**1. Introduction**

The high-speed railway (HSR) has become a common solution to relieve the pressure on transportation systems worldwide, especially in China. HSR provides a fast and robust travel option that enhances the movement of people as a critical national infrastructure system. In China, the construction of HSR is extending to the mountainous areas; the poor construction environment and the complex and diverse climate make the construction personnel face various risks, some of which even threaten the safety of life [1]. When the HSR line passes through adverse geological sections, manual excavation and reinforcement are required [2]. Accidents such as slope instability, slump, gushing water, mechanical injury, electric shock, and falls are prone to occur during slope construction [3]. Especially in recent years, more and more slope disasters have caused extensive losses worldwide of human life and property [4]. Therefore, it is vital to develop a safety risk assessment system to avoid or mitigate those slope disasters.

The high cutting slope refers to a soil slope with a height greater than 20 m and less than 100 m or a rocky slope with a height greater than 30 m and less than 100 m [5]. The study of high cutting slope construction originated from the study of slope stability, which is important for the safety of slope construction. Slope stability is generally influenced

**Citation:** Huang, J.; Zeng, X.; Fu, J.; Han, Y.; Chen, H. Safety Risk Assessment Using a BP Neural Network of High Cutting Slope Construction in High-Speed Railway. *Buildings* **2022**, *12*, 598. https:// doi.org/10.3390/buildings12050598

Academic Editors: Yongjian Ke, Jingxiao Zhang and Simon P. Philbin

Received: 18 March 2022 Accepted: 1 May 2022 Published: 5 May 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

by soil, hydrology, vegetation, earthquakes, climate, geological conditions, groundwater, slope height, slope rate, and other factors [6]. The study of risk in slope engineering started in the 1980s, and the initial stage of the research was mainly to clarify the existence of inherent uncertainty in geotechnical engineering and to try to characterize the uncertainty of geotechnical engineering by using probabilistic methods [7].

Current studies generally use reliability analysis, the limit equilibrium method, and the strength reduction method for slope stability. Reliability analysis was applied to the study of slope sexual stability using soil parameter data extracted from field and laboratory data, and the relative contribution of the uncertainty of different parameters to slope reliability varies [8]. The impact of uncertainty on the reliability and performance evaluation of slope design is often significant. Traditional safety factor-based slope practices can not explicitly address uncertainty and thus affect the adequacy of predictions [9]. For simple homogeneous soil slopes, the calculation results of the limit equilibrium method and strength reduction method are essentially the same [10].

For slope construction safety, the stability of slopes has also been analyzed using kinematic laws and digital elevation models. Ref. [11] used kinematic laws and digital elevation models for the study area to develop probabilistic risk maps for planar, tipping, and wedge damage. By comparing the actual fault distribution in the area with the probabilistic risk map prepared for the study area, it was found that the identified faults were located in the higher risk areas on the probabilistic risk map. Ref. [12] analyzed the fundamental changes of a particle subjected to flow dynamics, deposition, and erosion processes at high slope angles. Ref. [13] developed a nonlinear mathematical model for the degradation of sensitive clay soils after peak undrained shear strength based on experimental results.

In summary, the existing research mainly focuses on the stability analysis of slopes and the analysis of landslide hazard risk during the operation period of HSR, while the research on the safety risks occurring during the construction period of HSR is relatively rare. In actual engineering practice, the existing analysis of sliding stability of high cutting slopes mostly adopts the deterministic analysis method, which determines whether the damage will occur by calculating the safety coefficient of anti-sliding stability. The deterministic analysis method is more frequently used because the calculation is relatively simple and the result is more intuitive. However, there are a lot of uncertain parameters in the actual construction process of the high cutting slope of HSR, and the deterministic analysis method can not consider the influence of parameter uncertainty. Therefore, consideration of random factors and their construction dynamics in the analysis of the high cutting slope of HSR deserves further discussion and has important research value.

In 1943, the first neuronal M-P model was proposed by McCulloch-Pitts, and the research on neural networks began [14,15]. Since then, more derivative models of neural networks have emerged. After Rosenblatt's first perceptron model in 1957, many influential models have been proposed [16,17]. Neural networks rapidly developed and were used within different fields [18]. Neural networks have various functions, such as learning, training, simulation, storage, and error removal, which allow them to develop rapidly in many fields and achieve great success in signal processing, pattern recognition, etc. In recent years, more and more scholars have applied them in the research of artificial intelligence [19–25]. Scholars have applied BP neural networks to construction risk assessment and achieved a large number of results, which fully demonstrate the feasibility of BP neural networks for construction risk assessment [2,26–28]. A BP neural network is a nonlinear dynamical system that constructs a model to realize nonlinear analysis by learning and understanding historical data. Compared with the conventional linear analysis methods, a BP neural network has the following advantages [29,30]: (i) it can process data with ambiguous feature performance and logical relationships; (ii) it can process nonlinear characteristic random noisy data; and (iii) it does not require an in-depth understanding of the simulation process. In the case of having more uncertainty, the neural network model can fully

demonstrate its superiority in processing data. Based on the above advantages, a BP neural network was selected as the model for risk evaluation in this study.

The paper is organized as follows. Section 2 introduces the data and methods, which includes factor identification and classification (Sections 2.1–2.3), construction safety risk assessment index system (Section 2.4), risk classification criteria (Section 2.5), and assessment model (Section 2.6). Section 3 presents a case study to verify the practicality of the proposed model and discusses the results, then, major conclusions and implications are drawn (Section 4).

#### **2. Data and Methods**

Many factors that are not interconnected are stimulated by a certain condition to produce a chain reaction leading to the existence of risk. Thus, the existence of accidents is not caused by a single factor. The construction safety risk of the high cutting slope of HSR has the characteristics of suddenness, damage, complexity, objectivity, and development. This also determines the unpredictability and diversity of its risk-influencing factors.

This study started with the technical specification of railway roadbed risk management to grasp the process of high cutting slope engineering of HSR and the common accidents and problems in the process of slope construction. Our goal was to make it easier to understand construction safety risks. Through literature review and practical research on slope stability, the main influencing factors of instability were studied. The occurrence of accidents is often related to people, materials, the environment, construction management, and other factors. Therefore, through the collection of relevant information and cases to supplement the construction safety risk factors of HSR, the personnel factors and construction management factors were fully considered to form a comprehensive list of construction safety risks.

#### *2.1. Construction Safety Risk Identification Based on Technical Specifications*

Technical code for risk management of railway subgrade engineering [31] gives the influencing factors of the construction safety risks of the high cutting slope, which play a reference role in the selection of risk factors in this study. Construction safety risk factors identified for the high cutting slope in HSR are shown in Table 1.


**Table 1.** Construction safety risk factors based on technical specifications.

#### *2.2. Construction Safety Risk Identification Based on Documentary Data*

Through combing and screening statistics of related literature, the factors affecting the construction safety of the high cutting slope in HSR were derived, as shown in Table 2.


**Table 2.** Construction safety risk factors based on literature.

#### *2.3. Construction Safety Risk Identification Based on Statistical Analysis of Cases*

The construction safety risk identification was carried out through the high cutting slopes related to HK and HSH, two high-speed railways in China, and the risk identification table for the statistical analysis of the cases was formed as shown in Table 3.

**Table 3.** Construction safety risk identification based on statistical analysis of cases.


#### *2.4. Construction Safety Risk Assessment Index System for High Cut Slope of HSR*

Through SPSS software for analysis, combined with engineering practice, the construction safety risk factors were classified and summarized according to the principle of systemic feasibility. The secondary risk indicators include 5 items such as personnel risk, and the tertiary risk indicators include 39 items such as earth excavation. The risk assessment index system is formed in Table 4.

**Table 4.** Safety risk assessment index system for high cutting slope construction of HSR.


#### *2.5. Risk Classification Criteria of Safety in Construction*

With a large number of risks and a variety of risk control measures in the construction of high cutting slopes in HSR., it is necessary to evaluate risks reasonably, effectively, and objectively, select appropriate risk control measures, and carry out scientific engineering decisions and risk evaluation. A key part of the evaluation is the need to study the corresponding risk acceptance criteria and control countermeasures. According to the Technical Code for Risk Management of Railway Construction Engineering [47], the risk acceptance criteria for high cutting slopes in HSR are shown in Table 5.

**Table 5.** Risk acceptance criteria.


*2.6. BP Neural Network Model*

2.6.1. Design of Network Topology

According to the risk assessment index system established above, combined with the BP network theory, three levels of indicators are used as the input layer, and risk levels are the output layer. Among them, the input layer has 39 indicators, and the output layer is the project risk level. The trial-and-error method was adopted to determine the number of hidden nodes corresponding to the fastest convergence and smallest error of the network. The operating mechanism diagram is shown in Figure 1.

2.6.2. Select the Activation Function of the Feedforward Neural Network

In this model, the maximum number of trainings is set to 20,000, after which the training is terminated. The error accuracy is set as 1 × <sup>10</sup><sup>−</sup>6, and the operation is terminated when the accuracy is less than this error number. The model of this training is nonlinear, and the data need to be normalized to a certain extent before being brought in; therefore, the S-type function was chosen for this model.

#### 2.6.3. Selection of Samples

The processing of samples directly affects the generalization mapping ability of BP networks [48]. When selecting the samples, we need to consider the engineering requirements and characteristics [49,50]. In this study, the sample parameters were obtained via a questionnaire survey; a total of 216 high cutting slopes in HSR of HK, HF, YG, and HSH were selected for the collection. The data were quantified by combining Table 7 and the method of expert interrogation. If the collected samples are evenly distributed, it is more conducive to the training of neural networks and can make a better prediction of the risk level of the cases.

#### 2.6.4. Pretreatment of Input and Output Data

The collected data were divided into input data and output data, of which 80% were used as training samples and 20% as testing samples. The processed data of input nodes were regarded as the input layer, which was denoted by *x*. The processed data of output nodes were regarded as the output layer, which was denoted by *y*. In this study, the number of samples obtained was 216, denoted by m. The network inputs and outputs are shown in Table 6.

**Table 6.** Inputs and outputs data of network.


Each indicator has a different dimension; if the initial data are used directly, it will be difficult to ensure that indicators are in the same dimension, which will make the BP network converge slowly. If the indicators have the same dimension, the S-shaped function in the BP network can be fully utilized and the saturation area of the function can be avoided, thus enhancing the sensitivity of the BP neural network to the indicators. Therefore, it is important to reduce the magnitude of the variation of the sample values and to lock the interval of the definition domain of the samples within a certain range. This ensures that the derivative values of the input function are within the appropriate interval and have an important role in the training of the neural network and the prediction of the samples. Therefore, in this study, the collected sample data were normalized to reduce the magnitude variation of the predicted values. Firstly, each risk indicator was evaluated by the table of construction safety risk assessment of high cutting slopes in HSR (Table 7) and the method of expert interrogation. The statistical data were then normalized to obtain the risk value of relevant indicators. For example, the transformation of construction technology risk (CT) is shown as Formulas (1)–(3). The expression of the input value of the whole indicators system is shown as Formula (4).

$$CT\_i = \sum\_{j=1}^{11} CT\_{ij} / 11 \ i = (1, 2, \dots, 11) \tag{1}$$

$$CT\_i = \frac{ct\_i - X(\text{min})}{X(\text{max}) - X(\text{min})} \ (i = 1, 2, 3, \dots, 11) \tag{2}$$

*CT* = (*CT*1, *CT*2,..., *CT*11) (3)

$$All = \begin{pmatrix} \mathbf{C} \mathbf{T} \mathbf{'} \mathbf{M} \mathbf{E} \mathbf{'} \mathbf{P} \mathbf{'} \mathbf{E} \mathbf{'} \mathbf{C} \mathbf{M} \end{pmatrix}^T \tag{4}$$

**Table 7.** Construction safety risk evaluation levels.


According to Table 5, combined with engineering practice, the construction safety risk evaluation levels can be divided into four levels, as shown in Table 7.

#### 2.6.5. Selection of Initial Parameters

In this study, the BP neural network toolbox in MATLAB was used for simulation training, and the appropriate model parameters played a decisive role in the training quality and accuracy. The network creation function was debugged in the toolbox operation interface of the BP neural network, which is the first step to building the network object. Then, the transfer function was debugged. The transfer function represents the input and output objects with a correlation function using the logsig function. The learning function is to adjust the local error value size, and the training function is to adjust the global error value size; learngdm was chosen as the learning function, traingdx as the training function, and the network error performance function was the default MSE function of the toolbox. The network model parameters are set in Table 8.

**Table 8.** BP network model parameters.


2.6.6. Objective Function of Network Training

The initial expected predicted value of the objective function is *Xk*(*k* = 1, 2, ··· , *N*), the output value of the final function is ∧ *Xk* = (*k* = 1, 2, ··· , *N*), and the prediction error e is *e* = (*e*1,*e*2, ··· ,*eN*) = *<sup>x</sup>*<sup>1</sup> <sup>−</sup> <sup>∧</sup> *<sup>x</sup>*1, *<sup>x</sup>*<sup>2</sup> <sup>−</sup> *<sup>x</sup>*2, ··· , <sup>∧</sup> *xN* <sup>−</sup> <sup>∧</sup> *xN* . In the study, *SSE* was used to represent the evaluation value of neural network training maturity, which is shown in Formula (5).

$$SSE = \frac{1}{2} \sum \left( \mathbf{x}\_k - \stackrel{\wedge}{\mathbf{x}}\_k \right)^2 \tag{5}$$

where, *xk* is the expected output and <sup>∧</sup> *xk* is the actual output.

Simulation training was performed according to the neural network toolbox to achieve the minimum error criterion. If the trained neural network does not meet the error criterion, the BP neural network model parameters need to be readjusted to achieve a suitable neural network structure.

#### 2.6.7. Selection of Output Node

The output node refers to the final information output, which is also the global control of the neural network training. The output nodes should be selected with reasonable and high credibility as often as possible to facilitate the collection of data and to normalize the sample data to obtain the output data that are beneficial to the neural network training. The sample data of the output nodes in this study were based on the risk levels corresponding to Table 7.

#### **3. Results**

#### *3.1. Case Background*

Hefei-Fuzhou HSR is an important part of Beijing-Fuzhou HRR; DK592 + 532.00~ + 562.00 is a section of the high cutting slope (Figure 2). The area is low and hilly with gentle terrain and developed vegetation. The groundwater is bedrock fracture water, which is more developed. The groundwater is not chemically erosive (judged by the chloride ion content, without chloride salt erosive).

**Figure 2.** The high cutting slope of section DK592 + 532.00~ + 562.00.
