LIMITS OF LENGTH OF OVERTHRUST BLOCKS 341 



zero toward the origin of stress. With this limited movement there would 

 be small opportunity for the development of a gouge which might serve 

 as a lubricant. Such attrition as might occur would probably result in a 

 breccia whereby the frictional resistance would be increased. 



From these considerations as well as the probability that the coefficient 

 of friction increases with increasing pressure, it is assumed that the co- 

 efficient of friction on the rupture plane postulated is not less than that 

 determined for similar rocks experimentally under slight pressures. 

 1 By substituting the assumed values for S, iv, and / in the equation 



2S 



AB = -77—; — ; ; > we maY obtain a concrete expression for AB — that 



(/ -J- tan a) w 



is, the limiting value for the length of an overthrust wedge of the crust, 



measured in the direction of the thrusting for any angle of thrust. Since 



/ is the doubtful factor in the equation, the doubt may be recognized by 



adopting a series of values for that factor. 



Limiting Values for Length of overthrust Prism 



a / = .5 f = A / = .3 



2° 20 miles 25 miles 32 miles 



5° 18 miles 22 miles 26 miles 



10° 16 miles 19 miles 23 miles 



20° 12 miles 14 miles 16 miles 



In arriving at these values for AB, S has been taken at 15 tons per 

 square inch, or 2,160 tons per square foot, which is the maximum crush- 

 ing load for the strongest rocks at the surface. Any diminution of this 

 factor would proportionally reduce the value of AB. It is probable that 

 the proper value for S is between the crushing load and the shearing 

 strength, and this would be notably less than the value assumed. 



The Limits of Movement of overthrust Blocks 



The elastic rebound theory of faulting teaches that when a slip occurs 

 on a fault, both sides of the fault move suddenly, each in an opposite 

 direction, and that the amount of movement is limited to that necessary 

 to relieve the elastic strain in the rocks. The stress which generates the 

 strain may be persistent, so that by repetition of relief by slip the aggre- 

 gate relative displacement may be large. The relief from strain at every 

 slip may, and probably does, involve an equal amount of fling on each 

 side of the fault; but the aggregate effect of repeated slips may be that 

 of a mobile block moving past a passive block, the former advancing with 

 each slip, while the latter simply oscillates between the positions of strain 



