Earth pressures and stability of retaining walls - The Mechanics of Soils and Foundations - page 395

Example 24.2: Depth of a propped wall Figure 24.18(a) shows a wall propped at the
top retaining dry sand. The unknown depth of penetration is d . For a factor of safety
F s

φ s φ c / F s is φ s 20 ◦ . Hence, = 1.6 the safe angle of friction, given by tan = tan =

from Eqs (24.3) and (24.4),

tan 2 45 ◦ − φ a

1
2

tan 2 35 ◦ = K a = = 0.5

tan 2 45 ◦ + φ a tan 2 55 ◦ =

1
2

K p = = 2.0

With the depth H measured from the ground level on either side of the wall

1
2

H 2 K a

1
2

d ) 2

1
2

d ) 2 kN

= γ = × × + × = +

P a 20 (5 5(5

1
2

H 2 K p

1
2

d 2 20 d 2 kN P p = γ = × 20 × × 2 =

The distributions of active and passive earth pressures and the active and passive forces
are shown in Fig. 24.l8(b). Taking moments about the top of the wall and noting that
the forces P a and P p act at the centres of the triangular areas (i.e. 3 H above the base),

5

3 d

d ) 2

2
3 (5

20 d 2

2

5(5 + × + d ) = × +

Figure 24.18 Analysis of a propped retaining wall - Examples 24.2 and 24.3.