Side-by-Side Box Beam Bridge Life-Cycle Cost Analysis For or Better Inv nvestment nt and nd Engi ngine neering ng Decisions ons By Nabil Grace, Ph.D., PE Elin Jensen, Ph.D. University Distinguished Professor Associate Professor Director, Center for Innovative Materials Center (CIMR) Civil Engineering Department Chair, Civil Engineering Department Lawrence Technological University, MI. US-Japan Workshop Sapporo, Hokkaido, Japan October, 2009 Spo pons nsored by d by Nationa nal Scienc nce Founda undation n
The LCCA Methodology • Establish design alternatives • Determine activity timing • Estimate costs (agency and user) • Compute life-cycle costs • Analyze the results
Classification of Project LCC Project Life-Cycle Cost Level 1 Agency User By Entity that Incurs Cost Level 2 By Life-Cycle OM&R Demolition OM&R Demolition Construction Construction Cost Category Level 3 By Elemental Breakdown of Project Engineers estimate Element Non- New-Material Element 1 N Elemental Introduction
User Cost ( ) × L L − × w × AADT AADT N Travel time Costs = S a S n L = length of affected roadway over which cars drive; S a = traffic speed during bridge work activity; S n = normal traffic speed; AADT = Annual Average Daily Traffic; N = number of days of road work; w = hourly time value of drivers; ( L ) × L − × r × AADT AADT N Vehicle Operating Costs = S a S n r = hourly vehicle operating cost; A a - A n × c a ( ) Crash Costs = L × AADT AADT × × N A a = during-construction accident rates per vehicle-mile; A n = normal accident rates per vehicle-mile; c a = cost per accident.
Inflation and Discounting The real discount rate ( r ) r = [(1 + d ) / (1 + i )] – 1 = ( d – i ) / (1 + i ) ≈ d – i Where: r = real discount rate, i = inflation rate, d = nominal discount rate (also called interest rate, funding rate)
LCC Calculations T ∑ C = t LCC ( ) + t 0 1 r = t t = sum of all costs incurred at time t C t r = real discount rate for converting time t costs r T = number of time periods in the analysis period
General Plan of Bridge Cas ase S e Study Bridge dimensions are in ft. 120 60 60 Dimensions are in inch 46 36 110 (SPAN 1) 55 (SPAN 2) 55 28 (6) 15mm Ф STRANDS (4) A06 BARS 46 15 beams
Establish Design Alternatives • Bridge with black steel reinforcement and with cathodic protection • Bridge with epoxy-coated steel reinforcement • Bridge with CFRP reinforcement
The LCCA Methodology • Establish design alternatives • Determine activity timing • Estimate costs (agency and user) • Compute life-cycle costs • Analyze the results
Determine Activity Timing Activity Timeline of Black Steel Bridge Construction Beam End Repair Deck Patch Cathodic protection maintenance Deck Shallow Overlay Superstructure Replacement Deck Replacement Beam Replacement 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Year Routine inspection every two years Detailed inspection every five years Cathodic protection maintenance every year
Determine Activity Timing The same activity timing with black steel bridge except cathodic protection activity Activity Timeline of Epoxy-coated Steel Bridge Deck Shallow Overlay Construction Beam End Repair Deck Patch Superstructure Replacement Deck Replacement Beam Replacement 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Year Routine inspection every two years Detailed inspection every five years
Determine Activity Timing Activity Timeline for CFRP Bridge Construction Deck Shallow Overlay Deck Replacement 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 year Detailed inspection every ten years
The LCCA Methodology • Establish design alternatives • Determine activity timing • Estimate costs (agency and user) • Compute life-cycle costs • Analyze the results
The LCCA Methodology • Establish design alternatives • Determine activity timing • Estimate costs (agency and user) • Compute life-cycle costs • Analyze the results
Medium span bridge with High-traffic-below and High-traffic-above Bridge Life-Cycle Cost Black Steel Bridge Epoxy-Coated Steel Bridge CFRP Bridge $7,000,000 Construction Deck Shallow Overlay 5.98 Deck Replacement Superstructure replacement $6,000,000 5.63 $5,000,000 Life-cycle cost $4,000,000 Breakeven year $3,000,000 2.29 $2,000,000 20 $1,000,000 $0 0 10 20 30 40 50 60 70 80 90 100 Year
Medium span bridge with High-traffic-below and High-traffic-above Bridge Life-Cycle Cost Comparison $7.00 Superstructure Replacement 5.98 Superstructure Demolition 5.63 $6.00 Cathodic Protection Update $1.23 Life-Cycle Cost (million dollar) Cathodic Protection Maintenance $1.24 $5.00 Beam Replacement Beam End Repair $4.00 $1.32 $1.32 Deck Replacement Deck Shallow Overlay $3.00 2.29 Deck Patch $1.85 $1.85 $0.51 Detailed Inspection $2.00 $0.60 Routine Inspection $1.00 Initial Cathodic Protection $0.11 $1.03 Initial Construction Cost $0.61 $0.59 $0.00 Black Steel Epoxy-Coated CFRP Bridge Steel Bridge Bridge
Sensitivity Analysis • Sensitivity analysis studies the manner of how the most optimal target solution or function (Output), would be affected by changes in the value of one or more parameters (Input) of a model, while the rest of them remain unchanged.
Sensitivity Analysis Tornado chart • Tornado chart shows a graphical representation of the changes produced in the target optimal solution or function whenever a specific quantity or value in a model ’ s parameters changes.
Sensitivity Analysis Tornado Chart of Black Steel Bridge Top 5 sensitive parameters Initial value parameter -10% parameter +10% Normal driving speed S n below bridge $5.301 $6.985 70 mph Real discount rate $5.344 $6.726 3% Driving speed reduction below bridge $5.511 $6.504 25 mph Normal driving speed S n over bridge $5.698 $6.393 45 mph AADT below bridge $5.681 $6.235 100,000 $4.0 $4.5 $5.0 $5.5 $5.98 $6.5 $7.0 Life-Cycle Cost (million dollar)
Sensitivity Analysis Tornado Chart of Epoxy-Coated Steel Bridge Top 5 sensitive parameters Initial value parameter -10% parameter +10% Normal driving speed Sn below bridge $4.955 $6.640 70 mph Real discount rate $5.025 $6.350 3% Driving speed reduction below bridge $5.165 $6.159 25 mph 45 mph Normal driving speed Sn over bridge $5.389 $5.995 100,000 AADT below bridge $5.335 $5.889 $4.0 $4.5 $5.0 $5.63 $6.0 $6.5 $7.0 Life-Cycle Cost (million dollar)
Sensitivity Analysis Tornado Chart of CFRP Bridge parameter -10% parameter +10% Top 5 sensitive parameters Initial value Real discount rate $2.028 $2.476 3% Normal driving speed Sn below bridge $2.048 $2.500 70 mph Driving speed reduction below bridge $2.104 $2.371 25 mph Superstructure construction unit $2.169 $2.291 $110 / SFT cost of traditional bridge $2.175 $2.310 Normal driving speed Sn over bridge 45 mph $1.6 $1.8 $2.0 $2.29 $2.4 $2.6 Life-Cycle Cost (million dollar)
Parameter Study Short-span bridge Parameter Medium-span bridge Long-span bridge (30ft - 60ft) (60ft - 110ft) (110ft - ) Matrix Double span (60ft) Double span (122ft) Double span (45ft) Low traffic C C N/C above bridge Low traffic below Bridge High traffic C C N/C above bridge Low traffic C C C above bridge Medium traffic below bridge High traffic N/C C C above bridge Low traffic N/C C C above bridge High traffic Below bridge High traffic N/C C C above bridge C: Considered N/C : Not considered (Not so common)
Long span Box Beam Bridge (122 ft span) Initial cost ratio 1 : 1.01 : 1.78 Initial cost ratio 1 : 1.01 : 1.78 LCC ratio 1: 0.96 : 0.45 9.0 LCC ratio 1: 0.97 : 0.51 8.0 Initial Cost 7.0 Life-cycle Cost 6.0 5.0 4.0 6.98 8.33 6.80 7.99 3.0 2.0 3.57 3.79 2.17 2.17 1.0 1.22 1.23 1.22 1.23 0.0 Black Steel Epoxy-Coated Steel CFRP Black Steel Epoxy-Coated Steel CFRP High-traffic-below & High-traffic-above High-traffic-below & Low-traffic-above Initial cost ratio 1 : 1.01 : 1.78 9.0 Initial cost ratio 1 : 1.01 : 1.78 8.0 LCC ratio 1: 0.95 : 0.49 LCC ratio 1: 0.97 : 0.57 7.0 6.0 5.0 4.0 7.19 3.0 5.84 6.85 5.66 2.0 3.54 3.31 2.17 2.17 1.0 1.22 1.23 1.22 1.23 0.0 Black Steel Epoxy-Coated Steel CFRP Black Steel Epoxy-Coated Steel CFRP Medium-traffic-below & High-traffic-above Medium-traffic-below & Low-traffic-above
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