Modeling of Blast-Loaded Steel Cables

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1 Modeling of Blast-Loaded Steel Cables John M. H. Puryear, PE, Protection Engineering Consultants, Austin, TX, USA Matt Barsotti, Protection Engineering Consultants, Austin, TX, USA David J. Stevens, PhD, PE, Protection Engineering Consultants, San Antonio, TX, USA Eric B. Williamson, PhD, PE, University of Texas, Austin, TX, USA Eric L. Sammarco, PE, University of Texas, Austin, TX, USA Vincent P. Chiarito, USACE Engineer Research and Development Center, Vicksburg, MS 15 th ISIEMS, Potsdam, Germany; September 2013 Distribution Statement A: Approved for public release; distribution is unlimited. Introduction PEC and UT Austin are collaborating to develop the Anti-Terrorism Planner for Bridges (ATP-B) software tool ATP-B is fast-running software to estimate bridge component damage PEC has developed an algorithm for predicting the damage and residual capacity of steel cables subjected to explosive threats. 1

Sammarco, PE, University of Texas, Austin, TX, USA Vincent P.

2 Motivation Steel cables critical to many bridges Cables Easy to access Attractive targets Vulnerability to blast little understood Fast-running algorithm to predict: Damage to cable cross section Residual capacity By ZENsan ( Methodology Empirical data Test series by USACE Engineer Research and Development Center (ERDC) Additional data required to support algorithm for cases of interest Augment empirical data with synthetic data from LS-DYNA simulation Infer best-fit curves to predict damage and residual capacity 2

0) Methodology Empirical data Test series by USACE Engineer Research and Development Center (ERDC) Additional data required to support

3 Methodology Establish cable modeling approach Validate cable model against applicable ERDC tests Parametrically generate synthetic data from validated model Infer a results plane and calculate bestfit curves to describe empirical and synthetic data Explosive Threat Two Types of Explosive Threat Primitive Sophisticated 3

model Infer a results plane and calculate bestfit curves to describe empirical

4 Strand Element Formulation Cable composed of distinct strands Element formulations considered for strands: Eulerian fluid Solid elements Combined beam elements for wires Strand Element Formulation Most effective formulation: Entire strand as beam element Null shell element wrapper Shell element wrapper to couple beam to fluid (explosive and air) Nodes of beam and shell joined using constrained nodal rigid bodies (CNRB) 4

effective formulation: Entire strand as beam element Null shell element wrapper Shell element wrapper to

5 Strand Element Formulation Cross Section Constitutive Models Strand (beam element) *MAT_PLASTIC_KINEMATIC Cowper-Symonds parameters critical to failure prediction Shell wrapper *MAT_NULL Zero strength so no structural contribution 5

Cowper-Symonds parameters critical to failure prediction

6 Explosive Constitutive Models Assumed C-4 *MAT_HIGH_EXPLOSIVE_BURN *EOS_JWL Air *MAT_NULL Contact & FSI Strand-to-strand contact *CONTACT_SINGLE_SURFACE Penalty formulation Stiffness and damping through trial and error No artificial failures No excessive rebound Fluid structure interaction (FSI) ALE domain Lagrangian strands Eulerian explosive and air *CONSTRAINED_LAGRANGE_IN_SOLID 6

damping through trial and error No artificial failures No excessive rebound Fluid structure

7 Model Validation Two validation cases from ERDC test data Sophisticated threat Tensioned cable Untensioned cable Post-Test Condition: Untensioned 19-Strand Cable Model Validation Explosive detonates and loads cable ALE domain is deactivated to reduce run time Remainder of simulation is Lagrangian Results for untensioned cable: Numerical: 26% of cross section failed Experimental: 23% of cross section failed 7

detonates and loads cable ALE domain is deactivated to reduce run time Remainder of simulation is

8 Model Validation Parametric Simulations Variables Tension (% GUTS 1 ): 0%, 20%, 40% Strand count: 19, 31, 61 Clear standoff: 0 & 2 in. (5cm) Charge weight: typ. 7 weights per strand count Synthetic data supports fast-running predictive algorithm 1 Guaranteed ultimate tensile strength 8

9 Predictive Algorithm Describe synthetic data in a results plane Dependent variable: residual capacity (% GUTS) Independent variable: scaled weight Scaled weight (w scaled ) from: Charge weight (w) Standoff/clearing factor (F DC ) Clear standoff Outer diameter cable bundle Cross-sectional area of cable (A C ) Predictive Algorithm Standoff (s) Outer Diameter of Cover upon which Explosives are Attached (D A ) Outer Diameter of Cable Bundle (D C ) Scaled Weight Parameters 9

Clear standoff Outer diameter cable bundle Cross-sectional area of cable (A C ) Predictive Algorithm Standoff (s)

10 Predictive Algorithm (1) (3) (4) Predictive Algorithm Standoff/clearing factor (F DC ) to maximize R 2 values R 2 values from 0.78 to 0.94 Plots 1 through 3 distinguish by strand count and service tension (%GUTS) Plot 4 distinguishes only by service tension 10

11 Predictive Algorithm Synthetic curves (0% tension) under-reported damage 13% compared to ERDC data 13% offset applied to all synthetic curves Predictive Algorithm 11

12 Conclusions Algorithm to predict cable damage and residual capacity Primitive and sophisticated threats Good agreement with ERDC data for most cases Accuracy within bounds for blast phenomena Recommendations Additional tests with tensioned cables Few tensioned tests with unprotected cable in ERDC data Assess 20% and 40% GUTS curves Effect of covers Test additional cable types e.g. 2-inch (5cm) suspender cable Strand-free layup may change response Test additional cable sizes, e.g. 55, 61, 75, 91 or 108 strands 12

tensioned tests with unprotected cable in ERDC data Assess 20% and 40% GUTS curves Effect of covers Test additional cable types e.

13 Acknowledgements The US Army Engineer Research and Development Center (ERDC) was program manager for this work. Funding was provided by the Department of Homeland Security (DHS), Science and Technology Directorate, Infrastructure Protection and Disaster Management Division Acknowledgement Permission to publish was granted by Director, Geotechnical & Structures Laboratory, US Army Engineer Research and Development Center 13

Directorate, Infrastructure Protection and Disaster Management Division Acknowledgement Permission to

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SBEDS. 31st DOD Explosives Safety Seminar. (Single degree of freedom Blast Effects Design Spreadsheets ) San Antonio, Texas 24-26 August 2004

SBEDS. 31st DOD Explosives Safety Seminar. (Single degree of freedom Blast Effects Design Spreadsheets ) San Antonio, Texas 24-26 August 2004 31st DOD Explosives Safety Seminar San Antonio, Texas 24-26 August 2004 SBEDS (Single degree of freedom Blast Effects Spreadsheets ) Dale Nebuda, P.E. U.S. Army Corps of Engineers Chuck Oswald, Ph.D.,