Reliability-Based Load and Resistance Factors Design for Offshore Jacket Platforms in the Bohai Bay:Calibration on Design Factors

For the fulfillment of the probability-based structural design for the offshore jacket platforms in the Bohai Bay, the design factors of loads, resistance and load combinations are much necessary to be calibrated according to the proposed target reliability index. Firstly, the limit states function for the offshore jacket platforms is introduced. Then, four approaches to calibrate the factors of load and resistance are presented and compared. Afterwards, the methods to calibrate the load combination factors are developed. Finally, the factors of load, resistance and load combination for the offshore jacket platforms in the Bohai Bay are calibrated and the corresponding design formulae are recommended. The results are proved to be rational in practice, and also illustrate that the proposed target reliability index for offshore jacket platforms in the Bohai Bay is also appropriate.

Calibration of LRFD Format for Steel Jacket OffshorePlatform in China Offshore Area(2): Load, Resistance and Load Combination Factors

Adopting the load and resistance factor design format, the design method for steel jaeket platform structures is developed. Firstly, the limit state equations and design format for steel jacket platform structures are introduced. Then, the ratio of live load effect to dead load effect is estimated. The target reliabilities for design of offshore structures in China offshore area are calibrated by past practice in API RP2A-WSD code. The load and resistance factors are optimized by minimizing the difference within the target reliability and the resulting reliability over the range of load effect ratios. Considering the concurrence of different loads, load combination factors are obtained through an optimization process, and the relation between the load combination factor and load correlation coefficient is established. Finally, the design formulae for steel jacket structures in China offshore area are recommended.

Estimation of load and resistance factors using the thirdmoment method based on the 3P-Iognormal distribution

Load and resistance factors are generally obtained using the first order reliability method(FORM)in which the design point should be determined and derivative-based iterations used.In this article,the thirdmoment reliability index,based on the three-parameter lognormal(3P-lognormal)distribution,is investigated.A simple method based on the third-moment method for estimating load and resistance factors is then proposed,and a simple formula for the target mean resistance is also presented to avoid iterative computations.Unlike the currently used method,the proposed method can be used to determine load and resistance factors,even when the probability density functions(PDFs)of the basic random variables are not available.Moreover,the proposed method does not require the iterative computation of derivatives or any design points.Thus,the method provides a more convenient and effective way to estimate load and resistance factors in practical engineering applications.Numerical examples are presented to demonstrate the advantages of the proposed third moment method for determining load and resistance factors.

Bridge pier failure probabilities under combined hazard effects of scour, truck and earthquake. Part Ⅰ: occurrence probabilities

In many regions of the world, a bridge will experience multiple extreme hazards during its expected service life. The current American Association of State Highway and Transportation Officials （AASHTO） load and resistance factor design （LRFD） specifications are formulated based on failure probabilities, which are fully calibrated for dead load and nonextreme live loads. Design against earthquake loads is established separately. Design against scour effect is also formulated separately by using the concept of capacity reduction （or increased scour depth）. Furthermore, scour effect cannot be linked directly to an LRFD limit state equation, because the latter is formulated using force-based analysis. This paper （in two parts） presents a probability-based procedure to estimate the combined hazard effects on bridges due to truck, earthquake and scour, by treating the effect of scour as an equivalent load effect so that it can be included in reliability-based bridge failure calculations. In Part I of this series, the general principle of treating the scour depth as an equivalent load effect is presented. The individual and combined partial failure probabilities due to truck, earthquake and scour effects are described. To explain the method of including non-force-based natural hazards effects, two types of common scour failures are considered. In Part 11, the corresponding bridge failure probability, the occurrence of scour as well as simultaneously having both truck load and equivalent scour load are quantitatively discussed.

Bridge pier failure probabilities under combined hazard effects of scour, truck and earthquake. Part Ⅱ: failure probabilities

In many regions of the world, a bridge will experience multiple extreme hazards during its expected service life. The current American Association of State Highway and Transportation Officials （AASHTO） load and resistance factor design （LRFD） specifications are formulated based on failure probabilities, which are fully calibrated for dead load and non-extreme live loads. Design against earthquake load effect is established separately. Design against scour effect is also formulated separately by using the concept of capacity reduction （or increased scour depth）. Furthermore, scour effect cannot be linked directly to an LRFD limit state equation because the latter is formulated using force-based analysis. This paper （in two parts） presents a probability-based procedure to estimate the combined hazard effects on bridges due to truck, earthquake and scour, by treating the effect of scour as an equivalent load effect so that it can be included in reliability-based failure calculations. In Part I of this series, the general principle for treating the scour depth as an equivalent load effect is presented. In Part II, the corresponding bridge failure probability, the occurrence of scour as well as simultaneously having both truck load and equivalent scour load effect are quantitatively discussed. The key formulae of the conditional partial failure probabilities and the necessary conditions are established. In order to illustrate the methodology, an example of dead, truck, earthquake and scour effects on a simple bridge pile foundation is represented.

Towards establishing practical multi-hazard bridge design limit states

In the U.S., the current Load and Resistance Factor Design （LRFD） Specifications for highway bridges is a reliability-based formulation that considers failure probabilities of bridge components due to the actions of typical dead load and frequent vehicular loads. Various extreme load effects, such as earthquake and vessel collision, are on the same reliability-based platform. Since these extreme loads are time variables, combining them with not considered frequent. non- extreme loads is a significant challenge. The number of design limit state equations based on these failure probabilities can be unrealistically large and unnecessary from the view point of practical applications. Based on the opinion of AASHTO State Bridge Engineers, many load combinations are insignificant in their states. This paper describes the formulation of a criterion to include only the necessary load combinations to establish the design limit states. This criterion is established by examining the total failure probabilities for all possible time-invariant and time varying load combinations and breaking them down into partial terms. Then, important load combinations can be readily determined quantitatively,

Performance of reliability-based design formats in geotechnical applications

Geotechnical design codes and guidelines are all switching from traditional factor of safety design to modern load and resistance factor design(LRFD)or partial factor design(PFD),in the belief that the latter two bring more flexibility and reliability consistency across various design scenarios,thus produce safe and cost-effective design outcomes.This paper first reviews the LRFD and PFD developed for geotechnical applications.A total of seven methods to calibrate the load and resistance factors are also introduced.The ability of the LRFD and PFD to produce designs with consistent reliability is examined and compared to that of a traditional factor of safety method using two examples of the bearing capacity of strip footings and the global stability of soil nail walls.Results showed that the framework of LRFD offers no apparent advantages over working stress design(WSD)in achieving more consistent reliability for geotechnical structures;the dispersion in design probabilities of failure could be five to seven orders of magnitude difference.The variation will be reduced to three orders if using the PFD.Neither reducing the variability in soil shear strength parameters nor allocating partial resistance factors with respect to soil types would efficiently harmonize the reliability levels when dealing with multiple soil layer conditions.In addition,the uniformity of reliability levels is insensitive to calibrations with or without presetting the load factors.This study provides insights into the LRFD and PFD frameworks currently developed for geotechnical applications.