Time-dependent Reliability Assessment Research Articles

Time-dependent reliability of strengthened PSC box-girder bridge using phased and incremental static analyses

Prestressed concrete (PSC) box-girder bridges are extensively used in highway and railway construction. Excessive long-term deflection and unexpected cracks however are often observed. To achieve deflection control and/or to restore the bearing capacity of bridges, structural strengthening measures are frequently adopted. This paper proposes an approach based on probabilistic finite element analyses to evaluate the time-dependent reliabilities of strengthened PSC box-girder bridges. The time-dependent behaviour of the girders is simulated considering concrete shrinkage, creep and cracking, corrosion and stress relaxation of steel, etc. In particular, phased analysis is adopted to account for the existing damage and stress conditions prior to strengthening, and the incremental static analysis method is used to calculate the structural reliabilities. Application is made to the time-dependent reliability assessment of a PSC box-girder bridge, and the effectiveness of three strengthening methods including externally bonded steel plates, fibre reinforced polymer (FRP) composites and external post-tensioning is compared. The presented study provides references to reliability-based design and optimization of strengthening strategies for PSC box-girder bridges.

Time-dependent reliability of ageing structures: an approximate approach

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.

Simplified Method for Time-Dependent Reliability Analysis of Aging Bridges Subjected to Nonstationary Loads

The performance of existing bridges may deteriorate in time due to aggressive environmental or operating conditions in service, which may eventually cause changes in structural resistance and reliability beyond the baseline assumed for new ones. In addition, the increasing trend of live loads applied to the bridges, which has been reported in many researches, also contributes to the reduction of structural reliability. In order to perform time-dependent reliability assessment for aging bridges subjected to nonstationary loading process with improved efficiency, a simplified method is proposed in this paper, where lower dimensional integral is involved in the calculation of reliability. With the proposed method, time-dependent reliability of a real aging RC bridge is conducted, and the effect of nonstationarity in load intensity on structural reliability is investigated. It is found that structural reliability is sensitive to the increase of load intensity, and is less sensitive to the varying mechanism of load intensity.

Time-dependent reliability assessment of offshore jacket platforms

The reliability assessment method has been developed into a widely used method to conduct safety assessment of jacket platforms. Traditionally, the structural resistance is considered to be a constant during the design reference time. However, platform structures degrade over time. Therefore, a reliability assessment method that considers the resistance degradation will be better suited. A time-dependent reliability assessment of the offshore jacket platform was studied in this paper. The base shear capacity was considered as the resistance of the platform. For the resistance probability model of the jacket platform, the corrosion effect was considered for the degradation of the resistance. A proper corrosion model was studied. For the load effect probability model, the typhoon load effect, containing wind, wave and current loads, was used. At last, an example platform was studied using the proposed method and the results showed that the method could be used in practical engineering applications.

Time-dependent reliability of aging structures in the presence of non-stationary loads and degradation

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.

A global procedure for the time-dependent reliability assessment of crane structural members

This paper aims at developing a probabilistic fatigue assessment procedure for crane structural members, using a structural reliability method, namely the stress–strength interference method. A crane member strength law is found by fitting fatigue life distribution parameters using finite element results and experimental data. The stress model is developed by using on-site data to determine probabilistic parametric distributions defining crane member loading. The efficiency of the proposed stress–strength interference method for tower crane member reliability assessment in fatigue is demonstrated on a jib chord member connection.

Fatigue reliability evaluation of structural components under random loadings

An efficient method for time-dependent fatigue reliability assessment of mechanical components under random loadings is proposed. Normally, fatigue damage induced by random loading is high-cycle fatigue problem. The randomness of high-cycle fatigue damage is treated in two aspects. The first one is the uncertainty quantification from the external random loading. The second one is the uncertainty quantification of the fatigue property of the structural component. The former is characterized by Gaussian distribution derived from the rainflow cycle distribution, median stress-life ( S- N) curve, and the linear damage accumulation rule. The latter is described with the probabilistic stress-life ( P- S- N) curve based on log-normal distribution. The proposed method has colligated these two aspects together to evaluate the expectation and confidence interval of fatigue reliability. Finally, a numerical example is provided to verify the effectiveness of the developed approach. A comparison with bootstrap method is also carried out. The comparative result has shown rational accuracy of the proposed method.

Time-dependent analysis of cable trusses -Part I. Closed-form computational model

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine\'s forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

Time-dependent analysis of cable trusses -Part II. Simulation-based reliability assessment

One of the possible alternatives of simulation-based time-dependent reliability assessment of pre-stressed biconcave and biconvex cable trusses, the Monte Carlo method, is applied in this paper. The influence of an excessive deflection of cable truss (caused by creep of cables and rheologic changes) on its time-dependent serviceability is investigated. Attention is given to the definition of the basic random variables and their statistical functions (basic, mutually dependent random variables such as the pre-stressing forces of the bottom and top cable, structural geometry, the Young's modulus of elasticity of the cables, and the independent variables, such as permanent load, wind, snow and thermal actions). Then, the determination of the response of the cable truss to the loading effects, and the definition of the limiting values considering serviceability of the structure are performed. The potential of the method, using direct Monte Carlo technique for simulation-based time-dependent reliability assessment as a powerful tool, is emphasized. Results obtained by the First order reliability method (FORM) are compared with those obtained by the Monte Carlo simulation technique.

Time-Dependent Reliability of PSC Box-Girder Bridge Considering Creep, Shrinkage, and Corrosion

Bridge performance undergoes time-varying changes when exposed to aggressive environments. While much work has been done on bridge reliability under corrosion, little is known about the effects of creep and shrinkage on the reliability of concrete bridges. In this paper, the CEB-FIP model for creep and shrinkage is applied by using finite-element (FE) analysis in conjunction with probabilistic considerations. Verification is made by comparing the analytical findings with existing test data. More specifically, a time-dependent reliability assessment is made for a composite prestressed concrete (PSC) box-girder bridge exposed to a chloride environment. This realized via an advanced probabilistic FE method. The postcracking behavior of the thin-walled box girder is described using composite degenerated shell elements, and importance sampling is used to improve the efficiency of the reliability analyses. It is shown that concrete creep and shrinkage dominate during the early stages of bridge structure deterio...

Time-dependent analysis and simulation-based reliability assessment of suspended cables with rheological properties

The intention of the paper is to illustrate the ability of the probabilistic time-dependent reliability assessment procedure applied to non-linear suspended cable structure with rheological properties, when a rope made from the high strength synthetic fibres is used in order to demonstrate the new qualitatively different concept. Attention is turned to the individual main steps in the assessment procedure, i.e. to the selection of an appropriate method of structural analysis and to derivation of an appropriate closed-form and discrete analytical models, analysis of random variables representing individual actions (four basic random variables, such as structural geometry, cable’s modulus of elasticity and creep strain increments and loading, are considered), evaluation of the structural response with respect to the interaction of the random variables considering a history of the time-dependent action effects and to the definition of the limiting values considering serviceability of cable structure. The potential of the method using direct Monte Carlo technique as one of the possible alternatives for simulation-based time-dependent reliability assessment as a powerful tool is emphasized. The influence of an excessive deflection of suspended cable (caused by creep of cable and rheologic changes) on its serviceability in required time is investigated and illustrative examples are performed.

Time-dependent reliability of textile-strengthened RC structures under consideration of fuzzy randomness

The reliability of civil engineering structures is time-dependent. By means of strengthening it is possible to improve the load-bearing capacity and serviceability of structures and simultaneously to increase structural reliability. In this paper, we focus on the time-dependent reliability assessment of RC structures strengthened by textile-reinforced fine-grade concrete layers. The paper starts with a short introduction concerning textile strengthening of RC structures and the underlying mechanical model. The uncertain material parameters of textile-strengthened structures are then investigated. The uncertain parameters are quantified as fuzzy variables or fuzzy random variables. In order to take account of the latter in the assessment of the time-dependent reliability a new fuzzy probabilistic safety concept is presented. The fuzzy adaptive importance sampling (FAIS) method is introduced. The algorithm is demonstrated with an example. The uncertainty of the input parameters is comprehensively reflected in the uncertainty of the computed fuzzy reliability index. The assessment of the uncertain results is discussed.

A time-dependent corrosion wastage model for seawater ballast tank structures of ships

For assessment of time-dependent reliability or risk of aging ship structures, it is essential to have a mathematical model which provides the statistical characteristics (mean, variance, distribution) of corrosion wastage as a function of time (i.e., ship age). The aim of the present work is to develop such a model for low alloy carbon steel plates used for the structure of seawater ballast tanks in ships. Measurement data of structural wastage due to corrosion for such ship steel plates is collected and the statistical characteristics of corrosion loss and rate are quantified by statistical analysis in terms of ship age. The results and insights developed in the present study will be useful for predicting the wastage of corrosion in seawater ballast tank structures of ships. They will also be useful for designing corrosion tolerant structures subjected to the seawater environment.

Assessment of time-dependent reliability of reinforced concrete columns with uncertain load eccentricity

An approach for the time-dependent reliability analysis of reinforced concrete (RC) columns considering the correlation between the axial load and the bending moment or the uncertainty in the load eccentricity is presented. The approach recursively uses the efficient first-order reliability method for the time-dependent reliability analysis. The proposed approach is more efficient than the ones used in the literature for the reliability analysis of RC columns. The proposed approach is used to carry out sensitivity analyses of the reliability of short RC columns to the time-dependent live load effects and to the correlation between the axial load and the bending moment. Results of the analyses suggest that the reliability of RC columns can be sensitive to the correlation between the axial load and the bending moment due to live load. The differences between the reliability indices obtained by considering the live load modeled as a pulse process and as an extreme variate can be large.Key words: reliability, load, time-dependent, time-independent, uncertainty, correlation, concrete, reinforcement, column.

Assessment of time-dependent reliability of reinforced concrete columns with uncertain load eccentricity

Assessment of time-dependent reliability of reinforced concrete columns with uncertain load eccentricity

Time-dependent reliability assessment for mass concrete structures

Under the influences of random thermal creep stresses, the safety of mass concrete structures could be described by time-dependent reliability. In this paper, based on probabilistic finite element method (PFEM), numerical methods for the time-dependent reliability assessment are presented. By using the presented methods, various kinds of random variability including non-stationary temperature of concrete, modulus of elasticity, creep compliance and strength parameters of concrete can be conveniently taken into account. The suggested method is useful for the mass concrete structural design and safety evaluation when random factors should be taken into account.