Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 155

and the graphical N-sigma rule provides a straightforward means for characterizing the
uncertainty in the shear strength envelope.

3.6 CoMPutIng ProbabIlItY oF FaIlure

Four methods of computing probability of failure are described in this chapter. To illustrate
these methods, they are used to calculate the probability of failure of the cantilever retaining
wall shown in Figure 3.16. Three possible modes of failure will be considered for each method:

• sliding on the silty sand layer overlying the foundation clay,
• sliding beneath the silty sand layer, at the top of the clay foundation, and
• bearing capacity failure in the clay foundation.

Calculation of probabilities of failure for these modes of failure begins with conventional
deterministic analyses to calculate factors of safety against sliding on the granular layer,
sliding in the clay, and bearing capacity failure.

3.6.1 Deterministic analyses
The wall dimensions and properties for this example are shown in Figure 3.16. The rein-
forced concrete footing was cast on a 10 cm thick layer of silty sand to prevent softening
of the clay foundation when the wet concrete was poured for the wall footing. As a result,
sliding can occur on top of the silty sand layer or on top of the clay foundation, depending

4.8 kN/m 2

0.30 m

11.4°

∑ γ eq=7.1 kN/m 3
∑ γ bf=18.9 kN/m 3
∑ Surcharge = 4.8 kN/m 2
∑ Ks=surcharge coeƒcient =
0.25
∑ Vertical shear coe ƒ cient =
Kv = 0.1

7.2 m

6.10 m

E v

E h

(assumed to be
0.4H)

Silysand layer beneath
concrete, μ = 0.5

2.9 m

0.61 m

0.46 m

0.46 m

Saturated clay foundation,
S u =120 kPa 4.3 m

Figure 3.16 Cantilever retaining wall with silty sand backfill.