between Z and C. Let P = resultant active pressure on wall; R 1 and R 2 = resultant passive
pressure above and below center of rotation, respectively.
The position of Z may be found by applying statics. But to simplify the calculations,
these assumptions are made: The active pressure extends from A to C; the passive pres-
sure to the left of the wall extends from B to C; and R 2 acts at C. Figure YIb illustrates
these assumptions.
By taking moments with respect to C and substituting values for R 1 and R 2 ,
d=
«ycj«-i(23)- Substitute numerical values and solve for d
Thus, 45° + Y2(f> = 61°; 45° - Y 2 ^ = 29°. By Eqs. 15 and 16, Cp/Ca = (tan 61°/tan 29°)
2
=
10.6; d'= 5/[(10.6)
1/3
- 1] = 4.2 ft (1.3 m). Add 20 percent of the computed value to pro-
vide a factor of safety and to allow for the development of R 2. Thus, penetration =
4.2(1.2) = 5.0 ft (1.5m).
ANCHORED BULKHEAD ANALYSIS
Sheet piling is to function as a retaining wall 20 ft (6.1 m) high, anchored by tie rods
placed 3 ft (0.9 m) from the top at an 8-ft (2.4-m) spacing. The soil weighs 110 lb/ft
3
(17.28 kN/m^3 ), and its angle of internal friction is 32°. The backfill has a horizontal sur-
face and carries a surcharge of 200 lb/ft
2
(9.58 kPa). Applying the equivalent-beam
method, determine the depth of penetration to secure a fixed earth support, the tension in
the tie rod, and the maximum bending moment in the piling.
Calculation Procedure:
- Locate C and construct the net-pressure diagram for AC
Refer to Fig. 13«. The depth of penetration is readily calculated if stability is the sole cri-
terion. However, when the depth is increased beyond this minimum value, the tension in
(a) Anchored
bulkhead
FIGURE 13(b) Free-body diagram
of AC(c) Free-body diagram
of CD