2. Wall Stability Checks

The wall has two failure modes: 1) Wall parts may not be strong enough to resist the acting forces, 2) the wall as a rigid body may be displaced or overturned by the earth pressure acting on it. The latter will be discussed in this section to ensure that the retaining wall is stable by checking stability against overturning, sliding, and allowable soil bearing pressure.

Note: two cases are being examined. Case 1 where surcharge load is applied to point a (see Figure 3), and Case 2 where surcharge load is applied to point b.

2.1. Wall Overturning Check

Case 1 governs for wall overturning since it generated the highest overturning with the least resistance.

Weights and moments about the front edge of the wall are shown in the following table (See figure 2 and design data section):

Table 1 - Weights and Moments about the Front Edge

Component Weights

W, kips

x, ft

Mr, ft-kip

W1

1.36

4.08

5.55

W2

0.68

4.67

3.18

W3

2.19

4.88

10.69

W4

0.25

4.42

1.11

W5

0.90

1.88

1.69

W6

0.54

4.86

2.62

W7

7.57

7.42

56.17

Total

13.49

81.00

The overturning moment is equal to:

Factor of Safety against overturning:

2.2. Soil Bearing Pressure

The distance of the resultant force from the base slab front edge is:

The resultant is barely outside the middle third of the foundation (it is assumed that the bearing pressure becomes zero exactly at the edge of the heel as shown in Figure 2). The maximum soil pressure at the toe is calculated as follows:

Reference 1 (Figure 16.5c)

Reference 1 (Figure 16.5c)

The soil pressure values calculated for Case 1. The soil pressure values for Case 2 do not govern for overturning and sliding. However, values calculated from Case 2 are needed for foundation flexural design as follows:

Reference 1 (Figure 16.5a)

Reference 1 (Figure 16.5a)

2.3. Wall Sliding Check

Case 1 also governs for sliding since it produces the least pressure and corresponding friction resistance.

The coefficient of friction that applies for the length along the heel and key is 0.5, while the coefficient of friction for the length in front of the key is equal to the internal soil friction, that is, tan 30ᴼ = 0.577. More information about selecting the friction coefficient can be found in the reference in chapter 16 section 4. (for case where surcharge load is applied to point a):

Friction, toe:

Friction, heel and key:

Passive earth pressure:

Note that the top 1.5 ft layer of soil is discounted in this check as unreliable.

Total:

Factor of Safety against sliding:

Thus, the retaining wall with the selected geometry is externally stable.