*2.3. Extension, Relative Risk, Repair Cost, and Rainfall at Failure by Terrain Type*

First, by totaling the extensions of forest road segments by topographic type, we obtained the percentage of topographic types on an extension basis. The percentage of the landforms that were damaged was also calculated by adding up the extensions of the damaged segments by landform type. By comparing these data, the characteristics of failure in each landform type were examined in terms of the extension of failure.

Next, we calculated the relative risk of each landform type with respect to the other categories in order to examine the extent to which the susceptibility to failure differs by landform type. For example, the relative risk of the streamside category is calculated as the ratio of the probability of failure in the streamside category to the probability of failure in the other categories. Since the relative risk of each landform category represents the likelihood of failure relative to the other categories, it is also possible to compare the likelihood of failure among landforms. In order to clarify the relationship between topographic form categories and failure rates, a test of independence was conducted using the χ-square distribution. The null hypothesis of the χ-squared test is that the two variables, i.e., a given landform category and loss rate, are independent. If the null hypothesis is rejected, it suggests that there is some relationship between the two variables, i.e., the category may have an effect on the susceptibility to damage. Finally, we examined whether

the cost of repair and rainfall at the time of failure differed by terrain type. While repair costs and rainfall were recorded on a per-loss basis from the Forest Road Facility Failure Assessment Document, the topographic configuration differed on a per forest road segment basis. Therefore, depending on the length of the failure, a single failure may consist of segments of multiple terrain categories. In this case, the category with the highest number of segments was treated as the topographic category of the failure in question. The Kruskal– Wallis test was performed to determine whether the samples were drawn from the same population (or different populations with the same distribution) by comparing the median repair cost and rainfall at the time of failure for each topographic category group. If the null hypothesis is rejected, it suggests that not all samples may have been obtained from the same continuously distributed population. In this case, a further multiple comparison test is performed to determine whether there is a significant difference between any of the groups.

The rainfall at the time of failure recorded in the Forest Road Facility Failure Assessment Document was obtained from the nearest meteorological station (Automated Meteorological Data Acquisition System). These meteorological stations are located at intervals of about 17 km, and 45 of them are located in Nagano Prefecture (Figure 7) [31].

**Figure 7.** Distribution of meteorological stations established in Nagano Prefecture.

#### **3. Results**

#### *3.1. Percentage of Forest Roads Damaged by Segment Categories*

Figure 8 shows the percentage of all forest road segments and damaged forest road segments by terrain type category.

**Figure 8.** Percentage of all forest road segments and damaged forest road segments by terrain type category." Mixed" indicates segments that fall into both streamside and zero-order basin landforms.

The bar graph in the upper row of Figure 8 shows the percentage of forest road segment categories calculated for the 207 routes; 15% was streamside, 26% zero-order basin, 3% in both categories ("mixed"), 4% was stream crossing, and 53% was of other types.

The bar graph in the lower row of Figure 8 shows the percentage of forest road segment categories calculated for the failure segments; 42% was streamside, 18% zero-order basin, 8% in both categories, 7% was stream crossing, and 25% was of other types. By extension, 75% of the forest road failures that occurred in the target area occurred along streams or stream crossing or zero-order basins, indicating that forest road failures along streams are most common.

#### *3.2. Relative Risk of Forest Road Segment Categories*

The number of damaged and undamaged segments was recorded for each forest road segment category, and the relative risk to forest road segments in the "other" category was calculated (Figure 9). The χ<sup>2</sup> test results showed that the ratio of the number of damaged to undamaged forest road segments in the "other" category was significantly higher than that in the "other" category for all categories. The relative risk for forest road segments in the "other" category was higher along streams and zero-order basins, in that order. The streamside was about 6.0 times more likely to be damaged, stream crossings were about 4.6 times more likely to be damaged, and zero-order basins were about 1.9 times more likely to be damaged than the other categories.

#### *3.3. Failure Characteristics by Forest Road Segment Category*

#### 3.3.1. Failure Repair Costs

Figure 10 shows the distribution of repair costs for the 287 damaged areas where repair costs were available (USD 1 = JPY 135.96 as of 7 March 2023). Only a small percentage of the failures were applicable to stream crossings (failures in which stream crossing segments were in the majority), so they were excluded from the analysis. The median and mean repair cost for all the damaged sites was approximately 2.33 million yen and 2.94 million yen, respectively (USD 16,946 and 21,584, respectively, as of 7 March 2023). The Kruskal–Wallis test was conducted for the three forest road segment categories, and the null hypothesis that all samples were derived from the same distribution with a 5% risk rate was not rejected. It is considered necessary to consider factors other than topographic morphology in analyzing the causes of damage that lead to high repair costs.

**Figure 9.** Cross tabulation table of forest road segment topography form and damage status. Rows correspond to the topographic form of the forest road segment, and columns correspond to the damage status.

**Figure 10.** Repair cost by risk category for each area damaged by failure. The line in each box represents the median of the sample; the upper and lower ends of each box represent the upper and lower quartiles, respectively.

#### 3.3.2. Amount of Rainfall

The distribution of the maximum 1 h rainfall and maximum 24 h rainfall for the rainfall events that triggered the forest road failures are shown in Figures 11 and 12, respectively. The maximum and minimum values for 1 h potential rainfall [32] and 24 h potential rainfall [33] at the target sites are plotted in the figures as reference values. The median maximum 1 h rainfall for all the damaged locations was 15.5 mm/h. The Kruskal– Wallis test was performed for the three forest road segment categories. However, the null hypothesis that all samples were derived from the same distribution with a 5% risk rate was not rejected. The quartile range of maximum 1 h rainfall at the damaged sites being located between the maximum and minimum values of 1-year potential rainfall suggests that forest road failures can occur even when the intensity of the maximum 1 h rainfall is not extreme. The median maximum 24 h rainfall intensity for all damaged sites was 175 mm/24 h. The Kruskal–Wallis test was conducted for the three forest road segment categories. The null hypothesis that all samples were derived from the same distribution with a 5% risk rate was rejected. Multiple comparisons showed that the mean maximum 24-h rainfall at the time of damage for the streamside category was significantly higher than the mean for the other categories at a 5% risk rate. The first quartile of the streamside category was higher than the other categories and exceeded the 30-year potential rainfall in some areas.

**Figure 11.** Distribution of maximum hourly rainfall in the damaged area. The line in each box represents the median of the sample; the upper and lower ends of each box represent the upper and lower quartiles, respectively.

**Figure 12.** Distribution of maximum 24 h rainfall in the damaged area. The line in each box represents the median of the sample; the upper and lower ends of each box represent the upper and lower quartiles, respectively.

#### **4. Discussion**

Streamside forest road segments accounted for only 15% of the total length of forest roads analyzed, but 42% of the road segments that were damaged. Furthermore, the relative risk of the streamside forest road segment was about 6.0 times higher than that of the other categories of forest road segments, indicating that it was the most likely terrain type to be damaged in this analysis. From the perspectives of both the length of failure and the relative risk, it is clear that the most important issue in the target area is the prevention of failure on the streamside forest road segments. The Forestry Agency supports the planning and improvement of trunk forest roads important for failure prevention and conducts projects to promote the strengthening of forest roads [34]. Countermeasures along stream segments will be particularly important for the resilience of Japan's forest roads against failures.

In previous studies evaluating the environmental impact of forest roads, distance to streams [35,36] and avoidance of stream crossings [37] have been used as one evaluation index. This study found that proximity to a stream is also an important evaluation indicator for forest road maintenance in terms of the susceptibility of forest roads to damage. Jing et al. [38] studied the spatial relationship between road and river networks in central China and noted that road and river networks were closely related spatially, with the density of high-standard roads increasing the closer they were to rivers. In Japan, there is a history of forest roads being located along streams because of the preference for timber haul-out routes using progressive gradients before the 1960s, when the driving performance of timber transport vehicles was low [39]. Especially when forest roads located along streams play a key role in the road network, they need to be subject to maintenance and improvement because of the significant disruption that would result from their destruction. The mean maximum 24-h rainfall at the time of the failure of a forest road segment along a stream was significantly higher than the mean for other geomorphic categories at a 5% risk rate. The frequency of extreme precipitation events per degree of warming also increased, and these trends were reported to be greater in Europe and Japan than in the United States and Australia [40]. Future changes in rainfall patterns may further increase the risk of damage, especially along streamside forest roads, and the relationship between failure and rainfall should continue to be investigated.

Even in terrain forms that were considered to be at high risk of failure in previous studies, the ease of failure in terms of relative risk differed by several fold. In studies of forest road evaluation based on multi-criteria evaluation, the AHP method has been used to determine the importance of different criteria [12,35–37]. Through interviews with experts and others, evaluations have been made, for example, that Criterion A is twice as important as Criterion B. However, these evaluations are based on the subjective opinions of experts. With regard to the weight of the criteria for failure, a more objective evaluation may be possible by accumulating statistical knowledge.

The topographic morphology of the forest road segments analyzed in this study could not explain the difference in failure repair costs. According to Watanabe et al. [41], who studied the past repair costs of 1504 forest roads in Nagano Prefecture, Japan, the standard deviation of the repair cost of one forest road failure amounts to about 26.2 million yen. Therefore, it is considered necessary to first investigate the characteristics of the failure in detail, especially for the failure with high repair costs.

In this study, we were able to obtain five years of inventory data on forest road failure by the prefectural government, which allowed us to statistically analyze the characteristics of forest road failure. In Japan, such inventory data are temporarily maintained by administrative departments but are discarded after a certain period of time because of a lack of familiarity with how to utilize them. As revealed in this study, some knowledge can be obtained only by collecting data on forest road failure on a scale of several hundred routes. Therefore, it is important to establish a system to compile a database of forest road failure inventories in the future. In this study, we focused on forest road failure that occurred more than 10 years ago, so we were unable to consider the presence, location, and condition of structures (drainage facilities, retaining walls, road surface pavement) that existed before the damage occurred. In Japan, it is rare to record information on such forest road structures in normal times because the value of their use is not well known. Since these structures are essential for a more accurate assessment of the risk of forest road failure, it is desirable to investigate their location and other information prior to the occurrence of a failure. Recently, studies have evaluated the degree of damage to failure-risk forest road surfaces by remote sensing [42–44]. Although it is labor-intensive to survey all forest roads immediately, it is also important to combine techniques to determine the functional status of forest road structures in a labor-saving manner, focusing on forest roads composed of segments at high risk of failure, as identified in this study and to build an inventory data of the structures.

There are various types of failure to forest roads, and it is necessary to construct an evaluation model of failure risk and prioritize countermeasures according to the cause and risk of failure. For example, in a forest road segment that runs alongside a stream, the nourishing force of the stream is considered to be the dominant failure factor, and reinforcement of the fill slope may be a more important failure risk reduction method than the placement of cross-drainage ditches. In this study, forest road segments were classified in terms of topography, and comparisons were made regarding the length of forest road failure, the relative probability of occurrence, repair cost, and induced rainfall intensity in each category. The results showed the importance of responding to forest road failures

along streams, which was revealed by the analysis based on a large number of data for a wide area of the prefecture.
