t 'lOl ] 



LXVIII. On the Pressure of the Earth agahist Eevetemcnti 

 and Be taming Walls. By Mr. Thomas Tredgold. 



JLt has been observed, in making experiments on the strength of 

 revctcments, that the pressure of the earth increases in a certain 

 degree, the stability of the wall*. To account for this increase 

 of stabiHtv, the writer of an article on the subject, in the Ency- 

 clopcediii iMetropoliianaf, has adopted the method of resolving 

 the force, resulting from the pressure of the earth, that appears 

 to hiive been first practised by Rondelet X : but this method is 

 evidently inferior to the one used by Coulomb and Prony, as it 

 does not indicate the angle of fracture ; consequently does not 

 give the maximum pressure of the earth ; and when the cohe- 

 sion is omitted, it is much inferior even in point of simj)licity. 



The cohesion of the earth, which is so strongly objected to by 

 the writer above mentioned, is not a necessary appendage to 

 Coulomb's Theorv, and would, perhaps, be better left out; also, 

 similar ol)jections might be U'ged against introducing the cohe- 

 sion of the mortar in calculating the strength of the wall. 



But to return to the stability imparted to the wall by the pres- 

 sure of the earth. — It appears to result partly from friction ; as it 

 must be evident no motioli could take place without friction 

 against the back of the wall. I will, therefore, attempt to in- 

 clude its effect in an investigation of the pressure of the earth. 

 Let ABCD (Plate IV. fig. 12) represent a section of the wall ; and 

 BDE a section of the prism of earth that slides forward in the 

 case of fracture, DE representing the plane of fracture, which we 

 will suppose to be a plane surface. 



Put W=: the weigljt of the prism of earth acting against the 

 wall. 

 R= the resistance of the wall, or the horizontal force that 



retains the sliding prism on the plane of fracture. 

 a= the angle which the plane of fracture makes with tlie 



horizon. 

 f— the friction when the pressure is unity. 

 /;= the height of the wall =BD. 

 And, S= the weight of a cube of earth whose side is unity. 



It is shown, by writers on mechanics, that when a body is 

 sustained upon an inclined plane, and is in equilibrio, the whole 



~ . , ,. . TM-v • \V (sin. o — /"cos. fl) ... 



force HI the direction ED is = — ^ :: ~. (A) 



radius ^ 



• Col. Pasley's " Course of Military Instruction," vol. iii. chap. xxv. 

 ■f Art. Mechanic!, section xxv. p;>rt i. 

 J L'Artde Butir, tome iii. p. 128. 



Vol. f)!. No.242. June 1818. C c This 



