such a degree that under sufficient pressure, water can be forced through a 
slab of granite 6 inches thick. While extremely strong in compression, rock 
is therefore relatively weak in tension, and most of the rock failure methods 
in use Or Suggested are designed to take advantage of this weakness—actual 
failure occurs in tension although the method may apply pressure at a point 
or shear Over an area. 
Most of the rock destruction methods in use and historically 
important use indentors of one form or another, but stress patterns and 
true causes of failure are not well known. An excellent discussion of rock 
indentation is given in Cheatham (1968). Figure 62 (Hartman, 1959) illus- 
trates the method by which spalling over a large area can be induced by a 
sharp indentor. Figure 63a shows a point load on an infinite half space. 
When second-order effects are considered, it is found that the line A-A has 
increased in length, after indentation and the material is therefore under 
tension. Two-dimensional elasticity theory shows that in the linear solution 
the surface well away from the indentor is stress free. Figure 63b is a sketch 
of the Hertz solution for a two-dimensional mechanical indentor. Clearly, 
some similar line is under tension here also. Along these radial lines of 
tension some maximum value exists, as does a random distribution of 
microscopic cracks. If Figures 63a and 63b are thought of as viewed from 
above down onto the halfspace and axially along the indentor, the lines of 
constant surface tension will be concentric circles. Thus, along some jagged 
circle near the maximum tension region and depending upon the particular 
pattern of Griffith cracks, a gross circle should appear and penetrate into the 
surface (Figure 63c), leaving an unsupported column opposing the loading 
force. Tension is produced in this column upon loading according to Poisson's 
expansion theory. 
Whether or not this brief discussion accurately describes local failure 
induced by indentors, it seems clear that most successful techniques for 
drilling and crushing hard rocks take advantage of the material’s weakness 
in tension by these or similar mechanisms. Cutters with teeth which roll 
over the surface of attack, whether they be steel, diamond, carbides, or 
whatever should similarly create high stresses. The rapid development of 
these cutters has depended upon a combination of improvement in roller 
materials and in methods of creating the very high forces normal to the 
work face necessary to achieve rapid cutting. Within the last year, improved 
cutters have successfully worked very strong rock which a few years ago 
would have been considered impossible to cut. 
The following section is a discussion of proposed and sometimes tried 
methods for causing local failure of rock by impact or other energy transfer 
methods. A later section discusses the use of vibration in enhancing fragmen- 
tation without the large forces characteristic of current boring machines. 
79 
