STATISTICALLY-BASED AIR BLAST LOAD FACTORS BASED ON IMPRECISE PARAMETER STATISTICS FOR REINFORCED CONCRETE WALL

  • : Ms Word, Ms Word Format
  • : 70 Pages
  • : ₦3000
  • : 1-5 Chapters
  •  
  • Click to DOWNLOAD Materials

STATISTICALLY-BASED AIR BLAST LOAD FACTORS BASED ON IMPRECISE PARAMETER STATISTICS FOR REINFORCED CONCRETE WALL

ABSTRACT

 

The determination of acceptable air blast load factors for Load and Resistance Factor Design (LRFD) is complicated due to highly variable loads and to non-linear and rate dependent material and structural response that can result. This has resulted in the use of blast load factors that are set equal to unity since load uncertainty, which is typically used as a probabilistic basis for developing LRFD load factors, is not considered. A precise distribution of random variables also has been required for load and resistance factor determination in LRFD. However, in the case where their distributions are uncertain due to insufficient data, such as for blast events, assumptions will be made that overlook uncertainties that should be accounted in the derivation. In this study, a combination of Response Surface Metamodels (RSM), Monte Carlo Simulations (MCS), and Probability Box (P-Box) that incorporate nonlinear finite element models were used to derive statistically-based blast load factors for LRFD. Load factor development centered on a case study involving a reinforced concrete (RC) cantilevered wall subjected to free air blasts. The resulting load factor was found to be 1.41 when precise parameter statistics were assumed. This blast load factor was then used to design a new RC cantilevered wall and this new wall was found to have its reliability close to the target value. However, when parameter uncertainty was considered, the resulting load factors based on P-Box representation were found to be a range between 1.16 and 1.74, indicating that there was a possibility that the load factor of 1.41 obtained from precise parameter statistic assumptions could be unreliable.

 

 

TABLE OF CONTENTS

List of Figures………………………………………………………………………………………………………. vi 

List of Tables……………………………………………………………………………………………………….. ix

 

Acknowledgement…..……………..………………………………………………….…..….. x

Chapter 1 Introduction……………………………………..……………………………….. 1

1.1 Overview……………..…………….…..…………………………………….….. 1

1.2 Problem Statement …..…..………….……..………….…………….………….. 4

1.3 Objectives….………………………..………..………………………………….. 4

1.4 Scopes………………………………..………..………………………………….. 5

1.5 Tasks……….………………………..………..………………………………….. 5

Chapter 2 History and Background for Load and Resistance Factor Development..……… 7

2.1 Reliability Approaches to Determine Load and Resistance Factors………….… 7

2.2 Development of Reinforced Concrete Load and Resistance Factors………….. 15

2.3 Conclusions..………………………………..……………………….………….. 21

Chapter 3 Statistically-based Air Blast Load Factor Development.…..………..…………22

3.1 Introduction and Backgrounds………….………………………….…..……….. 22

3.2 Parameter Statistics………………………………..………………..………….. 24

3.3 Finite Element Modeling…………………………..…………………..…..….. 28

3.4 Reliability Analysis of Reinforced Concrete Members Nonlinear

Responses under Blast………………………….…..…………………..…..….. 34

3.5 The RSM and MCS Method..………….…………..…………………..…..….. 37

3.6 Case Study…………………………..……………..…………………..…..….. 47

3.7 Summary and Conclusions…..……………………..…………………..…..….. 66

 

 

TABLE OF CONTENTS (cont’d)

Chapter 4 Uncertain Distributed Parameter Applications for Statistically-based

Air Blast Load Factor Determination..…………………………………..…….. 69

4.1 Introduction and Backgrounds……………………………………….………….. 69

4.2 Parameter Statistic Uncertainty in Blast Resistant Design…………………….. 70

4.3 P-Box Application for Parameters with Imprecise Distribution………………..72

4.4 Air Blast Load Factor Development by Accounting Parameter

Statistic Uncertainty………………………..………………..…..……………… 79

4.5 Summary and Conclusions…..……………..…………………………..…..….. 85

Chapter 5 Conclusion, Impact, and Future Research………………………..……..….…. 87

5.1 Summary and Conclusions…..……………..…………………………..…..….. 87

5.2 Impact………………….…………………..………………………………….. 89 5.3 Area of Future Research……………………………………………………….. 90

References…..…………………………..……..…………………..………………………….. 91

Appendix A…..….……………………..……..………………..…………………………….. 97

Appendix B…..….……………………..……..………………..…………………………….108

Chapter 1

Introduction

 

1.1 Overview

Load and Resistance Factor Design (LRFD) is a statistically based structural design methodology that is used for many structures, components, and material types. The concept considers uncertainties in structural loads (S) and member capacities or resistance (R) and applies load factors () and resistance factors () to S and R to ensure that the structure’s resistance will be greater than the anticipated load effects during its lifetime. This LRFD definition can be explained using Equation1-1,

𝑅𝑛 ≥ 𝑖𝑆𝑛𝑖                                                                           (Eq.1-1)

in which Rn and Sn are the nominal strengths and loads, respectively. The load factors are influenced by the degree of accuracy of load effect calculations and their variation during the structure’s lifetime. On the other hand, the resistance factors are influenced by the probability of structural members being under-strength due to variations in material properties and component dimensions, inaccuracies in design equations, degrees of ductility, and their importance in the design (ACI, 2008). The application of LRFD can be found in many design codes, such as the

American Concrete Institute’s (ACIs) Building Code Requirements for Structural Concrete (ACI

318-08) (ACI, 2008), the American Institute of Steel Construction’s (AISCs) Manual of Steel Construction (AISC, 2006), or the American Association of State Highway and Transportation Officials’ (AASHTOs) LRFD Bridge Design Specifications (AASHTO, 2004).

The development of  and   found in these codes for low probability, extreme events such a seismic event has been traditionally based on limiting structural responses so that structural elements can retain most of their original load-carrying capacity. However, blast resistant design often allows for structural elements to experience large plastic deformations where the structural elements could be failed and alternate load-carrying mechanisms could be developed to resist progressive collapse. Therefore, many assumptions that form the basis for the development of conventional design load and resistance factors might not be valid for blast loads, and factors that have been developed for conventional design might not be applicable to blast design (Dusenberry, 2010). However, many blast resistant design guidelines suggest using a conservative resistance factor of 1.0 because: 1) material strength is shown to increase due to strain-rate effects during a blast event and 2) the air blast pressure time history is idealized and likely conservative (Department of Defense, 2008). Those guidelines, on the hand, suggest a unity blast load factor based on a conservative assumption for low-probability, extreme events like blast, not based on statistical information of blast load parameters that contradict the underpinnings of LRFD. The literature states that difficulties associated with statistically-based blast load factor development arise from complexities related to predicting structural response under blast and determining joint probability density functions of random variables (Cormie et al., 2005; Campidelli et al., 2013) that are required when performing reliability analyses. Therefore, the current study developed a methodology to overcome these two shortcomings by: 1) applying Response Surface Metamodeling (RSM) techniques centered on fully-nonlinear finite element models to develop mathematical functions for predicting structural response under blast and 2) applying Monte Carlo Simulation (MCS) techniques in conjunction with the RSM functions and a thorough survey of available data related to reinforced concrete structure blast reliability to develop an empirical response probability distribution that was further used to determine subsequent blast load factors. The proposed method was demonstrated by the case of a blast-resistant reinforced concrete cantilevered wall that was originally designed using a traditional, single-degree of freedom (SDOF) approach.

Not only limiting nonlinearity of the response, early development of load and resistance factors also simplified incorporated parameter statistics so that the traditional reliability method (e.g. First Order Second Moment (FOSM) method, Advance First Order Second Moment (AFOSM or ASM) method) could be performed (MacGregor, 1976; Winter, 1979). For example, precise normal or lognormal distributions, incorporating statistical independency were assumed when determining load and resistance factors for a RC beam under typical dead load and live load (MacGregor, 1976). This simplification is valid for these typical loadings when their extensive statistical information is available. Parameter statistics for blast loads, on the other hand, have been found to be highly uncertain because statistical studies for blast are limited and their results are normally unavailable due to security concern (Low and Hao, 2002; Bogosian et al., 2002; and Hao et al., 2010). When parameter distributions are uncertain, it has been reported that assuming different distributions can provide a significant difference of the subsequent reliability results (Zhou et al., 1999, Jimenez et al., 2009; Haldar and Mahadevan, 2000). Therefore, for circumstances where parameter distributions are imprecise such as in blast, traditional reliability analysis methods (e.g. FOSM, AFOSM, Monte Carlo Simulation (MCS)) that depend on precise parameter distributions may give inaccurate results and can, ultimately, affect the subsequent load and resistance factors. Therefore, the current study developed a methodology that implemented Probability Box (P-Box), to account parameter statistic uncertainty, in conjunction with RSM method and the iteration method (Allen et al., 2005) to determine subsequent blast load factors when parameter statistic uncertainty is included. The proposed P-Box method was demonstrated using the same case study used to demonstrate the RSM and MCS method discussed previously so that the blast load factors resulted from precise and uncertain parameter statistics can be compared.

 

 

 

 

1.2 Problem Statement

There is an extensive series of load and resistance factors available for many loading types, including blast loads, for LRFD. The development of these factors is typically based on extensive statistical information of parameters related to resistance and loads. However, for blast resistant design, there is no evidence of statistically-based blast load factor while most design guidelines provide only its simple, conservative version as a unity applied for a low probability, extreme event. This shortcoming comes from complex responses of structures under blast load and, as a result, a lack of explicit nonlinear response functions that are required when performing reliability analyses and subsequently determining probabilistic blast load factors. Moreover, parameter statistics related to blast loads have been found to be highly uncertain due to limited statistical information for blast load parameters and this contradicts the requirement of precise distribution when using traditional reliability methods.

 

1.3 Objectives

The primary objective of this study is to develop a methodology that can systematically determine statistically-based blast load factors used for blast resistant reinforced concrete deign when such design factors have been conservatively assumed as a unity based on low-probability, high-consequence characteristic of blast event. The secondary objective is to develop another methodology used in conjunction the previous methodology to provide blast load factors that are resulted not only from blast load parameter statistics but also from the statistic uncertainty found in the literature.

 

 

 

 

1.4 Scope

The scope of this study focused on development of a modified reliability method to determine blast load factors for isolated reinforced concrete retaining wall under an ultimate strength limit state when variations of material strength, geometry imperfection, and loading statistical information obtained from the literature. The ultimate strength limit state for flexure was considered because it is the typical design criteria for structures under extreme events and the retaining wall was chosen because this type of structures is commonly used as a blast resistant structure. Single Degree of Freedom (SDOF), a traditional design approach for blast resistant design, was used to design the wall and the reliability from using this method, considered as the current state of blast resistant design, could be investigated. The development was also based on experimental programs done by Finite Element Models (FEMs) which were created and validated against theoretical calculation and published blast test results. The validated FEMs were then used in conjunction with Response Surface Metamodels (RSM) and Central Composite Design (CCD) to simulate response data points that were further used to develop response predicting functions of the wall. The developed response functions were then used in conjunction with MCS and P-Box to determine the subsequent blast load factors.

 

1.5 Tasks

To accomplish the objectives, the research will be organized as follows:

  • The completion of a literature search that presents background on: the development of load and resistance factors for reinforced concrete; traditionally implemented tools for the reliability based load and resistance factors derivation; the application of PBA to reliability analyses when random variable distributions are not well-established; the availability of statistical information for random variables related to this study; the development of load and resistance factors for structures subjected to blast loads; the development of nonlinear response functions using RSMs; and the modeling techniques for computational study of reinforced concrete members subjected to blast loads using LS-DYNA.
  • The development of RSMs that are implemented to predict the nonlinear response of reinforced concrete members under blast loads and to determine subsequent blast load factors when precise parameter statistics are assumed.
  • The development, application and validation of P-Boxes and a modified reliability method to determine blast load factors that account parameter statistic uncertainty.

This section summarizes the tasks that are needed to be done to complete the present study. Details for each task will be discussed in the subsequent chapters.

STATISTICALLY-BASED AIR BLAST LOAD FACTORS BASED ON IMPRECISE PARAMETER STATISTICS FOR REINFORCED CONCRETE WALL

Sharing is caring!

Leave a Reply