urban flood modeling simulation of flood in a dense urban area using 2d shallow water equations
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URBAN FLOOD MODELING
Simulation of flood in a dense urban area using 2D Shallow
water equations
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Flood Event
• City: Southern French city of Nimes
• Event : 03 Oct 1988
• Cause: Downpour of 420 mm in 8 hours
• Return period: 150-250 years
• Depths observed: 3 m
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Modeled Zone
• Suburban area: ‘Richelieu’• Dimensions: 1400 m along N-S, 1050-
220 m along E-W• Boundaries: Northern and eastern
side by railway embankment, western by hills
• Building type: Military barracks, hospital, regular network of narrow streets
• Long. slope: >1%• Flood cause: Storm runoff
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Data for Model Development
• X-sections: 200 of 60 streets
• Typical profile: 11 points
• Flood marks: Map and 99 marls • Hydrograph: Rainfall-Runoff
transformation
• No. of hydrographs: Two, east and west
• Sewage network : Decoupled; interaction capacity<10% Qmax
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Mesh Generation
• Junction profiles: Generated, linear interpolation on altitude
• Buildings: Impermeable
• DEM: 25000 pts
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Reference Calculation
• Dx streets: 25 m• Mesh density: 100 cells at
crossroads, 30-60 in each street
• Manning’s ‘n’ and 0.025 and 0.1 m2/s• Time step: 0.01 sec• Simulation time: 10 hrs• Outflow b.c: Fr=1• Initial condition: dry bed
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Flood Progression
• High velocity (3-4 m/s) and supercritical flow on streets aligned along N-S axis.
• Small velocities(0.5-0.7 m/s) and subcritical flow occurs in streets aligned along E-W axis.
• The time to peak in streets correspond with time to peak of the eastern hydrograph.
• Flow at crossroads is generally complex with mixed flow regime.
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Comparison Parameter
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Comparison with Observations• Flooded zone extent correctly simulated.• Measurement with peak values of depth.• About 40% overestimated and 60%
underestimated.• The max. difference is 1.6 m and the average
difference is 0.41 m• Good agreement in the northern zone• Strong underestimated in the narrow streets (43
cm) • Slight overestimation in the southern part (16 cm)
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Sensitivity Tests 1: Inflow and Storage Effects
1A: Inflow increased by 20%
• To check hydrological uncertainties.
• Depths increase by 12.5 cm
• Higher increase in the upstream zone than in the downstream and the southern part.
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Sensitivity Tests 1: Inflow and Storage Effects
1B: Rainfall vol. taken into account• Rainfall (61 mm/hr) falling over the
simulated zone added to the inflow hydrographs
• The rainfall vol. (212,000 cu.m) is very small compared to the flood hydrographs (3600,000 cu.m)
• Limited effect. Peak water depths increased by about 4 cm.
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Sensitivity Tests 1: Inflow and Storage Effects
1C: Creation of a Storage Zone• Reference case computation assumed
watertight buildings with no storage in lawns, parks, basements etc.
• The military barracks (l’ecole d’artillerie aerienne) are the largest open space.
• Volume stored is about 80,000 cu.m.• A very small reduction of peak water
depths at d/s is observed (about 1 cm)
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Sensitivity Tests 2: Roughness and Kinematic Viscosity Coefficients
2A: Effect of Kin. Viscosity • represents turbulence and the
heterogeneity over the vertical.=khu*, k=0.01, k=0.1 m2/s.
• Small to no effect on computed depths.
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Sensitivity Tests 2: Roughness and Kinematic Viscosity Coefficients
2B: Effect of Manning’s ‘n’• ‘n’ represents the effect of friction on the bottom,
walls, irregularities, obstacles to flow.• n increased to 0.033 from 0.025.• Depths overall increase by 10 cm.• Depth increased at Faita-Sully junction thus
decreasing the discharge in the d/s sections.• Flow regime strongly altered at crossroads and
changes from supercritical to subcritical (fig).
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• Underestimation decreased in the central zone, overestimated depths in the northern zone and in the southern zone.
• Globally the depths increase and improve but locally there is worsening.
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Sensitivity Tests 2: Roughness and Kinematic Viscosity Coefficients
2C: Different Manning’s ‘n’• n=0.05 selected for the central part
comprising of narrow streets meeting at right angle to each other. This accounts for increased friction due to walls and presence of parked cars. Elsewhere n is same as that of reference calculation
• Results improved significantly in the central zone where dh reduced to 23 cm from 43 cm.
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Sensitivity Tests 3: Downstream Boundary Conditions
3A: Zero depth gradient boundary • The d/s b.c is changed to a zero depth
gradient condition for subcritical flow and no d/s influence for supercritical flow.
• Depth increases in the streets in the vicinity of the d/s boundary
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Sensitivity Tests 3: Downstream Boundary Conditions
3B: Representation of backwater effect• To simulate backwater effect of the
outlying areas upon the modeled zone, flow prevented from leaving through S1, S2 and S10.
• Flow strongly affected in the whole southern zone and flow depths increase as far up as the southern part of the central zone
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• Whereas the choice of b,c affects the flow only in the close vicinity of the exit the choice of exit has a far greater influence in the upstream zone extending upto four streets backwards.
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Sensitivity Tests 4: Simplification of the Street Profile
3B: 4 point, 5 point and 7 point profiles
• To reduce the data requirement and calculation times
• For 11, 7, 5, 4 points cells at the junction are 64, 16, 4 and 1 respectively.
• The general form of the results remains same except that depths are increased by about 10 cm.
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• The 7 and 11 point calculation results are very similar
• In 5 and 4 point versions of the calculations flow detail at a junction is averaged out e.g if a flow at a junction is mainly subcritical with a small supercritical area. The model calculates an average subcritical flow depth.
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RESULTS SUMMARY
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Conclusions
• 2D Shallow water equations in complete form were used, without interaction with sewage network to model urban flood.
• The results showed a standard deviation of 50 cm which is on the higher side but reflects the uncertainty in flood marks, insufficient topographical data, missing information about mobile obstructions, wall irregularities etc.
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• Kinematic viscosity seems to exercise negligible to no influence on he results.
• Manning,s ‘n’ strongly affects the flow but no single value can be determined to correctly represent all the zones.
• Assigning each zone an ‘n’ reflecting its structural characteristics seems to be the best strategy.
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Recommendations• The input hydrographs should be precisely
calculated for an accurate peak water depth map creation.
• If the rainfall volume is small compared to the input hydrograph volume than there effect is going to be negligible and can be neglected.
• If the storage volume is small compared to the input hydrograph volume they can be safely neglected.
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• Different friction coefficients should be applied to various homogeneous urban zones, depending on the width of the streets and fixed and mobile obstacles that may increase the resistance to flow.
• Collecting information about the flooded areas just downstream from the studied zone is important in establishing an accurate outflow boundary condition.
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• A 5 point representation for a street profile can represent a fairly good estimate for the general overview of the flood dynamics reducing data needed and calculation times
• However, if information about local depths is available than a more precise description of the streets is required to calibrate the model.
• Use of a 2d code to assess the flood progression through an urban zone is a convenient tool for hydraulic engineers and urban planners.