Evaluation of tunnel support structure reliability

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

A logical framework is developed for load and resistance factor design (LRFD) of slopes based on reliability analysis. LRFD of slopes with resistance factors developed in this manner ensures that a target probability of slope failure is not exceeded. Three different target probabilities of failure (0.0001, 0.001 and 0.01) are considered in this report. The ultimate limit state for slope stability (formation of a slip surface and considerable movement along this slip surface) is defined using the Bishop simplified method with a factor of safety equal to unity. Gaussian random field theory is used to generate random realizations of a slope with values of strength and unit weight at any given point of the slope that differ from their mean by a random amount. A slope stability analysis is then performed for each slope realization to find the most critical slip surface and the corresponding driving and resisting moments. The probability of slope failure is calculated by counting the number of slope realizations for which the factor of safety did not exceed 1 and dividing that number by the total number of realizations. The mean of the soil parameters is adjusted and this process repeated until the calculated probability of failure reaches to the target probability of failure. Optimal resistance and load factors are obtained by dividing the resisting and driving moments corresponding to the most probable ultimate limit state by the nominal values of resisting and driving moments. The main goal of this study was to provide specific values of resistance and load factors to implement in limit states and load resistance design of slopes in the context of transportation infrastructure. This report discusses the concepts of load and resistance factors, target probability of failure and the ultimate limit state equation in the context of slope stability analysis. It then presents a detailed algorithm for resistance factor calculation by using reliability analysis. Six cases of real slopes designed and constructed by the Indiana Department of Transportation (INDOT) are examined by using undrained shear strengths in order to illustrate the LRFD procedure and validate the recommended resistance and load factors.

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.

This paper presents the application of a reliability based design methodology for interference between trawl gear and pipelines, and the associated cost savings in subsea rock installation. As part of Wintershall Norge's Maria development project, a 26 km long 14″ production flowline with DEH (Direct Electrical Heating) and a 46 km (43 km + 3 km infield) long 12″ water injection pipeline has been installed and left exposed on the seabed. The seabed topography in the area is un-even and scarred by iceberg ploughmarks, leading to a significant number of large free spans. Furthermore, fishing activity must be taken into account in the design of these pipelines. According to DNV-RP-F111, if the trawl gear hits in a free span, the pull-over load will be significantly higher than if it hits a section in contact with the seabed. Preliminary analysis indicated that by using the LRFD (Load and Resistance Factor Design) approach as per DNV-RP-F111, a large number of free spans would require rock infill in order to limit the trawl pull-over load. In order to optimize the design and potentially reduce the requirement for free span infill, an optimised methodology based on SRA (Structural Reliability Analysis) was proposed by Wintershall, developed by DNV GL and implemented by Subsea 7 during detail design phase. The optimised methodology involves FE analyses of the sensitivity to various parameters and Monte Carlo simulations, in order to quantitatively assess the probability of failure. Specific FE models analysing the bending moment capacity and response were established. The various input parameters were assessed and included as distributions if deemed required from the sensitivity analysis. Finally, a Monte Carlo simulation was performed to calculate the probability of failure. It was demonstrated that the target safety levels defined by DNV-OS-F101 were reached without free span infill, and hence significant savings in subsea rock installation could be achieved without any deviation from the DNV-OS-F101 code. Cost saving due to reduced subsea rock installation scope is estimated to 7.6 mill Euro. Wintershall facilitated a close dialogue between DNV GL and Subsea 7 throughout the work progress. This resulted in a constructive and open approach, ensuring efficient delivery of the detailed design in line with project schedule. The work carried out has demonstrated two relevant examples where performing a SRA, as opposed to a LRFD, has resulted in a significant reduction of seabed intervention requirements and an associated cost saving, while still being in compliance with DNV-OS-F101 target safety levels. To our knowledge this is the first time the SRA method has been applied for trawl interference design on a live project, and on a CRA (Corrosion Resistant Alloy) lined pipeline with DEH system attached. The success was made possible by close collaboration between the parties involved; Wintershall, DNV GL and Subsea 7.

Achieving uniform reliability is a desired intent of design standards based on Load and Resistance Factor Design (LRFD) methodology. The design standard for offshore wind turbines, the IEC 61400-3 (IEC, 2009), also follows the LRFD. This standard is based on European experience and it may not necessarily represent offshore environment in the US waters, where several offshore wind farms are being planned. For these reasons, it is of interest to investigate factors that may influence the reliability of offshore wind turbines under various levels of wind and wave loads. We evaluate the reliability index, which is a measure of the probability of failure, for the ultimate limit state associated with the fore-aft tower bending moment at the mudline for offshore wind turbines with fixed support structures. We compare reliability index for various values of characteristic levels and coefficients of variation of wind and wave loads, as well as for various ratios of hydrodynamic to aerodynamic loads. These parameters represent different sites and turbine designs. Using the combined wind and wave load effect model for offshore wind turbines proposed by Tarp-Johansen (2005), we show that the range of reliability levels are reasonably uniform under various combinations of wind and wave loads. This meets the intent of codes based on the LRFD. Since large diameter monopile support structures tend to be dominated by inertia forces, while jacket support structures with smaller diameter members are often dominated by drag forces, we also employ a more general wave load formulation that models both drag and inertia forces. We include this wave load model in the combined wind and wave load effect model for offshore wind turbines, and estimate resulting reliability levels. Results show that dragonly case results in smaller estimates of reliability index than the inertia-only case. Moreover, for inertia-dominated cases, reliability levels are found to be even more uniform than those for drag-dominated case. Introduction Several design codes, including the IEC 61400-3 (IEC, 2009) standard for offshore wind turbines, are based on the Load and Resistance Factor Design (LRFD). Designs of an entire class of structures based on the LRFD methodology tend to have a uniform reliability. On the other hand, different designs in a class of structures may have quite different reliability levels if working stress design methodology is followed. LRFD is particularly useful for loads that exhibit considerable variability. Offshore wind turbines are influenced by wind as well as wave loads, both of which can exhibit significant variability. Therefore, it is of interest to understand influence of various factors on the reliability of offshore wind turbines under various levels of wind and wave loads. Understanding reliability levels is even more important for relatively new industries like offshore wind energy for which the design practice is still evolving. The first edition of IEC 61400-3, the Design Requirements for Offshore Wind Turbines (IEC, 2009), was issued only recently in 2009. This standard is based more on the European experience, where the offshore wind industry is about a decade old. Lately, there has been considerable interest in developing offshore wind farms in the US waters. Care has to be used in applying IEC standards in the US where offshore environment is quite different than that in Europe. The offshore oil and gas industry is quite mature in the US, and American standards for design of fixed-bottom offshore structures exist, such as API RP 2A-LRFD (API, 2003) and API RP 2A-WSD (API, 2005). However, these standards were not intended for wind turbines, which are active machines instead of passive structures, and for which loads on support structures are mainly dominated by aerodynamic loads.

This study concerns the prediction of tensile capacity as governed by concrete cone failure of single anchors placed in uncracked, unreinforced concrete and located far from a free edge and far from other anchors. A total of approximately 801 data points is available from tests on such anchors. A total of 31 data points consisting of data on high-strength anchors previously compiled by Klingner et al., 1 Collins et al., 2 and Cannon is accessible from tests on single anchors failing by fracture of anchor steel. Using common definitions and nomenclature for all variables and material properties, each data set is placed in a database using SI units and concrete cube strengths. The concrete cone failure data are then plotted against capacities predicted by three existing methods: 1) the 45 deg cone method of ACI 349-90, Appendix B; 2) a variable angle cone method (VAC); and 3) the concrete capacity method (CC method). Observed data are compared against these existing methods in terms of average square error and load and resistance factor design (LRFD). Finally, using the principles of load and resistance factor design (LRFD) and following the design procedure of ACI 349-90, Appendix B, the probability of steel or concrete failure under known loads and the probability of concrete failure under unlimited loads are calculated. Based on those comparisons, each approach is evaluated with respect to accuracy and suitability for use in design. For single tension anchors with embedment depths less than 8 in., all three capacity prediction methods fit most of the data relatively well. However, the CC method is more accurate and has a distinctly lower probability offailure when the embedment depth is greater than 8 in.

The design of shallow foundations typically proceeds by using the load and resistance factor design (LRFD) methodology to avoid various limit states with some probability. This paper looks at the sliding limit state of shallow foundations, and the sliding resistance factors required for the LRFD approach are estimated using reliability analyses of surface strip foundations. Cohesive and frictional soils are separately studied under wind loading conditions. Monte Carlo simulations are used to estimate the sliding failure probability of foundation designs on cohesive soils, and an analytical method is developed for frictional soils. The results indicate the existence of a “worst case” correlation length for cohesive soils, and the sliding resistance factor required to achieve target maximum lifetime failure probabilities is around 0.4–0.65 for moderate soil variability. For frictional soils, the required sliding resistance factor is about 0.5–0.85 for ν ϕ′ = 0.15. Overall, the sliding resistance factors recommended here agree well with the resistance factors of ϕ gu = 0.6 for cohesive soils and ϕ gu = 0.8 for frictional soils stipulated by geotechnical LRFD code provisions in Canada. The analyses can be used to estimate the reliability of current designs and can also aid the calibration of geotechnical design codes.

The estimation of reliability in timber structures is a procedure complicated by the time-dependent nature of timber failure, coupled with the complex structural behaviour of timber systems. Prior to the implementation of probabilistic concepts, design recommendations given in British Standards were based on permissible stress design, and a similar procedure of allowable stress design employed in the United States. While permissible stress specifications are easy to use, their application results in an inability to achieve a desired uniform level of reliability. Such situations have led to the implementation of probability-based limit states such as load and resistance factor design (LRFD), based on calculating the ‘probability of failure’. The statistical variations and uncertainties in loading and material properties are now established and incorporated into the design process. This change in design philosophy has resulted in the development of new design standards such as Eurocode 5: Design of Timber Structures which is to replace the permissible stress codes of BS 5268. A review of the development of limit states design has been undertaken, and includes the design methods employed prior to the introduction of probability-based design. This review focuses attention on the LRFD format, and although this is not the only probabilistic format available, it is the format that has evolved as the most widely adopted technique.

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 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 parameters for load and resistance factor design (LRFD) of driven piles using dynamic methods are presented based on a database of 218 pile cases in Florida. Eight dynamic methods were studied: ENR, modified ENR, FDOT, and Gates driving formulas, Case Analysis with Wave Analysis Program (CAPWAP), Case Method for Pile Driving Analyzer (PDA), Paikowsky's energy method, and Sakai's energy method. It was demonstrated that the modern methods based on wave mechanics, such as CAPWAP, PDA, and Paikowsky's energy methods, are roughly twice as cost effective to reach the target reliability indices of 2.0 to 2.5 (failure probability = 0.62 to 2.5%) as the ENR and modified ENR driving formulas. The Gates formula, when used separately on piles with Davisson capacities smaller or larger than 1779 kN, has an accuracy comparable to the modern methods. The utilizable measured Davisson capacity, defined as φ/λ (ratio of resistance/mean capacity) obtained from testing at beginning of redrive (BOR), is only slightly larger than the end of drive (EOD) values. Furthermore, past practice with driving formulas reveals the existence of a large redundancy in pile groups against failure. The latter suggests the use of a lower relatively reliability target index, βT = 2.0 (pf = 2.5%) for single pile design. Also, the utilizable measured Davisson capacity, φ/λ, for all the dynamic methods studied, is quite similar to published values (Lai et al. 1995; Sidi 1985) for static estimates from in situ tests.

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.

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.

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.