21 drainage areas were carefully selected according to 5 major geological units throughout Japan. An examination was done based on data about volumes of slope failure produced during several years period by means of repetitive airphoto interpretation. The main results obtained in this study are as follows: (1) Volumes of slope failure production vary distinctly according to geological units. For example, granite areas product 1, 260 m3/km2/y, whereas Quaternary volcanic areas product 70 m3/km2/y. However, such volumes also vary according to duration in a same area. This fact implies that other factors including geology influence production of slope failure. (2) Factors of topography and rainfall were then analysed to examine the relationship with volumes of slope failure production. A particular attention is paid to the following, in which the volumes have a direct relation with the ratio of relief to length of a drainage area and an inverse one with the ratio of area of less than 20° in slope gradient to the whole area, both in an exponential function. (3) When the geologically identified data of the volumes of slope failure production and reservoir sedimentation are dealt with in a relatively long term such as a decade, both show a good positive correlation. This means that the latter could be predicted through the former in Japan as far as geology of an area is known.
The authors examine whether or not the fractures in the rock mass are statistically self-similar by using the box counting method and the method using the distribution function of fracture trace length. Further, a method to estimate the fracture distribution of the universal set from a certain subset, are proposed. In order to obtain the data over a wide range, fracture maps at some different scales are used. The objective districts were Asahi Mountain-land (here after called Gr. H) in Yamagata Prefecture and Hatsukari in Yamanashi Prefecture, in which granite and andesite are distributed, respectively. At some different scales of those rock mass, the fractal properties of the fracture trace length and the spatial distribution of fractures (fracture pattern) were investigated. The results are surmmarized as follows: 1) The distribution of fracture trace length shows the fractal distribution, and the fracture pattern on a 2-D plane is described by the fractal geometry. The fracture trace length has the fractal property in the range from 10-2 m to 105 m. 2) In estimating the fractal dimension Dl by using the distribution of fracture trace length, the data from the mean length of the fracture trace to 0.8 times the side length of the measured area give a meaningful result. Using the box counting method, the fractal dimension Dg of fracture pattern should be estimated on the side length of box ranging from 1/2 times grid side length to 1/32 times one. 3) The fracture pattern has a statistical self-similarity. The fractal dimension Dg of the pattern is generally smaller than two. Hence, there is a non-uniformity of the spatial fracture distribution. 4) The fracture trace length distribution N of universal set at ηu×ηu area is expressed by the equation N=N′ (ηu/ηs) Dg. (N′ : Average distribution of the subsets, ηs×ηs: Area of the subset)
Recently, the relationship between lineaments and fracture systems has been discussed by some statistic approach. In this study, the criterias for the interpretation of lineaments using Landsat TM, Spot and aerial photograph imagery are proposed for the detection of fractured zones through lineaments. In order to clarify this criteria which are divided into 6 ranks, ranging from A to F, the six sites including USA are studied. Field evidence shows that many lineaments coincide with faults or joints and it's probability of the coincidence between lineaments and faults or joints is restricted by the length of lineaments. The lineaments length of the 100 percent probability to coincide lineaments with faults or joints agree with the linear part which is called fractal distribution in the relationship between lineaments length and frequency. In addition, the relationship between lineaments criteria and the width of the fractured zones have a good harmony. High ranking lineaments are very useful in the interpretation of geological structures.