Component Reliability Indices Research Articles

Optimization of bridge maintenance strategies based on multiple limit states and monitoring

Visual inspections, diagnostic instrumentation and monitoring of bridges are essential for determination of intervention planning. Nowadays, a great challenge is to use bridge monitoring to determine optimal maintenance strategies. Indeed, monitoring data allow updating the knowledge on the structural performance and can significantly affect the intervention strategy. A methodology for structural reliability analysis of superstructures of steel girder bridges incorporating monitoring results is presented. Component reliability indices are computed for the slab and the girders and a time-variant performance analysis is conducted by considering corrosion. This allows dealing with structural capacity and serviceability with respect to permanent deformation under overload. Continuous and simultaneous measurements at discrete points of the bridge superstructure, provided by monitoring, allow to update some parameters of the serviceability limit state function and to perform a fatigue reliability analysis for several bridge components. The consideration of multiple limit states can lead to different optimal maintenance solutions, if taken individually or simultaneously. The aim of this paper is to show the impact of considering a global approach rather than an individual one when determining optimal maintenance strategies associated with several bridge limit states. The approach is illustrated on an existing highway bridge.

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.

Seismic reliability assessment of external stability of reinforced soil walls using pseudo-dynamic method

The paper presents a method for the evaluation of external stability of reinforced soil walls subjected to earthquakes in the framework of the pseudo-dynamic method. The seismic reliability of the wall is evaluated by considering the different possible failure modes such as sliding along the base, overturning about the toe point of the wall, bearing capacity and the eccentricity of the resultant force. The analysis is performed considering properties of the reinforced backfill, foundation soil below the base of the wall, length of the geosynthetic reinforcement and characteristics of earthquake ground motions such as shear wave and primary wave velocity as random variables. The optimum length of reinforcement needed to maintain stability against four modes of failure by targeting various component reliability indices is obtained. Differences between pseudo-static and pseudo-dynamic methods are clearly highlighted in the paper. A complete analysis of pseudo-static and pseudo-dynamic methodologies shows that the pseudo-dynamic method results in realistic design values for the length of geosynthetic reinforcement under earthquake conditions.

Reliability measures for pile foundations based on cone penetration test data

The in situ behaviour of pile foundations is considerably influenced by variability in soil properties. Cone penetration (CPT) data are often used to determine the pile ultimate capacity. A wider range of values of the ultimate capacity are predicted when different CPT-based methods are used, as compared to using pile load test results. The present study considers inherent soil variability, measurement, and transformation variability. The undrained shear strength obtained from CPT data is considered to be a random variable. An approach to obtain load–settlement curves and the associated statistics from CPT data is suggested. Component reliability indices, based on ultimate limit state (ULS) and serviceability limit state (SLS) criteria, and system reliability indices combining ULS and SLS are evaluated. The variability in the pile–soil interface parameters and pile ultimate capacity is quantified in a Monte Carlo framework using the measured data. The effects of variability, scale of fluctuation, and limiting serviceability settlement on the reliability of pile foundations are also examined. A geotechnical database from the Konaseema site in India is utilized as an example. It is shown that the reliability based design of pile foundations considering spatial variability of soil, along with the variables associated with pile–soil interface properties, enables a rational choice of design loads.

Structural Reliability Analysis of Composite Advanced Sail for Virginia Class Submarine

A structural reliability model is developed for a large composite submarine sail structure. Random variables include material strength and stiffness properties as well as load. Limit states are formulated in terms of material strength parameters and buckling resistance. A series system reliability model that bases structural performance on first component failure is used. A total of 205 random variables and 117 limit states compose the structural system model. Most component reliability indices ranged from 3 to 7, with overall system failure governed by material in-plane shear with a reliability index of 1.84. A probabilistic sensitivity analysis determined that load and material strength were the most significant random variables, while material stiffness parameters were unimportant. Significant computational effort was saved by reducing the number of random variables to the most influential set. The effects of correlation and random variable probability distribution were explored. It was found that correlation has little effect on results, but probability distribution is significant. Recommendations are made to improve performance.

Target reliability based design optimization of anchored cantilever sheet pile walls

In this study, the stability of anchored cantilever sheet pile wall in sandy soils is investigated using reliability analysis. Targeted stability is formulated as an optimization problem in the framework of an inverse first order reliability method. A sensitivity analysis is conducted to investigate the effect of parameters influencing the stability of sheet pile wall. Backfill soil properties, soil – steel pile interface friction angle, depth of the water table from the top of the sheet pile wall, total depth of embedment below the dredge line, yield strength of steel, section modulus of steel sheet pile, and anchor pull are all treated as random variables. The sheet pile wall system is modeled as a series of failure mode combination. Penetration depth, anchor pull, and section modulus are calculated for various target component and system reliability indices based on three limit states. These are: rotational failure about the position of the anchor rod, expressed in terms of moment ratio; sliding failure mode, expressed in terms of force ratio; and flexural failure of the steel sheet pile wall, expressed in terms of the section modulus ratio. An attempt is made to propose reliability based design charts considering the failure criteria as well as the variability in the parameters. The results of the study are compared with studies in the literature.

Structural health monitoring and reliability estimation: Long span truss bridge application with environmental monitoring data

The main objective of this study is to present the reliability estimation studies for the main truss components as well as the entire structural system of a long span truss bridge which is the longest in its category in the USA. It is possible to assess the safety level of a long span bridge by using a probabilistic approach in terms of its component and system reliability indices. However, most of the older long span bridges were designed based on allowable stress design and it is not possible to quantify their reliability. The reliability analysis in this study is based on the distributions estimated for dead, live and wind loads. The bridge was also subjected to long term structural health monitoring where large amount of input and response data have been collected. Analysis of the long term monitoring data revealed distinct structural behavior in terms of patterns and magnitudes under various external loading effects. As an example, it is shown that the structural responses due to temperature are not very easy to conceptualize and subsequently model using conventional analysis methods. In order to explore the effects of temperature on the structure and to include the long term monitoring data in reliability estimation, temperature-induced responses are also incorporated in the analysis. It is seen that the responses due to temperature have a significant effect on the overall system reliability.

Reliability assessment of excavation systems considering both stability and serviceability performance

Excavation projects related to urban redevelopment and infrastructure improvement are often governed by serviceability-based design, rather than failure prevention criteria. Deformation tolerance specifications are often prescribed based on minimizing potential damage to adjacent structures. A risk-based approach to serviceability performance that systematically incorporates design parameter uncertainty will allow engineers to address soil uncertainty in performance-based design. This paper demonstrates the use of various kinds of reliability methods, such as response surface method (RSM), first-order reliability method (FORM), second-order reliability method (SORM), adaptive importance sampling (AIS), Monte Carlo simulation (MCS) and system reliability, to assess the risk of stability and/or serviceability failure of an entire excavation support system throughout the entire construction process. By considering multiple failure modes (including serviceability criteria) of an excavation, the component and system reliability indices for each excavation step are assessed during the entire excavation process. Sensitivity analyses are conducted for the system reliability calculations, which demonstrate that the adjacent structure damage potential limit state function is the dominant factor for determining excavation system reliability. An example is presented to show how the serviceability performance for braced excavation problems can be assessed based on the system reliability index.

SIMPLIFIED ASSESSING OF SUBSTATION-ORIGINATED OUTAGES IN ANALYSIS OF TRANSMISSION SYSTEM RELIABILITY

In order to minimize the effects of substation-related outages on performance of the composite system, the power system planners have to assess their effects. The present paper is specifically concerned with a relatively simple method of substation reliability analysis based on failure modes and effect analysis. More influential failure events are screened basing on reliability indices of substation components. The further analysis considers only a relatively small number of screened events. So the method enables to analyze and compare different substation configurations, to elaborate measures to improve system operation, to incorporate substation-related outages in evaluation of the reliability of the composite system etc. relatively simply without using special complicated computer programs.

Lifetime Performance Analysis of Existing Reinforced Concrete Bridges. II: Application

This study, being the second part of a two-part paper, presents the application of a lifetime performance analysis methodology to three reinforced concrete bridges located in an existing bridge network in Colorado. The focus of this paper is on reinforced concrete slabs and girders of these bridges. The limit state equations were previously derived in the companion paper by grouping the random variables, deterministic parameters, and constant coefficients in such a way that the formulas are applicable to reinforced concrete slabs and girders in general. The results presented in this paper for reinforced concrete slabs and girders are part of a larger study focusing on lifetime performance analysis of multiple bridge types in a selected bridge network. The bridges are individually described herein, followed by the presentation of the performance analysis results including both initial reliability indices and lifetime reliability profiles. Once the values associated with random variables, deterministic parameters, and constant coefficients are assigned, component reliability indices for the slab and the girders are calculated for each bridge. Detailed results are presented for an individual bridge, whereas the lifetime reliability profiles are presented for all bridges. For time-variant performance analysis, special emphasis is placed on the chloride penetration modeling in reinforced concrete, theoretical basis of which was presented in the companion paper.

System-level load–strength interference based reliability modeling of k-out-of-n system

The issue of information loss in the process of system reliability modeling through conventional load–strength interference analysis is discussed first, and the reason why it is impossible to construct dependent system reliability model simply by means of component reliability index is demonstrated. Then, an approach to modeling the reliability of dependent system with common cause failure (CCF) is presented. The approach is based on system-level load–strength interference analysis and a concept of ‘conditional failure probability of component’ as well. With the opinion that load randomness is the direct cause of failure dependence, a discrete type system reliability model is developed via the conditional component failure probability concept. At last, the model's capabilities to estimate system reliability with CCF effect and to predict high multiplicity failure probability based on low multiplicity failure event data are proved.

Optimal reliability design in an electrical distribution system via a polynomial-time algorithm

In this paper, the optimal design of reliability indices in an electrical distribution system and their impact to planning are studied. By formulating the cost due to interrupted KVA-hour, initial interruption cost, and modification cost in terms of component reliability indices, an optimization problem is derived while simultaneously considering multiple load points and feeder capacity limits, resulting in a nonlinear programming problem. To solve this nonlinear programming problem, an effective polynomial-time algorithm is presented. The numerical test shows that not only significant savings can be achieved, but also information on identifying value-saving feeder/components can be revealed as well. This is a valuable tool to distribution planning/operations.

Use of numeric methods for calculating the reliability indices of damaged structural components

Methods used to calculate the reliability indices of structural components (the distribution function of remaining life, the probability of failure-free service, and the risk function) as applies to problems of the propagation of defects under a cyclic load are examined. The potentials of the method of “numeric experiments” are demonstrated in an example of the calculation of crack kinetics in a branch pipe in tension with bending. The reliability indices are calculated for a plane element with a crack by means of numeric integration of determining equations. It is possible to solve problems with different laws governing crack propagation and forms of density distribution for the size of the initial defect within the framework of these methods. A combination of approaches of fracture mechanics and reliability theory with numeric methods of calculation make it possible to evaluate the reliability indices of a defective structural component.