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 500 kPa and standard deviation= 200 kPa.
Settlement is log-normally distributed with mean=1.5 cm and standard deviation =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).
Calculate the probability that the footing will fail.