SIMPLIFIED NUMERICAL BRIDGE MODEL SUBJECT TO BLAST LOADS

SIMPLIFIED NUMERICAL BRIDGE MODEL SUBJECT TO BLAST LOADS

ABSTRACT

  Damage to a pier column will take a bridge out-of-service, or worse, lead to a complete bridge failure. Besides the importance of civilian safety, maintaining bridge serviceability is imperative to civilian and military transport, while discontinuous transportation networks have rippling effects on economy and community.  With the increase of blast attacks on transportation networks and structures, researchers and design engineers are seeking understanding of the behavior of transportation structures subject to blast loading. Increased numerical modeling capabilities allow researchers to consider material, structural, and load effects on structure response at limited expense.  However, researchers must carefully consider modeling parameters to appropriately represent the nonlinear material and geometric behavior inherent to a blast event.  Numerical model simulations vary vastly in complexity and are handicapped by programming assumptions. A balance of numerical model fidelity, simulation behavior accuracy and general applicability must be found to develop design criterion for blast loads on bridge components. This study considers the effects of four modeling parameters: aspect ratio, boundary conditions, longitudinal reinforcement ratio and standoff distance in a simplified and a complex numerical simulation.  The simplified model considers several discrete mass elements connected by linear elements to model the subject column, whereas the complex model considers continuum elements, material models accounting for degradation and failure, and a built-in blast load application software.  The scope of the project was to evaluate the performance of the simplified model considering the   complex model as the baseline for comparison.  It is believed that the differences in load application, material behavior, and stiffness have the largest impact on the simplified model.  Implementation of the load application and stiffness must be carefully considered in the development of a simplified model.  

TABLE OF CONTENTS

List of Figures…………………………………………………………………………………………………… viii List of Tables……………………………………………………………………………………………………… xi   Acknowledgments ………………………………………………………………………………………. xii Chapter 1 Introduction ………………………………………………………………………………… 1 1.1 Background …………………………………………………………………………………… 11.2 Problem Statement ………………………………………………………………………….. 2 1.3 Objectives ……………………………………………………………………………………… 21.4 Scope ……………………………………………………………………………………………. 3 1.5 Task List ……………………………………………………………………………………….. 4 Chapter 2 Literature Review ………………………………………………………………………… 6 2.1 Blast Loading…………………………………………………………………………………. 6 2.1.1 Blast Wave Propagation Programs ……………………………………………. 8 2.2 Blast Analysis Methods …………………………………………………………………… 9 2.3 Model Assumptions, Parameters, and Materials …………………………………… 12 2.3.1 Model Assumptions ……………………………………………………………….. 122.3.2 Parameters ……………………………………………………………………………. 14 2.3.3 Material Models …………………………………………………………………….. 15 2.4 Finite Elements ………………………………………………………………………………. 19 2.5 Simplified Models ………………………………………………………………………….. 21 2.6 Summary ………………………………………………………………………………………. 25 Chapter 3 Simplified Numerical Bridge Model ……………………………………………….. 27 3.1 Simplified Bridge Numerical Model ………………………………………………….. 273.2 Blast Loads ……………………………………………………………………………………. 283.3 Analysis ………………………………………………………………………………………… 29 3.4 Summary ………………………………………………………………………………………. 31 Chapter 4 LS-DYNA Finite Element Model …………………………………………………… 32 4.1 Finite Elements ………………………………………………………………………………. 324.2 Boundary Conditions ………………………………………………………………………. 33 4.3 Element Constraints/Coupling…………………………………………………………… 354.4 Material Models ……………………………………………………………………………… 374.5 Blast Loads ……………………………………………………………………………………. 384.6 Analysis Method …………………………………………………………………………….. 38 4.7 Summary ………………………………………………………………………………………. 39Chapter 5 Numerical Simulation Parametric Studies ………………………………………… 41 5.1 Constants ………………………………………………………………………………………. 41 5.2 Varied Parameters …………………………………………………………………………… 43 5.2.1 Column Aspect Ratio ……………………………………………………………… 44 5.2.2 Longitudinal Reinforcement Ratio ……………………………………………. 455.2.3 Boundary Conditions ……………………………………………………………… 46 5.2.4 Standoff Distance …………………………………………………………………… 46 5.3 Summary ………………………………………………………………………………………. 47 Chapter 6 Numerical Simulation Results………………………………………………………… 49 6.1 Blast Loading Comparison ……………………………………………………………….. 49 6.2 Group 1 Results ……………………………………………………………………………… 51 6.2.1 Group 1 Moment Envelope ……………………………………………………… 51 6.2.2 Group 1 Shear Envelope………………………………………………………….. 51 6.2.3 Group 1 Deflected Shape ………………………………………………………… 53 6.3 Group 2 Results ……………………………………………………………………………… 54 6.3.1 Group 2 Moment Envelope ……………………………………………………… 55 6.3.2 Group 2 Shear Envelope………………………………………………………….. 55 6.3.3 Group 2 Deflected Shape ………………………………………………………… 57 6.4 Group 3 Results ……………………………………………………………………………… 58 6.4.1 Group 3 Moment Envelope ……………………………………………………… 59 6.4.2 Group 3 Shear Envelope………………………………………………………….. 60 6.4.3 Group 3 Deflected Shape ………………………………………………………… 61 6.5 Group 4 Results ……………………………………………………………………………… 62 6.5.1 Group 4 Moment Envelope ……………………………………………………… 63 6.5.2 Group 4 Shear Envelope………………………………………………………….. 63 6.5.3 Group 4 Deflected Shape ………………………………………………………… 65 6.6 Group 5 Results ……………………………………………………………………………… 67 6.6.1 Group 5 Moment Envelope ……………………………………………………… 67 6.6.2 Group 5 Shear Envelope………………………………………………………….. 67 6.6.3 Group 5 Deflected Shape ………………………………………………………… 69 6.7 Group 6 Results ……………………………………………………………………………… 70 6.7.1 Group 6 Moment Envelope ……………………………………………………… 71 6.7.2 Group 6 Shear Envelope………………………………………………………….. 71 6.7.3 Group 6 Deflected Shape ………………………………………………………… 73 6.8 Group 7 Results ……………………………………………………………………………… 74 6.8.1 Group 7 Moment Envelope ……………………………………………………… 756.8.2 Group 7 Shear Envelope………………………………………………………….. 76 6.8.3 Group 7 Deflected Shape ………………………………………………………… 77 6.9 Group 8 Results ……………………………………………………………………………… 78 6.9.1 Group 8 Moment Envelope ……………………………………………………… 78 6.9.2 Group 8 Shear Envelope………………………………………………………….. 78 6.9.3 Group 8 Deflected Shape ………………………………………………………… 80 6.10 Deflection-Time History ………………………………………………………………… 816.11 Discussion …………………………………………………………………………………… 86Chapter 7 Summary, Conclusions, and Recommendations ………………………………… 92 7.1 Summary and Conclusions ……………………………………………………………….. 927.2 Recommendations …………………………………………………………………………… 93 7.3 Future Research ……………………………………………………………………………… 94 7.3.1 Element Stiffness …………………………………………………………………… 94 7.3.2 Loads …………………………………………………………………………………… 947.3.3 Boundary Conditions ……………………………………………………………… 947.3.4 Modeling Parameters ……………………………………………………………… 95 7.3.5 Reinforcement……………………………………………………………………….. 95 References ………………………………………………………………………………………………… 96 Chapter 1  

Introduction

1.1 Background

Recent events have increased the demand to design and retrofit structures to resist blast loads.  Much of the published research and guidelines on blast resistant design is related to buildings and public safety, however, bridge engineers also must consider the risks associated with short duration, high intensity, blast loads. Recommendations for Bridge and Tunnel Security (FHWA, 2003) offers suggestions to improve security and reduce bridge and tunnel vulnerability.  Security features for signature bridges, such as the Brooklyn Bridge or the Golden Gate Bridge are in place; however, these features are not implemented for many of the most critical transportation links.  These links must be protected against blast load to ensure a safe and reliable transportation network. Currently, the American Association of State Highway and Transportation Officials (AASHTO) LRFD Bridge Design Specifications contain no specific guidelines for the analysis and design of bridges to resist blast loading.  Other specifications, such as the U.S. Department of Defense’s Unified Facilities Criteria (UFC) 3-340-02 Structures to Resist the Effects of Accidental Explosions presents methods of design for facilities but has no bridge-specific information. Supporting pier columns are considered one of the most critical and vulnerable parts of a bridge (NCHRP, 2010).  If a column collapses, multiple spans or the entire structure may collapse.  An increasing number of engineers are beginning to consider the structural integrity of bridges in response to blast loading because of the importance of bridge pier columns with respect to maintaining structural integrity.

1.2 Problem Statement

There is a need for specification development for analysis and design of bridges under blast loading.  This study will focus on the analysis of bridge columns subjected to blast loads, which is important to the development of a comprehensive specification. There are many methods available to engineers to predict blast loads and the response of bridge components.  However, there are no guidelines or design specifications from AASHTO or FHWA for simplified analyses that can be used efficiently in conjunction with a blast design process.  Sophisticated models are not practical because they involve large computational requirements, costly software, and time commitments that are not available to the practicing engineer.  In addition, detailed models are not always warranted because of high uncertainties associated with the size and location of the explosive (NCHRP Report 645).  As a result, a need exists to develop and validate efficient bridge-specific simplified modeling techniques that provide economical and accurate results.  

1.3 Objectives

This study will investigate the accuracy of simplified models in efforts to develop new design guidelines and specifications. The objective of this study is to evaluate the effectiveness of a proposed simplified model of bridge columns under blast loading.  The accuracy and limitations of the simplified modeling technique are examined by comparing shear, moment, and deformation magnitudes over the time-history of a blast event for the columns studied to validated, advanced, finite element analysis (FEA) results.

1.4 Scope

This study investigates the effects of blast loading on round, concrete bridge columns by comparing the results of high-level, detailed, dynamic, finite element analyses (FEA) using LS-DYNA to a proposed, simplified numerical simulation technique using SAP2000.  The simplified numerical simulation is a multi-degree of freedom (MDOF), uncoupled analysis composed of linear elements and discrete masses that represent the column mass and the superstructure mass analyzed in SAP2000.  The LS-DYNA finite element model, composed of solid and beam elements, features a MDOF coupled approach involving an explicit, dynamic, time-history analysis. A parametric study using LS-DYNA and SAP2000 was completed to investigate the performance of the simplified modeling technique and possible limitations as compared to the LS-DYNA models.  CONWEP was used to generate the blast loads used in the LS-DYNA and SAP2000 models. All of the columns considered in this study have the following parameters: x A diameter of 1524 mm (60 in); x Concrete compressive strength of 27.57 MPa (4000 psi);  x Grade 60 reinforcement;  x Concrete cover of 76.2 mm (3 in); x Column axial load of 0.12(f’_c A_g); x Transverse reinforcement ratio equal to the maximum of

• Ag ·¸¸ f’fyc and Us t 0.18 f’fyc ;

ȡs t 0.45¨¨ Ac -1¹ © x Charge weight of 226.8 kg (500 lb) TNT; x A column height of 7620 mm (25 ft) or 16,764 mm (55 ft);  x A longitudinal reinforcement ratio of 1% or 2%; x A standoff distance of 1.22 m (4.0 ft) or 7.62 m (25.0 ft); x Boundary conditions of a free cantilever, propped cantilever, or construction joint at the base of the column.

1.5 Task List

The following tasks were completed to accomplish the objectives of this study:

1. Literature Review

A literature review was completed to determine the current state of practice related to simplified modeling of bridge columns with blast loading.  Blast loading origins and available blast analysis methods were also examined.  Modeling techniques, assumptions, parameters, and material models were investigated to help with the decisions for the LS-DYNA and SAP2000 models for this study.

2. Computational Modeling

Simplified numerical simulations of blast loading on bridge columns were conducted in SAP 2000 based on a previously established procedure (John Lobo, personal communication, Jan. 2012) that simplifies the blast loading and analyses.  The simplified numerical simulation developed by Lobo was explored in this study; and analyses were completed based on this method.  Detailed finite element models were created with LS-DYNA with blast loads generated using CONWEP, which is an empirically-based blast load function.

3. Parametric Study

Varied parameters include: 1) aspect ratio; 2) longitudinal reinforcement ratio; 3) boundary conditions; and 4) scaled distance.

4. Computational Results and Comparison

Data from the SAP2000 and LS-DYNA models were compared to determine the effectiveness of the simplified model.  Output data that were compared include deflected shape, moment envelopes, and shear envelopes.

5. Conclusions and Recommendations

After the results from the LS-DYNA and SAP2000 models were compared, limitations of the simplified model were outlined. Recommendations on how to make the simplified model more accurate are provided in terms of load determination and analysis method.  Recommendations on how to implement simplified analysis of bridge pier columns under blast loading into design specifications are also provided.

SIMPLIFIED NUMERICAL BRIDGE MODEL SUBJECT TO BLAST LOADS