70 einstein-johnson. SEDIMENT TRANSPORT [Ch. 3 



dition for movement is related to the specific gravity of the bed ma- 

 terial and to such mechanical properties as grain size, grain distribu- 

 tion, and grain form. 



Numerous flume experiments have been conducted to obtain a rela- 

 tionship between these various factors at the point of general move- 

 ment. Kramer (1935), one of the first to attempt to formulate a 

 criterion for defining critical conditions, used experimental data from 

 all available sources and developed a formula in terms of sand size and 

 distribution. In later investigations at the U. S. Waterways Experi- 

 ment Station (1935), Kramer's criteria and data were used and a 

 modified formula was derived. 



Still later Chang (1939) analyzed all available data and also pre- 

 sented a formula for the critical tractive force in terms of the mechani- 

 cal properties of the material. Numerous experiments were conducted 

 at the University of Iowa (Mavis, Ho, and Tu, 1935) to establish a 

 relationship between a competent bottom velocity, corresponding to 

 impending motion of the stream bed, and the size and specific gravity 

 of the bed material. Somewhat later Mavis and Laushey (1949) re- 

 analyzed the Iowa data and presented a new relationship between 

 critical bottom velocity and size and specific weight of the material. 



The practical purpose of relationships between critical conditions 

 for movement and the sediment characteristics is to establish permis- 

 sible velocities in the design of earth canals. Also, in many bed-load 

 formulas the rate of transportation is expressed as a function of the 

 difference between the tractive force and the critical tractive force 

 of the material in the bed. Although the theory underlying this rea- 

 soning, namely, that the transportation is a function of the "residual 

 tractive force," is perhaps correct, in the practical case the critical 

 tractive force is relatively small compared to the total tractive force, 

 and its inclusion in a bed-load formula becomes primarily one of aca- 

 demic interest. 



REFERENCES 



Brown, C. B. (1945). Rates of sediment production in southwestern United 

 States: U. S. Dept. Agr. Soil Cons. Service, SCS-TP-58, Jan. 1945, 40 pages. 



Chang, Y. L. (1939). Laboratory investigation of flume traction and transpor- 

 tation: Trans. Amer. Soc. Civ. Engrs., vol. 104, pp. 1246-1313. 



DuBoys, P. (1879). Le Rhone et les rivieres a lit affouillable: Ann. ponts et 

 chaussees, 5 ser., tome 18, pp. 141-195. 



Eakin, Henry M. (1936). Silting of reservoirs: U. S. Dept. Agr., Tech. Bull. 524, 

 168 pages (revised by C. B. Brown, 1939). 



Einstein, H. A. (1944). Bed-load transportation in Mountain Creek: U. S. 

 Dept. Agr. Soil Cons. Service, SCS-TP-55, 54 pages. 



