solidified soil formed by using a cement curing agent to improve fine silty sand has significantly smaller settlement and horizontal displacement after backfilling the foundation pit. The settlement of self-compacting solidified soil after backfilling is only one eleventh of that of fine silty sand, so it has good engineering application properties.

(2)

The settlement of self-compacting solidified soil for foundation pit backfilling decreases with the increase in the $E_{dw}$ and ${\mu }_{dw}$, and it increases with the increase in the $E_{pc}$, $E_{soil}$, $c_{soil}$, and ${\phi }_{soil}$. According to the grey relational grade, $E_{soil}$ has the greatest impact on the settlement of self-compacting solidified soil, with a grey relational grade of 0.8402. Except for the $E_{soil}$, the grey relational grade of other factors on the settlement of self-compacting solidified soil is above 0.5, and the values are close to each other.

(3)

After soil backfilling, the horizontal displacement of the diaphragm wall decreases with the increase in $E_{soil}$, $c_{soil}$, ${\phi }_{soil}$, $E_{dw}$, and $E_{pc}$, and it increases with the increase in ${\mu }_{dw}$. Among them, the horizontal displacement of the diaphragm wall is less affected by $c_{soil}$ and ${\mu }_{dw}$.

(4)

When traditional BP neural networks are used for predicting the settlement of self-compacting solidified soil, due to their random weights and biases, it may be the local optima when used for prediction. The genetic algorithm is used to optimize the weights and biases of BP neural networks, and it can effectively improve the computational efficiency and prediction accuracy of the neural network model. The GA-BP neural network settlement prediction model proposed in this paper has an R² of 0.9910 and an RMSE of only 0.0018 mm. In contrast, the BP neural network settlement prediction model has an R² of only 0.9674 and an RMSE of 0.0035 mm. The performance of the GA-BP neural network-based self-compacting solidified soil settlement prediction model for foundation pit backfilling is superior to that of the BP neural network-based settlement prediction model.