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Existing structures may suffer from resistance deterioration due to repeated attacks. The modeling of resistance deterioration is a critical ingredient in the reliability assessment and service life prediction of these degraded structures. In this paper, an explicit compound Poisson process-based model is developed to describe the shock deterioration of structural resistance, where the magnitude of each shock deterioration increment is modeled by a Gamma-distributed random variable. The moments (mean value and variance) and the distribution function of the cumulative shock deterioration are derived in a closed form, based on a proposed W-function. A method for the efficient calculation of the W-function is presented, which reduces to the Bessel type I function if the shock deterioration increment is exponentially distributed (a special case of Gamma distribution). The proposed shock deterioration model is applicable to either a stationary or a nonstationary Poisson process of random jumps. Subsequently, the overall resistance deterioration is modeled as the linear combination of gradual and shock deteriorations, based on which the proposed model can be used in the time-dependent reliability assessment of aging structures efficiently. A numerical example is presented to demonstrate the applicability of the proposed deterioration model by estimating the time-dependent reliability of an aging bridge. It is found that a smaller threshold for the degraded resistance leads to greater mean value and standard deviation of the time to failure, and this effect is enhanced by a smaller occurrence rate of the shock deterioration.

The use of underground spaces is becoming increasingly important in this era of rapid urbanization and population growth. However, underground spaces are susceptible to water ingress, which may trigger the deterioration of their structural performance and reduce their serviceability. This highlights the importance of the proper design of lining structures with an emphasis on water penetration. This study develops a reliability-based approach to guide the design of lining structures used for underground spaces. The equivalent depth of water seepage is considered for a two-dimensional lining structure in the presence of the randomness and spatial correlation of the water seepage distribution. The probabilistic behavior of the equivalent seepage depth that is derived serves as the basis for reliability-based design of lining structures. A simple design criterion is developed. An example is presented to demonstrate the applicability of the proposed approach.

Reliability assessment of engineered structures is a powerful and useful concept to estimate the structural capacity of withstanding hazardous events during their service lives. Taking into...

The durability design of reinforced concrete (RC) structures that are exposed to aggressive environmental attacks (e.g., corrosion due to chloride ingress in marine environment) plays a vital role in ensuring the structural serviceability within a reference period of interest. Existing approaches for the durability design and assessment of RC structures have, for the most part, not considered the spatial distribution of corrosion-related structural properties. In this paper, a closed-form approach is developed for durability assessment of RC structures, where the structural dimension, spatial variability, and correlation of structural properties such as the concrete cover thickness and the chloride diffusion coefficient are taken into account. The corrosion and crack initiations of an emerged tube tunnel segment that was used in the Hong Kong-Zhuhai-Macau bridge project were assessed to demonstrate the applicability of the proposed approach. The accuracy of the method was verified through a comparison with Monte Carlo simulation results based on two-dimensional random field modeling. The proposed method can be used to efficiently assess the durability performance of RC structures in the marine environment and has the potential to become an efficient tool to guide the durability design of RC structures subjected to corrosion.

Elastic cables have the advantages of desirable seismic mitigation effect, low cost, and convenient installation, and have been used widely in low-to-mid-span bridges. However, their utiliz...

The environmental or anthropogenic factors, to which the in-service bridges are subjected, are responsible for the reduction of bridge performance, and finally lead to great service risk for bridges and increase the probability of substantial economic losses. Probability-based estimate of bridge resistance is an essential indicator for the bridge condition evaluation and for optimization of bridge maintenance/repair decisions. It places an emphasis on the proper probabilistic models of structural properties and assessment methods. Making full use of historical service load information may improve the accuracy of bridge performance assessment with reduced epistemic uncertainty for existing aging bridges. In to-date analyses to update the bridge resistance with past service information, the models of resistance deterioration have been assumed as either deterministic or fully correlated, which may differ significantly from the realistic case. With this regard, this paper proposes a novel method for updating the resistance of service-proven bridges with a realistic deterioration model. The Gamma stochastic process has been suggested in the literature to describe the probabilistic behavior of structural time-dependent resistance and thus is adopted in this paper. An illustrative bridge is presented to demonstrate the applicability of the proposed method. Parametric examples are conducted to investigate the role of resistance deterioration model in the updated estimate of bridge resistance with historical service information. Keywords: Existing aging bridges, Historical load information, Resistance updating, Gamma deterioration process, Bridge safety

Electric power systems play a critical role in assuring modern society’s functionalities. Earthquakes are one of the most destructive natural hazards that affect the serviceability of electricity t...

Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing the seismic behaviour of bridges subjected to moderate to high seismicity due to its simplicity. However, in existing analysis methods, the generation of pushover curve needs tremendous amount of computational costs and requires skills, which may halter its application in practice, implying the importance of developing practice-oriented analysis method with improved efficiency. Moreover, the bridge pier performance has been modelled as deterministic, indicating that the variation associated with the pier material and mechanical properties remains unaddressed. The correlation in the performance of different piers also exists due to the common design provisions and construction conditions but has neither been taken into account. This paper develops a simplified pushover analysis procedure for the seismic assessment of simply supported RC bridges. With the proposed method, the pushover curve of the bridge can be obtained explicitly without complex finite element modelling. A random factor is introduced to reflect the uncertainty in relation to the pushover curve. The correlation in the pier performance is considered by employing the Gaussian copula function to construct the joint probability distribution. Illustrative examples are presented to demonstrate the applicability of the method and to investigate the impact of variation and correlation in bridge pier behaviour on the seismic performance assessment. Keywords: Seismic assessment, Simply supported RC bridge, Nonlinear analysis, Simplified method, Variation in pier behaviour, Correlation in pier behaviour

In probabilistic analyses and structural reliability assessments, it is often difficult or infeasible to reliably identify the proper probabilistic models for the uncertain variables due to limited supporting databases, e.g., limited observed samples or physics-based inference. To address this difficulty, a probability-bounding approach can be utilized to model such imprecise probabilistic information, i.e., considering the bounds of the (unknown) distribution function rather than postulating a single, precisely specified distribution function. Consequently, one can only estimate the bounds of the structural reliability instead of a point estimate. Current simulation technologies, however, sacrifice precision of the bound estimate in return for numerical efficiency through numerical simplifications. Hence, they produce overly conservative results in many practical cases. This paper proposes a linear programming-based method to perform reliability assessments subjected to imprecisely known random variables. The method computes the tight bounds of structural failure probability directly without the need of constructing the probability bounds of the input random variables. The method can further be used to construct the best-possible bounds for the distribution function of a random variable with incomplete statistical information.

Many existing bridges suffer from resistance deterioration due to environmental or operational attacks and thus may rate under the anticipated performance requirements. The proof load testing is a commonly used approach to evaluate whether the bridge would have the capacity of carrying a certain load. The magnitude of proof load will determine the safety level of the proven bridge. A proof load test, if not designed properly, may potentially cause structural damage and even collapse to the bridge. This implies that the load testing should be oriented by a probability-based framework in an attempt to control the failure probability of the bridge. However, the current engineering practice insufficiently considers the risk control of proof load testings. This paper presents a reliability-based framework to guide and optimize the proof load testing for existing bridges. A mathematical model is developed to compute the target proof load, where two types of constraints are considered simultaneously: the acceptable structural safety level and the economic costs. A numerical example is presented to demonstrate the applicability of the proposed method. The framework developed in this paper can be used in practical engineering as an auxiliary decision-making tool for bridge load testings.

The historical vehicles passed through an existing bridge can be regarded as proof-loading tests for the bridge, and, as a result, are evident of the bridge’s performance. Such service history information has been utilized to update the estimate of bridge resistance in previous studies with the help of a Bayesian method, where the resistance deterioration process was assumed to be independent of the vehicle load process. This assumption is, however, untenable in many cases where the deterioration stochastic process is statistically correlated with the load process (e.g., a greater load intensity may affect/accelerate the deterioration of structural resistance and the accumulation of structural fragility). With this regard, this paper investigates the effect of correlation between the resistance deterioration and load processes on updating the resistance of aging bridges with prior service load information. The copula function is employed to model the joint distribution of the correlated deterioration and load processes, with which the correlation is measured by the Kendall’s tau. A new method is developed in this paper to assess the updated bridge resistance taking into consideration the deterioration-load dependency in an explicit form. The applicability of the proposed method is illustrated using an existing RC beam bridge. The sensitivity analysis is conducted to examine how the deterioration-load dependency affects the updated resistance of service-proven aging bridges.

An important element of time-dependent reliability analysis of civil structures is choosing a proper model for the applied loads. Stochastic process theory has been widely used in existing ...

Tropical cyclones (TCs) are among the most costly natural hazards affecting civil construction in coastal areas, which have caused extensive economic losses and social disruption world-widely. Moreover, the intensity and/or frequency of future TCs have been projected to change with time due to the potential impacts of climate change, indicating the potential of ever larger TC damages for coastal regions. The estimate of future TC damage should be conducted under a probability-based framework, taking into account the uncertainties associated with both the TC characteristics (e.g., intensity and frequency) and the vulnerability of the coastal communities of interest. In this paper, an explicit approach is developed to evaluate the TC damage for TC-prone areas considering the potential impacts of climate change. The mean value and variance, as well as the cumulative density function of cumulative TC damage are estimated quantitatively. The proposed method is applied to TC damage assessment of Hong Kong, China – a TC-prone area which has suffered severely from historical cyclones. Sensitivity analysis is also performed to investigate the impacts of the time-variant characteristics of both the TC process and the TC damage conditional on one TC event on the cumulative damage costs for coastal areas.

Aging of structural performance and significant external loads may impair structural safety and serviceability and cause potential economic losses. In the presence of uncertainties associated with both resistance deterioration and external loads, structural safety shall be estimated quantitatively under a probability-based framework. A stochastic load process is often auto-correlated on the temporal scale, with correlations arising from both the occurrence times and intensities. Moreover, a deterioration process is physically dependent on the load magnitudes. This paper investigates the impacts of load temporal correlation and deterioration-load dependency on time-variant structural reliability. The load occurrence process is modeled as a Poisson point process with correlated separation time between two load events. The correlation between the intensities of load events is described by the multi-variate Gaussian copula function. The resistance aging process is considered to be a combination of both gradual and shock deteriorations. Four candidate copula functions, namely Gaussian, Clayton, Gumbel and Frank, are considered to model the dependency of shock deterioration on load intensity. Two types of failure mechanisms are considered: the first is due to the load effect exceeding the resistance, and the second occurs when the cumulative damage within the considered service period reaches the permissible level. A simulation-based method is developed to estimate structural reliability considering the two failure modes. Illustrative examples are presented to demonstrate the applicability of the proposed method. Parametric studies are conducted to investigate the impacts of temporal correlation in loads and deterioration-load dependency on structural failure probability.

In-service civil structures are often subjected to repeated external loads (shock events), which may lead to an accumulation of structural damage and further an increase in the probability of structural failure. The shock actions are by nature stochastic with randomness arising from their intensities and occurrence times. A varying trend in future intensity and/or occurrence rate of many types of shock action has been projected in the literature, such as cyclone actions due to the potential impact of climate change. This article proposes a method to assess the structural reliability in the presence of uncertainty and non-stationarity in external shock events, with a limit state that the cumulative damage exceeds the permissible level. The mean value and variance of the cumulative damage are estimated with proposed closed-form solutions, and the gamma distribution is suggested to describe the probabilistic characteristics of the cumulative damage, whose accuracy is verified through a comparison with Monte Carlo simulation. Furthermore, the cumulative density function of structural service life is derived explicitly. Parametric studies are conducted to investigate the impact of non-stationarity in shock actions on structural reliability.

For a magnetic confinement fusion device, the superconducting magnets and busbars need to be insulated with one layer of solid insulation to isolate the high voltage potential from the ground. The insulation layer commonly consists of several interleaved layers of epoxy resin-impregnated glass fiber tapes and polyimide films. The traditional electrical inspection methods for such solidified insulation on the magnet and busbar are a DC voltage test or a Paschen test. These tests measure the quality of the insulation based on the value of leakage currents. However, even if there is a larger quantity of high dielectric strength material implemented, if there are some microcavities or delaminations in the insulation system, the leakage current may be limited to microampere levels under testing levels over dozens of kilovolts. Therefore, it is difficult to judge the insulation quality just by the magnitudes of leakage current. Under long-term operation, such imperceptible defects will worsen and finally completely break down the insulation because of partial discharge (PD) incidents. Therefore, a PD detection test is an important complement to the DC voltage and Paschen tests for magnet and busbar insulations in the field of fusion. It is known that the PD detection test is a mature technique in the electric power industry. In this paper, the PD characteristics of samples containing glass fiber-reinforced composite insulations for use with the superconducting busbar were presented and discussed. Various samples with different void contents were prepared and the PD behaviors were tested.

Civil infrastructure systems provide physical supports to a community’s functionalities and are expected to achieve acceptable safety levels subjected to extreme load effects. However, these systems may deteriorate with time as a result of aggressive environmental or operating conditions in service, implying that the system reliability may decline beyond the baseline as assumed for design. Moreover, the increasing trend of the external loads may also contribute to the reduction of the system reliability. In this paper, a semi-analytical method is proposed for assessing the reliability of aging systems subjected to non-stationary loads. The series system is considered, where the system failure is defined as the failure of any single component (structure) among the system. The application of the proposed method is illustrated using a representative series bridge network with several individual bridges. The role of parameters such as the variations in the load intensity, resistance correlation and number of ...

The ceramic honeycomb sandwich structures of 3 mol% yttria-stabilized tetragonal ZrO2 (3Y-TZP) material were fabricated by an additive manufacturing technique based on the digital light processing (DLP) system. The bending behaviour of hexagonal and square honeycomb sandwich structures was investigated with three-point bending test. The effects of geometric parameters, including the thickness of the face-sheet, the height of the cell, the thickness of the cell wall and the size of the cell, were studied through experiments carefully. The results illustrated that the bending strength of the ceramic honeycomb sandwich structure can reach 170 MPa at a relative density of 41.72%. The geometric parameters of the honeycomb core were more critical than the sandwich face-sheet. The cell size, cell wall thickness and cell height were found to be the preferred geometric parameter for justifying the bending resistance performance of the ceramic sandwich panel. Square honeycomb demonstrated better bending performance than the hexagonal honeycomb. This study provides a new basis for further studies on the ceramic lightweight structures.

Probabilistic damage assessment of a community under a scenario tropical cyclone needs to consider the collective damage of individual structures within the community. This involves modelling the spatial correlations of wind speeds and structural vulnerability between individual structures. Ignoring the spatial correlations can lead to unconservative assessment. However, the methods to model these two spatial correlations and their effects on damage assessment are limited. In this paper, a general probabilistic framework is proposed to analyze the correlated damage of spatially distributed building portfolios using joint fragility functions. Two cases are investigated: (1) the correlation of fragility functions of different buildings is given, and (2) the correlation of structural resistance is given from which the correlation of fragilities is computed. To demonstrate the framework, an example is provided to analyze the roof sheathing damage of a residential building portfolio under a cyclone event.

The intensity and/or frequency of hurricane storms may change due to the impact of potential climate change. This paper presents a probabilistic framework to assess the hurricane damage to residential constructions considering the non-stationarity and correlation in hurricane actions. The framework includes a non-stationary Poisson process of hurricane occurrence, a failure rate function of hurricane damage, and explicit formulas for evaluating the mean and variance of annual hurricane damage. The framework is illustrated using a case study of Miami-Dade County, Florida, where the current probabilistic models of hurricane intensity and occurrence rate were estimated by examining hurricane history in this area. The impacts of time-variant hurricane intensity and time-variant hurricane frequency on building damage are assessed individually using the developed framework. The paper also investigates the effects of correlation in hurricane wind speeds on hurricane damage.

Concrete structures may deteriorate over time due to aggressive service environments, leading to a reduction in their strengths, stiffnesses and reliabilities. In general, the assessment of time-dependent reliability of ageing structures must consider uncertainties in structural deterioration as well as non-stationarities in the structural load processes. This paper develops an approximate method for assessing the impact of structural deterioration and non-stationary live loads on structures, which requires only low-dimensional integration and reduces the cost of assessing time-dependent reliability over a service life extending to 50 years significantly. This approximate method is demonstrated through several examples. The importance of non-stationarities in the resistance and load processes on time-dependent reliability is illustrated and the accuracy of the method is confirmed in several cases utilising Monte Carlo simulation.

The safety of scaffold systems during construction is vital to prevent failures with catastrophic consequences. Engineering practice in the scaffolding industry, however, does not have a rational structural reliability basis as that used for buildings and bridges. The implementation of design clauses for scaffold systems in the current standards partially relies on judgement suffering from the lack of data. With this regard, a reliability-based limit state design approach is developed in this study, making full use of the advanced finite element (FE) method and the recently accumulated statistical data of scaffolding resistance and construction loads. A stochastic finite element method is used to obtain the probabilistic characteristics of the ultimate load-carrying capacities of typical scaffolding frames, accounting for the uncertainties associated with structural geometry, material and stiffness properties. The latest construction load survey data is utilized. System reliability assessment is then performed to develop new design criteria which are consistent with generally accepted structural reliability targets.

Civil infrastructure performance and reliability may be affected by deterioration in strength or stiffness caused by service or environmental conditions or by systemic changes in load beyond the baseline conditions assumed for design. These changes should be considered when assessing a structure for its continued future reliability in service. This paper presents an improved method for evaluating time-dependent reliability of structures taking these factors into account. The method enables the impact on safety and serviceability of non-stationarity in the load and resistance deterioration processes to be assessed quantitatively. Parametric analyses show that the reliability is sensitive to the load intensity at the end of the service period, moderately sensitive to the initial and final mean occurrence rates of load events and the nature of these increases in time, and relatively insensitive to the nature of the increase in mean load intensity. A realistic time-dependent model of structural resistance is proposed and the role played by the auto-covariance in the resistance degradation process is investigated. The auto-covariance in stochastic resistance plays a significant role in time-dependent reliability assessment. Assuming that the time-dependent resistance is ‘fully correlated’ generally gives a reasonable estimation of structural reliability, while assuming that the resistances are statistically independent at two points in time may cause the failure probability to be overestimated.

Severe hurricanes in coastal areas have caused enormous human and economic losses. Furthermore, the intensity and frequency of future hurricanes may increase due to the potential impact of ...

The successful past performance of an existing bridge is evidence of its resistance, which reduces the uncertainty associated with the resistance and so increases the bridge reliability. However, the resistance deterioration and increases in traffic load may negate this effect. In this paper, statistical techniques are used to combine the prior estimate of time-dependent resistance with new information from the service load history, thereby obtaining an updated estimate of bridge resistance, as well as an updated reliability for subsequent years. The application of the method is illustrated using an existing bridge. The influences of the intensity and nonstationarity of service load history and the shape and variance of deterioration function on updated estimates of bridge resistance and reliability are examined using parametric examples. It is found that the updated resistance of an existing bridge with ever-increasing traffic load is close to that of the same bridge with a stationary traffic loa...