(a) Resultant pressures (b)Mohr's circleFIGURE 8- Using the Mohr's circle, state the equation for p
Thus,
_ [cos B - (cos
2
00 - cos
2
<fr)°-
5
]wh
P
~ cos 0+(cos
2
6 -cos
2
<£)°-
5
^By substituting, w = 100 lb/ft^3 (15.71 kN/m^3 ); A = 12 ft (3.7 m); O = 15°; <£ = 34°; p =
0.321(100)(12) = 385 lb/ft^2 (18.4 kPa).
The lateral pressure that accompanies a slight displacement of the wall away from the
retained soil is termed active pressure; that which accompanies a slight displacement of
the wall toward the retained soil is termed passive pressure. By an analogous procedure,
the passive pressure is
[cos B + (cos
2
O - cos
2
ft)
0- 5
]wft
P~ cos0-(cos (^2) 0-cos (^2) <£)°-5(13)
The equations of active and passive pressure are often written as
Pa = C 0 Wh Pp = CpWh (14)
where the subscripts identify the type of pressure and Ca and Cp are the coefficients ap-
pearing in Eqs. 12 and 13, respectively.
In the special case where 0 = 0, these coefficients reduce to
1 - sin d>
C= TT^ = t- (^2) (45°-'/,<» (15)
1 + sin <b
<i-T^* ""^
450
-**
(16)
The planes of failure make an angle of 45° + VKJ) with the principal planes.