CHAPTER 19

PAGE Chapter 33

CHAPTER 33INSPECTION AND REPAIR STRATEGIES FOR CONCRETE BRIDGES

J.D. Srensen & P. Thoft-Christensen, Aalborg University, Denmark

ABSTRACT

In this paper an optimal inspection strategy for concrete bridges based on periodic routine and detailed inspections is presented.

The failure mode considered is corrosion of the reinforcement due to chlorides. A simple modelling of the corrosion and of the inspection strategy is presented. The optimal inspection strategy is determined from an optimization problem, where the design variables are time intervals between detailed inspections and the concrete cover. The strategy is illustrated on a simple structure, namely a reinforced concrete beam.

1. INTRODUCTION

Periodic inspection intervals for structures like bridges are in general determined on the basis of experience and practical convenience rather than rational methods. However, in the last decade there has been a growing interest in deriving inspection strategies on a more rational basis. In this paper optimal inspection strategies for bridges are investigated on the assumption that two different types of inspections are used, namely routine inspections and detailed inspections. Routine inspections typically take place at one year intervals while the detailed inspections are only performed every five years or so. Only failure due to corrosion of the reinforcement is considered. A model for corrosion is derived and the proposed strategy is applied to a simple structural element of a concrete bridge. The corresponding optimal inspection strategy is obtained from a complicated integer optimization problem. The object function is the estimated total cost in the expected lifetime of the bridge and the constraints are reliability based.

2. INSPECTION REGULATIONS

Traditionally inspection regulations for concrete bridges are based on three types of inspection:

1. Routine inspections.

2. Detailed inspections.

3. Special inspections.

The special inspections are only used when routine or detailed inspections show that there is a need for a more complete (and expensive) inspection. The special inspections are therefore not included in the regulations as inspections that are repeated within fixed intervals. It is therefore not relevant to include them in the optimal inspection strategies derived in the present paper.

The time intervals between routine and detailed inspections vary from country to country according to existing inspection regulations. To illustrate this, a number of regulations will be briefly described in this section. Most of the information shown here is obtained from the proceedings edited by Nowak & Absi [1].

Lemari [2] reports that technical guidelines for the inspection and maintenance of bridges were published in 1979 in France. According to these guidelines there are two types of inspection, namely permanent inspections performed by local agents and periodical inspections. The periodical inspections include a systematic yearly visit (relatively superficial) to all bridges more than 10 m long and a detailed inspection every five years for at least all bridges exceeding 120 m.

In Belgium a computer assisted bridge management scheme was developed in 1977 (see De Buck [3]). In Belgium the maintenance of bridges involves two activities: the control of the bridges and the repair and maintenance works. The control is based on three levels of inspection:

1. A routine inspection and annual survey.

2. "Type A" general inspection every 3 years.

3. "Type B" general specialized inspection when the "type A" inspection reveals the need for it.

In Denmark a bridge management system developed for the Danish State Railways consists of three modules (see Rostam [4]). Module B is the inspection module which comprises the following activities:

1. A superficial inspection.

2. A principal inspection (visual registration and evaluation of damage).

3. A special inspection (specially qualified inspection to be made when needed).

The observation and inspection of bridges in Germany is governed by the German code DIN 1076 (see Zichner [5]). It specifies:

1. Visual inspection of the general conditions without special equipment 4 times a year.

2. General inspection every three years.

3. Main inspection every six years.

4. Special survey in the event of accident or natural disaster that may affect the short-term safety of the structure.

In Switzerland it has been proposed to split bridge surveillance up into (see Favre [6]):

1. Routine inspections (every 15 months).

2. Periodic inspections (every 5 years).

3. Special inspections (according to needs).

In Italy the bridge structure supervision activities are regulated by the Ministry for Public Works Circular n.6736/61 (see Malisardi & Nebbia [7]). It is prescribed that an inspection should be carried out at least once every 3 months. At least once a year a more specialized inspection should take place.

It is seen from the data presented above that a routine type inspection is prescribed for every 3 to 15 months in the countries mentioned. Therefore, it seems reasonable to fix the intervals between routine inspections to 1 year. The 1 year interval is also convenient from a climate point of view.

The data for the detailed inspections deviate more, but intervals from 3 to 5 years seem to be the most commonly used. The time between detailed inspections is the unknown to be determined by the optimization problem formulated in this paper.

3. MODELLING OF CORROSION

As mentioned in the introduction only a single structural element in a concrete bridge is considered, viz. the T-beam shown in figure 1.

The beam is loaded by a bending moment kP, where P is an external load and k is a coefficient of influence. The concrete cover is modelled by c. The reinforcement is assumed to consist of n bars each with the diameter d. Let the total reinforcement area A(t) be modelled as a function of the time t. Then a safety margin MF(t) corresponding to failure of the beam is (in the normal case where the neutral line distance is less than h1)

(1)

where

is the yield stress of the reinforcement,

is the yield stress of the concrete in compression,

ZI is the uncertainty variable modelling the uncertainty connected with

estimating the moment capacity.

A reinforced concrete beam in a bridge structure is exposed to a large number of hazards, e.g. alternating load, extreme load, frost, acids, chlorides, de-icing salts, pollution and alkali aggregates. Several of these hazards have the effect that the reinforcement is exposed to corrosion. In this paper one of the most important sources of corrosion is considered, namely chlorides which have a de-passivation effect on the steel if the concentration is high enough. Chlorides that are in the concrete initially are found to be of much less importance than chlorides coming from rock salt used for de-icing roads, see Vassie [8].

A number of physical factors is of importance for corrosion of reinforcement generated by chlorides, namely low depth of concrete cover, leaking joints, faulty drainage, absence of waterproof membranes and the number and intensity of freeze-thaw cycles. However, in this paper only such cases are considered where the chloride concentration outside the concrete, the initial chloride concentration and the critical chloride concentration (starting corrosion) are given. Clearly the concentration of chlorides outside the concrete beam is highly dependent on the location of the beam in the structure.The time of corrosion initiation TI depends on the chloride concentration outside the beam, how fast the chlorides penetrate the concrete cover and on the critical chloride concentration. If the penetration process is modelled as a diffusion process, TI can be estimated from (see [9])

(2)

where

a is the coefficient of diffusion (= 400 mm2/year for water/cement ratio = 0.55)

cc is the critical chloride concentration (= 0.15)

c0 is the initial chloride concentration (= 0.04)

is the outer chloride concentration (= 0.2)

erf is the error function

The values shown in parenthesis are values used by Andersen & Lyck [9].

After initiation of corrosion in the reinforcement it is assumed that it propagates as local corrosion. All bars are assumed to corrode with the same velocity starting at the same time. The corrosion model shown in figure 2 is used in this paper.

The propagation velocity K is assumed to be constant

(3)

where

G = 200 /year for chloride initiated corrosion

kt = 1 at normal temperatures.

The total reinforcement area as a function of the time t then becomes

(4)

where

(5)4. MODELLING OF INSPECTION STRATEGY

As described in section 2 most national inspection programmes for concrete bridges consist of two types of inspection, namely routine inspections at fixed time intervals and detailed inspections at longer intervals (being a multiple of the ). If the routine inspections are performed with inspection quality q1and the detailed inspections with quality q2 the inspection programme can be modelled as shown in figure 3. Ti, i = 1,..., N, are the times of detailed inspections and T is the expected lifetime of the beam.

The detailed inspections are assumed to be performed at the time intervals

(6)

where Ni, i = 1,..., N, is a positive integer. The inspection method used for the detailed inspections are assumed to provide an estimate of the chloride concentration variation with the depth from the concrete surface and to give a picture of where corrosion (general and local) occurs. The inspection methods include such methods as visual inspection, measurements of half-cell potentials, resistance, chloride content and concrete quality.

A number of repair strategies can be chosen. In this paper it is assumed that the beam is repaired when corrosion of the reinforcement is detected. The repair is assumed to be immediate and complete (both concrete and reinforcement is replaced, if necessary). The routine inspections are assumed to be visual inspections. If corrosion has started and has developed to a certain degree, the concrete cover will flake off. The structure is assumed to be repaired if peelings are discovered during the inspections.

An optimal inspection and repair strategy can be determined from an optimization problem where the optimization variables are the total number of detailed inspections N, the time intervals between detailed inspections N1, N2,..., NN and the concrete cover c. In Thoft-Christensen & Srensen [10] a similar problem to determine an optimal inspection and repair strategy for a fatigue sensitive element (hot spot) in an offshore jacket structure is considered. The optimization problem considered here is:

(7)

(8)

(9)

(10)

The objective function is modelled as

(11)

where

(12)

is the initial cost,

(13)Is the inspection cost,

(14)

is the repair cost, and

(15)

is the cost of failure. CI0, CI1, CINl, CIN2, CR0 , and CF0 are constants.

E[Ri] is the expected number of repairs at the time i and Pf(i) is the probability of failure at the time i. In the optimization problem the influence on the cost from the rate of interest is neglected.

The reliability index is determined from

(16)

The total number of different repair courses (branches) is, see fig. 4. The safety margin corresponding to the event that the beam is repaired after a detailed inspection is written

(17)

where CM is the measured concentration of chlorides at the depth of the reinforcement. CM is estimated from

(18)

where ZD is a measuring uncertainty variable.

Correspondingly the safety margin for the event that repair is performed after a routine inspection is written

(19)

where c1 is a constant, , and ZR is a measuring uncertainty variable.

The probability of failure at the time t is determined by

(20)

(21)

where is the failure safety margin at the time t given repair at the time t1. and are the events that branches 1 and 2 occur, respectively. For example

(22)

For

(23)

where for example

(24)

Equation (23) is used if the second inspection is a routine inspection. If instead it is a detailed inspection Pf(t) is determined from

(25)

where for example

(26)

Correspondingly the expected number of repairs can be determined from

(27)

(28)

(29)

or if e.g. the first detailed inspection is performed at the third inspection

(30)

In order to be able to evaluate Pf(t) and E[R1] within a reasonable computer time the following simplifications are used in the example in section 5.

The inspections are grouped such that the routine inspections preceding a detailed inspection are treated as one group of inspections. Further, it is assumed that the probability of more than one repair is negligible. The probability of repair in [0, T1] is then approximated by

(31)

The probability of repair in ]T1, T2] is approximated by

(32)

The probability of repair in ]T2, T3] is approximated by

(33)

etc.

The probability of failure is approximated by

(34)The Constraint (8) in the optimization problem is approximated by

(35)

The probabilities and the sensitivity factors with respect to the optimization variables are determined using FORM (First Order Reliability Methods).

5. EXAMPLE

Consider the structural beam as shown in figure 1 with bl = 1500 mm, b2 = 400 mm, h1 = 300 mm, hn = 840 mm, d = 15 mm and n = 7. Let the beam be subjected to a bending moment kP, where k = 1500 mm and where the load P is modelled as a log-normally distributed stochastic variable P: LN(60,000 N, 12,000 N).

Further, let the yield stresses and be log-normally distributed:

: LN(36 N/mmz, 7.5 N/mm2); : LN(600 N/mmz, 60 N/mmZ).The variables in eq. (2) are modelled as:

a: LN(400 mmz/year, 80 mmz/year); cc = 0.15; c0 = 0.04; = 0.2.The propagation velocity K is modelled as:

K: LN(0.2 mm/year, 0.04 mm/year)

The model uncertainty variables are modelled as:

Z1: LN(l, 0.10); ZR: N(l, 0.10), N means normal distribution; ZD: LN(l, 0.05)

The constant c1 in eq. (19) is put equal to c1 = 0.5.

In the optimization problem (7) - (10) the parameters are chosen as

= 4.0; T = 70 years; = 1 year; = 30 mm, = 60 mm; and the costs are in 103 DKK: CI0 = 2000, CIN1= 200, CINI = 10, CIN2 = 100, CR0 = 200, and CF0 = 1000.

The optimization problem (7) - (10) is a mixed integer/pseudo-integer/real variable problem. It is solved sequentially for fixed N treating N1,, NN as real variables and using the NLPQL algorithm developed by Schittkowski [11]. The final values for N1,, NN are chosen as the integers closest to the final values. The result is: N = 5, N1 = 14, N2 = 13, N3 = 14, N4 = 13, N5 = 8, and c = 30 mm. This result is illustrated in figure 5.

The figure shows that the reliability index is only decreasing slightly for the first approximately 20 years (corresponding to the expected value of the initiation time T1 for the chloride to penetrate the concrete). Further, it is seen that each inspection (the detailed inspections and the routine inspections are grouped) gives only a small increase in the reliability index , i.e. the effect of the inspection on the reliability is in this example not significant.

The long time intervals between detailed inspections ( 13 - 14 years) in this example seem to be unrealistic. The reason for these large values could be that only corrosion due to chloride penetration is taken into account. The time intervals are highly sensitive to the input data.6. CONCLUSION

A method to determine an optimal inspection strategy for concrete bridges is presented. The failure mode considered is corrosion of the reinforcement due to chloride penetration. The inspection strategy is modelled on the basis of the current practice in many countries, where routine inspections are performed approximately once a year and detailed inspections are performed at longer intervals (three to five years).

The optimal inspection strategy is determined from an optimization problem, where the objective function is the expected total cost, and the constraints ensure that the reliability is satisfactory at any time. The design variables are the number of inspections, the time intervals between inspections and a design parameter (the concrete cover).

As an example a single reinforced concrete beam is considered. Using some simplifications with regard to determination of probabilities of failure and repair the optimal inspection strategy is determined. The example shows that inspections with the present modelling have only a small significance for the reliability index. However, the example indicates that the proposed procedure can be applied to more general examples where the total structural system is considered.

7. REFERENCES

[1] Bridge Evaluation, Repair and Rehabilitation. Proceedings of the 1st US-European Workshop. Editors A. S. Nowak & E. Absi. The University of Michigan, Ann Arbor, Michigan, USA, 1987.

[2] Lemari, P. Bridge Management and Maintenance in France. In [1], pp. 51-57.

[3] De Buck, J. Bridge Maintenance in Belgium. In [1], pp. 63-98.

[4] Rostam, S. Bridge Monitoring and Maintenance Strategy. In [1], pp. 146-153.

[5] Zichner, T. Disorder - Repair - Strengthening of Prestressed Concrete Bridges based on the Inspection of 43 Valley-Bridges. In [1], pp. 168-179.

[6] Favre, R. Methodology for the Monitoring of Bridges. In [1], pp. 197-208.

[7] Malisardi, L. & Nebbia, G. Supervision of Bridge and Tunnel Structures. In [1], pp. 219-233.

[8] Vassie, P. Reinforcement Corrosion and the Durability of Concrete Bridges. Proc. Instn. Civ. Engrs., Part 1, Vol. 76, 1984, pp. 713-723.

[9] Andersen, K. & Lyck, S. Optimal Repair Strategies for Concrete Bridges (in Danish). M.Sc. Thesis, University of Aalborg, 1988.

[10] Thoft-Christensen, P. & Srensen, J. D. Integrated Reliability-Based Optimal Design of Structures. Proc. IFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems. Springer-Verlag, Lecture Notes in Engineering, Vol. 33, 1987, pp. 385-398.

[11] Schittkowski, K. NLPQL : A FORTRAN Subroutine Solving Constrained Non-linear Programming Problems. Annals of Operations Research, 1986.

Figure 5. Reliability index EMBED Equation.DSMT4 as a function of time.

Figure 4. Repair realizations. 0 signifies non-repair and 1 signifies repair.

Figure 3. Inspection plan.

Figure 2. Model of local corrosion propagation.

EMBED Equation.DSMT4

Figure 1. Model of concrete beam.

Proceedings IFIP WG 7.5 Working Conference, London, UK, Sept. 1988. Springer Verlag 1989, pp. 325-335.

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