Optimal formula to estimate the quantity of sediment transport upstream of Al- Shamia Barrage

Optimal formula to estimate the quantity of sediment transport upstream of Al- Shamia Barrage

Prof. Dr. Saleh I. Khassaf Al-Saadi

Dr.Safaa K.Hashim AAL-Khalaf

Nasseem M. Sharba

University of Kufa/Faculty of Engineering/Civil Department

Abstract

This research was conducted to estimate the total amount of Sediment Load at the up-stream of Al- Shamia Barrage in middle of Iraq. For the analysis of the applicability of sediment transport formulas to the study site, eight equations were chosen for that purpose, namely:

(Engelund-Hansen, Inglis-Lacey, Ackers-White, Van Rijn, Yang, Fazle, Ariffin and Jasem)

The applicability of each formula was tested using data taken from field measurements of twenty-four sections along the study area (6 km) to measure all the hydraulic variables and characteristics of sediments transported. The bottom samples were obtained using a device (Van Veen Sample), which was manufactured by the researcher in addition to sampling the mixture (Water-Sediment) by using a factory device. Also, the hydraulic variables were found using (Acoustic Doppler Current Profile) device.

From the analysis, the equations (Engelund-Hansen and Fazle) are the closest to the true estimate in order to get the sediment discharge among other equations selected in the search within the hydraulic conditions of the site.

Key words: Sediment Transport, River Bed Degradation, Measurements.

List of symbols

1 = Critical particle mobility factor

, = Width of the river

= Concentration coefficient in the sediment transport function

, = Total sediment concentration

50 = Particle size for which 50 percent by weight of the sediments is finer

50 = Median grain size

, = Dimensionless particle diameter

= Particle mobility parameter

= Acceleration of gravity

, = Specific gravity

= Average depth of flow

= Water depth

= Exponent in the sediment transport function

= Manning roughness coefficient

= Volume rate of transport per unit length of surface

= Suspended sediment transport

= Total sediment discharge

, = Hydraulic radius

= Water surface slope

, = Shear velocity

= Mean flow velocity

= Critical velocity for start of suspension

= Fall velocity of particle

, = Specific density of water

= Shear stress along the bed

= Kinematic viscosity

1. Introduction

   Rivers and channels are considered to be important resources for water supply, irrigation, navigation, water power generation and other public uses. The presence and movement of sediment causes many problems. The deposition and erosion of solid material of the beds and banks of channel increases bed deformation, which in turn will reduce the depth of water in some places and reduce the ability of the water way for navigation or hydraulic purposes. However, the raising of the river bed by the deposited materials increases the flood range to a great extent. As a result, large sums of money have to be spent to maintain the course of the river necessary

   for the hydraulic requirements. (7)

   There is a number of equations to compute the total sediment load. Most of these equations have some theoretical and empirical bases. They were derived under very limited conditions of flow and sediment characteristics. All of them have shown good results when used to compute the sediment load for conditions similar to those under which they were derived. On the other hand, very poor results are obtained when they were applied for different conditions.

   The most important reason for choosing this site to study is the accumulation of sediment in the up-stream of Al-shamia Barrage. The sediment was amounted to about three meters, which led to the closure of four out of six gates. There was no direct study of this region by the researchers to estimate the amount of sediment.

2. Description of the Study Region

   The region of this study in the Euphrates basin is located between the towns of Kifil and Shinafiya, extending between latitudes 31 55' and 32 15' N and longitudes 43 55' and 44 45' E. Al-shamia Barrage is located on the Euphrates river at Al-Diwaniya city in Iraq.

   The maximum design discharge is 1100 m3/sec with the highest level of water by 22.5 m above sea level. It has six radial gates for water drainage is run electrically. Al-Shamia Barrage was constructed during 1986 to control the flow in the middle Euphrates region. Figure (1) shows reach study location.

   Reach study

   Al-Shamia Barrage

   Figure (1): Reach study location

   (m)	1.22	1.77	1.5
   (m2/sec)	1.25×10-6	1.21×10-6	1.21×10-6
   (m/sec)	0.013306	0.016724	0.018839
   (m/sec)	0.0424	0.051	0.047
   Sec. No	4	5	6
   (m3/sec)	57.94	33.14	31.33
   (m/sec)	0.459	0.489	0.326
   	2.69	2.68	2.68
   50 (mm)	0.173	0.18	0.182
   (m2)	126.2	67.8	96.2
   (m)	61.73	59.1	48.78
   (m)	2.04	1.15	1.97
   (m2/sec)	1.15×10-6	1.15×10-6	1.16×10-6
   (m/sec)	0.01889	0.020065	0.020298
   (m/sec)	0.0548	0.0411	0.0538
   Sec. No	7	8	9
   (m3/sec)	33.99	40.92	36
   (m/sec)	0.358	0.478	0.204
   	2.6	2.69	2.67
   50 (mm)	0.191	0.182	0.175
   (m2)	95	85.6	176.1
   (m)	90.33	52.21	77.64
   (m)	1.05	1.64	2.27
   (m2/sec)	1.17×10-6	1.15×10-6	1.16×10-6
   (m/sec)	0.020904	0.020539	0.018924
   (m/sec)	0.0393	0.0491	0.0578

   0.051

   (m)	1.22	1.77	1.5
   (m2/sec)	1.25×10-6	1.21×10-6	1.21×10-6
   (m/sec)	0.013306	0.016724	0.018839
   (m/sec)	0.0424	0.047
   Sec. No	4	5	6
   (m3/sec)	57.94	33.14	31.33
   (m/sec)	0.459	0.489	0.326
   	2.69	2.68	2.68
   50 (mm)	0.173	0.18	0.182
   (m2)	126.2	67.8	96.2
   (m)	61.73	59.1	48.78
   (m)	2.04	1.15	1.97
   (m2/sec)	1.15×10-6	1.15×10-6	1.16×10-6
   (m/sec)	0.01889	0.020065	0.020298
   (m/sec)	0.0548	0.0411	0.0538
   Sec. No	7	8	9
   (m3/sec)	33.99	40.92	36
   (m/sec)	0.358	0.478	0.204
   	2.6	2.69	2.67
   50 (mm)	0.191	0.182	0.175
   (m2)	95	85.6	176.1
   (m)	90.33	52.21	77.64
   (m)	1.05	1.64	2.27
   (m2/sec)	1.17×10-6	1.15×10-6	1.16×10-6
   (m/sec)	0.020904	0.020539	0.018924
   (m/sec)	0.0393	0.0491	0.0578

3. Field Measurement

   In this research, the data used for hydraulic and sediment characteristics were collected from 24 sections in the Euphrates River distributed along the study area upstream of Al-shamia Barrage. The collected data were discharge, velocity, width, cross- sectional area, and observed suspended sediment load from the field measurements. The flow depth in study reach ranged from (1 to 5) meters, with flow ranging from (28.5 to 62) m3/sec. The flow velocities ranges from (0.145 to 0.584) m/sec and the median sediment size (0.177) mm for the bed material composition was observed. Figure (2) shows the distribution of the

   sections along the search area.

   A summary of data used in the study is presented in Table (1).

   Figure (2): The position of cross sections in the reach study

   Table (1): Primary data and parameters

   Sec. No	1	2	3
   (m3/sec)	31.14	55.4	32.29
   (m/sec)	0.233	0.28	0.276
   	2.67	2.65	2.65
   50 (mm)	0.148	0.167	0.178
   (m2)	133.5	197.8	117
   (m)	109.28	111.95	77.75

   Sec. No	10	11	12
   (m3/sec)	28.58	38.61	34.48
   (m/sec)	0.306	0.352	0.386
   	2.65	2.72	2.68
   50 (mm)	0.181	0.18	0.17
   (m2)	93.4	109.7	89.4
   (m)	41.22	75.33	49.45
   (m)	2.27	1.46	1.81
   (m2/sec)	1.21×10-6	1.25×10-6	1.12×10-6
   (m/sec)	0.019165	0.019211	0.018629
   (m/sec)	0.0578	0.0464	0.0516
   Sec. No	13	14	15
   (m3/sec)	30	44.34	39.7
   (m/sec)	0.145	0.484	0.584
   	2.69	2.6	2.71
   50 (mm)	0.172	0.156	0.164
   (m2)	206.7	91.6	68
   (m)	83.98	79.56	58.86
   (m)	2.46	1.15	1.16
   (m2/sec)	1.07×10-6	1.15×10-6	1.02×10-6
   (m/sec)	0.019776	0.015068	0.019164
   (m/sec)	0.0602	0.0411	0.0413
   Sec. No	16	17	18
   (m3/sec)	53.85	33.98	33.8
   (m/sec)	0.251	0.393	0.262
   	2.69	2.68	2.68

   50 (mm)	0.162	0.176	0.186
   (m2)	214.6	86.4	129
   (m)	93.71	62.24	82.65
   (m)	2.29	1.39	1.56
   (m2/sec)	1.12×10-6	1.04×10-6	1.05×10-6
   (m/sec)	0.017268	0.020861	0.022619
   (m/sec)	0.058	0.0452	0.0479
   Sec. No	19	20	21
   (m3/sec)	62.03	34.99	50.45
   (m/sec)	0.253	0.378	0.382
   	2.66	2.65	2.66
   50 (mm)	0.189	0.179	0.186
   (m2)	245.1	92.5	132
   (m)	71.88	79.23	59.82
   (m)	3.41	1.17	2.21
   (m2/sec)	1.02 ×10-6	1×10-6	1×10-6
   (m/sec)	0.023429	0.021712	0.023174
   (m/sec)	0.0708	0.0415	0.057
   Sec. No	22	23	24
   (m3/sec)	33.89	33.96		57
   (m/sec)	0.406	0.405	0.234
   	2.65	2.65	2.67
   50 (mm)	0.183	0.208	0.185
   (m2)	83.4	83.8	244.1
   (m)	68.82	69.53	86.34
   (m)	1.21	1.21	2.83

   Sec. No	10	11	12
   (m3/sec)	28.58	38.61	34.48
   (m/sec)	0.306	0.352	0.386
   	2.65	2.72	2.68
   50 (mm)	0.181	0.18	0.17
   (m2)	93.4	109.7	89.4
   (m)	41.22	75.33	49.45
   (m)	2.27	1.46	1.81
   (m2/sec)	1.21×10-6	1.25×10-6	1.12×10-6
   (m/sec)	0.019165	0.019211	0.018629
   (m/sec)	0.0578	0.0464	0.0516
   Sec. No	13	14	15
   (m3/sec)	30	44.34	39.7
   (m/sec)	0.145	0.484	0.584
   	2.69	2.6	2.71
   50 (mm)	0.172	0.156	0.164
   (m2)	206.7	91.6	68
   (m)	83.98	79.56	58.86
   (m)	2.46	1.15	1.16
   (m2/sec)	1.07×10-6	1.15×10-6	1.02×10-6
   (m/sec)	0.019776	0.015068	0.019164
   (m/sec)	0.0602	0.0411	0.0413
   Sec. No	16	17	18
   (m3/sec)	53.85	33.98	33.8
   (m/sec)	0.251	0.393	0.262
   	2.69	2.68	2.68

   50 (mm)	0.162	0.176	0.186
   (m2)	214.6	86.4	129
   (m)	93.71	62.24	82.65
   (m)	2.29	1.39	1.56
   (m2/sec)	1.12×10-6	1.04×10-6	1.05×10-6
   (m/sec)	0.017268	0.020861	0.022619
   (m/sec)	0.058	0.0452	0.0479
   Sec. No	19	20	21
   (m3/sec)	62.03	34.99	50.45
   (m/sec)	0.253	0.378	0.382
   	2.66	2.65	2.66
   50 (mm)	0.189	0.179	0.186
   (m2)	245.1	92.5	132
   (m)	71.88	79.23	59.82
   (m)	3.41	1.17	2.21
   (m2/sec)	1.02 ×10-6	1×10-6	1×10-6
   (m/sec)	0.023429	0.021712	0.023174
   (m/sec)	0.0708	0.0415	0.057
   Sec. No	22	23	24
   (m3/sec)	33.89	33.96	57
   (m/sec)	0.406	0.405	0.234
   	2.65	2.65	2.67
   50 (mm)	0.183	0.208	0.185
   (m2)	83.4	83.8	244.1
   (m)	68.82	69.53	86.34
   (m)	1.21	1.21	2.83

   3 2 3

   3 2 3

   (m2/sec)	1×10-6	1×10-6	1×10-6
   (m/sec)	0.02248	0.025745	0.023099
   (m/sec)	0.0422	0.0422	0.0645

   (m2/sec)	1×10-6	1×10-6	1×10-6
   (m/sec)	0.02248	0.025745	0.023099
   (m/sec)	0.0422	0.0422	0.0645

   The actual expression used with the Inglis- Lacey approach to predict sediment transport is:

   = 0.562( ) ( ) ( ) (1)

4. Sediment Transport Formulas

There are two general categories of sediment transport model equations used to simulate the movement of sediment in natural rivers. One set of transport model equations separates the total sediment load into suspended and bed load, whereas the other

combines the two modes of transport and tracks only

• Ackers – White Formula

  Ackers and White (1973) (1) used dimensional analysis based on flow power concept, as explained by Bagnold, in order to express sediment transport rate by several dimensionless parameters. Their proposed formula was as follows.

  = (50 ) ( ) [( ) 1] …(2)

  the total load (10). The formulas used in testing were

  1

  Engelund-Hansen, Inglis-Lacey, Yang, Van Rijn, Ackers-White, Fazle, Ariffin, and Jasem. Table (2) is

  showing summary of the sediment discharge variables

  The dimensionless particle is calculated by:

  by the investigators.

  = 50

  3 ( 1)

  2

  (3)

  Table (2): Summary of sediment parameters

  The particle mobility factor is calculated by:

  Author	Input parameters used
  Engelund- Hansen(1967)	, , 50 , ( 1) ( ) 50
  Inglis- Lacey(1968)	/ , / , /
  Ackers- White(1973)	50 / , / , / , ,
  Van Rijn(1984)	( ) , 50 , ( 1) ( 1) 50
  Yang(1973)	/ , / , 50 /
  Fazle(1998)	/( 1)50 , /
  Ariffin(2004)	/50 , / , / , /
  Jasem(2012)	, / , /50 , / , /

  Author	Input parameters used
  Engelund- Hansen(1967)	, , 50 , ( 1) ( ) 50
  Inglis- Lacey(1968)	/ , / , /
  Ackers- White(1973)	50 / , / , / , ,
  Van Rijn(1984)	( ) , 50 , ( 1) ( 1) 50
  Yang(1973)	/ , / , 50 /
  Fazle(1998)	/( 1)50 , /
  Ariffin(2004)	/50 , / , / , /
  Jasem(2012)	, / , /50 , / , /

  =

  [

  10

  ] 1 …(4)

  ( 1) 50

  5.66 ( 50 )

  • Engelund-Hansen Formula

    The dimensionally homogeneous equation for prediction of total sediment discharge rates in the Engelund-Hansen method is(4).

    2 50 3/2

    = 0.05

    ( 1) (( ) 50 )

    (5)

    The meanings of each symbol are presented in list of symbol.

• Inglis-Lacey formula

  The Inglis-Lacey formula was developed by Lacey (1947) (5) and Inglis (1968) by introducing the mean size and fall velocity of the bed sediment. The original Lacey regime relations were based on data from large stable irrigation canals. The formula itself is dimensionally homogeneous and it can be use with any consistent set of units.

• Yang's equation

Yang (1973) (11) proposed a sediment transport formula based on the concept of unit stream power, which can be utilized for the prediction of total bed material concentration transported in sand bed flumes and rivers. The formula is as follows:

= 5.435 0.286 ( 50 )

0.457 ( ) +

• Ariffin Formula

  Ariffin (2004) (2) had derived her sediment

  0.314 ( )] (

  ) …(6)

  transport equation based on regression. She had conducted tests on the robustness on the variables used

  The value

  is given by:

  in her equation. Her proposed equation is:

  = 1.156 × 105

  = ( 2.5

  ) +0.66 0 < 50

  < 70

  0.716

  0.975

  0.507

  2

  0.524

  ( 50 /)

  (50 ) ()

  ( )

  ( )

  .(13)

  (7)

  50

• Jasem Formula

  =2.05 70 <

  ..(8)

  Jasem (2012) (6) was studied the transportation of bed load and its entrapment have been estimated of up- stream Al-Abassiya Barrage. The equation is:

• Van Rijn formula

  Van Rijn (1984) cited in (8) developed an

  =

  ( ) 1.5( )0.5(

  ) 0.43 ( )0.67

  analytical relationship for sediment load transport in terms of the saltation height, particle velocity and bed

  50

  load concentration. The transport equation can be expressed in a simplified form when only the mean velocity, flow depth and particle size are known was given as:

  (14)

  Table (4-3) is showing the predicted and observed values of sediment discharge.

  = 0.005( ( ) )2.4(50 )1.2 (9)

  ( 1) 50

  Table (3): Predicted and observed values of sediment discharge in (kg/sec).

  = 0.012 ( ( ) )2.4(50 )()0.6

  Sec. No	1	2	3
  Ackers	0.44	0.88	0.55
  Engelund	1.54	3.71	1.96
  Inglis	0.47	0.77	0.48
  Yang	0.26	0.61	0.29
  Van Rijn	1.37	2.63	1.48
  Fazle	1.64	2.74	1.35
  Ariffin	4.89	10.15	6.19
  Jasem	10.68	13.98	9.32
  Observed	3.05	5.37	3.07
  Sec. No	4	5	6
  Ackers	3.27	2.21	2.1
  Engelund	6.41	3.62	0.79
  Inglis	2.91	4.49	0.55
  Yang	1.5	0.8	0.41
  Van Rijn	9.31	10.41	1.83
  Fazle	6.04	4.2	1.52
  Ariffin	16.06	9.21	9.86
  Jasem	18.72	15.29	9.07
  Observed	5.39	2.82	2.88
  Sec. No	7	8	9

  Sec. No	1	2	3
  Ackers	0.44	0.88	0.55
  Engelund	1.54	3.71	1.96
  Inglis	0.47	0.77	0.48
  Yang	0.26	0.61	0.29
  Van Rijn	1.37	2.63	1.48
  Fazle	1.64	2.74	1.35
  Ariffin	4.89	10.15	6.19
  Jasem	10.68	13.98	9.32
  Observed	3.05	5.37	3.07
  Sec. No	4	5	6
  Ackers	3.27	2.21	2.1
  Engelund	6.41	3.62	0.79
  Inglis	2.91	4.49	0.55
  Yang	1.5	0.8	0.41
  Van Rijn	9.31	10.41	1.83
  Fazle	6.04	4.2	1.52
  Ariffin	16.06	9.21	9.86
  Jasem	18.72	15.29	9.07
  Observed	5.39	2.82	2.88
  Sec. No	7	8	9

  ( 1) 50

  (10)

  =

  3 ( 1)

  2

  (11)

• Fazle Karim Formula

  Fazle Karim (1998)(3) in this analysis for developing the relation for total sediment discharge per unit width. The equation is:

  = 0.00139[

  ]2.97

  50

  50

  ( 1) 3

  ( 1)50

  ( )1.47 …(12)

  Fazle	1.28	3.38	2.68
  Ariffin	15.04	8.39	17.65
  Jasem	8.4	13.76	11.52
  Observed	6.51	2.9	5.25
  Sec. No	22	23	24
  Ackers	2.23	1.62	0.55
  Engelund	1.8	1.67	1.73
  Inglis	3.02	2.04	0.08
  Yang	0.58	0.55	0.43
  Van Rijn	5.53	4.8	0.73
  Fazle	2.49	2.05	1.09
  Ariffin	11.31	11.16	13.47
  Jasem	11.09	10.45	7.82
  Observed	2.54	2.89	5.07

  Ackers	0.98	4.35	0.41
  Engelund	1.81	2.47	1.19
  Inglis	2.2	4.05	0.06
  Yang	0.44	1.01	0.21
  Van Rijn	4.51	8.61	0.43
  Fazle	1.71	5.2	0.74
  Ariffin	8.38	14.54	6.86
  Jasem	12.02	15.46	6.77
  Observed	3.33	3.54	2.59
  Sec. No	10	11	12
  Ackers	1.42	0.67	3.4
  Engelund	1.58	1.69	1.2
  Inglis	0.24	0.93	1.38
  Yang	0.36	0.56	0.66
  Van Rijn	1.27	3.73	3.89
  Fazle	1.29	2.55	2.71
  Ariffin	6.88	7.58	10.88
  Jasem	8.29	12.86	11.75
  Observed	2.43	3.63	2.79
  Sec. No	13	14	15
  Ackers	0.12	4.62	5.43
  Engelund	0.54	3.56	4.1
  Inglis	0.01	11.7	16.41
  Yang	0.08	1.38	1.43
  Van Rijn	0.08	17.04	21.25
  Fazle	0.29	8.48	7.57
  Ariffin	4.5	11.89	13.98
  Jasem	4.08	21.88	19.04
  Observed	2.64	4.48	4.17
  Sec. No	16	17	18
  Ackers	0.85	2.04	0.56
  Engelund	3.24	2.07	1.12
  Inglis	0.25	2.51	0.39
  Yang	0.52	0.59	0.26
  Van Rijn	1.41	5.16	1.06
  Fazle	1.89	2.51	0.97
  Ariffin	10.77	10.38	8.61
  Jasem	10.91	11.24	7.42
  Observed	4.2	3.16	2.94
  Sec. No	19	20	21
  Ackers	0.71	1.65	2.71
  Engelund	1.48	1.97	1.03
  Inglis	0.08	3.63	0.87
  Yang	0.57	0.75	0.89
  Van Rijn	0.86	5.6	3.88

  Ariffin

  Ackers	0.98	4.35	0.41
  Engelund	1.81	2.47	1.19
  Inglis	2.2	4.05	0.06
  Yang	0.44	1.01	0.21
  Van Rijn	4.51	8.61	0.43
  Fazle	1.71	5.2	0.74
  Ariffin	8.38	14.54	6.86
  Jasem	12.02	15.46	6.77
  Observed	3.33	3.54	2.59
  Sec. No	10	11	12
  Ackers	1.42	0.67	3.4
  Engelund	1.58	1.69	1.2
  Inglis	0.24	0.93	1.38
  Yang	0.36	0.56	0.66
  Van Rijn	1.27	3.73	3.89
  Fazle	1.29	2.55	2.71
  Ariffin	6.88	7.58	10.88
  Jasem	8.29	12.86	11.75
  Observed	2.43	3.63	2.79
  Sec. No	13	14	15
  Ackers	0.12	4.62	5.43
  Engelund	0.54	3.56	4.1
  Inglis	0.01	11.7	16.41
  Yang	0.08	1.38	1.43
  Van Rijn	0.08	17.04	21.25
  Fazle	0.29	8.48	7.57
  4.5	11.89	13.98
  Jasem	4.08	21.88	19.04
  Observed	2.64	4.48	4.17
  Sec. No	16	17	18
  Ackers	0.85	2.04	0.56
  Engelund	3.24	2.07	1.12
  Inglis	0.25	2.51	0.39
  Yang	0.52	0.59	0.26
  Van Rijn	1.41	5.16	1.06
  Fazle	1.89	2.51	0.97
  Ariffin	10.77	10.38	8.61
  Jasem	10.91	11.24	7.42
  Observed	4.2	3.16	2.94
  Sec. No	19	20	21
  Ackers	0.71	1.65	2.71
  Engelund	1.48	1.97	1.03
  Inglis	0.08	3.63	0.87
  Yang	0.57	0.75	0.89
  Van Rijn	0.86	5.6	3.88

  • Comparison of Formulas precision

    With the intention of selecting the best formulas; there are two types of comparisons which are statistical relations and graphical comparison.

  • Comparison Using Statistical Relations

    Two methods are used in this research to evaluate the performance of each formula through comparing the measured sediment discharge with predicted sediment discharge.

  • Discrepancy Ratio

    To evaluate the difference between the measured and the predicted values, the discrepancy ratio was used as an error measure that is defined as: (11)

    Discrepancy Ratio = computed qs

    measured qs

    (15)

    If the discrepancy ratio is equal to one, then the predicted value is identical to the measured value. If the discrepancy ratio is larger than one, then the predicted value will be overestimating, and if the discrepancy ratio is smaller than one, it will be underestimating. The discrepancy ratio is scheduled with the ranges (0.75-1.25), (0.5-1.5), and (0.25-1.75). The results are shown in table (4).

    Table (4): Comparison between the computed and the measured values.

    Formula	Discrepancy ratio			N0. data
    	Percentage of data in the range
    	0.75-1.25	0.5-1.5	0.25-1.75
    Engelund -Hansen	16.6%	58.3%	87.5%	24
    Inglis- Lacey	12.5%	33.3%	41.6%	24
    Van Rijn	4%	29%	58.3%	24
    Ackers- White	29%	54%	58.3%	24
    Yang	.	.	25%	24
    Fazle	25%	62.5%	79%	24
    Ariffin	.	.	8.3%	24
    Jasem		4%	12.5%	24

    Table (5): Comparison using Root Mean Squared Error

    Formula	Engelund- Hansen	Inglis- Lacey	Van Rijn
    	1.96	4	5.25
    Formula	Ackers- White	Yang	Fazle
    	2.5	3.18	2.24
    Formula	Ariffin	Jasem
    	7.2	9

• Graphical Comparison

  A graphical comparison is conducted on the formulas by calculating the deviation of predicted sediment discharges from measured or by means of discrepancy ratio. Cited in (6)

  Predicted Sediment Discharge (kg/sec)

  Predicted Sediment Discharge (kg/sec)

  7

  6

  • Root Mean Squared Error

    The root mean squared error (RMSE) (9) value is a commonly used error measure. The sum of squares gives more weight to higher error values, and consequently higher error variances. The RMSE has the same units as the measured and calculated data. Smaller values indicate better agreement between the measured and the calculated values.

    5

    4

    3

    2

    1

    0

    0 1 2 3 4 5 6 7

    Observed Sediment Discharge (kg/sec)

    =

    =1

    2

    …(16)

    Figure (3): Comparison between measured and computed sediment load by using Engelund – Hansen Formula

    Figure (3): Comparison between measured and computed sediment load by using Engelund – Hansen Formula

    In which: observed sediment rate, is predicted sediment load and is the number of predicted values. The results are shown in table (5).

    Predicted Sediment Discharge (kg/sec)

    Predicted Sediment Discharge (kg/sec)

    21

    18

    15

    12

    9

    6

    3

    0

    0 3 6 9 12 15 18 21

    Observed Sediment Discharge (kg/sec)

    18

    Predicted Sediment Discharge (kg/sec)

    Predicted Sediment Discharge (kg/sec)

    16

    14

    12

    10

    8

    6

    4

    2

    0

    0 2 4 6 8 10 12 14 16 18

    Observed Sediment Discharge (kg/sec)

    Figure (6): Comparison between measured and computed sediment load by using Inglis-Lacey Formula.

    Figure (6): Comparison between measured and computed sediment load by using Inglis-Lacey Formula.

    Figure (4): Comparison between measured and computed sediment load by using Van Rijn Formula

    Predicted Sediment Discharge (kg/sec)

    Predicted Sediment Discharge (kg/sec)

    7
    6
    5
    4
    3
    2
    1
    0
    	0	1 2 3 4 5 6	7
    		Observed Sediment Discharge (kg/sec)
    Figure (5): Comparison between measured and computed sediment load by using Ackers-White Formula

    7
    6
    5
    4
    3
    2
    1
    0
    	0	1 2 3 4 5 6	7
    		Observed Sediment Discharge (kg/sec)
    Figure (5): Comparison between measured and computed sdiment load by using Ackers-White Formula

    7

    Predicted Sediment Discharge (kg/sec)

    Predicted Sediment Discharge (kg/sec)

    6

    5

    4

    3

    2

    1

    0

    0 1 2 3 4 5 6 7

    Observed Sediment Discharge (kg/sec)

    Figure (7): Comparison between measured and computed sediment load by using Yang Formula.

    9

    Predicted Sediment Discharge

    (kg/sec)

    Predicted Sediment Discharge

    (kg/sec)

    8

    7

    6

    5

    4

    3

    2

    1

    0

    0 1 2 3 4 5 6 7 8 9

    20

    Predicted Sediment Discharge (kg/sec)

    Predicted Sediment Discharge (kg/sec)

    18

    16

    14

    12

    10

    8

    6

    4

    2

    0

    0 2 4 6 8 10 12 14 16 18 20

    Observed Sediment Discharge (kg/sec)

    Observed Sediment Discharge (kg/sec)

    Figure (8): Comparison between measured and computed sediment load by using Fazle Karim Formula.

    Figure (10): Comparison between measured and computed sediment load by using Jasem Formula.

    Predicted Sediment Discharge (kg/sec)

    Predicted Sediment Discharge (kg/sec)

    18

    16

    14

    12

    10

    8

    6

    4

    2

    0

    0 2 4 6 8 10 12 14 16 18

    Observed Sediment Discharge (kg/sec)

    Figure (9): Comparison between measured and computed sediment load by using Ariffin Formula.

  • Conclusions

    Based on the results obtained in this study (Euphrates river up-stream of Al-shamia Barrage), The following conclusions can be made:

    1. The sediment particle size analysis showed that the bed material river is composed of Sand, Silt and Clay. The large portion of bed material is sandy material, with median grain size from (0.148 to 0.2) mm.

    2. Eight formulas used in the search to predict the total sediment load, the best performance were produced by Engelund formula followed by Fazle formula. The first one gave discrepancy ratio equal to 87.5% within the ranges (0.25-1.75) and RMSE equal to 1.96. While the second one gave 79% for the same ranges, and RMSE equal to 2.24.

• References

1. Akers, P. and W. R. White, "Sediment Transport: New Approach and Analysis", Journal Division, ASCE, Vol. 99, No. Hy 11, 1973.

2. Ariffin,J. and Suhaimi, A., T., "Development of Total Sediment Load Equation for Selected Rivers in Selangor", Research Management Institute, Universiti Teknologi Mara, 40450 Shah Alam, Selangor, Malaysia, October 2008.

3. Fazle, K., "Bed Material Discharge Prediction for Non Uniform Bed Sediments", Journal of Hydraulic Engineering, ASCE, Vol.124, No.6,1998.

4. Hassanzadeh, H., Faiznia, S., Shafai, B., M. and Motamed, A., "Estimate of Sediment Transport Rate at Karkheh River in Iran Using Selected Transport Formulas", World Applied Sciences Journal 13 (2): 376-384, ISSN 1818-4952, © IDOSI

   Publications, 2011.

5. Inglis, C. ,C., "Discussion of Systematic Evaluation of River System", By Neill,C. R., and Galuy, V. J., Journal of Water ways and Harbour Division, ASCE, Vol. 98, 1968.

6. Jasem, M., Hyder, "Estimation of Sediment Quantity up stream of Al-Abbasiya Barrage in Euphrates River", MSc. Thesis, Department of Civil Engineering, University of Kufa. 2012.

7. Khassaf, S., I., and Addab, H., F., "Development of Empirical Formula for Computing Sediment Load in Al-Meshkhab Regulator Channel", Jordan Journal of Civil Engineering, vol. 5, No.4, 2011.

8. Monowar, M., H. and Lutfor, M., R., " Sediment transport functions and their evaluation using data from large alluvial rivers of Bangladesh", Department of Water Resources Engineering, Bangladesh University of Engineering and Technology, IAHS Publ., no. 249, 1998.

9. Scheaffer, R., L., "Probability and Statistics for Engineer", brooks/Cole, USA, 2011.

10. Tianchun, H. and Yong, L. " Two-Dimensional Total Sediment Load Model Equations", Journal of Hydraulic Engineering © ASCE, 2008.

11. Yang, C. T., "Erosion and Sedimentation Manual", US Department of the Interior, 2006.