Towards Understanding Reliability Levels for Offshore Wind Turbines

API RP2A Load and Resistance Factor Design is a limit state design practice which is intended to replace the existing Working Stress Design practice for designing fixed offshore structures. Being in partial safety factor format, LRFD offers plenty of scope for influencing and improving design by calibrating the partial factors to suit regional environmental conditions and design practices. This paper presents the results from a joint industry project on the calibration of LRFD for Mediterranean Sea platforms. Advanced structural reliability methods formed the basis of the code calibration procedure which is briefly outlined. Probabilistic models for environmental and gravity loads and modelling uncertainties for tubular member and joint strength adopted in the reliability analysis are described. Comparisons of reliability indices for components designed under LRFD and WSD 18th Edition indicate that for the storm condition LRFDwould introduce a very small weight penalty whilst for the operating condition there would be a weight reduction. The application of LRFD would lead to significantly more uniform component reliability compared to WSD designs. Based on the proposed partial load factors for the MediterraneanSea the impact of LRFD to the design of jacket structures is assessed through verification studies of two typical platforms in the region. INTRODUCTION Regional variations in wave climate and design practice can be accounted for in LRFD-type design codes for offshore structures. The reliability based API RnA LRFD (Load andResistance Factor Design) [1], which has been proposed as an alternative to the Working Stress Design practice [2], takes into account the uncertainties associated with applied loads and structural component resistances and factors both loads and resistances. In contrast, in WSD only resistance factors are applied to derive allowable stresses. By explicitly defining partial factors for gravity and environmental loads it is possible to account for the variabilities in environmental conditions and design practices that exist worldwide. The partial load and resistance factors in the LRFD draft issue have been calibrated primarily for Gulf of Mexico structures [3]. Partial load factors for North Sea structures have beensubsequently proposed, based on the results of a joint industry project where advanced structural reliability methods were used for code calibration [4,5]. Following the conclusion of the North Sea adaptation the project was extended to adapt LRFD to the Mediterranean Sea [6]. Details of the underlying philosophy and procedures adopted for the calibration are given in [4]. This paper focuses on the work undertaken in the context of the Mediterranean Sea and presents the background information. Partial load factors for the in-place extreme and operating conditions have been derived using the same reliability based procedures to those adopted for the North Sea calibration. Based on the proposed load factors verification studies havebeen carried out for two typical jacket structures. The results are reported through comparisons of utilisation ratios for tubular members, legs and joints designed using LRFD and RP2A-18th Edition. They demonstrate potential effects of implementing LRFD to the Mediterranean Sea environment and highlight problem areas. Reference to the proposed LRFD version incorporatingrecommended Mediterranean Sea adjustments will be to LRFDMed.

American Electric Power (AEP) has traditionally designed foundations for self-supporting transmission line structures using allowable geotechnical capacities, empirical design procedures, and the same designs system-wide without considering variations in geology. However, the ASCE Manual 74 (ASCE, 1991) and others have encouraged the adoption of the Load and Resistance Factor Design (LRFD) approach. Therefore, AEP adopted the LRFD approach for updating their internal design standards. A significant advantage of LRFD is that the same format is used to design both structures and foundations. In addition, the designer has a useable framework to establish relative levels of reliability among the components of the transmission line system. And finally, the LRFD design procedure for foundations can easily address variations in geology. This paper describes the concepts employed by AEP in the implementation of the LRFD approach for steel grillage foundations for the AEP 765 kV Wyoming-Jackson's Ferry transmission line.

In the past, allowable stress design (ASD) was used to design steel structures. The allowable stresses used were determined from previous practice, with limited understanding of the reliability and risk performance provided by the structure. Engineering methods based on Load and Resistance Factor Design (LRFD) provide more accurate lifetime models of structures by providing risk-based load factors. Besides improved safety, cost savings can be provided through improved performance and, in some cases, by delaying rehabilitation. This research project develops LRFD-based engineering procedures for the evaluation and design of hydraulic steel structures (HSS). Hydraulic loads are a key element to the LRFD analysis. This report identifies the primary hydraulic loads and describes procedures that can be used to determine these hydraulic loads. Existing design guidance for HSS is described and presented in the individual chapters. The appendixes to the report provide examples of the procedures used to compute the hydrostatic, wave, and hydrodynamic loads. A new approach for determining wind-induced wave loads was developed. Design guidance for computing the hydrodynamic load was limited for many of the HSS. Additional research is recommended to improve capabilities for computing hydraulic loads. Details on these recommendations can be found in this report.

The load and resistance factor design (LRFD) approach employed in geotechnical design codes is often calibrated using the reliability-based design (RBD) method. However, the LRFD may not achieve the target safety level exactly. This paper makes comparisons between the LRFD and RBD by considering the ultimate and serviceability limit state design of strip foundations. The RBD is carried out via the Random Finite Element Method. It is found that the failure probability and the resulting foundation width for ULS obtained using the RBD increase with the soil spatial correlation length, gradually reaching a plateau. The comparison between the LRFD and RBD results for ULS suggests that the LRFD is conservative for low to medium soil variability, particularly at smaller correlation lengths. The reliability-based SLS design is less dependent on the soil correlation length, particularly for lower coefficients of variation of the soil elastic modulus. However, a resistance factor of 1.0 for SLS is unconservative, and resistance factors of 0.65, 0.7 and 0.8 are better aligned with the RBD when the target failure probabilities are 1×10−3, 1×10−2 and 1×10−1. The current study can be used to guide the design of shallow foundations and the calibration of the LRFD approach.

In this paper, the detail of Load and Resistance Factor Design (LRFD) approach which is based on reliability concept for the design of Reinforced Soil (RS) walls is presented. For conventional methods i.e Allowable Stress Design (ASD) Method, the factor of safety is applied only to resistance and loads are considered without variations. For LRFD method, factor of safeties are applied for both load and resistance. Due to availability of large statistical data and economy, this method is preferred. An attempt is made to solve one numerical example of geosynthetic RS walls due to soil selfweight plus permanent uniform surcharge using LRFD as well as other conventional methods (ASD) viz. FHWA, Modified Rankine, NCMA and B.S Code Methods and the results of the LRFD methods are compared with conventional design methods and concluding remarks are presented. The various equations are obtained based on various curves plotted by using ASD and LRFD approaches. From these equations it is clear that if FOS against tensile rupture is known for any RS wall having 7m height and same properties and environmental conditions as mentioned in current study then FOS against pullout failure and pullout capacity can be computed for these walls.

The use of the Load and Resistance Factor Design (LRFD) for Class 2 nuclear piping can be an alternative of the traditional Allowable Stress Design (ASD) method currently used in the ASME Boiler Pressure Vessel Code, Section III, Div. 1 providing the benefit of a known and consistent reliability for the designed piping. The design uncertainties and the necessary safety margin are evaluated for each equation for all service levels by considering the applied loads (e.g., earthquake, deadweight, internal pressure, etc.) and the resistance of steel, in the form of either the yield or ultimate strength, as separate variables described by their mean value, distribution, and coefficient of variation. The procedure yields different partial safety factors for each load and the resistance in opposition to the one safety factor used in each of the ASD equations of the Code. Although LRFD equations have been developed in the past, a range of possible partial safety factors were assigned to the variables, corresponding to different levels of reliability. This paper discusses the method used, namely calibration, for achieving same reliability as in the Code equations, and the progress made to assess a minimum target reliability index or else acceptable probability of failure for the LRFD equations that consider the earthquake load for pressurized pipes as well as the design for internal pressure for Class 2 nuclear pipes made of carbon steel.

ABSTRACT: Load and resistance factor design (LRFD) is now recommended in North American design codes for reinforced-soil structures, including internal stability limit states. The selection of load and resistance factors that appear in limit state equations is best carried out using reliability-based analysis. In this paper the conventional approach to compute the limit state for geosynthetic reinforcement tensile rupture is reviewed, and is then recast in a reliability-based analysis framework suitable for LRFD calibration using bias statistics. The paper describes how to compute bias statistics from product-specific laboratory creep tests for the reinforcement rupture limit state. A database of results from creep tests on 94 different geosynthetic products was collected from 21 different sources. A total of 1086 in-air tensile test results and 540 creep-rupture data points were examined. This database is used to compute virgin and creep-reduced strength bias statistics for three different geosynthetic product categories. The results of analysis show that variability in the prediction of creep-reduced strength is very low, and is probably captured by the magnitude of variance in the original tensile strength of the test specimens. This greatly simplifies future LRFD calibration for the geosynthetic rupture limit state. An important implication of this study for LRFD design is that creep strength reduction factors can be taken as deterministic. The paper also provides a summary of computed creep-reduction factors that is a useful reference for future estimates of this factor from laboratory creep testing, and for preliminary design purposes using allowable stress design or LRFD approaches.

Load and resistance factor design (LRFD) incorporates state-of-the-art analysis and design methodologies with load and resistance factors that are based on the known variability of applied loads and material properties. These load and resistance factors are calibrated from actual bridge statistics to ensure a uniform level of reliability. LRFD allows a bridge designer to focus on a design objective or limit state; doing so can lead to a similar probability of failure in each component of the bridge. Bridges designed with the LRFD specifications should have relatively uniform reliability levels; such uniformity should ensure superior serviceability and long-term maintainability. Bridge hydraulics engineers should have the option of and ability to perform scour calculations that incorporate similar probabilistic methods. With this objective in mind, NCHRP Project 24–34 was initiated in April 2010 to develop a risk–reliability-based methodology that was based on risk and reliability and that could be used in calculating bridge pier, abutment, and contraction scour at waterway crossings so that scour estimates could be linked to a probability. The developed probabilistic procedures will be consistent with LRFD approaches used by structural and geotechnical engineers. This paper discusses sources of uncertainty in hydrologic estimates as those sources relate to bridge scour computations and summarizes a conceptual approach to the problem.

Load and Resistance Factor Design (LRFD) shows promise as a viable alternative to the present working stress design (WSD) approach to foundation design. The key improvements of LRFD over the traditional Working Stress Design (WSD) are the ability to provide a more consistent level of reliability and the possibility of accounting for load and resistance uncertainties separately. In order for foundation design to be consistent with current structural design practice, the use of the same loads, load factors and load combinations would be required. In this study, we review the load factors presented in various LRFD Codes from the US, Canada and Europe. A simple firstorder second moment (FOSM) reliability analysis is presented to determine appropriate ranges for the values of the load factors. These values are compared with those proposed in the Codes. The comparisons between the analysis and the Codes show that the values of load factors given in the Codes generally fall within ranges consistent with the results of the FOSM analysis. For LRFD to gain acceptance in geotechnical engineering, a framework for the objective assessment of resistance factors is needed. Such a framework, based on reliability analysis is proposed in this study. Probability Density Functions (PDFs), representing design variable uncertainties, are required for analysis. A systematic approach to the selection of PDFs is presented. Such a procedure is a critical prerequisite to a rational probabilistic analysis in the development of LRFD methods in geotechnical engineering. Additionally, in order for LRFD to fulfill its promise for designs with more consistent reliability, the methods used to execute a design must be consistent with the methods assumed in the development of the LRFD factors. In this study, a methodology for the estimation of soil parameters for use in design equations is proposed that should allow for more statistical consistency in design inputs than is possible in traditional methods. Resistance factor values are dependent upon the values of load factors used. Thus, a method to adjust the resistance factors to account for code-specified load factors is also presented. Resistance factors for ultimate bearing capacity are computed using reliability analysis for shallow and deep foundations both in sand and in clay, for use with both ASCE-7 (1996) and AASHTO (1998) load factors. The various considered methods obtain their input parameters from the CPT, the SPT, or laboratory testing. Designers may wish to use design methods that are not considered in this

This paper proposes a Load and Resistance Factor Design (LRFD) approach for the bearing capacity design of a strip footing. The load factors used are as specified by the National Building Code of Canada. The resistance factors required to achieve a certain acceptable failure probability are estimated as a function of the spatial variability of the soil as well as by the level of “understanding” of the soil properties in the vicinity of the foundation. The analytical results are validated by simulation. The results are primarily intended to aid the development of the next generation of reliability-based geotechnical design codes, but can also be used to guide current designs. Introduction Design of a shallow footing typically begins with a site investigation aimed at determining the strength of the founding soil or rock. Once this information has been gathered, the geotechnical engineer is in a position to determine the footing dimensions required to avoid entering various limit states. The limit states that are usually considered in the footing design are serviceability limit states (typically deformation) and ultimate limit states. The latter is concerned with safety and includes the load-carrying capacity, or bearing capacity, of the footing. This paper develops a load and resistance factor design (LRFD) approach for strip footings designed against bearing capacity failure. The design goal is to determine the footing dimensions such that the resistance to the load, Ru, satisfies

What differentiates a beam from a plate girder? This may seem to be a trivial question. However, it is a necessary and important part of plate girder design when applying the Load and Resistance Factor Design (LRFD) Specification. Making this distinction and the compactness classification early in plate girder design is important when using the LRFD Specification. The significance of these items can be seen in the LRFD Manual flowcharts for the determination of flexural and shear design strength. With these flowcharts, this discussion will focus on the design of plate girders according to LRFD rules. An explanation of plate girder design in the LRFD Specification will include: flexural design strength, shear design strength, flexure-shear interaction, bearing strength under concentrated loads and stiffener design. Application of the LRFD method will show there is actually little difference between it and Allowable Stress Design (ASD) of plate girders.

Load combinations in Section 2 of ASCE Standard 7 are provided for both Load and Resistance Factor Design (LRFD) and for Allowable Stress Design (ASD). Included in Section 2 are combinations addressing counteracting load effects, where the permanent gravity (dead) load stabilizes the structural system. Counteracting effects occur most commonly when destabilizing forces occur due to wind uplift or lateral wind or earthquake effects. In the 1998 and subsequent editions of ASCE Standard 7, the load factor on nominal dead load in the corresponding ASD combinations has been 0.6 rather than 1.0 to achieve some measure of consistency between ASD and LRFD. This reduction has been questioned by some engineers. This paper examines the treatment of counteracting loads in ASD from a structural reliability viewpoint similar to that used to develop the ASCE 7-05 load combinations for LRFD, and explains why the reduction in the dead load factor was necessary to achieve consistent reliability between ASD and LRFD.

최근 구조물 기초 분야에 대한 한계상태설계법이 국제적인 기술표준으로 요구됨에 따라 연구기반이 미약한 연약지반 개량공법에 대한 하중저항계수설계법 개발의 필요성이 대두되었다. 본 연구는 신뢰성 분석을 통해 항타강관말뚝의 목표신뢰성지수 및 저항계수를 산정하여 기초 구조물에 대한 LRFD code를 개발하고자 하였다. 프로그램의 검증을 위해 광양지역 16개의 항타말뚝 재하시험 결과와 2008년 한국건설기술연구원에서 이용된 57개의 항타말뚝 재하시험 결과를 취합하였다. 구조물기초설계기준에서 제안하고 있는 두가지 정역학적 설계공식에 대해서 대표 측정지지력과 설계지지력을 비교함으로써 저항편향계수를 평가하였고, 저항편향계수의 통계특성을 이용하여 일차신뢰도법 및 몬테카를로 실뮬레이션에 의한 신뢰성 분석을 실시하였다. 그 결과, 항타강관말뚝의 목표 신뢰성지수 2.0, 2.33, 2.5에 대해서 선단부 N치 50이하인 경우 두 지지력 공식의 저항계수는 각각 0.611~0.684, 0.821~0.537, 선단부 N치 50이상인 경우 각각 0.608~0.545, 0.749~0.643으로 제안되었다. 본 연구결과는 향후 다양한 기초구조물 및 지반구조물의 하중저항계수설계법 개발을 위한 자료로서 그 활용성이 있을 것이다. Recently, the necessity of developing the load and resistance factor design(LRFD) for soft ground improvement method has been raised, since the limit state design is requested as international technical standard for the foundation of structures. In this study, to develop LRFD codes for foundation structures in Korea, target reliability index and resistance factor for static bearing capacity of driven steel pipe piles were calibrated in the framework of reliability theory. The 16 data(in Gwangyang) and the 57 data(Korea Institute of Construction Technology, 2008) sets of static load test and soil property tests conducted in the whole domestic area were collected along with available subsurface investigation results. The resistance bias factors were evaluated for the tow static design methods by comparing the representative measured bearing capacities with the expected design values. Reliability analysis was performed by two types of advanced methods : the First Order Reliability Method (FORM), and the Monte Carlo Simulation (MCS) method using resistance bias factor statistics. As a result, when target reliability indices of the driven pipe pile were selected as 2.0, 2.33, 2.5, resistance factor of two design methods for SPT N at pile tip less than 50 were evaluated as 0.611~0.684, 0.537~0.821 respectively, and STP N at pile tip more than 50 were evaluated as 0.545~0.608, 0.643~0.749 respectively. The result from this research will be useful for developing various foundations and soil structures under LRFD.

In order to control serviceability problems arising from excessive settlement of shallow footings, geotechnical design codes generally include specifications regarding maximum settlement which often govern the footing design. Once the footing has been designed and constructed, the actual settlement it experiences on a real three-dimensional soil mass can be quite different than expected, due to the soil’s spatial variability. Because of this generally large variability (compared to other engineering materials such as concrete and steel) and because this particular serviceability limit state often governs the design, it makes sense to consider a reliability-based approach to settlement design. This chapter looks in some detail at a Load and Resistance Factor Design (LRFD) approach to limiting footing settlement. In particular, the resistance factors required to achieve a certain level of settlement reliability as a function of soil variability and site investigation intensity are determined analytically using random field theory. Simplified approximate relationships are proposed and tested using simulation via the Random Finite Element Method. It is found that the simplified relationships are validated both by theory and simulation and so can be used to augment the calibration of geotechnical LRFD code provisions with respect to shallow foundation settlement.

This paper presents the results of load and resistance factor design (LRFD) calibration of the facing limit states for soil nail walls. The current AASHTO facing load model and a modified model together with the AASHTO facing resistance models for both permanent and temporary facing load cases are considered. The facing design includes flexure, punching shear, and headed-stud tensile limit states. The calibration of resistance factors captures uncertainty in the accuracy of the load and resistance models, uncertainties in the nominal load and resistance values at time of design, and bias dependencies between model bias and nominal values. Resistance factors are calibrated for a range of load factors and target reliability indexes. Example designs for facing limit states demonstrate the implementation of the calibrated resistance factors in a LRFD framework using the current AASHTO and modified load models for the permanent facing load case. The practical values of this study are calibrated load and resistance factors for facing limit states of soil nail walls that are of interest to code writers for future editions of LRFD codes in the United States and Canada.