56 



G. F. BECKER FINITE STRAIN IN ROCKS. 



strain ellipsoid, or the direction of maximum compression, will lie 

 between the line of pressure and the compressive axis of the additional 

 shear. 



When the rock is ruptured without sensible deformation the strain 

 under discussion will not be rotational and will be indistinguishable 

 from that which would result from a simple shear; for in the xy plane 

 one of the shears arising from direct pressure cooperates with the shear 

 resulting from the preliminary rotation, and their combined effect will 

 be greater than that of the second shear in the y z plane arising from the 

 direct pressure component. 



The character of the finite strain is best seen by an illustration such as 

 that in the diagram, figure 6, A. 



X\ 



Ftguee G. — Strained Cubes. 



The dotted squares are strained to the rhombs, drawn with full lines. A results from two shears 

 at 45° to one another, the ratio of each shear being 5/4. B results from a shear and a scission, the 

 ratio of each of the two shears involved being also 5/4. The central crosses mark the direction of 

 the ellipse axes. The angle R is the material angle through which one set of planes of maximum 

 tangential strain sweeps, and r is the other corresponding angle. In A, R — r = v — ^ = 2° 45'. In 

 B,R — r = 15° 21'. 



Inclined Pressure and unyielding Resistance. — When a tabular mass of 

 rock subjected to inclined pressure rests against a mass which does not 

 yield considerably, the free couple which results from the tangential 

 component of the pressure and the resistance of the supporting mass can 

 only be equilibrated by strain in the rock itself. The strain will then- 

 fore include as one component a shearing motion or scission. 



This strain is rotational, the angle of rotation being far greater in this 

 case than in that of a yielding support. The rotation is here of the same 

 order as the strain. Consequently one set of planes of maximum tan- 

 gential strain Avill sweep through the mass much more rapidly than the 

 other, and the difference in their action will be very pronounced. The 

 nature of the distortion is seen in figure 6, B. 



