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The three‐dimensional shape and velocity of propagating cracks in the hydrostatic stress condition were studied by using gelatin, the physical properties of which were controlled to be constant. Various liquids (with various densities, viscosities, and volumes as the governed parameters) were injected in gelatin to form liquid‐filled cracks. The directions of the crack growth and the propagation of an isolated crack are governed by the density difference between injected liquid and gelatin (Δρ), that is, a buoyancy. The propagation of a crack has two critical values: the first is the transition value to brittle fracture; the second is the value where segmentation begins to occur. The condition of a stable isolated crack formation is discussed. The crack shape of an isolated crack in the direction perpendicular to the crack plane is different from that of a growing crack with a fat tear drop form: the former has an elliptical top and a nearly flat bottom. The upper termination of an isolated crack in the vertical cross section has an elliptical shape, and the lower termination has a cusped shape. The lower part of the crack occupies the preexiting fracture which has formed by fracturing at the crack top. The crack thickness ( w )/crack height ( h ) ratio is proportional to Δρ A, if the elastic moduli are constant. The crack length l / h ratio increase with h in the primary fracture, while the l / h ratio decreases with h in the preexisting fracture except for air‐filled cracks. The ascending velocity of an isolated crack is proportional to Δρ 3 h 4 , that is, Δρ w 2 , if the other physical properties are constant. The height and length of a growing penny‐shaped crack are approximately proportional to A 3d 1/3 t 4/9 , so that the growth rate of height is in proportion to A 3d 3 t −5/9 ( A 3d is constant injection rale). Some comparisons with the two‐dimensional crack theory and applications for magma‐filled cracks are discussed on the basis of these results.
Akira Takada (Sun,) studied this question.