58 



G. F. BECKER — FINITE STRAIN IN ROCKS. 



to "do the most good." If so, the spacing can he determined if one can 

 succeed in expressing in exact terms the depotentialization of energy per 

 unit length of crack. 



The lines of maximum tangential strain make angles <o with the major 

 axis of the strain ellipse. When the strain is due to a pressure at a posi- 

 tive, acute angle <p with the fixed plane (parallel to o x), the major axis 

 makes an acute negative angle » with ox. That set of planes of maxi- 

 mum tangential strain which have the smaller range during the process 

 of strain, and upon which there is the least viscous resistance, then makes 

 an angle « -f- > with o x. 



Let w he the thickness of one of the sheets into which rupture may 

 divide the slab of rock, and let # he the angle which the diagonal between 

 the obtuse angles of the sheet makes with o x, as indicated in the follow- 

 ing diagram, figure 8. Then, if the thickness of the slab at the moment 

 of rupture is 2 /, a little consideration shows that — 



iv = 21 cos (y + <**") \ 1 — tan (y -\- to) cot # j- • 



It is evident that the total length of the cracks is inversely propor- 

 tional to the thickness of one sheet or to w. 



Figure 8.— Spacing of Fissures. 



To determine the relief of pressure it is convenient to begin by con- 

 sidering a mere change of strain. Suppose a slab to he in equilibrium 

 under the action of a simple, direct pressure. Let the mass now undergo 

 a small change in physical properties, such that it yields by a small 

 additional amount to the pressure. Then the potential energy of the 

 system is diminished in proportion to the amount of this secondary 

 yielding, measured in the direction of the force. Only one fiber passing 

 through the center of the mass, however, will move solely in the same 

 direction in which the pressure acts, all other particles moving on hyper- 

 bolic bines. 



If the pressure were inclined to the surface at an angle cr. the depoten- 

 tialization of energy under similar circumstances would also be measured 



