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ABSTRACT
Flood control is one of the most important and difficult tasks in river basin management in terms of present several uncertainties. This study aims to follow the risk management and coordination analysis in designing a riverine flood defence system, actually, a composite multi-section flood control levee system considering the aleatory and epistemic uncertainties using contagious distributions. A stochastic optimization model was developed based on Monte Carlo analysis for uncertainty propagation, and then the system's optimum dimensions were computed in the single-section and multi-section cases for overall comparisons. Using the concept of ‘scenario probability’, the coordination of the system and its individual components was analysed. The results indicated that by increasing the complexity (from a single-section to a multi-section model) and by the separation of uncertainties (into epistemic and aleatory), the coordination of the system decreases 130% and 30%, respectively. Moreover, it was found that when economic uncertainty was considered, unexpected results may be obtained so that by increasing the system dimensions the total cost decreases. Finally, after analysing the sample histograms of the system's components, several distributions have been suggested. When there are vast datasets that might be confusing for decision-makers, the systematic method proposed here makes risk management easier.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
| Abbreviations and symbols | ||
| aomr | = | the annual operation, maintenance and replacement |
| CDF | = | cumulative distribution function |
| CCDF | = | complementary cumulative distribution function |
| DE | = | differential evolutionary |
| GSA | = | global sensitivity analysis |
| LHS | = | Latin hypercube sampling |
| PDA | = | potential damage area |
| = | probability density functions | |
| RSM | = | response surface methodology |
| ACOSTtotal | = | annual total cost |
| ACOSTland | = | annual cost of purchasing lands |
| = | the area of the river channel in the section r | |
| = | the area of the levee section on the left (right) of the river reach r | |
| = | the area, wetted perimeter, and roughness coefficient in the right (left) floodplain in the reach r | |
| = | the bottom width of the levee on the left (right) of the river reach r | |
| = | cohesion coefficient | |
| crf | = | capital recovery factor |
| Clev | = | construction cost of the levee |
| CRlev | = | the cost of rebuilding the levees |
| Csy | = | the Skewness coefficient |
| Dr | = | flood damage in the river reach r |
| = | the (average) distance of an individual component j | |
| EADwith | = | expected annual damage or risk cost |
| fQ(Q) | = | the PDF of the peak discharges Q |
| FQ(Q) | = | the CDF of Q |
| = | the distance from the top of the river to the top of the levees in section r | |
| = | the height of the levee on the left (right) of the river reach r | |
| i | = | the interest rate |
| L | = | left |
| Lr | = | the length of the river reach r |
| = | the slope of the levee on the left (right) of the river reach r | |
| = | the average slopes of the floodplain in the PDA on the right (left) sides of the river in the reach r | |
| Nr | = | river reaches |
| n | = | useful life of the levees in years |
| = | the roughness coefficient in the right (left) floodplain in the reach r | |
| = | the roughness coefficient of the river channel in the section r | |
| Pi | = | the overall risk |
| Psc | = | Scenario probability |
| Psc_0.1 | = | Pscs corresponding to the risk of 0.1 |
| = | the wetted perimeter of the river channel in the section r | |
| = | the wetted perimeter and roughness coefficient in the right (left) floodplain in the reach r | |
| Qdes | = | the design peak discharge |
| Qj | = | the peak discharge |
| Qdes | = | design flood |
| qa_pb | = | a point with probability b on quantile a |
| R | = | right |
| r | = | the number of sections |
| Sr.riv | = | the longitudinal slope of the river channel in the section r |
| sc | = | the scenarios considered for the uncertainties |
| = | the top width of the levee on the left (right) of the river reach r | |
| ucostlev | = | the volumetric unit cost for the levee’s construction |
| uprcbuild | = | the unit price of buildings |
| = | the unit price of lands in the potential damage area on the left (right) of the river reach r | |
| X | = | random variable |
| = | the setback of the levee | |
| = | the setback on the left (right) of the river reach r | |
| Z | = | the normal variable |
| = | the safety factor of the levee slope on the right (left) side of the section r | |
| = | objective function | |
| β | = | the coefficient of OMR cost |
| = | the angle of the slope of the levee on the left (right) side of the river section r | |
| = | specific gravity | |
| = | internal friction angle | |
| μy | = | the mean of y |
| σy | = | the standard deviation |