714 WALTER H. BUCHER 



lines, v/ith the acute angles formed by their intersection facing the 

 direction of pressure. On specimens of Carrara marble used by 

 Rinne' this angle measured 60°, on those used by Karman^ it 

 measured 54°, while red sandstone (Buntsandstein) gave a value 

 as low as 38°. 



When the pressure is increased until rupture occurs, the plane 

 of fracture forms a symmetrical cone with an apical angle equaling 

 the angle of shear characteristic of the material. In this case, the 

 least principal stress equals the intermediate stress. Thereby its 

 position is made indefinite with reference to the infinite number 

 of directions in the plane common to the two lesser stresses, normal 

 to the greatest principal stress. The peculiar conical fracture is 

 the result.^ 



As soon, however, as any one of the infinite number of possible 

 directions in the plane normal to the greatest stress offers a mini- 

 mum of resistance, rupture occurs"* along two well-defined planes, 

 as indicated in Figure 3. Daubree's classical experiments on blocks 

 made of a mixture of plaster of Paris and beeswax^ correspond 

 directly to this case. 



^ F. Rinne, "Vergleichende Untersuchungen uber die Methoden zur Bestimmung 

 der Druckfestigkeit von Gesteinen," Neues Jahrb.f. Miner., etc., Vol. I (1967), 9.45. 



^Th. von Karman, "Festigkeitsversuche unter allseitigem Druck," Zeitschr. d. 

 Vereins deutscher Ingenieure, Vol. LV (191 1), pp. 1748-57. 



3 The remarkable fracturing in the form of parallel and interpenetrating cones 

 observed in the brittle white limestones of the Upper Jurassic along the intensely 

 shattered margin of the crypto-volcanic basin of Steinheim seems to be due to this con- 

 dition. W. Branco u. E. Fraas, "Das kryptovulkanische Becken von Steinheim," 

 Fhys. Abhandl. d. K. Preuss. Akad. d. Wissensch. (Berlin, 1905), pp. 36-38. 



4 In a cube where four directions offer an identical minimum of resistance, the 

 planes of fracture form a pyramid as may be seen in any ordinary crushing test. 



5 A. Daubree, "Etudes synthetiques de geologie experimentale" (Paris, 1879), 

 pp. 315 ff. and Figs. 93 and 94. For a copy of Fig. 93 see, e.g., Van Hise, "Principles 

 of North American Pre-Cambrian Geology,'' Sixteenth Ann. Rep. U.S.G.S. (1895), 

 Pt. I, p. 644, Fig. 126. Note in this figure the difference between Liiders' lines and 

 the final plane of shearing. The former, marked "R," do not, at first, correspond 

 to continuous internal surfaces. They represent purely local effects along individual 

 lines of stress. The establishment of large planes of shearing (marked "F") is a 

 later development. The difference between the two is shown strikingly on the right 

 side of the block, where the main fracture cuts diagonally across Liiders' lines. 

 This contrast between Liiders' lines and the final planes of rupture is met with in 

 all experiments. It seems to indicate that at first the greatest tension exists parallel 

 to the surface of the test specimen, due to the stretching of the horizontal dimensions 

 accompanying the vertical shortening. Rupture, on the other hand, gives dominance 

 to the direction of easiest movement in a radial direction. 



