138 cleaves. HIGHWAY ENGINEERING PROBLEMS [Ch. 7 



where W\ is the weight of the slice akfe which tends to produce failure, and Wi 

 is the weight of the slice kbdif which tends to resist it. 



For the determination of slopes with known shear characteristics 

 the authors say: 



... it is necessary to determine the diameter and position of the circle that 

 represents the surface along which sliding will occur. This circle, known as 

 the critical circle, must satisfy the requirement that the ratio between the 

 moment of the forces tending to resist the slide and the moment of the forces 

 tending to produce it must be a minimum. Hence, the investigation belongs 

 to the category of maximum and minimum problems exemplified by Coulomb's 

 theory . . . and the theory of passive earth pressure. . . . 



After the diameter and position of the critical circle have been determined, 

 the factor of safety G s of the slope with respect to failure may be computed by 

 means of the relation [see Fig. 1] 



moment of resisting forces TF 2 Z 2 + sr d\ei 



G s = 



moment of driving forces Wih 



wherein r represents the radius of the critical circle and die^ the length of the 

 surface of sliding. 



Many variations are required in accordance with data such as soil 

 differences and position relative to the water table. The computa- 

 tions will serve as a guide for design in trying to ascertain probable 

 failure. Because of the tremendous variations in soil, and soil and 

 rock combinations, and even rock slides wherein the end results are 

 similar to Sharpe's "slump" for soils, or Terzaghi and Peck's "slope 

 failure," the engineer must not place too much confidence in either 

 soil mechanics or purely geological interpretations alone. In such 

 problems these specialists form a natural team whose cooperation is 

 essential to further slide studies. 



SUBSIDENCE 



As defined by Sharpe (1938), "Subsidence is movement in which 

 there is no free side and surface material is displaced vertically down- 

 ward with little or no horizontal component." The causes of sub- 

 sidence are varied, and their end result evokes serious concern in high- 

 way construction. Chief among the types are settlement over coal 

 mines, compaction of unconsolidated sediments through drainage of 

 swamp lands, solution and removal by natural or artificial means of 

 salt, gypsum, and sulphur, depletion of oil fields, lowering of the water 

 table through excessive public and private usage, break-through over 

 sinkholes in limestone areas, changes in the "active" layer in regions 



