The China National Highway 109 New Line Expressway (Beijing Sixth Ring Road-City Boundary Section) (Figure 1), with a total length of 69.2 km, starts from the Beijing Sixth Ring Road to the east and ends at the Zhangjiajie city of Hebei Province. It serves the two cities and plays a vital role in communication and social development. To better include and assess the existing landslides and potentially related geohazard chain, the watersheds of the mountains on both sides of the line are taken as the research boundary. Compared with the equidistant expansion of 200 m along both sides in the traditional manner, it was helpful to take high-level disasters into account (Fan et al., 2019a).

The total study area of 628 km² was a typical mountainous landform with sandstone and basalt as the main strata, with only a few small inactive faults. According to remote sensing interpretation and the on-site investigation, 126 landslide disasters were found. All landslides were randomly distributed on two sides of the highway.

Different assessment models have significant impact on the results of landslide susceptibility mapping. At present, the commonly used landslide susceptibility evaluation models can be divided into knowledge-driven, data-driven, and physical model-driven models (Reichenbach et al., 2018). The knowledge-driven type of model has greater subjectivity, while the physical model-driven type requires a large number of accurate mechanical parameters, which limits the application of these two methods. Practice has proven that data-driven models have higher accuracy than the other two types (Reichenbach et al., 2018; Chen and Li, 2020). With the development of artificial intelligence, the machine learning model has become the most popular model in data-driven models, and a large amount of work has proven that the evaluation result of the machine learning model is better than that of the traditional statistical model (Reichenbach et al., 2018; Chen et al., 2021; Zhao et al., 2021). The common machine learning models include the random forest model, decision tree model, support vector machine, Bayesian model, and god-level network model. Each model has its advantages and disadvantages (Table 1).

Recently, scientists have also begun to apply the maximum entropy model, which was originally used and is still popular in the field of species habitat suitability assessment (Merow et al., 2013), in the evaluation of landslide susceptibility. The evaluation results have been effective and better than models as support vector machines and artificial neural networks (Chen et al., 2017; Teimouri and Nalivan, 2020). At the same time, according to the basic theory of landslide assessment, future landslides will occur in similar areas where landslides have occurred in the past, which is consistent with the basic theory of species habitat suitability assessment (Reichenbach et al., 2018). Therefore, the choice of a maximum entropy model could achieve a better result to support linear engineering optimization and further verify the suitability of this interdisciplinary evaluation model for landslide assessment to enrich the optional model and guide actual production.

MaxEnt is a machine learning model that quantitatively calculates the probability of landslide occurrence in the evaluation area using the Bayesian rule based on the geological environment indicators of the training landslide (Rahmati et al., 2016). The specific calculation principle is that the study area is divided into a finite pixel set X, with the assumption that x represents each computing unit. Then, x∈X in the study area and π(x) represents the probability distribution value of landslide occurrence in each computing unit 0<P(x) < 1. The sum of the probability values of all computing units is 1. The landslide value of the calculation grid is taken as the response variable y, if the calculation unit has a landslide, y = 1, otherwise it is 0. Therefore, the probability of the landslide conditional distribution P(y|x) can be expressed as follows: P ( y = 1 | x ) = P ( x | y = 1 ) P ( y = 1 ) P ( x ) , (1)

where P(y = 1|x) is the probability of a landslide at a specific point x; P(y|x = 1) is the probability of a landslide at a specific point x under the landslide distribution conditions, which is also π(x); P(y = 1) is the overall incidence of landslides; and P(x) is the probability of landslide occurrence at any point x.

Since P(x) indicates that any point x of all calculation units X in the study area is equal to 1/∣x∣, the aforementioned formula can be transformed into the following equation: P ( y = 1 | x ) = π ( x ) P ( y = 1 ) | X | . (2)

Considering the probabilities of landslide occurrence and nonoccurrence are equal, namely [P(y = 0) = P(y = 1) = 0.5], the equation can be further simplified as follows: P ( y = 1 | x ) = P ( x | y = 1 ) P ( x | y = 1 ) + P ( x | y = 0 ) . (3)

The application of the MaxEnt model directly depends on the conditional probability P(y = 1|x). The larger the conditional probability is, the greater the possibility of landslide occurrence will be. The event occurrence data π(x) can be used for modeling, instead of directly estimating P(y = 1|x). The value of π(x) estimated with the principle of maximum entropy is equal to the Gibbs probability distribution represented by the exponent. If n features (f _i , i = 1, 2,…,n) are considered, the Gibbs probability distribution can be defined as follows: q λ ( X ) = exp ( ∑ i = 1 n λ i f i ( x ) ) Z λ . (4)

In the formula, Z_λ is a normalization constant to ensure that the sum of q _λ (x) is 1. In the estimation of q _λ (x), the model uses the regularization I ₂ to find the distribution closest to the constraints to avoid overfitting. Therefore, the MaxEnt model maximizes the processing of log-likelihood. If the event occurs m times within the study area, the difference between the log-likelihood and the regularization should be maximized, which is expressed as follows: 1 m ∑ i = 1 n I n [ q λ ( x i ) ] − ∑ j = 1 n β j | λ j | , (5) where β _j is the regularization parameter of the jth feature f _j . The maximum entropy model finds that the Gibbs distribution not only conforms to the existing data but also has good generalization significance.

The landslide susceptibility mapping based on the MaxEnt model mainly included the following steps.

1 Building an assessment index system: collecting landslide database elements, such as geological maps, digital elevation models, and other data, to determine the evaluation index system;

The data source of used indexes in this study is given in Table 2. All the layers are resampled to 30 m resolution on the pixel. All the indicators can be seen in Figure 2. The quantitative evaluation of the landslide susceptibility could be achieved by setting the distribution ratio of the training data and the verification data, the number of training times, and the output type recommended by Merow et al. (2013). The main parameters that needed to be set were the data split ratio and the training times. The rest of the parameters were related options such as whether to produce the ROC curve and the output type. According to the previous studies (Merow et al., 2013; Chen et al., 2017; Reichenbach et al., 2018), 80% of the landslide data of the 126 landslides, about 111 landslides, were used for the training of the model, and the remaining 20% landslide were used for the verification model. The number of training times for the model was 100. The calculation output type was a logical calculation, and the output format was the ASCII type. The line for jackknife analysis options was selected (Figure 3).

Using the receiver operating characteristic curve and the area under the curve, the model accuracy and the partition results were tested. As shown in Figure 4, the training model value reached 80.2%, and the verification accuracy reached 82.1%. According to the evaluation standard of the ROC–AUC value (Reichenbach et al., 2018), the value of the ROC–AUC was good when the value was calculated between 0.8 and 0.9. Therefore, both model training and verification achieved good prediction accuracy, and the results had a certain credibility.

The calculated value of the MaxEnt model was in the range from 0 to 1. The larger the value was, the greater chance there was that the landslide was prone to happen. The results were divided into five categories using the natural breakpoints, namely, the very low-susceptibility area (0–0.144), low-susceptibility area (0.114–0.296), medium-susceptibility area (0.296–0.436), high-susceptibility area (0.436–0.584), and very high-susceptibility area (0.584–0.993). The spatial distribution of the landslide susceptibility grades is shown in Figure 5. It can be seen that very high-susceptibility areas of landslides were mainly distributed on two sides of the middle section of the newly built line, and the ends of the east and west sides near the cities experienced heavy human activity. The very low- and low-susceptibility areas were distributed in places without human influence or with few human influences.

With the help of grid statistical analysis tools on the GIS platform, the areas of different levels can be quantified. As shown in Figure 6, very low-susceptibility landslide-prone areas accounted for 2% of the total, the low-susceptibility landslide-prone areas accounted for 10%, the medium-susceptibility landslide-prone areas accounted for 16%, the high-susceptibility landslide-prone areas accounted for 32%, and the area of very high-susceptibility level accounted for 40%. In the results of the landslide susceptibility mapping, 90 (72%) of the 126 landslides were located in two categories: high-susceptibility area and very high-susceptibility area.

At the same time, to better evaluate the usefulness of the results, we used the %LR_class index to evaluate the prediction performance. The criterion of the %LR_class index was defined according to the area ratio of each grade predicted by the model and the proportion of predicted landslide points. The greater the value of %LR_class was, the better the prediction result of the model would be. This index %LR_class = S/A, where S is the proportion of landslide sites in each stability grade and A is the area of each stability grade predicted by the model. After calculating the index to be 2.25, it was determined that the evaluation results had an excellent performance (Chen et al., 2017; Viet et al., 2018). Therefore, the assessment results were comprehensively evaluated in terms of the performance of the model from different aspects. All the results showed good directness, and they could be used to support linear engineering optimization.

Using the GIS extraction tool, the pixels of the different susceptibility levels of the new and old highways were passed through. It was found that for the new highway, as marked by a continuous dark line in Figure 7, only 10% was in the very high-susceptibility area, and the other four levels were distributed evenly, at about 20%. However, for the old highway, as marked by a dash dark line in Figure 7, 26% of the highway was in a very high level, 32% was in the high-susceptibility areas, 25% was in the medium-susceptibility areas, and the low- and very low-susceptibility areas together only made up 17%. Therefore, the newly built road faced fewer threats than the old road, especially in very high- and high-susceptibility regions, which had reduced threats of about 16% and 13%, separately, which also supported the necessity of building the proposed road and the rationality of the new route selection work.

Selecting the jackknife option in the MaxEnt model could reveal the impact of different evaluation indicators on the susceptibility evaluation results (Merow et al., 2013; Chen et al., 2017). After the calculation of the changing relationship between one index and the corresponding ROC value, the contribution rates of all the assessed indexes could be exported. As shown in Figure 6, all the indexes for the evaluation results were greater than zero, indicating that all of the indicators had certain roles for the model. Additionally, it could be seen that the six indexes, namely, the slope, aspect, distance from the road, NDVI, elevation, surface roughness, and land use type, had nearly a 90% impact on the landslide evaluation results in total, while the other indexes contributed less to the landslide rate.

The results of this analysis were consistent with field surveys and related experiences (Su et al., 2021). The slope aspect affected the weathering of the rock and soil, which in turn affected the internal mass movement after the infiltration of rainwater. The distance from the road reflected the negative effect of human activities on the local environment. The NDVI represented the ecological restoration after the occurrence of landslides (Tehraniand Janalipour, 2020). Sparser than the stable slope area, the corresponding NDVI value was also smaller, and it could thus be used to distinguish the landslide area and the non-landslide area (Tehrani et al., 2021). The elevation affected the in situ stress distribution, weathering, and other factors of the slope. The surface roughness indicated the difference between the landslide occurrence area and the non-landslide area after mass transport.

The facts determined by Hakan (2022) are interesting and remarkable. Compared with the study area in Arhavi and this research, it was clearly shown that the roads passed through different landforms and construction technology (Tanyas et al., 2020). The former road was mainly located on the mountainside, which caused two more types of damage to the upper and lower slopes, compared to the majority on the slope toe in the road for this research. At the same time, the road in this research was planned to have a low retaining wall at the foot of the slope influenced by cutting regions and vegetation recovery actions, rather than simply leaving the soil and rock exposed.

It should be noted that while humans have caused many deadly landslides for engineering projections, there have also been numerous conveniences for people’s lives. However, compared with earthquake-induced landslides that have almost occurred during a short period, road-related landslides need a longer time to evolve to an unstable status. Hence, this provides more time and opportunities to prevent unfortunate events. Previously determined facts (Fan et al., 2019b; 2019c) have strongly proven that proper low-cost monitoring equipment can achieve successful landslide warnings before landslide failure to prevent property damage.

At the same time, as shown in Figure 7, the new road shows a better situation than the existing road from the aspect of length percentages in different susceptibility levels, but it should be noted that the situation may change from a low threat to a middle or high threat with new road and frequency of human activities involved.