Calibration of Load and Resistance Factors for Breakwater Foundation Design. Application on Different Types of Superstructures

Load and resistance factor design is an efficient design approach that provides a system of consistent design solutions. This study aims to determine the load and resistance factors needed for the design of breakwater foundations within a probabilistic framework. In the study, four typical types of Korean breakwaters, namely, rubble mound breakwaters, vertical composite caisson breakwaters, perforated caisson breakwaters, and horizontal composite breakwaters, are investigated. The bearing capacity of breakwater foundations under wave loading conditions is thoroughly examined. Two levels of the target reliability index (RI) of 2.5 and 3.0 are selected to implement the load and resistance factors calibration using Monte Carlo simulations with 100,000 cycles. The normalized resistance factors are found to be lower for the higher target RI as expected. Their ranges are from 0.668 to 0.687 for the target RI of 2.5 and from 0.576 to 0.634 for the target RI of 3.0.

Improved Calculation of Load and Resistance Factors Based on Third-Moment Method

Load and resistance factor design (LRFD) is widely used in building codes for reliability design. In the calculation of load and resistance factors, the third-moment method (3M) has been proposed to overcome the shortcomings (e.g., inevitable iterative computation, requirement of probability density functions (PDFs) of random variables) of other methods. With the existing 3M method, the iterative is simplified to one computation, and the PDFs of random variables are not required. In this paper, the computation of load and resistance factors is further simplified to no iterations. Furthermore, the accuracy of the proposed method is proved to be higher than the existing 3M methods. Additionally, with the proposed method, the limitations regarding applicable range in the existing 3M methods are avoided. With several examples, the comparison of the existing 3M method, the ASCE method, the Mori method, and the proposed method is given. The results show that the proposed method is accurate, simple, safe, and saves material.

Calibration of Load and Resistance Factors for Breakwater Foundations under the Earthquake Loading

This study investigates the system stability of breakwater foundations subjected to earthquakes from a probabilistic point of view. A fully probabilistic approach, i.e., a combination of the Monte Carlo simulation and Bishop’s simplified method, has been developed to evaluate the system failure probability of foundation damage, one of the prevailing failures encountered during earthquakes. Twelve sections of perforated caisson breakwaters located around Korea were chosen as case studies. First, the reliability analysis was performed for all the breakwaters at existing conditions; then, the calibration process involving the estimation of load and resistance factors was conducted for 12 breakwaters at three levels of the target reliability index. As the performance function, used in the stability analysis of breakwater foundations, is defined based on an implicit shape with a high-dimensional space of variables, the calibration process of load and resistance factors becomes cumbersome and complicated. Therefore, this study has proposed a sensitivity analysis to be implemented prior to the calibration process to elicit the effects of variables on the stability of each breakwater, which, thereafter, effectively directs the calibration process. The results of this study indicate that the failures in the foundation of breakwaters frequently occur in different modes. Therefore, the failure probability should be estimated considering all possible failure modes of the foundation. The sensitivity results elucidate that the soil strength parameters are the dominant variables, contributing to the stability of foundations, whereas the seismic coefficient presents the negative effect, causing the insecurity of breakwaters. In particular, the deadweights, though directly contributing to the seismic forces, show a small effect on the stability of foundations. The calibration shows that the load factors slightly vary with an increase in the target reliability index and set 1.10 for three safety levels. In contrast, the resistance factor exhibits an inverse relationship with the specified reliability index. Especially when the load factor equals 1.10, the resistance factors are 0.90, 0.85, and 0.80, corresponding to the reliability index of 2.0, 2.5, and 3.0, respectively. Eventually, it is proved that the sensitivity analysis prior to the calibration process makes the procedure more efficient. Accordingly, the iteration of simulation execution is diminished, and the convergence is quickly accomplished.

Safety Factor for Drilled Shaft Foundations Subjected to Wind-Induced Torsion

Public transportation agencies commonly use drilled shaft foundations as support of mast arm traffic signs and signal pole structures. These structures and their foundations are subjected to wind-induced torsion. Design provisions can be found in AASHTO specifications for structural supports for highway signs, luminaires and traffic signals; nevertheless, those standards do not provide guidance to estimate the torsional resistance of drilled shaft foundations, or what an appropriate factor of safety (or resistance factor) for design could be. Although load and resistance factors format is desired because AASHTO is moving in that direction, still many Departments of Transportation design requirements are based on factors of safety. In this study, a probabilistic approach is used to recommend a rational procedure to determine factors of safety that consider the uncertainties and the consequences of failure. This procedure can be modified for load and resistance factors design calibration, as well. The skin friction approach was calibrated employing reliability analysis, available statistics, published experimental data, and simulations. However, a lack of field test data has been noticed. Factors of safety for cohesive, cohesionless, and layered soils are recommended. They are presented as a function of the target reliability index, and which in-situ test is performed to obtain the soil strength properties. Three alternatives were considered: standard penetration test, cone penetration test, and vane shear test. The procedure described can be used by practitioners to select appropriate factors of safety based on local conditions when statistical parameters from a particular site investigation are available.

Load and resistance factors for prestressed concrete girder bridges

There has been a considerable progress in the reliability-based code development procedures. The load and resistance factors in the AASHTO bridge design code were determined using the statistical parameters from the 1970's and early 1980’s. Load and resistance factors were determined by first fixing the load factors and then calculating resistance factors. Load factors were selected so that the factored load corresponds to two standard deviations from the mean value and the resistance factors were calculated so that the reliability index is close to the target value. However, from the theoretical point of view, the load and resistance factors are to be determined as coordinates of the so-called “design point” that corresponds to less than two standard deviations from the mean. Therefore, the optimum load and resistance factors are about 10% lower than what is in the AASHTO LRFD Code. The objective of this paper is to revisit the original calibration and recalculate the load and resistance factors as coordinates of the “design point” for prestressed concrete girder bridges. The recommended new load and resistance factors provide a consistent reliability and a rational safety margin.

Reliability Estimation for Highway Bridges

Structural reliability analysis is necessary to predict the uncertainties which may endanger the safety of structures during their lifetime. Structural uncertainties are associated with design, construction and operation stages. In design of structures, different limit states or failure functions are suggested to be considered by design specifications. Load and resistance factors are two essential parameters which have significant impact on evaluating the uncertainties. These load and resistance factors are commonly determined using structural reliability methods. The purpose of this study is to determine the reliability index for a typical highway bridge by considering the maximum moment generated by vehicle live loads on the bridge as a random variable. The limit state function was formulated and reliability index was determined using the First Order Reliability Methods (FORM) method.