*2.1. Dataset*

The difficulty in collecting forest road failure data over a wide area is that the larger the field survey area, the more labor is required. Therefore, it was difficult to obtain a forest road failure data set with a sample size sufficient for statistical analysis. On the other hand, in Japan, for the purpose of applying for government subsidies, the location and details of repair work are recorded in an administrative document ("Forest Road Facility Failure Assessment Document"). The failure is subject to certain conditions, such as there being a repair cost of more than 400,000 yen/point (As of 2006–2010, USD 2942 as of 7 March 2023) and the failure being caused by a rainfall event with 24 h of rainfall of 80 mm or more. The data in this document include the date of occurrence of the failure and its triggers, the distance from the start of the forest road to the damaged place, the repair cost, and the length of the segment of the road where the repair was required (Table 1).


**Table 1.** Items listed in the Forest Road Facility Failure Assessment Document and examples of how to complete the document.

However, since this document was created for administrative purposes only, it was supposed to be discarded after a five-year retention period and has not been used for research on forest road failures. In this study, we were able to obtain the "Forest Road Facility Failure Assessment Document" prepared in Nagano Prefecture between 2006 and 2010. Based on this document, an inventory of forest road failures was compiled. Among the forest road failures in the document, 10 failures caused by factors other than heavy rainfall (snowmelt) were excluded from the data. The forest roads covered in this study include those used primarily for timber extraction as well as those used for public purposes.

Nagano Prefecture is in the central region of Japan's Honshu Island and has mountainous characteristics, with forests covering 78% of its total area (approximately 1.06 million ha) [27] (Figure 2). In the Nagano Prefecture, 1962, forest roads totaling approximately 4904 km in length have been established as of the 2019 fiscal year, and the average forest road density is 7.1 m/ha [27]. Forest road counting is based on road identification codes. At least 207 roads, comprising approximately 10.7% of all roads, have experienced failures due to rainfall events during 2006–2010 (Figure 3a). The total number of damaged forest roads due to rainfall events during 2006–2010 was 701. Of these, 526 were identified as failure locations according to the forest road vector data (Figure 3b). The analysis in this study covers the 526 failures that occurred along these 207 routes. The median and mean number of the damaged locations (locations/line) for each forest road were 1 and 3, respectively. In 79% of the lines, the number of damaged points per line was less than 3 (Figure 4).

**Figure 2.** Map showing the research site. White lines indicate all forest roads in the Nagano Prefecture. In the figure on the right, no public roads other than forest roads are shown, so the forest roads are shown as if they exist independently. The forest road vector data shown in the figure was created by Nagano Prefecture.
