Load And Resistance Factor Design Research Articles

Improved Wave Equation Analysis for Piles in Soil-Based Intermediate Geomaterials with LRFD Recommendations and Economic Impact Assessment

The Wave Equation Analysis of Pile Driving (WEAP) has been widely used to determine drivability, predict static resistance, and assure the integrity of piles in soils. Assigning static and dynamic properties of Soil-based Intermediate Geomaterials (S-IGMs) remains a challenge in WEAP, partly attributed to IGMs that act as transition geomaterials between soil and hard rock. Furthermore, reliable static analysis methods for unit resistance predictions are rarely available for driven piles in S-IGMs in the default WEAP method. To alleviate these challenges, this study presents improved WEAP methods for steel piles driven in S-IGMs, including proposed damping parameters and Load and Resistance Factor Design (LRFD) recommendations based on newly developed static analysis methods and the classification of S-IGMs. A back calculation approach is used to generate the appropriate damping parameters for S-IGMs for three distinct subsurface conditions utilizing a database of 34 steel H- and pipe piles. Newly developed WEAP and LRFD procedures are also recommended. Additional independent 22 test pile data are used to compare and evaluate the accuracy and efficiency of the proposed WEAP methods with the default WEAP method. Compared with the default WEAP, bearing graph analysis results revealed that the selected proposed WEAP method, on average, reduces the underprediction of pile resistances by 6% and improves the reliability with a 43% reduction in the coefficient of variation (COV). Calibrated resistance factors for the proposed WEAP method increase to as high as 0.75 compared to the current AASHTO recommendation of 0.50. An economic impact assessment reveals that the proposed WEAP method is more efficient than the default WEAP method as the average difference in steel weight for 32 test piles is 0.06 kg/kN, almost close to zero, reducing the construction challenges in the current engineering practice.

Resistance Factor Spectra for the Ultimate Limit State of the National Building Code of Canada

Over the years, structural engineering codes and specifications in Canada and elsewhere have moved from an allowable stress design (ASD) approach to a load and resistance factor design (LRFD) philosophy. LRFD methodology takes better account of the inherent variability in both loading and resistance by providing different factors of safety for loads of distinct natures with regard to their probability of overload, frequency of occurrences and changes in point of application. The method also results in safer structures because it considers the behavior at collapse. While resistance factors for traditional construction materials based on LRFD in the National Building Code (NBC) of Canada are available, they cannot be used for non-conventional ones. This is because the resistance of such materials due to various load effects has unique bias factors (λR) and coefficients of variation (VR), which greatly impact their reliability index (β). In this study, relationships between the resistance factor ϕ and critical load effects from the NBC load combinations at ultimate limit states are developed for a wide range of resistance bias factors and coefficients of variation. The relationships are presented in the form of charts that are useful for researchers and code-writing professionals who have expertise in the various fields of structural engineering but lack proper background in reliability theory. The developed spectra showed that for the same ϕ, β increases with an increase in the live-to-dead load (L/D) ratio until it reaches 1; thereafter, the shape of the relationship will depend on the statistics of the resistance as well as on the magnitude of ϕ. For a small ϕ and VR, β will keep increasing with an increase in the L/D ratio from 1 until 3, albeit at a lesser rate. For L/D > 3, the relationship between the critical β and applied load is just about constant. This finding is also true for load combinations involving snow and wind. Application of the method is illustrated by a practical example involving the shear strength of a corrugated web steel beam.

Resistance factors for reliability based-design of geogrid reinforced soil foundations against ultimate and serviceability limit state

In the recent decades, the use of geosynthetics to improve the overall soil’s bearing capacity and settlement behavior under shallow foundations has become a major topic. Despite several studies that have been carried out on Reinforced Soil Foundations (RSF), no design specifications have been set to design RSF against the Ultimate and Serviceability Limit State (ULS and SLS) in any of the established codes. This paper presents the development of resistance factors based on the Load and Resistance Factor design (LRFD) approach against the ULS and SLS for strip footing resting on C−ϕ soils. The resistance factors are developed using a spreadsheet-based reliability model based on the First Order Reliability Method (FORM) to be consistent with the ASCE-7 load factors. The resistance factors are calibrated at a targeted probability failure (Pf) of 0.13499% and 0.00317% for ULS and 2.27%, for SLS. A Finite Element Model (FEM) is developed to validate three analytical solutions to establish the reliability model. The FEM results showed an agreement with the analytical solutions. For ULS the developed resistance factors at Pf= 0.13499% ranged from 0.33 to 0.9 assuming lognormally distributed variables and 0.25 to 0.89 assuming normally distributed variables. The resistance factors against SLS at Pf= 2.27%. ranged from 0.39 to 0.85 considering lognormally distributed variables and 0.35 to 0.83 considering normally distributed variables.

Comparative study on semi-probabilistic design methods to calibrate load and resistance factors for sliding stability design of caisson breakwaters

The partial safety factor method commonly necessitates a set of multiplying factors (MFs) to modify the basic variables; hence, when multiple variables are included, it is complicated for design practice. Conversely, the load and resistance factor design (LRFD) format is more practical since it utilizes fewer factors to adjust loads and resistance. This study carries out a comparative study of the two semi-probabilistic design formats and four calibration methods to determine the more suitable design approach and establish associated factors for sliding stability designs of caisson breakwaters under wave and seismic conditions. To fulfill the aforementioned purposes, 12 perforated caisson breakwaters are first selected; thereafter, four calibration methods, which include a closed-form solution and three scenarios based on Monte Carlo simulation (MCS), are executed to determine individual MFs for each case. The final single set of MFs for design practice is calibrated via an optimization process. The present study shows that the two design formats can provide similar solutions. Hence, the LRFD-based concept is recommended to be applied owing to its easier implementation in code calibrations and design practices. Moreover, the performance of the shifting-technique-MCS-based calibration (the simplest simulation) is thoroughly investigated, and it is then found that this approach must be used with care if the target safety considerably varies from the initial safety level. In the present work, an efficient and accurate approximation method to specify the final MFs set is proposed because the optimization-based calibrations to determine the final set of MFs are time-consuming and expensive to evaluate.

Estimation of confidence in the calculated resistance factor for simple limit states with limited data for load and resistance model bias

Estimation of the resistance factor in load and resistance factor design (LRFD) calibration for simple soil-structure limit states is most often based on model bias data of limited size. Frequently, the bias data are only available or required for the resistance term. In this paper, the confidence in the estimate of the mean of the resistance factor is computed for the case of one resistance factor and one load factor where limited model bias data are available for both load and resistance terms. The bootstrap method is used to compute synthetic load and resistance bias data sets from which confidence intervals on the point (mean) estimate of the resistance factor and load factor are computed. A closed-form solution is used to calculate the resistance factor for a single prescribed load factor and target reliability index, bias data, and nominal load and resistance variables that are lognormally distributed. However, the approach is general using Monte Carlo simulation. The method is demonstrated using the case of the internal stability pullout limit state for steel strip mechanically stabilized earth (MSE) walls. The example demonstrates the quantitative influence on pullout design using upper and lower 95% confidence interval limits for load and resistance factors.

ASD and LRFD: Reliability comparison for designs subjected to wind loads

Current design practice in the United States allows engineers to use either Allowable Strength Design (ASD) or Load and Resistance Factor Design (LRFD) method, under the assumption that both methods provide similar levels of economy (available design strengths) and safety (probabilities of failure and reliability indices) regardless of the design conditions. Recent studies have demonstrated that significant differences in economy can arise between ASD- and LRFD-based designs subjected to combinations of gravity and wind loads, suggesting inconsistencies between the safety levels. This study investigates the safety levels provided by the ASD and LRFD methods for such design cases. The safety levels were estimated using a formal reliability analysis with consideration of geometrically non-linear second-order effects. The reliability analysis was performed using Monte Carlo simulations with appropriate probability distributions for the random variables associated with both resistance and loads. The findings of this study indicate that generally accepted uniformity of reliabilities achieved by the ASD and LRFD methods does not hold for design cases governed by wind loads. The safety levels achieved by using the ASD method are less consistent than those achieved by using the LRFD method. The use of the ASD method generally entails the acceptance of failure risks many times greater than for those of the LRFD method, and target safety levels lower than those stipulated by the ASCE 7 Standard. These results highlight the need for a reevaluation of the current design practices to ensure that the required target levels of structural safety are consistently met.

Derivation of stainless steel material factors for European and U.S. design standards

Modern structural design standards are based on the Limit State Design (LSD) philosophy, also known as Load and Resistance Factor Design (LRFD), which involves the use of resistance functions with accompanying safety factors that are based on a statistical evaluation of relevant experimental data, carried out within the framework of a probabilistic reliability theory. This paper presents the derivation of material factors for the yield strength and ultimate tensile strength of austenitic, duplex and ferritic stainless steels, and their associated coefficients of variation (COV) for use in evaluating the safety factors for the European design code EN 1993-1-4 and the American design codes Specification for Structural Stainless Steel Buildings (ANSI/AISC 370–21) and Specification for the Design of Cold-Formed Stainless Steel Structural Members (ASCE/SEI 8–22). Separate material factors and associated COV values are required for the U.S. and European design codes due to the different minimum specified strength values that are given in the respective product standards. The material factors were derived by analysing a large amount of material data provided by different stainless steel producers, which encompassed a wide range of stainless steels and material thicknesses.

Structural reliability assessment of steel bridges using OSIM visual inspection data and Bayesian updating

Structural reliability theories are used in the calibration of load and resistance factor design (LRFD) in the Canadian Highway Bridge Design Code (CHBDC). The LRFD approach contains certain assumptions about uncertainties in the load and capacity estimation that prevent it from fully exploiting the information gathered during visual inspections. This paper presents a reliability-based framework for analyzing the visual inspection data obtained according to the Ontario structure inspection manual (OSIM). Existing deterioration models are adapted. The Bayesian interference is utilized to estimate the updated structural properties according to the prior information from the bridge maintenance and deterioration models and the new information collected from visual inspections. The criteria set by the CHBDC are used to analyze components and systems reliability. The value of the proposed framework for bridge evaluation and optimizing maintenance is demonstrated through the full implementation of a case-study bridge in the Canadian Province of NB.

Evaluation of the Earth Pressure Acting on Concrete Box Culverts

Earth pressure on concrete box culverts is a key component of design and load-rating decisions. The American Association of State Highway and Transportation Officials has revised the design guidelines over the years to impose greater design/rating earth pressures for buried structures. Currently, the Iowa Department of Transportation uses the maximum and minimum lateral earth pressure of 36/18 lb/ft3 specified for load factor design (LFD) and allowable stress design (ASD) and 60/30 lb/ft3 for load and resistance factor design (LRFD). The objective of this research is to monitor and evaluate the real earth pressures acting on deep-buried culvert structures. To achieve this objective, two concrete box culverts–one in Ida County and the other in Crawford County–were monitored for more than 2.5 years and 1 year, respectively, to identify the realistic design soil pressure. The captured pressure, strain, and temperature data were analyzed to find the relation between the temperature and earth pressure experienced by the culverts. The measured vertical and lateral pressures were compared with the specified design pressure loading. The monitoring results from both culverts led to the consistent conclusion that the earth pressure experienced by the culverts was two to six times that of the design values with the LRFD and LFD/ASD methods. This paper revealed that the earth pressure acting on the deeply embedded culvert could be higher than the design-specified value. Further research was recommended to investigate the relation between the soil weight and culvert vertical/lateral pressure for Iowa design specifications.

ASD and LRFD lateral load combinations: Comparison of required strength and reliability for design of structural steel

ASCE 7, Minimum Design Loads for Buildings and Other Structures, provides load combinations for both Load and Resistance Factor Design (LRFD) and for Allowable Stress Design (ASD), defining the required strength of structural members and connections. Similarly, the AISC Specification for Structural Steel Buildings provides resistance factors for LRFD and safety factors for ASD to be applied to the nominal strength for each limit state, permitting design using either method in conjunction with the corresponding load combinations in ASCE 7. Previous publications have demonstrated that similar designs (with similar levels of reliability) result from the application of LRFD and ASD for cases in which the governing load combination has live load as the principal load. This study presents comparison of ASD and LRFD demands, and corresponding reliability indices, from ASCE 7 lateral load combinations, determined with different proportions of dead, live, wind, and seismic load effects and a range of levels of second-order effects. The findings indicate that the generally accepted uniformity between the two design methods established for gravity load combinations does not always extend to lateral load combinations. For a range of conditions, design using ASD load combinations provides significantly lower reliability than using LRFD and does not meet the ASCE 7 reliability target.

Reducing the uncertainty of ULS load estimates in offshore structural design

The design process of any offshore structure, including Wave Energy Converters (WECs), aims to assess a series of critical conditions, often encapsulated in the concept of ‘limit states’, that define the ‘design boarders’ across which a structure is unlikely to respond satisfactorily, potentially leading to functional failure(s). The Load and Resistance Factor Design (LRFD) method aims to quantify such ‘design boarders’ with adequate safety margins on both the loading and the resistance sides of the design inequality. An inherent risk of such approach is that the definition of ‘adequate’ may be clouded by multiple sources of uncertainty, making it challenging to assess if a system is likely to be under- or over-designed from inception.
 Although overall guidance for the design process of a WEC can be sought from related industries – see e.g. [1], and while noting that generic guidance for WEC design is available in e.g. [2], there is at present limited (practical) guidance on how to derive estimates of long-term return period loads. In recent work, comparative assessments of different load estimation methods have been made, illustrating the dependence of the outputs on the underlying method – see e.g. [3]. Additionally, and in connection with the assessment of extreme loads acting on WECs, the load post-processing methodology was identified in [4] as the major contributor to the uncertainty in Ultimate Limit State (ULS) load estimates.
 This paper presents a novel post-processing methodology to assess the uncertainty when estimating ULS loads acting on an offshore structure. To assess which  statistical distributions are best suited to estimate long-term extreme loads, goodness-of-fit tests were performed using a series of input load time-series. The methodology was applied to evaluate the 50-year return load acting on the foundation of a generic Submerged Pressure Differential (SPD) WEC, based on the generic configuration originally defined in [5]. Results suggest that current conventional practices based on visual inspection(s) may lead to the selection of non-representative fitting functions which, in turn, likely lead to inaccurate extreme load estimations.
 Ultimately, the methodology described in this paper aims to contribute to a probabilistic approach to the definition of suitable safety factors, which in turn is expected to reduce the uncertainty in key design metrics and the risk of either under- or over-design.
 This study was conducted as part of the H2020 VALID and H2020 IMPACT projects.
 References
 [1] DNVGL-ST-0437. (2016). Loads and site conditions for wind turbines.
 [2] IEC/TS 62600-2. (2019). Marine energy — Wave, tidal and other water current converters Part 2: Design requirements for marine energy systems.
 [3] Michelen, C., Coe, R. Comparison of Methods for Estimating Short-Term Extreme Response of Wave Energy Converters, Sandia National Laboratories, SAND2015-6890C.
 [4] Atcheson, M., Cruz, J., Martins, T., Johannesson, P., Svensson, T. (2019). Quantification of load uncertainties in the design process of a WEC, Proc. 13th European Wave and Tidal Energy Conference (EWTEC 2019), Naples, Italy.
 [5] Babarit, A., Hals, J., Muliawan, M.J. et al. (2012). Numerical benchmarking study of a selection of wave energy converters. Renewable Energy 41, 44-63.

Reliability analysis framework for shallow foundations resting on reinforced cohesionless soils

Improving soil mechanical properties using reinforcement inclusions has become of major interest to many researchers. Accordingly, several numerical, analytical, and experimental studies have been conducted to explore the improvement of soil’s mechanical properties under shallow foundations. However, a comprehensive Reinforced Soil Foundations (RSF) design framework has not been established. This paper introduces a novel design framework for RSF based on the Load and Resistance Factor Design (LRFD) approach. Resistance factors for improved bearing capacity are computed using the First Order Reliability Method (FORM) for strip and square footings resting on loose sandy soil. A spreadsheet-based model is developed to compute the resistance factors at a targeted reliability index (βT) equal to 3 for ASCE-7 2000, AASHTO 1998, and EC7 (DA2) load factors. The resistance factors developed using ASCE-7 load factors ranged from 0.2 to 0.55 and 0.27 to 0.7 for a geogrid tensile strength of 45 kN/m and 160 kN/m, respectively. Load factors of different established design codes had a significant effect on the developed resistance factors. Soils with high frictional angles and embedment ratios resulted in conservative resistance factors. Moreover, the computed resistance factors for square footings were slightly higher in reinforced cases and lower for unreinforced cases than in strip footings.

Design and Full-Scale Testing of New MASH Test Level 4 (TL-4) Alaska 2-Tube Bridge Rail

The purpose of this project was to design and test a new Alaska multi-state 2-tube bridge rail meeting the safety-performance evaluation guidelines included in the American Association of State Highway and Transportation Officials (AASHTO) Manual for Assessing Safety Hardware (MASH), Second Edition 2016. The new 2-tube bridge rail designed and tested for this project was crash tested in accordance with MASH Test Level 4 (TL-4). Three crash tests were performed. The new bridge rail is 38 in. tall from the top of asphalt overlay and anchors to a 10 in. high by 18 in. wide curb. The curb was cast on top of a 35 ¾ in. wide deck cantilever that varied in thickness from 6 in. at the extreme field side edge to 12 in. at the exterior girder element. The posts were spaced on 10 ft centers. The posts were anchored to the concrete curb and deck using four 7/8 in. diameter A449 anchor bolts. The two-tube rail elements consisted of two HSS7 × 5 × 3/8 tubular elements. The calculated strength of the design was 77 kip at a height of 30 in. The bridge rail was considered acceptable for strength as per the AASHTO Load and Resistance Factor Design (LRFD) Section 13 Bridge Design Specifications. A test specimen of the bridge rail was constructed and crash tested per MASH TL-4. The new two-tube bridge rail met all the performance requirements of MASH TL-4. Details of the design and testing of the new bridge rail are provided in this paper.

From Reliability-Based Design to Resilience-Based Design

Abstract Reliability-based design has been a widely used methodology in the design of engineering structures. For example, the structural design standards in many countries have adopted the load and resistance factor design (LRFD) method. In recent years, the concept of resilience-based design has emerged, which additionally takes into account the posthazard functionality loss and recovery process of a structure. Under this context, the following questions naturally arise: can we establish a linkage between reliability-based design and resilience-based design? Does there exist a simple resilience-based design criterion that takes a similar form of LRFD? This paper addresses these questions, and the answer is “yes”. To this end, a new concept of structural resilience capacity is proposed, which is a generalization of structural load bearing capacity (resistance). The probabilistic characteristics (mean value, variance, probability distribution function) of resilience capacity are derived. Applying the concept of resilience capacity, this paper explicitly shows the relationship between the following four items: time-invariant reliability-, time-invariant resilience-, time-dependent reliability-, and time-dependent resilience-based design methods. Furthermore, an LRFD-like design criterion is proposed for structural resilience-based design, namely, load and resilience capacity factor design (LRCFD), whose applicability is demonstrated through an example. The LRCFD method can also be used, in conjunction with LRFD, to achieve reliability and resilience goals simultaneously of the designed structure.

Integrating Energy-Based Limit State Functions to Optimize Target Reliability of Bridge Pile for Seismic Events

The target reliability index is a safety and economic measure used to stipulate the optimal reliability level for structural elements. The conventional load and resistance factor design (LRFD) philosophy is premised on limit state functions that ignore structural performance by disregarding the structural stored energy capacity. Indeed, two significant concerns have yet to be adequately addressed within structural failure and safety analysis. The first pertains to the careful consideration of failure modes. The second involves the relationship between target reliability and hazard intensity. The main goal of this research is to propose a new energy-based limit state function to incorporate the performance-based design and LRFD philosophies concerning the target reliability of bridge substructure systems, including piles. The proposed energy-based limit state function can thoroughly examine a structure’s behavior in the presence of a natural disaster. This study’s reliability analysis corresponds to the seismic performance levels. The elastic and plastic energy resistance of pile elements is quantified concerning the various performance levels subjected to the loading scenarios. The uncertainties of soil and structural resistance and the structure’s dynamic response are considered and a new energy-based limit state function established. To validate the proposed limit state function, several finite element method models are examined to capture the probability energy distribution for structural resistance and loading conditions. Finally, the structural target reliability indices for the bridge piles are delineated using the proposed optimization approaches.

Optimal Design of Planar Steel Frames Using the Hybrid Teaching–Learning and Charged System Search Algorithm

In this study, a novel effective algorithm called HTC which results from a hybridization process between the teaching–learning-based optimization (TLBO) and charged system search (CSS) algorithms is proposed and utilized to optimize planar steel frames. Among the features of the proposed algorithm, simplicity and low number of setting parameters can be mentioned. The main goals of this hybridization process are to establish a balance between exploration and exploitation, increase the rate of convergence, and avoid getting trapped in the local optimal point. Moreover, the purpose of optimizing steel frames is to calculate their minimum weight by choosing suitable sections as well as considering the stress and displacement constraints in accordance with the requirements of the AISC design regulations using the load and resistance factor design (LRFD) method. To evaluate the performance of the HTC algorithm, standard benchmark steel frames are examined, and the results of the proposed algorithm are compared with other metaheuristic optimization methods. According to the outcomes of the comparison, the proposed algorithm has better performance than the other methods.

Improved Design Shear Method for the Bolted Cold-Formed Steel Clip-Angle Connector

In this paper, the ultimate shear capacity of the 3-bolt cold-formed steel clip-angle between the cold-formed steel (CFS) beam and column is evaluated through 54 laboratory tests. A series of experiments were conducted by varying (1) thickness, and (2) aspect ratio (L/D) of clip-angles for different depths (D) and widths (A). The experimental program consists of three phases of tests: (1) Phase-I: direct shear load tests on clip-angle attached to a CFS column through 4.6-grade bolts; (2) Phase-II: CFS column replaced with a hot-rolled steel (HRS) column, since the CFS column experienced bearing failure in Phase-I; and (3) Phase-III: 10.9-grade bolts used instead of 4.6, as the 4.6-grade bolts subjected to bolt shear failure in Phase-II. Failure modes observed in the test specimens are (1) shear local buckling of clip-angle; (2) column bearing failure; (3) bolt shear failure; and (4) tear failure in clip-angle. Design shear equations from the literature, for the bolted clip-angle, were found to be inefficient for the high-grade steel (fy=375 MPa to 550 MPa), and conservative for the commonly available low-grade steel (fy=275 MPa). Hence a new shear strength equation is suggested for the clip-angle from the collated data of the present study and past research work. A comparative study between 2-bolt and 3-bolt clip-angle configurations was conducted to evaluate the increase in shear strength. Reliability studies were conducted, and corresponding resistance and safety factors were suggested for the design shear strength calculation corresponding to load and resistance factor design (LRFD), limit state design (LSD), and allowable strength design (ASD) methods.

Unified Flexural Resistance Design Method and Evaluation Frame for the B-Regions of RC Flexural Members—Theory and Application

The load and resistance factor design (LRFD) method is normally used to design B-regions of reinforced concrete (RC) flexural members. The design includes many checks corresponding to different limit states. The LRFD method requires many loop calculation steps in the design, demonstrating its relative inefficiency. It cannot be applied to compare limit states directly and quantitatively. Different design limit states are separated and isolated. How to improve the analytical calculation efficiency of the LRFD method and to realize direct and quantitative comparisons between limit states are very important problems in structural engineering. This paper presents an innovative unified flexural resistance design (UFRD) method and a unified flexural resistance evaluation (UFRE) frame to solve these problems to some extent. The main contents include the unified flexural resistance (UFR) principles, formulas for the unified flexural resistance design (UFRD) method, the operation procedure to facilitate its usage, the UFRE framework to compare limit states, and three examples. The results show that the UFRD method can provide the same design outcomes as the LRFD one. However, UFRD calculations are simpler, requiring at most 20% of the calculation steps of the LRFD method. The UFRE frame can make different limit states compare with each other directly and quantitatively, which cannot be realized by the LRFD method. It helps expose some potential and insufficient flexural resistance hazards for some limit states, such as the only 10% relative strength reservation of one example. Thus, the UFRD method and the UFRE frame supplement and develop the LRFD method to some degree. The simplicity and practicality of the approach and the frame make them appropriate for many applications.

Calibrating resistance factor for LRFD of deep foundation under lateral loading condition with serviceability limit state

Deep foundations are often used to support bridges and buildings when the surface soils are not sufficiently strong. In this study, the resistance factor (RF) in the load and resistance factor design (LRFD) for laterally loaded drilled shafts as deep foundation was calibrated and proposed. The serviceability limit state (SLS) associated with allowable displacement was targeted as it frequently governs the design of deep foundation. For this purpose, a database was established for rigid piles, such as drilled shafts, by collecting various load test results from full-scale field tests, centrifuge tests, and 1-g model tests. The normalized load–displacement curves were introduced, and uncertainties were captured and characterized based on the normalized hyperbolic relationship. The statistical properties of load and resistance were evaluated and introduced into the Monte Carlo simulation, which was performed for calibrating RF according to the allowable displacement and target reliability index. The relationship between the SLS RF and the allowable displacement was proposed and compared with the factor of safety for the conventional design method for laterally loaded drilled shafts.

Bayesian updating on resistance factors of H-Piles with axial load tests

In the Load and Resistance Factor Design (LRFD) of piles, several design codes recommend higher resistance factors if load tests are conducted. However, no information is provided on how these resistance factors are determined. In this paper, a probabilistic approach based on Bayes' theorem and the First Order Reliability Method (FORM) is proposed to calibrate resistance factors for different numbers of load tests and the corresponding test results. In addition, within-site variability, design methods, types of piles, and ground conditions can also be considered. The proposed approach applied to H-piles under axial load tests shows consistent results with current design codes. Results show that resistance factors are significantly increased even if only one positive test is observed among all the tests. For low variability sites, the differences of resistance factors between various design methods are significantly reduced if one or more tests are positive, while for high variability sites, the differences of resistance factors are only slightly decreased, indicating that design methods should be considered in the latter case. Most of the increase in resistance factors is achieved with a small number of tests. For β-Method used in clay sites, 80% of the increase in resistance factors is achieved with two, four and five consecutive positive tests are observed for low, medium and high variability sites, respectively.