Strain localization effect on system reliability based design of bridge abutments under earthquake loading

The component and system reliability based design of bridge abutments under earthquake loading is presented in the paper. Planar failure surface has been used in conjunction with pseudo-dynamic approach to compute seismic active earth pressures on an abutment. The pseudo-dynamic method, considers the effect of phase difference in shear waves, soil amplification along with the horizontal seismic accelerations, strain localization in backfill soil and associated post-peak reduction in the shear resistance from peak to residual values along a previously formed failure plane. Four modes of stability viz. sliding, overturning, eccentricity and bearing capacity of the foundation soil are considered in the analysis. The series system reliability is computed with an assumption of independent failure modes. The lower and upper bounds of system reliability are also computed by taking into account the correlations between four failure modes, which is evaluated using the direction cosines of the tangent planes at the most probable points of failure.

Influence of strain localization on reliability based design of bridge abutments using pseudo-dynamic method

The paper focuses on reliability based design of bridge abutments when subjected to earthquake loading. Planar failure surface has been used in conjunction with pseudo-dynamic approach to compute the seismic active earth pressures on the bridge abutment. The proposed pseudo dynamic method, considers the effects of strain localization in the backfill soil and associated post-peak reduction in the shear resistance from peak to residual values along a previously formed failure plane, phase difference in shear waves and soil amplification along with the horizontal seismic accelerations. Four modes of stability viz. sliding, overturning, eccentricity and bearing capacity of the foundation soil are considered for the reliability analysis. The influence of various design parameters on the seismic reliability indices against four modes of failure is presented, following the suggestions of Japan Road Association, Caltrans Bridge Design Specifications and U.S Department of the Army.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Performance and reliability of Gd2O3 and stacked Gd2O3-Eu2O3 metal-insulator-metal capacitors

Gd2O3-based metal-insulator-metal capacitors have been characterized with single layer (Gd2O3) and bilayer (Gd2O3/Eu2O3 and Eu2O3/Gd2O3) stacks for analog and DRAM applications. Although single layer Gd2O3 capacitors provide highest capacitance density (15 fF/mu m(2)), they suffer from high leakage current density, poor capacitance density-voltage linearity, and reliability. The stacked dielectrics help to reduce leakage current density (1.2x10(-5) A/cm(2) and 2.7 x 10(-5) A/cm(2) for Gd2O3/Eu2O3 and Eu2O3/Gd2O3, respectively, at -1 V), improve quadratic voltage coefficient of capacitance (331 ppm/V-2 and 374 ppm/V-2 for Gd2O3/Eu2O3 and Eu2O3/Gd2O3, respectively, at 1 MHz), and improve reliability, with a marginal reduction in capacitance density. This is attributed to lower trap heights as determined from Poole-Frenkel conduction mechanism, and lower defect density as determined from electrode polarization model.

Characterizing drought using the reliability-resilience-vulnerability concept

This study borrows the measures developed for the operation of water resources systems as a means of characterizing droughts in a given region. It is argued that the common approach of assessing drought using a univariate measure (severity or reliability) is inadequate as decision makers need assessment of the other facets considered here. It is proposed that the joint distribution of reliability, resilience, and vulnerability (referred to as RRV in a reservoir operation context), assessed using soil moisture data over the study region, be used to characterize droughts. Use is made of copulas to quantify the joint distribution between these variables. As reliability and resilience vary in a nonlinear but almost deterministic way, the joint probability distribution of only resilience and vulnerability is modeled. Recognizing the negative association between the two variables, a Plackett copula is used to formulate the joint distribution. The developed drought index, referred to as the drought management index (DMI), is able to differentiate the drought proneness of a given area when compared to other areas. An assessment of the sensitivity of the DMI to the length of the data segments used in evaluation indicates relative stability is achieved if the data segments are 5years or longer. The proposed approach is illustrated with reference to the Malaprabha River basin in India, using four adjoining Climate Prediction Center grid cells of soil moisture data that cover an area of approximately 12,000 km(2). (C) 2013 American Society of Civil Engineers.

System Reliability Analysis of Flexible Pavements

The uncertainty in material properties and traffic characterization in the design of flexible pavements has led to significant efforts in recent years to incorporate reliability methods and probabilistic design procedures for the design, rehabilitation, and maintenance of pavements. In the mechanistic-empirical (ME) design of pavements, despite the fact that there are multiple failure modes, the design criteria applied in the majority of analytical pavement design methods guard only against fatigue cracking and subgrade rutting, which are usually considered as independent failure events. This study carries out the reliability analysis for a flexible pavement section for these failure criteria based on the first-order reliability method (FORM) and the second-order reliability method (SORM) techniques and the crude Monte Carlo simulation. Through a sensitivity analysis, the most critical parameter affecting the design reliability for both fatigue and rutting failure criteria was identified as the surface layer thickness. However, reliability analysis in pavement design is most useful if it can be efficiently and accurately applied to components of pavement design and the combination of these components in an overall system analysis. The study shows that for the pavement section considered, there is a high degree of dependence between the two failure modes, and demonstrates that the probability of simultaneous occurrence of failures can be almost as high as the probability of component failures. Thus, the need to consider the system reliability in the pavement analysis is highlighted, and the study indicates that the improvement of pavement performance should be tackled in the light of reducing this undesirable event of simultaneous failure and not merely the consideration of the more critical failure mode. Furthermore, this probability of simultaneous occurrence of failures is seen to increase considerably with small increments in the mean traffic loads, which also results in wider system reliability bounds. The study also advocates the use of narrow bounds to the probability of failure, which provides a better estimate of the probability of failure, as validated from the results obtained from Monte Carlo simulation (MCS).

Approach for the use of MSW settlement predictions in the assessment of landfill capacity based on reliability analysis

In the analysis and design of municipal solid waste (MSW) landfills, there are many uncertainties associated with the properties of MSW during and after MSW placement. Several studies are performed involving different laboratory and field tests to understand the complex behavior and properties of MSW, and based on these studies, different models are proposed for the analysis of time dependent settlement response of MSW. For the analysis of MSW settlement, it is very important to account for the variability of model parameters that reflect different processes such as primary compression under loading, mechanical creep and biodegradation. In this paper, regression equations based on response surface method (RSM) are used to represent the complex behavior of MSW using a newly developed constitutive model. An approach to assess landfill capacities and develop landfill closure plans based on prediction of landfill settlements is proposed. The variability associated with model parameters relating to primary compression, mechanical creep and biodegradation are used to examine their influence on MSW settlement using reliability analysis framework and influence of various parameters on the settlement of MSW are estimated through sensitivity analysis. (C) 2013 Elsevier Ltd. All rights reserved.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Target reliability-based optimisation for internal seismic stability of reinforced soil structures

In this paper, an approach for target component and system reliability-based design optimisation (RBDO) to evaluate safety for the internal seismic stability of geosynthetic-reinforced soil (GRS) structures is presented. Three modes of failure are considered: tension failure of the bottom-most layer of reinforcement, pullout failure of the topmost layer of reinforcement, and total pullout failure of all reinforcement layers. The analysis is performed by treating backfill properties, geometric and strength properties of reinforcement as random variables. The optimum number of reinforcement layers and optimum pullout length needed to maintain stability against tension failure, pullout failure and total pullout failure for different coefficients of variation of friction angle of the backfill, design strength of the reinforcement and horizontal seismic acceleration coefficients by targeting various system reliability indices are proposed. The results provide guidelines for the total length of reinforcement required, considering the variability of backfill as well as seismic coefficients. One illustrative example is presented to explain the evaluation of reliability for internal stability of reinforced soil structures using the proposed approach. In the second illustration (the stability of five walls), the Kushiro wall subjected to the Kushiro-Oki earthquake, the Seiken wall subjected to the Chiba-ken Toho-Oki earthquake, the Ta Kung wall subjected to the Ji-Ji earthquake, and the Gould and Valencia walls subjected to Northridge earthquake are re-examined.

Estimation of time variant reliability of randomly parametered non-linear vibrating systems

The problem of time variant reliability analysis of randomly parametered and randomly driven nonlinear vibrating systems is considered. The study combines two Monte Carlo variance reduction strategies into a single framework to tackle the problem. The first of these strategies is based on the application of the Girsanov transformation to account for the randomness in dynamic excitations, and the second approach is fashioned after the subset simulation method to deal with randomness in system parameters. Illustrative examples include study of single/multi degree of freedom linear/non-linear inelastic randomly parametered building frame models driven by stationary/non-stationary, white/filtered white noise support acceleration. The estimated reliability measures are demonstrated to compare well with results from direct Monte Carlo simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Reliability-based load and resistance factor design approach for external seismic stability of reinforced soil walls

Load and resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. The evaluation of load and resistance factors for the reinforced soil walls based on reliability theory is presented. A first order reliability method (FORM) is used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analysis is conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. The proposed procedure includes the variability associated with reinforced backfill, retained backfill, foundation soil, horizontal seismic acceleration and surcharge load acting on the wall. Partial factors needed to maintain the stability against three modes of failure by targeting component reliability index of 3.0 are obtained for various values of coefficients of variation (COV) of friction angle of backfill and foundation soil, distributed dead load surcharge, cohesion of the foundation soil and horizontal seismic acceleration. A comparative study between LRFD and allowable stress design (ASD) is also presented with a design example. (C) 2014 Elsevier Ltd. All rights reserved.

Reliability Assessment of a Storm Water Drain Network

Most of the cities in India are undergoing rapid development in recent decades, and many rural localities are undergoing transformation to urban hotspots. These developments have associated land use/land cover (LULC) change that effects runoff response from catchments, which is often evident in the form of increase in runoff peaks, volume and velocity in drain network. Often most of the existing storm water drains are in dilapidated stage owing to improper maintenance or inadequate design. The drains are conventionally designed using procedures that are based on some anticipated future conditions. Further, values of parameters/variables associated with design of the network are traditionally considered to be deterministic. However, in reality, the parameters/variables have uncertainty due to natural and/or inherent randomness. There is a need to consider the uncertainties for designing a storm water drain network that can effectively convey the discharge. The present study evaluates performance of an existing storm water drain network in Bangalore, India, through reliability analysis by Advance First Order Second Moment (AFOSM) method. In the reliability analysis, parameters that are considered to be random variables are roughness coefficient, slope and conduit dimensions. Performance of the existing network is evaluated considering three failure modes. The first failure mode occurs when runoff exceeds capacity of the storm water drain network, while the second failure mode occurs when the actual flow velocity in the storm water drain network exceeds the maximum allowable velocity for erosion control, whereas the third failure mode occurs when the minimum flow velocity is less than the minimum allowable velocity for deposition control. In the analysis, runoff generated from subcatchments of the study area and flow velocity in storm water drains are estimated using Storm Water Management Model (SWMM). Results from the study are presented and discussed. The reliability values are low under the three failure modes, indicating a need to redesign several of the conduits to improve their reliability. This study finds use in devising plans for expansion of the Bangalore storm water drain system. (C) 2015 The Authors. Published by Elsevier B.V.

Girsanov Transformation-Based Reliability Modeling and Testing of Actively Controlled Structures

The problem of estimation of the time-variant reliability of actively controlled structural dynamical systems under stochastic excitations is considered. Monte Carlo simulations, reinforced with Girsanov transformation-based sampling variance reduction, are used to tackle the problem. In this approach, the external excitations are biased by an additional artificial control force. The conflicting objectives of the two control forces-one designed to reduce structural responses and the other to promote limit-state violations (but to reduce sampling variance)-are noted. The control for variance reduction is fashioned after design-point oscillations based on a first-order reliability method. It is shown that for structures that are amenable to laboratory testing, the reliability can be estimated experimentally with reduced testing times by devising a procedure based on the ideas of the Girsanov transformation. Illustrative examples include studies on a building frame with a magnetorheologic damper-based isolation system subject to nonstationary random earthquake excitations. (C) 2014 American Society of Civil Engineers.

Markov chain splitting methods in structural reliability integral estimation

Monte Carlo simulation methods involving splitting of Markov chains have been used in evaluation of multi-fold integrals in different application areas. We examine in this paper the performance of these methods in the context of evaluation of reliability integrals from the point of view of characterizing the sampling fluctuations. The methods discussed include the Au-Beck subset simulation, Holmes-Diaconis-Ross method, and generalized splitting algorithm. A few improvisations based on first order reliability method are suggested to select algorithmic parameters of the latter two methods. The bias and sampling variance of the alternative estimators are discussed. Also, an approximation to the sampling distribution of some of these estimators is obtained. Illustrative examples involving component and series system reliability analyses are presented with a view to bring out the relative merits of alternative methods. (C) 2015 Elsevier Ltd. All rights reserved.

System reliability of randomly vibrating structures: Computational modeling and laboratory testing

The problem of determination of system reliability of randomly vibrating structures arises in many application areas of engineering. We discuss in this paper approaches based on Monte Carlo simulations and laboratory testing to tackle problems of time variant system reliability estimation. The strategy we adopt is based on the application of Girsanov's transformation to the governing stochastic differential equations which enables estimation of probability of failure with significantly reduced number of samples than what is needed in a direct simulation study. Notably, we show that the ideas from Girsanov's transformation based Monte Carlo simulations can be extended to conduct laboratory testing to assess system reliability of engineering structures with reduced number of samples and hence with reduced testing times. Illustrative examples include computational studies on a 10 degree of freedom nonlinear system model and laboratory/computational investigations on road load response of an automotive system tested on a four post Lest rig. (C) 2015 Elsevier Ltd. All rights reserved.