Planning of Bridges
Dr. Shahzad Rahman

• Traffic Studies
• Hydrotechnical Studies
• Geotechnical Studies
• Environmental Considerations
• Alternatives for Bridge Type
• Economic Feasibility
• Bridge Selection and Detailed Design

Existing Network
Traffic Studies
New Road Link
City Center
New Bridge

• Traffic studies need to be carried out to ascertain the amount of traffic that will utilize the New or Widened Bridge
• This is needed to determine Economic
Feasibility of the Bridge
• For this Services of a Transportation
Planner and or Traffic Engineer are
Required
• Such Studies are done with help of Traffic
Software such as TransCAD, EMME2 etc.

• Traffic Studies should provide following information
– Traffic on Bridge immediately after opening
– Amount of traffic at various times during life of the
Bridge
– Traffic Mix i.e. number of motorcars, buses, heavy trucks and other vehicles
– Effect of the new link on existing road network
– Predominant Origin and Destination of traffic that will use the Bridge
– Strategic importance of the new/improved Bridge

Hydrotechnical Studies
• A thorough understanding of the river and river regime is crucial to planning of Bridge over a river
• Hydrotechnical Studies should include:
• Topographic Survey 2km upstream and
2km downstream for small rivers including
Longitudinal section and X-sections
• For big rivers 5kms U/S and 2kms D/S should be surveyed
• Navigational Requirements

• Scale of the topographic map
– 1:2000 for small rivers
– 1:5000 for large rivers
• The High Flood Levels and the
Observed Flood Level should be indicated map
• Sufficient Number of x-sections should be taken and HFL and
OFL marked on them
• River Bed surveying would require soundings

• Catchment Area Map
• Scale recommended
– 1:50,000 or
– 1:25,000
• Map can be made using GT Sheets available from Survey of Pakistan
• All Reservoirs, Rain
Gauges Stns., River
Gauge Stns., should be marked on map
Catchment of River Indus

River Catchment Area

River Catchment Boundaries with Tributaries

River Catchment Boundaries with Sub-Basin Boundaries

• Following Hydrological Data should be collected:
• Rainfall Data from Rain Gauge Stations in the Catchment Area
• Isohyetal Map of the Catchment Area showing contours of Annual Rainfall
• Hydrographs of Floods at River Gauge
Stations
• Flow Velocities
• Sediment Load in River Flow during floods

Example of an ISOHYETAL MAP

Example of River Hydrograph

Example of a River Hydrograph

• AASHTO Gives Following Guidelines for Estimating
Design Flood Levels

• AASHTO Gives Following Guidelines for Estimating
Design Flood Levels

• CANADIAN MINISTRY OF TRANSPORTATION
Gives Following Guidelines for Estimating Design Flood Levels

• CANADIAN MINISTRY OF TRANSPORTATION
Gives Following Guidelines for Estimating Design Flood Levels

FREEBOARD REQUIREMENTS
• CANADIAN MINISTRY OF TRANSPORTATION
Gives Following Guidelines for Estimating Freeboard Requirements

• Flood Peak Discharge at Stream or River Location
Depends upon:
• Catchment Area Characteristics
– Size and shape of catchment area
– Nature of catchment soil and vegetation
– Elevation differences in catchment and between catchment and bridge site location
• Rainfall Climatic Characteristics
– Rainfall intensity duration and its spatial distribution
• Stream/River Characteristics
– Slope of the river
– Baseline flow in the river
– River Regulation Facilities/ Dams, Barrages on the river

1. Empirical Methods
2. Flood Frequency Analysis
3. Rational Method

Empirical Methods of Peak Flood Estimation
• Empirical Formulae have been determined that relate Catchment Area and other weather or river parameters to Peak Flood Discharge
• Popular Formulae for Indo-Pak are:
– Dickens Formula
Q

825 A
3 / 4
Q = Discharge in Cusecs
A = Catchment Area in Sq. Miles
– Inglis Formula
– Ryve’s Formula
Q

7000
A

4
A
Q

C A
2 / 3
C = 450 for areas within 15 miles off coast
560 between 15 – 100 miles off coast

• Usable at gauged sites where river discharge data is available for sufficient time in past
• Following Methods are commonly used
– Normal Distribution Method
– Log-Normal Distribution
– Log-Plot Graphical Method

• Normal Distribution Method
– Based on Assumption that events follow the shape of Standard Normal Distribution Curve

Q
P

Q
M

K
Tr

Q
Q
Q
P
= Discharge Associated with Probability of Occurrence P
QM = Mean Discharge over the data set
σQ = Standard Deviation of the Discharge data set
KTr = Frequency factor corresponding to Probability of Occurrence P

Example
Flood Frequency Analysis Normal Distribution Method
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Actual
Year Year Max Flood Xi - Xavg (Xi - Xavg)
2
(No.) Q
(cumecs) (cumecs) (cumecs
2
)
7
8
5
6
3
4
1
2
9
10
11
12
16
32
48
14
26
42
17
35
13
21
18
16
2.9
18.9
-6.1
11.9
-7.1
8.9
24.9
-9.1
-10.1
-2.1
-5.1
-7.1
8.3
356.3
37.5
141.0
50.8
78.8
618.8
83.3
102.5
4.5
26.3
50.8
Ranked Flow
(Decending
Order)
35
32
26
25
48
45
42
35
23
21
21
20
Rank Probability Return Period
R P = R/n Tr = 1/P
7
8
5
6
3
4
1
2
9
10
11
12
0.04
0.08
0.13
0.17
0.21
0.25
0.29
0.33
0.38
0.42
0.46
0.50
(yrs)
24.00
12.00
8.00
6.00
4.80
4.00
3.43
3.00
2.67
2.40
2.18
2.00

Actual
Year
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
18
19
20
21
22
23
24
13
14
15
16
17
Year
(No.)
Max Flood Xi - Xavg (Xi - Xavg)
2
Q
(cumecs) (cumecs) (cumecs
2
)
14
12
17
25
15
21
15
20
15
35
45
23
-3.1
-8.1
11.9
21.9
-0.1
-9.1
-11.1
-6.1
1.9
-8.1
-2.1
-8.1
9.8
66.0
141.0
478.5
0.0
83.3
123.8
37.5
3.5
66.0
4.5
66.0
Ranked Flow
(Decending
Order)
15
15
15
14
14
13
12
18
17
17
16
16
Rank Probability Return Period
R P = R/n Tr = 1/P
(yrs)
18
19
20
21
22
23
24
13
14
15
16
17
0.54
0.58
0.63
0.67
0.71
0.75
0.79
0.83
0.88
0.92
0.96
1.00
1.85
1.71
1.60
1.50
1.41
1.33
1.26
1.20
1.14
1.09
1.04
1.00
Sample Pts = n =
Mean Qm = M
Sum of Squares =
Variance =
S 2 
24
23.125
n
1

1

( x j

 x ) 2 
V

( n
S

2
1 )

Standard Deviation =  
V

Coefficient of Variation = Cv = σ/M =
Skewness Coefficient = SC = 3 Cv + Cv
3
=
Input Return Period (Years) = Tr =
Probability = p = 1/ Tr
Flood Estimate = Qt =
2638.6
114.72
10.71
0 . 4 6 3
1.49
100 Input Value
0.01

Input Return Period (Years) = Tr =
Probability = p = 1/ Tr
Flood Estimate = Qt =
100 Input Value
0.01
w
 ln p
1
2 w = 3.03485528
K
Tr
 w

2 .
51557
1

1 .
532788

0 .
802853 w

0 .
w
189269
 w
0 .
010328
2 
0 .
w
2
001308 w
3
K
Tr
=
Flood Estimate = Qt =
Q t
 Q m

Ktr

2.32678649
Qt = 48.05
Cumecs
10
1
1 10
Series1
Log. (Series1)
100

• Yields better Results
Compared to Normal
Distribution Method ln Q
P
 ln Q
M

K
Tr
 ln Q
Log Q or Ln Q lnQ
P lnQ
M
σ lnQ
K
Tr
Q
P
= Log of Discharge Associated with Probability of Occurrence P
= Mean of Log Discharge over the data set
= Standard Deviation of the Log of Discharge data set
= Frequency factor corresponding to Probability of Occurrence P
= Antilog (ln Q
P
) = Discharge Associated with Probability of Occurrence P

Example of Peak Flood Estimation Flood
Log-Plot Method
Log Plot Discharge Vs Return Period
80
70
60
50
40
30
20
Observed Discharge
Log. (Observed Discharge) y = 12.724Ln(x) + 11.733
10
0
1 10
Retun Period (Yrs)
Trendline Equation is
Qt = 12.724 Ln(Tr) + 11.213
For Return Period Tr =
Qt = 12.724 Ln (50) + 11.213 =
For Return Period Tr =
Qt = 12.724 Ln (100) + 11.213 =
50 yrs
100 yrs
61.0
69.8
cumecs cumecs
100

• Attempts to give estimate of Design Discharge taking into account:
– The Catchment Characteristics
– Rainfall Intensity
– Discharge Characteristics of the Catchment
Q

C I
T
A
Q = Design Discharge
I
T
= Average rainfall intensity (in/hr) for some recurrence interval, T during that period of time equal to Tc.
Tc = Time of Concentration
A = Area of the catchment in Sq. miles
C = Runoff coefficient; fraction of runoff, expressed as a dimensionless decimal fraction, that appears as surface runoff from the contributing drainage area.

• Time of Concentration can be estimated using
Barnsby Williams Formula which is widely used by US Highway Engineers
Tc

0 .
9 L
A
0 .
1
S
0 .
2
L = Length of Stream in Miles
A = Area of the catchment in Sq. miles
S = Average grade from source to site in percent

Area Characteristic
Steep Bare Rock
Steep Rock with Woods
Plateau with light cover
Densely built-up areas
Residential areas
Stiff Clayey soils
Loam
Suburbs with gardens
Sandy soils
Jungle area
Parks, Lawns, Fields
Run-off Coefficient C
0.90
0.80
0.70
0.90 – 0.70
0.70 – 0.50
0.50
0.40 – 0.30
0.30
0.1 – 0.20
0.10 – 0.25
0.25 - 0.50

• Geotechnical Studies should provide the following Information:
• The types of Rocks, Dips, Faults and
Fissures
• Subsoil Ground Water Level, Quality,
Artesian Conditions if any
• Location and extent of soft layers
• Identification of hard bearing strata
• Physical properties of soil layers

Example Geological Profile:
Cross section of the soil on the route of the Paris
The diagram above shows the crossing over the Seine via the Bir Hakeim bridge and the limestone quarries under Trocadéro

Example: Cross section of the Kansas River, west of Silver Lake, Kansas
Typical Borehole

Source: Building Code of Pakistan

Source: Geological Survey of Pakistan

• Impact on Following Features of Environment need to considered:
– River Ecology which includes:
• Marine Life
• Wildlife along river banks
• Riverbed
• Flora and fauna along river banks
– Impact upon dwellings along the river if any
– Impact upon urban environment if the bridge in an urban area
– Possible impact upon archeological sites in vicinity

• Economic Analysis is Required at
Feasibility Stage to justify expenditure of public or private funds
• A Bridge is the most expensive part of a road transportation network
• Types of Economic Analyses
– Cost Benefit Ratio Analysis
– Internal Rate of Return (IRR) Analysis

Bridge Economic Analysis/
Life Cycle Cost Analysis (LCCA)
Time
Project Life

• The objective of LCCA is to
– Estimate the costs associated with the Project during Construction an its service life. These include routine maintenance costs +
Major Rehab Costs
– Estimate the Benefits that will accrue from the Project including time savings to road users, benefits to business activities etc.
– Bring down the costs and benefits to a common reference pt. in time i.e. just prior to start of project (decision making time)
– Facilitate decision making about economic feasibility by calculating quantifiable yardsticks such as Benefit to Cost Ratio
(BCR) and Internal Rate of Return (IRR)
• Note: Salvage Value may be taken as a Benefit
This includes cost of the Right-of-Way and substructure

• An economic analysis procedure that uses engineering inputs
• Compares competing alternatives considering all significant costs
• Expresses results in equivalent dollars
(present worth)

• Normally equal for all alternatives
• Should include at least one major rehabilitation
• Needed to capture the true economic benefit of each alternative
• Bridge design today is based on a probabilistic model of 100 years

Bridge Economic Analysis/
Life Cycle Cost Analysis (LCCA)
Time
Problem:
Project Life
• Costs and Benefits Change over the life of the Project
• Amount of Money/Benefit accrued some time in future is worth less in terms of Today’s money
• Same is the case with the benefits accrued over time
• The Problem now is as to How to find the Worth of a Financial Amount in
Future in terms of Today’s Money
• This is accomplished by using the instrument of “DISCOUNT RATE”

Bridge Economic Analysis/
Life Cycle Cost Analysis (LCCA)
DISCOUNT RATE:
The annual effective discount rate is the annual interest divided by the capital including that interest, which is the interest rate divided by 100% plus the interest rate. It is the annual discount factor to be applied to the future cash flow, to find the discount, subtracted from a future value to find the value one year earlier.
For example, suppose there is an investment made of $95 and pays $100 in a year's time. The discount rate according the given definition is:
Discount Rate
 d

100

100
95

5 .
0 %
Interest Rate is calculated as $ 95 as Base
Interest Rate
 i

100

95
95

5 .
26 %
Interest Rate and Discount Rate are Related as Follows
Discount Rate
 d
 i
1
 i
 i
 i
2

• Thus Discount Rate is that rate which can be used to obtain the Present Value of Money that is spent or collected in future
Cost/ Benefit Projected
Backward
Cn
Year n
Co
Time
Bo
Bn
Project
Life
Net Present value of Cost incurred = Co = (1 - d) n
Cn
In Year n
Net Present value of Cost incurred = Bo = (1 - d) n
Bn
In Year n

• A first estimate of appropriate Discount rate can be made as follows:
Estimate of
Discount Rate = Federal Bank Lending Rate – Average Long-term Inflation Rate
Note: By subtracting the Inflation Rate in arriving at a Discount Rate the effect of Inflation can be removed from consideration during
Economic Analysis
The Discount Rate after subtracting the Inflation Rate is also
Referred to as the “Real Discount Rate”
Govt. of Pakistan uses a Discount Rate of 6-7% for economic analysis
Asian Development Bank uses a Discount rate of 12% for evaluation of projects
Discount Rate is less than the Real interest Rate as Governments do not take a purely commercial view of an infrastructure project

Present Worth
Initial Cost
Rehabilitation Cost
Salvage
Costs
Maintenance and
Inspection
Cost
Years
Salvage
Value

Formula for Cost
Benefit Ratio
Benefit To Cost Ratio =
Present Value of Benefits
Present Value of Costs

L 
0
( 1
 d ) n
L 
0
( 1
 d ) n
Bn
Cn
Where L = Life Span of the Project in Years d = Discount Rate
Bn = Benefit in year n
Cn = Cost incurred in year n

• Net Present Worth/ Value = NPW or NPV is defined as follows:
NPW = NPV = Present Value of Benefits – Present Value of Costs
Note: If a Number of alternatives are being compared, the alternative that has the highest Net Present Worth is the preferable one and will also have the higher Benefit to Cost Ratio

• IRR may be defined as that Discount Rate at which the Benefit to Cost Ratio (BCR) of a Project becomes exactly 1.0
• It is a better measure of economic viability of a project compared to Benefit to Cost
Ratio
• It is a good indicator of how much inflation increase and interest rate hike a project can tolerate and still be viable

pwf

( 1
 d ) n pwf = Present Worth Factor for discount rate d and year n d = Discount rate n = Number of year when the cost/ benefit will occur
Alternate Formula (Usually Adopted) pwf

1

1
 d
 n

• Discounts all future costs and benefits to the present:
PW = FC + t=L
 pwf [MC+IC+FRC+UC] + pwf [S] t=0
PW = Present Worth/ Value of the Project t
FC = First (Initial) Cost
= Time Period of Analysis (ranges from 0

L)
MC = Maintenance Costs
IC = Inspection Costs
FRC = Future Rehabilitation Costs
UC = Users Costs
S = Salvage Values or Costs pwf = Present Worth Factor

• Normally equal for all alternatives
• Should include at least one major rehabilitation
– Needed to capture the true economic benefit of each alternative
• Bridge design today is based on a probabilistic model of
100 years

• Annual cost associated with the upkeep of the structure
• Information is difficult to obtain for a given project
• Cost varies on the basis of size of the structure
(sqft)
• Best Guess Values
– Frequency - Annual
– Concrete 0.05 % of Initial Cost
– Structural Steel 0.05 % of Initial Cost

• Should be taken for all alternatives preferably every two years
• Cost varies on the basis of size of the structure
(sqft) and by construction material
• Best Guess Values
– Frequency - Biannual
– Concrete 0.15 % of Initial Cost
– Structural Steel 0.20 % of Initial Cost

• Only applies to structural steel structures but excludes weathering steel
• Should occur every 20 years
• Cost varies on the basis of size of the structure
(sqft)
• Best Guess Values
– Frequency – every 20 years
– Concrete 0.0 % of Initial Cost
– Structural Steel 7.0 % of Initial Cost

• The frequency is not only a function of time but also the growing traffic volume and the structural beam system
• Cost varies on the basis of size of the structure (sqft) and structural beam system
• Best Guess Values
– Frequency
• First occurrence – Concrete 40 years
• First occurrence – Structural Steel 35 years
• Annual traffic growth rate .75 % (shortens rehab cycles)
– Concrete
– Structural Steel
20.0 % of Initial Cost
22.0 % of Initial Cost

• Occurs once at end of life of structure
• Difference between
– Removal cost
– Salvage value
• Best Guess Values
– Removal cost 10 % of Initial Cost
– Salvage Value – Concrete - 0 % of Initial Cost
– Salvage Value – Structural Steel - 2 % of Initial Cost

Monetizable Benefits
• Time savings to road users
• Growth in economic activity
• Saving of Vehicular wear and tear
• Reduction of accidents if applicable
Other Non-Monetizable Benefits
• Strategic Benefits

Carry out an Economic Analysis of a Proposed Bridge given the following Data:
= 12,000 Vehicles per Day Estimated Average Annualized Daily Traffic is
With the Following Mix of Traffic
Cars
Trucks
Buses
Assume that the Traffic Growth Rate is Geometric over the
Life Span of the Bridge
Bridge Life Span
The Construction Cost is spread over 2 years
The Trade and economic benefits are estimated to be
Annual Growth Rate of Trade Benefits is Geometric at the rate of over the
Life Span of the Bridge
The Bridge would Result in Time Saving of to Road Users
Average Time Value of Single Road User
=
=
=
=
=
=
=
=
=
=
10,000
1,000
1,000
1.2 %
80 years
200.0 Million Rs.
10.0 Million Rs. per year
2.0 %
1 hour
50.0 Rs. Per Hour

Assume that the Bridge would require:
Annual Maintenance
Major Rehabilitation after every 30 years
Salvage Value of Piers and Abutments
Salvage Cost is assumed to be
Average Occupancy Of a Single Car
Average Occupancy Of a Single Truck
Average Occupancy Of a Single Bus
Calculate the Present Worth, Net Present Worth,
Benefit to Cost Ratio of the Bridge at Discount Rate =
Calculate the Internal Rate of Return of the Bridge
=
=
=
=
=
=
=
0.03 % of Construction Cost
20.0 % of Construction Cost
25 % of Construction Cost
0.0 %
3.0 Passengers
2.0 Passengers
50 Passengers
6.0 %

Benefits in Time Saving Upon Bridge Opening
Vehicle
Type
Cars
Buses
Trucks
Number Occupancy Time Saving Time Value
10,000
1,000
1,000
(Persons)
3.0
50.0
2.0
Total Benefit Per Year
Assumed to then Grow at Geometrically at the Rate of 1.2% per year
(hrs)
1.0
1.0
1.0
(Rs.per Hour)
=
Benefit
(Rs.)
50.0
1,500,000
50.0
2,500,000
50.0
100,000
4,100,000

Actual Year Year No.
2018
2019
2020
2021
2022
2023
2024
2025
2026
2010
2011
2012
2013
2014
2015
2016
2017
0
1
4
5
2
3
6
7
8
9
10
11
12
13
14
15
16
Present Worth
Factor (PWF)
Construction/
Maintenance
Cost
(1-d)^n (Rs.)
1.0000
100,000,000
0.9400
100,000,000
0.8836
0.8306
0.7807
0.7339
0.6899
0.6485
0.6096
0.5730
0.5386
0.5063
0.4759
0.4474
0.4205
0.3953
0.3716
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
Benefit:
Time
Saving Rehab Cost Total Costs
(Rs.) (Rs.)
100,000,000
100,000,000
(Rs.)
-
60,000 4,100,000
60,000 4,149,200
60,000 4,198,400
60,000 4,247,600
60,000 4,296,800
60,000 4,346,000
60,000 4,395,200
60,000 4,444,400
60,000 4,493,600
60,000 4,542,800
60,000 4,592,000
60,000 4,641,200
60,000 4,690,400
60,000 4,739,600
60,000 4,788,800
Benefit:
Trade/
Economic
(Rs.)
10,000,000
10,200,000
10,400,000
10,600,000
10,800,000
11,000,000
11,200,000
11,400,000
11,600,000
11,800,000
12,000,000
12,200,000
12,400,000
12,600,000
12,800,000
Salvage
Benefit
(Rs.)
Total
Benefits
Total
Discounted
Costs
(Rs.) (Rs.)
100,000,000
94,000,000
14,100,000
14,349,200
14,598,400
14,847,600
15,096,800
15,346,000
15,595,200
15,844,400
16,093,600
16,342,800
16,592,000
16,841,200
17,090,400
17,339,600
17,588,800
53,016
49,835
46,845
44,034
41,392
38,909
36,574
34,380
32,317
30,378
28,555
26,842
25,231
23,718
22,294
Total
Discounted
Benefits
(Rs.)
-
-
12,458,760
11,918,216
11,397,686
10,896,713
10,414,826
9,951,537
9,506,350
9,078,759
8,668,256
8,274,330
7,896,470
7,534,165
7,186,910
6,854,202
6,535,546
Net Benefit
(Rs.)
(100,000,000)
(100,000,000)
14,040,000
14,289,200
14,538,400
14,787,600
15,036,800
15,286,000
15,535,200
15,784,400
16,033,600
16,282,800
16,532,000
16,781,200
17,030,400
17,279,600
17,528,800

2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
42
43
44
45
46
37
38
39
40
41
47
48
49
50
32
33
34
35
36
27
28
29
30
31
22
23
24
25
26
17
18
19
20
21
Actual Year Year No.
Present Worth
Factor (PWF)
(1-d)^n
0.1013
0.0952
0.0895
0.0842
0.0791
0.0744
0.0699
0.0657
0.0618
0.0581
0.0546
0.0513
0.0482
0.0453
0.1881
0.1768
0.1662
0.1563
0.1469
0.1381
0.1298
0.1220
0.1147
0.1078
0.3493
0.3283
0.3086
0.2901
0.2727
0.2563
0.2410
0.2265
0.2129
0.2001
Construction/
Maintenance
Cost
(Rs.)
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
Rehab Cost Total Costs
(Rs.) (Rs.)
40,000,000
Benefit:
Time
Saving
(Rs.)
60,000 4,838,000
60,000 4,887,200
60,000 4,936,400
60,000 4,985,600
60,000 5,034,800
60,000 5,084,000
60,000 5,133,200
60,000 5,182,400
60,000 5,231,600
60,000 5,280,800
60,000 5,330,000
60,000 5,379,200
60,000 5,428,400
40,060,000 5,477,600
60,000 5,526,800
60,000 5,576,000
60,000 5,625,200
60,000 5,674,400
60,000 5,723,600
60,000 5,772,800
60,000 5,822,000
60,000 5,871,200
60,000 5,920,400
60,000 5,969,600
60,000 6,018,800
60,000 6,068,000
60,000 6,117,200
60,000 6,166,400
60,000 6,215,600
60,000 6,264,800
60,000 6,314,000
60,000 6,363,200
60,000 6,412,400
60,000 6,461,600
Benefit:
Trade/
Economic
(Rs.)
13,000,000
13,200,000
13,400,000
13,600,000
13,800,000
14,000,000
14,200,000
14,400,000
14,600,000
14,800,000
15,000,000
15,200,000
15,400,000
15,600,000
15,800,000
16,000,000
16,200,000
16,400,000
16,600,000
16,800,000
17,000,000
17,200,000
17,400,000
17,600,000
17,800,000
18,000,000
18,200,000
18,400,000
18,600,000
18,800,000
19,000,000
19,200,000
19,400,000
19,600,000
Salvage
Benefit
(Rs.)
Total
Discounted
Costs
(Rs.)
20,957
19,699
18,517
17,406
16,362
15,380
14,457
13,590
12,775
12,008
11,288
10,610
9,974
6,259,600
8,813
8,284
7,787
7,320
6,881
6,468
6,080
5,715
5,372
5,050
4,747
4,462
4,194
3,943
3,706
3,484
3,275
3,078
2,893
2,720
Total
Benefits
(Rs.)
17,838,000
18,087,200
18,336,400
18,585,600
18,834,800
19,084,000
19,333,200
19,582,400
19,831,600
20,080,800
20,330,000
20,579,200
20,828,400
21,077,600
21,326,800
21,576,000
21,825,200
22,074,400
22,323,600
22,572,800
22,822,000
23,071,200
23,320,400
23,569,600
23,818,800
24,068,000
24,317,200
24,566,400
24,815,600
25,064,800
25,314,000
25,563,200
25,812,400
26,061,600
Total
Discounted
Benefits
(Rs.)
6,230,454
5,938,445
5,659,047
5,391,799
5,136,247
4,891,952
4,658,482
4,435,416
4,222,349
4,018,882
3,824,630
3,639,221
3,462,292
3,293,493
3,132,486
2,978,943
2,832,549
2,692,997
2,559,995
2,433,258
2,312,514
2,197,499
2,087,961
1,983,656
1,884,351
1,789,822
1,699,853
1,614,236
1,532,774
1,455,276
1,381,560
1,311,451
1,244,782
1,181,391
Net Benefit
(Rs.)
17,778,000
18,027,200
18,276,400
18,525,600
18,774,800
19,024,000
19,273,200
19,522,400
19,771,600
20,020,800
20,270,000
20,519,200
20,768,400
(18,982,400)
21,266,800
21,516,000
21,765,200
22,014,400
22,263,600
22,512,800
22,762,000
23,011,200
23,260,400
23,509,600
23,758,800
24,008,000
24,257,200
24,506,400
24,755,600
25,004,800
25,254,000
25,503,200
25,752,400
26,001,600

2082
2083
2084
2085
2086
2087
2088
2089
2074
2075
2076
2077
2078
2079
2080
2081
2090
2091
Total
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
72
73
74
75
76
77
78
79
80
81
64
65
66
67
68
69
70
71
56
57
58
59
60
61
62
63
51
52
53
54
55
Actual Year Year No.
Present Worth
Factor (PWF)
Construction/
Maintenance
Cost
(1-d)^n
0.0191
0.0179
0.0168
0.0158
0.0149
0.0140
0.0132
0.0124
0.0116
0.0109
0.0103
0.0097
0.0091
0.0085
0.0080
0.0075
0.0071
0.0067
0.0426
0.0401
0.0377
0.0354
0.0333
0.0313
0.0294
0.0276
0.0260
0.0244
0.0230
0.0216
0.0203
(Rs.)
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
Benefit:
Time
Saving Rehab Cost Total Costs
(Rs.)
40,000,000
(Rs.) (Rs.)
60,000 6,510,800
60,000 6,560,000
60,000 6,609,200
60,000 6,658,400
60,000 6,707,600
60,000 6,756,800
60,000 6,806,000
60,000 6,855,200
60,000 6,904,400
40,060,000 6,953,600
60,000 7,002,800
60,000 7,052,000
60,000 7,101,200
60,000 7,150,400
60,000 7,199,600
60,000 7,248,800
60,000 7,298,000
60,000 7,347,200
60,000 7,396,400
60,000 7,445,600
60,000 7,494,800
60,000 7,544,000
60,000 7,593,200
60,000 7,642,400
60,000 7,691,600
60,000 7,740,800
60,000 7,790,000
60,000 7,839,200
60,000 7,888,400
60,000 7,937,600
60,000 7,986,800
Benefit:
Trade/
Economic
(Rs.)
19,800,000
20,000,000
20,200,000
20,400,000
20,600,000
20,800,000
21,000,000
21,200,000
21,400,000
21,600,000
21,800,000
22,000,000
22,200,000
22,400,000
22,600,000
22,800,000
23,000,000
23,200,000
23,400,000
23,600,000
23,800,000
24,000,000
24,200,000
24,400,000
24,600,000
24,800,000
25,000,000
25,200,000
25,400,000
25,600,000
25,800,000
Salvage
Benefit
(Rs.)
50,000,000
Total
Benefits
(Rs.)
26,310,800
26,560,000
26,809,200
27,058,400
27,307,600
27,556,800
27,806,000
28,055,200
28,304,400
28,553,600
28,802,800
29,052,000
29,301,200
29,550,400
29,799,600
30,048,800
30,298,000
30,547,200
30,796,400
31,045,600
31,294,800
31,544,000
31,793,200
32,042,400
32,291,600
32,540,800
32,790,000
33,039,200
33,288,400
33,537,600
83,786,800
Total
Discounted
Costs
(Rs.)
2,557
2,403
2,259
2,124
1,996
1,876
1,764
1,658
1,558
978,098
1,377
1,294
1,217
1,144
1,075
1,011
950
893
839
789
742
697
655
616
579
544
512
481
452
425
399
202,104,198
Total
Discounted
Benefits
(Rs.)
1,121,126
1,063,840
1,009,393
957,649
908,480
861,764
817,384
775,227
735,186
697,159
661,049
626,762
594,210
563,308
533,975
506,134
479,712
454,638
430,846
408,272
386,856
366,541
347,270
328,993
311,658
295,220
279,632
264,851
250,838
237,553
557,868
261,516,182
Net Benefit
(Rs.)
26,250,800
26,500,000
26,749,200
26,998,400
27,247,600
27,496,800
27,746,000
27,995,200
28,244,400
(11,506,400)
28,742,800
28,992,000
29,241,200
29,490,400
29,739,600
29,988,800
30,238,000
30,487,200
30,736,400
30,985,600
31,234,800
31,484,000
31,733,200
31,982,400
32,231,600
32,480,800
32,730,000
32,979,200
33,228,400
33,477,600
83,726,800
Total Discounted Costs =
Total Discounted Benefits =
Present Worth =
Net Present Worth =
202,104,198
261,516,182
202,104,198
59,411,984
Rs.
Rs.
Rs.
Rs.
Benefit to Cost Ratio =
Internal Rate of Return (IRR) =
1.294
8.028%