1096Kb - River Engineering and Urban Drainage Research Centre

Temporal variation of scour depth at Complex Abutment
Reza Mohammadpour1*, ,Aminuddin Ab. Ghani 2 ,Nor Azazi Zakaria3
1
,Post-Doc/ researcher River Engineering and Urban Drainage Research Centre (REDAC), Universiti
Sains Malaysia, Engineering Campus, Seri Ampangan, 14300 Nibong Tebal, Penang, Malaysia. Email:
[email protected]
2
3
Professor and Deputy Director, REDAC, Universiti Sains Malaysia, Engineering Campus, Seri
Ampangan, 14300 Nibong Tebal, Penang, Malaysia.
Professor and Director, REDAC, Universiti Sains Malaysia, Engineering Campus, Seri Ampangan,
14300 Nibong Tebal, Penang, Malaysia.
*corresponding author: Email: [email protected]
Abutment scour is a main problem in collapse of bridges. Local scour around abutment is a
complicated problem that has been investigated significantly over last years. In this study,
temporal variation of local scour at complex abutment is investigated analytically. The complex
abutments were included a rectangular abutment founded on a larger rectangular foundation. A
series of laboratory experiments was conducted to collect data for model application. The
temporal variation of scour depth were collected at uniform and complex abutment under the
clear-water scour condition. The top surface foundation was located below the initial bed at
three different positions with respect to the general level of the channel bed. The mathematical
model proposed in this paper is able to predict the temporal variation of scour depth around
uniform and complex abutment. The variation of scour depth with time was estimated based on
the sediment transport equation. Equilibrium local scour depth is reached when the bed-shear
stress tends to critical bed-shear stress in the scour hole. Reasonably good agreement was also
noticed between the corresponding observed and computed values of temporal scour depth
around uniform and complex abutment.
Keywords: Scour; Complex abutment; Bridge foundations; Scour time, Scour mechanism
Introduction
The local scour around piers and abutments are a main problem in collapse of bridges. The
contraction of flow by abutment/pier changes the flow structure and leads to local scour around
the abutment/pier. In the vicinity of the abutment, the vortex flow develops the local scour hole.
The type of local scour around abutment is classified into clear-water and live-bed scour. The
clear-water scour occurs when the sediment is removed from scour hole but no supply from
approaching flow. In the live-bed scour condition, in additional to remove sediment around
abutment/pier, the flow carries the upstream sediment into the scour hole.
A large number of real abutments/piers are non-uniform in shape and consist of different kind
of components (Sheppard and Glasser 2004). Such abutments/piers are named here as complex
(or non-uniform) abutments/piers. A vertical wall complex abutment can be defined as
rectangular abutment resting on larger foundation or caisson. The time variation of local scour
around abutment is an essential aspect to the hydraulic engineering (Dey and Barbhuiya, 2005).
Most investigations have been carried out on abutment/pier with uniform cross section, but due
to geotechnical and financial reasons, actual abutment/pier is built on foundations with piles
(Melville and Raudkivi, 1996; Mia and Nago, 2003; Coleman, 2005, Ataie-Ashtiani et al.,
2010). Similarly, most equations recommended on the time variation of local scour around
uniform abutment (Dey and Barbhuiya, 2005, Cardoso and Fael, 2010, Ballio and Orsi,
2001,Coleman et al., 2003, Oliveto and Hager, 2002, Yanmaz and Kose, 2007). Furthermore, a
number of studies have been undertaken to forecast the local scour at complex piers under clearwater conditions (Jones 1989; Parola et al. 1996; Sheppard et al. 1995; Melville and Coleman
2000; Mia and Nago, 2003; Coleman 2005).
Due to effect of foundation or pile, the flow pattern around complex abutment/pier is more
complicate than uniform abutment/pier (Kumar et al., 2012).
In spite of using the uniform abutment, there is limited information about the effect of the
foundation or pile cap on the complex abutments (Mohammadpour, 2013a). If the effect of
foundation geometry was integrated into the methods of estimation of the scour depth, however,
the conservative approach would be unnecessary. Furthermore, abutment scour failure may be
reduced by proper design of the foundation. Since the temporal variation of scour at complex
abutment was not studied in detail, then an attempt to investigate about time variation of local
scour at complex abutment seems to be very necessary.
The main objective of this study is to experimentally study time variation of the local scour
around complex abutment. The short abutments with a ratio of abutment length/flow depth<1
(Melville, 1992), were chosen at all experiments. The experiments were conducted under the
clear water conditions at different abutment with uniform and non-uniform (complex) shape.
2 Experimental Setup
A rectangular cross section flume with dimension of 6.0 m long, 0.6 m wide, and 0.6 m deep
was chosen to conduct the experiments. The flume was equipped with a 0.25 cm deep sand
recess through the channel and several floatable screens were placed at the entrance of the flume
to reduce the flow turbulence. To adjust the water level at desired depth, a controlling gate was
used at the end of the channel. A camera inside the transparent abutment with a ruler were used
to measure the scour depth at the nose of the abutment at different time (Fig 1).
Fig. 1) transparent abutment and ruler with camera
Three short uniform abutment and four short complex abutment were used in this study
(Table 1). The vertical-wall shape was chosen for both uniform and complex abutment (Fig. 2).
To avoid the effect of flow depth on local scour, the ratio of abutment length (L) to flow depth
(y) was considered smaller than one, L/y<1 (Melville, 1992). For all the experiments uniform
sand was used with d50 = 0.60 mm and geometric standard deviation, σD=1.20. To maintain the
clear water condition, the flow velocity was set close to the critical velocity of sediment (U/Uc
between 0.94 and 1), where Uc was estimated using the Shields diagram and expressions given by
Melville and Coleman (2000).
At the end of each experiment, water was drained off carefully without any disturbance in
the local scour, and a point gauge with an accuracy of  1 mm was used to measure the
topography of scour hole around abutments.
Table 1) Abutment-Geometry Characteristics for the Present Study
Foundation
Abutment
Length ratio
Experiment
No.
Abutment
Type
Lf (cm)
Bf (cm)
L (cm)
Lf(cm)
AB 1
Uniform
-
-
4.0
-
-
AB 2
Uniform
-
-
5.5
-
-
AB 3
Uniform
-
-
7.0
-
-
FA 21
Complex
5.5
11.0
4.0
0.73
0.73
FA 33
Complex
9.0
18.0
7.0
0.78
0.78
FA 42
Complex
12.0
24.0
5.5
0.46
0.46
FA 43
Complex
12.0
24.0
7.0
0.58
0.58
(L/Lf)
Fig. 2) Complex vertical-wall abutment
2 Test duration
The time-dependent of local scour at abutment was investigated in several studies, and
different definition was recommended for equilibrium scour depth. In clear water condition the
equilibrium scour depth is reached asymptotically with time (Melville, 1992; Melville and
Chiew, 1999).
According to Ettema (1980), the scour depth does not increase “appreciably” in the
equilibrium time. Melville and Chiew (1999) defined the equilibrium time for piers when the
scour depth did not change by more than 5% of the pier diameter over a period of 24 hours (or no
more than 1% of diameter within 5 hours). Oliveto and Hager (2002) indicated that development
of the scour hole never stops. Feal et al. (2006) reported that almost between 146 and 509 hours
(approximately from 6 to 21 days) may be required to reach such a condition in vertical wall
abutments. However, from a practical standpoint, it is very difficult to perform a wide range of
experiments with such a long duration. Then, in the practical tests, the duration of experiments
was selected based on other criteria. Kumar et al. (1999) stopped their experiments for pier when
the scour depth did not change by more than 1 mm over a period of 3 hours. Mia and Nago
(2003) stopped their tests when the variation of scour depth was less than 1 mm scour by 1 hour.
Mohammadpour et al. (2013) indicated that the most of scour occurs during the first hours of
experiments. Their result showed that approximately 80-90% of the scour depth at abutment
occurred during the initial 20-40% of the equilibrium time. Similar result was reported for the
local scour around piers.
In this study a long-time experiments was conducted for uniform abutment of AB-II (~67 hrs)
and AB-III (~84 hrs). The result shows that 96% equilibrium scour depth is obtained after 42 hrs
(2500 min). After this time in uniform abutment, the variation of scour depth for each time
interval of 7 hrs was less than 1 mm. Since the peak flood flow may not last long enough to
develop equilibrium scour depth, the duration of 42 hrs was chosen as a criterion for further at
complex and uniform abutments.
3 Scour Zones and Scouring Process
To investigate the effects of foundation level (Z) on a complex abutment, three foundation
locations (cases) were considered depending on the foundation level (Fig. 2). In Case I, the
foundation level was located below the scour hole. In Case II, the scour depth reached the top of
the foundation, and the horseshoe vortices in front of the abutment were weakened by the
foundation. In Case III, the foundation top was located within the scour hole. In Fig. 2, the
instantaneous scour depth for Case I, Case II and Case III is shown with dst,I , dst,II and dst,III
respectively.
For small abutment sizes, high Z and low flow depths, the equilibrium scour depth at complex
abutment may occur in Case I. Also, this occurs when the depth of the top level of foundation
(Z) is greater than the equilibrium scour depth (dsm). In this case, the complex abutment is similar
to uniform abutment. Melville (1992) suggested a value of 2L for
the maximum equilibrium
scour depth at uniform abutment. However, if the scouring reaches to Z level and foundation
limits the development of scouring, then instantaneous scour depth (dst,II) remains constant
at Z, which is represented as Case II. This condition occurs for 1.2≤Z/L≤2 (Mohammadpour,
2013). On the other hand, the further scouring that occurs generally for large abutments, low Z
and high flow depths, the foundation gets exposed. This zone is considered as Case III in which
the foundation size (Lf) influences on the scour hole. All three cases is shown in Fig. 2b and 2c.
In this study, the effect of foundation was investigated on complex abutment. Therefore, the Z
value was kept less than 2.0L in the all experiments.
Fig. 3) Three cases for complex abutment below the initial bed
a)plan view; b)section A-A; c)section B-B
3 Proposed Model for uniform Abutment
The bed-load sediment transport theory recommended by Yalin (1977) was used to develop a
model for time variation of local scour at uniform and complex abutment. The sediment transport
rate at any time can be defined by the following equation:


q wt
1
 k st 1 
Ln1  a st 
 s d 50 u*t
 a st

(1)
where qwt = the sediment transport rate in weight per unit movable width of the scour hole;
Δ=(ρs–ρ)/ρ ; ρs = mass density of sediment; ρ= mass density of water; γs =ρs g ; d50=median size
of sediment; g= acceleration of gravity; u*t=(τt /ρ)0.5; τt =bed-shear stress at the abutment nose at
time t; k=constant to be determined; st= excess dimensionless tractive force at time t which can
be expressed by:
2
u 
st   *t   1
 u*c 
(2)
Where u*c=(τc /ρ)0.5 and τc = sediment critical shear stress. The a value can be obtained from the
following equation:
a  2.45
u*c
(  s   ) 0.4 gd 50
(3)
The volumetric sediment transport rate per unit movable width (qst) can be determined as:
q st 
q wt
 s
(4)
The qst can be determined using the Equation (1) and (4) as:


1
q st  k d 50 u*t st 1 
Ln1  a st 
 a st

(5)
The scour hole around abutment can be approximated by half a frustum of inverted cone where
the angle of frustum is equal to angle of bed sediment repose Ø. If suppose that the shape of
scour hole remains almost unchanged and just becomes bigger with respect to time with a
diameter at base equal to abutment length (L). Volumetric expressions of the scour hole can be
derived regarding to this approximation. Similar assumption was also considered by Yanmaz
and Altinbilek (1991), and Mia and (2003) to develop the scour depth around piers. As shown
in Fig. 4, the volume of scour hole around uniform abutment can be calculated as :
Qvt 

dst
y
2 
2
dz  BLd st
(6)
0
Where B=the width of abutment (Fig. 1); L=abutment length; y and z are time dependent
coordinates of scour hole. Writing y in terms of z as shown in Fig. 4 and integrating leads to:
Qvt 
 L2
2
d st 
L
2 tan 
d st2 

6 tan 2 
d st3  BL d st
Fig. 4) Geometric definition of scour hole around uniform abutment
(7)
Regarding to Fig. 4, the surface width of the scour hole at time t, is dst /tanØ. Therefore, the
volume of the scour hole per unit movable width of the scour hole at time t, can be determined
as:
q vt 
Qvt

L
 L2

d st2 
d st 
tan   BL tan 
2
2
 d st  6 tan 


 tan  
(8)
The solution of this equation for dst can be expressed as:
q st 
6 tan 

 6 BL 3L2  2
3L
 tan   tan 

qvt  
2
4 
 
(9)
Where qvt should be defined. The primary vortex at different time is shown in Fig. 5. The A0
shows the cross section area of primary vortex before scouring, and Ast is the cross section area
of primary vortex within scour hole during the scour process at time t.
Fig. 5) Primary vortex in front of uniform abutment
a) before scouring, At=A0; b) during scouring, At=A0+Ast
In this figure, total area of primary vortex (At) can be explained as:
(10)
At=A0+Ast
It have been Assumed that before starting scour, the shape of primary vortex is circular therefore
(kothyari et al., 1992; Dey and Barbhuiya; 2005):
A0 

4
(11)
Dv2
Barbhuiya (2003) suggested the following equation to calculated Dv at vertical-wall abutment:
 y
Dv  0.295L 
 L
0.205
(12)
and
Ast 
d
1 d st2
 0.087 st
2 tan 
tan 
(13)
Where Dv =diameter of primary vortex; y= flow depth and L= abutment length.
With increase in local scour hole, the area of primary vortex increases and also the shear stress
under the vortex decreases ( Melville, 1975; Hjorth, 1977). The scour initiates at vertical-wall
abutment when u* ≥0.5uc* (Dey and Barbhuiya, 2005), where u*=shear velocity of approach flow
and uc* = critical shear velocity of bed sediment . To estimate the flow shear velocity, the
logarithmic mean flow velocity for rough bed can be used as:
U
h
 5.75 log
6
u*
2d 50
(14)
The flow velocity and shear stress around abutments were investigated by Ahmad and
Rajaratnam (2000). They found that the bed shear stress increases substantially near the
abutment, and reaching to a maximum value at the abutment nose. The shear stress at the nose of
abutment was estimated equal to 3.63 times of bed shear stress (τ*) before scour begins (At=A0).
With respect to u*t u*   *t  * , the temporal variation of bed shear velocity at any time of t at
nose of abutment (u*t) can be determined using the equation of Kothyari et al. (1992) as:
A 
u*t  1.91u*  0 
 At 
C
(15)


In the equilibrium condition (ds=dse), the area of scour depth (Ast=Ase) is equal to 0.5 d se2 tan  .
In this state, the scour depth at nose of abutment is fixed and equal to dse, then u*t can be
supposed equal to u*c and another form of above equation for equilibrium time is:
u*t
1.91u*
 A0 

 
A
A

se 
 0
C
(16)
In Fig. 6, the experimental data from present and previous studies was used to estimate the
coefficient of C. The best fit line with the experimental data gives a coefficient C=0.16.
The constant of k in Equation (5) was found using the experimental data. First, the
q st d 50 u*t was plotted verses 1  ast . The qst was estimated from experimental scour depth at any

time step of n using the sediment transport rate as q st  q vt n  q vtn 1
 t
n
 t n 1  . As shown in Fig.
6a, the value of k was determined based on Equation (5) and trial and error equal to 4.0. Then
the Equation (5) can be rewritten as:


1
q st  4.0 d 50 u*t st 1 
Ln1  a s t 
 a st

(17)
The depth of scour at any time step n can be determined in terms of qvt as:
d st n 
6 tan 

 6 BL 3 L2 
3L
 tan 2  

tan 
q vt n  
4 
2
 
(18)
And
(19)
n
qvtn   qsti
i 0
Fig. 6) Primary vortex in front of uniform abutment
Fig. 6) Determination of k value for abutment
The following steps have been evolved for the computational of scour depth at abutment under
clear water condition:
1) Calculation of the fixed value of A0 , u* and u*c using equations (11) , (12) and (14).
2) In first time step (t0=0 and n=0), no scour is happened (dst 0 = 0 and qst 0 = 0) then Ast=0,
and At=A0 , therefore using Equation (15) it can be found that u*t0=1.91 u*. Computation of
st0 and a using Equations (2) and (3) respectively in this condition.
3) For next time step (n=1), determine qst1 using Equation (17).
4) Compute qvt1=qst0+qst1 using Equation (19) and calculation of dst1 using equation (18).
5) Determine total cross section (At) using Equations (11) to (13) based on the last dst .
6) Compute new values of st and u*t using the Equations (2) and (15) respectively.
7) Estimation of the new value of qstn for next step using Equation (17) and calculate qvtn
using Equation (19).
8) Calculate dst using Equation (18) for new time step tn=tn-1+1.
9) Steps 4 to 9 can be repeated to obtain the variation of scour depth until u*t=u*c.
3 Proposed Model for variation of local scour around complex Abutment
In this paper, proposed method for computation of temporal variation of scour depth at complex
abutment (dsct) is presented for the cases where the foundation is located under the initial bed
level (Fig. 3). As mentioned previously, three condition arise for calculation of local scour.
In Case-I, the foundation level is located under the scour hole and there is no effect of
foundation. In this case the proposed methodology for uniform abutment in last section can be
used.
For Case-II,
In Case II the principal vortices in front of the abutment are weakened by the foundation
and, the scour depth is confined by the top of the foundation. Mohammadpour (2013) indicated
that this case can be observed in range of 1< Z/L < 2 and the depth of scour is approximately
equal to foundation level (ds ~ Z). In such as case, the foundation is similar to obstacle and the
principal vortex rests on the top surface of the foundation. No further scour occurs around the
upstream portion of footing during this condition, and the principal vortex just expands the
volume of scour hole in the sides and downstream of the abutment.
In Case-III (0 < Z/L ≤ 1), at first, the principal vortex increases the scour depth to the top of
foundation, and the scour depth is similar to uniform abutment. Then, the scour depth is
considered to be fixed at Z level up to such time as the vortex expands horizontally over the top
rigid surface of the foundation at the upstream nose of the abutment. This time is equal to
duration of scour process at uniform abutment for a depth equal to the maximum lateral
dimension of scour hole (Ws in Fig. 7). Since the foundation level (Z) change the effect of vortex
in front of abutment and influence on this time, then a correlation factor of α was used to
determine the equivalent scour depth (des) for this time as:
 Bf  B 
Z
 
d es   
 2  tan 
(20)
where α is a correction factor between 0.00 and 1.00. This factor is recommended due to effect
of the vortex which is produced between the top of foundation and initial bed level. When
foundation is located in the bed level (Z=0), the α=1.0 and α decreases with increasing Z.
Fig. 7) Schematic diagram of scour process around complex abutment
As long as the principal vortex reaches to the outer edge of the top of the foundation, and a part
of the foundation will also be exposed to the flow (dst > Z). In such a scenario, the methodology
for computation of the temporal variation of scour depth is based on the principal vortices in
front of both abutment and foundation. As indicated in Fig. 8, the principal vortices are classified
in three groups, the vortex in front of abutment and on the initial bed level(A0), the vortex
between top of foundation and initial bed (Ast,I) and the vortex in front of the foundation (Ast,II).
The principal vortex between initial bed and top of foundation (Ast,I) is a function of foundation
level (Z) and the dimension of foundation in front of abutment (Bu). The Bu decreases the effect
of this vortex, then a correction factor of K should be used to consider the effect of Z and Bu on
the area of vortex in this region. Then, total area of principal vortices (At) can be explained as:
(21)
At=A0+K Ast,I + Ast,II
Similar to uniform abutment, the shape of vortex for A0 and Ast,II was considered circular and
triangle respectively, then the Equation (11) was used for A0. However, to estimate Ast,II , it was
noted that the depth of scour in this area is equal to dst –Z. Furthermore, a trapezoid shape was
assumed for calculation of vortex in Ast,I , therefore the area of vortices in Ast,I and Ast,II can be
written as:
 B f  B d sct 
Z2
 Z 
Ast , I  

tan  
tan 
 2
Ast , II

1 d sct  Z

2 tan 

2
 0.087
d
Z
tan 
sct
(22)

Fig. 8) Principal vortices in front of complex abutment
(23)
Regarding to Fig. 9 and Equation 6, the following equations were developed for estimation of
scour hole volume per unit width of scour (qvt) at complex abutments:
q vtc 
Qvt

d 
 L f  L  sct 
tan  


 
  L2f
 Lf 2
3
d sct 
d sct  
 Bf Lf

 2
2 tan 

d sct   6 tan 2 

 L f  L 

tan  

1


 d sct  B f L f  BL Z 



The numerical solution was used to estimate dst in the this equation.
Fig. 9) Geometric definition of scour hole at complex abutment
(24)
4. Result and discussion:
Table 2 shows the result of all experimental for both uniform and complex abutments. The
AB w used for uniform abutment when Z >2L (Case I) and FA for complex abutment when Z is
located in range of 0 and 2L (Cases II and III). Mohammadpour (2013) showed that in range of 1
< Z/L < 2, the depth of scour decreases with increasing the foundation level and reaches a
minimum at a value of Z/L ≈1. In the next step (0<Z/L≤1), due to effect of the vortex in front of
foundation, the scour depth increases with decrease in the Z.
Table 2) Summary of Experimental Results for the Present Study
I
AB 1
Q
(lit/sec)
18
0.96
time
(min)
3052
I
AB 2
18.6
0.98
4004
5.5
-
0.5
-
1.73
I
AB 3
16
0.95
5080
7
-
0.72
-
1.68
II
FA 21
18
0.96
3000
4
1.5
0.36
0.38
1.50
III
FA 21
18.3
0.96
2500
4
3.5
0.36
0.88
0.88
III
FA21
18.4
0.98
2133
4
5
0.38
1.25
1.25
II
FA33
18.0
0.95
2136
7
1
0.64
0.14
1.73
II
FA33
17.7
0.98
2316
7
5
0.66
0.71
1.47
II
FA33
19.4
0.97
2822
7
7
0.61
1.00
1.07
II
FA42
20.0
0.97
2262
5.5
1
0.46
0.20
1.58
II
FA42
17.65
0.99
2905
5.5
5
0.54
0.91
1.33
III
FA42
20.8
0.99
3033
5.5
7
0.46
1.27
1.27
III
FA42
20
0.98
3206
5.5
8
0.46
1.45
1.45
II
FA43
18.5
0.95
2248
7
3
0.62
0.43
2.07
II
FA43
17.9
0.97
2641
7
5
0.65
0.71
2.01
III
FA43
18
0.97
3430
7
7
0.64
1.00
1.00
III
FA43
18.4
0.96
3498
7
8
0.63
1.14
1.14
III
FA43
18.5
0.95
3512
7
9
0.62
1.29
1.29
Case Experiment
U/Uc
L
(cm)
4
Z
(cm)
-
L/y
Z/L
ds/L
0.36
-
1.68
3.1. Estimation of α and K at complex abutment
As mentioned the coefficient of α and K were employed to determine the effect of foundation on
time and depth of scour at complex abutments respectively. The experimental data was used to
find these coefficients. The variation of α in terms of foundation level (Z) is shown in Fig. 10,
and the following equation can be expressed for estimation of α :
Z
L
  0.5   1.0
for 0  Z  2 L
(25)
Fig. 10) Variation of α in terms of Z/L
The result indicates that for Z=0 (α =1.0), the foundation has high effect on time for development
of local scour. The value of α decreases with increase in foundation level ratio (Z/L), and for
Z=2L the value of α is equal to 0.0 where the effect of foundation is eliminated. Melville (1992)
showed that the maximum scour depth around uniform abutment is 2L. The Equation (20) and
(23) also confirms that for Z=2L, the time of equivalent local scour at complex abutment (dest) is
same to uniform abutment.
The K value was proposed to consider the effect of foundation level (Z) and its dimension (Bu ,
Fig. 8) on depth of scour regarding to principal vortex between top of foundation and initial bed.
As shown in Fig. 11, the collected data was categorized in two groups and two following
equations were recommended for variation of K based on the Z/L and Bu/L (Fig. 11):
2
Z 
Z 
K  5.0    5.0    1.61
L
L
2
Z
Z 
K  8.20   7.9 0   2.70
L
L
 B  Z 
for  u    0.3
 L  L 
(26)
 B  Z 
for  u    0.3
 L  L 
(27)
Fig. 11) Variation of K-value in terms of Z/L and Bu/L
The computation for temporal variation of scour depth can be carried out as per the flow chart
given in Fig. 12.
Fig. 13) Algorithm for computation of the temporal variation of scour depth at complex
abutment
3.1. Time variation of local scour at uniform abutment
Fig. 13 shows a comparison between the observed and calculated temporal variation of scour
depth at uniform short abutment for some data of Cardoso and Battess (1999), Ballio and Orsi
(2001), Dey and Barbhuiya (2005), and the present study. Most of runs in this figure correspond
to long-duration experiments. The depth of scour and time were normalized using equilibrium
scour depth (dse) and time (te) respectively. A good agreement was found between the computed
scour depth using the presented method and the observed data for all runs. The calculated results
were plotted until a fraction of equilibrium scour time. It was found that the bed-shear stress at
the nose of abutment was equal to or just less than the critical shear stress for the corresponding
scour depth obtained according to their prediction. Since in the experiment runs, development of
the scour hole never stop (Oliveto and Hager, 2002), then the best result was obtained when the
difference between u*t and u*c was between 0.07 to 0.1.
Fig. 13) Comparison of observed and computed temporal variation of scour depth at uniform
abutment
In Fig. 14, the observed equilibrium scour depths were compared with predicted equilibrium
scour depths using the proposed method for data of Dongol (1994) , Ballio and Orsi(2001), Dey
and Barbhuiya (2005), and the present study. The collected experimental data cover a wide range
of variables such as abutment length ratio (L/y) ranging from 0.16 to 1.00, flow intensity (U/Uc)
ranging from 0.95 to 1.00, and sediment coarseness (L/d50) ranging from 10 to 462. As shown in
Fig. 13, the proposed model predicts the equilibrium scour depth with a maximum of 25% error.
Therefore, for a wide range of data, prediction of temporal scour depth, the accuracy of presented
model is satisfactory.
Fig. 14) Comparison between observed and computed equilibrium scour depth at uniform
abutment using proposed method
3.2. Time variation of local scour at complex abutment
Fig. 15 shows a comparison between the computed temporal variation of scour depth at complex
abutment and the corresponding observed values for some of the data in the present study.
Reasonably good agreement was noticed between the corresponding observed and computed
values. The results show that the foundation decreases the depth of scour when it is located in
suitable depth. For example for FA 33, the scour depth ratio (ds/L) decreases from 1.73 to 1.07
(Table 2) when the foundation is increased from 1.0 cm (Z/L=0.14) to 5.0 cm (Z/L=0.71)
respectively (Table 2). As shown in Fig. 14, a perfect agreement is obtained between the
computed and observed scour values in the most of tests. Furthermore, the presented method
mostly predicts the scour depth at equilibrium time with high accuracy. Similar to uniform
abutment, the best result at complex abutment was observed when the difference of u*t and u*c
was between 0.07 and 0.1. The method proposed in this paper is noticed to estimate the scour
depth at uniform and complex abutment with reasonably high accuracy, and therefore it can be
practically employed to design a proper foundation level for complex abutment.
Fig. 15) Comparison between observed and computed equilibrium scour depth at complex
abutment using proposed method
Conclusion
In this study, temporal variation of local scour at short uniform and complex abutment (L/Y<1)
was investigated experimentally under the clear water conditions. A design method is presented
for prediction of the temporal variation of local scour at uniform abutments based on the
technique proposed by Mia and Nago (2003). The proposed method has produced suitable
prediction for temporal variation of scour depth at uniform abutment for the data collected from
the present study and previous studies.
Another method has also been recommended for computation of temporal variation of scour
depth at complex abutment while the top of the foundation was located below the initial bed
level at three different cases. The concept primary vortex (kothyari et al., 1992; Barbhuiya,
2003) was used to estimate the effect of foundation at complex abutment. The experimental data
collected in this study was utilized for validation of proposed method. . Reasonably good
agreement was also noticed between the corresponding observed and computed values of scour
depth around complex abutment.
.
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