Prediction of Buildings’ Settlements Induced by Deep Foundation Pit Construction Based on LSTM-RA-ANN

Abstract

In view of the shortcomings of existing methods for predicting the settlement of surrounding buildings caused by deep foundation pit construction, this study uses the monitoring data of a foundation pit project in Shanghai and divides the construction process of the pit into three working conditions, that is, enclosure construction, earthwork excavation, and basement support construction. The attention mechanism and residual update are integrated into the artificial neural network (ANN) model, and the root-mean-square error, average absolute error, and determination coefficient are used as the evaluation indices of the model. The artificial neural network prediction model LSTM-RA-ANN for building settlements in deep foundation pit construction was then established. The prediction performance of the model was also analysed under different working conditions, and the influences of the main factors (including the soil parameter, monitoring point location, activation function, hyperparameter, and input number) on the evaluation index was further explored. The results indicate that the performances of the established LSTM-RA-ANN model are closely related to the construction conditions, the predicted settlements agree well with the monitored ones in three working conditions with the greatest errors occurring at a later time of the working conditions, and the prediction accuracy of the great–small order corresponds to basement support, enclosure construction, and earthwork excavation respectively. The farther the monitoring point is from the edge of the pit, the better the model performance is. The activation function, initial learning rate, and maximum iteration batch have a great influence on the evaluation indices of the model, while the number of input points has little effect on the evaluation indices. These results may serve as a reference for the safe construction and normal operation of foundation pit engineering.

1. Introduction

At present, the number of foundation pits is increasing, and most of them are found in the busy areas of cities. The stability of the pit excavation itself and its potential impact on the surrounding buildings and structures have become a primary consideration in engineering construction [1]. A large number of studies have been carried out on the impact of pit construction on the settlement of surrounding buildings, and the commonly used methods include regression analysis, grey theory, time-series analysis, neural network analysis, and other [2] methods. However, these methods have certain limitations: regression analysis belongs to a static data processing method, while the pit construction monitoring data are dynamic data; grey theory has high data requirements, requiring the data to show an exponential increase or monotonicity, while the pit monitoring data do not have monotonicity, mostly presenting complex nonlinear characteristics; and time-series analysis is a statistical method, and the use of extrapolation time cannot be too long; Among the commonly used neural network analysis methods, the back propagation (BP) neural network is the most widely used, but the BP neural network is greatly affected by the initial value, slower convergence, longer iteration time, and being prone to local extreme value problems.

Currently, some scholars use deep-learning models to study the impact of pit construction on the settlement of surrounding buildings. Among the deep-learning models, the long short-term memory (LSTM) network [3] has a large advantage in temporal data processing, which can overcome the problem of gradient explosion and gradient disappearance in the process of back propagation, and can effectively capture both long-term and short-term information [4], and can carry out dynamic feature extraction for successively related data, and has been used in machine translation, information retrieval, image processing, text recognition [5], intelligent question and answer, speech recognition, and data prediction [6], and other fields, and has also found some applications in the field of geotechnical engineering. LSTM is a gated recurrent neural network that adds a gating mechanism to control the transmission of information in a neural network based on a simple recurrent neural network [7,8,9]. Chen et al. [10] applied the deep-learning algorithm LSTM to predict the long-term settlement of the reclamation settlement, and applied the LSTM-based model to the reclamation of Kansai International Airport (KIA) and Chek Lap Kok Airport (CLKA). The results show that the LSTM-based model can accurately capture the long-term settlement of KIA. The developed model has a great generalisation capability and can be directly applied to other projects. Hong et al. [11] found LSTM can be successfully used to predict consolidation settlements and provide highly accurate predictions for soft ground construction engineering. Xu et al. [12] explored the effects of random errors and environmental parameters on the prediction of dam settlement, and proposed a prediction model based on a multi-input LSTM network and random error extraction. With the settlement data of concrete-faced rock fill dams, the analysis showed that the removal of random errors can significantly improve the short-term prediction performance, and the consideration of environmental parameters can significantly improve the long-term prediction performance. Ding et al. [13] established four different machine-learning methods (the radial basis function (RBF) neural network, back propagation neural network (BPNN), generalised regression neural network (GRNN), and Gaussian prior (GP) regression model) for settlement prediction, and it was found that the GP model had the best prediction performance. Many scholars have attempted to optimise LSTM models using various methods. Peng et al. [14] introduced an improved LSTM model and a weighted Markov model to predict sluice deformation. The method utilises the Seagull Optimisation Algorithm (SOA) to optimise the hyperparameters of the neural network structure in the LSTM, mainly to improve the model. The analysis results show that the proposed model has the highest R², as well as the smallest RMSE value and absolute relative error for the monitoring data of the four monitoring points. Alotaibi et al. [15] took advantage of convolutional neural networks (CNNs) to optimise LSTM models to improve the low learning effectiveness. Kang et al. [16] added the attention mechanism to the LSTM model so that the model can pay more attention to the parameters with higher weights. A sensitivity analysis based on the Pearson correlation coefficient can improve the prediction efficiency and reduce irrelevant input parameters. It was found that the LSTM attention model has a higher accuracy compared to the LSTM model.

Several other scholars have investigated the problem of time-series data prediction using combinatorial models. Cao et al. [17] proposed a model of fully integrated empirical modal decomposition with adaptive noise long- and short-term memory (CEEMDAN-LSTM model); CEEMDAN divides one-dimensional data into multidimensional data by a model of fully integrated empirical modal decomposition. Experimental results show that this deep-learning method performs better compared to existing machine-learning techniques and algorithms. Lu and Li [5] proposed a combined deep-learning model for pollutant concentration prediction, and found that the combined model can enhance the generalisation ability of the model. Lee and Kim [18] developed a sequence-to-sequence mechanism combined with a bidirectional LSTM to predict the inflow rate. The results show that the model has a good prediction accuracy. Li et al. [19] used a deep-pocketed bidirectional LSTM neural network with a self-attention mechanism to capture the temporal dependencies of the original sensor data, and the method can deal with various missing data scenarios in a dam monitoring system. Sheng and Xiang [20] proposed a method to predict the settlement deformation of deep foundation pits based on the combination model of complementary ensemble empirical mode decomposition (CEEMD) and LSTM, and the results showed that the combination model has better prediction results. Zhang et al. [21] proposed a hybrid spatio-temporal depth prediction model with both principal and spatio-temporal blocks. Experiments showed that the spatio-temporal relationship between the surface settlement data obtained from different monitoring points within the network is dynamic during metro pit excavation, and the STdeep model exhibits the best performance and excellent stability. Zhou et al. [22] used the particle swarm algorithm (PSO) to optimise the number of neurons, dropout, and batch-size in the structure of LSTM network, and found that the PSO-LSTM model can accurately describe the dynamic evolution process of the buried pipelines, and has a better prediction accuracy than the improved Gaussian curve method and the LSTM neural network model.

At present, although some theoretical models have been established for predicting the impact of pit construction on building and surface settlement, the pit construction process is cumbersome, there are many working conditions, and different working conditions have different impacts on the buildings around the pit; at the same time, there are many parameters in the existing surface settlement prediction model, which makes it difficult to capture the key information of the settlement data. Therefore, there is a need to establish a dynamic prediction model for building settlement with a higher accuracy, fewer parameters, and clear working conditions. To this end, this paper divides the pit construction into different working conditions and creates a fusion neural network model LSTM-RA-ANN (which stands for long short-term memory, residual, and attention-based artificial neural network) for building settlement prediction, which is useful for the dynamic prediction of building settlement caused by the pit construction, safe construction, and normal operation of foundation pit projects.

2. Overview of the Project and Layout of Measurement Points

2.1. Overview of the Project and Layout of Measurement Points

The pit project is located in the downtown area of Shanghai, adjacent to the metro station on the east and residential buildings on the remaining three sides. The pit area is about 7800 square meters, divided into two areas: Area I is the area of the underground joint construction section, which has been completed, and Area II has an area of 5720 square meters, with a three-level basement and an excavation depth of 15.4–15.9 m. The enclosure structure is a 1 m-thick diaphragm wall, with triaxial hydraulic soil-mixing piles on both sides of the wall to reinforce the channel wall, and three reinforced concrete supports in the vertical direction, but a fourth steel angle support is set up in the northeastern corner of the local area. The periphery of the pit is reinforced with triaxial soil-mixing piles for skirt reinforcement, the width of reinforcement is 8 m, and the depth of reinforcement is 6.0–7.0 m below the bottom of the pit. Among the buildings around the pit, the nearest place on the north side is a five-storey shallow foundation brick–concrete structure residential building, which is about 9 m away from the enclosing edge line; on the west side, it is close to two six-storey shallow foundation brick–concrete structure residential buildings, which is about 9 m away from the enclosing edge line; on the east side, it is close to the underground station, and the distance is about 34.17 m; the nearest place on the south side is a six-storey residential building with a shallow foundation of a brick–concrete structure, which is about 13 m away from the edge line of the enclosure; the surrounding buildings are represented by F, G, H, I, and J. Buildings F and G are concrete buildings, and buildings H, I, and J are brick–concrete buildings.

The plan layout of settlement monitoring points for deep foundation pit construction buildings is shown in Figure 1, where F1 is the first monitoring point of building F, and other monitoring point symbols’ definitions are by analogy (for example, G2 is the second monitoring point of building G).

The main basis for monitoring is the ‘Foundation Pit Engineering Construction Monitoring Regulations’ (DG/TJ08-2001-2016) [23]. For monitoring, the settlement monitoring points are set up using the L-type peg arrangement method on the buildings arranged within the range of 2 H (H is the depth of the pit excavation) around the foundation pit construction area, and at least 3 points of elevation data are set up outside the range of 3 H around the foundation pit, and the co-ordinates of the control points are obtained through the establishment of a levelling measurement monitoring network. The elevation of each monitoring point is measured by the line work point, and the initial value is measured before construction, the difference between the current elevation and the previous elevation is taken as the current settlement, and the difference between the current elevation and the initial elevation is taken as the cumulative settlement. In this study, the monitoring of surface settlement and building settlement was carried out using an electronic level, and the accuracy of the monitoring data was in percentile in millimeters. The monitoring alarm value is as follows: the maximum settlement rate reaches 2.0 mm/d, or the cumulative settlement reaches 20 mm.

The soil layers within the excavation depth of the pit are the ②₁ layer, ③₁ layer, ④ layer, and ⑤₁ layer, and the soil at the bottom of the pit is mainly the ④ or ⑤₁ layer. According to the investigation report and ref. [24], when the soil is the same, the physical and mechanical properties of the soil layers within the excavation range of the pit are shown in

Table 1. Parameters of soil layers in excavation site.

Soil Layer Number	Soil Layer Name	Es/MPa	c/kPa	φ/(°)	ν	h/m
②1	silty clay	9.0	20	19	0.31	2.0
③1	silty chalky clay	10.0	12	18.5	0.38	2.8
④	silty clay	2.2	11	12	0.39	2.4
⑤1	loam	6.3	19	12.5	0.32	4.7

. In Table 1, Es is the compression modulus, c is the cohesion, φ is the internal friction angle, ν is the Poisson’s ratio, and h is the thickness of soil layer.

2.2. Pit Construction Conditions

The pit construction is divided into three conditions as shown in

Table 2. Classification of deep foundation pit construction conditions.

Construction Conditions	Construction Process
Condition 1 (enclosure construction)	Reinforcement of the trench wall on both sides of the ground wall; partially grouted pile construction;
	enclosure construction of diaphragm wall.
Condition 2 (earth excavation construction)	First earth excavation, first concrete support, trestle concrete, concrete maintenance;
	second earth excavation, second concrete support, concrete maintenance;
	third earth excavation, third concrete support, concrete maintenance;
	fourth earth excavation, setting bedding, and waterproof layer.
Condition 3 (basement support construction)	Concrete maintenance, removal of the third course of support, replacement of the top plate of the third basement wall, steel pipes and steel sections, and construction of diagonal bracing in Zone I;
	concrete maintenance, removal of the second course of support, replacement of the top plate of the second basement wall, steel pipes and steel sections;
	concrete maintenance, removal of the first course of support, replacement of the top plate of the first basement wall, steel pipes and steel sections.

, and the schematic diagram of the construction process is shown in Figure 2.

3. RA-LSTM-ANN Model Building

3.1. Long Short-Term Memory Neural Network (LSTM)

Long short-term memory (LSTM) is a variant of the recurrent neural network (RNN), which can solve the problem of the long-time dependence of the RNN structure by setting up a special ‘gate’ structure to selectively remember LSTM information [25,26,27]. Since it is difficult to obtain the sample features well and this can easily lead to underfitting, this paper uses multi-layer LSTM network cells to improve the prediction ability of the network. The structure of the LSTM cells is shown in Figure 3, in which x_t denotes the input of the moment t, y_t denotes the output of the moment t, h_t−1 denotes the input information of the moment (t − 1), h_t denotes the input information of the moment t, C_t−1 denotes the input information of the moment (t − 1), C_t−1 denotes the input information of the moment (t − 1), C_t denotes the memory cell of moment t, σ denotes the sigmoid activation function, and tanh denotes the hyperbolic tangent function.

3.2. Residual Network

Residual networks use residual blocks as the basic unit of the network, which not only mitigates the gradient vanishing or gradient explosion problem of deep networks, but also can be used to solve the network degradation problem caused by the increase in depth in the network. At the time of the study, residual-stacking LSTM was used to enhance the analysis of short- and medium-term information features under different working conditions by adding layers of residual connections in the model. The residual network consists of a series of residual blocks and a residual block can be represented as:

$$y=F(x,\{W_i\})+x$$

(1)

In Formula (1), $x$ and $y$ are the input and output vectors; and $F(x,\{W_i\})$ is the residual network to be learnt.

The structure of residual mapping is shown in Figure 4. In the figure, the residual mapping is divided into two parts: the curve part is the constant mapping ($y=x$), and the straight line part is the residual mapping, and the residual network obtains the optimal solution of the network by fitting (residual).

3.3. Attention Mechanisms

Traditional LSTM networks are prone to problems such as information confusion, information loss, and a limited learning ability when processing input information. The network model built in this paper has inputs from both single-monitoring point data and multi-monitoring point data; therefore, an attention layer is introduced before the full connectivity layer to assign weights to the computed data. The function of the attention layer is to assign the weights of the features learnt from the model to the input vectors in the next step, to weight the features whose prediction results are more relevant to the input data, to emphasise the role of key feature data in the prediction of the LSTM network, and then synthesise the weighted vectors with the input vectors of the existing layer, to generate a new vector and input it to the whole connection layer, and then finally to extract the relationship between the features by using non-linear transformation. The non-linear transformation of the fully connected layer is used to extract the relationship between the features and map them to the output space.

3.4. Fusion Modeling

The framework of the settlement prediction network model built in this paper is shown in Figure 5. In the figure, the input layer contains soil layer parameters and settlement sequences of monitoring points; the output of the first LSTM layer is passed to the residual network in addition to the next LSTM layer; the overall model contains the basic recurrent unit consisting of two LSTM layers followed by a residual network; the information of the residual network is passed to the next residual layer in addition to the next LSTM layer; the LSTM layer is mainly used for remembering important information and ignoring the less important information; and the residual network implements jump connections between different network layers, which is used to maintain the model performance, obtain long-range dependency, and avoid losing valid information.

3.5. Data Preprocessing

Interfered by various factors (precipitation, etc.), the monitoring data may contain a lot of noise. In order to avoid the influence of noise on the model performance, noise reduction is performed before the raw data are imported. At the same time, in order to reduce the influence of the magnitude on the prediction results of building settlement and improve the generalisation ability of the network, the input data are scaled to [0, 1] for the dimensionless processing, and the processing formula is:

$$y_i=(x_i-\stackrel{\wedge }{x})/s$$

(2)

In Formula (2), $y_i$ is the dimensionless input data, $x_i$ is the original input data,$\stackrel{\wedge }{x}$ is the mean value of the original data, and $s$ is the standard deviation of the original data.

The monitoring frequency is not consistent in different working conditions, and the actual monitoring data recording interval may be different. Therefore, this paper uses the spline interpolation method to transform the monitoring data, so that the monitoring data under the same operating conditions become a sequence of data with equal intervals, and the monitoring interval after interpolation is uniformly transformed to once a day.

3.6. Indices for Model Evaluation

In this paper, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) are used to evaluate the model prediction effectiveness, which are calculated as:

$$\mathrm{RMSE}=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{(y_i-{\stackrel{\wedge }{y}}_i)}^2}}$$

(3)

$$\mathrm{MAE}=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|y_i-{\stackrel{\wedge }{y}}_i\right|}$$

(4)

$$R^2=\frac{{\displaystyle \sum _{i=1}^n{\left({\stackrel{\wedge }{y}}_i-\overline{y}\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(5)

In the aforementioned formulae, ${\stackrel{\wedge }{y}}_i$ denotes the predicted value, $\overline{y}$ denotes the average of the monitored values, $y_i$ denotes the monitored value, and n denotes the total number of samples. The smaller the RMSE and MAE are, and the closer the R² is to 1, the more reliable the model is.

3.7. Model Validation

In order to verify the accuracy of the LSTM-RA-ANN model constructed in this paper, the settlement monitoring data of F1 under the enclosure construction condition are used for the validation and comparative analysis of the performance of the constructed model and the traditional LSTM model in predicting the settlement. The hyperparameters of the model are selected as the initial learning rate, minimum iteration batch, maximum iteration period, and number of hidden units. After several training sessions, the hyperparameters of the model are as follows: initial learning rate 0.06, minimum iteration batch 20, maximum iteration period 400, and the number of hidden units 32. The Adam algorithm is used for loss transfer, the training step size is set to 5, and the data training mode of ‘5 + 1’ is adopted (the settlement monitoring data of the first five days are used to predict the settlement value of the sixth day), and the output is in the form of a single-step output. Considering the consistency of the comparison conditions, these settings were still used for the basic parameters of the model for subsequent analyses. Using the proposed LSTM-RA-ANN model and the conventional LSTM model, the settlement prediction results for monitoring point F1 were obtained in Figure 6.

As can be seen in Figure 6, for monitoring point F1, the coefficient of determination of the LSTM-RA-ANN model proposed in this paper is much higher than that of the traditional LSTM model, which is 4.5 times that of the traditional model; the RMSE and MAE are 0.54 times and 0.57 times that of the traditional LSTM model, respectively. In terms of the overall agreement, the predicted settlement values from the LSTM-RA-ANN model in this paper are in better agreement with the monitoring values than those from the traditional LSTM model.

4. Prediction of Building Settlement under Different Pit Construction Conditions

The following is an analysis of the prediction of the settlement of different buildings under the three aforementioned pit construction conditions (enclosure construction, earth excavation, and basement support). For the study, 75% and 25% of the dataset are used as the training and test sets, respectively.

4.1. Enclosure Construction

The construction period of the enclosure was 150 working days in total, and a total of 47 isochronous monitoring data were obtained from each monitoring point, and 42 sets of data were constructed as the dataset by adopting the training mode of ‘5 + 1’. The settlement prediction results are shown in Figure 7. For comparison, the settlement monitoring values are also marked in the figure (later, the same).

As can be seen from Figure 7, during the enclosure construction period, the predicted values are in good agreement with the monitored values when using the constructed LSTM-RA-ANN model for settlement prediction. In terms of different moments, the largest moments of prediction error (absolute value of the ratio of the monitoring value–predicted value difference to the monitoring value, the dashed box moments in the figure, and, later, the same) for the five buildings were the 10th, 3rd, 11th, 11th, and 6th days (the blue dotted box in the figure is at the moment when, after the same), and most of these moments were distributed in the latter half of the present working condition.

4.2. Earth Excavation

The construction period of earth excavation was 143 working days in total, and 105 isochronous monitoring data were obtained from each monitoring point, constructing 100 sets of data as a dataset. The settlement prediction results are shown in Figure 8. As can be seen from Figure 8, the settlement prediction–monitoring values of the LSTM-RA-ANN model under the earth excavation construction condition have a high degree of agreement. As far as different moments are concerned, the maximum moments of prediction errors for the five buildings are the 20th, 15th, 18th, 22nd, and 24th days, which are distributed in the second half of this working condition.

4.3. Basement Support

The construction period of the basement support was 67 working days in total, and 65 isochronous monitoring data were obtained from each monitoring point to construct 60 data sets. The settlement prediction results under this working condition are shown in Figure 9, where it can be seen that the settlement prediction using the model developed in this paper also has a high degree of agreement between the predicted values and the monitoring values during the basement support construction working condition. In terms of different moments, the maximum prediction error moments for the five buildings are on the 7th, 6th, 12th, 14th, and 15th days, respectively, which mostly occur in the second half of the condition.

4.4. Comparison of Assessment Indicators under Different Working Conditions

Using the proposed LSTM-RA-ANN model for the prediction of building settlement, the calculation results of the assessment indices under different working conditions are shown in Figure 9. As can be seen in Figure 9, when the building settlement is predicted using the proposed LSTM-RA-ANN model, the trends of RMSE and MAE are basically synchronised with each other, with the range of change from 0.14 to 2.50; under the three conditions, the RMSE and MAE of Building I are larger because the buildings on both sides of Building I are closely connected, and the settlement prediction value is more affected by the environment.

Figure 10 also shows that the prediction accuracy is closely related to the construction conditions: the average values of RMSE for enclosure construction, earth excavation construction, and basement support construction are 0.50, 1.60, and 0.51, respectively; the average values of MAE are 0.46, 1.34, and 0.40, respectively; the average values of R² are 0.89, 0.97, and 0.78, respectively; and the prediction accuracies corresponding to the construction conditions are as follows: basement support > enclosure construction > earth excavation construction; during the basement support construction, the RMSE and MAE fluctuate the least, 0.24–0.62 and 0.18–0.58, respectively, which may be related to the fact that all the concrete support removal adopts the static cutting method; in the enclosure construction, the RMSE and MAE change a little bit more; in the excavation construction, the RMSE and MAE fluctuate more, which may be due to the fact that, during earth excavation, there is a large gravity change in the vicinity of the building, which leads to a large change in the trend of the settlement monitoring values at the monitoring points, which, in turn, may affect the predictive performance of the model.

5. Influence of Major Factors on the Performance of Building Settlement Prediction

The influence of the main factors on the effectiveness of building settlement prediction is discussed below, using the monitoring data of the enclosure construction condition as an example. These factors mainly include the soil layer parameters, monitoring point location, activation function, hyperparameters, and number of input points.

5.1. Soil Parameters

The results of the calculation of the model assessment indicators for the network input layer with the effect of the inclusion of soil parameters and without them are shown in

Table 3. Model evaluation indices considering influences of soil parameters on settlements.

Building Number	No Input of Soil Parameters			Input Soil Layer Parameters
	RMSE	MAE	R2	RMSE	MAE	R2
building F	0.18	0.16	0.94	0.20	0.18	0.94
building G	0.45	0.39	0.84	0.17	0.15	0.97
building H	0.36	0.31	0.71	0.32	0.29	0.98
building I	0.64	0.61	0.95	0.61	0.55	0.98
building J	0.24	0.21	0.89	0.26	0.22	0.96

.

As can be seen from Table 3, when the input layer is not inputted with soil parameters, the average values of RMSE and MAE are 0.37 and 0.34, respectively, and the mean value of R² is 0.87—the model performs better, and the prediction of building I is the best; while when the inputted soil parameters are inputted, the average values of RMSE and MAE are 0.31 and 0.28, respectively, and the mean value of R² is 0.97—the model performs better, and the prediction of building G is the best. Therefore, the input of soil layer parameters in the input layer of the LSTM-RA-ANN model leads to an improvement in the prediction accuracy: the mean values of RMSE, MAE, and R² are 0.84, 0.82, and 1.11 times higher than those when the effect of the soil layer is not taken into account, respectively, but the soil layer parameters do not have a significant overall effect on the model performance. Nevertheless, when the soil parameters are input, the predicted settlements are closer to the real ones, and the established model exhibits a better performance.

5.2. Location of Monitoring Points

The model performance metrics for monitoring points F1–F3 were obtained using the proposed LSTM-RA-ANN model (shown in

Table 4. Model evaluation indices considering influences of monitoring point locations on settlements.

Monitoring Point	Distance from Pit Edge (m)	RMSE	MAE	R2
F1	60	0.14	0.15	0.96
F2	55	0.18	0.17	0.95
F3	50	0.19	0.18	0.93

).

As can be seen from Table 4, the greater the distance of the monitoring point from the edge of the foundation pit, the better the assessment indicators. Compared with monitoring point F3, when the distance from the edge of the deep foundation pit increased by 5 m (F2), the RMSE decreased by 5%, the MAE decreased by 6%, and the R² increased by 2%; when the distance from the edge of the deep foundation pit increased by 10 m (F1), the RMSE decreased by 26%, the MAE decreased by 17%, and the R² increased by 2%. This is because the greater the distance from the edge of the deep foundation pit is, the further it is from the deep foundation pit construction area, the less it is affected by the deep foundation pit when it is being constructed, and the higher the prediction accuracy of the model is.

5.3. Activation Function

Different activation functions will have a certain impact on the prediction result when predicting sedimentation; this paper mainly compares the effects of three activation functions, relu (rectified linear unit), softplus, and tanh, on the prediction and evaluation indices of the LSTM-RA-ANN model. The relu function is a kind of linear and unsaturated activation function, which provides relatively wide activation boundaries, and can effectively solve the problem of gradient disappearance; the functional expression is Formula (6). The softplus function is similar to the relu function, but it is smoother than the corresponding curve of the relu function, and the functional expression is Formula (7). tanh is a saturated activation function, and the functional expression is Formula (8). Using different activation functions in the constructed LSTM-RA-ANN model, the calculation results of the model assessment indicators at monitoring point F1 are shown in

Table 5. Model evaluation indices under various activation functions for monitoring point F1.

Type of Activation Function	RMSE	MAE	R2
relu	0.16	0.17	0.95
softplus	0.25	0.19	0.89
tanh	0.29	0.20	0.90

.

$$\mathrm{relu}\left(x\right) = \max (0, x)$$

(6)

$$\mathrm{softplus}(x{) = \ln (1+\mathrm{e}}^x)$$

(7)

$$f(x) = \tanh (x) = \frac{2}{1+e^{-2x}}-1$$

(8)

As can be seen from Table 5, when using the proposed LSTM-RA-ANN model, it is optimal when using the relu activation function: compared to using the softplus activation function, the RMSE is reduced by 36%, the MAE by 11%, and the R² increases by 7%; and compared to using the tanh activation function, the RMSE is reduced by 45%, the MAE is reduced by 15%, and the R² increases by 6%. Therefore, the activation function has a greater impact on the model performance.

5.4. Hyperparameter

The hyperparameters in sedimentation prediction will have some influence on the model prediction results. Using the proposed LSTM-RA-ANN model, the calculated results of the model evaluation indices at monitoring point F1 with different hyperparameters (the initial learning rate, maximum iteration batch, and maximum iteration period) are shown in

Table 6. Model evaluation indices under various hyperparameters for monitoring point F1.

Hyperparameter Type	Hyperparameter Size	RMSE	MAE	R2
Initial learning rate	0.06	0.14	0.13	0.86
	0.08	0.16	0.19	0.85
	0.10	0.27	0.20	0.73
Maximum iteration batch	15	0.20	0.26	0.65
	20	0.14	0.14	0.79
	25	0.30	0.38	0.60
Maximum iteration period	400	0.13	0.15	0.80
	600	0.14	0.16	0.79
	800	0.12	0.14	0.82

.

As can be seen from Table 6, the model performs best when the initial learning rate is 0.06, the maximum iteration batch is 20, and the maximum iteration period is 800 when the proposed LSTM-RA-ANN model is used for the prediction of settlement at monitoring point F1. When the initial learning rate was increased from 0.06 to 0.08, the RMSE increased by 14%, the MAE increased by 46%, and the R² decreased by 1%; when the initial learning rate was increased from 0.06 to 0.10, the RMSE increased by 93%, the MAE increased by 54%, and the R² decreased by 15%. With a maximum iteration batch of 15 and 25, R² is only 0.65 and 0.60, respectively, which is 18% and 24% smaller than with a maximum iteration batch of 20. A maximum iteration period of 800 slightly outperforms the model at a maximum period of 400 and 600, but the difference is small. Therefore, the hyperparameters that have a greater impact on model performance are the initial learning rate and the maximum iteration batch.

5.5. Input Number

Using the proposed LSTM-RA-ANN model to predict the settlement of different buildings, the results of the evaluation index calculation when the number of input points is different are shown in Figure 11. From Figure 11a,b, the trends of RMSE and MAE are basically the same when inputting single-point and multi-point monitoring values, with the average values of RMSE being 0.50 and 0.31, and the average values of MAE being 0.46 and 0.28, respectively, From Figure 11c, the mean value of R² is 0.89, and the mean value of R² is 0.97. The mean values of RMSE, MAE, and R² are 0.92 times, 0.90 times, and 1.1 times higher than those of the single-point values, so the prediction accuracy of the multiple-point values is higher than that of the single-point values, but the difference is not significant.

6. Conclusions

In this paper, using the monitoring data of the settlement of the surrounding buildings triggered by the pit construction, an artificial neural network prediction model LSTM-RA-ANN (which stands for long short-term memory, residual, and attention-based artificial neural network), which integrates the attention mechanism and the residual updating, was established to analyse the prediction performance of the model for building settlement under three types of pit construction conditions, such as enclosure construction, earth excavation construction, and basement support construction, and obtained the following conclusions:

(1) The evaluation indices of the constructed LSTM-RA-ANN model are closely related to the construction conditions, and the average values of RMSE for the enclosure construction, earth excavation construction, and basement support construction are 0.50, 1.60, and 0.51, the average values of MAE are 0.46, 1.34, and 0.40, and the average values of R² are 0.89, 0.97, and 0.78, respectively, and the prediction accuracy of the great–small order corresponds to the following: basement support, enclosure construction, and earthwork excavation, respectively.

(2) When the LSTM-RA-ANN model is used to predict the building settlement, the average values of RMSE, MAE, and R² of the model without inputting the soil layer parameter in the input layer are 0.37, 0.34, and 0.87, respectively; the presence or absence of the soil layer parameter in the input layer does not have a significant effect on the overall performance of the model.

(3) The larger the distance between the monitoring point and the edge of the deep foundation pit, the better the model prediction performance: when the distance from the edge of the deep foundation pit is increased by 5 m, the RMSE decreases by 5%, the MAE decreases by 6%, and the R² increases by 2%; when the distance from the edge of the deep foundation pit is increased by 10 m, the RMSE decreases by 26%, the MAE decreases by 17%, and the R² increases by 2%.

(4) The activation function, the initial learning rate, and the maximum iteration batch have a greater influence on the prediction and evaluation indices of the LSTM-RA-ANN model; compared with the input single-point monitoring values, the average values of RMSE, MAE, and R² of the model change to 0.92, 0.90, and 1.10 times, respectively, when the input multi-point monitoring values are inputted, which has a slightly higher prediction accuracy but not much change in the overall performance.