with the horizontal. Superimpose the drawing containing the spiral on the main drawing,
orienting it in such a manner that O lies on L and the spiral passes through B and C 1. On
the main drawing, indicate the position of the center of the spiral, and designate this point
as O 1. Line ^C 1 is normal to the spiral at C 1 because it makes an angle </> with the radius
vector, and the spiral is therefore vertical at C 1.
- Compute the total weight W of the soil above the failure line
Draw the action line of Wby applying these approximations:
Area of wedge =
2
A(AB)AC 1 c = 0.44C 1 (21)
Scale the lever arms a and b.
- Evaluate P by taking moments with respect to O 1
Since R passes through this point,
bW
P=- (22)
- Select a second point C 2 on the ground surface; repeat
the foregoing procedure
- Continue this process until the maximum value of P is obtained
After investigating this problem intensively, Peckworth concluded that the distance AC to
the true failure line varies between OAh and 0.5/j, where h is the depth of the trench. It is
therefore advisable to select some point that lies within this range as the first trial position
ofC.
THRUST ON A BULKHEAD
The retaining structure in Fig. 1 Ia supports earth that weighs 114 lb/ft^3 (17.91 kN/m^3 ) in
the dry state, is 42 percent porous, and has an angle of internal friction of 34° in both the
(a) Retaining structure (b) Pressure diagram
FIGURE 11
Tie
Water
surface
