Concept:
Return period (T):- It is defined as the average time interval after which a flood of given discharge is equalled or exceeded.
\({\bf{T}} = \frac{1}{{\bf{p}}}\)
Where,
p = probability of occurrence or exceedance of an event with rank ‘m’.
The probability of occurrence or exceedance is given by three methods:-
Method |
Probability(p) |
Weibull Method |
\(\frac{{\rm{m}}}{{{\rm{N}} + 1}}\) |
California Method |
\(\frac{{\rm{m}}}{{\rm{N}}}\) |
Hazen Method |
\(\frac{{\left( {{\rm{m}} - 0.5} \right)}}{{\rm{N}}}\) |
N = Total number of events
Thus as per Weibul method,
\({\rm{p}} = \frac{{\rm{m}}}{{{\rm{N}} + 1}}\)
\(\therefore {\rm{T}} = \frac{1}{{\rm{p}}} = \frac{{\left( {{\rm{N}} + 1} \right)}}{{\rm{m}}}\)
Hence the required return period is (N+1)/m
Important Point:
Hydraulic structures design are based on risk assessment and this is done by analyzing the return period of the design discharge.
Risk is defined as the probability of exceedance at least once in the designed life of the structure and Reliability is the probability of non-occurrence of the event in the design life.