*2.2. Classification of Forest Road Segments*

The Forest Road Facility Failure Assessment Document obtained for this study does not record the type of failure. In other words, it is not possible to determine whether the failure is the road surface, cut slope, fill, or road body. However, since the location data of the failures are recorded, the topographical features of failures can be clarified by analysis. Since it is possible to infer to some extent the causes of road failure from the topographical features of the failures, we decided to classify failures from the viewpoint of topographical features.

**Figure 3.** Number of forest road routes and failures analyzed. (**a**) Two hundred-seven routes where the failure occurred were included in the analysis. (**b**) Failures for which location information on both the failure and the forest road route has been developed are included in the analysis.

**Figure 4.** Distribution of the number of failures according to route.

To accurately assess the risk of failure, it is desirable to consider the presence or absence of structures, such as drainage facilities, as well as their types and functional status. However, in order to conduct an analysis that takes structures into account, it is necessary to record the presence and absence of structures, their types, and their functional status prior to the occurrence of a failure. In this study, due to the availability of data, it is not possible to obtain information on structures prior to the occurrence of the failure since the study deals with forest road failure that occurred from 2006 to 2010. Therefore, the structural information was not considered in the analysis of the failure in this study. Even if the above structural information could be obtained and failure classification was performed considering both structures and topography, it is expected that the results would be complicated because a single failure belongs to multiple categories. Since the purpose of this study is to statistically understand the morphological characteristics of the elucidated failure events rather than to strictly describe the risk of forest road failure, we believe that a concise approach to classifying failure based on topographical factors alone is effective. Even without considering structural information, the identification of topographic features that are prone to forest road failure can, paradoxically, identify the characteristics of areas where structures are not functioning properly.

Referring to previous studies [16–20], forest road segments were classified into three categories, namely streamsides, including stream crossings (Figure 5), around concave landforms such as zero-order basins (Figure 6), and "others" that do not fall into either of these categories. A category for the slope was also considered. However, steep slopes were not included in the categories because they are a more universal landform type and could be mixed with other landform types, complicating categorization. Lithology and geology were not included for the same reason. In Japan, the Geospatial Information Authority of Japan provides spatial information on landslide landforms, geology, and faults. However, not all landslide landforms and faults have been databased, and it is possible that some small-scale landslides, especially in short sections of forest roads, have not been extracted, so they were not used in the evaluation categories. However, since a high-resolution DEM was used in this study, it is likely that the characteristics of erosional landforms, such as fault zones and landslide landforms, were also taken into account as erosion heights, which will be discussed later.

**Figure 6.** Image of a forest road segment that falls into the zero-order basin category. Note: The points in the figure represent the center coordinates of the segment.

First, each forest road was equally divided into 5 m intervals. The division process is performed by creating a new apex every 5 m from the beginning point of the forest road. The apex of the division' refers to each vertex created by this process. In this study, the apex of the division represented the center of the forest road segment. The presence or absence of forest road segment failure was determined based on the positional relationship between the forest road segment feature and the failure feature. First, line features (vertex interval: 5 m) were created from The Forest Road Facility Failure Assessment Document to indicate the forest road segments where forest road failure occurred. Next, a nearest neighbor search was conducted from each vertex of the failure line feature to the forest road segment center point set. The forest road segment that corresponded to the nearest neighbor was defined as the damaged segment.

Next, the forest road segments were classified into three categories using a Digital Elevation Model (DEM). The DEM used was a 1 m resolution DEM created from an aerial laser survey conducted by Nagano Prefecture in 2013, which was resampled to a 5 m resolution.

#### 2.2.1. Streamside

The raster data representing the water system lines were converted into vector data, which were equally divided into 5 m intervals, as was the case with forest roads. The nearest waterline vertex was searched from each forest road vertex, and its distance was obtained. The forest road vertices within 15 m of the waterline were defined as forest road segments along the stream. In this study, stream features were created from a DEM with a 5-m cell size. Therefore, we used 15 m, the distance of 3 cells in the DEM, as a guide to represent the adjacent range of the stream.

#### 2.2.2. Stream Crossing

Stream line features and forest road line features were determined to intersect, and forest road segments that intersected were defined as stream crossings.

#### 2.2.3. Zero-Order Basin

As a method for estimating zero-order basins, Shirasawa et al. [28] developed and validated a method using three landform quantities; erosion height, uneroded height, and erosion rate were considered to represent the degree of erosion. The erosion height is calculated as the difference between the summit level map and the base level map, which contains the highest and lowest elevation points in an area [29]. The amount of topography represented by the erosion height depends on the sampling grid size of the DEM. Kühni and Pfiffner [29] analyzed the morphology of valleys incised by major rivers in the Swiss Alps by using a 10 km square smoothing filter. In this study, erosion heights were determined using a smoothing filter of 30 m square to evaluate erosion due to surface failure, following the method of Shirasawa et al. [28]. Shirasawa et al. [28] determined the threshold of erosion heights representing zero-order basins by examining erosion heights on shallow landslides. The erosion height was used to simplify the method of estimating the zero-order basins. Some studies have used curvature to assess the risk of surface failure, but the assessment model uses multiple factors other than curvature [30]. Since it has been suggested that the erosion height calculated from the tangent peak surface and the tangent valley surface could be used to estimate the zero-order basin with a single indicator, we used the erosion height instead of the curvature in this study.

However, in this study, it was not possible to collect a sufficient sample of damaged slope areas. Therefore, cells with erosion heights of 2.5 m or more were treated as zero-order basins with reference to the relative risk values. The erosion height tends to be high around the waterline, and the area around the waterline is also defined as a concave landform according to the defining parameters used in this study. In this study, we wanted to make a clear distinction between streamside and zero-order basins in terms of topographic scale. Therefore, we masked the erosion heights of cells located 15 m around the waterline to avoid confusion between the two landforms. Zero-order basins defined in this study represent unchanneled landforms with a catchment area of 1 ha or less. Even under these conditions, forest road segments located along a stream with a zero-order basin on the backslope fall into both the along-stream and around-concave landform categories.

At each forest road apex, a concave cell was examined for the presence of a concave cell at 20 m in the transverse direction. The 20 m cell was examined to avoid evaluating the forest road slope as a concave cell. The vertices where concave cells were present were defined as the forest road segment around the concave cell. Although a simplified method was used in this study, there is room for further study of the evaluation method for the area zero-order basin.
