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 Akronqhuang@uakron.edu