09:00 〜 09:15
[SVC31-07] Geometric rules behind columnar joints
★Invited Papers
キーワード：柱状節理、多角形パターン、熱収縮、自己組織化、ドローン空撮、ガンベル分布
Nature often favors regular polygonal patterns. For example, polygonal patterns are observed in various objects: muskmelon netting, wasp nests, bubble clusters, and cracks on the surface of dry soil. Particularly in polygonal crack systems, the entire surface of the fractured medium is divided into numerous polygonal cells with irregular side lengths and cell areas. The most important observation is that the geometric properties of polygonal patterns are very similar across many systems despite considerable differences in chemical composition and spatial length scale; this strongly suggests the existence of a common physico-chemical rule for polygonal crack formation. However, few attempts have been made to quantify this geometric similarity and statistical distribution.
As a case study, we examined the statistics on the crack pattern geometry observed on exposed surfaces of columnar joints in Japan. A columnar joint is a spectacular geological structure composed of an array of well-ordered prismatic columns with polygonal sections. The quasi-regularity in the column's cross section is a consequence of inward penetration of cracks driven by thermal contraction of the original hot lava. The formation of columnar joints begins with a superficial random crack network that occurs during the initial cooling phase of the solidified lava surface. As cooling progresses into the interior of the lava, cracks penetrate the solidified lava body and gradually spontaneously form regular polygonal fracture networks. In principle, the typical column diameter depends on the cooling rate of lava, whereby slower cooling rates produce large-diameter columns and vice-versa. In addition, an argument based on the least-work principle leads to a conjecture that each polygon tends to be a cyclic polygon, that is, a polygon with vertices upon which a circle can be circumscribed. However, considering the formation mechanism, the polygonal pattern observed on the outcrop surface of actual columnar joints should deviate from the ideal cyclic polygon due to the effects of random cracking that occurs during the initial cooling phase. The two competing effects, preference to and deviation from cyclic polygons, will regulate the degree of geometric fluctuation in the columnar section. If it is true, then a unified rule regarding the fluctuation in polygonal cracking at the surface can be established.
In order to test this hypothesis, field surveys were conducted at four sites in Japan: (1) Tatami-ishi in Okinawa (O-site), (2) Tatami-ga-fuchi in Yamaguchi (Y-site), (3) Hi-no-misaki in Shimane (Sm-site), and (4) Tawara-iso in Shizuoka (Sz-site). Three sites (O, Sm, and Sz) are positioned along the seacoast and the remaining site (Y) is situated inland. At each locality, the columnar joint exposed surface was photographed from above by a drone and the geometric statistics of the polygonal cracks were calculated by image analysis. The geometrical data were then used to quantify the geometric deviation of the constituent polygons from the cyclic polygon.
From the results, we found that the statistical deviation in polygon geometry observed at real columnar joints falls into a special class of probability distribution curves called Gumbel distribution. This distribution is a probability distribution widely used to statistically describe the strength of brittle materials. Surprisingly, this fact is true for all the data obtained from different survey sites, despite large differences in location environment, lithologic composition, and typical column size. This finding implies that the geometric fluctuation in polygonal cracking at columnar joints is regulated by the Gumbel distribution.
As a case study, we examined the statistics on the crack pattern geometry observed on exposed surfaces of columnar joints in Japan. A columnar joint is a spectacular geological structure composed of an array of well-ordered prismatic columns with polygonal sections. The quasi-regularity in the column's cross section is a consequence of inward penetration of cracks driven by thermal contraction of the original hot lava. The formation of columnar joints begins with a superficial random crack network that occurs during the initial cooling phase of the solidified lava surface. As cooling progresses into the interior of the lava, cracks penetrate the solidified lava body and gradually spontaneously form regular polygonal fracture networks. In principle, the typical column diameter depends on the cooling rate of lava, whereby slower cooling rates produce large-diameter columns and vice-versa. In addition, an argument based on the least-work principle leads to a conjecture that each polygon tends to be a cyclic polygon, that is, a polygon with vertices upon which a circle can be circumscribed. However, considering the formation mechanism, the polygonal pattern observed on the outcrop surface of actual columnar joints should deviate from the ideal cyclic polygon due to the effects of random cracking that occurs during the initial cooling phase. The two competing effects, preference to and deviation from cyclic polygons, will regulate the degree of geometric fluctuation in the columnar section. If it is true, then a unified rule regarding the fluctuation in polygonal cracking at the surface can be established.
In order to test this hypothesis, field surveys were conducted at four sites in Japan: (1) Tatami-ishi in Okinawa (O-site), (2) Tatami-ga-fuchi in Yamaguchi (Y-site), (3) Hi-no-misaki in Shimane (Sm-site), and (4) Tawara-iso in Shizuoka (Sz-site). Three sites (O, Sm, and Sz) are positioned along the seacoast and the remaining site (Y) is situated inland. At each locality, the columnar joint exposed surface was photographed from above by a drone and the geometric statistics of the polygonal cracks were calculated by image analysis. The geometrical data were then used to quantify the geometric deviation of the constituent polygons from the cyclic polygon.
From the results, we found that the statistical deviation in polygon geometry observed at real columnar joints falls into a special class of probability distribution curves called Gumbel distribution. This distribution is a probability distribution widely used to statistically describe the strength of brittle materials. Surprisingly, this fact is true for all the data obtained from different survey sites, despite large differences in location environment, lithologic composition, and typical column size. This finding implies that the geometric fluctuation in polygonal cracking at columnar joints is regulated by the Gumbel distribution.