*Tetsuhiko Yoshimura*^{1}* and Kouichi Kanzaki*^{2}

^{1}Assistant Professor, Forest Engineering, Faculty of Agriculture, Kyoto University, Japan.^{2}Professor, Forest Engineering, Faculty of Agriculture, Kyoto University, Japan.

**Abstract**

In most mountains in Japan, it is very difficult to construct forest roads because the topography is very steep and slope failures often occur when constructing them. Therefore, it is very important to locate forest roads on stable slopes. In a former study, we made a quantitative risk assessment estimating the degrees of slope failure potentials using topographic maps. The objective of this study is to support decision-making for the layout of forest roads in mountainous areas based on the risk assessment. In particular, this study focused on decision-making based on the selection of passing points of forest roads using the fuzzy theory. The advantage of this method is that a computer can make the decision on where to lay out forest roads automatically as if it were a human being. It makes it much easier to plan forest roads in mountainous areas avoiding the danger that the areas considered collapse.

**List of technical terms:**

1. Risk assessment - It is very important to make a rational decision. By this method, the risk must be properly estimated in advance. In this study, the risk caused by constructing forest roads is employed for planning a forest road network.2. Slope failure potentials: The possibility of landslide occurrence.

3. Fuzzy expert system: This is the expert system using the fuzzy theory. The advantage of this system is that a computer can make a decision as if it were a specialist.

**Introduction**

In Japan, forest road networks are the essential basis of modern and sustainable forest production. However, one of the major problems that is that slope failures often occur when constructing forest roads especially in steep mountainous areas. Until now, little attention has been paid to the risk of slope failures when planning forest roads in those areas. We believe that it is most important to lay them out on stable slopes where slope failures rarely occur.

In a former study (Yoshimura *et al.* 1995), we made a quantitative risk assessment estimating the degrees of slope failure potentials using topographic maps. In addition, the degrees of slope failure potentials were calculated automatically using DEM (Yoshimura *et al.* 1996). It could be applied to GIS, which made it much easier to plan forest roads in steep mountainous areas.

Until now, planning of forest road networks has already been discussed many times, for example, Kanzaki (1966), Kobayashi (1975, 1980), Kitagawa (1972) and Sakai (1995). However, there is no precedent for a routing system based on the risk assessment as developed in this study which focuses on decision making based on the selection of passing points of forest roads using the fuzzy theory and the graph theory. It makes it possible for a computer to lay them out automatically as if it were a human being.

**Method**

*1. Slope failure potentials calculated by using DEM*

The factors used to estimate the degrees of slope failure potentials were inclinations, cross-sections of slopes, turning points of inclinations and catchment areas. When they were applied to GIS, it was necessary to obtain them automatically using DEM (Yoshimura *et al.* 1996, Takeuchi *et al. 1992,* Watanabe *et al.* 1993). Then, we calculated the slope failure potentials according to the method reported in a former study (Yoshimura *et al.* 1995). In this study, it was applied to Higashiyama mountains in Kyoto (Figure 1). The intervals of meshes were 20 m.

**Figure 1. Slope failure potentials calculated automatically**

*2. Method of laying out a forest road*

When a forest road network was planned in steep mountainous areas, we suggested that a forest road network consisting of vertical main roads and horizontal branch roads like a fish bone, was more suitable (Yoshimura *et al.* 1993, Ohashi 1992, Ohashi *et al.* 1989). In the present study, we developed a system for laying out a forest road automatically. This system was found suitable especially for a vertical main road. The methodology was as follows:

1. The meshes, where the degrees of slope failure potentials were below a constant value, were selected as possible passing points. In this study, that value was set at 0.0.2. The starting point and the ending point were decided at will.

3. A computer decided the routes by connecting some of those selected meshes. They often became the points where the directions of the routes were changed and were also suitable for the landings. This was a very important point.

4. When two passing points were connected, the methodology of selecting a next point was based on the fuzzy theory. Suppose you select point P' as the next point from P. The point which was evaluated the highest would be selected as P'. In the evaluation, the membership functions shown in Figure 2(a) ~(d) were used and then P' was evaluated by the following equations (1) ~ (3) (Tanaka, 1991):

IF X_{1}is A_{1}^{i}and ··· x_{n}is A_{n}^{i}THEN y

^{i}= c_{o}^{i}+ c_{1}^{i}x_{1}+ ··· + c_{n}^{i}x_{n}(i = 1, 2, ···, n) (1)

where i is a number of a rule, l is the total number of rules, A_{K}^{i} (k = 1, 2,..., n) is the fuzzy set, x_{k} is a variable of input, y^{i} is output from a rule i and c_{k}^{i} is a parameter of a rule i. Then, the estimated values (y) are obtained as follows:

_{}

where

_{}

In this equation, m A_{k}^{i} (x_{k}) is membership values of the fuzzy set A_{k}^{i} at x_{k}. In this study, the equation (1) is expressed as follows:

IF x_{1} is "Big" THEN y^{1} *=* -50x_{1} (Very Small) (4)

IF x_{2} is "Big" THEN y^{2} *=* -100x_{2} (Very Small) (5)

IF x_{1} is "Medium or Small" and x_{2} is "Medium or Small" and x_{3} is "Big or Medium" and x_{4} is "Big or Medium"

THEN y^{3} = 0.3x_{1} - 10x_{2} + 0.5x_{3} + 3x_{4} (Big) (6)

IF x_{1} is "Medium or Small" and x_{2} is "Medium or Small" and x_{3} is "Big or Medium" and x_{4} is "Small"

THEN y^{4} = 0.2x_{1} - 15x_{2}+ 0.3x_{3} + 2x_{4} (Medium) (7)

IF x_{1} is "Medium or Small" and x_{2} is "Medium or Small" and x_{3} is "Small" and x_{4} is "Big or Medium"

THEN y^{5} = 0.1x_{1} - 20x_{2} + 0.1x_{3} + x_{4} (Small) (8)

IF x_{1} is "Medium or Small" and x_{2} is "Medium or Small" and x_{3} is "Small" and x_{4} is "Small"

THEN y^{6} *=* -5x_{1} - 25x_{2} - 0.5x_{3} - 10x_{4} (Very Small) (9)

where:

x_{1}is the distance between P and P',

x_{2}is the gradient between P and P'.

The horizontal distance towards the point of the end (x_{3}) and the vertical distance towards the point of the end (x_{4}) are defined as:

x_{3 }= d_{1 }- d_{2}(10)

x_{4 }= |d_{3}| - |d_{4}| (11)

where d_{1} and d_{2} are the horizontal distance between P and E (the point of the end) and between P' and E, respectively. Moreover, d_{3} and d_{4} are (E - P) and (E - P') in vertical levels, respectively. Here, the level of a mesh is defined as the average level of four corners.

**Figure 2(a). Membership function. Distance between P and P'**

**Figure 2(b). Membership function. Gradient of a forest road**

**Figure 2(c). Membership function. Horizontal distance of the approach**

**Figure 2(d). Membership function. Vertical distance of the approach**

5) We connected P to P' applying the Dijkstra method in the graph theory. It was already applied to the layout of a forest road by Kobayashi (1975) and was a very useful way to decide routes of forest roads. In this method, the value of each section between every two adjacent meshes was evaluated according to the following equation (Sakai *et al.* 1994):

E = W x F (12)

where E is the evaluated value, F is the average degree of slope failure potentials of two adjacent meshes, W is a coefficient which is defined as:

W = 1 (g < 8) (13)W = (g/8)

^{2}(8 £ g < 24) (14)W=¥ (g>=24) (15)

where g is the gradient between two adjacent meshes. We limited the maximum gradient of a forest road to 24 percent according to the results of the former experiment (Deki *et al.* 1990), in which it was concluded that the maximum gradient of a forest road for 4WD cars was 30 percent and a margin of about 5 percent was allowed for the cars' capacity to climb a hill, the conditions of the road surface and the psychological load of a driver.

**Results**

Figure 3 shows the forest road laid out by the above-mentioned expert system using the fuzzy theory. In this figure, the seven points A ~ G indicate the passing points determined using the fuzzy theory. In this figure, 'A' is the starting point and 'G' is the ending point, both of which were decided at will. The expert system selected the safety areas as the passing points of forest roads, which were approaching the point of the end. These passing points were also suitable for landings or forks of forest roads. In this process, the gradient of a forest road was also important.

After that, they were connected by using the Dijkstra method (Figure 4). As a result, the route decided by the expert system was rather good and seemed to be of practical use.

**Conclusions**

We have developed the expert system laying out a forest road automatically based on the risk assessment. In this way, the risk of slope failure occurrence by constructing forest roads would be minimized. In addition, if there was precious vegetation which should not be crossed, the degrees of slope failure potentials could be changed to make sure that the forest roads would avoid those areas. It can also be expected that the above-mentioned way of planning a forest road would contribute greatly not only to the prevention of landslides and soil disturbance but would also reduce construction and maintenance costs. In another paper, we will show the method of optimizing a forest road network including branch roads.

**Acknowledgements**

This study was conducted to realize the ideas that Mr Keizaburo Ohashi, a leading forest owner in the Osaka Prefecture, had about forestry management. We also thank Dr Kunihiko Numata, Dr Tetsurou Sakai and Mr Hajime Yamasaki (all of Kyoto University) for their assistance and advice.

**Figure 3. Passing points determined using the graph theory**

**Figure 4. A forest road laid out by using the fuzzy theory**

**References**

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^{1}The titles are tentative translations from Japanese by the authors of this paper.