Determination of Barge Flotilla Impact Loads on Pile Founded Concrete Guide Walls with Rock Filled Timber Cribbing

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Determination of Barge Flotilla Impact Loads on Pile Founded Concrete Guide Walls with Rock Filled Timber Cribbing
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1 online resource (110 p.)
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english
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Rodrigues, Charles Rosario
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University of Florida
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Gainesville, Fla.
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Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering, Civil and Coastal Engineering
Committee Chair:
CONSOLAZIO,GARY R
Committee Co-Chair:
HAMILTON,HOMER ROBERT,III

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Subjects / Keywords:
finite-element -- guide-walls -- impact -- mrld3 -- rock-fill
Civil and Coastal Engineering -- Dissertations, Academic -- UF
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Civil Engineering thesis, M.S.
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theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Abstract:
The objective of this study was to quantify peak impact forces due to barge flotilla impacts on pile founded concrete guide walls with rock filled timber cribbing using numerical finite element (FE) models. High resolution finite element model was built for pile founded guide wall with rock filled timber cribbing in accord with as-built plans of Mississippi River Lock and Dam 3 (MRLD3). The FE model generation for MRLD3 was carried out in four stages. The first stage focused on development of a FE model of the concrete guide wall and timber piles for MRLD3. The second stage focused on development of a simplified representation of the supporting soil profile in the form of soil curves. The third stage focused on development of a simplified FE model of the rock filled timber cribbing substructure for MRLD3. The fourth stage consisted of unifying the guide wall and timber pile model with the soil curves and the simplified rock fill model to form an accurate FE representation of the MRLD3 guide wall. High resolution FE models of various barge flotillas were then used in combination with MRLD3 guide wall model for barge impact testing for varying impact conditions. The contact forces resulting from barge flotilla impacts were recorded to quantify the peak impact forces.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Charles Rosario Rodrigues.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
Local:
Adviser: CONSOLAZIO,GARY R.
Local:
Co-adviser: HAMILTON,HOMER ROBERT,III.

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lcc - LD1780 2014
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UFE0046771:00001


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DETERMINATION OF BARGE FLOTILLA IMPACT LOADS ON PILE FOUNDED CONCRETE GUIDE WALLS WITH ROCK FILLED TIMBER CRIBBING By CHARLES ROSARIO RODRIGUES A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2014

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2014 Charles Rosario Rodrigues

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This thesis is dedicated to my loving family, to my parents who supported and encouraged me throughout my life and my brother who has always been helpful and understanding.

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4 ACKNOWLEDGMENTS I feel immensely happy and privileged to finish my Maste rs of Science degree from the University of Florida Coming to the United State s was the first time I had been outside my home country India and the Department of Civil and Coastal Engineering at the University of Florida made my stay a m emorable experience. The thesis marks an end to the wonderful two years I spent here, and m any of the people I encountered made the time special. I would like to thank United States Army Corps of Engineers for partially funding my ogram and providing a platform for my thesis research. I would like to thank Dr. Consolazio for his constant motivation and guidance towards the completion of this project. I would like to thank John Wilkes for being a great mentor and a helping hand on th is project. I would like to thank my family and friends for their support and understanding throughout the process. Last, but certainly not the least, I would like to thank the faculty from the Internationa l Students Services Office who were a second family for me and many other i nternational s tudents.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 12 ABSTRA CT ................................ ................................ ................................ ................................ ... 13 CHAPTER 1 INTRODUCTION AND BACKGROUND ................................ ................................ ........... 14 1.1 Introduction ................................ ................................ ................................ ....................... 14 1.2 Objectiv e ................................ ................................ ................................ ........................... 15 1.3 Scope of Work ................................ ................................ ................................ .................. 15 2 BARGE FLOTILLA FINITE ELEMENT MODEL ................................ .............................. 17 2.1 Introduction ................................ ................................ ................................ ....................... 17 2.2 Modeling of Barges ................................ ................................ ................................ .......... 18 2.2.1 Impacting Barge ................................ ................................ ................................ ..... 18 2.2.2 Impacting Barge Internal Contact ................................ ................................ ....... 19 2.2.3 Non Impacting (Decimated) Barges ................................ ................................ ....... 20 2.3 Modeling Barge Interactions ................................ ................................ ............................ 21 2.4 External Loading (Gravity and Buoyancy) ................................ ................................ ....... 22 3 FINITE ELEMENT MODELING OF PILE FOUNDED GUIDE WALLS ......................... 29 3.1 Introduction ................................ ................................ ................................ ....................... 29 3.2 Structural Components of Pile Founded Guide Wall Models ................................ .......... 30 3.2.1 Plain Concrete Guide Wall ................................ ................................ ..................... 31 3.2.2 Timber Piles ................................ ................................ ................................ ............ 32 3.2.3 Guide Wall to Timber Pile Connection ................................ ................................ .. 34 3.2.4 Rock Filled Timber Cribbing Substructure ................................ ............................ 34 3.2.4.1 Timber Cribbing ................................ ................................ ........................... 35 3.2.4.2 Corner Overlapping Elements ................................ ................................ ...... 36 3.2.4.3 Pile Casing ................................ ................................ ................................ .... 37 3.2.4.4 Rock Fill ................................ ................................ ................................ ....... 37 3.3 Soil Components of Pile Founded Guide Wall Models ................................ ................... 39 3.3.1 Foundation Soils ................................ ................................ ................................ ..... 39 3.3.2 Rock Filled Timber Cribbing ................................ ................................ ................. 42 3.3.2.1 Rock Pile Interaction Curves ................................ ................................ ....... 42

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6 3.3.2.2 Rock Fill Mass ................................ ................................ ............................. 43 3.4 External Loading of Pile Founded Guide Wall Models ................................ ................... 44 3.4.1 Gravity Loading ................................ ................................ ................................ ...... 44 3.4.2 Buoyancy Loading ................................ ................................ ................................ .. 45 3.5 Barge Flotilla and PFGW Contact Impact Loading ................................ ......................... 45 4 DETERMINATION OF IMPACT FORCES ON PILE FOUNDED GUIDE WALLS ........ 69 4.1 Introduction ................................ ................................ ................................ ....................... 69 4.2 Development of Impact Conditions ................................ ................................ .................. 69 4.3 Sensitivity Studies ................................ ................................ ................................ ............ 70 4.4 Typical Impact Simulation ................................ ................................ ............................... 72 4.5 Effect of Rock Filled Timber Cribbing on Impact Forces ................................ ................ 73 4.6 General Trends in the Impact Force Results ................................ ................................ ..... 74 4.6.1 Effect of Barge Flotilla Length ................................ ................................ ............... 74 4.6.2 Effect of Barge Flotilla Width ................................ ................................ ................ 75 5 SUMMARY AND CONCLUSIONS ................................ ................................ ..................... 83 APPENDIX A IMPACT FORCE TIME HISTORIES FROM PILE FOUNDED GUIDE WALL MRLD3 SIMULATIONS ................................ ................................ ................................ ....... 84 B ADDITIONAL STUDIES WITH PFGW MODELS ................................ ............................. 92 B.1 Size of Discrete Elements (Shear Box Simulations) ................................ ........................ 92 B.2 Compaction Algorithm ................................ ................................ ................................ .... 93 B.3 Validation of Development Pile Interaction Curves ................................ ........................ 94 C ROCK MASS DISTRIBUTION ................................ ................................ .......................... 103 REFERENCES ................................ ................................ ................................ ............................ 107 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 110

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7 LIST OF TABLES Table page 2 1 Jumbo hopper barge flotilla dimensions and weights ................................ ........................ 24 3 1 Soil properties at MRLD3 ................................ ................................ ................................ .. 47 3 2 Soil profile near USACE MRLD3 STA 7+00 ................................ ................................ ... 47 3 3 Definitive soil parameters for pfgw study part a) (FB MultiPier input data) ................. 47 3 4 Definitive soil parameters for pfgw study part b) (FB MultiPier input data) ................. 48 4 1 Impact conditions for barge impact studies on MRLD3 ................................ .................... 76 4 2 Comparative peak impact forces for MRLD2 and MRLD3 ................................ .............. 76

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8 LIST OF FIGURES Figure page 2 1 Typical 3x5 barge flotilla in transit ................................ ................................ .................... 24 2 2 Jumbo hopper barge schematics ................................ ................................ ........................ 25 2 3 Jumbo hopper barge flotilla schematics ................................ ................................ ............. 25 2 4 Flotilla impact simulation model consisting of a single impacting barge model, multiple non impacting barge models, and target structure ................................ ............... 26 2 5 Jumbo hopper barge FE model ................................ ................................ .......................... 26 2 6 Barge bow zone ................................ ................................ ................................ .................. 27 2 7 Par tial rigidization of high reso lution impacting barge FE model ................................ ..... 27 2 8 Non impacting barge FE model ................................ ................................ ......................... 28 2 9 Typical lashing configuration on barge flotilla ................................ ................................ .. 28 2 10 Barge buoyancy spring schematic ................................ ................................ ..................... 28 3 1 Mississippi River Lock and Dam No. 3 (MRLD3) ................................ ............................ 48 3 2 Mississippi River Lock and Dam No. 2 (MRLD2) ................................ ............................ 48 3 3 As built plans of Lower Pool Interior Monoliths (LPIMs) at MRLD3 .............................. 49 3 4 Isometric view of the MRLD3 single monolith PFGW FE model ................................ .... 50 3 5 Interior monolith PFGW cross section for LPIM at MRLD3 ................................ ........... 51 3 6 Cross sections of MRLD3 FE guide wall model ................................ ............................... 51 3 7 Isometric view of guide wall portion of MRLD3 FE model ................................ ............. 52 3 8 Elevation view of pile group A at MRLD3 ................................ ................................ ....... 52 3 9 Elevation view of pile group B at MRLD3 ................................ ................................ ........ 53 3 10 Constrained nodal rigid body at guide wall to piling connection ................................ ..... 54 3 11 Constrained nodal rigid bodies (CNRBs) at guide wall piling interface for FE model of LPIM PFGW at MRLD ................................ ................................ ................................ 55 3 12 MRLD3 timber cribbing ................................ ................................ ................................ .... 56

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9 3 13 Foundation casing and base confinement ................................ ................................ .......... 57 3 14 Corner overlapping elements modeled as beams every 10ft. ................................ ............ 58 3 15 Rigid links from pile case elements to beam ends ................................ ............................. 59 3 16 Pile casing capable of bending ................................ ................................ ........................... 60 3 17 Assembly of MRLD3 substructure (without soil springs) for rock curve generation ....... 61 3 18 Soil profile from MRLD3 ................................ ................................ ................................ .. 62 3 19 FB MultiPier timber pile model using soil information from MRLD3 STA 6+00 ........... 62 3 20 Typical soil force displacement curves used in FE model ................................ ................ 63 3 21 FE model of MRLD3 LPIM PFGW illustrating soils springs ................................ ........... 64 3 22 Typical rock springs ................................ ................................ ................................ ........... 65 3 23 Rock pile interaction curve for MRLD3 substructure at depth = 126in ............................ 66 3 24 Application of damping during an MRLD3 FE initia lization simulation .......................... 67 3 25 Hydrostatic loading conditions applied to MRLD3 PFGW model ................................ .... 67 3 26 Illustration of contact between 2x3 barge flotilla and MRLD3 FE model ........................ 68 4 1 Dynamic barge flotilla impact conditions for MRLD3 ................................ ..................... 77 4 2 Position of initial contact for impact on MRLD3 ................................ .............................. 77 4 3 Comparative force time histories for 2x3 4fps 20deg impact simulations on MRLD3 using one monolith model and three monolith model ................................ ....................... 78 4 4 Comparative displacement time histories for 2x3 4fps 20deg impact simulations on MRLD3 using 1 monolith model and 3 monolith model ................................ ................... 78 4 5 Force time histories for 2x3 4 FPS 20 DEG MRLD3 ................................ .............. 79 4 6 Continued rotation of the barge flotilla lead row during impac ................................ ......... 80 4 7 Comparative force time histories for MRLD3 (with cribbing) and MRLD2 (without cribbing) for same impact condition 2x3 4 FPS 20 DEG ................................ .......... 81 4 8 Comparative displacement time histories for MRLD3 (with cribbing) and MRLD2 (without cribbing) for same impact condition 2x3 4 FPS 20 DEG ........................... 81 4 9 Force time histories for 6FPS 10DEG impact condition on MRLD2 ............................ 82

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10 4 10 Force time histories for 4FPS 15DEG impact condition for varying barge width ......... 82 A.1 1x3 2 FPS 5 MRLD3 ................................ ................................ ............................... 85 A.2 1x3 4 FPS 20 MRLD3 ................................ ................................ ............................. 85 A. 3 1x3 6 FPS 25 MRLD3 ................................ ................................ ............................. 86 A.4 2x3 6 FPS 10 MRLD3 ................................ ................................ ............................. 86 A.5 2x3 4 FPS 15 MRLD3 ................................ ................................ ............................. 87 A.6 2x3 4 FPS 20 MRLD3 ................................ ................................ ............................. 87 A.7 2x3 4 FPS 25 MRLD3 ................................ ................................ ............................. 88 A.8 3x3 6 FPS 10 MRLD3 ................................ ................................ ............................. 88 A.9 3x3 4 FPS 15 MRLD3 ................................ ................................ ............................. 89 A.10 3x3 6 FPS 15 MRLD3 ................................ ................................ ............................. 89 A.11 3x5 2 FPS 5 MRLD3 ................................ ................................ ............................... 90 A.12 3x5 4 FPS 5 MRLD3 ................................ ................................ ............................... 90 A.13 3x5 6 FPS 10 MRLD3 ................................ ................................ ............................. 91 A.14 3x5 6 FPS 15 MRLD3 ................................ ................................ ............................. 91 B 1 Typical sectional view shear box simulation setup ................................ ........................... 95 B 2 burden pressure ............... 95 B 3 burden pressure ................. 96 B 4 ....... 96 B 5 Effect of change in o ....... 97 B 6 Load applied per node at the top of the timber piles ................................ .......................... 97 B 7 Total Shear Force at level 1 (depth 0 18 in) ................................ ................................ .... 98 B 8 Total Shear Force at level 2 (depth 18 36 in) ................................ ................................ .. 98 B 9 Total Shear F orce at level 3 (depth 36 54 in) ................................ ................................ .. 99 B 10 Total Shear Force at level 4 (depth 54 72 in) ................................ ................................ .. 99

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11 B 11 Total Shear Force at level 5 (depth 72 90 in) ................................ ................................ 100 B 12 Total Shear Force at level 6 (depth 90 108 in) ................................ .............................. 100 B 13 Total Shear Force at level 7 (depth 108 126 in) ................................ ............................ 101 B 14 Total Shear Force at level 8 (depth 126 144 in) ................................ ............................ 101 B 15 Total Shear Force at level 9 (depth 144 162 in) ................................ ............................ 102

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12 LIST OF ABBREVIATIONS CNRB Constrained Nodal Rigid Bodies FE Finite Element LPIM Lower Pool Interior Monolith M RLD2 Mississippi River Lock and Dam 2 M RLD3 M ississippi River Lock and Dam 3 MRLD24 Mississippi River Lock and Dam 24 MRLD25 Mississippi River Lock and Dam 25 PFGW Pile Founded Guide Wall SPT Standard Penetration Test UF University of Florida UPIM Upper Pool Interior Monolith USACE United States Army Corps of Engineers

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13 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science DETERMINATION OF BARGE FLOTILLA IMPACT LOADS ON PILE FOUNDED CONCRETE GUIDE WALLS WITH ROCK FILLED TIMBER CRIBBING By Charles Rosario Rodrigues M ay 2014 Chair: Gary Consolazio Major: Civil Engineering The objective of this study was to quantify peak impact forces due to barge flotilla impacts on pile founded concrete guide walls w ith rock filled timber cribbing using numerical finite element (FE) models. High resolution finite element model was built for pile founded guide wall with rock filled timber cribbing in accord with as built plans of Mississippi River Lock and Dam 3 (MRLD3). The FE model generation for MRLD3 was carrie d out in four stages. The first stage focused on development of a FE model of the concrete guide wall and timber piles for MRLD3. The second stage focused on develop ment of a simplified representation of the supporting soil profile in the form of soil curves. The third stage focused on development of a simplified FE model of the rock filled timber cribbing substructure for MRLD3 The fourth stage consisted of unifying the guide wall and timber pile model with the soil curves and the simplified roc k fill model to form an accurate FE representation of the MRLD3 guide wall. High resolution FE models of various barge flotilla s were then used in combination with MRLD3 guide wa ll model for barge impact testing for varying impact conditions. The contact f orces resulting from barge flotilla impacts were recorded to quantify the peak impact forces.

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14 CHAPTER 1 INTRODUCTION AND BACKGROUND 1 1 Introduction The United States Army Corps of Engineers (USACE) maintains over 11,000 miles of inland waterways throughout the United States. Tow powered barge flotillas are used to transport bulk materials such as coal, grains, sand, and gravel along these waterways. N avigational structures along these inland waterways maintain the most feasible means of transport without altering the natural flow of the water body Guide walls and bullnose structures are the primary examples of navigational structures installed to guid e the barge flotillas into the lock, provide mooring facilities for the tows, and protect the dam and/or lock from any event (barge impact or otherwise) that may result in damage to and/or shutdown of the lock and/or dam. Thus, i t is common for guide walls to be impacted by barge flotillas as the later attempt to align and enter the lock As such, guide walls need to be designed for oblique barge flotilla impacts. Although USACE provides guidelines for designing such navigational structures, the structural engineer designing such guide walls may not be able to predict accurate barge impact forces USACE is in the process of improving the guidelines for the design of these navigational structures Various barge impact studies, both experimental and numerical, were carried out by USACE and the University of Florida (UF), Civil and Coastal Engineering Department. Full Robert C. Byrd Lock and Dam, Gallipolis Ferry, West Vi lock approach wall at Winfield Lock and Dam, Winfield, West Virginia. Preceding analytical studies have been performed by UF using nonlinear dynamic finite element (FE) techniques to simulate impact events with FE mod els representing hurricane protective structures rigid walls, semi flexible walls (Winfield), bullnose structures, and flexible timber guide walls. However, the

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15 amount of research of barge impacts on pile founded concrete guide walls is fairly limited. Du e to the amount of damage and risk associated with physical experimentation of barge impact on guide walls, the opportunities for full scale barge impact tests are limited to low velocity impacts. Thus, higher energy impact events causing significant damag e to the impacting barge and/or navigational structure are better addressed using numerical simulation. The present study focuses on development of pile founded guide wall models and quantifying peak impact forces from barge impacts using barge flotilla FE models developed during preceding studies. It should be noted that this study is part of an ongoing research (Consolazio et al. 2014) and the study presented herein is a partial adaptation of the same. 1 2 Objective The present study focuses on development and barge impact simulation of pile founded guide walls with rock filled timber cribbing substructure. The study uses nonlinear dynamic FE impact simulation techniques to quantify time var ying (transient) barge flotilla impact forces on pile founded guide wall structures over a range of different impact conditions (flotilla size, impact speed, impact angle etc.) to quantify peak barge impact forces. 1 3 Scope of W ork The study presented in this document quantifies oblique barge flotilla impact loads on navigation protective structures using high resolution dynamic nonlinear FE simulation techniques. Specifically, the barg e flotilla impact study focuses on Mississippi River Lock and Dam 3 (MRLD3). Focus in these simulations is on glancing impacts (angles 25) with approach speeds between 1 and 6 ft/sec (FPS). Determination of barge flotilla impact forces on this pile foun ded guide wall structure is accomplished as described below. The lower pool interior monoliths (LPIM) at MRLD3 consist of a guide wall resting on a series of battered and plumb piles whose partial depth is surrounded by rocks, confined by timber

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16 cribbing, and the remnant depth is anchored in soil. The development of the MRLD3 FE guide wall model and quantification of impact loads is accomplished by completing the following tasks: Develop FE model of LPIM at MRLD3 with piling foundation Development of a roc k filled timber cribbing substructure FE model for determining rock pile interaction (force deformation) curves and integrating the same into MRLD3 FE model Development of soil resistance curves for integration into MRLD3 model Conduct dynamic FE impact si mulations to quantify impact forces over a range of typical impact angles and initial velocities.

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17 CHAPTER 2 BARGE FLOTILLA FINITE ELEMENT MODEL 2 1 Int roduction Barge models used in this study are created using the methodology described in Development of Finite Element Models for Studying Multi barge Flotilla Impacts (Consolazio et al. 2012), Development of Multi Barge Flotilla Finite Element Models for Use in Probabilistic Barge Impact Analysis of Flexible Walls (Consolazio and Walters 2012), Determination of Multi barge Flotilla Impact Loads on Bullnose Structures and Flexible Timber Guide Walls (Consolazio and Wilkes 2013). This chapter has been direct ly adapted from Determination of Barge Flotilla Impact Loads on Pile Founded Concrete Guide Walls and Development of a Unified Impact Load Prediction Model for Navigational Structures ( Consolazio et al. 2014 ) and is presented as part of this document only to aid the reader in understanding the interaction between a barge flotilla and a guide wall, as will be discussed later. In the sections that follow, key aspects of the barge flotilla models are summarized, and noteworthy modifications to the previously d eveloped models, necessary for the present study, are described. This study quantifies loads imparted to large mass pile founded guide walls during barge flotilla impact events. A flotilla (e.g., Figure 2 1 ) is an assembly of individual barges of similar size and configuration which are connected together by steel wire ropes known as lashings. The flotilla models in this study are comprised of fully loaded jumbo hopper barges. All FE simulations performed for this s tudy utilize a highly discretized, high resolution, impacting barge model. This high resolution barge model is attached to lower resolution non impacting barge models to form a given flotilla configuration. The maximum size flotilla of interest in this stu dy is a 3x5, which includes a total of fifteen (15) barges comprised of three (3) strings with five (5) barges per string. Additionally, three other flotilla configurations are modeled: 1x3, 2x3, 3x3.

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18 Each barge flotilla model is comprised of a series of jumbo hopper river barges measuring 195 ft long by 35 ft wide and weighing 2000 tons each (where 1 ton = 2000 lbf). Two versions of this jumbo hopper river barge are included in all flotilla models used in this study: single raked and double raked. Single raked barges are raked (tapered through the depth) at the bow only (Figure 2 2 .a), whereas double raked barges are raked at both the bow and stern (Figure 2 2 .b). In configuring a flotilla, single raked barges are positioned in exterior rows while double raked barges are positioned in interior rows. Two (2) of the four (4) flotilla configurations used in this study are illustrated in Figure 2 3 Overall dimensions and weights of all flotilla configurations used in this study are listed in Table 2 1 2 2 Modeling of B arges Two types of individual barge FE models are used within each flotil la model (Figure 2 4 ). A single high resolution barge, referred to as the impacting barge, is the onl y barge to make physical contact with the target structure (pile founded guide wall). The high level of discretization associated with the impacting barge is necessary to enable accurate representation of the contact interaction between the target structur e and impacting barge. The remaining low resolution barges within a given flotilla are referred to as non impacting barges. The primary role of non impacting barges is to facilitate modeling the dynamic response resulting from barge to barge contact and la shing interactions of adjacent barges during impact. Note the non impacting barges do not make contact with the target structure at any point in time during the impact event. 2 2 1 Impacting B arge The high resolution impacting FE barge model is composed of more than 900,000 nonlinear shell elements. The barge structural model is consistent with available detailed structural plans and is made up of three barge zones: the bow zone, the stern zone, and the

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19 hopper zone. Each zone is discretely modeled with internal structural members and external plate surfaces. Internal structural members consist of angle, channel, or gusset plate sections. Internal member thicknesses and external plate thicknesses vary between 5/16 in. and 5/8 in., as determined from structural plans. Figure 2 5 shows a rendering of th e impacting barge. Illustration of the mesh discretization in the bow zone is shown (Figure 2 6 .b). The material de finition for this high resolution impacting barge model has a nonlinear constitutive relationship (effective true stress vs. effective plastic strain) representing A36 structural steel with Cowper Symonds strain rate parameters provided in Consolazio and W alters (2012). All components are defined by 4 node, fully integrated shell elements with sufficient mesh density to allow for local buckling and local material failure. Material failure is represented in the simulation models by element deletion, and is s pecified to occur at an effective plastic strain of 0.2 in./in. Additional information regarding the steel material model is available in the semi flexible wall (Winfield) study report (Consolazio and Walters, 2012). A majority of the impacting barge is rigidized ( Figure 2 7 ) for computational efficiency and barge to barge contact compatibility Rigidization is a process in which the material definition for chosen components (solid elements, shell elements, beam elements, etc.) within an LS DYNA model are switched to a rigid material model. Thus, mass related inertial properties are maintained but no internal stra ins or deformations occur. Rigidization is constrained to regions sufficiently distant from the impacting starboard bow corner such that the remaining deformable portion extends well beyond areas involved in force crush interactions during oblique impact e vents, thereby not affecting force deformation behavior of barge wall contact. 2 2 2 Impacting B arge I nternal C ontact An LS DYNA self contact algorithm is used to account for the structural stiffness of the deformable region of the high resolution barge model (Figure 2 7 ). In accord with literature and

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20 previous USACE funded barge impact studies, (Consolazio et al. 2010), (Consolazio et al. 2012), (Consolazio and Walters 2012), and (Consola zio and Wilkes 2013), static and dynamic coefficients of friction ( ) for intra barge steel to steel (self) contact have constant values of 0.55 and 0.45, respectively. The rigidized portion of the high resolution barge model cannot deform, and thus self c ontact is omitted. 2 2 3 Non Impacting (Decimated) B arges The primary role of non impacting FE barge models is to accurately represent mass related inerti al properties and inter barge behavior in an efficient manner. Thus, performing an analysis with multiple high resolution barges is neither computationally feasible nor an effective or judicious use of computational resources. Due to the exorbitant comput ational expense of performing an analysis with a nearly one million element high resolution barge model, it is impractical and unnecessarily inefficient to utilize a fully discretized high resolution deformable barge model in any non impacting position wit hin a given flotilla. Therefore, each non impacting barge is modeled in a way that retains the external geometry of a high resolution barge, as well than the hi gh resolution barge FE model. The dynamic inter barge behavior is accounted for with contact and lashings. impacting barge model (Figure 2 8 ) consists of approximately 4,000 shell elements, as compared to the 900,000 shell elements included in the high resolution impacting barge model. Shell elements defining external geometry of each non impacting barge are modeled with rigid material definitions, thus no internal structural elements are required or included. Inertial and mass properties, quantified from the high resolution barge

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21 model, are assigned to each non impacting barge to ensure a ppropriate dynamic behavior during impact. 2 3 Modeling Barge I nteractions Barges are connected with steel wire rope, or lashings, to form a cohesive unit (for navigation) known as a flotilla. Lashings, anchored to steel cleats and wrapped around bitts (cylindrical steel posts), both of which are integral to the barge deck, are t ensioned with turnbuckles, shackles, or similar (Figure 2 9 ) to improve maneuverability during navigation. Adjacent barges are connected by encircling the barge bits in a specified pattern, referred to as a lashing configuration Lashings are layered on top of each other when more than one configuration is required at the same location. Diffe rent configurations are used to lash different barge pairs (end to end, side to side, or diagonal) and to resist different loads imposed by common flotilla maneuvers. Seven different lashing configurations, in either a port or starboard location, are used in this study. For 3x FE flotilla models, lashing configurations are consistent with those used in the full scale barge impact tests conducted by the USACE at Gallipolis Locks (Patev et al. 2003) and in previous analytical barge impact studie s (rigid wall (Consolazio et al. 2012 ), semi flexible (Winfield) wall ( Consolazio and Walters 2012) and bullnose (Consolazio and Wilkes, 2013) As compared to these previous studies, which made use of 3x flotilla models only, an updated group of lashing configuration s is used for FE flotillas of smaller width. These configurations more suitable to 1x and 2x flotillas were developed during the preceding flexible timber guide wall study (Consolazio and Wilkes, 2013). Each wire rope within the FE model is assigned an ap propriate geometric configuration; a set of material properties that represent the nonlinear stiffness of the lashing; and a failure criterion based on ultimate capacity. Depending upon the location of the wire rope within the

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22 overall flotilla, an appropri ate ultimate tensile of either 90 kips (for 1 in. diameter wire rope) or 120 kips (for 1.25 in. diameter wire rope) is assigned. By including a wire rope (lashing) failure criterion, each flotilla model has the ability to experience either full or partial break up wherein the individual barges are free to separate from one another and move independently. This feature of the flotilla model is particularly important in terms of quantifying impact loads on pile founded structures, where lashing failures may oc cur during high energy impacts. For a detailed description of the FE (mathematical) modeling of the lashing element s see Consolazio et al. (2012). Inter barge behavior is described with a combination of both lashings and contact, where contact definition s counter balance lashings forces between adjacent barge models. Contact accounts for separating (tensile) forces while lashings account for joining (compressive) forces between adjacent barge models. All barge regions in contact with adjacent barge models are defined with rigid material models, from either being in a decimated barge or through rigidization in a deformable barge, and hence inter barge contact stiffness cannot be calculated from deformations. Thus, inter barge separation forces are accounted for with rigid to rigid contact definitions, which reference force deformation curves developed from crushing two adjacent high resolution deformable barge models. The nonlinear force deformation curves extracted from the results of each quasi static crus hing simulation for the various barge to barge contact stiffnesses (side to side, bow to bow, and bow to stern) is detailed in the rigid wall report (Consolazio et al., 2012). 2 4 External L oading ( G ravity and B uoyancy) In each impact simulation conducted in this study, the effects of both gravitational forces and buoyancy forces acting on the barge flotilla are included. Buoyant uplift forces underneath each barge are modeled by introducing individual buoyancy springs over the bottom surface of

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23 the barge model. For the high resolution impacting barge model, approximately 26,400 discrete springs are attached to the barge bottom nodes, whereas each non impacting barge employs approximately 900 buoyancy springs. The stiffness of each buoyancy spring is computed by determining the tributary area of the barge bottom surface supported by the spring, and then multiplying this value by the density of water (62.4 lbf/ft3). By using a large number of s prings with relatively small tributary areas, the resulting stiffness values are small, thereby precluding the development of unrealistically concentrated buoyant forces during barge motions. Each buoyancy spring is 200 in. in length and connects to a support node (above the barge) that is freely able to translate in the horizontal plane (Figure 2 10 ) but restrained against vertical motion. As such, th is able to translate arbitrarily large distances in the horizontal plane (plan view) without resistance. Vertical motions of the barge, however, cause appropriate changes in the distribution of vertical uplift forces, which are based on changes in the submerged depth of the barge. Because the buoyancy springs are always in tension, the vertical support node of each spring ce of the barge. Consequently, the buoyancy springs remain vertical at all points in time during the simulation, regardless of the horizontal motions that the flotilla may undergo. This is particularly beneficial should a partial or full flotilla breakup o ccur during a simulation. Additional aspects of buoyancy modeling, such as calibration of the buoyancy springs and gapping of buoyant springs at the raked barge bow, are described in Consolazio et al. (2012).

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24 Table 2 1 Jumbo hopper barge flotilla dimensions and weights Flotilla Size Flotilla Length (ft) Flotilla Width (ft) Flotilla Weight (tons) 1 x 3 585 35 6,000 2 x 3 585 70 12,000 3 x 3 585 105 18,000 3 x 5 975 105 30,000 Figure 2 1 Typical 3x5 barge flotilla in transit (after USACE 2007)

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25 a) b) Figure 2 2 Jumbo hopper barge schematics: a) Single raked barge; b) Double raked barge a) b) c) d) Figure 2 3 Jumbo hopper barge flotilla schematics: a) 3x5 plan view; b) 3x5 elevation view; c) 1x3 plan v iew; d) 1x3 elevation view

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26 Figure 2 4 Flotilla impact simulation model consisting of a single impacting barge model, multiple non impacting barge models, and target structure (Note: only key geometric edge lines are shown; element mesh not shown for clarity) a) b) Figure 2 5 Jumbo hopper barge FE model (mesh not shown for clarity): a) Perspective view; b) Exploded view

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27 a) b) Figure 2 6 Barge bow zone: a) Structural configuration; b) FE mesh Figure 2 7 Partial rigidization of high resolution impacting barge FE model : (mesh not shown for clarity)

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28 Figure 2 8 Non impacting barge FE model (mesh shown) Figure 2 9 Typical lashing configuration on barge flotilla Figure 2 10 Barge buoyancy spring schematic

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29 CHAPTER 3 FINITE ELEMENT MODE LING OF PILE FOUNDED GUIDE WALLS 3 1 Introduction The USACE maintains a significant inventory of large mass concrete guide walls on timber piling foundations, herein referred to as pile founded guide walls (PFGWs). This study quantifies forces generated during oblique angle flotilla impacts against PFGW s tructures using FE analysis. The MRLD3 FE model, is developed from the lower pool interior monoliths (LPIM) at Mississippi River Lock and Dam No. 3 (MRLD3) in Welch, Minnesota (Figure 3 1 ). For the purposes of discussion and laying a guideline for the development of MRLD3 FE model, PFGW FE model developed from the upper pool interior monoliths (UPIM) at Mississippi River Lock and Dam No. 2 (MRLD2) in Hastings, Minnesota (Figure 3 2 ), is also refer red in this report. In summary, the two types of PFGWs FE models discussed in this study, for purposes of quantifying oblique angle barge impact forces, include: PFGW with typical timber piling foundation : MRLD2 (Figure 3 2 ) PFGW with rock filled timber cribbing foundation: MRLD3 (Figure 3 1 and 3 3 ) USACE provided an as built plan sheet of guide walls at MRLD2, MRLD3 (Figure 3 3 ), Mississippi River Lock and Dam No. 24 (MRLD24), and Mississippi River Lock and Dam No. 25 (MRLD25). Interior guide walls at these four lock structures are representative of typical PFGW structures for purposes of performing FE impact simulations. The MR LD3 FE model, which includes a rock filled timber cribbing substructure, is developed from the as built plans of LPIMs at MRLD3 (Figure 3 3 ). The MRLD3 FE model is representative of the USACE inventory of PFGWs with rock filled timber cribbing substructures. Interior guide walls are selected from the lock system for barge impact analysis as due to a l ower (lateral) stiffness, in comparison to other portions of the lock system, are often impacted by barge flotillas, and

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30 complement a previous study of impacts with bullnose structures (Consolazio and Wilkes, 2013). In short, the FE model developed for th is study (Figure 3 4 ) represents the most vulnerable portion of the USACE PFGW inventory. It is an ticipated that the predicted impact forces for MRLD3 guide wall will be representative and are likely to be generated on similarly constructed PFGWs with rock filled timber cribbing. The MRLD3 LPIMs, and thus the MRLD3 FE model, include a plain concrete g uide wall, rock filled timber cribbing substructure, and timber piling foundation. The plain concrete guide wall is modeled with solid elements, the timber piles with beam elements, the timber cribbing with shell elements, and the rock fill with discrete e lements. The plain concrete wall and timber piling are defined as linear elastic materials. The timber cribbing is defined with a rigid material model and the rocks are modeled using a discrete rigid material model. The structural components are linear ela stic as this study intends to quantify (conservative) impact loads representative of forces generated on structures of similar construction and configuration. Linear elastic behavior ensures individual structural components do not limit the impact force in a manner specific to the FE models presented herein. Nonlinear single degree of freedom spring elements represent the stiffness contributions of foundation soil, rock fill, and backfill soil. The primary objective in modeling the MRLD3 guide walls is to q uantify the effect of a rock filled timber cribbing substructure on peak flotilla impact forces The MRLD3 (Figure 3 4 ) FE model is discussed in further detail in the following sections. 3 2 Structural C omponents of P ile F ounded G uide W all M odels The interior monoliths at MRLD3 consist of plain concrete walls supported by a combination of rock filled timber cribbing and timber piling (Figure 3 5 b). The plain concrete walls and the supporting timber piling are defined with linear elastic material models. Timber cribbing is defined with a rigid material model and the rocks are modeled using a di screte rigid

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31 material model. The modeling techniques used to represent these structural components and the connections between them are discussed in detail in the following sections. 3 2 1 Plain C oncrete G uide W all The plain concrete guide walls are modeled with 8 node solid brick elements with cubic tha n approximately twice the size of the smallest impacting shell elements ( on the face of the deformable barge bow). Maintaining a size ratio no greater than 2:1 for elements in contact is suggested for impact simulations, e.g. the accuracy of detecting pene tration is compromised with an increase in mesh resolution disparity between the contacting surfaces. The concrete wall is sectional (Figure 3 6 ) and isometric view (Figure 3 7 ) of the LS DYNA model. The geometry of the bottom surface of the MRLD3 LPIM guide wall is inexact due to the transition from plain concrete wall to cribbing and/or rock fill. For purposes of deve loping a 661.0 (Figure 3 5 3 6 As per as built plan, construction of the UPIM guide walls at MRLD2 was completed in plans for MRLD2, MRLD3, MRLD24, and MRLD25, no additional information was obtained regarding concrete materials; e.g. minimum s trength, aggregate size requirements, sieve testing, codes, specifications, etc. As such, reasonably conservative materials properties are selected. For example, increasing the density of any PFGW component will increase the mass, thereby increasing peak i mpact force. Thus, a higher material density is understood to be conservative. Consequently, normal weight

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32 concrete, with a density 145 pounds per designation, practices at the time of construction, and ag e of the structure, a compressive strength c Modulus, from compressive strength using a current concrete industry method, a reasonable lower end value of 2,500 ks selected from literature review (McCormac and Nelson, 2005). In summary, the plain concrete guide wall for the MRLD3 FE model uses a linear elastic material model with of 145 pcf, of 2, 500 ksi, and of 0.16. 3 2 2 Timber P iles All timber piles in this study are modeled using resultant beam elements. As such, the beam elements (and nodes ) are positioned along the pile centerlines. Pile element nodes are are in length. For the MRLD3 FE model, two alternating sets of pile groups support the guide wall. This matrix of pile length and embedment depth yields a col lection of piles with six (6) different pile tip elevations below the base of the MRLD3 guide wall (Figure 3 8 and 3 9 ). The pile layout center. Each pile group set includes five pile group s, three sets of pile group A (Figure 3 8 ) and two sets of pile group B (Figure 3 9 ). Within these sets, pile groups are arranged in an alternating fashion, with the two (interior) sets of pile g roup B being bordered by the three sets of pile group A; i.e. each set contains an A B A B A arrangement. The spacing between an exterior pile group

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33 Section stiffness for all timber pile beam elements is specified by defining an area and section, section properties include an area of 133.1 in 2 rectangular moments of inertia of 1017.9 in 4 (about both local axes), and polar moment of inertia of 2035.8 in 4 Although it is known timber piling is tapered, with the given diameter representing the cross with a constant cross out its entire length. Multiple specifications were reviewed to select the most appropriate material properties from a review of literature from FHWA, USDOT, U SDA, FDOT, AWPA, NDS, ASTM, and USACE. As previously stated, increasing the density of any PFGW component will increase mass and inertial properties, thereby increasing peak impact forces. Thus, as with modeling of the plain concrete wall, using a reasonab ly high material density for timber piling is conservative. As such, an upper end density of 50.0 pcf is selected. Timber piling at Mississippi River Lock and Dam 6 (MRLD6) in Trempealeau, WI includes elm, maple, hickory, ash, oak, species (USACE, 2012). As no additional information regarding the timber used in the construction of PFGWs in either the Upper Mississippi or other regions throughout the United States, the substantial amount of timber needed for construction of a PFGW, e. wide range of wood species, as documented for MRLD6, is typical. In the interest of conservatism, and without additional information, a lower end elastic modulus of 1,000 ks i, is for wood. In summary, all beam elements representing timber piling are defined as a linear elastic material with of 50 pcf, of 1,000 ksi, and of 0 .10.

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34 3 2 3 Guide Wall to T imber P ile C onnection cross section with these embedment depths, the guide wall pile interface is understood to behave as a fixed connection. As discussed, timber piles are modeled with beam elements and the guide wall is modeled with solid elements. To connect these two struct ural components, nodes along the base of the guide wall solid elements are merged with coincident nodes along the tops of the timber pile beam elements; i.e. the timber piles are connected to the concrete wall through nodal merging. B ecause solid ( brick ) e lement node s do not have rotational degree s of freedom, nodally merging the beam elements (timber piles) to the solid elements (concrete guide wall) would represent a pinned connection as opposed to a fixed connection. In order to model a fixed pile head c onnection, a connection capable to transferring moments is needed between the guide wall and timber pile. The selected connection mechanism used in this study is the constrained nodal rigid body (CNRB). The coincident, or merged, pile to wall interface nod e is defined as the master node. The additional (slave) nodes included in the node (Figure 3 10 ). Constraining these additional four guide wall nodes to the merged wall pile node r behavior of the guide wall to pile connection. These CNRBs are installed at all guide wall to pile connections for the FE model, i.e. all eighty piles in the MR LD3 FE model (Figure 3 11 ). 3 2 4 Rock Filled Timber Cribbing Substructure The substructure of MRLD3 is split in two types of substructures : one consisting of only the timber piles that are completely embedded in soil and the other made of timber piles timber cribbing. The rock filled timber cribbing is

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35 unique to MRLD3 and the modeling techniques adopt ed in this study are site specific. Due to the complexity involved in modeling the rock filled timber substructure, a separate FE model is created that focuses on modeling the rock filled timber cribbing. This model, which consists of timber cribbing, corn er overlapping elements, pile casing and rock fill is discussed in the following sections. 3 2 4 1 Timber C ribbing long 10 x 12 timber elements that are stacked orthogonal to each other on the shorter side The timber cribbing ( Figure 3 12 ) in the MRLD3 substructure only serves the purpose of holding the rocks in place; i.e., the cribbing is not attached to the timber piles supporting the guide wall. For the develop consistent with the thickness of the timber elements shown in the as built plan s (Figure 3 3 ) provided by USACE. The timber cribbing ( Figure 3 12 only to support the discrete elements in place and does not to provide any direct structural The timber cribbing ( Figure 3 13 ) modeled as shell elements in FE model (also referred as the are placed such that the base of the shell elements coincide with th e beam (timber pile) node at the specified depth. The foundation casing is modeled to rest on horizontal rollers, to avoid any

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36 in the USACE plans) helps to avo id any discrete elements from falling out of the foundation casing which may occur due to relative displacement between shell elements at different levels. thick timber cribbing (also referred as base confinement) is modeled to reflect the end of the timber cribbing and the beginning of the soil strata. The base confinement ca rries the load of all discrete approximation. By transferring the vertical load to the rollers instead of transferring the same to the soil springs, the resista nce of the soil springs remains unaltered (due to the presence of rocks) during an impact and will provide conservative peak impact forces. The FE model representing the foundation casing and the base confinement is shown in Figure 3 13 3 2 4 2 Corner O verlapping E lements and torsion. from the base of the guide wall to the first soil spring (i.e. 18in below the soil strata). The er) as a diameter. The connection between the corner overlapping elements and the base of the guide wall is same as the guide wall to timber pile connection as de scribed in § 3 2 3 The FE model of the overlapping corners is anchored in soil as a displacement control mechanism for the guide wall. To have minimal effect on the axial capacity of the timber piles, the overlapping corner elements are modeled only along the outer periphery of the guide wall. Figure 3 14 shows over lapping elements modeled every 10ft along the length of the guide wall.

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37 3 2 4 3 Pile C asing As previously described in § 3 2 2 the timber piles are mode led using beam elements for MRLD3. However, these beam elements are not capable of physically interacting (i.e. contact) with surrounding elements. To capture the effect of rock fill interacting with beam elements, four no de fully integrated elastic shell elements are modeled about each beam node that lie within the timber cribbing. The thickness of shell elements is restricted connected to the beam nodes using constrained nodal rigid bodies (CNR B) as shown in Figure 3 15 Ev two adjacent battered prisms. Clear spacing between two adjacent prisms helps to avoid flexural locking and allows the beams to bend freely, as shown in Figure 3 16 The combination of rigid links (prism ends beam nodes) and the ability to define contact betwe en shell elements and discrete elements makes it possible to simulate rocks interacting with timber piles in LS DYNA. 3 2 4 4 Rock F ill It has been noted by the USACE that the rock fill in structures like MRLD3 structures often dislodge from the timber cribbing, indicating that the rock fill may not be optimally compacted in its present state If the rock fill i s under compacted, there may be no contact between the base of the guide wall and the top of rocks and hence no direct vertical load transfer from the guide wall to the rocks. This emphasize s that the load w ill flow from the guide wall into the piles and f rom the piles into the s oil foundation. The rock fill thus provides only lateral

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38 stability to the timber piles by interacting with them and by shear transfer due to mutual interaction of different layers of rocks. As the actual rock properties of the rock fill are unavailable with USACE, some assumptions are made to model the rock filling. Basalt rock, a generic rock type used for rock foundations, is assumed to model the rock fill in the timber cribbing. Basalt rock properties of density of 165pcf, modulu the FE model. The rocks are modeled using fully integrated quadratic 8 node solid elements with nodal rotations and discrete rigid material formulation Discrete elements (DE) are a mesh free modeling technique but their physical presence is modeled as spherical elements in LS DYNA. The spherical presence of discrete elements makes them capable of physical interaction (rolling, sliding, etc.) with each other and surrounding elements. A sliding friction coefficient of 0.30 and rolling friction coefficient 0.01 are used along with a damping coefficient of 0.20 to define an inelastic contact between the discrete elements and the shell elements that represent the foundation casing and pil e casing. Contact between two discrete elements is established by defining control properties for discrete elements. A normal damping coefficient of 0.70, tangential damping coefficient of 0.41, static friction coefficient of 0.57 and rolling friction coef ficient of 0.10 are used to control the contact between discrete elements. The friction coefficients used are in agreement with those suggested in conference proceeding presented by N Karajan et al., 2013. and hence, the discrete elements used to model rocks must As documented in Appendix B 1 the sizes of discrete elements do not significantly affect the shear resistance of the rock fill. Hence, for

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39 compaction algorithm described in Appendix B 2 required to compact the rock filling. A FE model with discrete elements in their fi nal position in the substructure is shown in Figure 3 17 3 3 Soil C omponents of Pile F ounded G uide W all M odels Soil representation is based on geotechnical data provided by the USACE. The provided soil data is expanded for use in FB MultiPier (FB Pier version 4) using empirical rela tionships. Nonlinear soils curves, extracted from FB MultiPier, are integrated into LS DYNA models with the use of lateral and vertical spring elements. Modeling of rock fill is based on data from the developers of LS DYNA, Livermore Software Technology Co rporation (LSTC). The rock filled timber cribbing is discretely modeled, with separate DYNA models, for application as soil curves to the timber pilling in the MRLD3 FE models with lateral spring elements. The modeling techniques used to represent the foun dation soils and rock filled timber cribbing are discussed in detail in the following sections. 3 3 1 Foundation S oils To model soil resistance, the USACE provided soil data from the MRLD3 site. The selected soil profile (Figure 3 18 ) was taken from MRLD3 (USACE, 2013). Soil properties corresponding to the layers included in this profile are highlighted in Table 3 1 This soil profile and the associated soil parameters, being representative in nature, provide the basis for the soil foundation characterization MRLD3 FE models. The soil near STA 6+00 at MRLD3 (Figur e 3 18 ) and the associated layer properties (Table 3 1 ) is representative of PFGW foundations and thus used in MRLD3 FE models. Table 3 2 correlates the USACE provided soil descriptions with the corresponding soil types as defined in FB MultiPier. For each layer, SPT blow counts (Figure 3 18 ) and soil parameters (Table 3 1 ) are taken directly from the provided geotechnical report (USACE, 2013). These SPT blow counts are

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40 7+00 centerline (Figure 3 18 principal strains at 50 and 100% are unavailable and thus calculated using known empirical relationships, e.g. Tomlinson, Kulhawy and Mayne, Skempton, etc. The resulting profile of calculated soil strength parameters are shown in Table 3 3 An FB MultiPier model (Fig ure 3 19 ) is developed using this profile (Table 3 2 ) of soil parameters (Table 3 3 ). The FE model (Figure 3 19 mber pile, with an 3 3 ). T he timber pile is elements in the LS DYNA models. The resulting static nonlinear force displacement soil curves (Figure 3 20 ) from this FB MultiPier model are extracted from each pile node, re sampled, mirrored if needed, and integrated into LS DYNA FE models (Figur e 3 21 ). Horizontal and vertical soil resistance is represented in the LS DYNA models using corresponding FB MultiPier model (Figure 3 19 ). These soil elements include p x and p y springs in the horizontal direction for lateral resistance, and t z and q z springs in th e vertical direction for skin friction and pile tip bearing resistance, respectively. The lateral, p x and p y, springs are modeled to undergo loading and unloading, where the loading curve is nonlinear and the unloading curve is linear and parallel to the initial portion of the loading curve (Figure 3 20 a). As there are two soil springs representing l ateral stiffness, both springs include a tensile and compressive component. The vertical skin friction, t z, springs are modeled to undergo nonlinear elastic force deformation. The vertical pile tip, q z, springs are modeled as compression only nonlinear e lastic elements. In order to achieve these desired behaviors, the

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41 force deformation curves (Figure 3 20 ) calculated by FB MultiPier are re sampled (and mirrored) prior to integration into the LS DYNA models. In the case of the lateral resisting, p x and p y, and skin friction, t z springs, the force deformation curves from FB MultiPier are mirrored us ing Mathcad in addition to re sampling. The pile tip, q z springs are resampled without mirroring as compression only resistance is modeled. Specifically, these modified force deformation curves are integrated into LS DYNA models with curve definition refe rences in the soils spring material models. As with the soil spring elements employed in previous research studies, translational restraints, required for each soil spring type, require element axes be oriented parallel to global axes (Consolazio et al. 20 02). The FB MultiPier timber pile model (used for development of the foundation soil springs) accounts for the overburden pressure of full depth backfill soils. Although backfill is not specifically modeled in the FB MultiPier timber pile model (Figure 3 19 ), the model includes from said water level is equivalent to the overburden pressure from full depth backfill soils, an additional FB MultiPier retaining wall model with both foundation and backfill soils is developed. The soil curves from the retaining wall model match the soi l curves from the timber pile model, thus verifying the single pile model accurately accounts for the stiffening effects of overburden pressures from backfill soils. An increase in the stiffness of any PFGW component will increase the peak impact forces. T hus using (reasonably) stiff curves for foundation soils is conservative. This stiffening effect (on the foundation soils) from overburden pressure is therefore included in the interest of conservatism. Again, stiffening effects from overburden pressures d ue to full depth backfill are accounted for in the nonlinear foundation soil curves (Figure 3 20 ).

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42 3 3 2 Rock F illed T imber C ribbing The rock filled timber cribbing of MRLD3 substructure is modeled using a combination of discrete elements, beam elements and shell elements of varying thickness. To generate a computationally efficient model, the rock filled timber cribbing model, describe d in 3 2 4 is simplified as lateral rock springs. These lateral rock springs are defined in pairs (along the length development of rock pile interaction curves for defining the rock springs is described in the following section. 3 3 2 1 Rock P ile I nteraction C urves Rock springs along global X axis (perpendicular to the length of the guide wall) and global Y axis (along the le ngth of the guide wall) are used in the MRLD3 (FE model that includes the guide wall and timber piles) to yield a response similar to the rock filled timber cribbing substructure, but in a computationally efficient way. These rock springs have stiffness cu rves generated based on the shear response of the rock filled timber cribbing (Section 3 2 4 ) with MRLD3 soil profile and represent a site specific simplification of the substructure. To generate the stiffness curves for the rock springs, four distinct pseudo static simulations are performed on MRLD3 substructure. Each simulation focuses on shearing th e top nodes of the timber piles in one particular direction (say global positive X direction). These nodes are fixed rotationally to resemble the fixed connection between guide wall and timber piles. The shear and displacement response of the timber piles within the timber cribbing are recorded. The relative shear response between two adjacent beam elements is then paired with the total displacement of the shared node to yield force deformation curve. By averaging the force deformation curves for all nodes at a given elevation a representative force deformation curve is generated for an elevation. A similar simulation is repeated for shearing in the global

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43 negative X direction, to generate a force deformation curve. The force deformation curve for positive a nd negative X axis loading are paired and sorted. The sorted force deformation curve is averaged and decimated every 150 points to filter out any oscillations arising from FE results. The sorted force deformation curve (rock pile interaction curve) represe nts stiffness curve for rock springs along global X axis. The same process is repeated for global Y axis to generate stiffness curves (rock pile interaction curves) for rock springs along global Y axis. Using the stiffness curves generated from the above p rocess, elastic non linear 1 dof discrete beams similar to soil springs (except for the stiffness) are defined in the final FE model of MRLD3. A typical section along MRLD3 highlighting only the rock springs is shown in Figure 3 22 Due to under compacted nature of the rock fill and non linearity of the stiffness curves it is assumed that the rock fill will beh ave elastically and hence the loading and the unloading is represented by the same stiffness curve. To validate the simplification process of rock filled timber cribbing into equivalent rock springs, a pseudo static simulation was performed by shearing the timber piles with rock and soil springs. The total shear response of the simplified model at any given depth is in close agreement total shear response of the rock filled timber cribbing, at the same depth (See Appendix B 3 ). An example of rock pile interaction Figure 3 23 a) and Figure 3 23 b) 3 3 2 2 Rock F ill M ass To capture the inertial properties of the rock fill, the total mass of the rock fill is distributed across the timber cribbing based on tributary volumes. Mass can be added directly to nodes in LS DYNA using *ELEMENT_MASS card. A detailed explanation of the mass distribution is explained below in Appendix C Depending upon the location of the pile node, one of three mass values is attached. If the node is at the pile guide wall interface, an added point

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44 mass of 1.451 x 10 3 kip sec 2 /in is attached. If the node is at the pile soil interface, an added point mass of 1.088 x 10 3 kip sec 2 /in is attached. For any node that lies within the timber cribbing, an added point mass of 2.176 x 10 3 kip sec 2 /in is attached. 3 4 External L oading of P ile F ounded G uide W all M odels Effects of both gravitational and buoyancy forces are included in all dynamic impact simulations performed for this study. Prior to initi ating an impact simulation, in which the barge flotilla is prescribed an initial velocity, the integrated flotilla guide wall model undergoes a gravity initialization simulation. This initialization simulation is performed to achieve static equilibrium und er self weight and hydrostatic pressures. Additionally, a unique initialization simulation must be performed for each simulated impact that differs in any condition other than initial velocity. Details regarding the application of gravity and buoyancy duri ng the initialization simulation are discussed below. 3 4 1 Gravity Loading Gravity is modeled in such a way that equilibrium is achieved prior to in itiating the impact simulation. Specifically, self weight of all structural members is applied in an instantaneous and constant manner. The initialization simulation takes place over the course of one second of simulation time, which is a sufficient length of time for integrated barge PFGW models to reliably reach static equilibrium under gravity and buoyancy loads. With the aid of critical damping, the computational cost of reaching static equilibrium is minimized, i.e. integrated barge PFGW models reach e quilibrium under the gravity loads in an efficient manner. Gravity loads, hydrostatic loads, and critical damping (for the first 0.99 seconds) are applied as a constant value before the first time step; i.e. 0.0 seconds. Critical damping is applied to the flotilla and PFGW separately, and removed from both prior to the completion of the initialization

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45 simulation at 0.99 seconds. From 0.99 to 1.00 seconds, the flotilla and PFGW remain at their equilibrium positions, without critical damping. 3 4 2 Buoyancy Loading As with gravity, hydrostatic loads are applied in an instantaneous and constant manner during the initialization simulation. Again, equilibrium of the integrated barge PFGW model is achieved under the combined application of applied hydrostatic loads and c ritical damping over the course of one second of simulation time. Results from an impact / water elevation sensitivity study (performed on MRLD2, Consolazio et al. 2014) identify most conservative impact elevation, with respect to peak impact force and pil e demands, corresponds to the lowest water elevation. Thus, the lowest water elevation condition is used for the parametric matrix of impact simulations with the MRLD3 FE model. For impacts against the MRLD3 FE model, the impact elevation corresponds to a (Figure 3 25 ). Although fully loaded hopper barge, weight = 2000 tons, drafts at an approximate providing sufficient water depth for a fully loaded hopper barge. 3 5 Barge F lotilla and PFGW C ontact I mpact L oading Integrating barge flotilla and PFGW models requires defining contact between the impacting barge and the given PFGW. This contact definitio n generates the force time histories that are presented in this study. Because interaction between the flotilla and PFGW models is limited to the starboard bow corner of the deformable barge and a portion of the vertical face, or impact side, of the concre te wall (Figure 3 26 ), computational efficiency is achieved by limiting contact definition referen ces to the portions of the deformable barge and guide wall that can potentially come into contact. Specifically, Barge PFGW contact is defined with a set of nodes in the (deformable region of the) starboard bow corner of the impacting barge and a set of

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46 segments along the lower portion of the vertical face of the PFGW. In accord with literature and previous USACE funded barge impact studies, (Consolazio et al. 2010), (Consolazio et al. 2012), (Consolazio and Walters 2012), and (Consolazio and Wilkes 2013) static and dynamic coefficients of friction ( ) between the steel barge and concrete wall have constant values of 0.50 and 0.45, respectively. Additionally, the PFGW models are positioned (in the longitudinal direction) to maximize impact forces prior to integrating the barge and PFGW models. It is understood impact forces generated during a centerline impact are conservative compared to those generated from other potential barge positions because the longitudinal centerline is the stiffest region (in the lateral direction) along the length of a monolith. Analysis of multiple impact simulations revealed the location of the impacting bow corner at the time peak impact force is within of contact for even the most extreme impact conditions modeled in this study. The PFGW guide walls are therefore span of the impacted monolith. Thus, the PFGW mod el is positioned to ensure peak impact will occur at (or just prior to) the longitudinal mid span of the given PFGW.

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47 Table 3 1 Soil properties at MRLD3 ( Source: USACE) Q (UU) S (CD) UNIT m (pcf) sat (pcf) c (tsf) (deg) (tsf) (deg) DESCRIPTION Q L 115.5 115.2 0.21 0 0 33 Lacustrine Sediment Q L1 112.0 113.0 0.31 0 0 32 Glacio Lacustrine Sediments Q L2 112.0 113.0 0.31 0 0 32 Lacustrine Sediment (Deep) Mostly CL E f 104.0 123.0 0 30 0 30 Fill (Fine to Medium Sand, Q f(upper) 121.6 121.6 0 29 0 29 Fluvial sands Q f(middle) 121.5 121.5 0 29 0 29 Fluvial sands Q f(lower) 122.6 122.6 0 32 0 32 Fluvial sands Q o 136.5 136.5 0 52 0 45 Glacial Outwash Table 3 2 Soil profile near USACE MRLD3 STA 7+00 (Data source for soil profile generation: USACE) Unit Layer Layer Depth Soil Description (as per USACE definitions) Soil Type (FB MultiPier) Q f(upper) 1 Fluvial Sands Cohesionless Q L1 2 Glacio Lacustrine Sediments Cohesive Q f(middle) & Q f(lower) 3 Fluvial Sands Cohesionless Table 3 3 Definitive soil parameters for pfgw study part a) (FB MultiPier input data) Unit Layer Depth (pcf) (psf) K q c (ksi) R t (kip) Q f(upper) 1 121.6 29 0.515 Q L1 2 113.0 310 Q f(middle) Q f(lower) 3 122.6 29 32 0.470 1.011 114.3 : unit weight : internal angle of friction c u : undrained shear strength K: coefficient of lateral earth pressure q c : ultimate unit end bearing R t : axial bearing failure E 50 : major principal strain at 50 E 100 : major principal strain at 100

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48 Table 3 4 Definitive soil parameters for pfgw study part b) (FB MultiPier input data) Unit Layer Depth E 50 E 100 G (ksi) f s (psf) E s (pci) Q f(upper) 1 0.542 0.25 0 126.0 34.09 Q L1 2 0.02 0.06 9.581 0.42 168.0 487.0 Q f(middle) Q f(lower) 3 0.978 0.25 373.2 562.3 131.9 G: shear modulus f s : ultimate unit skin friction E s : subgrade modulus Figure 3 1 Mississippi River Lock and Dam No. 3 (MRLD3) (Source: United States Army Corps of Engineers) Figure 3 2 Mississippi River Lock and Dam No. 2 (MRLD2) (Source: United States Army Corps of Engineers)

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49 Figure 3 3 As built plans of Lower Pool Interior Monoliths (LPIMs) at MRLD 3 (Source: U.S. Army Corps of Engineers)

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50 a) b) Figure 3 4 Isometric view of the MRLD3 single monolith PFGW FE model: for clarity; b) Pile beam elements (black ), rock spring elements (red), and soil spring elements (blue) rendered as lines

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51 Figure 3 5 Interior monolith PFGW cross section for LPIM at MRLD3 (Source credit: U.S. Army Corps of Engi neers) Figure 3 6 Cross sections of MRLD3 FE guide wall model

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52 Figure 3 7 Isometric view of guide wall portion of MRLD3 FE model Figure 3 8 Elevation view of pile group A at MRLD3:

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53 Figure 3 9 Elevation view of pile group B at MRLD3:

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54 Figure 3 10 Const rained nodal rigid body at guide wall to piling connection

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55 Figure 3 11 Constrained nodal rigid bodies (CNRBs) at guide wall piling interface for FE model of LPIM PFGW at MRLD

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56 Figure 3 12 MRLD3 timber cribbing (Not a FE model)

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57 Figure 3 13 Foundation casing and base confinement (FE model)

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58 Figure 3 14 Corner overlapping elements modeled as beams every 10ft.

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59 Figure 3 15 Rigid links from pile case elements to beam ends

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60 Figure 3 16 Pile casing capable of bending: a) un deflected shape b) def lected shape

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61 Figure 3 17 Assembly of MRLD3 substructure (without soil springs) for rock curve generation

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62 Figure 3 18 Soil profile from MRLD3 (Source: USACE) a) b) Figure 3 19 FB MultiPier timber pile model using soil information from MRLD3 STA 6+00: a) Soil profile with soil strength parameter shown per layer; b) 3 D rendering of mode l

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63 Figure 3 20 Typical soil force displacement curves used in FE model: a) P x, p soil surface; c) T z curve at pile tip ( surface)

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64 Figure 3 21 FE model of MRLD3 LPIM PFGW illustrating soils springs section of monolith without timber pilings shown for clarity)

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65 Figure 3 22 Typical rock springs (blue: along X axis, red: along Y axis)

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66 a ) b ) Figure 3 23 Rock pile interaction curve for MRLD3 substructure at depth = 126in along: a) Global X axis and b) Global Y axis

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67 Figure 3 24 Applicat ion of damping during an MRLD3 FE initialization simulation Figure 3 25 Hydrostatic loading conditions applied to MRLD3 PFGW model

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68 Figure 3 26 Illustration of contact between 2x3 barge flotilla and MRLD3 FE model (Rock springs and soil springs not shown)

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69 CHAPTER 4 DETERMINATION OF IMPACT FORCES ON PILE FOUNDED GUIDE WALLS 4 1 Introduction To quantify barge impact loads on pile founded guide walls, the guide wall model discussed in Chapter 3 is merged with four different flotilla configurations to form barge guide wall impact models. In total, 14 dynamic barge impact simulations are conducte d on MRLD3. Impact forces presented in this chapter are dynamic contact forces between the high resolution deformable impacting barge model and the concrete guide wall model. All forces are in the horizontal plane and have been resolved into the direction normal to (perpendicular to) the guide wall structure. Furthermore, all results are low pass filtered at approximately 10 Hz so that the quantified impact forces are not unduly influenced by higher frequency oscillations present in the FE results. Since th e focus of this study is to quantify peak barge impact forces, which typically lie in the first three pulses, the impact simulations for all parametric studies are terminated after t wo pulses or after complete loss of contact or after total impact duration of 3.5 seconds. 4 2 Development of I mpact C onditions The impact conditions for parametric study are based on the possibility of an impact condition occurring. This study covers barge impac ts occurring at angles of obliquity ( ) from 5 to 25 with the impact velocity varying (V 0 ) from 2 to 6 FPS ( Figure 4 1 ). As revealed by previous oblique impact studies (Consolazio and Wilkes, 2013), the momentum of the lead row of the impacting barge flotilla model has the greatest effect on the peak barge im pact forces. Hence only four (4 ) distinct barge configurations are us ed in this study. For barge configurations dams it is hi ghly unlikely for a barge flotilla with three strings to impact a guide wall model at

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70 20 or 25. Hence, impact studies for higher angles of obliquity are restricted only to 1x3 and 2x3 barge flotilla models. The development process for MRLD2 FE model refe rred to in the following sections is very similar to MRLD3. The significant difference in MRLD2 and MRLD3 wall model is that, MRLD2 does not have a rock filled timber cribbing and hence the soil strata starts immediately below the guide base of the guide w all. The mass of MRLD2 guide wall and MRLD3 guide wall (excluding the rock fill) are approximately the same. For a detailed understanding of MRLD2 FE model formulation refer to Consolazio et al. 2014. A summary of the impact conditions used for parametric study and their resulting peak impact forces is presented in Table 4 1 4. 3 Sensitivity Studies Apart from the barge flotilla configuration, the speed of the impacting barge and the angle of impact, there are numerous other factors (guide wall to pile connection, presence of adjacent monoliths, impact elevat ion, and presence of backfill) that can affect the barge impact forces. A series of simulation sets are performed on MRLD2, as described in (Consolazio et al. 2014), to quantify the effect of a given impact condition parameter on force results (time histor y characteristics and peak value). A majority of these simulations are performed to determine a conservative set of consistent impact conditions for use in the parametric matrix of simulations. Due to the similarity between MRLD2 and MRLD3, all sensitivity studies performed for MRLD2, except for the adjacent monolith investigation, are assumed to be consistent for MRLD3 FE model. As a result of the sensitivity studies, all impact simulations are conducted without backfill soil and are associated with the lo west water pool elevation, with the barge flotilla positioned

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71 upstream of the mid span of the guide wall being impacted ( Figure 4 2 ). Since, locks and dams are made of multiple guide wall monoliths placed side by side, it is essential to understand the effect of multiple monoliths on peak impact forces. Barge flotilla impact studies are thus carried out on single monolith and three monolith models to quantify the difference in peak barge impact forces due to presence of multiple monoliths. For simulations with multiple monoliths, both static and dynamic inter monolith coefficients of friction are a constant 0.60 per ACI §11.6.4.3 (ACI 2011). The three monolith model has one monolith placed Since the major concern of the sensitivity study was to understand the difference in peak impact forces and displacements of the guide wall, the simulation for one monolith was terminated after 1.5sec of impact duration. Comparative impact force time histories a nd displacement response of MRLD3 subjected to the same impact condition, 2x3 20deg 4fps, are presented ( Figure 4 3 and Figure 4 4 ) for 1.5sec impact duration. As is evident from Figure 4 3 the peak impact forces for a single monolith and 3 monolith models are approximately the same (10% increase). However, the co mparative displacement time histories ( Figure 4 4 ) show a reduction of approximately 30% in the total displacement of the guide wall with three monoliths. For a three monolith model, the peak impact forces are appr oximately 10% higher with a displacement reduction of almost 30%. For the purposes of this study, all impact simulations on MRLD3 are conducted using three monoliths, with one guide wall monolith on either side (upstream and downstream) of the guide wall m onolith being impacted by the barge flotilla. It should be noted that the impact forces presented in this chapter for MRLD3 are only for the center monolith that is being impacted.

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72 4. 4 Typical I mpact S imulation To describe b arge flotilla guide wall behavior during an impact event, an example impact simulation is discussed in the following section. Since the behavioral response of the guide wall and the barge flotilla, for any given guide wall, remains approximately the same f or all impact conditions, representative impact simulation is presented for MRLD3 guide wall. in which it is anchored, making MRLD3 substructure more flexible than MRLD2. The large mass of MRLD3 guide wall sitting on top of a relatively flexible timber pile matrix raises the possibility for a dynamic response on impact. To investigate the difference between a guide wall with and without rock filled timber cribbing, M RLD3 was subjected to the same impact conditions as MRLD2 (model without rock filled timber cribbing; Consolazio et al. 2014). Figure 4 5 shows a typical force time history for barge guide wall impact at high angles of obliquity, highlighting multiple impact pulses and durations of zero contact force. During the impact, the flotilla goes through a three stage fle xing action ( Figure 4 6 .). The first stage involves the rotation of the lead row without any rotation of the trailing r ows, whi ch is responsible for the first impact pulse. Due to the inertial resistance of the guide wall, the lead row flexe s away from the guide wall and loses contact with the guide wall. This loss in contact leads to zero force on the force time history. Due to the inherent motion of the flotilla, it again impacts the downstream side of the guide wall, generating a second impact pulse and starts transitioning in to the second stage of the flexing action. During this stage, the lead row of the barge flotill a has already rotated by some amount. The additional force due to the ongoing impact rotates the lead row further and forces the immediate trailing row to rotate and align itself with the lead row. The third stage involves the flotilla completely realignin g itself before another impact. When the barge makes another contact with the guide wall, it is already rotated and the

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73 flotilla makes contact at a lower angle of obliquity. After a series of low energy pulse s the flotilla has lost significant kinetic ener gy, and no longer flexes significantly during the impact. 4 5 Effect of Rock Filled Timber Cribbing on Impact Forces To compare the peak barge impact forces on guide walls with and without rock filled timber cribbing, MRLD2 and MRLD3 are subjected to the same impact conditions. This section discusses a comparison of force time histories of 2x3 4fps 20deg impact on both M RLD2 and MRLD3. In spite of the different force time histories produced from the impact studies on MRLD2 and MRLD3, as shown in Figure 4 7 it is worth noting that the initial impact forces, for both the guide walls, are approximately the same. This is can be attributed to the fact that the peak impact force is almost always the first impact pulse, whi ch is a consequence of the initial contact of the bow with the guide wall. Since, the mass of the guide wall of a single monolith of MRLD2 and MRLD3 are almost the same, the peak impact force were anticipated to be approximately the same. The difference in the stiffness of MRLD2 and MRLD3, due to the cribbing, is also reflected in the impact force time histories. The impact pulse duration for MRLD3 is consistently smaller and has only one peak impact force per pulse. The combination of high impact force and flexibility of the MRLD3 guide wall leads to short impact pulse. Since the contact duration between the MRLD3 and the barge flotilla is very small, it fails to cause significant flexing action of the barge flotilla, leading to a single well defined peak f orce for every impact pulse. To highlight the difference in the flexibility of both the structures, a comparative response time history is presented in Figure 4 8 The displacement response presented here is resolved normal to the guide wall. As can be clearly seen from Figure 4 8 MRLD2 displaces from its initial position after the impact and then fluctuates about a displacement of approximately 0.5 in. In case of MRLD3, the stiffness is so low that the guide wall displaces

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74 about 8. 7 5 in from its initial position before slowly starting to return to its original position. Based on the force time histories and the displacement responses ( Figure 4 7 and Figure 4 8 ) of both the guide walls, it can be concluded that the initial impact force is a direct consequence of the inertia of the guide walls. On the other hand, the flexibility and the stiffness contribution of the guide wall and the fl otilla are reflected in the impact pulse geometry. A comparative summary of peak barge impact forces are presented in Table 4 2 It can be seen that for high energy impact conditions (large flotilla size, high angle of obliquity and high velocity), MRLD2 (without cribbing) produces peak impac t forces that are 10 20% higher than those produced by MRLD3 (with cribbing). I t is thus reasonable to use the peak impact forces f rom impact conditions on MRLD2 as design guidelines. 4 6 Ge neral Trends in the Impact Force Results As mentioned in previous section, the peak impact forces due to the barge flotilla impacting MRLD2 and MRLD3 are approximately the same. Since MRLD2 has a huge matrix of simulations (51 impact conditions with 4 barg e configurations, Consolazio et al. 2014), the general trends for peak barge impact force for pile founded guide walls are studied on MRLD2 and are assumed to be consistent with MRLD3. The following section discusses the general trends that can be consiste ntly observed in peak impact forces and the force time histories due to varying impact conditions on MRLD2. 4 6 1 Effect of B arge F lotilla L ength Comparing force time histories for barge flotilla models with increased number of rows for same number of strings, under the same impact condition (speed and angle of impact), yielded that the peak impact forces are approximately the same. This behavior is consistent with previous studies (Consolazio and Walters, 2012) that suggest that the peak impact forces are a direct consequence of the momentum of the lead row of the impacting barge and not the

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75 momentum of the entire barge flotilla. To illustrate this, a comparative force time history for 10deg 6fps impact condition is presented in Figure 4 9 for both, 3x3 and 3x5 barge flotilla. As is evident from the plot, the first impact pulse traces the same path throughout the force pulse. The first force pulse represents the first contact between the bow and the guide wall and is responsible for the lea d row rotation. As a result, all the force time histories for 3x3 and 3x5 barge flotilla configuration have the same force time histories for the first impact pulse, except for the minor difference in the peak impact forces. 4 6 2 Effect of B arge F lotilla W idth The peak impact force is produced due to the impact of the bow on the guide wall, which captures many complex interactions like the contact between barges, the tensioning among the lashings, etc. It is thus reasonable to assume that the peak impact force will increase proportionally with the size of the impacting barge flotilla. It has been pointed out in previous works (Consolazio and Walters, 2012) that the change in the number of rows of the impacting barge flotilla have no significant difference on the peak impact force, for a given barge width. On the other hand, if the width of the flotilla is varied, an increase in flotilla width is accompanied by an increase in the peak impact force and the force pulse width. This behavior is consistently reported throughout the simulation matrix for MRLD2.

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76 Table 4 1 Impact conditions for barge impact studies on MRLD3 Flotilla Size Impact Speed (V 0 ) Impact Angle On Wall ( ) Impact Force (kip) 1 x 3 2 FPS 5 93 1 x 3 4 FPS 20 421 1 x 3 6 FPS 25 608 2 x 3 6 FPS 10 358 2 x 3 4 FPS 15 381 2 x 3 4 FPS 20 468 2 x 3 4 FPS 25 530 3 x 3 6 FPS 10 364 3 x 3 4 FPS 15 399 3 x 3 6 FPS 15 478 3 x 5 2 FPS 5 177 3 x 5 4 FPS 5 164 3 x 5 6 FPS 10 423 3 x 5 6 FPS 15 478 Table 4 2 Comparative peak impact forces for MRLD2 and MRLD3 Impact condition Peak normal impact force on MRLD2 (kip) Peak normal impact force on MRLD3 (kip) % by which MRLD2 force is greater than MRLD3 force 1x3 5 2 FPS 70 93 32.9 1x3 20 4 FPS 424 421 0.7 1x3 25 6 FPS 523 608 16.3 2x3 10 6 FPS 388 358 7.7 2x3 15 4 FPS 417 381 8.6 2x3 20 4 FPS 496 468 5.7 2x3 25 4 FPS 314 530 68.8 3x3 10 6 FPS 443 364 17.8 3x3 15 4 FPS 494 399 19.2 3x3 15 6 FPS 596 478 19.8 3x5 5 2 FPS 128 177 38.3 3x5 5 4 FPS 227 164 27.8 3x5 10 6 FPS 446 423 5.2 3x5 15 6 FPS 596 478 19.8

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77 Figure 4 1 Dynamic barge flotilla impact conditions for MRLD3 Figure 4 2 Position of initial contact for impact on MRLD3

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78 Figure 4 3 Comparative force time histories for 2x3 4fps 20deg impact simulations on MRLD3 using one monolith model and three monolith model Figure 4 4 Comparative displacement time histories for 2x3 4fps 20deg impact simulations on MRLD3 using 1 mo nolith model and 3 monolith model

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79 Figure 4 5 Force time histories for 2 x3 4 FPS 20 DEG MRLD3

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80 Figure 4 6 Continued rotation of the barge flotilla lead row during impact (Note that the displacements are magnified by a scale factor of 10 to highlight the rotation of the flotilla)

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81 Figure 4 7 Comparative force time histories for MRLD3 (with cribbing) and MRLD2 (without cribbing) for same impact condition 2 x3 4 FPS 20 DEG Figure 4 8 Comparative displacement time histories for MRLD3 (with cribbing) and MRLD2 (without cribbing) for same impact condition 2 x3 4 FPS 20 DEG

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82 Figure 4 9 Force time histories for 6FPS 10DEG impact condition on MRLD2 Figure 4 10 Force time histories for 4FPS 15DEG impact condition for varying barge width

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83 CHAPTER 5 SUMMARY AND CONCLUSIONS To quantify peak barge impact force on pile founded guide walls, dynamic barge impact simulations are conducted on MRLD3. Using 3 distinct barge flotilla configurations, impact simulations are carried out on pile founded guide walls for angles of obliquity ranging from 5 to 20 with the impact velocities ranging from 1FPS to 6FPS. Fifty one distinct dynamic impact conditions were developed for MRLD2 and six dynamic impact conditions for MRLD3. A comparison of force time histories for MRLD2 and MRLD3 indicated that the peak impact forces estimated from the dynamic barge impact studies on MRLD2 are conservative and representative for both pile founded guide walls, with and without cribbing. The peak impact forces for MRLD2 and MRLD3 indicate that the peak impact forces are a consequence of the inertial resistance of the guide wall. General trends observed in MRLD2 are consistent with previous findings (Consolazio and Walters, 2012) and are expected to be the same for MRLD3. For a barge flotilla of a given width, the length of the guide wall has little to no difference on the peak impact force. The peak impact force and the impact pulse width change proportionally with the size of the impacting barge, i.e. for the same impact conditions, the peak im pact force of a 3x3 flotilla will be greater than a 2x3 flotilla, which in turn will be greater than the peak impact force for a 1x3 barge flotilla. The data and the results from this study will be integrated with previous barge impact studies on guide wal ls, hurricane protection structures, etc. to develop a unified load prediction model (Consolazio et al. 2014).

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84 APPENDIX A IMPACT FORCE TIME HISTORIES FROM PILE FOUNDED GUIDE WALL MRLD 3 SIMULATIONS Individual force time histories for all barge PFGW MRLD3 impact simulations conducted in this study are plotted on the following pages. Each plot includes a trace o f the normal impact force in the horizontal plane All impact forces presented herein correspond to the contact force time histories between the high resolution impacting (deformable) barge model and the PFGW MRLD 2 model. Also note that all forces presented in this appendix have been low pass filtered using the procedure described e arlier in this report. The nomenclature used in each figure caption, to identify the impact condition that is plotted, is of the form: NSxNR SPEED ANGLE where: NS = number of barge strings (barge columns) in the flotilla NR = number of barge rows i n the flotilla SPEED = impact speed in ft/sec (FPS) ANGLE = impact angle in degrees For additional information regarding the barge PFGW MRLD3 impact conditions for which impact forces are plotted in this appendix, see Chapter 4.

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85 Figure A 1 1x3 2 FPS 5 MRLD3 Figure A 2 1x3 4 FPS 20 MRLD3

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86 Figure A 3 1x3 6 FPS 25 MRLD3 Figure A 4 2x3 6 FPS 10 MRLD3

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87 Figure A 5 2x3 4 FPS 15 MRLD3 Figure A 6 2x3 4 FPS 20 MRLD3

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88 Figure A 7 2x3 4 FPS 25 MRLD3 Figure A 8 3x3 6 FPS 10 MRLD3

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89 Figure A 9 3x3 4 FPS 15 MRLD3 Figure A 10 3x3 6 FPS 15 MRLD3

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90 Figure A 11 3x5 2 FPS 5 MRLD3 Figure A 12 3x5 4 FPS 5 MRLD3

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91 Figure A 13 3x5 6 FPS 10 MRLD3 Figure A 14 3x5 6 FPS 15 MRLD3

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92 APPENDIX B ADDITIONAL STUDIES WITH PFGW MODELS B 1 Size of D iscrete E lements ( S hear B ox S imulations ) The shear force b etween two layers of rocks could be a function of the over burden pressure. To quantify the effect of change in size of discrete elements and change of overburden pressure on the shear transfer, a sensitivity study is performed. The maximum opening in the timber cri simulation setup ( Figure B 1 ) consists of two boxes made of fully integrated shell elements ; depending upon the investigation. The lower box would remain fixed in all four simulations. The upper box would be sheared along the top edge of the lower box along its longitudinal direction at the Due to the absence of any other external force, the total shear force between two layers of discrete elements was the contact force exerted by the discrete elements on the confining upper box. Following simulations were performed t o estimate the effect of change of over burden pressure and change in size of discrete elements on the total shear force: Simulation 1: 12in diameter discrete elements, 12ft overburden. Simulation 2: 12in diameter discrete elements 9ft overburden. Simulat ion 3: 18in diameter discrete elements 12ft overburden. Simulation 4: 18in diameter discrete elements 9ft overburden. Comparing the total shear force of simulation 1 against simulation 3 and simulation 2 against simulation 4 indicated that for a given o ver burden depth the change in shear force due to change in the size of discrete elements is approximately in range of 10 15% and hence can be ignored. Hence, it can be assumed that discrete elements of different sizes (with same material

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93 properties) will produce similar shear resistance. Comparing the total shear force of simulation 1 against simulation 2 ( Figure B 4 ) and simulation 3 against simulation 4 ( Figure B 5 ) indicated that for a given size of discrete el ements increase in over burden pressure would increase the total shear force. Figure B 3 and Figure B 2 the reduction in shear ter discrete elements are used. B 2 Compaction Algorithm Based on report site observations for cribbed guide walls, it is assumed in this study that the rock fill is not optimally compacted. Compaction of discrete elements with the timber cribbing was achieved as a result of number of simulations that focused only on achieving compaction. The final state of compaction of discrete elements was achieved by working through the following steps: Generate a model with only the foundation casing, base confinement and discrete elements. The discrete elements are placed in a rectangular grid and given contact definitions of water, instead of rocks, to achieve better compaction. Subject the model to a non linear (sine wave) displacement to simulate compaction process. The final position of discrete elements is noted. A new model is created with foundation casing, base confinement, timber piles, pile casing and discrete elements. The initial position of discrete elements is taken from previously noted final position. The di screte element contact definitions are updated to rock properties. This model is initiated in LS DYNA. The discrete elements with initial penetrations are noted. A new model is created similar to previous model, but excludes any discrete elements that were noted as initial penetrations. The model is subjected to non linear (sine wave) displacement to simulate compacting motion. The final position of discrete elements is noted.

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94 The final model now contains discrete elements that placed such that they represent the closest approximation of compacted rock fill B 3 Validation of D evelopment P ile I nter action C urves The rock filled timber cribbing model with discrete elements (DE) was simplified into 1DOF nonlinear rock springs that were used in the final MRLD3 model. A study was conducted on MRLD3 substructure (timber piles, soil springs and rock spring s/DE) to verify the process of simplifying the model from using discrete elements into using rock springs. The pile guide wall connection nodes were loaded with a ramp load as shown in Figure B 6 This was done for the model with discrete elements and for the simplified model containing rock springs. The total shear force at every beam level was computed and compare d. The comparative plots ( Figure B 7 through Figure B 15 ) indicate that the force time histories for model with DE and model with rock springs are fairly close. The model with rock springs consistently over estimated the total shea r force at any layer, leading to a conservative modeling approach. Note: The soil stratum starts at 144 in below the base of the guide wall and the base confinement is modeled at a depth of 138 in. However for modeling the rock springs, rock pile interacti on curves were also defined for depth 144 in, to capture an approximation of the rock and soil interacting at the rock soil layer. It was thus initially expected that the total shear force from rock filled timber cribbing model may not match the simplified rock spring model at level nine (9).

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95 Figure B 1 Typical sectional view shear box simulation setup Figure B 2 Effect of change in diameter on total shear force burden pressure

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96 Figure B 3 burden pressure Figure B 4 E ffect of change in over burd discrete elements o n total shear force

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97 Figure B 5 E ff ect of change in over burden Figure B 6 Load applied per node at the top of the timber piles

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98 Figure B 7 Total Shear Force at level 1 (depth 0 18 in) Figure B 8 Total Shear Force at level 2 (depth 18 36 in)

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99 Figure B 9 Total Shear Force at level 3 (depth 36 54 in) Figure B 10 Total Shear Force at level 4 (depth 54 72 in)

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100 Figure B 11 Total Shear Force at level 5 (depth 72 90 in) Figure B 12 Total Shear Force at level 6 (depth 90 108 in)

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101 Figure B 13 Total Shear Force at level 7 (depth 108 126 in) Figure B 14 Total Shear Force at level 8 (depth 126 144 in)

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102 Figure B 15 Total Shear Force at level 9 (depth 144 162 in)

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103 APPENDIX C ROCK MASS DISTRIBUTION

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107 REFERENCES American Forest and Paper Association, National Design Specifications for Wood Construction 2001. Timber Piling Design and Construction Manual 2002. Consolazio, G. R., McVay, M. C., Cowan, D. R., Davidson, M. T., and Getter, D. J., Structures Research Report No. 51117 Engineering and Industrial Experiment Station, Univ. of Florida, Gainesville, FL, 2008. Consolazio, G. R., Davidson, M. T., and Cowan, D. deformation relati onships for barge Transportation Research Record 2131 Transportation Research Board, Washington, DC, 3 14, 2009. Consolazio, G.R., Davidson, M.T., and Getter, D.J., Development and support of dynamic numerical modeling of aberr ant rake barges impacting hurricane protection structures subjected to forces from a hurricane environment Final report to U.S. Army Corps of Engineers, Structures Research Report 2010/83710, University of Florida, Department of Civil and Co astal Engineer ing, 112 p., 2010 Consolazio, G.R., Walters, R.A., Harper, Z.S., Development of Finite Element Models for Studying Multi Barge Flotilla Impacts Final report to U.S. Army Corps of Engineers, Structures Research Report 2012/87754, University of Florida, De partment of Civil and C oastal Engineering, 61 p., 2012 Consolazio, G.R., Walters, R.A., Development Of Multi Barge Flotilla Finite Element Models For Use In Probabilistic Barge Impact Analysis Of Flexible Walls Final report to U.S. Army Corps of Engineer s, Structures Research Report 2012/94753, University of Florida, Department of Civil and Coastal Engineering, 79 p., 2012. Consolazio, G.R., W ilkes J R ., and Rodrigues, C.R., Determination of Barge Flotilla Impact Loads on Pile Founded Concrete Guide Wall s and Development of a Unified Impact Load Prediction Model for Navigational Structures Final report to U.S. Army Corps of Engineers, Structures Research Report 2014 / 104971 University of Florida, Department of Civil and Coastal Engineering, 79 p., 201 4 Coduto, D. P., Foundation Design, Principles and Practice, Second Edition 1994. Das, B. M., Principles of Foundation Engineering Third Edition, 1995. FB MultiPier, FB Florida Bridge Software Institute, University of Florida, Gainesville, Florida 2013. Florida Department of Transportation and Federal Highway Administration, Procedural Manual: Reclassify Unknown Foundation Bridges 2009.

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108 Ge tter, D. J., and Consolazio, G. deformation for brid ge Transportation Research Record 2251 Transportation Research Board, Washington, DC, 3 15, 2011. Goldsmith, W., Impact: The Theory and Physical Behaviour of Colliding Solids Dover Publica tions, Inc., 2001 Kulhawy F. H., Mayne, P. W., Manual on Estimating Soil Properties for Foundation Design Electric Power Research Institute, EL 6800, 1990. Lambe T. W. Soil Mechanics 1969. Liao, S. S. C., Whitman, R. V., Overburden Correction Factors for SPT in Sand Journal of Geotechnical Engineering, A.S.C.E., v. 112:3, p. 373 377, 1986. LSTC, LS 971 Livermore Software Technology Corporation, Livermore, CA, 2009. Karajan, N., Han, Z., Teng H., Wang, J., Interaction Possibilities of Bonded and Loose Particles in LS DYNA Information day: Multiphysics with LS DYNA, Livermore Software Technology Corporation, Livermore, CA, 2013 McCarthy, D. F., Essentials of Soil Mechanics and Foundations Seventh Edition, 2006. Skempton, A. W., Standard penetration test procedures and the effects in sands of overburden pressure, relative density, particle size, ageing and consolidation Geotechnique 36(3): 425 447, 1986. U.S. Army Corps of Engineers, 2007 Flood Control and Navigation Maps: Mississippi River U.S. Army Corps of Engineers, Washington D.C., 2007. U.S. Army Corps of Engineers, Lock and Dam 3 General Re Evaluation Report, Geotechnical and Geology 2013. U.S. Army Corps of Engineers, Mississippi River Lock & Dam N o. 2, Landward Lock Contract No. 4 1945. U.S. Army Corps of Engineers, Mississippi River Lock & Dam No. 3, Lock, Masonry Upper and Lower Guide Walls 1934. U.S. Army Corps of Engineers, Mississippi River Lock & Dam No. 24, Lock, Masonry Upper and Lo wer Guide Walls 1936. U.S. Army Corps of Engineers, Mississippi River Lock & Dam No. 25, Lock, Masonry Upper and Lower Guide Walls 1933. U. S. Army Corps of Engineers, Engineering and Design: Settlement Analysis Engineering Manual EM 1110 1 1904, 1990.

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109 U.S. Army Corps of Engineers, Upper Mississippi Rives Locks and Dams 2012. U.S. Department of Agriculture, Deriving Allowable Properties of Lumber: A Practical Guide for Interpretation of ASTM Standards General Technical Report, FPL 20, Forest Products Laboratory, 1978. U.S. Department of Agriculture, Wood Handbook: Wood as an Engineering Material General Technical Report, FPL GTR 190, 2010. U.S. Department of Transportation and Federal Highway Administration, Allowable Stresses in Piles Report No. FHW A/RD 83/059, 1983.

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110 BIOGRAPHICAL SKETCH Charles Rodrigues was born in Kolhapur, Maharashtra, India in 1990. In August 2008, he enrolled in the University of Pune in India, where he received the degree of Bachelor of civil engineering in May 2012. In August 2012, he then enrolled at the University of Florida where he received the degree of Master of Science in civil engineering in May 2014, with emphasis in structural engine ering.