Influence of structural deterioration over time on the optimal time interval for inspection and maintenance of structures

doi:10.1016/j.engstruct.2014.01.012

Engineering Structures

Volume 61, 1 March 2014, Pages 22-30

https://doi.org/10.1016/j.engstruct.2014.01.012 Get rights and content

Abstract

The influence of the time variation of the structural demand and/or of the structural capacity on the optimal time interval (based on a cost–benefit analysis) for inspection and maintenance of offshore structures is analyzed. Reliability is expressed in terms of the expected number of failures over a time interval by means of closed-form mathematical expressions which consider the structural degradation. The mathematical expressions are incorporated into the cost optimization formulation. Three scenarios are considered: (1) structural demand (for a given intensity) varies in time, while structural capacity remains constant, (2) structural capacity deteriorates over a time interval, while structural demand remains constant, (3) both structural capacity and structural demand vary simultaneously over time. The optimal time interval for inspection and maintenance corresponds to the lowest cost of inspection, repair and failure. The cost optimization is applied to an offshore jacket platform. The damage condition is given by the fatigue crack size at critical joints. It is shown that in order to estimate the optimal time interval for inspection and maintenance of the structure, it is necessary to take into account the variation in time of both its structural capacity and its structural demand (case 3); if one of them were ignored, the optimal time interval could be overestimated.

Introduction

Structures are subjected to loads that can lead to degradation of the structural mechanical properties as time goes by, which leads to the decreasing of the structural capacity while the structural demand increases. As a consequence, the structural reliability is modified; therefore, it is convenient to develop tools oriented to evaluate the structural reliability considering that the structural capacity and/or the structural demand change(s) over time. After the structural reliability is known, an optimization analysis can be applied in order to find the optimal time interval for inspection and maintenance of the structure. The results of the optimization analysis will depend on the hypothesis made about the variation in time of the structural capacity and of the structural demand.

To establish an optimization model, Forsell [1] formulated the problem by minimizing the total cost. The problem has been studied by using probability-based methods [2]. Later, reliability formulations were introduced into probability-based design codes [3], [4], [5], [6], [7], [8] and optimal design criteria were developed on the basis of probability concepts [9], [10], [11], [12], [13]. During the last fifteen years several authors have applied the concept of time-dependent reliability index to optimize the life cycle of deteriorating structures without structural maintenance [14], [15], [16], as well as with structural maintenance [16]. Later, maintenance programs for existing structures using the concept of multiobjective optimization were developed considering different optimization objectives: i.e., (a) minimizing the maintenance cost and maximizing the load-carrying capacity and durability [17], (b) minimizing the cost and maximizing the structural performance [18], (c) minimizing the maximum condition index, maximizing the minimum safety index, and minimizing the present value of cumulative maintenance cost [19], [20], [21], and (d) minimizing the maximum probability of failure, maximizing the minimum redundancy index, and minimizing the life-cycle cost [22]. A criterion to find optimal time intervals for maintenance based on multiobjective optimization which considers confidence factors obtained by means of closed-form expressions, damage index and the expected cumulative total cost of structures with degrading structural properties, has been developed [23]. Recently a generalized probabilistic framework for optimum inspection and maintenance planning that maximizes the expected service life and minimizes the total life-cycle cost has been formulated [24].

For the particular case of offshore structures, the degradation of structural properties is mainly due to fatigue phenomena caused by waves continuously acting on the structures. The mechanical deterioration caused by fatigue is reflected by cracking of the tubular joints, giving place to a decrease of the resistance capacity of the structural system, and as a consequence, an increase in its structural demand (for a given maximum wave height). The idea behind inspecting an offshore structural system is to detect the presence and growth of size cracks, in order to perform the necessary repairs and maintenance to the structure later on. Several authors have developed inspections and maintenance plans for offshore structures: (a) based on risk and reliability of welded connections subject to fatigue [25], [26], [27]; (b) using methodologies that take into account fatigue sensitivity analyses in steel joints [28]; (c) implementing simplified approaches and using practical design parameters such as fatigue design factors [29] and/or reserve strength ratios [30]; (d) considering the damage caused by fatigue, buckling and dents on structural elements [31]; and (e) using Bayesian techniques [32].

The main objective of the present study is to analyze the influence of the time variation of the structural demand and/or of the structural capacity on the optimal time interval (based on a cost–benefit analysis) for inspection and maintenance of offshore structures. Three scenarios are considered: (1) structural demand (for a given intensity) varies in time, while structural capacity remains constant, (2) structural capacity deteriorates over a time interval, while structural demand remains constant, (3) both structural capacity and structural demand vary simultaneously over time.

The optimal interval for inspection and maintenance corresponds here to the lowest total cost associated with inspection, repair and failure, considering risk and reliability of the structure.

The difference between the present study and those mentioned above is that in this paper reliability is expressed in terms of the expected number of failures over a time interval by means of simplified closed-form mathematical expressions that take into account the structural deterioration over time. None of the methods above has solved the problem by means of this simplified approach. The mathematical expressions are then incorporated into the cost optimization formulation. Besides, it is demonstrated that for estimating the optimal interval of inspection and maintenance of a deteriorating structure, the variation in time of both structural capacity and structural demand (for a given maximum wave height) must be taken into account (case 3), otherwise the optimal time interval could be overestimated.

Section snippets

Expected total present value of the cost function over a time interval

The expected total cost function is defined as the summation of the total expected cost, $\overline{C}$ , of inspection (I), repair (R), and failure (F) at the end of a time interval [0, Δt) as follows: ${\overline{C}}_{Total} (0, Δ t) = {\overline{C}}_{I} (0, Δ t) + {\overline{C}}_{R} (0, Δ t) + {\overline{C}}_{F} (0, Δ t)$ where ${\overline{C}}_{I} (0, Δ t)$ , ${\overline{C}}_{R} (0, Δ t)$ and ${\overline{C}}_{F} (0, Δ t)$ are the present value of the expected cost of inspection, repair and failure, respectively. The optimal interval corresponds to the lowest cost over the design life of the structure. The present value of the expected cost ${\overline{C}}_{I} (0,$

Evaluation of structural reliability

In this paper, structural reliability is expressed by means of the expected number of structural failures at the end of the time interval, ${\overline{η}}_{F} (0, Δ t)$ , which is an extension of the expected annual structural failure rate concept (ν(t), [39]). Based on the simplified approach proposed by Cornell and collaborators [40], [41] to evaluate the reliability of structures subject to seismic loads, and later on, extended by Torres and Ruiz [42], it is possible to obtain ${\overline{η}}_{F} (0, Δ t)$ as shown in Eq. (16). It

Illustrative example

In this section the optimal interval for inspection and maintenance a jacket offshore platform during its design life (DL) is formulated, assuming the following hypotheses:

(a)
The structure survives up to the end of the time interval of interest.
(b)
Intervals between inspections are equidistant.
(c)
The damage is accumulated on the critical nodes.
(d)
The elements recover their fully capacity after repair.

The expected total function cost given by Eq. (1), is expressed as follows (using Eqs. (7), (11), (15)): ${\overline{C}}_{}$

Conclusions

The influence of the structural deterioration over time on the optimal time interval for inspection and maintenance of structures was analyzed. The structural reliability is expressed by means of simple closed-form mathematical expressions which are incorporated into the cost–benefit analysis. The criterion was applied to a fixed steel jacket platform located in Campeche Bay, Mexico. The results indicate that the variation in time of the structural capacity (case 2) has a greater influence than

Acknowledgements

Thanks are given to D. De León (formerly at IMP) for his valuable comments related to the reliability analysis of the marine platform. This research project had the support of DGAPA-UNAM (PAPIIT IN107011 and IN102114). The first author thanks CONACYT for the economical support to develop his PhD research.

References (60)

D.M. Frangopol
A reliability-based optimization technique for automatic plastic design
Comput Method Appl Mech
(1984)
L. Esteva et al.
Life-cycle optimization in the establishment of performance-acceptance parameters for seismic design
Struct Saf
(2002)
P. Thoft-Christensen
Assessment of the reliability profiles for concrete bridges
Eng Struct
(1998)
M. Liu et al.
Optimal bridge maintenance planning based on probabilistic performance prediction
Eng Struct
(2004)
M.A. Torres et al.
Structural reliability evaluation considering capacity degradation over time
Eng Struct
(2007)
J.R. Newman et al.
An empirical stress intensity factor equation for the surface crack
Eng Fract Mech
(1981)
C. Forsell
Ekonomi och Byggnadsvasen (Economy and construction)
Sunt Fornoft
(1924)
A.M. Freudenthal
Safety and the probability of structural failure
Trans ASCE
(1956)
C.A. Cornell
A probability-based structural code
J Am Concr I
(1969)
N.C. Lind
Consistent partial safety factors
J Struct Div ASCE
(1971)

E. Rosenblueth et al.

Reliability basis for some Mexican codes

Probabilistic design of reinforced concrete buildings

(1972)

Ditlevsen O. Structural reliability analysis and the invariance problem. Report no. 22. University of Waterloo, Solid...

A.H.-S. Ang et al.

Reliability bases of structural safety and design

J Struct Div ASCE

(1974)

A.M. Hasofer et al.

Exact and invariant second moment code format

J Eng Mech Div ASCE

(1974)

E. Rosenblueth et al.

Reliability optimization in isostatic structures

J Eng Mech Div ASCE

(1971)

Mau ST. Optimum design of structures with a minimum expected cost criterion. Report no. 340. Cornell University,...

F. Moses

Design for reliability-concepts and applications

D.M. Frangopol et al.

Reliability-based life-cycle management of highway bridges

J Comput Civil Eng

(2001)

J.S. Kong et al.

Life-cycle reliability-based maintenance cost optimization of deteriorating structures with emphasis on bridges

J Struct Eng ASCE

(2003)

A. Miyamoto et al.

Bridge management system and maintenance optimization for existing bridges

Comput-Aided Civ Infrastruct Eng

(2000)

H. Furuta et al.

Optimal bridge maintenance planning using improved multi-objective genetic algorithm

Struct Infrastruct Eng

(2006)

L.C. Neves et al.

Probabilistic lifetime-oriented multiobjective optimization of bridge maintenance: single maintenance type

J Struct Eng ASCE

(2006)

L.C. Neves et al.

Probabilistic lifetime-oriented multiobjective optimization of bridge maintenance: combination of maintenance types

J Struct Eng ASCE

(2006)

N.M. Okasha et al.

Lifetime-oriented multi-objective optimization of structural maintenance considering system reliability, redundancy and life-cycle cost using GA

Struct Saf

(2009)

D. Tolentino et al.

Time intervals for maintenance of offshore structures based on multiobjective optimization

Math Probl Eng

(2013)

S. Kim et al.

Generalized probabilistic framework for optimum inspection and maintenance planning

J Struct Eng ASCE

(2013)

R. Skjong

(1985)

Madsen HO, Sørensen JD, Olsen R. Optimal inspection planning for fatigue damage of offshore structures. ICOSSAR. San...

Sørensen JD, Faber MH, Rackwitz R, Thoft-Christensen P. Modeling in optimal inspection and repair. In: 10th...

P. Thoft-Christensen et al.

Optimal strategies for inspection and repair of structural systems

Civil Eng Syst

(1987)

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View full text

Influence of structural deterioration over time on the optimal time interval for inspection and maintenance of structures

Abstract

Introduction

Section snippets

Expected total present value of the cost function over a time interval

Evaluation of structural reliability

Illustrative example

Conclusions

Acknowledgements

Comput Method Appl Mech

Struct Saf

Eng Struct

Eng Struct

Eng Struct

Eng Fract Mech

Ekonomi och Byggnadsvasen (Economy and construction)

Sunt Fornoft

Safety and the probability of structural failure

Trans ASCE

A probability-based structural code

J Am Concr I

Consistent partial safety factors

J Struct Div ASCE

Reliability basis for some Mexican codes

Probabilistic design of reinforced concrete buildings

Reliability bases of structural safety and design

J Struct Div ASCE

Exact and invariant second moment code format

J Eng Mech Div ASCE

Reliability optimization in isostatic structures

J Eng Mech Div ASCE

Design for reliability-concepts and applications

Reliability-based life-cycle management of highway bridges

J Comput Civil Eng

Life-cycle reliability-based maintenance cost optimization of deteriorating structures with emphasis on bridges

J Struct Eng ASCE

Bridge management system and maintenance optimization for existing bridges

Comput-Aided Civ Infrastruct Eng

Optimal bridge maintenance planning using improved multi-objective genetic algorithm

Struct Infrastruct Eng

Probabilistic lifetime-oriented multiobjective optimization of bridge maintenance: single maintenance type

J Struct Eng ASCE

Probabilistic lifetime-oriented multiobjective optimization of bridge maintenance: combination of maintenance types

J Struct Eng ASCE

Lifetime-oriented multi-objective optimization of structural maintenance considering system reliability, redundancy and life-cycle cost using GA

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Time intervals for maintenance of offshore structures based on multiobjective optimization

Math Probl Eng

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J Struct Eng ASCE

Optimal strategies for inspection and repair of structural systems

Civil Eng Syst