Safety-based Bridge Maintenance Management

Transcription

1 Safety-based Bridge Maintenance Management Ib ENEVOLDSEN Project director M.Sc. Ph.D Copenhagen, Denmark Finn M. JENSEN M.Sc., Ph.D. Copenhagen, Denmark Born 1963, received M.Sc. & Ph.D. degree in structural safety from Aalborg University. Project Director for probabilistic-based bridge assessment and safetybased bridge management at RAMBOLL. Summary Born 1965, received M.Sc. & Ph.D. degree in structural safety from Aalborg University. Specialist in probabilistic-based inspections and management of existing bridges. This paper describes a practical 10-phase approach for establishing safety-based bridge maintenance management plans for existing bridges based on probabilistic techniques. The purpose of the management plan is to extend the service lifetime defined as the time until the required safety level can no longer be satisfied. The idea is to apply a probabilistic format for the individual bridge, which does not necessarily have to fulfil the specific requirements of a general code as long as the overall level of safety defined by the code is satisfied. The approach is presented including description of a probability-based safety modelling for critical failure modes, modelling of stochastic variables, calculation of the safety of the non-deteriorated and deteriorated bridge, analysis of various actions and finally establishment of the cost-optimal safety-based bridge maintenance management plan. The approach has proven its practical worth on actual bridges owned by the Danish Road Directorate with savings of more than 10 million. Keywords: Bridges; management; safety; probabilistic; decision analysis; rehabilitation; deterioration; cost-optimal. 1. Introduction The situation for many bridge owners in the industrialised part of the world can be characterised as a combination of an old deteriorating bridge stock and limited budgets. Most of the older bridges are designed for a load level considerably smaller than today's demand. In some cases the bridges, furthermore, often act as bottlenecks in the infrastructure system, which for both rehabilitation and strengthening projects involves high road user inconvenience costs. The traditional bridge management approach can be described as an appearance-based approach because the management of bridge maintenance is primarily based on the outcome of periodical principal inspections combined with special inspections of selected bridges. The result of these inspections, both principal and special, forms the input for a decision process for the bridge maintenance and the management of the bridge maintenance. This decision process typically involves cost-benefit analysis of various actions including rehabilitation and repair options. Each of these options are defined with direct and indirect (user inconvenience) costs and impact on the lifetime based on deterioration models and engineering experience. The option resulting in the smallest net-present worth value or longest lifetime for lowest investment is then chosen. The inspections typically include information on the degree of deterioration of various parts of the inspected bridges. The actual remaining structural load carrying capacity of individual elements or the whole bridge is usually not accessed, and subsequently is not an integral part of the maintenance management. However, if the inspector based on the appearance of the bridge becomes suspicious concerning the load carrying capacity a safety analysis can be performed as a part of the inspection. The described appearance-based approach basically requires that the bridges are maintained at a level which often in practice corresponds to the appearance or standard of the bridge when it was constructed. By doing this it is implicitly assumed that the structural safety requirements for the bridge are satisfied. The appearance-based approach then becomes problematic in at least three situations: 1) when the desired or required load level is higher than the design load, 2) when the degree of bridge deterioration is so severe that a major rehabilitation is not possible or economically

2 feasible and 3) when the budgets for maintaining a bridge standard close to as-built standard are insufficient. In contradiction to the above-described traditional appearance-based approach a new direction is seen in e.g. Canada, USA, UK and Denmark. A new paradigm is introduced which includes safetybased bridge maintenance management. The basic idea is that when it becomes impossible or too costly to maintain bridges to as-built standard, the bridge owners must at least ensure that the bridges are safe for the users. Therefore, safety-based bridge maintenance management becomes attractive because it allows bridge owners to extend the service lifetime by reducing or postponing costly rehabilitation projects without compromising the required level of safety. A Safety-based Bridge Maintenance Management plan can be based on a deterministic or a probabilistic approach. In the probabilistic-based approach the plan is established based on probability analysis in which the probability of failure P f of the deteriorating bridge is calculated. I.e. the idea is to apply a probabilistic format for the individual bridge, which does not necessarily have to fulfil the specific requirements of a general code, as long as the overall level of safety defined by the code is satisfied. By use of a model for the present and future deterioration including uncertainties, P f as a function of time may be determined. The lifetime is then determined as a criteria time, that is the time until the probability of failure becomes higher than a criteria typically defined by the authorities in e.g. background documents for the relevant codes. This criterion is typically a requirement for the maximum allowable formal annual probability of failure. Hereby, the lifetime is directly associated with the safety of the bridge. Based on this, any action (e.g. collection of information, rehabilitation or strengthening) imposed on the bridge at any time to increase the safety (in order to keep P f lower than the required criteria) must be associated with a change of criteria time and a related cost. The establishment of a probabilistic-based management plan then includes a classical decision analysis problem, see e.g. [1], in which the optimal action or combination of actions at the optimal time(s) must be determined from solution of an optimisation problem with the minimum cost as result (longest service lifetime at lowest cost). The probabilistic approach provides a rational manner of including estimates of the deterioration and deterioration rate with related uncertainties of e.g. concrete and reinforcement. The probabilistic approach also provides information about the importance of individual parameters that govern the bridge safety. This is the basic tool for inspection planning by focusing on important parts of the structure and for suggestion of repair and rehabilitation actions. This level of information does further support the optimal lifetime spending of budgets. Based on this it is seen that a probabilistic-based approach is superior to a traditional deterministic-based approach and will theoretically always lead to lower costs than a deterministic approach. This paper describes a practical approach for establishing Safety-based Bridge Maintenance Management plans for existing bridges. The approach has proven its worth in RAMBOLL s practical implementation on bridges for the Danish Road Directorate resulting in large cost savings. 2. Practical Approach for Establishing of a Safety-Based Bridge Maintenance Management Plan In the following a practical approach for establishing of a safety-based bridge management plan for a particular bridge is described by use of a 10-phase procedure. The procedure is suitable for bridges in all countries, although national requirements and principles of probabilistic-based analyses must be used. The phases, described in the following, can be listed as: Phase 0. Fact-finding (previous inspections, analyses, etc.) Phase 1. Definition of problem Phase 2. Safety requirements for the bridge as a maximum yearly probability of failure Phase 3. Deterministic models for identification of the critical failure modes Phase 4. Development of a probability-based safety model for critical failure modes. Phase 5. Modelling of stochastic variables Phase 6. Calculation of the safety of the non-deteriorated bridge Phase 7. Calculation of the safety when taking deterioration into account Phase 8. Analysis of various repair and rehabilitation actions Phase 9. Requirements for the visual appearance (may be required by bridge owner) Phase 10. Making the cost-optimal safety-based bridge maintenance management plan

3 2.1 Phase 0 Fact-finding The first phase in any safety evaluation of any bridge is fact-finding. The bridge is inspected and all previously obtained information on the condition of the bridge is made available and evaluated. This seems to be obvious but, however, very important to stress because old information such as asbuilt drawings, testing of materials and design calculations can be valuable because some uncertainties a-priori can be reduced considerably. 2.2 Phase 1 Definition of problem The development of an optimal management plan requires information on expected future maintenance budgets, the importance of the bridge and the importance of the bridge for road users. This and the safety requirements for the bridge are defined in co-operation with the bridge owner. 2.3 Phase 2 Safety requirements for the bridge The legal basis, from either national or international authorities, establishes the fundamental requirement for the application of a probabilistic-based assessment. For the Nordic countries (Denmark, Finland, Iceland, Norway and Sweden) the background documentation behind the structural codes Recommendation for Loading and Safety Regulations for Structural Design, see [2], describes the requirement in the ultimate limit state for the structural safety specified with reference to failure types and failure consequences, i.e. safety class with requirements for the formal yearly probability of failure P f. Furthermore, [2] specifies the principles of modelling of uncertainties including model uncertainties. From Table 1 it is seen that if it is possible to calculate the formal yearly probability of failure P f or the corresponding reliability index β, it is possible to determine whether the requirements for the safety are fulfilled or not. Table 1. Safety requirements in the Ultimate Limit State specified as the formal yearly probability of failure P f and the corresponding reliability index β, [2]. Failure consequence (Safety class) Failure type I, Ductile failure with remaining capacity Failure type II, Ductile failure without remaining capacity Failure type III, Brittle failure Less Serious (Low safety class) P f 10-3 ; β 3.09 P f 10-4 ; β 3.71 P f 10-5 ; β 4.26 Serious (Normal safety class) P f 10-4 ; β 3.71 P f 10-5 ; β 4.26 P f 10-6 ; β 4.75 Very Serious (High safety class) P f 10-5 ; β 4.26 P f 10-6 ; β 4.75 P f 10-7 ; β 5.20 Similar requirements for the structural safety can be obtained directly or indirectly from e.g. Eurocode 1, [3], or ISO [4]. It is also possible from e.g. statistical decision analysis to determine the optimal safety level, see e.g. [5]. This is, however, often unacceptable for the bridge owner because in many cases the obtained requirements for the safety will be lower than what is normally accepted, because the applied requirements for the structural safety are in general often also based on highly political decisions. 2.4 Phase 3 Deterministic models for identification of the critical failure modes Because it is too expensive to establish a safety-based management plan including many failure modes, it is necessary to identify the critical failure modes before steps 4 to 10. The critical failure modes are determined from combination of three sub-approaches: 1) traditional deterministic determination of load carrying capacity utilisation, 2) information on the approximate degree and location of deterioration and 3) sensitivity analysis in order to evaluate whether the conclusion on identified critical failure modes is stable due to variations in information and modelling. From this it is seen that safety-based management plans never are established without the traditional deterministic analysis functions as a pre-evaluation. 2.5 Phase 4 Development of a probabilistic-based safety model for critical failure modes 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,

4 - identify critical areas for inspection or monitoring, - include detailed information on deterioration, loading, failure mechanisms, test results 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. The obvious choice for the development of a probabilistic-based safety model is then to apply the First Order Reliability Method (FORM) also know as the β-method or the reliability safety index (β) method, see [5], [6] or [7]. FORM is the obvious choice because it is efficient for the relevant small probability levels and includes a rational method of taking the uncertainties related to the specific problem into account in a rational and consistent manor. Further, it is by use of FORM (opposite to deterministic code-based approaches) possible to include new information from e.g. inspection or test results. FORM does basically require a formulation and programming of the specific critical limit states identified as described in section 2.4 and a modelling of the uncertain variables as stochastic variables as described in the next section. 2.6 Phase 5 Modelling of stochastic variables The uncertain variables in the critical limit states related to load, resistance and modelling are modelled as stochastic variables with corresponding statistical distributions and parameters in agreement with the specific project material and level of knowledge concerning materials, loads and mechanical modelling. The stochastic modelling is performed according to the principles and specifications in the background documentation for the relevant code. As mentioned the background information in [2] is applied in the Nordic countries. It is usually advantageous to make a separate stochastic modelling of the traffic load specific to the bridge in question. A specific model is not as conservative as a general modelling of traffic loads, which has to be valid for a larger group of bridges. By developing an individual modelling of traffic loads a higher safety can be obtained. In general, the stochastic modelling of the resistance variables (based on information from the specific bridge) and the bridge specific model for traffic load effects used in a probabilistic-based assessment avoid the unnecessary conservatism present in many deterministic codes. Based on the traffic populations, the load combinations are made. Several situations can be relevant. However, the basic cases for a two-lane bridge with a relatively small influence length (< ~ 40 m) are in general: 1) Appearance and meeting of ordinary trucks with ordinary trucks and 2) Appearance and meeting of special heavy transports with ordinary trucks. For both cases the extreme distribution function of the load effects can be obtained from so-called thinned Poisson processes, see [8] and [9]. The obtained distributions are further obtained based on modelling of a) the number, configuration and weight of the trucks, b) the longitudinal and transverse appearance in the bridge lanes, c) the dynamic amplification of the static truck load, d) the mechanical models for the relation between traffic load and traffic load effects and e) the relative importance for the reliability of load in the actual lanes, see also e.g. [10]. 2.7 Phase 6 Calculation of the safety of the non-deteriorated bridge The reliability index or the probability of failure is calculated for critical failure modes determined in phase 3 using the probability-based safety model developed in phase 4 and the stochastic modelling from phase 5. In addition, a sensitivity analysis is usually performed in order to identify the important parameters that govern the safety of the bridge. (This is a part of the input for uncertainty modelling of deterioration in phase 7 and planning of actions, inspections etc. in phase 8). The safety evaluation of the non-deteriorated bridge is important because the result gives the margin for a safety-based bridge management plan when taking deterioration into account. (It is clear that a reliability index of β = 9 for the non-deteriorated bridge leaves more space for deterioration and possible actions than β = 5 when the safety requirement is e.g. β 4.75). 2.8 Phase 7 Calculation of the safety when taking deterioration into account In order to be able to estimate the safety when taking deterioration into account it is essential to model the characteristics of structural parts (e.g. remaining areas or reduced strength of e.g. posttensioning cables or groups of reinforcements bars) that are deteriorating and from phase 6

5 identified as important for the structural safety as stochastic variables. This is based on available information from previous inspections performed on the bridge and from e.g. previous repairs. Basically the stochastic modelling is based on judgements from experienced bridge inspectors and deterioration experts who should all state the expected values and express their uncertainties in the judgement. It is clear that the judgement of the present degree of deterioration can be updated based on inspections, which is therefore a natural action to consider in phase 8. For the future deterioration some modelling is necessary. In the literature it is relatively easy to find mathematical models for deterioration of various structural parts. However, many of these models seem academic and most always be calibrated and updated based on inspections. It is therefore recommended to base the modelling simply on rates of deterioration modelled as stochastic variables. The parameters for the statistical distributions of these deterioration rates are also assigned based on statements by bridge deterioration experts. This modelling can and must be updated based on future inspections as a part of the safety-based maintenance management. The key issue here is that the rational treatment of the uncertainties related to the deterioration including inspection and updating is more important than the specific mathematical model for deterioration. Hereby, the reliability index as a function of time can be estimated for each of the critical failure modes. Using this, the safety requirement (from phase 2), and the criteria time the corresponding service lifetime can be determined for each failure mode and for the bridge as a whole. 2.9 Phase 8 Analysis of various repair and rehabilitation actions This phase 8 together with phase 10 forms a classical statistical decision theoretical problem with posterior analysis, see e.g. [1]. The core idea is to assign a statistical distribution to future outcomes of uncertain variables, here typically changes in deterioration rates and/or degrees as a consequence of taken imagined actions in the future. A formulation in the framework of decision theory does then integrate the uncertain expert judgements of individual deterioration rates or degrees of individual structural parts into rational decision support in consistent agreement with the expert judgements. In order to establish the management plan a number of possible actions must be analysed. These actions may be divided into 3 categories related to traffic (better modelling, registration by e.g. weigh-in-motion or restrictions), repair/rehabilitation and information updating by inspections or testing, respectively. Hereafter, the change in either information level or change in the rate of deterioration is estimated for each of the actions and combination of actions. Theoretically, an infinite number of actions and combination of actions can be imagined. However, engineering judgements can reduce the possible number of actions. For the change in level of information or estimated change in the rate of deterioration, the updated probability of failure is calculated using the developed probabilistic-based assessment model. This change in reliability is equivalent to a change in criteria time or change in remaining service lifetime Phase 9 Requirements for the visual appearance This phase 9 is basically a phase not belonging to a strict safety-based management plan because the visual appearance is not a part of the bridge safety. However, in order to establish a management plan in phase 10 it is often required by the bridge owner that specific requirements for the visual appearance of the bridge are fulfilled. These requirements are formulated in co-operation with the bridge owner and influence the management models by introducing periodical inspections as known from appearance-based management Phase 10 Making the cost-optimal safety-based bridge maintenance management plan In order to establish the cost-optimal safety-based bridge maintenance management plan the cost of the individual actions and combination of actions are determined from a net-present value calculation including both direct cost and indirect cost (road user inconvenience cost). A net-present cost value of the action at the optimal postponed time is also made. This gives a list of corresponding remaining service lifetimes and associated costs. Based on this it is possible to determine the cost-optimal management plan in which most lifetime is obtained at the lowest cost. In practice the safety-based bridge maintenance management plan contains a list of actions that have to be performed at specified times. Furthermore, it is important to stress that the safety-based maintenance

6 plan is adaptive and must be updated according to any performed action and obtained new information regarding the condition of the bridge. I.e. the safety-based management plan must be maintained in the remaining lifetime of the bridge. 3. Practical Experience with the Approach The above descriptions may at first impression look theoretical but the approach was developed and implemented for specific bridges for the Danish Road Directorate and has shown to be a practical, efficient and well focused approach. A safety-based maintenance management plan based on the approach has been implemented for the Skovdiget West Bridge in 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. Using deterministic load carrying calculations combined with traditional lifetime estimates the bridge would either require major rehabilitation or replacement. Applying a probabilistic-based management plan postponed a major rehabilitation and gave a saving of more than 10 million compared to using a traditional deterministic analysis and lifetime estimation. This is described in details in [11]. For the moment RAMBOLL is working with the implementation of a similar plan for the Storstrom bridge, a 3.5 km long bridge from 1935 at which the management plan is established for the concrete slab bridge deck supporting a two-lane road and a sidewalk. 4. Conclusions Safety-based bridge maintenance management is an attractive approach for extension of the service lifetime, thereby giving bridge owners the possibility of reducing or postponing costly rehabilitation projects, which would not otherwise be possible using a traditional deterministic analysis. In safetybased bridge maintenance management plans the lifetime is directly associated with the safety of the bridge. Based on this, any action imposed on the bridge at any time to increase the safety in order to keep the probability of failure below the required level is associated with a change of lifetime and a related cost. The establishment of a safety-based bridge maintenance management plan then includes a classical decision analysis problem, in which the optimal action or combination of actions at the optimal time(s) must be determined from solution of an optimisation problem with the minimum cost as result. A practical 10-phase procedure for establishment of a safety-based bridge maintenance management plan is presented. The most important conclusion is, however, that procedure has been proven to work in practical cases at bridges for the Danish Road Directorate with savings of more than 10 million compared to traditional deterministic analysis. 5. References [1] Benjamin J. R. & Cornell C. A. Probability, Statistics and Decision for Civil Engineers, McGraw-Hill, 1970 [2] Nordic Committee for Building Structures (NKB),Recommendation for Loading and Safety Regulations for Structural Design, NKB report no. 35, 1978 & NKB report no. 55, [3] Eurocode ENV : 1995 Basis of design and actions on structures Part 1: Basis of Design, September [4] General principles on reliability for structures, ISO , [5] Ditlevsen O. & Madsen H.O., Structural Reliability Methods, John Wiley, [6] Madsen H.O., Krenk S, & Lind N.C., Methods of Structural Safety, Prentice-Hall, [7] Melchers, R.E., Structural Reliability Analysis and Prediction, 2nd ed. John Wiley, [8] Ditlevsen O. & Madsen H.O. Stochastic Vehicle-Queue-Load Model for Large Bridges Journal of Engineering Mechanics. Vol 120, No. 9, pp , [9] Ditlevsen O. Traffic Loads on Large Bridges Modelled as White-Noise Fields Journal of Engineering Mechanics. Vol 120, No. 4, pp , 1994 [10] Enevoldsen, I. Probabilistic-Based Assessment of Bridges Proceedings 16 th Congress of IABSE, Lucerne 2000, Switzerland, September 18-21, 2000 [11] Jensen F.M., Knudsen A., Enevoldsen I. & Stoltzner E. Probabilistic-Based Bridge Management implemented at Skovdiget West Bridge. Bridge Management 4 (M. J. Ryall, G.A.R. Parke & J.E. Harding edts.), pp , Thomas Telford, 2000.