LONG-TERM SEISMIC PERFORMANCE OF RC STRUCTURES IN AN AGGRESSIVE ENVIRONMENT
For structures located in a moderately or highly aggressive environment, multiple environmental and mechanical stressors lead to deterioration of structural performance. Such deterioration will reduce the service life of structures and increase the life-cycle cost of maintenance actions. Various environmental stressors affect the degradation mechanisms of structures. However, the exact influence of these stressors is difficult to predict, as their influence vary in time and space. Because of the presence of such uncertainties, long-term structural performance must be predicted based on probabilistic concepts and methods, and life-cycle reliability assessment methodologies must be established. Design, assessment and performance of deteriorating structures are major issues for the application of probabilistic methods in life-cycle analysis.
Many researchers have reported theoretical predictions of structural performance as a function of time. Even though some accurate structural models have been developed for corroded reinforced concrete structures subjected to monotonic flexure and/or shear, studies on seismic performance including corrosion damage are scarce. Earthquakes are still a dominant hazard to structures in many parts of the world. For the lifetime assessment of structures in aggressive environments and earthquake prone regions, the effects of corrosion on seismic performance need to be taken into consideration. Within this context, life-cycle seismic reliability of reinforced concrete (RC) structures in a marine environment is discussed.
Figure 1 shows the flowchart describing the framework for computing the life-cycle seismic reliability of RC bridge structures in a marine environment. This flowchart consists of three main parts: (a) determining the seismic capacity of corroded RC structures based on inspection results and monitoring, and predicting the seismic fragility curve (PART (a)); (b) two kinds of hazards combining the seismic hazard and the hazard associated with airborne chlorides (PART (b)); and (c) estimating the time-dependent structural reliability including updating (PART (c)).
In PART (a), experimental data on the seismic performance of corroded RC structures are collected from the existing literature, and the relationship between material deterioration and structural capacity is experimentally investigated. Then, based on the experimental results, numerical models for evaluating capacities of corroded RC structures are presented. These models must predict not only the structural strength but also the hysteresis loops and displacement ductility. For existing structures, inspection results obtained from non-destructive testing methods can become input data for numerical analysis to evaluate their seismic capacity. This makes it possible to improve the accuracy of predicting the seismic capacity of corroded structural components.
Regarding PART (b), in seismic reliability assessment and prediction of RC structures located in an aggressive environment, two kinds of hazards must be accounted for: seismic hazards and hazards associated with other environmental stressors. Unlike conventional probabilistic seismic hazard analysis (PSHA), environmental hazard assessment lacks significant research. Therefore, the appropriate methodology for quantifying environmental influences must be established. Whereas the seismic demand depends on the results of seismic hazard assessment, the deterioration of seismic capacity depends on the environmental hazard assessment. Based on the seismic capacity and hazard assessment obtained from PARTS (a) and (b), an analysis of the life-cycle reliability of structures under earthquake excitations, including corrosion damage, is presented in PART (c). Results provided by visual inspection, nondestructive inspection, and/or monitoring can update the random variable used in time-dependent reliability analysis, and improve the accuracy of the present and future failure probability of failure.
Seismic Capacity of RC Columns in a Marine Environment
The probabilistic assessment of structures under seismic hazard has developed rapidly over the last two decades. A probabilistic methodology developed by Cornell and his co-workers for seismic risk assessment of moment-resisting steel frames has been widely used. The potential of this methodology to provide seismic risk assessments of RC bridge structures has been investigated. In addition, several researchers have discussed the fragility curve, which expresses the probability of a structure reaching a certain damage state under a given ground motion intensity. This fragility curve plays an important role in the overall seismic risk assessment of structures. The purpose of these past studies was to present more efficient computational methods for estimating the seismic reliability of bridges.
However, little attention has been devoted to the assessment of the seismic reliability of corroded structures. Since corrosion accelerates the vulnerability of bridges subjected to seismic hazard, it is important to consider the effect of corrosion on lifetime seismic reliability of bridges in earthquake-prone regions and aggressive environments. Since ductility loss frequently occurs when considering the response of corroding structures even under monotonic loads, the intensity of corrosion process could have a considerable influence on the behavior of RC columns under cyclic loads. Performing the analysis at the section level using the reduced steel rebar cross-section may be an oversimplification to evaluate the seismic capacity such as a ductility capacity used in the reliability estimation of deteriorating RC structures. As a result, it is difficult to determine whether the seismic safety of deteriorated bridge pier with corrosion cracks in a marine environment as shown in Fig. 2 is compromised, or to explain how long this bridge pier will have a safety level above a prescribed threshold. Improving the understanding of the influence that corrosion has on the seismic performance of structures is needed.
Recently, there have been experimental studies on corroded columns subjected to cyclic loading. These experiment shows that as the amounts of corrosion of the longitudinal rebar increases, the displacement ductility capacities and flexural capacities of beams decrease. It is impossible to simulate the behavior of corroded RC member subjected to cyclic loading by using a very simple model such as design equation in seismic design code. To establish a numerical method for analyzing corroded RC members, it is necessary to consider the effects of cracking of concrete cover due to expansion of corrosion products and bond degradation between concrete and steel on the seismic capacity, together with the reductions of cross-section of rebars.
It is necessary in seismic reliability analysis to relate deformation demands placed on structural components with the probability of reaching specific levels of damage. The onset of buckling of longitudinal rebars in RC component is a key damage state. This is because rebar buckling requires extensive repairs. Figure 3 shows an example of plastic hinge analysis to evaluate the plastic rotation and displacement ductility at the onset of rebar buckling of corroded RC bridge pier. Using the steel corrosion amount and concrete deterioration derived from measurements of corroded specimens, computational results are in good agreement with the experimental results as shown in Fig. 4. A combined experiment and analysis assessment procedure can provide reliable techniques to assess the seismic capacity of corroding RC structures.
To reach satisfactory computational results on the capacity of an existing RC structure, the key problem is the collection of reliable data on the corrosion level and concrete deterioration in the field. What is actually important and difficult in numerical simulation is how to accurately predict the degree and location of material deterioration in a real structure and how to adequately represent them in terms of input data in the structural analysis. In particular, since ductility capacity and energy dissipation depend strongly on localized condition of reinforcements in the plastic hinge, further research is needed on the modelling of spatial variability of steel corrosion, even though some researchers reported spatial time-dependent reliability analysis. Recently, X-ray technology has been applied to the visualization of concrete cracking to investigate the behavior of fracture process zone in concrete. This lab. established the digital picture processing method for X-ray photography to estimate the amount of corrosion products in RC components. Figure 5 shows pictures of corroded tensile rebar in singly RC beam using X-ray. In addition, corrosion cracks on bottom surface using digital camera and geometry of RC beam are shown in Fig. 5. This beam was corroded by electric corrosion. The pictures using X-ray were taken at Wxray, g = 0.0%, 2.9%, 9,7%, 19.7%, 25.6%, and 27.3%, where Wxray, g is the averaged steel weight loss of tensile rebar within the constant-moment region. After taking the pictures with Wxray, g = 27.3 %, the beam was tested under a monotonically increasing load until failure by using a four-point bending setup. The steel weight loss was estimated based on pictures using X-ray taken from various angles. As shown in Fig. 5, as the steel weight loss increases, the diameter of tensile rebar decreases and crack width on bottom surface increases. Figure 6 shows the relationship between distance from left loading point in Fig. 5 and local steel weight loss of tensile rebar along the rebar, Wxray, l. Figures 5 and 6 indicate that the location with maximum Wxray, l depends on Wxray, g. Also, the difference between maximum and minimum Wxray, l ranges from 10 % to 15 %, independent of Wxray, g, when Wxray, g is larger than 9.7 %. Using X-ray technology, corrosion process in RC component can be observed continuously. These experiments will help improving the accuracy of estimation of the corrosion distribution and corrosion amount of rebar.
When a computational model to evaluate the seismic capacity of corroded RC structures is established, the effect of corrosion amount of rebars on fragility curve can be examined. Figure 7 depicts an example of fragility curve of RC bridge pier with steel corrosion amount in plastic hinge Cw = 0%, 20%, and 40%. The vertical axis in Fig. 7 represents the conditional failure probability of seismic demand De exceeding the seismic capacity Ca given seismic intensity (i.e. maximum velocity at the bedrock). The fragility is estimated from the ratio of the number of times De exceeds Ca to the total number of Monte Carlo Simulations. De is calculated by nonlinear dynamic analysis using a number of ground motions. Ca is evaluated as displacement ductility at the onset of rebar buckling of corroded RC bridge pier by buckling analysis. It should be noted that in fragility analysis, the differences of seismic and airborne chloride hazards among bridges are not taken into consideration. Combining the evaluations of De and Ca with hazard analysis associated with earthquake and airborne chloride, respectively, life-cycle reliability of bridge pier can be obtained. In the fragility analysis, an RC bridge pier was modeled as single degree of freedom (SDOF), and the longitudinal rebars buckling of this pier was considered as the sole limit state when estimating the fragility. To capture the true demands on RC bridges, the nonlinear dynamic analytical model of RC bridge used in seismic fragility analysis must be enhanced. Also, to evaluate failure probability of RC bridge, additional limit states need to be considered (e.g. limit state for corroded steel bearing).
Using this information, the relationship between time, amount of corrosion and seismic capacity could be established as shown in Fig. 8. Using the relationship between time and amount of steel corrosion provided by the analysis of material transport and material deterioration, the prediction of seismic fragility at any time after construction could be provided. For future prediction of seismic capacity, some parameters used in the analysis of material transport and material deterioration have to be updated based on information provided by inspection and monitoring on site (see Fig.1), and the effect of the location of structures in a marine environment on their seismic capacity must be taken into consideration. In addition, to predict seismic performance accurately, further studies are needed on the interaction between microscopic chloride and water diffusion and internal damage of concrete component due to seismic loading.
Hazard Assessment
In conventional seismic hazard analysis, it is assumed that earthquakes occur randomly and independently. The annual probability that the random intensity at a specific site will exceed a value is
(1)
This probability is
(2)
Attenuation relationships, also called ground-motion prediction equations, play a key role in PSHA. When the attenuation uncertainty is involved, the random intensity is
(3)
Then Eqn. (2) can be expressed as
(4)
The seismic hazard curve is obtained from Eqn. (1) for various values of seismic intensity. Figure 9 shows the example of seismic hazard curves in Japan.
Earthquake environment is quantified by seismic hazard curve as indicated in Fig. 9. A marine environment should be quantitatively assessed and the evaluation results should be reflected in the estimation of life-cycle performance of RC structures. Even though many probabilistic methods for the evaluation of deterioration of RC bridges subjected to chloride attacks have been reported and a probabilistic framework for life-cycle analysis of RC structures has been established, prior studies have not taken into consideration the hazard associated with marine environment.
The probabilistic model of hazard associated with airborne chlorides taking into account the spatial-temporal variation was proposed by this lab. As shown in Fig. 10, the amount of airborne chlorides decreases with increasing the distance from the coastline, as does the seismic intensity (e.g., the peak ground acceleration attenuates with distance from seismic source). Since in Japan the wind usually blows from west to east, the structures near the Sea of Japan (East Sea) have suffered most from severe damages due to airborne chlorides. The speeds of wind, the ratio of sea wind (defined as the percentage of time during one day when the wind is blowing from sea toward land), significant wave height, and the distance from the coastline affect the amount of airborne chlorides. The attenuation relation associated with airborne chloride can be obtained from measured airborne chlorides. The ratio of sea wind, average wind speed u, and significant wave height h are obtained from the meteorological data collected. Then, to obtain the hazard curve associated with airborne chlorides, similar equations to those used to obtain seismic hazard curves can be used. The probability that Cair at a specific site will exceed a prescribed value cair is
(5)
Figure 11 shows the probability of exceedance of various amounts of airborne chlorides in City A at d = 1.0 km, City B at d = 0.1 km, and City C at d = 0.1 km. Figure 12 shows the relationships between the mean of steel weight loss and time for RC bridge pier, assuming that RC bridge pier is located in City A, City B and City C. The means of steel weight loss in Fig. 12 depends on hazard curve associated with airborne chloride. Based on the hazard assessment associated with airborne chlorides, the effect of different marine environment and distance from the coastline on bridge performance can be quantified.
These hazard curves indicate the large uncertainties involved in the evaluation of marine environment. These uncertainties affect the seismic reliability of RC structures. In order to develop a rational maintenance strategy, it is necessary to try to reduce the epistemic uncertainties associated with hazard assessment, in particular the scatter on attenuation relations. In PSHA, the issue of avoiding physically unrealizable ground-motion amplitudes becomes important. From a physical point of view for hazard assessment associated with airborne chlorides, spatial spread has to be modeled instead of simply attenuation relation. Also, the effects of precipitation and the differences in coastal topography (e.g., sand beach and reef) on the amount of airborne chlorides need to be considered.
Life-Cycle Seismic Reliability Including Corrosion Damage
When only seismic hazard and one limit state are considered, the expected risk is
(6)
In the calculation of the conditional probability P[S |Γ=α] of structures subjected to aggressive environment (e.g. marine environment), the effect of corrosion on this probability has to be taken into consideration. In seismic reliability analysis of structures in marine environment, the structural capacity such as the displacement at the occurrence of buckling of longitudinal rebars of RC bridge pier depends on the results of hazard associated with airborne chlorides; however, the demand depends on the results of seismic hazard assessment. By assuming that seismic capacity and demand are statistically independent and that the occurrence of earthquake is modeled as a Poisson’s process, the annual probability of exceedance of seismic capacity Ca under earthquake excitation at t years after construction can be expressed by the total probability theorem as
(7)
During a given time interval T, the cumulative-time failure probability pf of bridge pier subjected to both seismic hazard and hazard associated with airborne chlorides is
(8)
It is assumed in Eqn. (8) that the events associated with the failure probabilities at different times t are statistically independent. However, in reality, they are dependent through the strength. There have been studies providing seismic hazard estimates based on non-Poissonian seismicity. Since the lifetime of the structure is much shorter than the return period of earthquake, the assumption of using the same seismic hazard curve p0 (γ) for time interval T could be acceptable. However, further research on the effect of the degree of correlation among the random variables at different times, and time-dependent seismic hazard on life-cycle reliability of structures is needed.
The relationships between cumulative-time failure probability and time after construction of RC bridge pier are shown in Fig. 13, using the seismic hazard curves in Fig. 9 and airborne chloride hazard curves in Fig. 11. To examine the effect of corrosion on the safety of the bridge pier, cumulative-time failure probabilities without deterioration (i.e. annual failure probability pfa(t) does not depend on time after construction) are also shown in Figure 13. At the beginning, the failure probability of the bridge piers only depends on the seismic hazard, and the RC bridge pier located in City A has the highest failure probability. However, as shown in Figure 11, the probability of exceedance of a prescribed amount of airborne chloride in City C is much higher than that in City A. The cumulative-time failure probability of RC bridge pier in City C increases with time due to chloride attack. The difference between the cumulative-time failure probability associated with both seismic and airborne chloride hazards and that associated with seismic hazard alone is the largest for City C. Finally, at 50 years after construction, the cumulative-time failure probability of RC bridge pier in City C is the highest, although the seismicity in City C is the lowest among three cities. Regarding RC structures in an earthquake region and marine environment, the decision on seismic retrofit, and/or repair due to material deterioration should be supported by the multiple hazard assessments of environments surrounding the structure analyzed. Even though randomness (or aleatory uncertainty) cannot be reduced, improvement in our knowledge or in the accuracy of predictive models will reduce the epistemic uncertainty. This means that for existing structures, the uncertainties associated with predictions can be reduced by the effective use of information obtained from visual inspections, field test data regarding structural performance, and/or monitoring. This information helps engineers to improve accuracy of structural condition prediction. However, the updated random variables do not follow, in general, widely used PDFs (such as normal, lognormal, etc.). The difficulties of the solution in Bayesian updating depend on the relationships between observed physical quantities, such as inspection results, and the PDFs of associated random variables. For problems in which all these relationships are linear and all random variables are modeled as Gaussian, a closed form solution exists. When nonlinear relations or non-Gaussian variables are involved, a rigorous theoretical approach is generally impossible to implement in realistic cases. An approximate solution can, however, be found by using several approaches. Monte Carlo (MC) approach is in general used because of its versatility. MC based methods for non-linear filtering technique have been developed since 1990s. These methods include MC filter, Bootstrap filter, recursive MCS, sequential MCS, the Sampling Importance Resampling (SIR) method, and the Sequential Importance Sampling with Resampling (SISR). Figure 14 shows the procedure for estimating the time-dependent reliability of existing RC structures using MC-based reliability analysis. As previously indicated, the information obtained from inspection and/or monitoring can be used to reduce epistemic uncertainties and, consequently, to better estimate the seismic reliability of RC structures in an aggressive environment.
DEVELOPMENT OF BRIDGE PIER WITH VARIABLE SURFACE INCORPORATED INTO FRICTION PENDULUM ISOLATION SYSTEM
Bridge piers with constant curved surface incorporated into friction pendulum isolation system (FPIS) was previously presented. However, this bridge pier under strong excitations shows large uplift of superstructure, and causes large lateral force to bridge pier due to constant curved surface. In this study, the surface combining with curve and line in FPIS has been developed. Proposed bridge pier has oscillation frequency decreasing with sliding displacement, and the restoring force has an upper bound so that the force transmitted to the bridge pier is very limited. Based on the shaking table test (see Fig. 15) and analytical approach (see Fig. 16), optimal variable surface to maximize the seismic performance of bridge has been identified.
