Hydraulic Calculation Of Minor Bridge At Ch. 1+800: Reconstruction

PROJECT: Preparation of Detailed Project Report for Begumganj - Sultanganj on NH-46 in the State of Madhya Pradesh for up-gradation to Two Lanes with paved shoulder / Four lane configuration

HYDRAULIC CALCULATION OF MINOR BRIDGE AT CH. 1+800

RECONSTRUCTION

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

Abstract of Hydraulic Particulars * Discharge using Emperical formulae * Discharge using A - V method * Design Discharge * Modified HFL * Linear Water way and Afflux Catchment area Existing Proposed span arrangement Design Discharge Design Velocity

174.137 sq. km 3x14 m 5 X15 m

LBL

1260.48 Cumecs 2.71 m/s 498.192 m

HFL Afflux

503.192 m 0.150 m

Vertical Clearance Soffit Level Existing FLR Proposed FRL

1.200 m 504.542 m 504.932 m 506.117

Hydraulic Report

High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

Hydraulic Report

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

BRIDGE CHAINAGE AT 1+700 Various Dischargeof Hydraulic Particulars * Discharge using Emperical and Rational formulae * Discharge using A - V method * Design Discharge Discharge in Upstream side

772.764

Discharge in SOC side

838.739

Discharge in Downstream side

797.306

Average Discharge of upstream,soc and downstream

802.936

Discharge calculted as per SUH

1905.25

Discharge from Dickens Formula

671.11

Discharge from Rational Formula

840.32

Design Dischage

1260.483

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

Flood Estimation Catchment area, A = I

174.137 sq. km

Emperical formula Dicken's formula Discharge, Q = C x A(3/4) Constant, C = Discharge, Q =

Ref.- IRC cl.no. -

SP 13- 2004 4.2

14 671.11 Cumecs

Hydraulic Report

Discharge calculation by Synthetic Unitgraph Method 1

2

Description Name and Number of Subzone Name of Site Name of Place Name of Stream Shape of the Catchment Location

= = = = =

Topography

=

= =

Betwa 1c Rly bridge 761/1225 Jhansi-Manikpur(CR) Barma Fan Lat 23°-36'-11.27" Long78°-21'-49.88" Moderate Steep Slope

Design data Catchment Area (A) = Length of Longest Stream (L) = Length of Longest Stream from cg to site (Lc) = Unit Duration of Unitgraph (tr) = =

Loss Rate

173.65 35.49 16.05 1.00

sqkm km km hr

2.30

mm/hr

from Toposheet from Toposheet

(Table no-4) from central water comission report

2.3 3

Computation of Equivalent Stream Slope (S) Sl. No. 1 1 2 3 4 6 7 8

Reduced distance Reduced levels (kms) (m) 2 3 0.000 480.000 5.243 500.000 16.041 520.000 26.249 540.000 31.351 560.000 35.202 580.000 35.486 600.000

Li(Di-1+Di) L2 Determination of Synthetic 1-hr Unitgraph Parameters L/ S tr Slope (S) = S

4

(table T-1) from central water comission report zone betwa1c

Li (kms) 4 0.000 5.243 10.798 10.208 31.351 3.851 0.284 x =

= =

Di (m) 5 0 20.00 40.00 60.00 80.00 100.00 120.00

Di-1 + Di (m) 6 0 20.00 60.00 100.00 140.00 180.00 220.00 Sum 14.25 m/km

Li(Di-1 + Di) (mxkm) 7 0 104.86 647.88 1020.80 4389.14 693.18 62.48 17942.92

2.490 1.0 hr

Time lag from center of unit rainfall duration to Peak of unit hydrograph in hrs.

qp =1.331(L/S)-0.492

0.850 cumec/sqkm

Unit rain fall duration in hrs.

tp =2.195(qp)^(-0.944)

=

2.561 hr

2.50 say

Peak discharge of unit hydrograph per unit area per sq.km. in cumecs

W50 = 2.040(qp)-1.265

=

2.412 hrs

=

1.44 hrs

=

0.87 hrs

Width of UH at 50% of peak discharge (Qp) in hrs.

W75 = 1.250(qp) -0.864 Width of UH at 75% of peak discharge (Qp) in hrs.

WR50 = 0.739(qp)-0968

Width of UH at 50% of Qp bet. Raisign limb and Qp ordinate in hrs.

WR75 =0.500(qp)-0.813

=

0.57 hrs

Width of UH at 75% of Qp bet. Raisign limb and Qp ordinate in hrs.

TB =5.04537(tp)0.71637

=

9.70 hrs

=

3.00 hrs

=

147.53 cumec

Base Period of UH in hrs.

tm = tp + tr/2 Time from start of raising limb to peak of UH in hrs.

Qp = qp x A Peak discharge of unit hydrograph in hrs.

10.00 say

Q in Cumecs

UG Ordinates from above formulaes X-value 0 0.00 tm-WR50 2.13 tm-WR75 2.43 tm 3.00 tm+W75-WR75 3.87 tm+W50-WR50 4.55 TB 10.00

Time in hrs

Y-value 0.00 0 Qp*0.5 73.77 Qp*0.75 110.65 Qp*1.0 147.53 Qp*0.75 110.65 Qp*0.5 73.77 0

0.00

160.00 140.00 f(x) = 14.1677486507549 x² + 7.5696901279205 x − 0.234062640606144 f(x) = − 119.524039743573 ln(x) + 270.283958429898 120.00 100.00 80.00 60.00 40.00 20.00 0.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00

UG Ordinates from graph(from equation for rising and recession limb) Abcissa values from the values from Adjusted first equation values the Second equation 0 0.00 0.00 0.10 0.66 0.66 0.20 1.85 1.85 0.30 3.31 3.31 0.40 5.06 5.06 0.50 7.09 7.09 0.60 9.41 9.41 1.00 21.50 21.50 2.00 71.58 71.58 2.92 142.73 142.73 142.72 3.84 110.02 110.02 4.55 89.74 89.74 9.25 4.96 4.96 9.28 4.57 4.57 9.29 4.44 4.44 9.40 3.04 3.04 9.53 1.39 1.39 9.55 1.14 1.14 9.58 0.77 0.77 9.60 0.52 0.52 9.62 0.27 0.27 9.64 0.00 0.00 484.05 Total 1.0 Depth (d) = S Qi = (A * D) / (0.36 * tr) = 484.05

5

UG Ordinates from graph

6

7

8

Design Storm Duration Design Storm Duration (TD)= Design Storm Rainfall 100 year-24hour Point rainfall Conversion factor for TD-hour i.e .'. 50Year TD - Hour Point Rainfall

Q in Cumecs

Time in hours Adjusted values 0 0.00 0.10 0.66 0.4 5.06 0.5 7.09 0.6 9.41 1 21.50 2 71.58 2.920647148716 142.73 3.84 110.02 4.55 89.74 9.25 4.96 9.28 4.57 9.29 4.44 9.4 3.04 9.53 1.39 9.55 1.14 9.58 0.77 9.6 0.52 9.62 0.27 9.641849381541 0.00 Total 478.90

Synthetic Unit Hydrograph

150 135 120 105 90 75 60 45 30 15 0

142.73

110.02 89.74 71.58

21.50 9.41 7.09 5.06 0.66 0.00 0

15

Time in hours

1.1* tp

3.00

=

= = =

1.1 x

32 0.68 21.76

2.6 =

cm

.'. 50 year TD hour Areal Rainfall

=

say

Plate No 10 from Fig.10 as per base period

3.0 and 0.8458 18.405

3.00

cm

Storm Areal Rainfall From Page No. 4 Areal reduction factor corresponding to storm duration TD i.e hours =

9

4.96 4.57 4.44 3.04 1.39 1.14 0.77 0.52 0.27 10

5

C.A of sq.km 173.649

(table no 6 or Fig -11) from central water comission report

cm

Time Distribution of input storm from fig. 11 of CWC Publication for sub zone 3(d) and hourly effective rainfall increments Rainfall Loss rate/ Distribution Storm rainfall in Effective hourly increments in hour (in coefficient Cm rain fall cm cm) Time 1 2 3 5 6 4 1.00 0.50 9.20 0.230 8.97 9.20 2.00 0.69 12.70 0.230 3.27 3.50 3.00 0.80 14.72 0.230 1.79 2.02 4.00 0.88 16.20 0.230 1.24 1.47 5.00 0.92 16.93 0.230 0.51 0.74 6.00 0.97 17.853 0.230 0.69 0.92 7.00 1 18.405 0.230 0.32 0.55 Design Base flow = Total Base flow for C.A =

0.018 0.018 x

cumec/m2 173.65 =

Table no- 5 from central water comission report

3.126

Cumecs

10 100 year flood peak Time in hours

SUG ordinates

Rainfall Excess ordinates Arrangement

Direct runoff

0 1.00 2.00 2.92 3.84 4.55 9.25 9.28

0.00 9.41 21.50 71.58 142.73 110.02 89.74 4.96

0.00 0.51 0.69 1.79 8.97 3.27 1.24 0.51

0.00 4.762 14.843 128.449 1280.647 359.418 111.496 2.509

Total Base flow Peak dischare

1902.13 3.13 1905.25

cumecs. cumecs. cumecs.

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800 BRIDGE CHAINAGE AT 1+700

II Rational Formula Catchment Area (A) Coefficient of Runoff (C)

=

174.137 sqkm

=

14.000

Clause 4.2 SP-13

=

0.700

Clause 4.9, Table 2, SP-13

=

22.53

km

=

180.00

m

=

4.686

hours Clause 4.7, SP 13

=

7.00

cm

=

1.0

hr

=

2.462

cm/hr Clause 4.8, SP 13

=

671.11

cumecs

=

840.32

cumecs

Percentage Coeficient of Runoff for the Catchment Characteristics (P)

Distance from the Critical Point to the Culvert in K.M (L) Fall in Level from critical point to the culvert in M (H) tc = Time of concentration in Hr. tc = (.87 X L3 / H).385 Rainfall in cm (F) Time in hr (T)

Ref SP:13 record

Critical Intensity of Rainfall in cm per hr (Ic) Ic =F/T*((T+1)F/T*((T+1)/(tc+1)) 1

Calculation of Discharge By Dicken's Formula Q = C*( A )3/4

II

Calculation of Discharge By Rational Formula Q =0.028*P*A*Ic*100

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800 Bed Slope / Longitudinal Slope of River/ stream S. No. length LBL 0 498.942 1 40.00 498.917 2 80.00 498.892 3 120.00 498.867 4 160.00 498.842 5 200.00 498.817 6 240.00 498.792 7 280.00 498.767 8 320.00 498.742 9 360.00 498.717 10 400.00 498.632 11 440.00 498.547 12 480.00 498.462 13 520.00 498.377 14 560.00 498.292 15 600.00 498.207 16 640.00 498.122 17 680.00 498.037 18 720.00 497.952 19 760.00 497.867 20 800.00 497.782 21 840.00 497.697 22 880.00 497.612 23 920.00 497.527 24 960.00 497.442 25 1000.00 497.442 26

Bed lev el

Bed slope =

0.0015 - ve sign indicate Down Ward Slope

f(x) = − 0.001652991452991 x + 499.145418803419

BED SLOPE

Chainage in m

Hydraulic Report

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800 Flood Estimation by Area-Velocity Method H.F.L = 503.942 m Bed slope So = 0.00150 Rugosity coefficient, n=

Cross section at

L.B.L Spread length 0.0350

S.No.

H.F.L

Length (m)

Bed Level

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942 503.942

37.5 32.1 26.8 21.4 16.1 10.7 5.4 0.0 5.4 10.7 16.1 21.4 26.8 32.1 37.5

503.553 501.964 501.241 500.585 499.060 499.056 498.987 498.942 498.943 498.946 498.967 499.445 500.234 501.492 503.637

= =

500.00

m U/S IRC SP 13-2014(Table 3.12)

498.942 m 75.00 m IRC SP 13-2014 ( Table 5.1 )

D.O.F

A.D.O.F

Distance

Area

W.P

0.389 0.000 0.000 0.000 0.000 1.978 1.183 5.357 6.338 5.588 2.701 2.339 5.357 12.531 5.406 3.357 3.029 5.357 16.225 5.397 4.882 4.119 5.357 22.067 5.570 4.886 4.884 5.357 26.164 5.357 4.955 4.921 5.357 26.360 5.358 5.000 4.977 5.357 26.665 5.357 4.999 5.000 5.357 26.783 5.357 4.996 4.998 5.357 26.773 5.357 4.975 4.986 5.357 26.709 5.357 4.497 4.736 5.357 25.372 5.378 3.708 4.103 5.357 21.978 5.415 2.450 3.079 5.357 16.495 5.503 0.305 1.378 5.357 7.380 5.771 Total (Cross sectional Area, A) = 287.840 sq. m Wetted Perimeter, R in m = 76.171 Abbreviations

Hydraulic Radius, Velocity, V

=

= = Discharge, Q = = Bed Level

505.000 504.000 503.000 502.000 501.000 500.000 499.000 498.000 497.000 496.000

R=A/P= 1 n

  R  

3.779 m 2 3

 V

1 2

H.F.L. -

High Flood Level

Ref:-(IRC SP-13.2014 cl.no.-(5.4))

   

3.779^(2/3) x (0.0015^0.5)/0.035) 2.68 m/sec A*V 287.84 x 2.6847 = 772.764 cumecs

D.O.F. A.D.O.F.W.P. L.B.L. -

Depth Of Flow Average Depth Of Flow Wetted Perimeter Lowest Bed Level

HFL

Chainage in m

Hydraulic Report

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

Flood Estimation by Area-Velocity Method H.F.L = 503.192 m L.B.L Bed slope So = 0.00150 Rugosity coefficient, n=

=

Spread length 0.0350

Cross section at Site of crossing 498.192 m

=

80.00 m IRC SP 13-2014 ( Table 5.1 )

S.No.

H.F.L

Length (m)

Bed Level

D.O.F

A.D.O.F

Distance

Area

W.P

1 2 3 4 5 6 7 8 9 10 11 12 13

503.192 503.192 503.192 503.192 503.192 503.192 503.192 503.192 503.192 503.192 503.192 503.192 503.192

40.0 32.0 24.0 16.0 8.0 4.0 0.0 4.0 8.0 16.0 24.0 32.0 40.0

503.037 500.737 499.537 498.792 498.194 498.193 498.192 498.193 498.195 498.261 498.266 500.246 502.600 499.419

0.155 2.455 3.655 4.400 4.998 4.999 5.000 4.999 4.997 4.931 4.926 2.946 0.592

0.000 1.305 3.055 4.027 4.699 4.999 5.000 5.000 4.998 4.964 4.928 3.936 1.769

0.000 8.000 8.000 8.000 8.000 4.000 4.000 4.000 4.000 8.000 8.000 8.000 8.000

0.000 10.440 24.440 32.220 37.592 19.994 19.998 19.998 19.991 39.710 39.428 31.489 14.153

0.000 8.000 8.089 8.035 8.022 4.000 4.000 4.000 4.000 8.000 8.000 8.241 8.339

Hydraulic Radius, Velocity, V = = = Discharge, Q

Bed Level

504.0 503.0 502.0 501.0 500.0 499.0 498.0 497.0 496.0 495.0

R=A/P= 1 n

  R  

Total (Cross sectional Area, A) = 309.452 sq. m 3.77328462 Wetted Perimeter, R in m = 80.727 Abbreviations H.F.L. High Flood Level Ref:-(IRC SP-13.2014 cl.no.-(5.4))

3.833 m 2 3

 V

1 2

   

3.8333^(2/3) x (0.0015^0.5)/0.035) 2.71 m/sec = A*V = 309.452 x 2.71

=

D.O.F. -

Depth Of Flow

A.D.O.F.W.P. L.B.L. -

Average Depth Of Flow Wetted Perimeter Lowest Bed Level

838.739 cumecs

HFL

Chainage in m

Hydraulic Report

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

Flood Estimation by Area-Velocity Method H.F.L = 502.442 m Bed slope So = 0.00150 Rugosity coefficient, n=

Cross section at

L.B.L Spread length 0.0350

= =

500.00

m D/S IRC SP 13-2014(Table 3.12)

497.442 m 75.00 m IRC SP 13-2014 ( Table 5.1 )

S.No.

H.F.L

Length (m)

Bed Level

D.O.F

A.D.O.F

Distance

Area

W.P

1 2 3 4 5 6 7 8 9 10

502.442 502.442 502.442 502.442 502.442 502.442 502.442 502.442 502.442 502.442

37.5 32.1 26.8 21.4 16.1 10.7 5.4 0.0 5.4 10.7

502.019 500.173 499.210 498.854 498.519 498.093 497.778 497.442 497.444 497.446

0.423 2.269 3.232 3.588 3.923 4.349 4.664 5.000 4.998 4.996

0.000 1.346 2.751 3.410 3.755 4.136 4.506 4.832 4.999 4.997

0.000 5.357 5.357 5.357 5.357 5.357 5.357 5.357 5.357 5.357

0.00 7.21 14.74 18.27 20.12 22.16 24.14 25.89 26.78 26.77

0.000 5.666 5.443 5.369 5.368 5.374 5.366 5.368 5.357 5.357

11

502.442

16.1

497.500

4.942

4.969

5.357

26.62

5.357

12

502.442

21.4

497.852

4.590

4.766

5.357

25.53

5.369

13

502.442

26.8

498.210

4.232

4.411

5.357

23.63

5.369

14

502.442

32.1

498.886

3.556

3.894

5.357

20.86

5.400

15

502.442

37.5

501.951

0.491

2.024

5.357

10.84

6.172

Total (Cross sectional Area, A) = 293.559 sq. m Wetted Perimeter, R in m = 76.335 Abbreviations Hydraulic Radius, Velocity, V

=

1 n

Bed Level

  R  

3.846 m 2 3

 V

1 2

3.8457^(2/3) x (0.0015^0.5)/0.035) 2.72 m/sec

=

A*V 293.559 x 2.716

=

H.F.L. -

High Flood Level

Ref:-(IRC SP-13.2014 cl.no.-(5.4))

   

= = Discharge, Q =

503.0 502.0 501.0 500.0 499.0 498.0 497.0 496.0 495.0 494.0

R=A/P=

D.O.F. A.D.O.F.W.P. L.B.L. -

Depth Of Flow Average Depth Of Flow Wetted Perimeter Lowest Bed Level

797.306 cumecs

HFL

Chainage in m

Hydraulic Report

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

1 Afflux Calculations By Molesworth formula

(IRC:5-2015 CL. No.106.6.2)

  V2   Au   0.015     1   17.89   Ae  2

Afflux =

Afflux =

((2.7104^2)/17.89)+0.015)x(((309.452/269.968776)^2)-1)

Velocity, V = Unobstructed area, Au =

2.71 m/sec 309.45 m2

Effective vent area, Ae =

269.97 m2

Afflux =

2 Linear Water Way: Discharge by Empericle Discharge by Area velocity (a) At U/s Side(b) At Bridge Side(c) At D/s SideDesign discharge (Q) = Velocity of river (V) = HFL = Lowest Bed level = Mean Depth of water (H) = Afflux = Required Linear water way =

0.15 m

671.11 m3/s

Q /( H  V )

Proposed vent way = 75-1*4-0.8*2 Silt Factor "f" = Linear Water Way = 4.8 

3. Fixing of Soffit Level Vertical clearance (Vc) required = required Soffit Level

Hence, provided Sofiit Level

Q

772.76 m3/s 838.74 m3/s 797.31 m3/s 1260.48 m3/s (SP 13 Para 6.2.1) 2.71 m/s 503.192 m 498.19 m 3.89 m 0.15 m = 1260.48/(2.7104 x (3.89+0.15) 115.11 m 69.40 m 4.5 (IRC:78-2014 CL. No.703.2.2.1) = 4.8*1260.48^0.5 170.42 m (IRC:5-2015 CL. No.106.5.1)

1.20 m 504.392 m

(As per Cl. No. 106.8.2 of IRC: - 5-2015)

504.542 m

Hydraulic Report

Project: Hydraulic calculation of High Level Bridge on Begumganj - Sultanganj on NH-46 at RD 1+800

1

Scour Depth: Design discharge

1260.5 m3/s 1260.5 m3/s 69.40 m 503.192 m 498.19 m

Design discharge for foundation Clear ventway HFL LBL dsm = 1.34 (Db2 / Ksf)^1/3

IRC 78 - 2014

where, Db = the discharge in cumecs per metre width. Ksf = silt factor Db = 23.61 cumecs/m

cl.703.2

Ksf = 4.500 dsm = 1.34 x (23.611^2 / 4.5)^(1/3) =

Max. depth of scour for Piers = Max. depth of scour for Abutment = Scour Level for Piers =

6.680

Foundation level for Abutments

m below HFL

2 x dsm =

13.360 m Below HFL 1.27 x dsm = 8.484 m Below HFL 489.832 m

Scour level for Abutments = Foundation Level for Piers

30% increase discharge IRC 78 - 2014 cl.No. 703.1.1 Silt factor Ksf as per

IRC 78 - 2014 cl. No.703.3.1.1 IRC 78 - 2014 of IRC 78 - 2014 cl. No.703.3.1.1

494.710 m = = = = =

( 489.832 - 2 ) 487.832 m

IRC 78-2014 cl.No.705.2.1

( 494.71 - 2 ) 492.710 m

IRC 78-2014 cl.No.705.2.1