*3.3. Estimation of Earthwork Volume and Earthwork Allocation Plan*

It was suggested by these results that SfM analysis is sufficiently accurate for soil volume calculations in units of cubic meters. However, there was room for further study on the accuracy of measurements under subsoil vegetation and at sharp slope conversion points. Therefore, we calculated the amount of earthwork for cut and fill at each stage. The results are shown in Figure 6.

**Figure 6.** Amount of earthwork for cut and fill at each stage.

It was estimated that 78.6 m3 of cut soil was generated on the morning of the first day of work (22 August), and another 5.49 m<sup>3</sup> was used as fill. In the early stage of the repair work, it was assumed that much of the cut soil was generated to shape collapsed areas and construct an access road to the lower part of the embankment. In the afternoon of 22 August, the cut, and fill volumes were 54.1 m3 and 41.4 m3, respectively. This was consistent with the fact that much soil was used during the formation of the log structure at the base of the fill. On the morning of 23 August, the cut decreased to 8.8 m<sup>3</sup> and the fill increased to 60.9 m3 when the log structure continued to be installed. The cut soil increased again to 23.6 m3 and the fill to 58.9 m3 when the upper portion of the embankment was re-excavated simultaneously with the formation of the fill in the afternoon of 23 August. On 24 August, the last day of the repair work, the cut was 6.2 m3 and the fill was 93.9 m3.

A simple comparison between before and after the repair work had a difference of 48.6 m3 for cut and 137.5 m<sup>3</sup> for fill, but when the amounts of earthwork at each stage were added up, 171.3 m3 for cut and 260.7 m3 for fill were performed. In the case of civil construction sites, the difference in the amount of earthwork before and after construction and the total amount of earthwork at each stage was not considered to be significantly different. However, it is necessary to temporarily bring in soil from another location or temporarily place cut soil in another location in forest work. The amount of cut and fill soil in this study was about 3.5 times and 1.9 times larger than that measured before and after the repair work. This is a significant error factor in estimating earth work volume and maintenance costs.

The cumulative earthwork volume at each stage is shown in Figure 7. The rate of change in the volume of loosened soil, the change in the volume of soil in the excavation of the ground soil volume (L), was calculated as 1.2 in calculating the amount of earthwork. The rate of change in the volume of compacted soil and the difference in soil volume in forming the ground soil volume into fill (C) was 0.9. The volume of the log structure embedded in the fill was not considered.

**Figure 7.** Cumulative amount of earthwork at each stage.

According to this figure, it can be seen that in the early stage of the repair work, when there was much cut soil, there was a maximum of about 100 m3 of cut soil. Securing a temporary storage place for this cut soil around the work site is necessary. On the other hand, the cut soil forms the embankment, and at some point, the soil for the embankment becomes insufficient. Therefore, it is necessary to secure soil from another location. This amount of fill was considered to be about 120 m3.

Figure 8 shows a 3D model of the earthwork sections at each stage. The cut and fill areas are shown in blue and red, respectively. In Figure 8f, showing the overall earthwork volume in the lower right corner, almost the entire missing fill area was covered with fill. The cut and fill areas were indicated in each step, making the procedure easy to understand. The entire fill was shown in blue, except for some parts, in Figure 8e. This is because the photographs after the repair work were not taken until three weeks after the completion of the repair work, and it is presumed that the entire fill has tightened and settled.

These results indicate that it may be difficult to accurately estimate the actual volume of earthwork in road construction on steep terrain where there are few temporary soil storage areas based only on the topography change between before and after construction. This study was conducted at a road repair site, and the procedure differed from that of earthwork during road construction. However, while constructing small-scale roads that do not require much artificial structures, the method of excavating the ground once and piling up topsoil blocks may be used to strengthen the road structure [32,33]. In addition to the topographical conditions, the capacity of the temporary soil storage area varies with the construction method. In steep terrain, it is necessary to determine the optimal construction procedures and earthwork volume in each step according to topographic conditions, road standards, and construction methods.

**Figure 8.** 3D model of the earthwork sections at each stage. (**a**) constructing an access road to the lower part of the embankment and the formation of the base, (**b**) forming the embankment base by earthwork and logs, (**c**) forming the lower part of the embankment by earthwork and logs, (**d**) forming the upper part of the embankment by earthwork and logs, (**e**) shaping the entire embankment, (**f**) overall earthwork.
