Structural Concrete - Hassoun

496 Chapter 14 Retaining Walls
The resultant, H p , acts at h ′ /3 from the base (Fig. 14.2). When the earth is surcharged at an
angle δ to the horizontal, then
( √ )
cos δ + cos2 δ − cos 2 φ
C p = cos δ
cos δ − √ cos 2 δ − cos 2 φ
wh
P p = C p wh and H p = C 2
p (14.9)
2
In this case H p acts at h ′ /3 and is inclined at an angle δ to the horizontal (Fig. 14.4). The
values of C p expressed by Eq. 14.9 for different values of δ and φ are shown in Table 14.3.
The values of φ and w vary with the type of backfill used. As a guide, common values of
φ and w are given in Table 14.1.
2. In Coulomb’s theory, the active soil pressure is assumed to be the result of the tendency of
a wedge of soil to slide against the surface of a retaining wall. Hence, Coulomb’s theory
is referred to as the wedge theory. While it takes into consideration the friction of the soil
on the retaining wall, it assumes that the surface of sliding is a plane, whereas in reality
it is slightly curved. The error in this assumption is negligible in calculating the active soil
pressure. Coulomb’s equations to calculate the active and passive soil pressure are as follows:
Figure 14.4
Passive soil pressure with surcharge.
Table 14.3 Values of C p
φ = C p
δ φ = 28 ∘ φ = 30 ∘ φ = 32 ∘ φ = 34 ∘ φ = 36 ∘ φ = 38 ∘ φ = 40 ∘
0 ∘ 2.77 3.00 3.25 3.54 3.85 4.20 4.60
10 ∘ 2.55 2.78 3.02 3.30 3.60 3.94 4.32
20 ∘ 1.92 2.13 2.36 2.61 2.89 3.19 3.53
25 ∘ 1.43 1.66 1.90 2.14 2.40 2.68 3.00
30 ∘ 0 0.87 1.31 1.57 1.83 2.10 2.38