Probabilistic-based Bridge Management Implemented at Skovdiget West Bridge

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1 Jensen et al, Page 1 Probabilistic-based Bridge Management Implemented at Skovdiget West Bridge F.M. JENSEN, A. KNUDSEN, I. ENEVOLDSEN, RAMBØLL, Denmark Bredevej 2, DK-2830 Virum, Denmark. fnj@ramboll.dk, phone: E. STOLTZNER, The Danish Road Directorate, Denmark. Niels Juels Gade 13, DK-1059 København K, Denmark. est@vd.dk, phone: ABSTRACT This paper describes the implementation of a probabilistic-based bridge management plan for the Skovdiget West Bridge, Denmark in Skovdiget West bridge is a 30 year old 220 m long post-tensioned concrete box-girder bridge with serious deterioration of both concrete, reinforcement and cables. By use of deterministic load carrying calculations combined with traditional lifetime estimates, the bridge would either require major rehabilitation or replacement. The application of a probabilistic-based management plan postponed major rehabilitation, repair and replacement, and gave a saving of more than EUR 10 million compared to use of a traditional deterministic analysis and lifetime estimation. KEYWORDS: probabilistic-based, management plan, decision analyses, rehabilitation, deterioration. INTRODUCTION Bridge owners today face the combination of an old deteriorating bridge stock and limited budgets. Additionally, many of these ageing bridges are vital for the infrastructural system, consequently rehabilitation projects are associated with large road user inconvenience costs. Probabilistic-based safety management and assessment tools were recently developed as an attractive approach for extension of the service lifetime, thereby giving bridge owners the possibility of reducing or postponing costly rehabilitation projects. Today, on selection of a repair and rehabilitation strategy for a deteriorating structure, the estimate of the remaining lifetime will often be based on experience. In order to avoid serious bridge failures a conservative estimate has to be used for prediction of the remaining lifetime. The use of a conservative estimate is necessary even for the most experienced bridge inspection engineer. Additionally, the effect on the extension of lifetime as a result of various repair and rehabilitation options is associated with some uncertainty due to the lack of an efficient tool to properly evaluate the effect. This uncertainty with respect to the remaining lifetime and the effect of repair and rehabilitation options means that there is a lack of information when determining the optimal bridge rehabilitation strategy, which may often lead to a non-optimal spending of budgets. By application of a probabilistic-based approach, the probability of failure P f of the deteriorating bridge is calculated. By use of a model for the deterioration, P f as a function of time may be determined. The lifetime is then determined as a criteria time, that is the time till the probability of failure passes a user-selected criteria. This criterion is typically a requirement to the maximum allowable probability of failure.

2 Jensen et al, Page 2 This way the lifetime can be directly associated with the safety of the bridge. In the probabilistic approach you still need to estimate the deterioration of concrete and reinforcement, but the uncertainties are included in a rational manner. Additionally, the probabilistic approach can be used to compare the various repair and rehabilitation options considered. The probabilistic approach also provides information about the importance of individual parameters that contribute to the safety. This supplies the bridge owner with a much better tool for inspection planning by focusing on important parts of the structure and for comparing repair and rehabilitation options. This level of information ensures optimal inspection planning and optimal lifetime spending of budgets. Recently, bridge owners have changed from the traditional approach for lifetime estimation and selection of repair strategies to a more advanced and individual approach in order to optimise budgets. The Danish Road Directorate has taken a lead in using the individual approach, and in 1998 the Danish Road Directorate in co-operation with RAMBØLL initiated work on the development of a probabilistic-based management plan for the Skovdiget West Bridge. By using a probabilistic-based management plan combined with a cost-optimal plan based on probabilistic-based assessment and decision analysis of several rehabilitation options the Danish Road Directorate was able to reduce and postpone a costly rehabilitation or replacement project due for the severely deteriorated Skovdiget West Bridge. HISTORY and STRUCTURAL SYSTEM The Skovdiget identical twin bridges are located Northwest of Copenhagen and were constructed in Each carries a 3-lane motorway across two local roads, a railroad and a parking area. The bridges carry a major approach road to Copenhagen. The average daily traffic is 53,000 vehicles. Each bridge is 220 m long, 20 m wide and has 12 spans. The bridges are concrete posttensioned, combined box-girder and beam-slab bridges. Figure 1. The West bridge seen from Southwest, 1999 (right). Below the midpoint of the West bridge looking North, Main box girder 3 is on the right and main box girder 4 on the left. The East bridge is seen on the right on the picture (left). Due to poor workmanship and unfortunate design, both bridges started to deteriorate shortly after construction. In the late 70 ies substantial damage was registered on both bridges. The damage was related to un-injected or poorly injected post-tensioned cable ducts, drainage was insufficient and poorly made, the area around gulley poorly made, a bad waterproofing on whole bridge deck and an uneven bridge deck. The gulley is located over main girder 4. The

3 Jensen et al, Page 3 water on the bridge deck around the gulley caused corrosion damage to reinforcement and cables and frost damage to the concrete. East Bridge Major repair was done on the East bridge in 1978 including partial concrete replacement of bridge deck (especially around the gulley), repair of post-tensioned cables (using vacuuminjection of partly injected cable ducts), new waterproofing, new base and wearing course and repair of the bearings and expansion joints. Since the repair in 1978, the East bridge has been inspected according to the normal guidelines for bridge inspections in Denmark. The East bridge was last inspected in 1998 and it was found in general to be in a good condition. West Bridge The cost of rehabilitation of the East bridge was EUR 3 million in A new bridge would cost EUR 8 mill. in Since the repair on the East bridge proved so costly, it was decided to leave the West bridge without repair. Instead it was decided to monitor the West bridge closely. The development of deterioration was to be monitored in order to determine when the safety was no longer acceptable. This has been done by close visual inspections 4 times a year. These inspections include a thorough visual inspection and measurements of crack widths and deformations. In addition to the frequent visual inspections and deformation measurements of selected structural parts, a test loading of the West bridge was carried out in 1984, 1988 and During the test loading the deformation of the main and secondary spans was measured while the bridge was loaded with 90 and 60 tonnes trucks. The test loading showed small deformations compared to the deformations when close to failure. Figure 2. Overview of the two Skovdiget bridges, location of lanes on West bridge (left). Picture from the last test loading performed on the West bridge in 1993 (right). The last special inspection was performed on the West bridge in The inspections were focused on the main girder no. 4 and especially the area around the gulley. It was found that the concrete in the area around the gulley was severely deteriorated, there was reinforcement with pitting corrosion, un-injected cables and cables with loose strands indicating total loss of load bearing capacity. The serious deterioration was primarily related to main girder number 4. Inspections in main girder 3 and the western wing showed only minor and local deterioration.

4 Jensen et al, Page 4 PROBABILISTIC-BASED MANAGEMENT PLAN A new test loading for Skovdiget West was due in 1998 (following a 4-5 year interval between tests). A test loading is costly and does not give sufficient information to be used for lifetime predictions, evaluation of the present and future load carrying capacity or information to decide between various rehabilitation options. Based on this fact combined with the results from the last special inspection in 1995, which locally showed severe deterioration, it was decided to implement a management plan based on probabilistic methods. By doing this the Danish Road Directorate obtains a better basis for decision, for minimising maintenance budgets and for extending the lifetime of the bridge - all with the prerequisite that the requirements to the overall safety are observed. Additionally, a model is obtained which may be used to financially and technically evaluate different repair and rehabilitation initiatives in the future. In the following the actual implementation of the probabilistic-based management plan for Skovdiget West is described. Formulation of problem The development of an optimal management plan requires information on expected future maintenance budgets, the value and the importance of the bridge and the importance of the bridge for road users. This in connection with the safety requirements for the bridge is decided in close co-operation with the bridge owner. Safety requirements for the bridge The legal basis, either national or international authorities, establishes the fundamental requirement for the application of a probabilistic-based assessment. For Skovdiget the background documentation behind the codes in the Nordic countries Recommendation for Loading and Safety Regulations for Structural Design, see [1], describes in detail how a probabilistic-based assessment can be performed in accordance with the requirements for the safety level in the Nordic countries. Furthermore, [1] specifies the principles of modelling of uncertainties including model uncertainties. The requirement in the ultimate limit state for the structural safety is in [1] specified with reference to failure types and failure consequences, i.e. safety class with requirements for the formal yearly probability of failure P f.. The formal probability of failure can, using the standard normal distribution function Φ, be related directly to the reliability index β by the relation β = -Φ -1 (P f ). Based on analysis of critical failure modes for Skovdiget West, the safety class high and limit state type failure with remaining bearing capacity is appropriate. This equals the limits on the probability of failure and corresponding reliability index to P f 10-5 and β Identification of critical failure modes The deterioration of Skovdiget is related to an overall deterioration of the whole bridge and a more concentrated deterioration around the gulley due to bad drainage. Initially, a deterministic analysis was made to identify the critical points and critical failure modes. A critical point is determined by the combination of load carrying capacity utilisation combined with deterioration at a given point for a given failure mode. These analyses identified main girder cross section at column supports and at construction joints in the long span on main girder 4 as primary critical points. The critical failure mode was combined bending and shear, with shear failure as the dominant failure mode. It was found that transverse girders, transverse ribs and wings on the main girders were less critical (secondary critical points).

5 Jensen et al, Page 5 Probabilistic-based assessment model The probabilistic-based safety assessment model is the core in the management model and must therefore be developed with a specified set of specifications. The model must be able to: - evaluate the safety now and in the remaining lifetime of the bridge, - analyse realistic failures and set of failures, - identify critical areas for monitoring, - include detailed information on deterioration, loading, failure mechanism, output from test loading, etc. - take into account the uncertainties related to strengths, loads, traffic, models, etc. - identify important parameters for the safety, sensitivity analysis, and - update the safety of the bridge based on new or updated information, e.g. results from a previous or a future test loading or inspections. For this project an influence model for the global bridge structure was developed based on elastic analysis. For the main girder cross section a capacity model was developed with the characteristics that: - the capacity of the cross section is maximised, - each reinforcement group and cable group may be modelled independently, and - the model is made operational for automatic inclusion into a general-purpose program for reliability analysis. The model developed is capable of realistic modelling of the variation of deterioration and by performance of an optimisation for load bearing capacity the extension of lifetime can be maximised. For Skovdiget West a model for main girder cross section capacity with separate modelling of 28 reinforcement groups was implemented, see Figure 3 (left). Since the concrete, reinforcement and cables below the gulley are more deteriorated than other parts of the cross section, a model for optimal force distribution was made, thereby ensuring that all remaining reinforcement is taken into account, see Figure 3 (right). Figure 3. For both main girders the reinforcement and cables were divided into a number of reinforcement groups each modelled individually (left). A model for optimal load carrying capacity of a main girder was made (right). Deterioration modelling Based on all available information from previous inspections performed on the West and East bridge and from the major repair of the East bridge in 1978, combined with experience in rate of deterioration for typical damages, the remaining reinforcement area for each individual reinforcement or cable group was estimated. This was done for three critical structural points identified earlier and for the years 1978 (major repair of East bridge), 1998 (now) and estimated for Each estimate was associated with a coefficient of variation depending on the information level available when making the estimate.

6 Jensen et al, Page 6 Stochastic Modelling & Traffic Modelling The uncertain variables related to traffic, load, resistance and modelling are modelled as stochastic variables with corresponding statistical distributions including parameters specific to Skovdiget West and the level of knowledge concerning materials, loads and mechanical modelling. For this project a separate stochastic modelling of the traffic load was made. The developed traffic model is specific to Skovdiget West and is therefore not as conservative as a general modelling of traffic loads, which has to be valid for a larger group of bridges. By development of an individual modelling of traffic loads a higher safety can be obtained. The Skovdiget model is based on combinations of thinned Poisson processes with extreme loads in two lanes, since extreme loading in three lanes was found to be unlikely based on the actual appearance of vehicles in lanes. Statistics of heavy vehicles just north of the bridge were used to develop the traffic load model specific to Skovdiget West. Calculation of safety taking deterioration into account Using the probabilistic-based assessment model, the deterioration modelling and the stochastic modelling of traffic, load, resistance and modelling, the reliability index as a function of time may be estimated. In Figure 4 (left) the reliability as a function of time is shown for the three critical points: - main girder 4, column support, south of long span, shear with moment failure check - main girder 4, construction joint south of long span, shear with moment failure check - main girder 3, column support south of long span, shear with moment failure check Figure 4. Reliability index for critical points as a function of time. Repair and rehabilitation options considered the management plan for Skovdiget West (right). The minimum required safety or reliability index is indicated in Figure 4 (left). The result of the analyses showed, with the given assumptions regarding the state of deterioration, that at present (1998) the safety of bridge is above the critical safety level. Using the estimates of future deterioration the criteria time or remaining lifetime is found to be 7-8 years. In addition the sensitivity analysis identified the critical parameters in the modelling and the critical reinforcement groups. This was later used to determine which groups needed to be inspected closely and which reinforcement groups were less important for the safety. Table 1 shows the approximate increase in reliability index when the standard deviation is halved. It is seen that a substantial increase in reliability index may be obtained if the uncertainty modelling can be improved. This means that detailed inspections of selected reinforcement groups are advantageous since they may lower the standard deviation - or even increase the estimated value - and thereby increase the safety of the bridge.

7 Jensen et al, Page 7 Table 1 Approximate increase in reliability index when reducing the standard deviation to 50% of the value used. Stochastic Variable G4,S409,1998 Column support G4,S409, 2008 Column support G4,S409,1998 Construction Joint G-4,S409, 2008 Construction Joint Self-weight Traffic load Yield stress, shear reinforcement Concrete compressive strength Shear reinforcement Post-tensioned cables Based on the result of this analysis several repair, rehabilitation and other initiatives were analysed to extend the lifetime of the bridge. Repair and rehabilitation options In order to choose the correct rehabilitation plan for extending the lifetime, a number of possible options were analysed. These may be divided into 3 categories related to: traffic, repair & rehabilitation and information updating, see Figure 4 (right). From the list of possible combinations of options the following were chosen for further analysis based on initial investigation of all combinations of options: 0) No initiative 1) Safety updating inspections 1-2) Safety updating inspections & test loading 1-3) Safety updating inspections & survival wearing course 1-4) Safety updating inspections & strengthening against shear failure 2) Test loading 3) Survival wearing course and new drainage system 4) Strengthening against shear failure at critical points To choose the best that is best technical and cost-optimal rehabilitation option, the change in either information level or change in the rate of deterioration was estimated for each of the 7 selected combinations shown above. For this change in level of information or estimated change in the rate of deterioration the change in reliability β was calculated using the developed probabilistic-based assessment model. This change in reliability is equivalent to a change in criteria time or change in remaining lifetime. Cost-optimal probabilistic-based management plan For each of the options a net-present value calculation was performed including both direct cost and indirect cost (road user inconvenience cost). A net-present value analysis of postponed options was also made. This gave a list of corresponding remaining lifetimes and costs to be used as input when selecting the optimal management plan. The cost optimal management plan was 1-3) Safety updating inspections & survival wearing course. The estimated criteria time after implementation of 1-3) was estimated to 15 years up from 7-8 years with an estimated cost of EUR 0.9 million. In addition to the proposed option the following was done in order to verify the model made and to update the management plan. - Safety controlling inspections to verify deterioration modelling of critical reinforcement groups. - Continuous periodical visual inspections and special inspections - Update of management plan based on safety updating and safety controlling inspections.

8 Jensen et al, Page 8 IMPLEMENTATION OF COST-OPTIMAL REHABILITATION PLAN The management plan was implemented in The management plan included detailed inspections to verify the assumptions and to update the management plan. Secondly, if inspections did not show deterioration not accounted for in the analysis, a new wearing course and a new drainage system was to be implemented at Skovdiget West bridge. Inspections in 1999 In 1999 two types of inspections were made. A number of safety controlling inspections to ensure that the overall assumptions about deterioration on the bridge were correct, and safety updating inspections at critical points identified during the analysis. The safety controlling inspections verified the overall assumptions regarding areas of critical deterioration. The safety updating inspections focused on critical areas and critical reinforcement groups identified during the previous reliability analysis, and extended the service life by 7-10 years due to more detailed deterioration information about the critical reinforcement groups. Rehabilitation in 1999 The second part of the management plan was initiated in 1999 after completion of the inspections and verification of the management plan. In the period July-September 1999 a new wearing course was put on the West bridge. The drainage system was altered by adding two new gulleys two metres on both sides from the old gulley. By doing this water was moved from the area around the old gulley where the deterioration was most severe. CONCLUSIONS In the present work a probabilistic-based management plan was implemented for Skovdiget West. Probabilistic-based safety management is an attractive approach for extension of the service lifetime, thereby giving bridge owners the possibility of reducing or postponing costly rehabilitation projects not otherwise possible using a traditional deterministic analysis. The applied approach included stochastic modelling of all the uncertainties of importance for the safety problem, a new load carrying capacity model taking variation in deterioration into account and a new traffic model specific to the bridge. The selection of the best technical and cost-optimal repair and rehabilitation option was done by using the probabilistic-based model in connection with net-present value estimates. The result was the implementation in of a cost-optimal plan based on probabilisticbased assessment and decision analyses of several rehabilitation options, giving a saving of more than EUR 10 million compared to traditional deterministic analysis. REFERENCES [1] Nordic Committee for Building Structures (NKB) Recommendation for Loading and Safety Regulations for Structural Design NKB report no. 35, 1978 & NKB report no. 55, [2] Danish Road Directorate (Vejdirektoratet) Rules for Determination of the Load Carrying Capacity of Existing Bridges", Danish Road Directorate, Written in Danish: "Beregningsregler for beregning af eksisterende broers bæreevne", Vejdirektoratet, Vejregeludvalget, April [3] Mohr, G.: Traffic on motorways, February [4] PROBAN, General Purpose Probabilistic Analysis Program, Veritas Sesam Systems, [5] H. O. Madsen, S. Krenk & N. C. Lind : Methods of Structural Safety, Prentice-Hall, [6] O. Ditlevsen & H. O. Madsen : Structural Reliability Methods John Wiley, 1996.