Uncertainties in predictive models for concrete structures performance can influence adversely the timing of management activities. A methodology has been developed that uses data obtained through proactive health monitoring to increase the confidence in predicted performance by reducing the associated uncertainties. Due to temporal and spatial variations associated with climatic changes, exposure conditions, workmanship, and concrete quality, the actual performance could vary at different locations of the member. In this respect, the use of multiple sensors may be beneficial, notwithstanding cost and other constraints. Two distinct cases are identified for which an updating methodology based on data from multiple sensors needs to be developed. In the first case the interest lies in improving the performance prediction for an entire member (or a structure) incorporating spatial and temporal effects. For this purpose, the member is divided into small zones with the assumption that a sensor can be located in each zone. In the second case, the objective is to minimise uncertainties in performance prediction, or to increase the redundancy of health monitoring systems, at critical locations. The development of updating methodologies for the above-mentioned scenarios is described in this paper. Its implications on the management activities, for example, establishing the timing of principal inspections, are evaluated and discussed.
In the UK, the Highways Agency is administering over 9,000 trunk road and motorway bridges that are valued at over
Visual inspections are widely used to aid maintenance management of almost all deterioration prone systems. Despite obvious benefits (e.g., simplicity, cost, and access to 100% of the visible surface), they are intermittent, subjective, and applicable only to exposed surfaces, and the need for access may involve disruption to normal operations. Further, the extent of damage cannot be estimated only by a surface examination; the signs of deterioration may not appear at the surface until it has caused severe internal damage, especially if the defect is not at, or close to, the surface. Furthermore, visual examinations can only provide qualitative information with respect to condition which may not relate explicitly or fully to safety.
Nondestructive examination (NDE) addresses several of these drawbacks and has gained popularity among the maintenance and management communities. The need to be in close vicinity of the area to be inspected is a major hurdle in its use for several applications, for example, bridges where it becomes costly primarily due to the indirect costs of bridge closure and traffic management. The “direct” and “indirect” data provided by NDE can often be related explicitly to safety levels but they are generally intermittent in both time and space.
In recent years, health monitoring methods are being developed as a continuation of the research into NDE methods. These range from simple methods (such as half-cell measurements) to more sophisticated technology such as corrosion risk sensors, possibly with remote sensing capability. These structural health monitoring (SHM) methods can provide real-time information on system deterioration characteristics, for example, Daly and Watts [
With regard to the spatial variability of deterioration processes, a major concern in the use of the above systems is that they only provide information at a small number of specific locations; careful thought has to be given as to how these results can be considered as representative (or not) for the element or entire system.
Unexpected results also pose many questions. If, for example, several sensors are installed at various locations in a system what should the conclusion be, if a sensor contradicts a similar closely located sensor? Alternatively, what if a sensor close to a known defect indicates a less severe condition, whereas another at some distance away indicates a worse condition, and so forth. Other possibilities include the absence of, or clearly erroneous, readings obtained from a particular sensor. But even when the sensors are free from obvious errors how confident should we be regarding their output, and to what extent can this information be used for performance prediction purposes?
The frequency of measurements required on a system depends primarily on the phenomenon being monitored; for example, the frequency of information obtained through sensors should be very high for live load measurements on a structure to avoid any important reading being missed out. On the other hand, if the phenomenon being monitored is corrosion in a concrete structure, the sensors, output need not be that frequent. Even though the process of health monitoring may be continuous in nature, the output from the sensors could either be of a continuous or a discrete form depending on the parameters being monitored and the type of sensors being used.
In a distinct strand of research, deterioration models have been developed to estimate and predict the performance of structures. Research on different materials, for example, concrete, steel, and masonry, in the area of performance prediction has lead to the development of predictive models for a range of conditions, to a varying degree of complexity. These models have the potential to provide information on materials’ deterioration, which can be continuous in time and space. The downside of the models is that uncertainties associated with the nature and rate of deterioration, the demand (past, present, and future), and other factors which influence the actual performance of these structures are considerable and subject to change during their service life. These uncertainties can be treated formally using probabilistic methods and an increasing shift towards probabilistic deterioration modelling is evident in the literature. The uncertainties in the deterioration modelling process can be reduced by introducing additional information, through a range of inspection and monitoring procedures carried out at different stages of the structure’s life, resulting in increased confidence in the predicted performance.
A methodology has been developed by the authors [
This paper describes the development of updating procedures incorporating information from multiple sensors with a view of predicting the performance of the monitored domain with increased confidence. These are demonstrated through application on concrete structures prone to chloride-induced deterioration.
In general, deterioration of concrete structures is associated with the corrosion of reinforcement embedded in concrete [
Generally aggressive agents penetrate from outside sources; for example, the amount of chloride cast into concrete is limited by design codes, but the problem starts as chloride ions ingress from outside. Whatever the source (de-icing salts, marine environment), the ingress is a complex phenomenon and involves different transport processes, for example, initial penetration, absorption and capillary suction, and diffusion. The deterioration processes in concrete have been modelled using a variety of approaches, for example, based on Fick’s 2nd law of diffusion [
Uncertainty in the variables involved in the deterioration process is generally modelled using random variables. Spatial variability of the deterioration process and lack of knowledge regarding its details also contribute towards the complexity in modelling deterioration and associated uncertainty (e.g., [
A typical model for the time to corrosion initiation based on Fick’s second law of diffusion is presented:
Distribution for the corrosion initiation time.
This curve can be interpreted in two different ways. The ordinate gives the probability that corrosion initiation at rebar level will be reached up to any particular point in time (abscissa). If an acceptable (tolerable) target probability can be specified, the curve could be used to estimate the point in time at which certain management actions are to be taken (e.g., if a target probability of 0.3 is considered, actions such as principal inspections would be needed after 10 years). On the other hand, assuming spatially uniform conditions, the ordinate may be interpreted as the fraction of the area of a member exhibiting corrosion activity normalized by the total area. In this case, the target (or threshold) would represent the maximum corrosion damage tolerated for any particular member or structure.
The mechanism of corrosion may be split into two phases, “initiation” and “propagation” [
During the initiation phase, the corrosion risk of a reinforced concrete structure can be monitored through either chloride content measurements, or by measuring the penetration of the threshold chloride contents, in the cover concrete. Chloride measurement probes have been developed though they appear to still be in the testing and validation stage. Corrosion risk probes have also been developed, and instruments available for this include the following: Ladder Arrangement (Figure Metallic Nail System; Expansion Ring System (Figure
Ladder arrangement [
Expansion Ring System [
The ladder arrangement can be installed in new structures or during repair works in existing structures. Expansion ring and Metallic nail systems can also be installed into existing structures without damaging the existing concrete cover. The working principle for all three systems is identical. Small pieces of steel are installed at various known depths into the cover concrete and the corrosion activity of these pieces is monitored. Corrosion initiation at these steel pieces gives an indication of the corrosion penetration depth into the cover concrete. A curve of the corrosion penetration depth is plotted against time, which can then be extrapolated to predict the time to corrosion initiation at the rebar level. It is worth mentioning that these instruments are still at their infancy but have delivered promising results in laboratory conditions. These are being tested on actual structures but very little is available in the current literature about their effectiveness in the field conditions.
Limitations in the use of predictive models and SHM methods in predicting future performances have been highlighted in the previous sections. There are clear benefits in combining the information from the two sources. However, this information is often diverse in quality and quantity and is subject to various uncertainty sources. Thus, a primary objective of combining prior information with monitoring data should be to combine uncertainties, whilst realising that there are different and diverse sources.
A powerful and versatile approach dealing with performance evaluation and prediction of systems in the presence of uncertainty is the Bayesian approach. This approach has had a significant impact in nuclear plants assessment and in the evaluation of healthcare system. More recently, similar techniques have been used successfully in offshore installations and steel bridges, for the planning and optimization of inspection and maintenance schedules [
A framework has been proposed that combines the information obtained from SHM with deterioration modelling to improve the confidence in the predicted performance [
Let the probability distribution for the ‘‘prior time to failure’’ at location
When the health monitoring system confirms the attainment of a limit state at the sensor location (confirmation of “failure”) at a given time (i.e., second updating scenario), the “time of failure” at the sensor location would be equal to the time of attainment of the limit state, that is,
Combining the two scenarios and using Bayesian event updating framework, the posterior distribution for the “time to failure” for a total of “
An inherent assumption in the above methodology is that there is only need to consider one location at which both prior and posterior (i.e., using monitored data) distributions are considered. In practice, the extent of deterioration varies considerably from one location to another. These variations can be attributed to the temporal and spatial effects of different variables involved in the deterioration process, within the element and/or for different elements of a system. The actual performance in such cases could be different for different elements of a system and even at different locations of the same element. In order to explore the application of the Bayesian methodology in cases where temporal and spatial influences are present, it is assumed that the monitored domain can be subdivided into a number of smaller zones with the possibility of installing sensors within each zone. The distance between the sensors, and hence the physical size of the zone, should be large enough to avoid any spatial correlation on sensor outputs. On the other hand, the zone should be small enough to justify the assumption of uniform performance over its entire physical size.
Multiple sensors may be deployed in another scenario, that is, to increase confidence in the performance prediction of a critical location, or when a robust/redundant monitoring system is required due to critical nature of a zone.
The two cases could exist in combination, for example, a bridge deck, as shown schematically in Figure
A structural member divided into five zones.
The updating procedure to account for data from multiple sensors needs to be developed for each of the two cases bearing in mind the nature of the decision that needs to be considered. In the former case (multiple sensors in different zones), the interest is to determine updated predicted performance for the entire system under consideration. In the later case (multiple sensors in the same zone), the interest lies in improving the confidence in prediction of performance within the individual zone, or to increase the redundancy of the monitoring system at critical locations.
Consider a system divided into a number of small zones and a sensor located in each zone. The outcome of health monitoring in this case would be the ‘‘actual time to failure’’ at certain depth of each zone. The difference between “times to failure” at certain depth in each of these zones could reflect the spatial variation of deterioration phenomenon (due to variation in microclimate, environmental characteristics or material properties, etc.). In this case, the “time to failure” at sensor location,
The distribution for posterior “time to failure” of the system,
In this case the objective is to either increase robustness of health monitoring instruments or to increase the confidence in prediction depending upon the critical nature of the zone under consideration. Hence, the sensors would be located relatively close to each other (within the same zone) and the assumption is that the deterioration would be uniform within that zone.
Bayesian updating can thus be applied for multiple sensors to improve confidence regarding prediction of performance of the zone under consideration. The posterior distribution for the “time to failure” using data from first sensor (that can be selected at random as the sequence is irrelevant) will be obtained from (
The above methodologies are explored in detail through a case study on a concrete member subjected to chloride-induced deterioration.
In this study the system updating methodology is applied to a bridge element prone to chloride-induced deterioration. In order to demonstrate the performance updating methodology for sensors in different zones, the element is hypothetically divided into five zones with a corrosion risk sensor located in each zone. For the purpose of demonstrating the updating methodology for multiple sensors installed within the same zone, three sensors are assumed within the same zone. The results for the two cases are presented separately in this paper to explore their characteristics.
Table
Distribution type and values of its parameters for basic random variables.
Parameter | Mean | C.O.V. | Distribution | Reference |
---|---|---|---|---|
|
3.5 Kg/m3 | 0.5 | Lognormal | Vu and Stewart [ |
|
5 × 10−5 m2/yr | |||
Model error ( |
1.0 | 0.2 | Normal | Vu and Stewart [ |
|
0.9 Kg/m3 | 0.19 | Uniform (0.6–1.2 Kg/m3) | Vu and Stewart [ |
|
1.0 | 0.2 | Lognormal | Lentz et al. [ |
|
40 mm | 0.1 | Normal | Chryssanthopoulos and Sterrit [ |
|
10, 20, and 30 mm (fully correlated) |
|
Normal | |
|
0.1 years | Deterministic |
Using these variables and the performance equation (
Prior corrosion initiation time at rebar level.
The posterior predicted performance (corrosion initiation times) assuming five sensors (at 10 mm cover depth) distributed along the plan (i.e., member divided into five zones) is shown in Figure
Corrosion initiation time at rebar level for different percentages of sensors showing initiation (at 10 mm depth).
It is clear from the figure that if all the sensors show the same output, that is, either corrosion initiation or passivity confirmation at a given point in time, the uncertainty associated with predicted performance is considerably less than in the case where even one sensor shows opposing results.
It can also be seen that uncertainty levels for the case when all sensors show corrosion initiation (COV = 0.48) is considerably less than the case when passivity is confirmed at the sensors (COV = 1.71). This is because the quality of information available with the initiation confirmation case being higher (i.e., the time to corrosion initiation at the sensor location becomes available) than the passivity confirmation case (i.e., the time to corrosion initiation at the sensor location is larger than the time of monitoring, but is still an unknown quantity).
Assuming that a management action (such as a principal inspection) will be required when the probability of corrosion initiation reaches 0.3, the time for next inspection, based entirely on the prior predictive model, is 10 years. It can be seen from Figure
The results (posterior corrosion initiation time) assuming one, two or three sensors in the same zone are shown in Figure
Effects of Bayesian updating for multiple sensors along the plan showing passivity confirmation.
It is clear that increasing the number of sensors in the same zone would increase the confidence regarding the prediction of performance (as COV for the corrosion initiation time is reducing continuously). Similar to the previous case, assuming the limiting value for the probability of corrosion initiation as 0.3, the timing for a management action (i.e., a Principal Inspection) can be evaluated. It can be seen from Figure
A similar trend can be seen for the case where the sensors show initiation of corrosion at year 1.0 (Figure
Effects of Bayesian updating for multiple sensors along the plan for initiation confirmation.
Uncertainties in the performance prediction of infrastructure facilities have a profound effect on the management decisions such as the timing of inspections and repairs. These uncertainties can be considerably reduced by effectively integrating the data obtained through health monitoring systems into the assessment and prediction procedures.
Due to the spatial effects of deterioration and/or to increase the redundancy of the monitoring systems, multiple sensors are required at various locations of the system. An approach for combining data from such multiple sensors is outlined in this paper. Two cases of updating have been identified and results for both of these have been summarized and discussed. It has been shown that the performance of a monitored domain representing a member, a structure, or an entire system can be updated using the proposed Bayesian procedures. Their application for chloride-induced deterioration in bridges has shown their effectiveness in reducing the associated uncertainties or in obtaining overall performance prediction of the member/structure by rationally combining similar data obtained through sensors at different locations. These methodologies can be used as a tool in the reliability-based management of structural systems to gain confidence in performance predictions and hence in the optimization of management activities such as repairs, maintenance, and inspections. With regard to the type of data being obtained (discrete versus continuous), it has been shown that continuous data can be converted to discrete form using limit state functions for simple applications. It is acknowledged here that the quality of information (obtained from the SHM) has a direct impact on the updated distribution; hence, the full potential of continuous data may not be apparent by using these procedures. The methodology needs to be refined and developed for such cases and this is the subject of ongoing research.
More research is also needed in other related aspects, for example, to establish the optimum number of sensors required and their distribution within the system to maximize the effectiveness of the health monitoring systems, and the development of procedures to incorporate/handle misinterpreted data and unexpected results.
Similarly, the methods for effective integration of the predicted performance of individual zones, and of the entire structure, into bridge management systems (i.e., optimization of inspection, maintenance and repair activities, etc.) need to be further developed/refined. The approach detailed herein would also benefit from being tested in the field.
The author would like to acknowledge Professor Marios Chryssanthopoulos at the University of Surrey and Professor Toula Onoufriou from Cyprus University of Technology for their unconditional support and advice during the course of this project. Their support has been vital for the success of this project and of course for the completion of his Ph.D. in this area. The author would also like to acknowledge the funding provided by the ORSAS and URS Scholarships to fund this study as part of his Ph.D.