Question

A concrete footing, exerting an applied pressure of 200 kPa on the soil, may fail from bearing capacity (B) or excessive settlement (S). Due to soil variation, the following are given:

• Bearing capacity is normally distributed with mean, μ=500 kPa and standard deviation, σ = 200 kPa

• Settlement is log-normally distributed with μ=1.5 cm and σ =0.3 cm.

• The probability that the footing fails in bearing capacity knowing that it had settled excessively is 0.2

• Maximum permissible settlement is 2.5 cm. (i.e. S> 2.5 cm is considered excessive settlement).

(a) Calculate the probability that the footing will fail.

(b) If the foundation system of a multistory building consists of 30 such footing, calculate the probability that none of the footing will fail.

Answer 1