Mean-value First-order Second-moment Method Research Articles

On computation of reliability index for tensile membrane structures based on limit state of deflection

PurposeThe present study is based on finding the structural response of a tensile membrane structure (TMS) through deformation. The intention of the present research is to develop a basic understanding of reliability analysis and deflection behavior of a pre-tensioned TMS. The mean value first-order second-moment method (MVFOSM) method is used here to evaluate stochastic moments of a performance function with random input variables. Results suggest the influence of modulus of elasticity, the thickness of the membrane, and edge span length are significant for reliability based TMS design.Design/methodology/approachA simple TMS is designed and simulated by applying external forces (along with prestress), as a manifestation of wind and snow load. A nonlinear analysis is executed to evaluate TMS deflection, followed by calculating the reliability index. Parametric study is done to consider the effect of membrane material, thickness and load location. First-order second moment (FOSM) is used to evaluative the reliability. A comparison of reliability index is done and deflection variations from μ − 3s to μ + 3s are accounted for in this approach.FindingsThe effectiveness of deflection is highlighted for the reliability assessment of TMS. Reliability and parametric study collectively examine the proposed geometry and material to facilitate infield design requirements. The estimated β value indicates that most suitable fabric material for a simple TMS should possess an elasticity modulus in the range of 1,000–1,500 MPa, the thickness may be considered to be around 1.00 mm, and additional adjustment of around 5–10 mm is suggested for edge length. The loading position in case of TMS structures can be a sensitive aspect where the rigidity of the surface is dependent on the pre-tensioning of the membrane.Research limitations/implicationsThe significance of the parametric study on material and loading for deflection of TMS is emphasized. Due to the lack of consolidated literature in the field combining reliability with deflection limits of a TMS, this work can be very useful for researchers.Practical implicationsThe present work outcome may facilitate practitioners in determining effective design methodology and material selection for TMS construction.Originality/valueThe significance of parametric study for serviceability criteria is emphasized. Parameters like pre-stress can be included in future parametric studies to witness in depth behavior of TMS. Due to lack of consolidated literature in the field combining reliability with deflection limits of a TMS, this work can be very useful for the researchers. The present work outcome may facilitate practitioners in determining effective design methodology and material selection for TMS construction.

Enhanced reliability assessment of punching shear resistance models for flat slabs without shear reinforcement

Punching shear is one of the main failure mechanisms in flat slabs. To prevent such failures, modern structural codes, as EN 1992-1-1, offer design provisions against punching shear. However, these provisions were calibrated based on experience, which can affect the precision of the resulting safety level. The use of modern reliability analysis techniques is required for a more precise evaluation of the safety level of these structural systems. This paper presents a comprehensive review of the state-of-the-art of reliability techniques where the safety level of design provisions for punching shear resistance without shear reinforcement is investigated. This study addresses three reliability analysis techniques: Mean-Value First Order Second Moment Method (MVFOSM), First-Order Second Moment Method (FOSM) and a Monte-Carlo simulation with Importance Sampling (MC-IS). Reliability indices β are used as a practical measurement of the safety level representing probabilities of failure. The parameters influencing the punching shear capacity without shear reinforcement were varied that the area of practical interest is covered. The estimated reliability indices β are evaluated and compared to a target safety level given by EN 1990 for a 50-year reference period where β is equal to 3.8. The results seem to confirm that the punching shear provisions for slabs without shear reinforcement according to EN 1992-1-1 achieve a required safety level, which is in accordance to the target level given by EN 1990. In addition, the study shows that the use of the techniques FOSM and MC-IS seems appropriate for determining the probability of failure of the design equation for the punching shear capacity without shear reinforcement. Furthermore, the study suggests that the method MVFOSM may not be suitable to assess the absolute safety level of such design equations. Finally, the study highlights the potential of using the aforementioned reliability analysis techniques and stresses the importance of modelling the uncertainties for a precise structural safety assessment of flat slabs without shear reinforcement.

Input‐variable sensitivity assessment for sediment transport relations

AbstractA methodology to assess input‐variable sensitivity for sediment transport relations is presented. The Mean Value First Order Second Moment Method (MVFOSM) is applied to two bed load transport equations showing that it may be used to rank all input variables in terms of how their specific variance affects the overall variance of the sediment transport estimation. In sites where data are scarce or nonexistent, the results obtained may be used to (i) determine what variables would have the largest impact when estimating sediment loads in the absence of field observations and (ii) design field campaigns to specifically measure those variables for which a given transport equation is most sensitive; in sites where data are readily available, the results would allow quantifying the effect that the variance associated with each input variable has on the variance of the sediment transport estimates. An application of the method to two transport relations using data from a tropical mountain river in Costa Rica is implemented to exemplify the potential of the method in places where input data are limited. Results are compared against Monte Carlo simulations to assess the reliability of the method and validate its results. For both of the sediment transport relations used in the sensitivity analysis, accurate knowledge of sediment size was found to have more impact on sediment transport predictions than precise knowledge of other input variables such as channel slope and flow discharge.

Target reliability index for serviceability limit state of single piles

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state (SLS) of single piles. This contributes to conducting the SLS reliability-based design (RBD) of piles. Based on a two-parameter, hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index (βsls) is obtained using the mean value first order second moment (MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation (MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement (slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety (FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

Incorporating serviceability limit state requirements into reliability-based analysis and design of piles

This study develops a novel reliability-based approach for the analysis and design of piles by incorporating Serviceability Limit State (SLS) requirements into Load and Resistance Factor Design (LRFD) for Ultimate Limit States (ULS). Three methods for reliability-based analysis and design, namely the Mean Value First Order Second Moment (MVFOSM) method, the Advanced First Order Second Moment (AFOSM) method, and the Monte Carlo Simulation (MCS) method, are employed for comparison. In order to expediently quantify model uncertainties for SLS and incorporate them into the process of reliability-based analysis and design of piles, the SLS model factor (or bias factor) is established based on a two-parameter, hyperbolic curve-fitting equation describing the load-settlement relation. Herein, the limiting tolerable foundation settlement (slt) is treated as a random variable. Four load test databases from South Africa presented by Dithinde et al. (2011) are compiled again to conduct reliability analysis and calculate resistance factors. The case studies illustrate that the AFOSM method has the higher accuracy than the MVFOSM method as verified using the MCS method. This study recommends the AFOSM method to perform reliability analysis and determine resistance factors for Reliability-Based Design (RBD).

Solution method of overtopping risk model for earth dams

Hydrologic risk analysis relies on a series of probabilistic analyses, and it is a complex problem in estimating the probability distributions of multiple independent and random variables. The goal of this study is to presents the procedure and application of a probability-based risk analysis methodology to evaluate earth dam overtopping risk that induced by concurrent flood and wind. The uncertainty arising from initial water surface level, flood, wind velocity, and dam height are discussed in this research. The improved Monte Carlo simulation and mean-value first-order second-moment method are used to solve the proposed dam overtopping risk model, respectively. The nonparametric kernel density estimation method, which can better learn the complex multimodal characteristic of probability density function than that of traditional parametric estimation method, is employed to improve the probability density function of initial water surface level. The latin hypercube sampling is introduced to generate uniform random number, which improves the efficient and stability compared with simple random sampling. Afterward, an application to the Dongwushi Reservoir in China illustrates that the dam overtopping risk computed using the improved Monte Carlo simulation is lower than that using mean-value first-order second-moment method. Furthermore, the sensitivity analysis show that initial water surface level is more sensitive to overtopping risk than wind velocity.

Reliability analyses of slope stability

ABSTRACT This paper proposes the coupling of reliability analysis methods with various mechanical approaches, for a slope stability assessment. Probabilistic strategies include Monte Carlo Simulation method (MCS), First and Second Order Reliability Methods (FORM, SORM), Mean-Value First-Order Second-Moment method (MFOSM) and Quadrature method (QM). Three mechanical models are considered: a Caquot-Taylor formula, a limit equilibrium method of Bishop and a finite element (FE) model based on the strength reduction method (SRM). The present study assumes both the cohesion and friction angle of the soil as uncertain input parameters, to be modelled as correlated random variables. The dependence of the slope reliability on the mechanical modelling and used probabilistic strategies is highlighted.

Reliability Assessment of Corrosion Initiation of Harbor Concrete Structure Using FOSM

Due to the uncertainty of variables in durability model, the probabilistic approach is increasing. Monte Carlo Simulation (MCS) is an easily accessible method, but requires a lot of repeated operations. This paper evaluated the effectiveness of First Order Second Moment method (FOSM), which is more convenient and time saving method than MCS, to predict the corrosion initiation in harbor concrete structure. Mean Value First Order Second Moment method (MV FOSM) and Advanced First Order Second Moment method (AFOSM) are applied to the error function solution of Fick's second law modeling chloride diffusion. Reliability index and failure probability based on MV FOSM and AFOSM are compared with the results by MCS. The comparison showed that AFOSM and MCS predict similar reliability indexes and MV FOSM underestimates the probability of corrosion initiation by chloride attack. Also, the sensitivity of variables in durability model to failure probability was evaluated on the basis of AFOSM. The results showed that AFOSM is a simple and efficient method to estimate the possibility of corrosion initiation in harbor concrete structures.

Comparison of Risk Calculation Methods for a Culvert

A comparative study of eight different risk calculation methods has been performed on the occurrence probability of inad- equate capacity of a culvert to pass floods. The five basic risk calculation methods used in this study are the mean-value first-order second-moment method, advanced first-order second-moment method, point estimate method, Latin hypercube sampling method, and Monte Carlo simulation. Two options each for the point estimation and Monte Carlo methods are also investigated. Building upon the first four basic calculation methods, three additional methods are suggested. They are the first-order second-moment mixed mode method, generalized mixed mode method, and significant component method. Within each of the first four basic methods risks are calculated, whenever possible, using two definitions of failure parameter, i.e., ~1! the performance function Z directly as a function of all the contributing variables; and ~2! separate calculations of loading and resistance ~capacity!. Logic trees are presented to illustrate possible causes of culvert failure, the ways to account for component factors such as those from hydraulics and hydrology and to combine the component risks for total risk. Risk of inadequate flow capacity for a five-foot diameter culvert is evaluated as an example. Three sets of uncertainty data for the random variables are used; the first set data is adopted from a study in the literature, in which uncertainties from loading dominate. The second set of data is hypothetical with resistance uncertainties as the major contribution to failure; whereas in the third set, loading and resistance have about equal contributions of uncertainties. The relative errors of computed risks with respect to Monte Carlo simulation results are compared. The results show that for conditions similar to those tested, most of the methods are computationally simpler than the Monte Carlo simulation, and can be used for risk calculation. Cautions to some of the methods are remarked.

STOCHASTIC WATER QUALITY ANALYSIS USING RELIABILITY METHOD1

ABSTRACT: This study developed a QUAL2E‐Reliability Analysis (QUAL2E‐RA) model for the stochastic water quality analysis of the downstream reach of the main Han River in Korea. The proposed model is based on the QUAL2E model and incorporates the Advanced First‐Order Second‐Moment (AFOSM) and Mean‐Value First‐Order Second‐Moment (MFOSM) methods. After the hydraulic characteristics from standard step method are identified, the optimal reaction coefficients are then estimated using the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method. Considering variations in river discharges, pollutant loads from tributaries, and reaction coefficients, the violation probabilities of existing water quality standards at several locations in the river were computed from the AFOSM and MFOSM methods, and the results were compared with those from the Monte Carlo method. The statistics of the three uncertainty analysis methods show that the outputs from the AFOSM and MFOSM methods are similar to those from the Monte Carlo method. From a practical model selection perspective, the MFOSM method is more attractive in terms of its computational simplicity and execution time.

Reliability-Based Design Format for Marine Structures

Recently there has been increased effort by classification societies and design authorities to bring reliability analysis into the design process. Typically these efforts involve using some reliability analysis method to calculate "partial safety factors" for design equations. The mean-value first-order second-moment method (MVFOSM), the advanced second-moment method (ASM), and an "exact" method have been used, or are being proposed for use, in the design of marine structures. In some recent work it has been shown that design formats based on the first two methods may result in engineering designs of different reliability levels than the ones specified in developing the design formats. These three methods are evaluated and a "reliability-conditioned (RC) method" is proposed in this paper. The proposed method overcomes the shortcomings of the MVFOSM and ASM methods and extends the concepts of the "exact" method in a more useful form to handle general types of problems. The RC method is believed to result in partial safety factors which give engineering designs of reliability levels equal to the specified ones.