Buried Pipeline Collapse Dynamic Evolution Processes and Their Settlement Prediction Based on PSO-LSTM

Abstract

Based on the unit life and death technology, the dynamic evolution process of soil loss is considered, and a pipe-soil nonlinear coupling model of buried pipelines passing through the collapse area is constructed. The analysis shows that after the third layer of soil is lost, the existence of the “pipe-soil separation” phenomenon can be confirmed, which then supplements the assumption that “pipe-soil is always in contact” in the elastic foundation beam theory. Calculation of settlement deformation of buried pipelines It needs to be divided into two stages: cooperative deformation and non-cooperative deformation. Taking the settlement prediction of buried pipelines as the goal, the particle swarm algorithm (PSO) was used to optimize the number of neurons, Dropout, and Batch-size in the long short-term memory network (LSTM) structure. The optimization results were 60, 0.001, and 100, respectively. The PSO-LSTM model proposed in this article can accurately describe the dynamic evolution process of buried pipelines and has better prediction accuracy than the modified Gaussian curve method and LSTM neural network model. The use of this model can provide a reference for safety risk management, disaster early warning, and intelligent monitoring when buried pipelines suffer from soil collapse disasters.

1. Introduction

Buried pipeline engineering is an important lifeline project for the country. However, the geological environment along the pipeline is complex and changeable, and collapse accidents occur frequently, causing huge losses to human life and property. Therefore, studying the dynamic evolution process of buried pipeline collapse and establishing a settlement prediction model to provide early warning and guarantee measures for the safe transportation of pipelines are important research topics to achieve sustainable development for mankind.

In recent years, many scholars have conducted a lot of research on pipe-soil collapse. In terms of mechanical analysis of buried pipelines under the action of soil collapse, most scholars’ research focuses on the establishment of a coupling model of pipe-soil action and the accurate results of the elastic foundation beam model. Although there have been a lot of studies on the mechanical analysis of buried pipelines suffering from soil collapse, there are few reports on the dynamic evolution process of buried pipeline collapse. In 2004, Iimura obtained monitoring settlement data to establish an elastic foundation beam model and proposed a stress prediction formula for buried pipelines in the settlement area [1]. In 2015, Kouretzis established a pipeline mechanics model for settlement and uplift and provided a simple method for calculating the internal force and strain of the pipeline [2]. In 2019, Kunyong established a model for the settlement of buried pipelines caused by tunnel excavation [3]. They gave the parameter that has the greatest impact on pipeline settlement as the elastic modulus of the soil and established the relationship between ground settlement and the settlement deformation of buried pipelines. In 2020, Wu carried out mechanical analysis work on buried polyethylene pipelines, and the results showed that the ground settlement rate has little effect on the ultimate bearing capacity of buried pipelines [4]. In 2022, Xiaohui studied the relationship between soil parameters, pipeline parameters, and settlement displacement under the action of foundation collapse and found that the mid-span pipeline had tensile stress and shear stress on both sides of the collapse zone [5]. In 2023, Pengchao established a stress prediction model for buried pipelines in melt settlement areas based on the support vector regression algorithm and gave working condition parameters to enhance the resistance of buried pipelines to deformation [6].

To sum up, the research focus of the above scholars in the field of pipeline engineering mainly focuses on the influencing factors of pipeline stress and strain and pipe-soil interaction. However, there is a relative lack of relevant research on the intelligent prediction of the non-uniform settlement of pipelines. In recent years, emerging neural network prediction methods have been widely proposed and used to reveal the inherent laws behind data due to their excellent autonomous learning and data analysis capabilities, especially in time series prediction. At present, some scholars have begun to apply neural network technology to the prediction of ground subsidence caused by engineering construction. Luobin used neural networks to establish a prediction model for ground subsidence caused by tunnel excavation [7]. Research results show that RNN (Recurrent Neural Network) exhibits higher stability and accuracy. Zhang used LSTM (long short-term memory network) in their research to predict the maximum surface settlement and longitudinal settlement curve caused by engineering construction [8]. Their research results showed that LSTM has excellent stability and can be applied to different types of projects. By comparing and analyzing different neural network models, it was found that, due to its good memory and selection functions, LSTM can comprehensively consider the spatiotemporal effects of deformation and settlement caused by engineering construction and the influence of construction parameters, thus demonstrating reliability and applicability in the prediction process. However, it should be noted that the prediction accuracy of the LSTM network is affected to a certain extent by the fluctuation of structural parameters, and improper network parameter settings may make it difficult to achieve the expected goals.

Based on the above research, this article adopts the PSO algorithm for parameter optimization, covering the number of neurons, Dropout, and Batch_size of the LSTM structure and comprehensively considering settlement data and related working condition parameters. A PSO-LSTM settlement prediction model was constructed to explore the dynamic evolution process of buried pipeline collapse. Based on the numerical analysis model of the dynamic evolution of buried pipeline collapse, the model is trained and tested using settlement data and corresponding input parameters. Three models, namely the modified Gaussian curve, LSTM, and PSO-LSTM, were used for comparative analysis of settlement prediction, which verified the reliability of the settlement prediction model based on PSO-LSTM proposed in this study for the dynamic evolution process of buried pipeline collapse. Based on unit life and death technology, this paper considers the dynamic evolution process of soil loss during the collapse process, constructs a pipe-soil nonlinear coupling model for buried pipelines passing through the collapse area, and uses the PSO algorithm to calculate the number of neurons, Dropout, and Batch- size to optimize parameters and establish a settlement prediction model for the dynamic evolution process of buried pipeline collapse based on PSO-LSTM. On the one hand, this model makes up for the inability of theoretical analysis methods to solve complex nonlinear problems, and on the other hand, it avoids the research difficulty caused by harsh experimental conditions. Compared with the traditional soil collapse simulation method of applying displacement load, this article adopts unit life and death technology. For applied research on collapse geological hazards, this technology can more realistically simulate soil loss during the gradual development of collapse. There is insufficient research content on intelligent prediction of the non-uniform settlement of pipelines. This settlement prediction model can provide a reference for safety risk management, disaster early warning, and intelligent monitoring when pipelines suffer from soil collapse disasters.

2. Pipe-Soil Collapse Analysis Model

Buried pipelines are laid under the surface, so the pipe-soil collapse analysis model is greatly affected by the surrounding soil. How to establish a reasonable pipe-soil interaction analysis model is particularly important. There are three main types so far: the elastic foundation beam model, the soil spring model, and the nonlinear contact model. The most famous elastic foundation beam model is Winkel’s local elastic foundation model. The principle is to simplify the foundation into many independent springs on a rigid base. The biggest disadvantage of this model is that it is mainly suitable for hand calculation and analysis of simple structures and is not suitable for large and complex structures. The core content of the soil spring model theory is to equate the soil medium around the pipeline into a series of springs, referred to as equivalent elastic-plastic springs. The degree of freedom of the spring depends on the movement form of the collapsed soil, and the stiffness of the spring depends on the soil quality of the soil covering the pipeline. The advantage of this model is that it is more computationally efficient than complex soil models. The disadvantage is that nonlinear behavior is ignored. Soil spring models are usually based on elastic behavior and therefore ignore the nonlinear behavior of soil, such as plastic deformation, friction effects, etc. In some cases, this may result in models with limited accuracy for soil behavior. The nonlinear contact model can truly describe the nonlinear friction process between pipe and soil. Existing numerical simulation research methods for soil collapse mainly use the method of applying displacement loads, and only some studies use unit life and death technology. This technology can more realistically simulate soil loss during the gradual development of collapse. Therefore, the pipe-soil nonlinear coupling model of buried pipelines passing through the collapse area constructed in this paper based on unit life and death technology is more in line with the applied research on collapse geological hazard problems.

2.1. Engineering Calculation Model

The ASCE-PD&C (2007) specification [9] provides a simple approximate calculation method to solve the problem of uneven settlement of pipe and soil. This method assumes that the bottom of the pipe is in constant contact with the soil and that the deformation curve of the soil is sinusoidal. This analysis method is elastic analysis, which has a certain guiding significance for nonlinear analysis. The uneven settlement deformation of pipe soil is shown in Figure 1.

Bending calculation theory used in engineering:

$$EI\frac{d^{2}y}{d{x}^2}=M$$

(1)

$$\frac{d^{2}y}{d{x}^2}=\frac{M}{EI}=\frac{1}{R}$$

(2)

where M is the bending moment, E is the elastic modulus, R is the radius of curvature, and I is the section moment of inertia.

Sinusoidal curve:

$$y=a\sin \frac{\pi x}{l}$$

(3)

where $l$ is the half-span length, $a$ is the deflection amplitude, and $\Delta$ is the total settlement displacement of the pipeline.

Mid-span curvature:

$$\frac{d^{2}y}{d{x}^2}=-a\frac{{\pi }^2}{l^2}=\frac{1}{R}$$

(4)

$$\Delta =2a$$

(5)

$$L=2l$$

(6)

The total pipeline settlement displacement can be obtained from Formulas (4)–(6):

$$\Delta =\frac{-L^2}{2{\pi }^{2}R}$$

(7)

Substituting Formula (1) into Formula (7), we can obtain the relationship between bending moment and settlement displacement:

$$\Delta =-\frac{L^{2}M}{2{\pi }^{2}EI}$$

(8)

2.2. Numerical Analysis Model

For the size parameters and boundary conditions of the physical geometric model, refer to Zhang Xu’s experiment [10]. The length of the pipe is 2.8 m, and the size of the tempered glass test box is 2.4 × 0.4 × 0.5 m³. The pipe is 20 cm longer than both ends of the test box, and slots are used to restrain the pipe. There is 25 cm of sand below the pipe, and two layers of dyed sand are laid above, totaling 4.5 cm thick. A strip with a width of 30 mm is placed under the test box, and a certain number of strips are extracted to simulate the collapse of the soil. A total of 90 cm sandbags were stacked above the test chamber, and three settlement markers were installed on the top of the pipe to record the settlement displacement of the pipe over time. The test model is shown in Figure 2.

The pipe material is PE100 pipe. Suileiman [11] studied the mechanical properties of pipes made of this material and proposed a hyperbolic constituent. As shown in Equation (9). The pipeline adopts the SHELL63 unit. Material parameters are shown in

Table 1. Pipeline material parameters.

Piping Material	Density (kg/m3)	Elastic Modulus (MPa)	Yield Stress (MPa)	Ultimate Stress (MPa)	Poisson Ratio
PE100	950	800	40	45	0.45

.

Hyperbolic constitutive equation:

$$\sigma =\frac{\epsilon }{a+b\epsilon }$$

(9)

The soil unit type is Solid45, and the constitutive model is the Drucker–Prager model [12,13]. Material parameters are shown in

Table 2. Soil material parameters.

Soil Type	Density (kg/m3)	Elastic Modulus (MPa)	Force of Cohesion (kPa)	Angle of Internal Friction (°)	Expansion Angle (°)	Poisson Ratio
sand	2000	10	20	20	0	0.3

.

The soil contact surface element type is Conta 174, and the pipe rigid surface element type is Targe 170. The two adopt the form of surface contact. The contact surface algorithm adopts the enhanced Lagrangian algorithm and the Coulomb friction model, and the friction coefficient is 0.4 [14,15,16]. The interaction mode of the contact surface is standard contact. The thickness of soil loss under the pipeline is 0.225 m. The soil loss process is divided into 8 steps. The parameters of the soil loss layer are shown in

Table 3. Soil loss layer.

Number of Layers	1	2	3	4	5	6	7	8
Thickness	0.016 m	0.032 m	0.032 m	0.032 m	0.016 m	0.032 m	0.032 m	0.032 m
Ratio	7.14%	21.42%	35.7%	49.98%	57.12%	71.4%	85.68%	100%

.

Boundary conditions [17,18,19] are imposed: vertical constraints are imposed on the front, rear, left, and right sides of the soil; fixed constraints are imposed on the bottom surface; and the top surface is free. A sandbag load is applied to the top surface to simulate the weight of the soil above. Vertical constraints are imposed on both ends of the tube. As shown in Figure 3.

2.3. Calculation Results and Analysis

Comparing the settlement displacement calculated by the pipe-soil finite element model established in this article with the settlement displacement recorded by the physical model test, the error is within 10%. The settlement displacement of the buried pipeline calculated using the engineering calculation model test formula 8 is compared with the finite element model results, and the error is within 5%. This error value shows that the results of this model are reliable. As shown in Figure 4.

It can be seen from Figure 4 that as the collapse width increases, the settlement displacement continues to increase. The collapse width is between 0.09 m and 0.27 m, and the settlement displacement increases rapidly. The collapse width is between 0.27 m and 0.54 m, and the settlement displacement increases slowly and levels off. This is due to the weakening of the pipe-soil interaction as the collapse width increases. The mechanical analysis of the dynamic evolution process of buried pipeline collapse is shown in Figure 5. (Note: In Figure 5 the color of the pipe represents the contact state of the pipe and soil; the red represents the contact, and the yellow represents the separation).

As the collapse process progresses, the Von-Mises stress and settlement displacement of the buried pipeline increase exponentially and have not reached the failure stress of the buried pipeline. As the collapse process progresses, the entire process, from the initial deformation of the pipe-soil structure to the tensile failure of the buried pipeline, can be divided into three stages: the top compression stage, the transition stage, and the bottom tension stage. Before the collapse depth reaches 80 mm, it is the top compression stage; between 80 mm and 160 mm, it is the transition stage; and after the collapse depth reaches 160 mm, it is the bottom tension stage. As the collapse process progresses, the distance difference between the settlement displacement of the soil and the settlement displacement of the buried pipeline gradually increases from zero. This shows that the pipe-soil deformation is coordinated in the early stage and non-coordinated in the later stage. When the collapse depth reaches 48 mm, “pipe and soil separate." This is because at this stage, the pipe initially sinks together with the soil, but the properties of the pipe and soil are different. The stiffness of the pipe is much greater than that of the soil. After a period of time, the pipe no longer moves together with the soil; the two movements appear to be out of sync. The pipeline begins to separate from the soil, and the suspended length continues to lengthen over time. However, the soil does not completely separate from the pipeline during this process, and the pipeline bears all the loads given by the soil. By comparing the section stresses at different locations of the buried pipeline, it can be concluded that the most dangerous section is the mid-span section. Through shear force and axial force, it can be concluded that axial stress is the control stress. By observing the stress levels at different locations in the same section, it can be concluded that the bottom of the pipe is the control point, and excessive tensile stress is the main cause of the failure of buried pipelines.

3. Dynamic Evolution Process of Underground Pipeline Collapse and Its Settlement Prediction

3.1. The Collapse Evolution Process of Soil Deformation

It can be seen from Figure 6, that with the loss of soil beneath the buried pipeline, the soil deformation shows the following characteristics:

(1)

First in the middle and then spreading to the surroundings, the middle deforms into a rhombus shape.

(2)

The maximum deformation continues to expand from the top downward until it penetrates the remaining soil.

(3)

In the early stage of penetration, the top deformation is greater than the bottom deformation. After penetration, it continues to develop, and the bottom deformation gradually becomes larger than the top deformation.

(4)

The maximum deformation of the soil develops from compression in the upper part to tension in the lower part as the soil loses.

3.2. Collapse Evolution Process of Buried Pipeline Deformation

It can be seen from Figure 7 that with the loss of soil beneath the buried pipeline, the deformation of the pipeline also shows similar characteristics to the deformation of the soil:

(1)

Diffusion occurs first in the middle and then around, and the middle deformation is a diamond.

(2)

The maximum deformation expands downward from the top until it penetrates the pipe.

(3)

In the early stage of penetration, the top deformation is greater than the bottom deformation. After penetration, it develops continuously. The tensile deformation at the bottom is slowly greater than the compressive deformation at the top. At the same time, the tensile area continues to expand from the middle to both ends.

(4)

The deformation of the pipeline is elliptical from the upper compression, and it is circular with the development of soil loss. The tops of both ends of the pipeline are compressed and developed into the tension of the middle collapse area.

3.3. The Collapse Evolution Process of Buried Pipeline Section Stress

As the collapse process progresses, the cross-sectional shape of the buried pipeline changes from crescent to oval and finally returns to a circle, as shown in Figure 8. This is because before the collapse begins, the buried pipeline is subject to the gravity load of the soil above and the support of the soil below. It reaches a mechanical balance, causing the cross-section of the buried pipeline to deflate into a crescent shape. As the collapse further develops, the soil below The loss of pipe leads to the continuous weakening of the support function of the lower part of the pipeline, and the cross-section of the underground pipe gradually returns from an elliptical shape to a circular shape. When the collapse depth reaches 192 mm, it completely returns to a circular shape. (Note: Point A is the top of the tube, point B is the bottom of the tube, and points C and D are points on both sides of the tube).

According to the literature [20,21,22], research shows that when the soil beneath the buried pipeline is lost, the maximum stress value of the pipeline appears at points A, B, C, and D of the pipeline cross-section. Therefore, in order to better analyze the failure mechanism of buried pipelines, we will further discuss and analyze the Von-Mises stress change rules at the top, bottom, and side of the cross-section of buried pipelines. As shown in Figure 9. The specific analysis is as follows:

(1)

In the early stage of collapse, that is, before the third layer of soil is lost, the stress on both sides of the pipe section is positive and in a state of tension. This is due to the squeezing effect of the soil on the pipe. As the collapse process evolves, the stress on both sides of the pipe section at the mid-span section position becomes negative and is in a compressed state. In the middle and late stages of collapse, that is, after the fifth layer of soil was lost, a new fluctuation value appeared between the edge of the collapse area and the middle of the span. This was due to the emergence of the “pipe-soil separation” phenomenon, accompanied by the generation of pipe-soil friction.

(2)

In the early stage of collapse, that is, before the third layer of soil is lost, the stress at the bottom point of the pipe section is negative and in a state of compression. As the collapse process evolves, the stress at the bottom point of the pipe section at the mid-span section is positive and in a state of tension. This is because with the loss of soil, the effect of soil weakens, and the settlement and deformation of the pipeline increase, resulting in increased tension at the bottom.

(3)

Before the fourth layer of soil collapses, the stress at the top of the pipe section is negative and in a state of compression. As the collapse process evolves, the stress at the bottom of the pipe section at the edge of the collapse area is positive and in a state of tension. This is due to the “step” shape of soil loss, which causes the bottom of the pipe to be sheared by the soil.

3.4. PSO-LSTM Settlement Prediction Model

This article refers to other people’s physical test models and calculation models provided by specifications to establish an analytical model of the dynamic evolution process of buried pipeline collapse. The analysis shows that the mid-span section is a dangerous section, the axial stress is the control stress, and the section control point is the bottom of the pipe. It is found that the characteristics of the collapse evolution process of buried pipelines and soil. The mechanical characteristic data, such as stress and structural deformation at different positions of the pipeline section, pipe-soil contact state, and settlement displacement during the dynamic evolution process of collapse, were obtained. Next, this article will establish a neural network prediction model and use its better independent learning and analysis capabilities to mine the inherent laws behind these mechanical characteristic data and output reasonable predicted settlement values.

3.4.1. LSTM structure

LSTM is a variant of Recurrent Neural Network (RNN) that aims to solve the problems of gradient disappearance and gradient explosion in RNN, making it better able to capture and remember dependencies in long sequences [23,24,25].

The main feature of LSTM is that it contains three gates and a cell state. These components work together to process sequence data. Here are the main components and functions of LSTM: The cell state is the internal memory unit in LSTM that can convey information throughout the sequence. Cell states can have information added or removed so that long-term dependencies are maintained. Input gates determine what information should be added to the cell state. It controls the importance of input information through the sigmoid activation function. The forget gate determines what information should be removed from the cell state. It controls the degree of forgetting of the cell state through the sigmoid activation function. The output gate determines which part of the cell state should be output to the next layer of the network, which is processed by a sigmoid activation function and a tanh activation function to generate the final output. Through the control of these gates, LSTM is able to effectively capture long-term dependencies as it can retain important information and discard unnecessary information, thus helping to avoid vanishing gradient or exploding gradient problems [26,27]. The specific principles are as follows:

(1)

Forgetting gate: The forgetting gate determines which information should be removed from the cell state. It controls the degree of forgetting of the cell state through the sigmoid activation function.

$$f^{\left(t\right)}=\sigma \left(W^{fC}{C}^{\left(t\right)}+W^{fh}{h}^{\left(t-1\right)}+b_f\right)$$

(10)

(2)

Input gate: The input gate determines which information should be added to the cell state. It controls the importance of input information through the sigmoid activation function.

$$i^{\left(t\right)}=\sigma \left(W^{iC}{C}^{\left(t\right)}+W^{ih}{h}^{\left(t-1\right)}+b_i\right)$$

(11)

$$g^{\left(t\right)}=tanh\left(W^{gC}{C}^{\left(t\right)}+W^{gh}{h}^{\left(t-1\right)}+b_g\right)$$

(12)

$$S^{\left(t\right)}=g^{\left(t\right)}\times i^{\left(t\right)}+S^{\left(t-1\right)}\times f^{\left(t\right)}$$

(13)

(3)

Output gate: The output gate determines which part of the cell state should be output to the next layer of the network and is processed by a sigmoid activation function and a tanh activation function to generate the final output.

$$o^{\left(t\right)}=\sigma \left(W^{oC}{C}^{\left(t\right)}+W^{oh}{h}^{\left(t-1\right)}+b_o\right)$$

(14)

Finally, combined with the output gate and the new internal state, the new hidden layer state $h^{\left(t\right)}$ is output.

$$h^{\left(t\right)}=tanh{S}^{\left(t\right)}\times o^{\left(t\right)}$$

(15)

3.4.2. Data Preparation

This paper selects 131 sets of settlement data from the numerical analysis model (each set of data has 1200 rows and 13 columns) and the corresponding working condition parameters: length along the pipeline, load sub-step, pipeline structural deformation at different positions in the section, axial stress of the pipeline at different positions in the section, and different cross sections. The positional pipeline Von-Mises stress, pipe-soil contact state, and settlement displacement are used as data sets, and the data set is divided into a training set and a verification set according to 8:2.

In order to improve the optimization efficiency of the optimization algorithm, the number of neurons, Dropout, and Batch_size are selected as the optimization objects of the PSO algorithm, and their value ranges are shown in

Table 4. Parameter range.

Optimization Parameters	The Number of Neurons	Dropout	Batch_Size
range	16–64	0.03–0.3	64–128

.

3.4.3. Model Building

Figure 10 shows the PSO-LSTM training process [28,29]. Randomly initialize the position information of each particle according to the hyperparameter value range. Secondly, an LSTM model is established based on the hyperparameter values corresponding to the particle positions, and the training data are used to train the model. Substitute the verification data into the trained model for prediction, and use the mean square error of the model on the verification data set as the particle fitness value.

3.4.4. Test Result

The particle swarm algorithm is performed based on the various parameters and constraints set above, and the resulting fitness change curve is shown in Figure 11.

As can be seen from Figure 11, when the number of iterations exceeds 2, the fitness value tends to converge, and the optimal solution of the population is selected when the number of iterations is 4 [number of neurons in the first layer, Dropout, Batch_size] = [60, 0.01, 100] is the combined value of the parameters to be optimized for the PSO-LSTM structure. When it reaches 12.5 epochs, the mean square error tends to be stable. At this time, the verification set of the model has reached good accuracy.

3.4.5. Results Comparison

To enhance the model’s evaluation reliability, we conducted a comparative study involving three prediction models: the modified Gaussian curve, LSTM, and PSO-LSTM. The results of the predictions are depicted in Figure 12.

As can be seen from Figure 12, LSTM can describe the development trend of the relationship between settlement displacement and the position along the pipeline, but the prediction accuracy is not good. The modified Gaussian curve performs well in predicting the settlement of buried pipelines in the mid-term of collapse but fails to make reasonable predictions in the early and late stages of collapse. Both PSO-LSTM and modified Gaussian curve fitting curves are better than LSTM, indicating that the parameter optimization method is effective and improves the prediction accuracy of LSTM, and the prediction accuracy of PSO-LSTM is higher than the modified Gaussian curve. It shows good trend prediction and has the highest accuracy throughout the collapse cycle, which shows that the model can dig out the length of the pipeline, load sub-steps, and pipe structure deformation at different positions in the section during the iterative training process. The internal laws of pipeline axial stress, pipeline Von-Mises stress at different positions of the cross-section, pipe-soil contact state, settlement displacement, and settlement value of buried pipelines output a more reasonable settlement prediction value. This shows that the model has better fitting accuracy and prediction performance and can predict the settlement of buried pipelines more accurately. The settlement prediction results obtained by using this model can provide real-time feedback on the operation of buried pipelines and provide timely early warning for safe pipeline transportation, thereby ensuring human production safety and avoiding property losses.

4. Discussion

4.1. Discussion on Soil Collapse Simulation Research Methods

For a long time, research on soil collapse has been mainly based on the mechanical analysis of the effect of soil collapse on buried pipelines [30,31], lacking the necessary dynamic evolution process of buried pipeline collapse. Soil collapse simulation techniques mainly include three types: manual removal of collapse areas, application of displacement loads, and unit life and death techniques. The method of manually removing the collapse area cannot simulate the nonlinear behavior of soil collapse and loss. The displacement load technology assumes that the surface along the collapse area has the same amount of subsidence and cannot truly simulate the distribution pattern of the displacement along the surface, which decreases from the center of the collapse to both sides. The unit life and death technology takes into account the dynamic evolution process of soil loss during the collapse process [32,33,34]. Since soil collapse is the result of the joint action of multiple factors and is concealed and sudden, in order to quickly and accurately predict the settlement displacement of buried pipelines, this paper constructs a settlement analysis of the dynamic evolution process of buried pipeline collapse based on the PSO-LSTM prediction model, which has higher prediction accuracy and a good prediction trend.

The above three different collapse simulation methods have concluded that there are certain differences in the mechanical analysis of buried pipelines subjected to collapse. In the discussion of dangerous sections, the applied displacement load method is used to simulate collapse. The dangerous section is located at the junction of the collapse area and the non-collapse area. However, the unit life-and-death technology used in this article simulates collapse, and the dangerous section is located in the mid-span. This is because the displacement load method is used, and the stress form of the buried pipeline is the strong shearing effect of the soil on the buried pipeline at the junction of the collapse area and the non-collapse area. Using unit life and death technology, the buried pipeline at the junction of the collapse area and the non-collapse area is subject to weak shearing by the soil. This is because with the loss of soil beneath the buried pipeline, the pipe-soil shearing effect continues to weaken, and this shearing effect has a great correlation with the cohesion, elastic modulus, and boundary conditions of the soil.

4.2. Discussion on the Generality of Research and Analysis Results

The pipe-soil nonlinear coupling model of the buried pipeline passing through the collapse area constructed in this article has been verified to a certain extent through on-site physical model tests and has been proven through the derivation of foreign normative theory publications that this model can provide a more accurate method. To predict the mechanical behavior of pipeline settlement caused by soil collapse. In addition, the main purpose of our work is to provide prediction and protection methods for engineering applications in buried pipeline-related fields. Nonetheless, the model proposed in this article can be modified and revised and may vary from region to region due to differences in local geological conditions. In order to study the damage mechanism of the collapse evolution process of buried pipelines, the settlement data used in this article cannot be 100% verified by the settlement data of actual projects. Further research in the future should use more on-site monitoring data on pipelines to obtain more consistent results. The actual foundation settlement characteristic data were collected, and relevant physical tests were carried out to verify the conclusions of the numerical model in this article.

4.3. Discussion on the Risk of Overfitting the PSO-LSTM Prediction Model

The PSO-LSTM (Particle Swarm Optimization-Long Short-Term Memory) model is a deep learning model that combines particle swarm optimization (PSO) and a long short-term memory network (LSTM). The goal of this model is to improve the performance of the model on the task by utilizing PSO to adjust the parameters of the LSTM. However, like other deep learning models [35,36,37], PSO-LSTM may also face the risk of overfitting, especially in tasks such as settlement displacement prediction. The following are the overfitting risks you may face when using the PSO-LSTM model: (1) If there is noise in the training data, the PSO-LSTM model may strive to adapt to the noise, resulting in overfitting to the training data. In this case, the model may perform well on the training set but poorly on unseen data. (2) The number of parameters in the PSO-LSTM model may be relatively large, especially when using PSO for parameter adjustment. If the model’s capacity is too large, it may learn details from the training data and fail to generalize to new data. (3) If the amount of available training data are insufficient, the model may rely too much on individual samples in the training set and fail to capture the distribution of the overall data. (4) During the training process, if the model goes through too many iterations, it may perform better and better on the training set, but there is no corresponding improvement in performance on the validation set or test set. This is a typical example of overfitting. Performance. (5) If too many or inappropriate features are selected during the modeling process, the model may overfit these features instead of the true data pattern. In order to mitigate the risk of overfitting the PSO-LSTM model, the following strategies can be adopted: (1) This article uses the regularization technology Dropout on the LSTM layer to reduce overfitting. (2) Use cross-validation to evaluate the performance of the model to ensure its generalization ability on different data sets. (3) Stop training when the model’s performance on the validation set no longer improves to prevent overfitting. (4) Increasing the amount of training data or introducing some changes through some data enhancement techniques can help improve the generalization ability of the model. (5) Carefully select features relevant to the task and avoid using too many irrelevant features. When establishing and adjusting the PSO-LSTM model, this article comprehensively considers the above factors to help the model reduce the risk of overfitting and improve its robustness and generalization ability.

5. Conclusions and Prospect

5.1. Conclusions

Based on unit life and death technology, this paper considers the dynamic evolution process of soil loss during the collapse process, constructs a pipe-soil nonlinear coupling model for buried pipelines passing through the collapse area, and uses the PSO algorithm to calculate the number of neurons, Dropout, and Batch- size to optimize parameters and establish a settlement prediction model for the dynamic evolution process of buried pipeline collapse based on PSO-LSTM. The following conclusions were drawn:

(1)

Based on the unit life and death technology, soil loss is simulated through the gradual failure of the mechanical effects of the collapse unit, which can accurately reflect the dynamic evolution process and mechanical characteristics of the collapse of the buried pipeline.

(2)

The axial stress is the control stress, the bottom of the mid-span pipe is the control point, and the mid-span section is the dangerous section. Excessive tensile stress is the main cause of the failure of buried pipelines.

(3)

Confirm the existence of the “pipe-soil separation” phenomenon, which occurs in the third layer of soil loss, and then supplement the assumption of the applicable prerequisite of “pipe-soil is always in contact” in the elastic foundation beam theory: settlement deformation of buried pipelines The calculation needs to be divided into two stages: cooperative deformation and non-cooperative deformation.

(4)

The collapse evolution process of buried pipeline deformation: first, the deformation first spreads from the middle to the surroundings, and the deformation in the middle takes on a “rhombus” shape; secondly, the maximum deformation continues to expand from the top downward until it “penetrates” the pipeline; the early stage of “penetration” is The deformation at the top is greater than the deformation at the bottom and continues to develop after “penetration”. The tensile deformation at the bottom is gradually greater than the compression deformation at the top.

(5)

Through the comparison of three settlement prediction models, the model in this paper shows good trend prediction and has the highest accuracy throughout the collapse cycle. This shows that the model can unearth the length of the pipeline, load sub-steps, top position of the pipe, position of the bottom of the pipe, positions of both sides of the pipe, material parameters, axial stress, pipe-soil contact status, and buried ground during the iterative training process. The internal laws of pipeline settlement values output a more reasonable settlement prediction value. The use of this model can provide a reference for safety risk management, disaster early warning, and intelligent monitoring when buried pipelines suffer from soil collapse disasters.

5.2. Prospect

Carry out mechanical analysis of buried pipelines using three different collapse simulation methods: manual removal of collapse areas, application of displacement loads, and unit life and death technology, and study the impact of soil cohesion, elastic modulus, and boundary conditions on the dangerous cross-section of buried pipelines. In order to further study the damage mechanism of the collapse evolution process of buried pipelines, relevant physical experiments were carried out to obtain more on-site measured data on buried pipelines to verify the relevant conclusions of this model.