EMBANKMENT WHEN ONE FACE IS SLANTING. 29 



or, 



(5) 



and the embankment will be overturned or not, according as 

 h > or < 4/[2 (-i) 2 + 3b(2a-b)~\ 



Con. If the embankment is rectangular, b = a, and (5) 

 becomes 



= ** (6) 



If the embankment is triangular, J = 0, and (5) becomes 



19. Embankment when the Face on the Water 

 Side is Slanting. Find the stability of an embankment 

 whose section is a trapezoid which 

 slants on both sides, viz., towards the 

 water and away from it. 



(1) Suppose the embankment to 

 yield to the pressure of the fluid by 

 turning round the outer edge A. 



Let ABCD be the cross-section of 

 the embankment. Since the pressure 

 of a fluid is always normal to the sur- 

 face with which it is in contact (Art. 

 4), the pressure on the slanting face BC, of this embank- 

 ment is inclined to the horizon, and hence the stability of 

 the embankment is caused by its weight and the vertical 

 pressure of the fluid on the face BC, while the effort to 

 overthrow it is caused by the horizontal pressure of the 

 fluid. 



Let P l and P 9 be the horizontal and vertical components 



