Evaluation Of Performance of Empirical Models for the Prediction of Local Scour At Bridge Piers (Case Study Chanchaga Bridge, Minna, Nigeria)

Evaluation Of Performance of Empirical Models for the Prediction of Local Scour At Bridge Piers (Case Study Chanchaga Bridge, Minna, Nigeria)

1,2BUSARI Afis Olumide*, 1,3GBADEBO Anthonia Olukemi, 1JIMOH Ibrahim Olayinka,

1TAKEET Olayinka Ezekiel, and 1ENIFU, Jennifer Ene

1Department of Civil Engineering, Federal University of Technology, Minna

P.M.B 65, Minna Niger State, Nigeria.

2Coastal and Hydraulic Engineering, TU732, Civil and Environmental Engineering Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

3UNESCO-IHE, Westvest 7, 2611 AX, Delft, The Netherlands

Abstract

Scour is the removal of sediment from streambeds and stream-banks and is caused by the erosive action of flowing water. It is more significant during high flow events under high velocity. Due to the complexity of stream dynamics, scour is often exacerbated at bridge piers and abutments, potentially undermining the structure and jeopardizing its stability. The accurate prediction of sediment scour depths near bridge piers under design storm conditions is very important in bridge design, especially when the bridge is located in an un-gauged catchment. The physical processes involved are very complex and difficult to analyze, and, thus, most design scour depth predictive equations are based on laboratory scale experimental results. Here, laboratory study was combined with onsite measurements to obtained relevant parameters. The parameters were fed into empirical models. Subsequently, the best empirical model is determined for estimation of local pier scour at downstream of the Tagwai intake weir among the numerous empirical models. This is

achieved by using consistency-correlation analysis which compared the measured depth of scour and calculated depth of scour obtained using selected empirical models.

Keywords: Bridge pier, Local scour, empirical models

1. Introduction

   Scour is the removal of sediment from streambeds and stream banks and is caused by the erosive action of flowing water. It can occur at anytime but is more significant during high flow events, when water is moving at a high velocity. Due to the complexity of stream dynamics, scour is often exacerbated at bridge piers and abutments, potentially undermining the structure and jeopardizing its stability (Peggy and Daniel, 1998). This often led to extremely high direct and indirect costs and, in extreme cases, the loss of human lives (Toth and Brandimarte, 2011).

   Scour has been discovered in recent time to be the paramount cause of bridge collapse. This is evident in number of bridge that has

   been reported damaged and subsequently collapse throughout the globe due to scour Peggy and Bilal, (1996). Nigeria has experience her fair share of the devastating effect of scour.

   Recently, Busari et al, (2013) evaluates the best probability distribution model for the prediction of rainfall- runoff for Tagwai basin, and suggested appropriate model for the estimation of annual runoff from the basin. The overflow from Tagwai (weir) is the chief source erosion to the downstream channel along which Chanchaga bridge is located. Pagliara and Carnacina, (2011) carried out laboratory experiment to investigate the effect of large woody debris on sediment scours at bridge piers and proposed relationships to predict the effect of drift accumulation on bridge pier scour, both in terms of relative maximum scour and temporal scour evolution.

   Scouring has long been acknowledged as a severe hazard to the performance of bridge piers. The total scour at a river crossing consists of three components that, in general, can be added together as explained by Richardson and Davies, (1995). They include general scour, contraction scour, and local scour, on the other hand divided scour into two major types, namely general scour and localized scour. Some other sub- divisions of scour can be found from (Stephen et al. 2003 and Mushair et al. 2004).

   Lagasse and Richardson, (2001) shows the flow and scour pattern at a circular pier (figure 1). The strong vortex motion caused by the existence of the pier entrains bed sediments within the vicinity of the pier base. According to Richardson and Davies,

   (1995) the separation of the flow at the sides of the pier produces wake vortices. These wake vortices are not stable and shed alternately from one side of the pier and then the other. It should be noted, however, that both the horseshoe and wake vortices erode material from the base region of the pier. The intensity of the wake vortices is drastically reduced with distance downstream, such that sediment deposition is common immediately downstream of the pier (Ahmed and Rajaratnam, 1998).

   This study evaluates the some empirical models used in estimation of bridge-pier scour, and assesses the empirical models that will provide a reliable design estimate of scour depth. The selected models were found to be adequate for the study area in terms of hydraulic conditions and associated model input parameters. The models evaluated in this study are equations that make use of the principal parameters that constitute the basic entity that influence the occurrence of bridge scour. The accuracy of result obtained from selected empirical models, by subjecting the calculated depth of scour and onsite measured depths of scour to consistency-correlation analysis.

   The aim of the study is mainly focus on determination of best empirical model that can be use to estimation of local pier scour at downstream of the Tagwai intake weir among the numerous empirical models. This was achieved by using consistency- correlation analysis on the measured depth of scour and calculated depth of scour. The principal objectives are: firstly, to carry out a much longer duration test than is currently reported at the site with a view to evaluating

   equations developed in estimation of the local scour at a bridge pier; secondly, to be assessed are common equations that describe the temporal development of pier scour, using correlation analysis to ascertain relativity in terms of accuracy of the some empirical models compare to the measured depth of bridge scour. Finally, to focus on determination and measurement of accurate parameters of the bridge that can be further be used for subsequent research on the bridge.

   The accurate prediction of sediment scour depths near bridge piers under design storm conditions is very important in bridge design. Under-prediction can result in costly bridge failure and possibly in the loss of lives, while over-prediction can result in wasted capital during the construction of a single bridge. The physical processes involved are very complex and difficult to analyze, and, thus, most design scour depth predictive equations are based on laboratory scale experimental results.

   Figure 1: Schematic local pier scour process

2. The Study Area

   The Chanchaga Bridge is situated at longitude 6 391-6 441E and latitude 9 34- 9 37 N across the river Chanchaga south west of Minna. The length of the bridge is about 256m, height of 6.1m and width of 10.5m. Throughout the year, the bridge experiences continuous flow of the water underneath it. This is due to the present of water retaining structure (weir) some few meters from upstream the bridge.

   The bridge which was built some 35 years ago to link the state capital to Abuja the Federal Capital Territory, the bridge has contributed immensely to social and political integration of people living in Minna and its environments. The bridge has also contributed to speedily economic growth of Chanchaga envrons and Minna by aiding easy transportation of goods, passenger and technology.

   The river flowing under the bridge originated from confluence of river Tagwai and Jidno South-west of Minna (see Figure 2). The river is perennial due to presence of a dam upstream the bridge, that help it to retain water during the raining season and discharge it during dry season. The

   catchment area of the river is about 120km2.

   There are secondary vegetation in the area which consists mainly of shrubs and open grass land. The landscape of the Chanchaga river area is made up of flat-lying to undulating terrains. The geology of the area is made up of Precambrian basement complex with varieties of igneous and metamorphic rock and sedimentary basin comprising of Alluvium found along valleys of the project area.

   The Chanchaga area has a population of about 12000 13000 inhabitants, the majority being the Gwaris. Most of these people in the area are subsistence farmers and fishermen. They practice mixed farming system.

   Figure 2: Chanchaga bridge, Minna-Nigeria

   The agricultural activities of the farmer is expected to change appreciably with the construction of the dam due to the occurrence of flooding and dry season farming which is expected to occur due to the dam constructed.

3. Framework for analysis

   The relation between the depth of scour at a bridge pier , and its dependent parameters can be written as:

   = [ , , , , ,

   , 50 , ,

   , , ()] (1)

   where are fluid density and kinematic viscosity respectively.

   is mean approach depth of flow and is the gravitational constant

   is the density of sediment

   50 is the bed sample median size

   is the critical bed shear velocity

   , is the pier width and

   is the shape and alignment factor

4. Selected empirical models

   Parameters obtained from field combined with the calculate parameters were fitted into the five empirical models adopted for this research to calculate depth of scour. Then, the depth of flow was varied while all other parameters remain unchanged. The depths of scour obtained from these empirical equations were compared with measured scour depth at different depth.

   The five empirical equations used in this research to calculate the depth of scour are:

   4.1 Richardson Davis Model

   The Richardson Davis model for estimating the depth of local scour at pier (HEC 18), colloquially called C.S.U equation, extends back about 35 years and has been updated several times to account for additional influence of the parameters.

   The Richardson and Davis equation predict maximum local pier scour depths for both live bed and clear pier scour. The equation is:

   = 212340.65 0.35 0.43 (2)

   is the mean approach velocity

   where

   1 1

   K1 = Correction factor for pier nose shape

   K2 = Correction factor for angle of attack of

   V = Vi Vi50

   R

   R

   Vc 50 Vi90

   (6)

   flow

   K3 = Correction factor for bed condition

   Vi50=0.645[D50/a]0.053Vc50 (7)

   K4 = Correction factor for armoring of bed

   V =0.645[D

   /a]0.053V

   (8)

   material

   i90

   90 c90

   = pier width (m)

   y = flow depth directly upstream of the pier (m)

   VR = Velocity ratio

   Vi = Average velocity in the main channel

   (m/s)

   Fr1 = Froude number directly upstream of the pier

   Vi50

   = approach velocity required to initiate

   scour at pier for grain size D50 (m/s)

   1

   1

   (3)

   Vi95

   = approach velocity required to initiate

   Table 1: Correction factor for pier nose shape K1

   Shape of pier nose	K1
   Square nose	1.1
   Round nose	1.0
   Circular cylinder	1.0
   Group cylinder	1.0
   Triangular	0.9

   Source: (Richardson and Davis, 1995)

   The correction factor for angle of attack of flow, 2 is calculated in the equation below:

   = [ + ]0.65 (4) Where

   L = pier length along the flow line (m)

   = angle of attack of the flow with respact to the pier

   K3 = 1.1

   4 = 0.4 0.25 ( 5)

   scour at pier for grain size D95 (m/s)

   Vc50 = critical velocity for D50 bed material size (m/s)

   Vc90 = critical velocity for D90 bed material size (m/s)

   Vc50=Kuy1/6D501/3 (9)

   Vc90=Kuy1/6D901/3 (10)

   Ku = 6.19

   Factors	Minimum bed material size	Minimum (K4) value
   K4	D500.002mm D950.02mm	0.4

   Factors	Minimum bed material size	Minimum (K4) value
   K4	D500.002mm D950.02mm	0.4

   Table 2: Correction factor for armoring of bed material (K4)

   Source: (Richardson and Davis, 1995)

   1. The Sheppard- Melville Model

      The Sheppard- Melville model builds on the

      3

      1.2 0,13

      1.2 0,13

      = 50 (16)

      0.4 +10.6

      method purposed by Sheppard and Melville,

      50

      50

      following more or less the same parameter, approach inherent in the Melville (1997) method. The model used an effective pier diameter (a*) the diameter of a circular pile

      that will experience the same equilibrium scour depth as the subject structure under

      And is the live bed peak velocity, much the same is in the Melville (1997) method.

      The sediment critical velocity, is calculated using shield curve

      the same flow sediments condition. In other

      words pier shape and alignment factor are

      = 0.6 (17)

      used to determine a* which then is used in the methods equation set. The Sheppard- Melville model comprises of two equations they are:

      For clear water scour (0.4< <1)

      Similarly,

      = 5Vc (18)

      = effective diameter

      = 0.86 + 0.97 [( )]4

      = 2.5

      (11) 4

      1

      2

      3 50

      = flow skew angle in radian

      For the live bed scour range (1< <VIP/ )

      1

      2.2 +

   2. Froehlich David Model

      Froehlish equation is based on onsite

      =

      1

      (12)

      measurements; the equation predicts the

      2.5

      expected maximum depth of local scour at a

      1

      3 50

      bridge and suggested safety factor that provides reasonable margin of error for

      For live bed scour range above the live peak

      ( > VIP/ )

      = 2.21 (13)

      design purposes. The model is described as follows:

      =

      .62 0.46 0.08

      0.32 0.2 (19)

      where

      50

      = 2.2 tanh

      0.4

      (14)

      = sin + cos (20)

      1

      2

      = 1 1.2 ln 2 (15)

      = projected width of the pier

   3. Gao Model

      The estimate maximum depth of local scour is given by:

      ys =

5. Methodology

   In this research project, the method adopted consists of mainly laboratory experiment on riverbed material granulometry, onsite

   measurements and desk study.

   0.46k 0.62 y0.45 D

   0.07 Vi V c

   (21)

   50 Vc V c

   1. Laboratory riverbed grading analysis

      0.14

      0.14

      = 17.6

      + 6.0 ×

      50

      The laboratory study involved the sediment

      0.72

      0.72

      10_7 10+ (22)

      50

      size distribution measurement and the specific gravity test.

      = 0,645 50

      0.53

      (23)

      Particle size distribution can be measured

      =[VC/V]9.35+2.23LogD50 (24)

      where, VC1 = Incipient velocity for local scour at pier and = 1 for clear water scour<1 for live bed scour.

      1. Melville Model

      The adopted maximum depth of local scour according to Melville is given by:

      = (25)

      using different methods. The adopted methods are the pipette method, the hydrometer method and the sieve analysis method.

      Five samples A, B, C, D, and E were taken from different spots on the site. Sample A, B, C, were taken downstream of the bridge and samples D and E were taken upstream between the weir and the bridge.

      % mass retained = weight of sample on sieve ×

      weight of original sample

      100

      The specific gravity of the soil sample was

      = 2.4a when y/a >1.4

      = 2(ya) 0.5 (26)

      determined using the density bottle method.

      The specific gravity of the soil sample (Gs) is calculated using the following,

      when 0.2y/a1.4

      = 4.5y when y/a<0.2

      Gs = M2 M1

      (M4 M1 ) (M3 M2 )

      (30)

      =

      (27)

      Where, M1 is mass of density bottle

      M2 is the mass of soil sample + density bottle

      = 0.6 (28)

      1/3 (29)

      1/3 (29)

      Vc50 = Ku1/6D50

      M3 is the mass of soil sample + density bottle + distilled water.

      M4 is the mass of water + density bottle

   2. Onsite measurement

      5.2.1 Measurement of Bankfull Discharge

      The discharge over the weir was measured and followed the relation:

      Q = LH3 2 (2g) (31)

      where the calibrated coefficient is given by

      = 2 1 + 4x 9 + 4x and x = H .

      D50 = Grain size = 0.3mm, D90 = 0.4mm

      a= pier width = 1.24m

      a*= effective diameter = 0.86m

      = flow skew angle in radian

      = critical velocity

      = live bed peak velocity pier shape

      = 2610 kg/m3.

      The computed rating curve obtained from

      3 3

      Hd site gauging after calibration is shown in

      Several values of the discharges obtained at the weir where used to plot a rating curve and the rating was correlated with measurement result obtained by Saidu, (2007).

      The parameters measured in the field are bridge pier geometry, hydraulic properties of the stream and bed sediment.

      Consistency-Correlation analysis is then carry out between each of the three results (calculated depth of scour) from three empirical models and the measured depth of scour to ascertain the degree of correlation of each result (calculated scour depth) obtained from three empirical models to the measured depth of scour.

6. Results and discussion

Parameters as measured and required for the estimation of local pier scour are as follows:

L= length of pier= 5.1m, 1 = = 0.84m V = approach velocity = 2.01m/s

= angle of the flow with respect to the pier

= 35o , VR = Velocity ratio

Figure 3. The discharge measurement match well with that measured (Saidu, 2007). Figure (5) showed bed material gradation for five different rainy seasons and the result indicates a sandy bed river of high temporal scale consistency. The d50 and d90 used in the analysis were obtained as particle size distribution that correspond to

50 and 90% sieve passing of sample respectively

Figure (4), showed the computed maximum scour depth from the empirical equation as compared to the seasonal measured value at the site. It was observed that two of the empirical models( Richardson and Melville overestimate the maximum scour depth.However, the other three empirical models (Sheppard, Gao and Froehlich) provide maximum depth of scour that are relatively close to that of the measured depth of scour. The over-prediction of the calculated scour depth from the aforementioned two models may be associated with time scale of 6 years measurement considered for the study. Their adequacy may be observed in the long term.

The three models under consideration were clearly presented in Figure (6). The estimation of Gao is relatively flat indicate less response to flow depth. More so, Gao model under-estimate and overestimate at respective higher and lower velocities of flows. This could be as a result of roughness

1.2

induced by channel vegetation resulting in erosion and deposition of bed materials. Similar trend was observed with Froehlich model with low flow gradient, but complete overestimation of scour depth for the given temporal scale.

Richardson Shappared

Frochlich Gao

Meloille Measured value

1 6

Height, H (m)

Height, H (m)

Depth of Scour (m)

Depth of Scour (m)

0.8 5

0.6 4

0.4

0.2

0

0 50 100 150 200 250 300

Discharge, Q (m3/s)

3

2

1

0

0.5 0.6 0.7 0.8 0.9

Depth of flow (m)

% passing

% passing

Figure 3: Computed rating curve Figure 4: depth of scour against depth of flow

100

90

80

70

60

50

40

30

20

10

0

sample B

sample C sample A sample D

sample E

100

90

80

70

60

50

40

30

20

10

0

sample B

sample C sample A sample D

sample E

0.01 0.1 1 10

Particle sizes (mm)

0.01 0.1 1 10

Particle sizes (mm)

Figure 5: Granulometry curve for the riverbed material (A, B and C are sample taken downstream of the bridge while C and D are the soil sample taken upstream of the bridge)

The trend observed by Sheppard model is most similar to the measured flow depth. Depth of scour increase with increase in velocity in almost linear proportion.

values close to zero. However, this is debatable and so we shall move on and consider the other normality assumption.

Due to this fact above, correlation analysis was carry out on each results obtained from

1.7

Depth of Scour (m)

Depth of Scour (m)

1.4

1.1

0.8

0.5

Shappared

Frochlich Gao

Measured value

0.6 0.7 0.8 0.9

the three empirical models with the measured scour depth.

Results (calculated depth of scour) obtained from the three models were compared using consistency correlation analysis. Measured depth of scour is taken as indeterminate variable is y, and calculated depth of scour which is determinate variable is x.

Depth of flow (m)

Figure 6: Comparison of calculated and measured

scour depth

=

2 2

(32)

1.5

Measured scour depth (m)

Measured scour depth (m)

1.3

1.1

0.9

0.7

0.5

Sheppard Froehlich Gao

Sheppard Froehlich Gao

0.5 0.7 0.9 1.1 1.3 1.5

Calculated scour depth (m)

Considering the correlation coefficient of determination () equalled to -0.989, -0.186 and -0.993 for Sheppard model, Froehlich models and Gao model, respectively. The values of r for the three empirical models showed that the Sheppard and Gao empirical models gives results (calculated depth of scour) that are quite strongly correlated with the measured depth of scour.

7. Conclusion

Figure 7: Depth of scour measured and the

predicted ones by models

Based on the above discussion, the degree of closeness of three results obtained cannot be ascertained with mere eye as can be observed from Figure (7). The scatter plot suggests a definite positive correlation between measured and calculated scour depth. However, there is possibly slight evidence of nonlinearity for calculated

Local scour depth at bridge pier has been estimated using five selected max depth based empirical models. The models results were compared with five years measured scour depth in live-bed conditions. Three models were selected on the basis of closeness to the measured values. Furthermore, consistency-correlation analysis was adopted; Sheppard and Gao models gave a results which are more correlated with the measured depth of scour

than results obtained from other empirical models. It should be noted that a lot of uncertainties are associated with measured depth because of noticeable interventions at the site such as water and sediment extraction downstream of the bridge by a block industry. Future study should consider the effect on these interventions on the morphodynamics of the river chanchaga.

.

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