application of life- cycle cost analysis in civil...
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Application of Life-cycle Cost Analysis In Civil Engineering
Qindan (‘Chindan’) Huang, Ph.D.Assistant Professor, Department of Civil Engineering
The University of Akron
Research Background – Life Cycle Cost Analysis
( ) ( ) ( ) ( )0, , ,mLCC t C LCL t C t= + +x x x x
Life cycle cost
Initial construction
cost
Life cycle loss
Operation and/or maintenance
costs
Associated with time-dependent
performance prediction
• Advantages of LCC analysis
Consideration of long-term structural performance
$t (years)
β(t)repair
Quantify performance using economic costs
Objective decision making information
considering uncertainties
• Life-cycle cost analysis (LCCA) is an economic methodology of system performance quantification over time, overcoming “upfront” cost (current performance) limitations
• General life cycle cost (LCC) formulation:
Project 1: Selection of cost-effective patch-repair materials for a corroded RC structure
• Motivation
• LCCA considering time-dependent reliability
• Illustration
• Results and discussion
Project 2: Vulnerability of winter maintenance material storage facilities
• Motivation
• Vulnerability of winter maintenance material
• Expected annual cost
• Results and discussion
Outline
Landmark NACE study on cost of corrosion
Add in growth in 15 years
Motivation
$276B: Annual direct cost of corrosion (NACE 1998)
$276B: Annual indirect cost of corrosion (what
consumers pay)
$550B: Inflation and growth from 1998 to 2016
= $1.1 Trillion:Total annual cost of corrosion
in U.S. (end of 2016)
• Annual cost of corrosion in the US is estimated to be over $1.1 Trillion in2016 (G2MT Laboratories, LLC)
• More than $85 billion of corrosion related costs belong to the highwaybridges (NACE 2002)
• About 15 to 35% of these costs can be saved, if optimum corrosionmanagement strategies are employed (NACE 2016)
• Most of the highway bridges in the U.S. are built ofsteel reinforced concrete (SRC) materials due totheir low initial costs
• Approximately 15% of SRC bridges in the U.S. arestructurally deficient due to corrosion
• Corrosion degrades the performance of SRC bridgeby
– reducing the diameter– changing yielding strength & ductility of rebars– deteriorating the bond at the steel-concrete
interface
Bottom flange of box beam with heavy strand corrosion (photo by: Caly J. Naito, Lehigh University)
Motivation
Before patch repair
After patch repair
• Patch-repair method is typically used forcorroded SRC bridge repair
• Patch-repair procedure:
Remove the chloride contaminated concretebeyond the rebars
Clean the corroded rebar
Replace the rebar if significantly corroded
Apply a patch repair concrete
Motivation
• In practice, the patch repair material selection is usually based on materialproperties, rather than evaluating the impact of the repair strategy on the life-cycle cost and long-term integrity of the repaired structure
• In the literature:
Usually repair techniques were compared, not patch repair materials
Most studies do not consider the after-repair long-term performance
Evaluations are mostly based on only ultimate limit states
The effect of pre-cracking due to shrinkage is ignored
Motivation
• To select optimum patch repair material using a reliability-based life-cyclecost analysis (LCCA)
Considering corrosion deterioration before and after repair
Considering time-dependent ultimate and serviceability performances
Considering pre-cracking due to early-age shrinkage
Based on life-cycle cost of each option
Research Goal
( ) ( ) ( ) ( )0, , ,mLCC t C LCL t C t= + +x x x x
Life cycle cost
Initial construction
cost
Life cycle loss
Operation and/or maintenance
costs
To compare LCC with different repair materials, two assumptions are made
• The repair is conducted when structural performance reaches to a threshold; thus, structural performance (i.e., LCL) is maintained about the same regardless patch repair material selected
• Maintenance costs are the same for all options, thus, LCC is:
( ),
1 1rep
i
nrep i
tm i
CC
r=∑=
+
discount rate
cost of each repair operation
time of ithrepair
number of repair
nrep is determined by the time-dependent of structural performance
Life Cycle Cost of Patch Repair Material
• The probability of failure at time t, Pf, k (t), is:
( ) ( )( ), , 0f k k k kP t P g C t D = ≤
capacity
kth limit state function(kth failure mode)
demand
( ) ( )1,1k f kt P tβ − = Φ −
inverse of CDF of standard normal variable
• The reliability index at time t, βk (t), is used for safety evaluation:
• Two failure modes are considered: ultimate and serviceability
Time-dependent Performance
β2T
β1T
β2(t)
Second repair
First repair
t1 t2
t (years)
t3
Third repair
t (years)
β1(t)
• Repair is conducted when either of reliability indexes reaches a defined threshold value
• Life-cycle cost is determined by number of repair during service life
Illustration of determining time-to-repair
The prediction of structural performance considering the following corrosion effects are considered: (Du et al. 2005)
• The reduction in rebar diameter at time t, db(t):
( ) ( ) 01
b bd t Q t d= −
( ) ( )[ ] 01 0.005
y yf t Q t f= −
• The reduction in rebar yielding strength at time t, fy(t):
yield strength of intact rebar
diameter of intact rebar
corrosion level at time t
Corrosion Effect
( ) ( ) ( )0
4.6 corr
in
b
i tQ t t t
d= −
corrosion initiation time
corrosion rate
Two important parameters for prediction of Q(t): corrosion rate & initiation time
(Du et al. 2005)
2
2
14 1
b
in
th
app
s
CtClD erfCl
−
=
−
chloride threshold value
chloride content at concrete surface
concrete cover
• Corrosion initiation time (tin) depends on material, geometry, & environmental properties
apparent diffusion coefficient
m
ref
c ref
tD D
t =
depends on type of concrete (pozzolanic
or not)
( )0.94 2.4 /3.154 10 w cm+× water-to-cementitious
ratio
reference time
(Mangat & Molloy 1994)
( ) /app c cr cr cr
D D w S D= +
crack width to spacing ratio
(Boulfiza et al. 2003)
diffusion coefficient inside the crack
Corrosion Initiation Time
( ) ( ) ( ) 0.215430340.926exp{8.37 0.618ln 1.69 1.05 10 2.32 }corr water c in icorri t Cl R t tT
σ ε−−= + − − ⋅ + − +
(Liu 1996)temperature
ohmic resistance
water soluble chloride
model error
( )[ ]exp 8.03 0.549 1 1.686c acid R c
R ln Cl σ ε= − + +
model erroracid soluble chloride
0.93 0.2722acid water da ci
Cl Cl σ ε+= −
12
b
water s
c
CCl Cl erfD t
= −
model error
• Corrosion rate (icorr) also depends on material, geometry, & environmental properties
Corrosion Rate
• Flexural failure mode
( ) ( ) ( )1,
f D Lg t M t M M= − +x
flexural moment capacity at time t
flexural moment due to dead load
flexural moment due to live load
( )( ) ( )
( ) ( ) ( )( )
for2
0.5 for2
s y f
f
s sf y sf y f f
aA t f t d a tM t
aA t A f t d A f t d t a t
− ≤ = − − + − >
Asfy
α1f'ca
dh
Asdb0 internal forces
MD +ML(external moment)
tf
beff
N.A.
Ultimate Performance
• Crack failure mode
( ) ( )2 ,limit,
cr crg t w w t= −x
crack width limit
crack width at time t
( ) ( )[ ] ( ) 0
0
0
0
10.5 1
0.5
d b
cr b b
b
b
b b
dw t d d t
d Cd C
α π−= −
+ +
(Thoft-Christensen 2001)
density ratio of rust products to steel
Serviceability Performance
Details of the RC bridge and its interior T-beam
Studied Structure
Three repair materials are considered:
• Normal strength concrete (NSC) with w/cm = 0.65
• High performance concrete (HPC) with w/cm = 0.35 & 8% silica fume (SF)
• HPC with w/cm = 0.35 & 30% fly ash (FA)
Time-to-repair (ti) is determined when β reaches:
• Ultimiate βT1 = 3.0 (pf ≈ 0.001 ), patch-repair after adding new rebar
• Serviceability βT2 = 0.0 (pf ≈ 0.5): patch-repair after cleaning rebar
Quantities Considered
r = 1%
Time-to-repair (ti) is determined by β(t) and βT
To calculate Crep,i:
• NSC: $200/m2
• HPC (with SF or FA): $225/m2
• New rebar: $1.8/kg
( ),
1 1rep
i
nrep i
trep i
CC
r=∑=
+
discount rate
cost of ith repair operation
time of ith repair
Quantities Considered (Cont.)
Type Random variable Mean (SD)
Geometrical
Cb (cm) 5.1 (1)tf (cm) 20 (10)
bw (cm) 53 (10)h (cm) 108 (10)
Mechanicalfy0 (MPa) 414 (41.4)
f′c, NSC (MPa) 28 (5.04)f′c, HPC (MPa) 50 (9)
Environmental T (K) 286 (8)
Corrosion parameters
Cs (kg/m3) 7.4 (1.5)Cth, BS (kg/m3) 1 (0.19)Cth, EC (kg/m3) 4.6 (0.87)
Model errorσicorr 0 (0.33)σRc 0 (0.12)σacid 0 (0.12)
Loaddead load (N) D (0.1D)live load (N) L (0.41L)
Crack width limit wcr, limit (mm) 0.5 (0.1)
Random Variables Used in Reliability Analysis
-4
-3
-2
-1
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80 90 100
Rel
iabi
lity
inde
x (β
)
Time (years)
Time-to-repairTime-to-repair
βT1 = 3
βT2= 0
• Both reliability indexes decrease with time
• The decrease in the flexural reliability is slower
• Serviceability limit state governs the failure mode of the structure
β1(t)
β2(t)
Time-dependent Reliability without Repair
k = 1: Ultimatek = 2: Serviceability
-2
-1
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80 90 100
Rel
iabi
lity
inde
x (β
)
Time (years)
βT1= 3.0
βT2 = 0.0
Ultimate (flexural only)Serviceability (cracking only)
If considering only flexural performance, nrepair = 2
If considering only cracking performance, nrepair = 8
NSC Used as Repair Material
Ultimate (flexural & cracking)Serviceability (flexural & cracking)
• If considering both flexural & cracking performances, nrepair = 9
• Both serviceability and ultimate failures should be considered
-2
-1
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80 90 100
Rel
iabi
lity
inde
x (β
)
Time (years)
βT1= 3.0
βT2 = 0.0
NSC Used as Repair Material
Ultimate (flexural only)Serviceability (cracking only)Ultimate (flexural & cracking)Serviceability (flexural & cracking)
Using HPC significantly reduces the number of repair operations• Flexural only: nrepair = 1• Cracking only: nrepair = 2• Flexural & Cracking: nrepair = 2
-1
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80 90 100
Rel
iabi
lity
inde
x (β
)
Time (years)
βT1= 3.0
βT2 = 0.0
HPC with 8% SF Used as Repair Material
Using HPC with 30% FA needs less repair than HPC with 8% SF• Flexural only: nrepair = 1• Cracking only: nrepair = 1• Flexural & Cracking: nrepair = 1
-2
-1
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80 90 100
Rel
iabi
lity
inde
x (β
)
Time (years)
Ultimate (flexural only)Serviceability (cracking only)Ultimate (flexural & cracking)Serviceability (flexural & cracking)
βT1= 3.0
βT2 = 0.0
HPC with 30% FA Used as Repair Material
Repair criteria Repair MaterialNSC HPC-SF HPC-FA
Flexural only $2200 $1400 $1400Cracking only $7500 $2400 $1500
Both flexural and cracking $8500 $2400 $1500
Life-cycle cost of repair strongly depends on the repair criteria
Considering both flexural and cracking increases repair costs
HPC considerably reduces life-cycle cost compared to NSC
HPC with FA is more effective than HPC with SF
Life Cycle Cost Comparison
Project 1: Selection of cost-effective patch-repair materials for a corroded RC structure
• Motivation
• LCCA considering time-dependent reliability
• Illustration
• Results and discussion
Project 2: Vulnerability of winter maintenance material storage facilities
• Motivation
• Vulnerability of winter maintenance material
• Expected annual cost
• Results and discussion
Outline
Motivation
• Annual cost of snow and ice controloperation in the US is estimated to beover $2.3 billion (Federal HighwayAdministration 2015)
• With limited budgets and increasing saltprices, agencies are optimizing theiroperations in all facets
• There is a dearth of study concerning risk assessment for depletion ofstorage facilities of winter maintenance material (i.e., salt, abrasives, anddeicing liquids)
Research Goal
• To determine the vulnerability of winter maintenance material (salt) storage facilities in Ohio State
• Using LCCA to determine the optimal material amount to purchase before winter season considering uncertainties
• The results of this study can assist Ohio DOT for short- and long-term facility planning
Vulnerability Evaluation
( )0≤−= DSPPf
• Ohio is comprised of 88 counties with a total of 221 salt storage facilities
County name Number of facilities
Storage capacity
(tons)
Number of trucks
Lane miles
(miles)Cuyahoga 6 25,600 35 643Franklin 7 23,500 59 614Henry 1 3,000 10 350
Medina 2 9,600 23 599
• Vulnerability of current storage facilities is evaluated using the probability of the material demand exceeding the material storage capacity
Storage capacity
Salt demand
Examples of Salt Storage Facility Data Collected
• Theoretically, the amount of salt used can be calculated using operator records of the amount of salt loaded; however, the records are not reliable
• With vehicle tracking and material application sensors on implemented in the plow trucks, the amount of material applied is tracked
Assuming the material application amounts are the same for the same snowfall level
Three snow fall levels are considered:
• i = 1: light (< 2in)• i = 2: moderate (2in ~ 6in)• i = 3: heavy (> 6in)
( )∑=
⋅+⋅=3
1,,
iiBiSi MMNLD κ
Salt applied per lane
mile
Brine applied per lane mile
Number of event with ithsnowfall levelLane miles
maintainedConvert factor from brine to
salt
Vulnerability Evaluation: Material Demand
Probability of Exceeding Salt Supply for Each County
• Among a total of 88 counties: 47 have a low probability (< 20%) 18 have a moderate probability (20%~40%) 23 have a high probability (> 40%) of
exceeding their salt supply
• The results are varied throughout the state, with no geographical trends emerging.
• Further analysis is needed to determine the underlying causes of exceeding the salt supply
• Random variables considered: lane miles maintained, storage capacity, annual number of snow events, material applied per lane miles
• First-order reliability method is applied
Vulnerability Evaluation: Results
Vulnerability Evaluation: Importance Measure
• Importance measure provides insight about which random variable has a larger impact on the variability of the limit state function in the reliability analysis
• It is unit-less and ranges from zero to one, with values closer to one having a higher influence on the probability of failure
County
Parameter Stark(Pf = 0.09%)
Washington(Pf = 26%)
Paulding(Pf = 61%)
Number of light events 0.315 0.4687 0.1049Number of moderate events 0.2711 0.0804 0.1352Number of heavy events 0.1286 0.04 0.0156Salt usage for light event 0.8315 0.8534 0.8898Salt usage for moderate event 0.3222 0.2062 0.4226Salt usage for heavy event 0.1247 0.0379 0.0145Brine usage for light event 0.0003 0.0003 0.0004Brine usage for moderate event 0.0001 0 0.0001Brine usage for heavy event 0.0001 0 0
• The amount of salt applied during light and moderate events are the two highest importance variables
• Next, the number of light and moderate events are also very important, indicating the importance of weather prediction
( ) ( ) ( ) ( )0, , ,mLCC t C LCL t C t= + +x x x x
Life cycle cost
Salt cost Life cycle loss
Operation and/or maintenance
costs
( )( )∑ +⋅
+=
N
nan EALCLCCE ,01
1][γ
Expected annual loss
• Expected LCC can be calculated using expected annual cost
Considering the present value of the future losses
Assuming annual snow intensity is independent
Constant discount rate per year
Expected annual cost of salt purchased
before the season
• Using expected annual cost, one can determine optimal salt amount to purchase
Life-cycle Cost Analysis
Expected annual cost
Expected Annual Loss
( ) ( ) rSD
slrSD
s dDSCdSDCEAL xx ∫∫≤>
−⋅⋅+−⋅⋅= αξ
• Expected annual loss is associated with the risk of having too much or too little salt
Cost due to purchasing additional salt
Cost due to storing the leftover salt
Increasing factor ≥ 1
Salt price before season Percentage of
salt loss
• As Pf describes the probability of being in the failure domain (i.e., D > S), the higher value of Pf indicates higher expected annual risk cost
• There is one optimum amount of material that should be purchased before the season: 7,000 tons for Region I, 4,000 tons for Region II, and 3,000 tons for Region III.
• The optimum number for Region I is the highest, as Region I is the area receiving lake effect snowfalls.
• Expected annual cost is calculated on three regions
Region I (northeast Ohio): 30in ~ >100in annual snowfall
Region II (northwest Ohio & central Ohio): 20in ~ 40in
Region III (southern Ohio): < 20in
EALC a += ,0Expected annual cost
Expected Annual Loss Results
Concluding Remarks
• Life-cycle-cost-analysis (LCCA) is an effective economic tool with a wide range
of civil engineering applications
• Through the two case studies, LCCA are useful for
– Unifying various performance criteria
– Demonstrating the cost-benefit of different systems
– Translating engineering information to decision making information (e.g., to
select cost-effective patch repair material, and to determine the optimal salt
amount to purchase)
• Critical aspects in LCCA are:
– Time-depend performance evaluation (e.g., deterioration modeling,
performance quantification)
– Stochastic event prediction (e.g., weather prediction)
Thank you&
Questions?
Qindan (‘Chindan’) Huang, Ph.D.Assistant Professor
Department of Civil Engineering, The University of [email protected]