28 EMBANKMENT WHEN ONE FACE IS VERTICAL. 



whose section has the form of a trapezoid when the water 

 stands at its brim. 



Let ABCD be the cross-section of the embankment ; 

 draw DE parallel to the vertical side BC ; let G and g be 

 the centres of gravity of the rectangle 

 and triangle respectively; draw the 

 vertical lines GH and ^K ; let AB 

 = a, DC = b, BC = h, iv = the 

 weight of each cubic foot of the ma- 

 terial, and Wj = the weight of a 

 cubic foot of water. 



The forces acting are the weight 

 of the wall, and the fluid pressure on 

 BC. As the embankment is uniform 

 throughout its length, and also the pressure on it, we may 

 determine the stability by taking only one foot in length. 

 Take BM = -J-BC, and M will be the centre of pressure 

 (Art. 16, Ex. 1, Cor.). The resultant P, of the pressure of 

 the water against the wall acts at M, and tends to turn the 

 embankment over its outer edge A. Hence, we have 



the moment of P = pressure of water on BC x AO 



(Art. 15) 



; (i) 



K E H 

 Fig. II 



the moment of AED = weight of AED x AK 



= (a b) hw x \ (aV) 



= i(a-ft)ftw; (2) 



the moment of EBCD = weight of EBCD x AH 



= bhw x (aW ; (3) 



the moment of ABCD = [l(aV)* + b(aib)]hw. (4) 



If the embankment be upon the point of overturning on 

 A, the moments in (1) and (4) are equal to each other, and 

 we have 



