PhD committee: Franck Schoefs (Director) Bruno Castanier Thomas Yeung

Probabilistic Modelling of Multiphasic Degradations for Maintenance Optimization of Infrastructures in Civil Engineering: application for a submerged reinforced concrete structure. A dissertation submitted by Boutros EL HAJJ to the University of Nantes for the degree of Doctor of Philosophy in Civil Engineering 23 rd of November 2015, Nantes, France PhD committee: Franck Schoefs (Director) Bruno Castanier Thomas Yeung

Probabilistic Modelling of Multiphasic Degradations for Maintenance Optimization of Infrastructures in Civil Engineering: application for a submerged reinforced concrete structure. To take into account uncertainties In the aim for optimized decision-making aid tools Non-destructive testing (NDT) Application: submerged RC structure Chloride rich environment Objective Build degradation modelling tools that allow a better integration in realistic dynamic maintenance optimization contexts Boutros EL HAJJ 2

Early examples of maintenance and rehabilitation management Management of infrastructures is an old occupation Rialto Bridge, Venice Built in 1181 Rome s aqueducts were rehabilitated and reused Maintenance was vital for the timber bridge 1444 collapsed due to overload by spectators during a wedding 1503: Wood to stone Pont du Gard, Nîmes Built around 40-60 BC 1703 repair works 1743 open to cars Now a touristic attractions Boutros EL HAJJ 3

Consequences of bad inspection/maintenance Tay Rail Bridge, Scotland February 1878: Inspections Satisfactory results Collapsed December 1878 Reichsbrücke, Austria Hayakawa wire bridge, Japan Mianus River Bridge, USA Collapsed 1976: lack of inspection techniques Collapsed 1980: lack of inspection and maintenance previous decade Collapsed 1983: inadequate inspection resources Somerton Bridge, Australia Collapsed 2008: poor maintenance Boutros EL HAJJ 4

Consequences of a failure I-35W Mississippi River Bridge, USA Built 1967 2007: collapsed killing 13 people and injuring 145 1990: rated "structurally deficient due to corrosion Approximately 75000 bridges in the US share the same rating (Anderson et al 2007) 2005: rated again "structurally deficient and in need for replacement $3.6 trillion/5 years to improve the US infrastructure to an acceptable level (ASCE report card, 2013) Boutros EL HAJJ 5

Maintenance impact Europe: 50 % of annual construction budget is currently spent on refurbishment and remediation (Duratinet project) Rotterdam, 1940 Europe: a large number of infrastructures were built after WW2 1/3 steel structures in the Atlantic area built more than 100 years ago Many structures require maintenance Many repaired structures display nonsatisfactory performances and need rehabilitation Boutros EL HAJJ 6

Introduction The importance of maintenance Maintenance management system Degradation model Predict the process of ageing in condition or in reliability Decision model Decide the optimal times of inspection and maintenance I. How to improve the evaluation, modelling and prediction of degradation for maintenance purposes? II. III. IV. How to be realistic? What to do with missing inspections and lost information? How to update and model the effect of a maintenance action after a decision? How to take the best decision throughout the operation time of the system? Illustrations Summary Conclusions and perspectives Boutros EL HAJJ 7

I. How to improve the evaluation, modelling and prediction of degradation for maintenance purposes? Inspections and monitoring techniques Maintenance management systems Decisions-making processes Inspections Sensors Preventive Corrective NDT, SDT Inc. Visual Condition-based Maintenance Condition assessment Maintenance decision Time-based Maintenance Is it time for maintenance? yes Maintenance action Decision making Risk assessment What qualities are required from a degradation model to be able to respond to these advancements? Boutros EL HAJJ 8

Classical degradation modelling approaches Physics-based models or White box models Simulation of the physics of measurable deterioration and failure Meta-models or Grey box models Based on measurable quantities indicating timedependent deterioration and failure (e.g., stochastic processes) Statistics-based models or Black box models (lifetime models) Describes the relation between time and failure (Nicolai 2008) (Frangopol et al. 2004) Boutros EL HAJJ 9

Characteristics of a good degradation model Modelling the pathology Predict the degradation evolution spatially Physical meanings into maintenance models Choice of indicators challenge benefit physics meta-model statistics Uncertainties Missing data or errors of acquisitions Fit to data Use all available information Integrate new data issued from NDT physics metamodel statistics Prognostic characteristic Predict the degradation evolution temporally Implementation maintenance systems Integrate in dynamic maintenance platforms Decision-making Un-observable indicators Non-stationarity physics metamodel statistics Maintenance effects (imperfect) Different insp. techniques physics metamodel statistics Boutros EL HAJJ 10

Degradation meta-model approaches Model the evolution of the degradation using observations Maintain the most critical aspects of the degradation Ease of integration in complex maintenance decision schemes Markov chains Lévy processes definition of the discrete states identification of the one-step transition matrix Brownian motion (Si et al. 2013) Gamma process (van Noortwijk 2009) non-monotonous evolution measurement error, fillers, etc. natural candidate (monotonous) self-explanatory parameters problems related to non-stationarity extensions Boutros EL HAJJ 11

Extensions to solve non-stationarity Non-Stationary evolution Covariates (Paroissin and Salami 2009) State-dependant degradation models Age-dependant degradation models (Nicolai, Dekker, and van Noortwijk 2007) Discrete-state (Markov Chains) Continuous-state (Lévy processes) Un-observable degradations Imperfect maintenance actions Individualisation State-based a robust procedure for the identification of input parameters Multivariate (Zouch et al. 2012; Mercier and Pham 2012) Monovariate (Vatn 2012) Boutros EL HAJJ 12

Monovariate state-dependant gamma process Definition 1 A stochastic process X = X t t > 0 is said to be a stationary gamma process with parameters α τ, β, where α > 0 and β > 0, if it satisfies the following properties: a) X 0 = 0 b) X t has independent positive increments c) X t has stationary increment t > 0 X t+τ X t ~ Ga α τ, β = βατ Γ(ατ xατ 1 e β.x Definition 2 A stochastic process G = G t t > 0 is said to be SDGP with parameters α G t τ, β, where α G t > 0 and β > 0, if it satisfies the following properties: a) G 0 = 0 b) G t has independent positive increments c) For a time interval τ > 0, we have: G t+τ G t ~ Ga α G t τ, β X G Ga α τ, β G t t Ga α G t τ, β t Transform the non-stationary process into pieces of stationary SDGP The SDGP is not a Lévy process anymore loses the infinite-divisibility property Boutros EL HAJJ 13

Items of the meta-models A small number of parameters A probabilistic pertinence and physical expertise Indicators of degradation and durability directly accessible through NDT Degradation analysis: Physical mechanism, degradation indicators, accessibility through NDT Physical meaning of the main probabilistic trends NDT META MODEL (Condition based) Maintenance modelling analysis: Decisions, inspections, maintenance actions and policies Modelling analysis: Statistical degradation modelling, stochastic processes, etc. State-dependent stochastic processes using information given by NDT Boutros EL HAJJ 14

Objectives Degradation analysis Study the pathology: here, chloride-induces corrosion Look into physical indicators Degradation analysis Modelling analysis Construction of the degradation model Propose estimation and calibration algorithm Maintenance analysis Catalogue potential maintenance actions Modelling the effect of an action in the model Discuss decision scenarios MM Maintenance analysis: Modelling analysis Degradation analysis Degradation analysis MM Maintenance analysis: MM Maintenance analysis: Modelling analysis Modelling analysis Argue and promote the use of condition based meta-models Boutros EL HAJJ 15

1 Degradation analysis: Chloride-induced corrosion of RC structures Chloride-induced corrosion of RC Structures RC cross-section Cl > Cl seuil Phase 1: Diffusion Diffusion of chlorides [Cl-] [Cl-] As l [Cl-] Phase2: Corrosion Initiation of corrosion σ > σ t Phase3: Propagation Cracking propagation Boutros EL HAJJ 16

Percentage of cumulative damage (%) 1 Degradation analysis: Choice of indicators 100 90 80 I: corrosion initiation C: cracking For each phase: A bivariate process written 70 60 50 40 30 20 10 0 End of functional service life, rehabilitation Initial cracking Diffusion Corrosion Deterioration I 0 5 10 15 20 25 C ρ t, θ t t 0 ρ t : condition indicator θ t : potential of evolution Choice of indicators: Accessibility via. NDT Representation of the degradation process Diffusion of chloride Corrosion of reinforcement Crack propagation ρ 1,t t 0 Cl : Chloride concentration θ 1,t t 0 PH ρ 2,t t 0 σ: Internal stress θ 2,t t 0 i corr : corrosion current density ρ 3,t t 0 a: Crack width θ 3,t t 0 i corr : corrosion current density Boutros EL HAJJ 17

1 Degradation analysis: Indicators tendencies ρ t : Condition indicator θ t : potential of evolution Phase 1 : Chloride diffusion Phase 2: Corrosion of the reinforcement Phase 3: Crack propagation Cl PH σ i corr a i corr Cl (%) σ (Mpa) a (mm) ρ 1,t t 0 unirnd 0.4 0.5 (Angst et al. 2009) ρ 2,t t 0 unirnd 2.7 3.1 3 ρ 3,t t 0 S-shaped L-shaped L-shaped PH i corr i corr θ 1,t t 0 L-shaped θ 2,t t 0 S-shaped θ 3,t t 0 S-shaped Boutros EL HAJJ 18

2 Modelling analysis: Construction of Bivariate State-Dependant Gamma Process cause-effect relation (mechanical) A uniform approach using SDGP applied to the third phase θ 3,t t 0 models i corr ρ 3,t t 0 represents a θ t : potential of evolution ρ t : Condition indicator (Δθ 3,Δρ 3 ) ~ Gamma distribution law α τ is the shape function (state-dependent) β is the scale parameter (constant) θ 3,t t 0 i corr E(Δθ 3 ) c 2 θ 3 c 2 1 α θ3 ρ 3, θ 3 = g 1 (ρ 3. c 3. e c 2 θ 0 t θ (c c 1 3 3. ρ 3 + c 4 a E(Δρ 3 ) α ρ3 ρ 3, θ 3, θ 3 = g 2 θ 3, θ 3. c 4. e c 5.ρ 3 ρ 3,t t 0 ρ 0 t ρ 3 c 6. θ 3 + θ 3 2 + c 7 Boutros EL HAJJ 19

2 Modelling analysis: State-dependant shape functions c 1 = 1, c 2 = 1, c 3 = 1, c 4 = 1.2, c 5 = 0.8, c 6 = 1.8, c 7 = 2, β ρ = 0.3, β θ = 0.3 θ t : potential of evolution ρ t : Condition indicator θ 3 c 2 1 α θ3 ρ 3, θ 3 = (c 3. ρ 3 + c 4. e c 2 α ρ3 ρ 3, θ 3, θ 3 = c 6. θ 3 + θ 3 2 + c 7. e c 5.ρ 3 Boutros EL HAJJ 20

Question I Positioned the problem Definition of the characteristics Summary I. How to improve the evaluation, modelling and prediction of degradation for maintenance purposes? Construction of the degradation meta-model II. How to be realistic? What to do with missing inspections and lost information? III. How to update and model the effect of a maintenance action after a decision? IV. How to take the best decision throughout the operation time of the system? Boutros EL HAJJ 21

II. How to be realistic? What to do with missing inspections and lost information? Size of the database ρ N = n T n T number of structures number of inspections N = 3 6 = 18 Truncated n = 3 Missing 1 2 3 4 5 6 Censored t T = 6 Maximum likelihood estimation (+fixed-point) Stochastic Estimation Maximization (SEM) Benefit of non-homogenous databases Boutros EL HAJJ 22

III. How to update and model the effect of a maintenance action after a decision? Maintenance action effects Speed ρ 1,t t 0 Cl Chlorides extraction Surface protection Level t E(Δθ) after maintenance before maintenance θ t : potential of evolution ρ t : Condition indicator S-shaped 1 st [Cl ] - ρ 2 nd & 3 rd i corr - θ m 1 (θ m 2 a 2 1 α s ρ, θ = m 1 g 1 (ρ. e a 2 m 2 θ L shaped 1 st ph - θ 2 nd stress - ρ 3 rd crack width - ρ k 1 E(Δρ) ρ α L ρ, θ = k 1 g 2 θ. e a 1.ρ Boutros EL HAJJ 23

IV. How to take the best decision throughout the operation time of the system? Decision model Assessment of the degradation Inspection Estimation Define condition indexes (CI) Define an estimation algorithm Decisions scenario Decisions plan τ D t τ ins = 2. τ D Inspections plan Decision based on the observed CI Decision based on the estimated CI τ ins t Bi variate process inter-inspection time interval inter-decision time interval Different inspection plans for ρ & θ Boutros EL HAJJ 24

5 Illustration: decision scenario Same inspection plans for ρ and θ Crack width θ t : potential of evolution ρ t : Condition indicator 4 CI = 0 : L (mm) 3 2 1 inspection/possible history crack width limit CI = 1 CI = 2 CI = 3 sqrt (x 0 0 2 4 6 8 10 12 14 16 18 20 Time Corrosion current density Time 6 0 1 2 3 4 5 6 7 8 9 10 11 12 : Ic ( A/cm 2 ) 5 4 3 2 CI Ins Ins Ins Ins Ins 0 0 0 0 0 0 0 0 0.01 0.04 0 0.12 0.34 1 1 0 0 0 0 0 0.02 0 0.05 0.18 0 0.7 0.64 0 1 2 0 0 0.02 0 0.05 0.1 0 0.79 0.78 1 0 0.02 0 0 0 2 4 6 8 10 12 14 16 18 Time 3 1 1 0.98 1 0.95 0.81 1 0.16 0.01 0 0 0 0 Boutros EL HAJJ 25

Illustration: Maintenance management Possible maintenance actions Phase 1 Phase 2 Phase 3 Chloride extraction [CE] Cathodic protection [CP2] Cathodic protection [CP3] Cathodic prevention [CP1] Concrete replacement [CR1] 263 /m² Concrete replacement + Steel cleaning [CR2] Concrete replacement + Steel replacement [CR3] 323 /m² 353 /m² Indirect cost: 2000 /m² Inspection = 25 /m² Inspection = 25 /m² Inspection = 10 /m² (Srifi 2012) Boutros EL HAJJ 26

Illustration: Maintenance management performance indexes and management policies [Cl ] CI = 7 CI = 8 CI = 9 Preventive Maintenance Do nothing Do nothing [CR1] t Stress CI = 6 [CR2] CI = 5 CI = 4 t Crack width CI=0 CI = 3 ρ t : Condition indicator Corrective Maintenance CI = 2 CI = 1 [CR3] t 5 years Expected Life-Costs and Condition indexes for PM and CM Policy PM CM PM CM PM CM Lifetime (years) 50 75 100 Annual cost ( /m²/year) 23.9 50 24 58 24.3 55 Condition Index 8.21 6.3 8.18 5.86 8.14 5.89 Boutros EL HAJJ 27

Illustration: Maintenance management Benefit Life-Costs ( /m²) and Condition indexes Policy PM CM Benefit Lifetime (years) 75 Inspections 466 200 + 133% Maintenance 1330 4142-68% Total cost 1765 4342-59% Annual cost ( /m²/year) 24 58-59% Condition Index 8.18 5.86 2.32 points PM: Preventive Maintenance CM: Corrective Maintenance Boutros EL HAJJ 28

Discussion State-based Condition Indexing ρ ρ 4 θ t : potential of evolution Decision graph for the 4th epoch ρ t : Condition indicator CI = 7 CI = 8 CI = 9 t ρ 3 3.5 3 2.5 2 1.5 1 0.5 One simulation ρ 3, θ 3 CI = 0 θ ρ State-based CIs 0 0 1 2 3 4 5 6 7 8 CI = 3 CI = 2 θ 3 CI = 1 CI based on a Pf Pf ρ i, θ i + + = P ρ + ρ i > L ρ = ρ i, θ = θ i = g x, y; ρ i, θ i dydx L ρ i θ i θ pf: probability of failure before the next inspection Boutros EL HAJJ 29

Discussion A Pf approach to state-based CIs Every iso-plan Iso-curve of equal pf Ex: pf = 0.05 Different CIs θ t : potential of evolution ρ t : Condition indicator Boutros EL HAJJ 30

Conclusions on the use of meta-models I The description of the ageing model: 1. Physical meaning To probabilistic trends 2. Input (NDT assessment) Output (decision parameters) complex physical models increasing complexity of NDT II In a CBM context: simple description, flexibility, calibration and statistical calculation implement and beneficial in a risk management framework III Evaluation of the Meta-model is done through state-dependant stochastic processes using NDT Available information Model Boutros EL HAJJ 31

Perspectives Different models of degradation (carbonation, etc.) Future tests under real databases (Surffeol, COST action) Confront the problem of lack of data Maintenance decision Pre-specifications of databases Boutros EL HAJJ 32

Perspectives Mathematical challenges Consider spatial variability of inspections Integration of measurement error Non-homogeneous database Integration of variability to β (e.g., state-dependant) Effect of the estimation process on low probabilities Loss of infinite-divisibility L 1 d 1 st pit 2 nd pit L 2 a 1 a 2 Boutros EL HAJJ 33

Thank you! Boutros EL HAJJ 34