Experimental study of local scour around a vertical pier in...

Scientia Iranica A (2014) 21(2), 241{250

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringwww.scientiairanica.com

Experimental study of local scour around a vertical pierin cohesive soils

M. Najafzadeh� and G.A. Barani

Department of Civil Engineering, Shahid Bahonar University, Kerman, P.O. BOX 76169133, Iran.

Received 6 March 2012; received in revised form 25 December 2012; accepted 21 October 2013

KEYWORDSLocal scour;Undrained shearstrength;Cohesive soils;Bridge pier;Froude number.

Abstract. Estimation of maximum scour depth is an important factor in designingstructures that are embedded in rivers. Using a hydraulic model, the mechanism of localscour around bridge piers embedded in cohesive soils has been studied. Experiments wereperformed in a ume; 22 m long, 0.77 m wide and 0.60 m deep, with a pier of 0.1 m indiameter. Also, three types of cohesive soil with di�erent percent clay were used. Whilechanging parameters, such as current velocity, ow depth, initial moisture content, claypercentage, and undrained shear strength, in each experiment, the scour depths weremeasured. The measured data were adjusted by hyperbolic law. Using dimensionalanalysis, a relationship between the ultimate scour depth and e�ective parameters wasdeveloped. Finally, the ultimate scour depths obtained by the experiments were comparedwith those calculated by empirical equations.c 2014 Sharif University of Technology. All rights reserved.

1. Introduction

Accomplished investigations into the mechanism oflocal scour around bridge piers show that the ap-proaching ow to piers produces a stagnation pressuregradient, due to the generation of a vertical velocitypro�le. This approaching ow, which acts as a down ow, is responsible for local scour around bridge piers.Partheniades [1], Partheniades and Paaswell [2], andChristensen and Das [3] carried out experiments oncohesive soils and found that the rate of scour in thesesoils depended on the percent of clay and initial com-paction, initial water content and shear strength. Clarket al. [4] and Melville [5] reported that the equilibriumscour depth is about 1 to 2.4 times the diameter of thebridge piers. Investigations by Kamphuis and Hall [6]and Herobich et al. [7] made it clear that the existenceof electro-chemical and chemical forces among the

*. Corresponding author. Tel.: +98 9169159830;Fax: +98 341 2114049E-mail addresses: Moha [email protected] (M.Najafzadeh); [email protected]. (G.A. Barani)

colloid particles of clay causes the scour phenomena tobe complicated. According to Parchure and Mehta [8],salinity has a major in uence on resistance, and, fora higher salinity, a higher resistance to erosion canbe expected. Ting et al. [9] used a physical model,which included �ve piers of di�erent diameter, threecohesive and two sandy soils, in order to investigate thelocal scour around bridge piers. Results showed thatat a low Reynolds number, scour depths around piersare the same. However, at a large Reynolds number,the resulted scour depths at the side of the piers weredeeper than those in front of the piers. Ansari et al. [10]used the results of experiments on cohesive soils of dif-ferent clay percentages, and presented a mathematicalmodel as a function of the physical properties of soils toevaluate scour depth. Rambabu et al. [11] investigatedthe ultimate local scour in a cohesive soil with 44% clayand found that the ultimate local scour depth dependson many parameters, including Froude number, pierReynolds number, critical shear stress, and saturatedundrained shear strength. Recently, Debnath andChaudhuri [12] investigated the e�ects of di�erentparameters on depth scour in cohesive soils. They

242 M. Najafzadeh and G.A. Barani/Scientia Iranica, Transactions A: Civil Engineering 21 (2014) 241{250

Figure 1. General view of experimental model (not to scale).

presented empirical equations based on the propertiesof cohesive soils. In this study, laboratory experimentswere carried out using three types of cohesive soil toinvestigate the in uence of undrained shear strength, ow characteristics, and initial moisture content onthe ultimate scour depth. Finally, using measureddata, linear and non-linear models were developed toestimate the ultimate scour depths. Comparisons weremade with eight equations, which were presented intwo groups of empirical equation. The �rst group,related to the pier scour in cohesive soils, includesAnsari et al. [10], Rambabu et al. [11], Debnath andChaudhuri [12], and the other group of equations,applied to pier scour in non-cohesive soils, includesShen et al. [13], Johnson [14], USDOT [15], andMelville [16].

2. Model description

Experiments were performed on a rectangular ce-mented channel measuring 22 m in length, 0.77 m inwidth, 0.6 m in depth and a longitudinal slope of 0.005,located in the hydraulic lab of the Civil EngineeringDepartment at Shahid Bahounar University, Kerman,Iran. Two storage tanks were located at two endsof the channel. The �rst tank with 4 � 3 � 2 m3

capacity and the second tank with 4 � 4 � 4 m3

capacity were located at the upstream and downstreamof the channel, respectively. A centrifugal pump wasinstalled in the second storage tank to recirculatewater through two pipes, 0.2 m in diameter, to the

upstream tank. Discharge control was performed bygate valves which were installed on the pipes. The�rst tank was divided into two sections, which wereconnected to each other from the bottom. Pumped-water discharged to the �rst section of this tank andentered the second section from the bottom to achieveuniformity of ow (Figure 1). The model pier, builtof cement, 0.1 m in diameter and 0.6 m in height,was installed in the center of the channel. Dischargewas measured using a calibrated rectangular weir,which was installed at the downstream end of thechannel.

3. Preparation of soil sample

Two types of soil were collected from two regions ofKerman, Mohyabad and Shahid Bahonar UniversityFarm. The hydrometer model, 152 H, was used todetermine the texture of these soils. Results showed52 percent clay from Mohyabad soil and 12 percentfrom the university farm soil. These soils were mixedwith 100, 90 and 80 percent of Mohyabad soil and 0,10 and 20 percent of university farm soil, respectively.Eventually, three types of soil were generated with 52,41 and 34 percent clay. The �rst clay soil, with 52percent clay, had a speci�c gravity, = 20:1 kN/m3,natural moisture content, NMC = 37:1%, liquid limit,WL = 45%, plastic limit, WP = 19%, plasticity index,PI = 26%, consistency index, IC = 0:3, and meandiameter, D50 = 5:5 � 10�3. The other properties ofclay soils are presented in Table 1.

M. Najafzadeh and G.A. Barani/Scientia Iranica, Transactions A: Civil Engineering 21 (2014) 241{250 243

Table 1. Physical properties of soils.

Soil properties Soil typesNo. 1 No. 2 No. 3

Speci�c gravity (kN/m3) 20.1 18.5 17.3Sand (%) 21 30 41Silt (%) 27 29 25Clay (%) 52 41 34D50 (mm) 0.0055 0.012 0.037Natural moisture content (%) 37.1 30.4 24.3Plastic limit (%) 19 15 13Liquid limit (%) 45 35 27Plasticity index (%) 26 20 14Consistency index 0.3 0.23 0.19

4. Experiments

To prepare the model for experiments, some water wasadded to each soil sample and covered by a plasticsheet for 24 hours to supply the required moisturecontent. The channel bed was covered with the moistsoil, 1.5 m long and 1.5 m thick, and compacted. Ahole was dug at the middle of the channel and a pierof 0.1 m diameter was installed in this hole. Later,the surface of the bed soil was compacted by a metalplate to remove air voids. Two ends of the compactedbed were regulated for a slope of 0.15 to 0.5 m (V&H)to prevent ow turbulence during experiments. Beforeeach experiment, a small mass of moist soil was cut andthe initial moisture content was measured. Also, theundrained shear strength of this was measured usinga direct shear test. For each experiment, a steady ow condition was established. Current velocity andbed elevation were measured by the current meter(Kenek VOA-101 type) and scour sensor (Kenek WH-406 type), respectively.

Using the Kenek VOA-101 current meter, owvelocity was measured at two depths (0.2 and 0.8 owdepth), two meters upstream of the pier. The averageof these two measured velocities was considered as the ow velocity. The maximum scour depth around thepier was measured 4 hours past the beginning of theexperiment. To access more accurate results, eachexperiment was carried three times under constant owdepth and approach velocity.

The average of the three measured data was usedin further computations. In cohesive soils, ultimatescour depth occurred after a long time. Briaud etal. [17] carried out their experiments in a ume testwith a circular pier and continued for 400 hours. Theyhad not observed the ultimate scour depth around thepier. Ting et al. [9] performed their experiments in claysoils and continued in the range of 16 to 227 hours; theycould not reach the ultimate scour condition. Rambabu

et al. [11] carried out their experiments in cohesive soilfor 4 hours and measured the scour depth; they usedthe hyperbolic law for correction of the measured localscour depths. Hence, in the present study, the durationof each experiment was considered to be 4 hours,then, the maximum scour depths were measured andcorrected using the hyperbolic law. Similar approachescan be found in many �elds of engineering. For exam-ple, in geotechnical science, Junhwan and Jongwan [18]estimated the bearing capacity for multiple footing insand using hyperbolic law, under the assumption thatunit load and settlement typically follow a power oran exponential equation, as described by Ghionna etal. [19] and Fonseca [20].

Based on the hyperbolic law, the relationshipbetween measured local scour depth (ds) and time (t)is:

dS(t) =t

a+ bt; (1)

and the ultimate scour depth (dsu) is:

dsu = limt!1(ds) =

1b; (2)

where ds(t) is the scour depth at instant time (t)from the beginning of the experiment, 1=a is the rateof initial scour (t = 0), which depends on hydraulicconditions and soil texture, and 1=b is the ultimatescour depth. Development of scour as a function oftime for soil no. 1 and four experiments are presentedin Figure 2. For each curve of Figure 2, time values (t)are divided by their correspond scour depths (ds) toobtain (t=ds) at each time (t). The relation betweent=ds and t is illustrated in Figure 3. In each lineof Figure 3, the inverse slope is the ultimate scourdepth and the intercept of the y-axis is the initialrate of scour. The validity of rectangular hyperbolabetween scour depth (ds) and time (t) was checked byRumbabu et al. [11]. Results show that the relationshipbetween t=ds and t is essentially a straight line, thus,con�rming the application of a rectangular hyperbolaformula.

Figure 2. Time development of the scour depth in the�rst type soil (52% clay).


Table 2. Experimental results.

Typesoil

Experimentno.

Flowdepthy0 (mm)

FlowvelocityU (mm/s)

Initialmoisturecontent

IMC (%)

Undrainedshear

strengthSu(kPa)

Observedscour depthds (mm)

Ultimatescourdepth

dsu (mm)

1 1 300 226 29.3 15 45 60

1 2 350 183 20.4 21.2 37 45.5

1 3 400 154 17.3 27.8 26 32

1 4 450 141 12.3 35.6 19 23.85

2 1 300 226 23 11.2 54 77.1

2 2 350 183 20.2 16.1 48 65.1

2 3 400 154 15 18.5 33 40.8

2 4 450 141 13.7 24.2 25 34.2

3 1 300 226 33.1 8.3 62 93

3 2 350 183 25.9 11.5 56 77

3 3 400 154 17.8 17.2 45 64

3 4 450 141 10.7 21.5 40 49.5

Figure 3. Estimation of the ultimate scour depth basedon hyperbolic law.

5. Dimensional analysis

The parameters that a�ect scour include the proper-ties of the ow and the physical properties of soil.Laursen [21], Bata [22], Chitale [23], Johnson [14], andthe United States Department of Transportation [15]suggest that the scour depth can be stated as afunction of dsu=y0 with related parameters. From theexperiments, the following function can be de�ned forultimate scour depth:

F (�w; �m; y0; �;D;C; IMC; Su; U; g; dsu) = 0; (3)

where �w, �m, y0, �, D, C, IMC, SU , g, and dsuare density of water, density of bed soil, ow depth, uid dynamic viscosity, pier diameter, clay percentage,initial moisture content, undrained shear strength, owvelocity, accelerated gravity, and ultimate scour depth,respectively.

Using dimensional analysis and selecting U , D,

Table 3. Results of non-dimensional parameters.

Su= :y0 C (%) Re Fr dsu=y0

2.48 52 22600 0.131 0.23.01 52 18300 0.098 0.133.45 52 15400 0.077 0.083.93 52 14100 0.067 0.052.01 41 22600 0.131 0.262.48 41 18300 0.098 0.192.5 41 15400 0.077 0.12.9 41 14100 0.067 0.071.6 34 22600 0.131 0.311.9 34 18300 0.098 0.222.48 34 15400 0.077 0.162.76 34 14100 0.067 0.11

and �m as repeating variables, we get Eq. (4):

f(IMC;dsuy0;SU :y0

;Fr;Re; C) = 0; (4)

where dsu=y0, SU= :y0, Fr, and Re are the dimen-sionless ultimate scour depth, dimensionless undrainedshear strength, Froude number and Pier Reynoldsnumber, respectively. Results of scour experimentsare shown in Table 2. In addition, Results of non-dimensional parameters are presented in Table 3.

The Re number (�wV D=�) is not an impor-tant parameter if the viscous e�ects are taken intoconsideration, but the Re in uences the frequencyof vortex shedding [24]. The Re number is not asigni�cant parameter if the ow around the pier isfully turbulent and is generally neglected in pier scour


studies [25]. In the present study, the range of Re isfrom 22600 to 14100, which is located in Debnath, and,in Chaudhuri [12], the range of the Re number is from59722 to 94272. As a result, the Re number may notbe an important parameter in local scour in cohesivematerials.

dsuy0

= f(Su :y0

;Fr; C; IMC): (5)

6. Discussion on parameters a�ecting the scour

In this section, e�ects of di�erent parameters on scourdepth are investigated based on dimensional analysis.

6.1. Undrained shear strength (Su) of bed soilSome of the physical properties of soil, such as con-sistency index, plastic and liquid limits, and moisturecontent, can be an important factor in estimating shearstrength [26,27]. Ting et al. [9] and Rambabu etal. [11] used soft clay soils with a consistency indexsmaller than 0.5 in their local experiments. Hence,in this study three soft clay soils, with consistencyindexes of 0.3, 0.23 and 0.19, were used. Variationsof initial moisture content at the beginning of eachexperiment caused the undrained shear strength tochange. Variations of ultimate scour depth (dsu=y0)against the undrained shear strength (Su) of bed soilare shown in Figure 4. From this, it can be found thatincreasing the undrained shear strength of soil causesa decrease in the ultimate local scour depth. Usingdata of Figure 4, by regression analysis, the followingequation resulted:

dsuy0

= 5:29 (Su)�1:27 : (6)

This equation can be applied to soft clay soils with aconsistency index smaller than 0.5. Rambabu et al. [11]experiments resulted in a power equation for these

Figure 4. Comparison of dsu=y0 as a function of SUbased on present data (unsaturated soil) and Rambabu etal. (2003) (saturated soil).

two parameters in saturated clay soil. The resultedcorrelation coe�cient was 0.81, while, in the presentstudy, it is 0.927. Further, using the experimentaldata of Debnath and Chaudhuri [12], Rambabu etal. [11], and Molinas et al. [28], the dimensionless scourdepth is plotted against dimensionless undrained shearstrength in Figure 5. As illustrated in this �gure,Molinas et al. [28], and Debnath and Chaudhuri [12]equations, which are proposed for unsaturated clay soilconditions, are in general agreement with the presentstudy. These comparisons show that plots can be usedfor the validation of �eld data from similar types ofunsaturated bed material.

6.2. The Froude number (Fr)Two parameters that a�ect the scour include thecurrent velocity and the ow depth, which are knownas the Froude number. Figure 6 demonstrates thevariation of ultimate scour depth as a function of theFroude number for all three soils. This �gure showsthat scour depths increase by increasing the Froudenumber. Also, for a speci�ed Froude number, the scourdepth decreases by increasing the clay percentage of thesoil. Comparison of dsu=y0 as a function of Fr, based

Figure 5. Comparison of dsu=y0 as a function of SU= :y0

based on present data and data from Molinas et al. (1998),Rambabu et al. (2003), and Debnath and Chaudhuri(2009) (clay soil of river Ganges) (35% < C < 100%).

Figure 6. Variation of dsu=y0 with Fr.


Figure 7. Comparison of dsu=y0 as a function of Fr basedon present data, and data from Ting et al. (2001),Rambabu et al. (2003) and Briaud et al. (2004).

Figure 8. Variation of dsu=y0 with IMC.

on pier scouring experiments on a clay bed, is madebetween the present data and that reported by Ting etal. [9], Rambabu et al. [11], and Briaud et al. [29] for25% < C < 65%, 0.061 < D < 0.273 m, and y0=D >2 (Figure 7). It is seen that the data of the presentstudy is in general agreement with that observed byTing et al. [9], Rambabu et al. [11], and Briaud etal. [29]. The scattering in the data was possibly due tothe variations in parameter between experiments suchas initial moisture content and clay percent.

6.3. Initial soil Moisture Content (IMC) andClay percentage (C)

The e�ect of initial soil moisture content on ultimatescour depth is shown in Figure 8. It is clear that byincreasing the IMC of unsaturated soil with di�erentclay percentages, the ultimate scour depth increases.Using the data of Figure 8 and regression analysis, thefollowing equation can be obtained:

dsuy0

= 1:023 IMC� 0:0471: (7)

For soil nos.1-3, with clay percentages of 52, 41, and34, by changing initial moisture content from 29.3%to 12.3%, 23% to 13.7%, and 33.1% to 10.7%, theultimate scour depths decrease to 60%, 55%, and 46%,

respectively. Honsy [30], through some experimentson di�erent clay soils, concluded that the scour depthdecreases by decreasing the IMC of the soil. Also,Debnath and Chaudhuri [12] experiments showed thatfor a moisture content ranging from 33.6% to 45.92%,the ultimate scour depth depended on the initial mois-ture content, and that for IMC < 24%, the ultimatescour depth decreased by increasing the clay contentof the soil. Also, according to Molinas et al. [28], andDebnath and Chaudhuri [12] experiments, when theinitial moisture content is less than 30%, dimensionlessultimate scour depth does not depend on the initialmoisture content.

Based on the mentioned investigations, thereare various suggestions regarding the e�ects of initialmoisture content on scour depth in cohesive soils.In this study, the range of the IMC varies between10.7% and 33.1%. Variation of dsu=y0 with IMCshows the low coe�cient correlation of 0.76 using plotscatter (Figure 8). This coe�cient correlation is thelowest coe�cient correlation compared to the dsu=y0with SU= :y0 and the dsu=y0 with Fr. Finally, it issuggested that it is better for IMC to be eliminatedfrom dimensional analysis.

7. Experimental results

Rambabu et al. [11] based their �ndings on the com-bination of some e�ective parameters of scour depth,and introduced a combined dimensionless parameter(�c), which is a function of the Froude number (Fr), themodel Reynolds number (Re), and the ratio of erosivecritical shear stress, to undrained shear strength in sat-urated mode (�c=Cu). Hence, in this investigation, bymultiplying, three combined dimensionless parametersresulted (�c), such as in Rambabu et al. [11]:

�c = Fr:Re:�cSu: (8)

Therefore, the Rambabu et al.'s [11] combined dimen-sionless equation can be written as below:

dsuD

= K(�c): (9)

The variation of dimensionless ultimate scour depthwas plotted against the variation of the combineddimensionless parameters in Figure 9. The followingequation obtained from the curves is based on claysoil properties and the hydraulic condition in the pierupstream:

dsuD

= 3:675(�c)0:355: (10)

The coe�cient of relation is 0.97. Hence, the aboveequation is suggested for the prediction of the ultimatescour depth based on the Rambabu et al.'s [11] com-


Figure 9. Relationship between dsu=D and combineddimensionless parameter (�c).

Figure 10. Plotting the result for Eq. (11).

bined dimensionless equation. After eliminating theIMC and Re number from Eq. (5), with dimensionlessparameters, a regression equation was obtained asfollows:

dsuy0

= 5565:05(Su :y0

)0:83:(C)�2:179:(Fr)2:306: (11)

The calculated values of the ultimate scour depths(dsu=y0), using Eq. (11), versus the ultimate scourdepths obtained through experiments, are presentedin Figure 10. The resulted correlation coe�cient isR2 = 0:97. Similar equations around a vertical pierhave been suggested by Herbich et al. [7] in coarsematerials for unsteady and varied conditions of ow,and by Molinas et al. [28], Rambabu et al. [11], andDebnath and Chaudhuri [12] in cohesive soil understeady ow.

8. Comparison of regression equation withempirical equations

The results of Eq. (2) have been compared with manyempirical equations. These equations are applied toestimate the scour depth in cohesive and non-cohesivesoils.

Ansari et al. [10], Rambau et al. [11], and Debnathand Chaudhuri [12] equations were used for comparisonwith Eq. (2) in cohesive soils, and Shen et al. [13],Johnson [14], USDOT [15], and Melville [15] equationswere used in non-cohesive soils.

The empirical equations used in cohesive soils are:

1. Ansari et al. [10]:

dsmcdsms

=6:02� 10:82( WW� ) + 5:41( WW� )2

(C�� )0:2; (12)

where:

C� =C:CU

( s � w):da; (13)

and:

�� =C tan('C) + (1� C) tan('S)

tan('S): (14)

In this equation, dsmc, dsms, W , W�, CU , 'C , 'S ,and da are maximum scour depth below the bedlevel for pier scour in cohesive soils, maximum scourdepth below the bed level for pier scour in non-cohesive soils, antecedent moisture content (%),antecedent moisture content required to saturatethe soil sample, cohesion, angle of repose or internalfriction for sand, angle of repose or internal frictionfor cohesive sediment, and arithmetic mean size ofthe sediment used for sand-clay mixture, respec-tively.

2. Rambau et al. [11]:

SUCD

= (Upg:y0

)0:641:(U:D�

)0:64:(CU s:y0

)�0:976;(15)

where SUC , CU , D, U , y0, s, and � are ulti-mate scour depth due to currents, undrained shearstrength of soil, diameter of obstruction, current ve-locity, ow depth, unit weight of soil, and kinematicviscosity of water, respectively.

3. Debnath and chaudhuri [12]:

dSD

= 2:05(Upg:D

)1:72:C�1:29:(�S�:U2 )�0:37; (16)

where ds, D, U , C, � and �S are maximumscour depth, pier diameter, approach velocity, claypercent, mass density of water, and undrained shearstrength, respectively. Also, the ranges of relatedparameters in Eqs. (12) and (15)-(17) are presentedin Tables 4 and 5.

Empirical equations used in non-cohesive soils are:


Table 4. Range of physical properties of bed soils used by Debnath and Chaudhurs (2009), Rambabu et al. (2003), Ansariet al. (2002), and Ting et al. (2001).

Researchers IMC (%) C (%) SU (kN/m2)

Debnath and Chaudhurs (2009) 20-45.92 20-100 5.7-12.7

Rambabu et al. (2003) 32.94 44 2.6-4.2

Ansari et al. (2002) 8.5-48.1 10-60 0-240

Ting et al. (2001) 26.18-39.28 25-65 12.51-39.56

Table 5. Range of hydraulic and geometry parametersdue to piers and ow condition uesd by Debnath andChaudhurs (2009), Rambabu et al. (2003), Ansari etal.(2002), and Ting et al. (2001).

U (m/s) D (m) y0 (m) dsu (mm)

0.514-0.818 0.12 0.35 58-2220.199-0.328 0.05-0.11 0.3-0.6 14.2-72.460.21-0.48 0.1125 0.05-0.18 11-179

0.204-0.608 0.025-0.11 0.16-0.4 8.4-134

1. Shen et al. [13]:

dsb

= 3:4(V 2

0gb

)0:67(d0

b)1=3; (17)

where g, V0, d0, b, and ds are gravity acceleration,current velocity, ow depth, pier diameter and scourdepth, respectively.

2. Johnson [14]:

dsd0

= 2:02F 0:210 (

bd0

)0:98��0:98; (18)

where ds, �, F0, d0, and b are scour depth, standarddeviation of sediment particle size distribution (� =pD84=D16), the Froude number, ow depth, and

diameter of pier, respectively.3. USDOT [15]:

dseyo

= K3(y0

D)�0:63Fr0:43; (19)

where K3, Fr, D, y0 and dse are equilibrium scourdepth, ow depth, diameter of pier, Froude number,and a constant value that is between 1.1 to 1.3.

4. Melville [16]:

dseD

= KlKdKyD; (20)

where Kl = V=VC if V=VC < 1 and Kl = 1,otherwise, Kd = 0:57 log (2:24D=D50) if D=D50 �25 and Kd = 1, otherwise and KyD = 2:4 ifD=y0 < 0:7, KyD = 2

py0=D if 0:7 � D=y0 � 5,

and KyD = 4:5 y0=D if D=y0 > 5.

Applying the measured data to the above empiri-

cal equations, scour depths are calculated. To comparethe ultimate scour depths with results of empiricalequations, Theil's coe�cient statistical test has beenused.

U =

�1n

nPi=1

�(dsc)i � (dsu)i

2�0:5

�1n

nPi=1

�(dsc)i

2�0:5

+�

1n

nPi=1

�(dsu)i

2�0:5 ;

(21)

where U is the Theil coe�cient (U = 0 for modelof perfect prediction and U = 1 for unsuccessfulmodel), dsc is the scour depth, which resulted from eachempirical equation, and n is the number of experiments.

The results of the statistical test show that theDebnath and Chaudhuri [12] equation is successful inpredicting scour depth in cohesive soils (U = 0:148).This equation is proposed for the unsaturated soilcondition. It seems that the high di�erence in the Theilcoe�cients is due to the e�ects of soil properties inthe empirical equations. Ansari et al. [10] proposedan equation based on moisture content, clay percent,plasticity index, angle of repose of the sediment, andbed sediment shear strength, whereas the Rambabuet al. [11] equation was presented under conditionsof initial moisture, saturated soil, and clay percentconstant. Based on Theil's coe�cient, Ansari et al. [10]and Rambabu et al. [11] equations were unsuccessfulin the prediction of scour depths (U = 0:47 and 0.74,respectively) because they are only valid for saturatedsoils. In this study, these equations were used forsaturated cohesive soils, while applying them for theprediction of scour depth in unsaturated cohesive soils(Figure 11).

The other group of equations include Eqs. (17)-(20), which are applied often for the prediction of scourdepths in non-cohesive soils. Results of statistical testsshow that the Johnson [14] equation, with U = 0:12,has the best prediction compared to Shen et al. [13], USDOT [15], and Melville [16]. The Johnson [16] equa-tion has parameters that include soil (bed sediments)properties, model geometry, ow depth and velocity,whereas the Shen et al. [13] equation has no soil (bedsediments) properties (Figure 12). As a result, it isnot valid enough for scour depth, and the maximumvalue of Theil's coe�cient is related to the Shen et


Figure 11. Comparison with calculated scour depthsobtained from Ansari et al. (2002), Rambabu et al.(2003), and Debnath and Chaudhurs (2009) formula andthe ultimate scour depths using hyperbolic law.

Figure 12. Comparison with calculated scour depthsobtained from Shen et al. (1969), Johnson (1992),USDOT (1993), and Melville (1997) formula and theultimate scour depths using hyperbolic law.

al. [13] equation (U = 0:34). Also, the Melville andUSDOT equations have the main three parameters (soilproperties, model geometry, and hydraulic conditions)and the values of their Theil coe�cients are 0.17 and0.18, respectively. These Theil coe�cients indicatedthe e�ects of soil properties on scour depth.

9. Conclusion

Scour depth around bridge piers can be a�ected byseveral parameters, such as undrained shear strength,Froude number, initial moisture content, and claypercentage. The ultimate scour depth decreases byincreasing the undrained shear strength of unsaturatedsoils, while it increases by increasing the Froude num-ber. Also, at a constant Froude number, the ultimatescour depth increases by decreasing clay percentage andthe percentage of moisture content of the soil.

Combining the ow Froude number, Reynolds

number and dimensionless undrained shear strength,a general equation for calculating the ultimate scourdepth was resulted, based on the Rambabu et alcombined dimensionless parameter. In this study,through experimental tests, the e�ect of current ve-locity, ow depth, initial moisture content, clay per-centage and undrained shear strength on scour arounda bridge pier has been investigated. Using dimensionalanalysis, a relationship between the ultimate scourdepth and e�ective parameters was developed. Theultimate scour depths were compared with calculatedscour depths that were calculated, using two groupsof empirical equations. In this study, the Theil'scoe�cient statistical test was used to determine theaccuracy of each group of equations. The results ofthe comparisons show that Debnath and Chaudhuri,and Johnson empirical equations have better agreementwith ultimate scour depth gained from experimentsthan from other equations in each group. It can beconcluded from comparisons of empirical equations incohesive soils that saturated and unsaturated condi-tions are signi�cant factors in predicting scour depth.Also, empirical equations in non-cohesive soils can beused for predicting scour depths in cohesive soils, whichare sometimes more accurate.

References

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2. Partheniades, E. and Paaswell, R.E. \Erodibility ofchannels with boundaries", J. Hydraul. Div. ASCE,96(3), pp. 755-771 (1970).

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18. Junhwan, L. and Jongwan, E. \Estimation of bearingcapacity for multiply footings in sands", ComputersGeotechn., 36(6), pp. 1000-1008 (2009).

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Biographies

Mohammad Najafzadeh received his BS degree inHydraulic Engineering,in 2006, from Shahid ChamranUniversity of Ahwaz, Iran, and a MEng degree inHydraulic Structures, in 2009, from Shahid BahonarUniversity of Kerman, Iran, where he is currently aPhD degree student. His research interests includescouring in cohesive soils, computational uid dynamic,and arti�cial intelligence approaches. He has publishedand presented many papers in various Journals and atmany national and international conferences.

Gholam Abbas Barani received his BS degree inCivil Engineering from Tehran University, Iran, in1973, and, in 1977, received his MEng degree fromthe University of California, Davis, USA, where heis currently working towards his PhD degree. Hisresearch interests include sediment scour in hydraulicstructures, water resource engineering, optimizationof reservoir operation, and hydrology. He has pub-lished more than 250 papers in various journals andpresented many others at national and internationalconferences.

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