A pile is designed to have a mean capacity of 20 tons: however, because of variabilities, the pile capacity is lognormally distributed with a coefficient of variation (c. o. v.) of 20%. Suppose the pile is subject to a maximum lifetime load that is also lognormally distributed with a mean of 10 tons and a cov of 30%. A number of piles may be tied together to form a pile group to resist an external load. Suppose the capacity of the pile group is the sum of the capacities of the individual piles. Consider a pile group that consists of two single piles as described above. Because of proximity, the capacities between the two piles are correlated with a correlation coefficient of 0.8. Let T denote the capacity of this pile group. Required:
Determine the mean value and c. o.v. of T, and calculate the probability of failure of the pile group by MCS.