The effects of tree belt along levee on levee break flows Susumu Yoshida, Yoshihisa Kawahara, Ryota Tsubaki, and Yuya Yamada Graduate School of Engineering / Department of Civil and Environmental Engineering, Hiroshima University, Kagamiyama, Higashi-Hiroshima, 739-8527, Japan
Introduction Accurate inundation prediction is essential
Experimental setup
in a large-scale channel to measure the water depth and hydrodynamic force acting on bulding.
to develop an effective plan to reduce the damage due to inundation. This requires the proper modeling of the effect of complex topography, especially building arrangement and effect of tree belt. The tree belt along levee is one of the traditional measures to mitigate the damage induced by levee-break inundation. In this study, we conduct a series of experiments
Main features of this study ● The synergistic effects of the tree belt and the urban topography is observed and discussed. ● Five cases of vegetation arrangements are compared, so that the effects of the vegetation arrangemen on the inundation flow are discussed and modeled.
Tree belt
Experimental channel
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Tree belt model
Close-up of urban model Force measuring building
1.20 m
Upstream reservoir
0.305 m
Levee break point
0.11 m
0.50 m
0.11 Wave height gauge Frame
0.11
Measuring point
Building model
Building model
9cm
Flow
y=1.50
model
x=0.305
(b) Measuring point of water level
Case2
Case3
Case5
Case4
0.115 Case 1 No vegetation.
Second peak
m
Case 2 3 rows, alligned.
Propagation front
4.0
0.035
Steady state
3.0
Case 4 5 rows, alligned.
2.0
2m
（a）t=1sec
Relative hydrodynamic forces
Hydrodynamic force (N)
Figure Experimental Channel.
Front
15
20
25
45
50
55
（b）t=2sec
60
Elapsed time (s)
Case 1 No vegetation.
Second peak
（c）t=4sec
Case 3 3 rows, staggered.
5.0 4.0
Re-reflection
3.0
Steady state
Case 5 5 rows, staggered.
2.0
（d）t=6sec
1.0 0.0 0
5
10
15
20
Elapsed time (s)
25
45
50
55
60
First state Second state Steady state
93
92
90
87
87 81
80
83 83
77 72
70 60 50 Case2
Case3
Case4
Case5
Figure Hydrodynamic forces acting on the building
100 90
Estimation neglecting cumulative effect (R2=0.67.)
Estimation considering cumulative effect (R2=0.82.)
82 81
81
1 F1 ＝ ρC d 1 AU 2 , 2
where F1 is drag force and subscript 1 denotes row number, ρ is the density of fluid, Cd is the coefficient of drag, A is projected area of the tree and U is representative velocity. For the second row, by introducing reduction rate of the drag coefficient r, drag force can be estimated as follows:
87 86 86
80
To estimate drag force of the tree belt in our experiment, drag force of the first row of tree belt can be estimated as follows:
83
1 F2 ＝ ρC d 1 rAU 2 . 2
78
77 72
70
70
where r = 0.68 for Case2 and Case4 and r = 1.00 for Case3 and Case5. This equation can be simplified as
68
F2 ＝αr ,
where α＝ 1 / 2ρC d AU 2 . Obviously, F1＝α. Now, total drag force of the tree belt can be estimated by the summation of drag forces of each row. If we neglect cumulative effects of multiple wake interaction, total drag force can be calculated as
60
Ft ＝α(n 1)r ,
50 Case 2
Case 3
Case 4
Case 5
Figure Estimation of relative hydrodynamic forces.
where n is number of row. If we consider cumulative effect of drag reduction, the total drag force is estimated as follows: 1－ r n Ft ＝α 1－ r Parameter α is determined empirically in this study. Assumption introduced in this estimation is quite bold, however the result considering cumulative effect represents the trend of experimental result well.
Front
Reflection 7.0
First peak
98
89
Case1
1.0
6.0
Experimental result
100 100 100 94
0.0
Hydrodynamic force (N)
Downstream weir
Figure Configulation of tree belts.
7.0
10
10.4 m Bed slope: 1/624
Urban model
100
5.0
3.0 m
(Unit:m)
Results
5
0.20 m
5.6 m
Upstream side weir
diameter
Figure Setup of force transducer and wave height gauges.
0
0.12 m
vegetation
21cm
First peak
0.12 m
20cm
gap 0.25mm
6.0
0.44 m
1.25 m
0.055 4.0 m
Flow
(a) Side view of measurement set up
0.21 m
1.55 m
0.11
(acrylic)
Fz
0.11
0.055
Tree-belt region
0.11
Relative hydrodynamic forces
transducer
Flange
Fx
0.11
1cm 1cm
Threecomponent force
Fy
0.11
Force transducer
（e）t=55sec (Steady state)
CFD water level distribution of Case 1
Figure Time-series of hydrodynamic forces in each case.
Conclusions
(1) Reduction rates of the hydro dynamic force acting on the building by installing different configulations of the vegetation model are measured. (2) Empirical formula for the reduction rate at the steady
state is proposed. Not shown in this poser but in the paper
(3) It is experimentally confirmed that the hydrostatic assumption is valid to estimate hydrodynamic force acting on the building, except in the phase of rapid change.
