EQUILIBRIUM TIME OF SCOUR NEAR WATER
ENGINEERING STRUCTURES ON RIVER FLOODPLAINS
Oskars Lauva, Boriss Gjunsburgs
[email protected]
1
Introduction
 River flooding is identified as one of the most important natural hazards in
the EU in terms of economic loss;
 Flood occurrence is projected to increase even further with climate change.
Main reason – general increase in winter precipitation;
 1997 floods in Poland and Czech Republic were responsible for losses of
about EUR 5.2 billion;
 Next three decades Extreme floods are likely to double with triple the
expected damage (at least EUR 4 billion per year);
 Despite the significant investment of researchers, hydraulic structures still
fail due to scouring processes;
 Water engineering structures change the natural flow:
– Contracted flow;
– Streamline concentration;
– water level change at the structure;
– Increased local flow velocity & vortex system.
2
Literature review
Since the scouring process at hydraulic structures is never
ending, threshold criteria are used for equilibrium time of
scour evaluation:
 Scour increase in 24 hours:
• < 5 % of pier diameter [Melville and Chiew, 1999];
• < 5 % of flow depth / abutments length [Coleman et al., 2003];
• < 5 % of 1/3 of pier diameter [Grimaldi et al., 2006];
 The proposed threshold criteria are only depending on the
size of the hydraulic structure, and not on hydraulic
parameters of the flow.
3
Literature review
Parameters used
Approach flow depth;
Approach flow velocity and critical
flow velocity;
Abutments length / pier diameter;
Froude number;
Median sand grain size and density.
Parameters avoided
Flow contraction;
Local flow velocity;
Bed stratification;
Flood duration, sequence,
probability and frequency.
Computation of sediment discharge in rivers: the contributions by
Levi and Studenitcnikov revisited. S. Evangelista, J. Govsha, M.
Greco, B. Gjunsburgs. – Journal of Hydraulic research, 2017.
4
Method
The differential equation of equilibrium for the bed sediment
movement under clear-water conditions was used (Levi’s formula for
sediment discharge):
dhs
dW
2
(1  p)
 ahs
dt
dt
(1  p)
dW
 Qs
dt
p – porosity of riverbed material, %;
W – volume of the scour hole, m3;
t – time, s;
Qs – sediment discharge out of the scour hole;
a - equal to 3/5 πm2 where m - steepness of the scour hole;
hs – scour depth, m;
A – parameter in Levi (1969) formula, A = f(, V0, Vl, di, hf);
B – width of the scour hole, equal to mhs, m.
Qs  AB  Vl 4
Levi (1969)
5
Method
Local flow velocity at the structure for any depth of scour:
Vlt 
Vl
h
1 s
2hf
Vl – local flow velocity at the structure, m/s;
hf – water depth in the floodplain, m.
Critical flow velocity at the structure can be determined by the
Studenicnikov (1964) formula:
V0  1,15 g d i 0,25h 0,25
f
g – acceleration due to gravity, m/s2;
di – grain size of the bed material, m.
6
Method
The critical flow velocity V0t at the structure for any depth of
scour hs is:
0,25

h 
V0t    3,6  d i0,25  hf0,25 1  s 
 2hf 
β - coefficient of critical flow velocity reduction near the structure (after
Rozovskij, 1956).
At a plain riverbed the formula for A is:
A
5,62  V0 
1
1 

 
Vl  d 0,25  h 0,25
i
f
1,25
V0t V0 
hs 
1 


Vlt
Vl  2hf 
At any depth of scour:
1,25 

hs 
5,62  V0 
1

1 

Ai 
1
0,25

 
Vl  2hf 


h

 d 0,25  h 0,25 1  s 
 2h 
i
f
f 

7
Method
Then Vl is replaced with Vlt and parameter A with Ai:
Qs  Ai  mhs  Vl4t  b
hs

h 
1  s 
 2hf 
4
b  Ai mVl4
After separating the variables and integrating:
a 3 m
Di  
b 5 A V 4
i l
3
m
Dequil 
4
5A
equil  Vl
Di – constant parameter in short time interval.
t  4 Di  hf2 N i  N 0 


tequil  4 Dequil  hf2 N equil  N 0
hequil
xequil  1 
1 6
1 5
2h f
N equil  xequil
 xequil
6
5
N0 = - 0,033 – constant to calculate scour
in the previous time step;
hequil – equilibrium scour depth, m.
8
Threshold condition
Ratio of critical flow velocity to the local one at the structure is
accepted as the point of equilibrium;
V0t  Vlt 
V0t
 1  tequil  
Vlt
The threshold criterion for the equilibrium time of scour
calculation checked and accepted is equal to:
1,25
h


V0t V0
equil 


1
 0,985


Vlt
Vl 
2hf 
9
Data computer-modelling
0,40
0,12
hs (scour depth)
0,10
0,30
0,08
0,25
0,20
0,06
0,15
0,04
V0t (critical velocity)
Calculated
Test results
0,10
0,05
Veleocities, m/s
2 experiment campaigns:
4 contraction rates;
3 flow intensities;
2 sand types;
24 test runs.
0,02
0,00
0,00
4
Time in hours
Test duration of
7 hours was
prolonged until
equilibrium was
reached.
6
20
8
Test EL2
7h
2
Depth of scour, cm
0
15
Calculated scour
development
10
Scour development
during test
5
h equil
Depth of scour, m
0,35
Vlt (local velocity)
0
0
1
2
Time in days
3
4
10
Computer-modelling results
TEST Q/Qb
AL1
AL2
AL3
AL4
AL5
AL6
AL7
AL8
AL9
AL10
AL12
5,27
5,69
5,55
3,66
3,87
3,78
2,60
2,69
2,65
1,56
1,67
Fr
0,078
0,103
0,124
0,078
0,103
0,124
0,078
0,103
0,124
0,078
0,124
tcomp (h) tform (h)
99,00
190,00
228,00
103,00
144,00
172,00
48,00
93,00
100,80
12,40
36,00
e (%)
95,93 -3,10
183,66 -3,34
238,78 4,73
119,10 15,63
152,02 5,57
158,37 -7,92
46,85 -2,40
103,12 10,88
95,63 -5,13
11,42 -7,90
32,26 -10,39
Increase in flow contraction
rate leads to equilibrium
time of scour increase.
Increase in flow intensity
results in equilibrium time
of scour increase.
Average (n=11) percent relative error is 7,0 %;
For d2=0,67 mm  7,4 % (n=11).
11
Theoretical analysis
Processing of experimental data and theoretical analysis of the
method showed that equilibrium time of scour depends on
 Q
V0 h hequil 
Fr
d

tequil  f 
; Pk ; Pkb ; ; ;
; ;

Q
i
h
V
h
h
f
l
f
f 
 b
Q/Qb – flow contraction rate;
Pk and Pkb – kinetic parameters of the flow;
Fr/i – ratio of the Froude number to the river slope;
d/hf – dimensionless sand grain size;
V0/Vl – ratio of the recalculated critical flow velocity to
the local flow velocity;
h/hf – relative flow depth;
hequil/hf – relative scour depth.
12
Graphical analysis
6
5
4
3
2
1
0
d2=0,67 mm
d1=0,24 mm
0
50
100
Time (h)
Time of scour increases by
increase in flow contraction.
Relative depth of scour
Contraction rate of the
flow
A graphical analysis of the processed data showed equilibrium
time of scour dependence from the following parameters:
4,0
d2=0,67 mm
3,0
2,0
1,0
d1=0,24 mm
0,0
0
100
200
Time (h)
300
As relative depth of scour
increases, time of scour
increases as well;
13
Time of scour increases by
increase in relative velocity of
the flow;
Froude number
0,15
Relative velocity of
the flow
Graphical analysis
3,0
2,5
2,0
1,5
1,0
0,5
0,0
d2=0,67 mm
d1=0,24 mm
0
0,10
0,05
100
200
Time [hours]
300
d1=0,24 mm
d2=0,67 mm
0,00
0
100
200
Time (h)
300
Time of scour increases by increase
in Froude number;
14
Conclusions
1. Proposed threshold criteria depend on physical parameters;
2. Differential equation of the bed sediment movement in clearwater conditions was used and a new method was worked out;
3. New hydraulic threshold criterion was proposed βV0t/Vlt=0,985;
4. Processed data revealed that with an increase in flow
contraction and approach flow Froude number, time of scour
increases as well;
5. Theoretical and graphical analysis of the method showed that
equilibrium time of scour depends on flow contraction, kinetic
parameters of the flow, relative depth of scour, Froude number
and relative velocity of the flow.
15
Thank you!
16