implosion of steel fibre reinforced concrete …...abstract implosion of steel fibre reinforced...

Implosion of Steel Fibre Reinforced Concrete Cvlinders

Under Hydrostatic Pressure

Joel Aaron Smith

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Civil Engineering

University of Toronto

O Copyright by Joel Aaron Smith 1999

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Abstract

Implosion of Steel Fibre Reinforced Concrete

Cylinders Under Hydrostatic Pressure Master of Applied Science 1999

by Joel Aaron Smith

Graduate Department of Civil Engineering

University of Toronto

This thesis describes an experimentai test program and subsequent analysis

devoted to the study of steel fibre reinforced concrete cylinders which implode under

hydrostatic water pressure. The cylinders mode1 components of gravity base structures

beneath oil and gas platforms in the North Sea.

Five cylinders were tested in the Hydraulic Test Facility at the University of

Toronto. They had an outer diameter of 6lOrnm, and a thickness of 19mrn. The Length-

to-outer-diarneter ratio varied fiom 1-0 to 2.5. The total volume of fibre reinforcement

was either 1% or 6% of the concrete volume.

The cyiiiden are analyzed using a method developed by Haynes and Nordby,

using Olsen's Method which is a popular design method, and finally using RASP~, a

reinforced concrete shell finite element program developed at the University of Toronto.

The results of the analyses are compared to ex perimental results.

Acknowledgments

1 would first and foremost like to acknowledge my profound appreciation to my

supervisor, Professor M E Coliins, Department of Civil Engineering, University of

Toronto, for enabüng me to research something from which 1 could take pluisure, and for

imparting to me =me of his knowledge, but also his enjoymemt of structural engineering.

1 thank the National Sciences and Engineering Research Council of Canada for its

financial support.

1 owe tremendous recognition and heartfelt thanks to Amr Helmy, who not only

designed my specimens, but helped me perform my first experimental test. 1 thank Dino

Angelakos and Steve Cairns for constnicting my specimens in the structurai laboratory.

1 am grateful for the help of Evan Bentz, who answered my many queries with

enthusiasm and insight, and also introduced me to his sectional anaiysis program,

~esponse-2000~. Special thanks go to Mr. P. Lee* who greeted me with instant help

whenever 1 barged into his office with a problem. 1 thank Professor F.J. Vecchio for the

use of his programs, RASP~, and ~ e r n ~ e s t ? The expertise of Roman Yaworsky with

pictures and illustrations is recognized.

1 would like to extend my gratitude to the management and personnel of the

structural laboratory. 1 want to thank John McDonald for his steadfast support, even

when 1 was in despair. 1 would also like to express my appreciation to Peter Heliopoulos

for his sometimes litigious, but inevitably very usefiil advice and knowledge. I am grateful

to Giovanni Buzzeo, and Allan McClenaghen for tolerating me and making me laugh in

the machine shop. 1 am gratefùl to Renzo Basset, Mehmet Cit& and Joel Babbin for

helping me to solve my many problems.

1 also want to tip my hat to my fellow students who not only helped me in the

structural laboratory, but also filled my tirne at the University of Toronto with dMks and

merriment, and made my t h e here an enjoyable one.

Table of Contents Acknowledgments

Summary

Table of Contents

List of Figures

List of Tables

Notation

1 Introduction

2 Background

2.1 Literature Review of Analysis Articles

2.2 Literature Review of Experimental Articles

2.3 The Hydraulic Test Facility at the University of

Toronto

3 Description of Specirnens

3.1 General

3.2 Construction of the Fibre Reinforced Concrete

C yIinders

3.3 End Conditions for the Implosion Tests

.* U

iii

3.4 Displacement Gauges for the Implosion Tests 23

4 Behaviour of Fibre Reinforced Concrete

Specimens

4.1 General

4.2 Slab Tests 4.2.1 DescriPtion of Fibre Reinforced Concrete S U S

4.2.2 Testing of Fibre Reinforced Concrete Slabs

4.2.3 Propert-es of Xorex Steel Fibres

4.2.4 M i l l i n g of Fibre Reinforced Concrete Slabs in Respome-2000

4.3 Line Load Tests

4.3.1 General Description

4.3.2 Tesling of the Implosion Spcimens U i r a Line Laad

4.3.3 Modeiiing the Implosion Spcimens Under a Line Laad Using

Respome-2000

4.2.4 Correlation of R e l t s with Program Tempest

4.4 Modelling the Fibre Reinforced Concrete in

Subsequent Analyses 4.4. I Undersîding the Behaviour of Fibre Reinforced Concrete

4.4.2 Implosion Specimen Properties used for Subsequent Analyses

5 Analysis of the Implosion Problem

5.1 Elastic Analysis 5.1.1 Firsf-Or&r Ineory

51.2 E M c Buckling liheory

5.2 Plasticity Reduction Factor 5.2.1 Ineiàstic Stabilityïheory

5.2.2 Waynes andNordby

5.3 Olsen's Method 5.3. t.r Descri,ption of the 19 78 M e t M

5.3.2 Revisions to Ohen 's Method

5.3.3 Anabsis Using Oken 's Method

5.4 RASP Analysis 5.4.1 RASP AnaIysis of Implosion

5.4.2 Cracking ut the Endr of the Specimens

6 Cornparison of Analysis with Experimental

Results

6.1 Pressure

6.2 Displacement and Strain 6.2- 1 General

6.2.2 Diqplacernents for Spcimen LD250F6

6.2.3 Diplacements for S-men LD250FI

6.2.4 Displacements for Spcimen LDI7SFI

6.2.5 Displaements for S'jxcimen D I TSF6

6.2.6 Diqlacements for Spcimen LDIOOFl

6.3 Failure Mode 6.3.1 General

6.3.2 Fdure Mode for Specimen LD250F6

6.3.3 Failure Mode for Spcimen LD250FI

6.3.4 F&e Mode for Spcimen LD175FI

6.3.5 FalIure Marie for S w m e n LDLD17SF6

7 Conclusion and Future Work

7.1 Conclusions

7.2 Future Work

References

Appendix A Manual for the Hydraulic Test

Facility

A. 1 How to Adapt Specimens to the Pressure Vesse1

A.2 How to Use the Hydraulic Test Facility

A.3 What Happens During A Test

A.4 Trouble-Shooting

AS Options

Appendix B Implosion Test Strain Results

B. 1 Specimen LD250F6

B.2 Specimen LD250F 1

B.3 Specimen LD175F1


B.5 Specimen LD 1 OOF 1

vii

List of Figures

1 Introduction Figure I . 1 Cross-section of the Draugen Gravity Base Structure

Figure 1.2 Photograph of Three of the Implosion Specimens

2 Background Figure 2.1 The Hydraulic Test Facility

3 Description of Specimens Figure 3.1 Formwork for Specimens

Figure 3.2 Average Compression Curves fkom Standard Cyünders with 6%

fibres

Figure 3.3 Average Compression Curves from Standard Cylinders 4 t h 1%

fibres

Figure 3.4 Epoxy Repair Technique

Figure 3.5 "Concresive Paste" Repair Technique

Figure 3.6 Detail Showing End Conditions

Figure 3.7 Steel Ring, and Grout Used to Prevent End Displacements

Figure 3.8 Rubber Gasket Used to Seai Against Leakage

Figure 3.9 Hexagonal Steel End Caps Anchored by Rebar

Figure 3.10 Surface Strain Gauges

Figure 3.11 Location of the Surface Strain Gauges GD l7SFl) Figure 3.12 Location of Undemater LVDTs (LDZSOF6)

Figure 3.13 Displacement Transducers Used for the Second Test

Figure 3.14 Sketch of the Displacement Transducer

Figure 3.15 Displacement Transducers Used for the Third, Fourth, and

viii

Fifth Tests

Behaviour of Fibre Reinforced Concrete

Specimens Fijgre 4.1 Modelling Fibre Orientation in the Implosion Specimens Using Slabs

Figure 4.2 Experimental Response of Slab Hd%

F i p e 4.3 Experimentai Response of Slab L6%

Figure 4.4 Experimentai Response of Slab Hl%

Figure 4.5 Experimental Response of Slab L 1 %

Figure 4.6 Stress-Strah Curve for the Fibres

Figure 4- 7 Cornparison of Expetimentai and Predicted Response of Slab H6%

Figure 4.8 Comparison of Experimentai and Predicted Response of Slab L6%

Figure 4.9 Comparison of Expenmental and Predicted Response of Slab Hl%

Figure 4.10 Comparison of Experimental and Predicted Response of Slab L 1 %

Figure 4.11 Lie Load Test of Specimen LD lOOF 1 under the Baldwin

Universal Testing Machine

Figure 4.12 Line Load Test of Specimen LD 100F6 under the Baldwin

Universal Testing Machine

Figure 4.13 Load-Deflection Curve for Specimen LDlOOFl Under a Line Load

Figure 4.14 Load- Deflection Curve for Specimen LD 100F6 Under a Line Load

Figure 4.15 Coordinate System Used in the Anaiysis of the Cylinder under a

Line Load

Figure 4.16 Moment Relations for a Cylinder Under a Line Load

Figure 4.17 Moment-Cuwature Plots for Specimen LD 1 OOF 1

Figure 4.18 Moment-Cuxvahire Plots for S pecimen LD lOOF6

Figure 4.19 Hoop and Longitudinal Strain for Specimen LD lOOF 1

Figure 4.20 Hoop and Longitudind Strain for Specimen LD100F6

Figure 4.21 Comparison of Responses O€ Specirnen LD 1 OOF6

Figure 4.22 Cornparison of Responses of Specimen LD lOOF 1

Figure 4.23 Tempest Mode1 48

Figure 4.24 Cornparison of laad-Displacement Response for Sepcimen LD lOOF6 49

Figure 4-25 Comparison of load-Displacement Response for Sepcirnen LD lOOFl49

Figure 4.26 Fibres Distributecl in the Concrete Mass

5 Analysis of the Implosion Problem Figure 5- I Implosion Pressure Calculateci From Buckling Theory for each

Specimen

Figure 5.2 Graphitai Solution o f q using Inelastic StabEty Theory

Figure 5.3 Graphical Solution of q using Haynes and Nordby Curve Fit

Figure 5-4 Location of Maximum w and 4 for Various Mode Shapes

Figure 5.5 Coordinate System Used in the Analysis of the Cylinder

Figure 5.6 Graphical Representation of Olsen's Method

Figure 5.7 Meshes Used to Model Specimen LD250F1 in RASP

Figure 5.8 Comparïson of Meshes Used to Model Specimen LD250F 1

Figure 5.9 Summary of RASP Analyses

Figure 5.10 Maximum Tensile Stresses Predicted by RASP

6 Comparison of Analysis with Experimental

Results Figure 6.1 Comparison of Displacements on Lefi Side of Specimen LD250F6

Figure 6.2 Comparison of Displacernents on Right Side of Specimen LD250F6

Figure 63 Displacement Pattern at Failure

Figure 64 Circuderentiai Strain for Specimen LD250F6

Figure 6.5 Comparison of Displacements for Specimen LD2SOF l

Figure 6.6 Cornparisan of Displacements for Specimen LDl7SFl

Figure 6.7 Cornparison of Displacements for Specimen LD l7SF6

Figure 6.8 Comparison of Displacements for S pecimen LD l OOF 1

Figure 9 Crack Observed in Specimen LD 1 OOF 1 After Test ing

Figure 6.10 Displacements ofLDlOOFl Assurning an Initidly Circular Shape

Figure 6. 1 1 Displacements of LD 1 OOFl Using the Actual Undefonned Shape 96

Figure 6.12 Failure of Specünen LD250F6 98

Figure 6.13 Failure of Spechen LD250F 1 99

Figure 6.14 Failure of Specimen LD 175F 1 100

Figure 6.15 Failure of Specimen LD 175F6 100

7 Conclusions and Future Work

Appendix A Manual for the Hydraulic Test Facility Figure A.1 Diagram of the Steel End Plate Used for the Implosion Specimens

Figure A.2 Upright Specimen in the Pressure Vessel

Figure A.3 Hoses Connecteci to the Primary Reservair

Figure A. 4 Front of the Primary Reservoir

Figure A.5 Relation between Oil Pressure and Rod Size for DifEerent Thread

Conditions

Figure A. 6 Proposed Sequence for Fastening the Specimen to the Steel Base

Plate

Figure A. 7 Portais Used for Drainage and as an Outlet for Cables fiom the

Specimen to the Outside of the Pressure Vessel

Figure A. 8 Proposed Method for Fastening Vessel Head to its Shell

Figure A. 9 Top of Pressure Vessel

Figure A. 10 The flow Meter

Figure A. l 1 Schematic of the Pump Control Unit

Figure A. 12 Test Sequence

Appendix B Implosion Test Strain Results Figure B. I Circumferentiai Strains fkom Specimen LD250F6

Figure B.2 tongitudinai Stnins from Specimen LD250F6

Figure B.3 Circumferentiai Strains fiom Specimen LD250F 1

Figure B. 4 Longitudinal Strains fiom Specimen LD2SOF 1

Figure B. 5 Circumferential S trains fiom S pecimen LD 1 7SF 1

Figure B. 6 Longitudinal Strains fiom Specimen LD17SF1

Figure B. 7 Circumferentid Strains from Specimen LD I7SF6

Figure B. 8 Longitudinal S trains fiom Specimen LD 1 7SF6

Figure B. 9 Circumferential S trains fiom Specimen LD 1 OOF 1

Figure B. 10 Longitudinal Strains fiom S pecimen LD 100Fl

xii

List of Tables

1 Introduction

2 Background

3 Description of Specimens Table 3.1 Variation of Specimen Geometry and Reinforcement Ratio

Table 3.2 Specimen Dimensions

Table 3.3 Variation in Specimen Diameter and Thickness

Table 3.4 Concrete MUc Design

Table 3.5 Concrete Properties

Table 3.6 Cornparison of Concrete Strengths of Small Cylinder With

and Without Fibres

4 Behaviour of Fibre Reinforced Concrete

Specimens Table 4.1 Slab Test Specimens

Table 4.2 Slab Properties

Table 4.3 Properties Used in Response-2000

Table 4.4 Properties Used in Response-2000 for Line Load Tests

Table 4.5 Percentage of Steel Modeled in Each Specimen

Table 4.6 Ratio pal

Table 4.7 Properties Used for Subsequent Implosion Analyses

5 Analysis of the Implosion Problem Table 5.1 Implosion Pressure and Displacements of Elastic Infinitely Long

Cylinder 57

Table 5.2 Maximum Values of Mx 57

Table 5.3 Comparison of Haynes and Nordby's Prediction to Experimental

Result s 64

Table 5.4 Cornparison of W.,, I W, with p,, I p, 72

Table 5.5 Results of Various Analyses Using Olsen's Method 74

Table 5.6 Comparison of RASP Implosion Strength with Experimental Results 79

6 Comparison of Analysis with Experimental

Results Table 6.1 Implosion Pressures

7 Conclusions and Future Work

Notation Concrete strength fiom standard cylinder tests

Yield strength of fibres

Ultimate strength of fibres

Strain when fibres start to pull-out

Young's Modulus of Steel

Young's Modulus of material

Width of slab or length of cylinder

Thickness of slab or cylinder

Cracking stress of concrete

Strain at maximum concrete stress

Radial displacement of cylinder

Outer radius of cylinder

Mean radius of cylinder

Outer diarneter of cyIinder

Length-to-Outer Diameter Ratio

Angle measured in hoop direction of cylinder

Distance dong length of cylinder

Radiai distance fiom center of cylinder

Reinforcement ratio

Effective reinforcernent ratio reduced due to unfavourable orientation of fibre

Total reinforcement ratio

Mode shape number in the hoop direction

Mode shape number in the longitudinal direction

Length of dab, fibre' cylinder under consideration

Cuwature at midspan of slab

Displacement at midspan of slab

XV

K

L k, k2

A

0

F

F n

P

Pmp. Pim

P- implodes

a h

Hoop moment

Bending moment in longitudinal direction of cyiinder

Internai moment capacity

Extemaily applied moment

Maximum bending moment produced by out-of-roundness of cylinder

Flexurai stifhess of cylinder, D = ~h~ I 12(1- V' )

Curvature of cylinder

Constants

Area of fibre

Angle of fibre fiom direction perpendicular to crack

Force in fibre along axis of fibre

Component of force in fibre along x-axis

Hydrostatic pressure applied to cylinder

Pressure when cylinder implodes

Critical buckling pressure for thin cyhders, or pressure when cylinder

Hoop stress in cylinder

Hoop stress in cylinder when it implodes

Cntical buckling stress, or hoop stress when cylinder implodes

Hoop stresses

Poisson's ratio

Scaling factor depending on cylinder georietcy

Displacement at top of column

Initial eccentricity of column

Moment of Inertia of weak axis of column

Axial load applied to cohmn

Elastic poisson's ratio

Plastic poisson's ratio

Tangent stifhess modulus

ES Secant stifhess modulus

, , Plasticity reduction factors

p. fi, 8, Factors accounting for contribution to bending resistance fkom shell action

wo Initial radial eccentricity of cyiinder

wi Maximum radial displacement of cylinder

W C ~ U ~ Maximum radial displacement of a cylinder of specined length

W , Maximum radial displacement of an Uinnitely long cyünder

U, V. W Unknown displacements

U1 V, W Displacements in the longitudinal, circuderential, and radiai diections

respectively

Po Unknown pressure

fi, p+. pr Pressure in the longitudinal, circumferential, and radial directions respectively

p~r- Critical buckling pressure for an infinitely long cylinder

P u Criticai buckling pressure for a cylinder of specified length

NI Fust-order hoop force, pr,

Introduction

In August 199i, as the concrete gravity base structure (GBS) of the Sleipner

offshore gas platform was being ballasted down for deck mating, a reinforced concrete

wall failed in shear. At the location of this failure, seawater began to rush into the

structure causing it to sink into the fjord. Very shortly after the concrete structure

submerged, the buo yancy cells imploded, total1 y destroying the structure. While nearly al1

of the investigations which followed this accident have concentrated on the initial failure

of the wail, the incident also raises serious questions about the accuracy of current design

procedures for implosion.

Figure 1.1 shows the cross-section for the concrete gravity base structure used for

the Draugen Platform. In designing such a structure, both the main shaft, which supports

the deck, and the small buoyancy cells, must be designed so that they have an acceptably

small risk of failing due to implosion.

Implosion causes a shaft or ce11 to crush before it can reach the failure pressure

calculated on the basis of first-order theory. ln other words, assurning that the shaft d l

retain a cylindrical shape during deformation can produce an u n d e design. In reality, the

members are not perfectly round initially, and so there are not ody first-order hoop

stresses, but aiso hoop moments corn the start. As the pressure increases, the out-of-

roundness increases, which in tum increases the hoop moments in the shaft. These

second-order hoop moments increase the compressive stresses beyond the £ira-order hoop

Introduction 2

Figure 1.1 Cross-section of the Draugen Gravity Base Structure

Introduction 3

stresses which can procipitate an early fiiilure. A varîety of methods have been developed

to analyze the implosion problem. Most of these methods were developed in the late

1970s and early 1980s when this method of construction was fint being implemented.

During the same period, a large number of tests were conducteci to ver@ the analysis

methods, and to determine which parameters had the greatest effect on implosion capacity.

The tests generally used hollow concrete cylinders with diameter-to-thickness ratios

sirnilar to the buoyancy cells and main sh&s of offshore platforms. Two parameters of

primary importance were the concrete strength and the length-to-diameter ratio of the

cylindersl. However, one parameter which to this author's knowledge was not adequately

investigated, was the importance of the arnount of reinforcement. Land-based reinforced

concrete structures traditionally contain about 1% by volume of reinforcement. However,

recent concrete offshore structures have typicaily contained about 6% by volume of

reinforcement.

This report presents the findings of five tests of fibre-reinforceci concrete cylinders

which failed by implosion under hydrostatic pressure in the Hydraulic Test Facility at the

University of Toronto. Three of the specimens are show in figure 1.2. The cylinders

varied in both strength and length-to-diameter ratio so that the relative importance of

these factors could be measured. AIso, the amount of fibre-reinforcement was changed

fiom 1% to 6% to permit an inquiry into the significance of a parameter which has been

much less studied.

In summary, the objectives of the research reported in this thesis are as follows:

1. To examine the feasibility of using steel fibre reinforced concrete models to study the

behaviour of heavily reinforced concrete offshore structures.

2. To ve* the importance of both concrete strength and length-to-diameter ratio on the

implosion capacity of concrete cylinders.

3. To determine the effect of reinforcement percentage on implosion capacity.

4. To detennine which of the various analysis methods best predicts the implosion

capacity of reinforced concrete cylinders.

Introduction 4

Figure 1.2 Photograph of Three of the Implosion Specimens

Chapter 2 of this thesis presents both a literature review and a description of the

Hydraulic Test Facility. Because a manual has not yet been produced to teach future

researchers how to use the Hydraulic Test Facility, Appendix A provides a very detailed

step-by-step manual describing the preparation of specimens, and the operation of the test

facility itself. Chapter 3 gives an account of how the implosion specimens were

constructed. Chapter 4 answers the first objective stated above, using the results of

various supplementary tests to investigate how fibre-reinforced concrete behaved in the

implosion specimens. Chapters 5 and 6 respond to the remaining three objectives, by first

presenting an analysis of the implosion specimens, and then a cornparison ofthe analysis to

test data.

Background

This section of the report performs threc tasks. First, a literature review

summarizes those articles deaiing with analysis of the implosion problern. The sources of

those procedures implemented in chapter 5 are descnbed in general ternis. They are aiso

comparai to papers whose analysis rnethods were not used in chapter 5. Next, a second

literature review discusses a variety of experimental prognims aimed at understanding

implosion. Finally, an account is made of the history of research performed using the

Hydrauiic Test Facility at the University of Toronto. This last part describes some aspects

of the Hydrauiic Test Facility, but for a much more detailed description of how the facility

operates, the reader is referred to the manual in Appendix A.

2.1 Literature Review of Analysis Articles

The method used to design offshore platforrns in the North Sea is Olsen's Method.

An article published in 1978 first described this approach2. We know that implosion

occurs when hollow cylinders cmsh before reaching their faiiure pressure caiculated on the

basis of first-order thcory. Olsen explains this by acknowledging that hoop stresses fiom

firstsrder theory me increased by hoop moments produced by the out-of-roundness of the

cylinder. Olsen's method has many benefits. First of ail, it incorporates a sectionai

analysis which directly accounts for reinforcement and materiai non-iinearity. Secondly, it

Background 6

uses out-of-roundness directly in the procedure. Thirdly, it is based purely on e n g i n e e ~ g

principles, and does not involve data fits. The 1978 article presents design charts based on

assumptions made with regard to material behaviour. When the method was implemented

in chapter 5, many of these assumptions were ignored, but the principles of the method are

still the same. It must be said here that some of the most usefiil research materiai

wncernhg this method came fiom Mr. Tor Ole Olsen of Dr. techn, Olav Olsen a s . This

information provided various unpublished revisions to Olsen's method.

When Olsen first published his article in 1978, he venfied its accuracy ushg data

from a second uitluential article published by Haynes and Nordby in 1976'. The paper

proposes an analysis procedure on the basis of an on-going experimental test program

conducted at the U.S. Naval Civil Engineering Laboratory in Port Heuneme. Haynes and

Nordby analyzed specimens using elastic buckling formulae modified by a plasticity

reduction factor used to account for inelastic material behaviour. The plasticity reduction

factor is in tum derived fiom a fit to experimental data. Chapter 5 implements this

procedure to compare it with results fiom Olsen's method.

The moa recent article dealing with analysis is written by Chen and ~boussa lah~ in

1991. The article explains a finite element analysis of the implosion problem. It describes

the matenal model in depth. However, the finite element mesh is axisymrnetnc, and

cannot therefore capture the initial out-of-roundness of the cylinder. This is interesting

because Chen participateci in writing an earlier article in conjunction with I3aynes4 in 1979

which explicitly accounts for initial out-of-roundness by using non-circular geometry in the

model. This is usually what makes a finite element model of the implosion problern

unique. Perhaps the emphasis on finite element models of implosion has shifted from

geometry to material characteristics Nevertheless, the finite element model in chapter 5

implements the earlier technique of using non-circular geometry in the finite element

modet.

The above articles described analysis methods used in chapter 5 . The rernaining

analysis papers descnbe methods which have similarities to those already discussed. In

1985, Agnes and ~akobsen' produced an article on behalf of Norwegian Contracton

which descnbes Olsen's method and the application of finite element models to the

implosion problem. The article suggests some revisions to Olsen's method, but not as

Background 7

many as described in this thesis. It aiso disusses a method of accounting for

imperfections in the f i t e element mode1 similar to Chen's earlier article, and d e m i e s

how to handle creep efkcts, which was not done herein.

In 1980, Leick and ode^ fiom Esso and Exxon respectively produced an article

which proposes two analysis methods, one which does not account for out-of-roundness

or reinforcement, and one which does. The former method is based on a modified Gerard

method for calcuiating the critical buckling stress of the cyiinders. The first method in

chapter five which implements the plasticity reduction factor is based on the regufar

Gerard's method. The modified procedure might give better results. The second method

described in the article is essentially Olsen's method, but implements conjugate bearn

theory into the solution-

2.2 Literature Review of Experimental Articles

The most recent reference to an experimentai study is written by ~umes' fkom Det

norske Veritas in Norway. The study involved four large reinforced concrete cylinders

that were tested to failure in the DnV's pressure vessel. This is the only test program

which this author could locate which deait specifically with concrete cylinders which

çontained reinforcement. Ali four specimens failed primarily due to high hoop

compressive stress in the cylinder walls. The article also has a good discussion on

lamination, which is important when analyzing the effècts of reinforcement, and which was

not covered in this report. Unfortunately, because the information covered in the article is

proprietary to a certain COSlMAR project, the results and detailed analysis are not

described in the article.

Arguably the most in depth experimental test program was done in 1978 by

Haynes and ~unge'. The paper described earlier written in conjunction with chen4 is

another exctllent article desaibing the same test program. The tests go a long way

toward hvestigating the effect of imperfections on implosion strength, and any future

implosion tests would do well :O follow the lead of these researchen in terms of

displacernent measurement. The 15 unreinforced concrete cylinders were instnimented

Background 8

with a central shafk with linear potentiometen on amis at dinerent elevations dong the

length of the cylinder which could be rotated around the entire circumfierence to obtain

displacement data Many of the cylinden were intentionally given an initial outsf-

roundness to cietennine its efféct. The article includes dimensional data, strength data,

support data, and implosion capacity- Some detailed plots of the geometry are displayed.

If there is any doubt left in the reader's rnind that cylinders really do deform in elliptical

and three-lobed shapes, then this article should dispel t hose doubts, because the

displacement patterns are clearly plotted in the article. This is an outstanding reference to

any friture experirnentai implosion study.

FinalIy, there is a technical report referenced in chapter 5 which de& with

reinforced concrete spheres. The report was written by ~lbertsen' in 1975, and is

responsible for the notion that reinforcement often has little effect on implosion strength.

It describes six tests; four tests of spheres with reinforcement and two tests of spheres

without reinforcement. Because chapter 5 discusses limitations of these tests, they will

not be described here. However, the article does deal extensively with the lamination

problem, and is good reading for anyone trying to understand the effect of reinforcement

on implosion strength.

2.3 The Hydraulic Test Facility at the University of Toronto

The main feature of the Hydraulic Test Facility is a large pressure vessel built by

the University of Toronto to test reinforced concrete specimens under water pressure-

The pressure vessel has an outside diameter of 2.59m , a wall thickness of 22mm, and is

4.32m hi& It has b a n certified for a safe intemal water pressure of 27Spsi. A schematic

of the pressure vessel is shown in Figure 2.1.

Figure 2.1 shows not only the pressure vessel, but also a number of other

wmponents nece- for a test. These include the water reservoirs, the elecuic pump,

the pump control unit, the pressure transducen, the data aquisition system, and the lights.

There are two water reservoirs in the facility, but because there was very little leakage

during the tests, and hence very little water demand, only one reservoir was used. The

Background 9

Background 10

reservoir stores water which in turn is fed to the 25 horsepower electric pump on demand.

The water fiom the pump then passes into the pressure vessel through a Venturi meter

which measures the water inflow rate. The pump is controlled by the pump control unit.

The pump control unit contains an Hitachi Electric Invertor which pennits the researcher

to adjust the fiequency of the pump fiom OHz to its maximum of 120Hz with an acniracy

of O. lHz. This permits very accurate control o f water pressure. The pump control unit

also displays the pressure fiom the pressure transducers. There are two pressure

transducers, both shown in Figure 2.1- The transducers agreed to within 2psi dunng any

of the implosion tests. The data acquisition system records the data fiom the strain gauges

and the displacement transducers inside the specimen. The lights permit obsecvation of

the test through the portal shown at the top of the vesse1 in Figure 2.1. A video carnera

was mounted on the portal so that the test could be recordeci.

Roman Koltuniuk, a Master's Degree student at the University of Toronto played

a large role in having the pressure vessel built in 19901°. He also built the first specimen

for the pressure vessel, a 1:7 scale mode1 of the buoyancy cornpartment of a small offshore

oil pladorm. The original purpose of the pressure vessel was to study the effects of water

pressure on the crackd surfaces of reinforceci concrete structures, and this specimen was

created for that purpose.

Amr Helmy finished work on the pressure vessel and brought the Hydraulic TWL

Facility into operation as part of his Master's Degree work in 1992". Helmy also

conducted a number of tests using the facility. In conjunction with Arlene Bristol, a fourth

year Bachelor's Degree student, he imploded six PVC elastic hollow cylindncal specimens

as pilot tests of the facility. He also tested Koltuniuk's sale model. Unfortunately, when

the specimen first cracked, there was so much water leakage into it that the 1.5

horsepower pump could not supply water quickly enough to continue the test until failure.

The specimen was repaird and now awaits testing. The new 25 horsepower pump can

maintain much higher pressures necessary for the new test.

The most impressive study yet pedormed by the facility was that of a 1: 13 scale

model of a typical upper dome-ceIl wall jundion of a storage ceIl fiom an eary Condeep

structure. The test, pertormed as pan of Amr Helmy's PhD requirementsl*, is one of the

very b a t tests yet conducted of the brittle shear failure which occurs at this junction. The

Background 1 1

specimen had an extemal diarneter of 1.531~1, a ce11 wall thickness of 56mm, a dome

thickness of 39mm and is 2.44m hia. Helmy also built the implosion specimens tested as

part of the work describeci in this thesis. Because both the shear failure, and the implosion

failure are so critical in the design of storage ceUs, Helmy's work is invaluable. In

surnrnary, the Hydraulic Test Facility, while relatively new, continues to be a beneficial

research tool.

Description of Specimens

Six fibre reinforced concrete cylindrical specimens were designed for testing. The

length-to-diameter ratio and the reuiforcement ratio varied as shown in Table 3.1. The

outer-diameter-to-thickness ratio is equal to 32.2. Typical values of this ratio for the

Draugen shaft in Figure 1.1 range fkom about 25 near the bottom to more than 33 toward

the top of the shaft. Therefore, the geometry of the specirnens is consistent with current

design geometry.

The first five specirnens in Table 3.1 were tested in the Hydraulic Test Facility

under hydrostatic load in order to determine their implosion strength. Four of the five

specimens imploded, while specimen LDlOOFl reached the verge of implosion, but

because the pressure inside the pressure vesse1 was about to exceed the tank's design

pressure, the test was stoppeci, and this specirnen did not implode. This allowed both

specimens LDlOOF 1 and LDlûûF6 to be tested in the Baldwin Universal Test Machine

under a line load dong the length of the specirnen. Using the Baldwin test machine

permittecl a cornparison of the relative ductility of a specimen containing 1-00!

reuiforcement and a specirnen containing 6 -0% reinforcement, which was impossible under

water pressure because the post-peak behaviour wouid not be measurable. Also, by

modeiing the Baldwin tests using a sectionai analysis program, we could estimate an

equivalent amount of continuous reinforcement to replace the steel fibres.

Table 3- I Variation of specimen geometry and reinforcement ratio

3.2 Construction of the Fibre Reinforced Concrete Cylinders

Specirnen Lû250F6

Amr Helmy, a doctorate student studying at the University of Toronto, designed

and buiit the six fibre reinforceci concrete cylinders. Table 3.2 sumar izes the dimensions

of aii the specimens. During construction, two 6mrn thick cardboard So~otubes were

used as fonns. Wooden formwork then suppomd the S o ~ o n i b e s . The drawing in

Figure 3.1 shows the fomwork built for the three dinerent lengths of cylinden. The plan

view and elevation view for each cylinder are separated into two halves. The le£t haif of

each view shows the exterior of the formwork while the right half of each view shows a

section. Each eighth tum of the Sonnotubes was supported by a 2x4 stud on the inside

and outside surfbas to ensure that the diameter of the specimens was consistent

throughout. The fomwork for the specimens with length-to-diameter ratios of 1.75 and

2.50 required an intermediate support dong the length of the Sonnotube to prevent

buiging.

Oiameter Ratio 2.50

by Volume 6.0%

Description of Specimens 14


LûlûûF6 1 737 1 635 1 286 1 305 1 - 19 EEective span length reduced by 4 inches to account for 2 inch steel ring at

Table 3.2 S pecimen Dimensions

each end of implosion specimens.

Specimen Lû2SOF6 LD25OF1 Lû175F1 LD175F6 LD1 ûûF1

The constmction technique led to some variation in both the diarneter of the

specimens, and the thickness of the specimens. Table 3.3 shows this variation for two

specimens; LD17SF6, and LD 100F1. No measurements were made for the remaining

specimens. We measured the variation in diameter using a stiff wooden fkame made to

bear against the specimen on one side, and with a dia1 gauge positioned on the opposite

side of the specimen. Only the variation in diameter could be measured in this way, not

the actual diameter itself. We measured the variation in thickness using two foot long

wooden calipers which were made to bear against the outside of the specimen, while a dia1

gauge on the inside of the specimen recordeci the thickness. Again, only the variation in

thickness was measured, not the absolute magnitude. The measurements were made on a

grid spaced 12Smm dong the length, and 120m around the circumference of the

specimen.

Table 3.3 Variation in Specimen Diameter and Thickness

Len~th (mm) 1626 1626 1169 1169 737

The reinforcement for the cylinders consisted of steel fibres. Cylinders contained

either 1% or 6% steel fibres by volume, as specified previously in Table 3.1. Dunng

casting, laboratory personnel mmc3y placed the fibres into the concrete fiom the top of

n ~ength' (mm) 1 524 1 524 1067 1067 635

Outer Diameter

(mm) 305 305 305 305

Diameter (mm) 286 286 286 286 286

Thickness (mm)

19 19 19 19

305 1 19

Description of S pechens 16

the formwork, .?id then vibrated the fonnwork until the fibres settied. Subsequent

dernolition of the specirnens shows that this method eveniy distributed the fibres through

the concrete m a s . The properties of the fibres will not be disaisseci in this chapter.

Chapter 4 is wholly devoted to a discussion of the behaviour of fibre reinforced concrete.

The compressive charactenstics of the concrete were determineci fiom tests using

standard sized 1SOmrn x 300mm concrete cylinders made fkom the sanie concrete as the

specimens and containing the same volumetnc percentage of steel fibres. Between two

and four samples were tested for each of the six specimens. The average value of the

maximum compressive stress reached by each cylinder and the compressive strain at this

stress are listed in Table 3.5. Furthemore, the average stress-strain curves for the

specimens are displayed in figures 3.2 and 3.3. It can be seen that samples with 6.0%

fibres were wnsistently more ductile than those with 1 .OO/o fibres.

The initial plan for the research was to maintain the compressive stress-strain

characteristics of the concrete reasonably consistent for al1 six specimens. While

nominally the same concrete mix was used for al1 six castings there was some variation in

concrete strength, and even more variation in concrete stifhess. Table 3.4 shows the

concrete mix design. Four O t the six casts were made in May, 1995. However, specimens

LD 100F1 and LD250F1 were cast in March, 1995. These two casts had approximately

the same rnix design, but as shown in table 3.5, their properties were slightly different

fiom the later casts.

Table 3.4 Concrete Mix Design

Description of Specirnens 17

Straln (m mlm)

- - - - - --

Figure 3.2 Average Compression Curves fiom Standard Cylinders with 6% fibres

O 1 2 3 4 5 6

Strrln (mmlm)

Figure 3.3 Average Compression Curves fiom Standard Cylinders with 1% fibres


Beuwse the standard sized cylinders contained fibres, and because typical standard

cylinder tests use plain concrete, an investigation was perforrned to determine if the

presence of fibres influenceci the concrete strength. Smaller concrete cylinders, sized

l O O m x 200mm, were tested in compression. Six smaü cylinders were cast with both

specirnens LD250F6, and LD175F6. Three of the six samples contained steel fibres, and

three were made of plain concrete. A cornparison of the compressive strenghs of the

smaii cylinders with and without steel fibres is displayed in Table 3.6. Below this, the

table also presents the average compressive strength fiom the tests of the lSOmrn x

3 0 0 m standard sized cylinders. The strength of smaller samples is generally 4% greater

than larger samples according to ~evi l le? This 4% adjusted strength is also presented in

Table 3.6.

Table 3.6 Cornparison of concrete strengths of small cylinders with and without fibres

1 Specimen 1 LD250F6 1 LD250F6 1 LD175F6 1 ~ ) 1 7 5 ~ 6 ] 1 ~ a r n ~ l e ' 1 wl fibres 1 wlo fibres / wl fibres 1 wlo fibres11

' lOOmrn x 200mm small cylinder '1 50mm x 300mrn large cylinder

- - - -

Large Cylinder strength2

3 Small cylinders are generaily 4% stronger than large cylinders

Average 26.3 26.5 28.2 26.1 3

Various conclusions can be drawn fiom Table 3.6. First of d l , steel fibres have

r 29.5

Adjusted for sire3 26.0 27.0 25.0

lïttle effea on the compressive strength of samples taken fiom specimen LD250F6.

27.4 27-7

26.0

Conversely, the compressive strength of samples with fibres taken fiom specirnen

26.1

LD lîSF6 increases 8% beyond those sarnples without fibres. The table also shows that

the tests of the large cylinders agrees well with the smaller cylinders. These results show

that the presence of fibres may have a small effect on the strength of cylindricai samples,

although fùrther testing would be required to ven& this conclusion. Even if fibres do

influence the strength of sarnples, the effect is less than 8%. Ultirnately, the implosion

analyses used the wncrete properties already specified in Table 3.5.


Because of the thinness of the implosion specimens, they were occasionally subject

to cracking during handling. Two repair techniques were implemented; an epoxy

technique, and a "wncresive paste" described shortly. The epoxy technique was used on

specimen LD250F6, shortly afler casting. The width of the cracks was increased to about

4mm by removing concrete matenal, and the epoxy tùlly filled the crack. An example of

this technique is shown in Figure 3.4. The "concresive paste," produced by Master

Builders, was used for both specimen LD 175F1, and specimen LD250F1, damaged Eear

the time of testing. The "concresive paste" is a two component, 100% solids, non-sag

epoxy adhesive used for sealing concrete. The paste has a compressive yield strength of

55.2MPa. Because it has a tensile strength of 13.8MPa, which is almost three times that

of the concrete, the paste dia not have to fully penetrate the crack. The crack was

enlarged to a depth of roughly 4rnm with a grinder, and the paste was plastered to a

thickness of about 4mm on the outside of the specimen, making the total thickness of

paste equal to 8mm on each side of a crack. An example of this technique is shown in

Figure 3.5.

Figure 3.4 Epoxy Repair Technique

Figure 3.5 "Concresive Paste" Repair Technique

3.3 End Conditions for the Implosion Tests

Previous testing suggests that end conditions have a significant eEect on implosion

strengthl. These previous tests used three models for end conditions; fkee ends, fixed

ends, and pinned ends. Free ends allow both rotation and displacement of the ends; fixed

ends dlow neither rotation nor displacement, and pimed ends allow rotation, but not

displacement. The pimed end concept most clearly represents the physical conditions

implemented in the specimens tested for this thesis.

To prevent displacement at the ends of the specimens, a 50mm high steel ring was

placed at both ends as shown in Figures 3.6, 3.7, and 3.8. The outside diameter of the

~ g s is 559mm and the inside diameter of the specimens is 572mm, leaving a 7mm gap

between the ring and the inside of the specimens. This gap was filleci with grout to a

depth of 40mrn and a cardboard Sonnotube, lOmm high, was placed below the grout to

prevent the grout fiom leaking out of the gap as shown in the detail of Figure 3.6. Next, a

Description of Specimens 21 - - - -- - - -- - -- --

mbber gasket covered the ends of the concrete specimen to prevent water fiom Ieaking

inside. Steel hexagonal plates shown in Figure 3.9 were anchored at each end of the

specimen using steel bars which threaded into nuts on the outside of the plates. To ensure

that the bars were tightened unifonnly, longitudinal strain gauges recorded the elongation

of the bars, and the elongation was kept unifonn around the specimen. See Figure 3.9.

The question remains whether this construction permits the ends o f the cylinder to

rotate. First of ail, there was very little bond between the grout and the steel ring, o r

between the grout and the inside of the concrete specimen. When the specimens

imploded, the grout fieely fell off both surfaces. This suggests that the ends were fiee t o

rotate. However, because the steel plate wss very tightly anchored to the ends, fiction

between the steel plate and the ends of the specimen would provide some resistance to

rotation. Because of the presence of the mbber gasket, and because the ends of the

cylinder had slightly rounded corners, this effect was reduced. As will be presented in

chapter 6 of this report, the first implosion test o f specimen LD250F6 used undemater

LVDTs to closely mode1 the end displacements. The displacernent pattern shown is

difficult to reconcile with anything other than a p i ~ e d end condition. Therefore, in the

analytical portions of this research, it was assumed that the ends of the cylinders are

pimed for the implosion tests.

Rubber Gasket 24'x22.5'~3/8'

Threoded Rads I I \ ~ i e c i m e n

Note: Cylindrical Dimensions are given as Outer Diarneter x Imer Diameter x height

Figure 3.6 Detail Showing End Conditions

Description of Specimens

Figure 3.7 Steel ring, and grout used to prevent end displacements

Figtre 3.8 Rubber gasket used to seal against leakage

Figure 3.9 Hexagonal steel end caps anchored by rebar

3.4 Displacement Gauges for the Implosion Tests

Implosion tests implemented both surface strain gauge rosettes and displacement

transducers to measure displacement. However, the location and type of displacement

transducers varied fiom test to test.

The strain gauge rosettes measured both longitudinal and circumferential strain on

opposite sides of the cylinders. Figure 3-10 shows how the strain gauges were mounted,

and Figure 3.11 shows their position on the inside of the cylinders. Two rosettes were

centered dong the length of the cylinders, and the remaining four rosettes were placed

8 5 m fiom the ends of the cylinders, or 35mm fiom the edge of the steel ring.

The first test was the only test to use underwater LVDTs. The intensity of the

implosion destroyed three of nine undenvater LVDTs, and subsequent tests used

displacement transducers which could be made with less expense in-house. The locations

Figure 3.10 Surface strain gauges Figure 3.11 Location of the

surface strain gauges (LD 175F 1)

of the underwater LVDTs are shown in Figure 3.12. This configuration permitted an

accurate representation of the end displacements which in turn gave an understanding of

whether the end conditions more closely represented a pinned case or a fixed case.

However, this configuration of LVDTs could not record the defonnation behaviour at the

midspan of the cylinder which is of primary concem for implosion tests.


18 Figure 3.12 Location of underwater LVDTs (LD250F6)

TOPLFT TOPRGHT

i

For the second test, no displacements were recorded at the ends, only at the

rnidspan. Rather than one LVDT at rnidspan, there were now four displacement

transducers, equally spaced around the inside of the cylinder, shown in Figure 3.13. The

tip of the transducers was giwn some pretension against the inside surface of the cylinder,

so that if the wall moved outwards, then the tip of the transducers would follow. These

displacement transducers each contained six 2mm strain gauges as shown in Figure

3.14(a). To calibrate the transducers, the tip of the transducers was given a known

displacement like that in @) and the change in strain was recorded for each strain gauge.

The response was very linear for the strain gauges in tension, but the gauges in

compression behaved poorly. It was dismvered that strain gauges on the outside of the

transducer, narneIy gauges 0,4, and 5 gave the best results, and the strain gauges 1,2, and

3 were ignored. Furthemore, ifthe tip of the displacement transducer rotates as s h o w in

(c), then the induced tension at O wül be balanceci by an i n c r d compression at 4.

Therefore, the displacement recorded was ultimately the average of the displacements

given by gauges O and 4.

TOPMLFT

MIDDLE +

BOTMLFT

TOPMRGHT

BOTMRGH I


Figure 3.13 Displacement transducers

used for the second test

Figure 3. I J Sketch of the displacement

transducer

The subsequent three tests used displacement transducers very similar to that in

Figure 3.14, but strain gauges were only placed at the outside positions as shown in Figure

3-15. This compensated for the problems of the inside strain gauges, and also, by

averaging al1 four gauges, then any rotation could be offset with greater accuracy.

Furthemore, the tip of these transducers was threaded into a plate which in tum was

epoxied to the inside surface of the specimen. This meant that if the wall of the specimen

moved outward (as often did occur), then the tip of the transducer would follow the wall.

Figure 3.15 Displacement Transducer

Used for the Third, Fourth, and Fifth Tests

Behaviour of Fibre

Reinforced Concrete

specimens

Due to the extreme variability in the properties of fibre reinforced concrete

depending on the size of the wncrete specimen, the distribution of fibre in the concrete,

and the type of steel fibre used, there is really no definitive model which accurately

predicts the behaviour of all kinds of fibre reinforced concrete- Some rnodels have been

proposed14, but the models do not use the type of steel fibre fiom this study, and the

models are based on tests of much thicker specimens than the current implosion

specimens. As a result, two expenmental prograrns were carried out to model the

behaviour of the fibre reinforced concrete used in the implosion specimens. The first

series of tests involved slabs 19mm thick, 140mm wide and 4 0 0m long. The second

series of tests involved specimens LD lOOFl and LD lOOF6 tested under a line load dong

the length of the specimen. Both of these testing programs are described in this section.

Behaviour of Fibre Reinforced Concrete 29

Ultimately, the goai of these programs is to define an equivaient amount of

continuous steel reinforcement which is representative of the discrete fibre reinforcement

used in the implosion specimens, and which can be used in subsequent implosion anaiysis.

The analysis methods first require properties of the steel reinforcement such as yield

strength, stiffness and rupture strain. These properties are more difficult to define for the

fibres, but an attempt has been made to correlate previous research with the fibres used in

this study. Secondly, the analysis methods require the area of steel reinforcement. To this

end, the h e load tests of specimens LD 1 OOFl and LD IOOF6 were analyzed in a sectionai

analysis program, and the steel area was varied until the sectional response best fit the

experimental response. In this way, an quivalent area of continuous steel reinforcement

could be defined using the data fiom tests with the discrete fibre reinforcement.

Once the properties and area of the equivalent steel reinforcement are defined, al1

information required for subsequent analyses is known. These properties are defined at

the end of the chapter.

4.2 Slab Tests

4.2. I Descriplion of Fibre Reinforced Concrete Shbs

The Slab Tests were designed to test two parameters: (i) the effect of casting - -

orientation on the orientation of fibres, and (ii) the effect of the percentage of fibres in the

concrete. Casting involved four sets o f three slabs each. The four sets are listed in Table

4.1. The slabs were 19rnm thick, 140rnm wide, and 400mm long. Note that the slabs

have the same thickness as the implosion specimens. Slabs cast horizontdy were cast

with the 400mm dimension horizontal and the 140mm àïmension vertical, while slabs cast

vertically had the 400mm dimension vertical and the 140mm dimension horizontal. The

cylindrid implosion specimens are cast in the upright position as shown in Figure 4.1.

Therefore, the horizontally cast slabs are intended to mode1 the orientation of fibres in the

hoop direction (H) of the implosion specimens, and the vertical casts are intended to

mode1 the orientation of fibres in the longitudinal direction (L) of the implosion specirnens

as shown in Figure 4.1.

Behaviour of Fibre Reinforceci Concrete 3 0

Table 4.1 Slab Test Specimens

Figure 4.1 Modelling fibre orientation in the implosion specimens using slabs

Hl%-A,B,P 1% HG%-A,B,P 6%

LI%+ 1% 6%

The mix design was identical to the mix designs used for implosion specimens

LD2SOF1, LD175F1, LD175F6, and LDlOOFd which al1 had concrete cylinder strengths

in the range fiom 25.OMPa to 27.6MPa. The average of these values was taken to be the

strength of the slabs. Therefore, the slab strength was assumed to be 26.OMPa. Similarly,

the average value of G,, was taken as 2 . 4 d m .

Hofïzontal Horizontal Vertical Vertical

4.2.2 Testing of Fibre Reinforced Concrete Siabs

Each set of slabs has three tests associated with it. Tests A and B are two-point

loading tests, and Test P is a single-point loading test. Table 4.2 indicates that set L1%

has only a single-point loading test associated with it. Because of the weakness of this

slab, the remaining two specimens broke during removal fiom the mold.

The single-point loading test used a 254mm span, and a single LVDT beneath the

center of the specirnen to masure vertical deflection. The two-point loading test useâ a

356mm span, and three LVDTs, one at the center of the span, and two at 50mm on either

side of the center. Using these t h deflections, curvature could be calculated directly.

The loads were 203mm apart.

Behaviour of Fibre Reidorced Concrete 3 1

The results from each test consist of the moment-curvature response, and the

modulus of rupture of the material. Because curvature could not be calculated fiom the

single LVDT used in the single-point loading tests, the curvature was approxirnately taken

ffom the following relation,

I C ~ , = i ZA,~~L* (4- 1)

In reality, the value 12 should vary as cutyature changes, but treating it as constant

through-out the response history was deemed sufficiently accurate. The modulus of

rupture was caldated based on the moment when the slabs first cracked.

The moment-curvature diagrams are shown in Figures 4.2 to 4.5. Each plot shows

the results fiom each individual test, as well as an average response curve. Table 4.2 gives

the calculated values for the modulus of rupture, the concrete strength, and the

compressive strain at the maximum compressive stress.

Table 4.2 Slab Properties

Slab s

A few things should be said with regard to the moment-curvature responses. Fist,

the set of slabs labelid Hd% have considerable ductitity, and the post-cracking capacity is

more than 50% higher than the cracking load. This is distinct fiom slab L6% which has

the same amount of fibres, but was cast in a different orientation. When the fibres are

placed in the concrete, and then vibrated, they tend to align parallel with the surface o n

which they are cast. This means that slab H6% should have fibres oriented dong its

length, whereas slab L6% should have fibres perpendicular to b length. In other words,

the fibres in slab H6% will be more likely to span any cracks which fotm, which should

make it more ductile. We might then expect slab Hl% to have higher ductility than LI%.

While this is not true, we can ascribe it to the fact that stabs with less reinforcement have a

more variable distribution of fibres, and hence the response is highly dependent on where

the slab first cracks. Evidently, the one slab labelled L1% cracked at a location where

Behaviour of Fibre Reinforceci Concrete 32

there were an anomaious number of fibres. It should also be mentioned that the specimens

with only 1% fibres were far more brittk than those with 6% fibres.

Figure 4.2 Experimental Response of Slab H6%

- -

Figure 4.3 Experimental Response of Slab L6Yo


Curvature (rdlkm)

Curvature (rdlkm)

Figure 4.4 Experimental Response of Slab Hl%

Figure 4.5 Experirnental Response of Slab L1%

4.2.3 Properlties of Xorex Steel Fibres

The slabs were ultimately modelled using Response-2000, a sectionai analysis

program developed at the University of Toronto. Response-2000 does not have the ability

to mode1 fibre reinforment directly; nor do most analysis methods. Therefore, the


primary purpose of the model was to discover how the discrete fibre reinforcement cwld

be modelled using continuous steel reinforcing bars.

Besides the area of the fibres, some properties of the fibres also had to be known

for the model. The type of fibre used was a ~ o r a r ~ wmgated steel fibre 38mm long

with lm comgations. The minimum tende strength was 828 MPa, and the stifniess

was 200000 MPa The stress-strain response used to model the fibres in Response-2000

is shown in Figure 4.6. This is not the load-deformation curve of the steel, but rather it is

the load-deformation arme of a steel fibre being pulied in direct tension fiom a concrete

sample in which the fibre is embedded. Therefore, the shape of this curve is largely based

on the concrete matrix around the fibres.

0 0.02 0.05 o. 1 0.1 5

Straln (mmlmm)

Figure 4.6 Stress-Strain Curve for the fibres

The pullsut of the steel fibres can be broken into three phases described in a paper

by Chanvillard and ~itcin". Since this work did not involve Xorex fibres specifically, the

data fiom these researchers was calibrated with pullout tests that did use Xorex fibres,

provided by the manufacturer. Once the concrete has cracked, then crushing cones

develop in the concrete as the fibre comgations unfold on either side of the crack. The

Behaviour of Fibre Reinforcd Concrete 35

initial d lhes s is stiU 200000MPa, and the cmshing continues until the stress in the steel is

200MPa-

The second phase involves the unfolding and straightening of the fibre as the fibre

becornes completely debonded from the matrix dong its print. Microswpic investigation

shows that the conaete does not crush at ail dong the print of the fibre, and so failure at

this stage involves only the yielding of the fibre. For Xorex fibres, this progressive

yielding allows the stress in the fibres to increase to 550MPa in relatively thick concrete

specirnens.

The third phase occurs after the fibre has yielded and debonded, when it begins to

slip out of the concrete without disturbing the concrete matrix- This progressive slip

theoreticaliy occurs until the steel is completely removed from the concrete, resulting in a

strain of 1.0. As the slip progresses, the stress in the fibres decreases to zero in a nearly

h e a r fashion.

The behaviour described above was not obsewed for either the slabs or the

implosion specimens. Only the first phase, in which the fibre stress increases to 200MPa

was consistent with results. When the second phase was modeled in Response-2000, the

increase in stress produced a curve incompatible with expenmental results. A flat yield

surface correlated best with expenmental results, and so a flat yield surface was used in

the model. This is shown as the lower curve in Figure 4.6. The fibres cannot maintain an

increase in stress because the specimens were so thin. In the initial phase, when the fibre

is unfolding in the vicinity of the crack, tende stresses are produced perpendicular to the

direction of the fibre, and the concrete delaminates. It was observed dunng testing that

chunks of concrete fell off in the vicinity of the cracks. Once the concrete has

delarninated, then the fibre can effectively take on no more load. There are still fibres

which were not on the surface, which cari maintain the load until they are completely

debonded, but the load cannot inc5ease.

Ideally, the fibre should be modelled with a plateau at 200MPa as shown in Figure

4.6, and also with a linear decay in stress after the plateau has ended. Response-2000

does not offer a reinforcing stress-strain model with a descending stress-strain curve, and

so this part of the fibre response was not included. This means that the post-peak

Behaviow of Fibre Reinforceci Concrete 36

behaviour of the slabs predicted by Response-2000 was much steeper than the observeci

post-peak behaviour.

Response-2000 does, however, allow the user to input a rupture strain, or the

strain at which a reidiorcing bar wiii fail. For fibres, this strain corresponds to the strain at

which the fibre is completely debonded fiom the concrete matrix, and begins to pull-out.

For the slab H6%, a rupture strain of 20 mmlm gave the best results. For the slabs HI%,

L6%, and LI%, a rupture strain of 9 d m gave the best results because these slabs were

less ductile.

4.2.4 M'IZing of Fibre Reinforced Concrete Slabs in Respome-2000

A sununary of the information input to Response-2000 is shown in Table 4.3.

Figures 4.7 to 4.10 show the correlation between expenmentai and predicted responses

fiom Response-2000. The post-peak response fiom the model is too steep because

Response-2000 cannot model the linear decay in stress of the fibres after debonding. The

initial slope fiom the tests is not steep enough because the tests showed that the slabs had

unreliably low stifhess. Perhaps there are other sources of initial deflection during the test

which were not recorded by the LVDTs, What is really important about these charts is

the response &er cracking, which shows the effect of the reinforcing bars. The excellent

correlation shows that the fibres c m be accurately modelled using continuous

reinforcement.

Table 4.3 Properties used in Response-2000

Steel Properties Concrete P roperties Slab Es ( M W fW ( M W fdt m'a) çQ,t Area fc (MPa) E, (mrn/m) f, (MPa)

(mmlm) (mm2) H6Oh 200000 200 200 20 48 26 2-4 62 L6Oh 200000 200 200 9 26 26 2.4 4.1 Hl% 200000 200 M O 9 7 26 2.4 5

Behaviour of Fibre Reinf'orced Concrete 37

O 100 200 300 400 500

Curvature (rdlkm)

Figure 4.7 Cornparison of Experimentai and Predicted Response of Slab H6%

Figure 4.8 Cornparison of Experirnentai and Predicted Response of Slab L6%

Behaviour of Fibre Reùrforced Concrete 38

Figure 4.9 Comparison of Experïmental and Predicted Response of Slab Hl%

Figure 4- 10 Comparison of Experimentai and Predicted Response of SIab LI%


4.3 Line Load Tests

4.3.1 Generai Descn'ption

The line load tests perfonned two fûnctions. First, they demonstrated the ductility

of the implosion specimens which could not be easily established by the pressure tests

which do not permit post-peak response. Second and most irnportantly, they provided the

best indication of how much steel fibre area is effective in the implosion specimens. In

other words, having 6% fibres by volume in the specimen does not mean that there is 6%

continuous steel reinforcement by area when andyzed. The line load tests determine what

hction of steel fibres are effective in resisting load.

The line load tests involved the testing of implosion specimens LDlOOFl and

LD IOOF6 under the Baldwin Universai Testing Frame. Specimen LD 100F6 had never yet

been tested, but specimen LDlOOFl had already been subjected to a pressure test. Only

one crack resulted fiom the pressure test, and it was repaired. The properties of the

concrete for both specimens were determined fiom standard cylinder tests as indicated in

part 2 of this report. The properties of the steel fibres used in the line load tests are

identical to those described in section 4.2.3.

4.3.2 Testing of the Implosion Spcimens Under a line Load

The testing method is shown in Figures 4.1 1 and 4.12 for specimens LD 100F1 and

LD100F6 respectively. There are two LVDTs placed inside the specimens at the 1/3

points to measure the change in the vertical diameter of the specirnen. There are four

LVDTs placed at the 1/3 points to measure the change in the horizontai diameter of the

specimen. There are also six sunace strain gauge rosettes on the sides of the specimen,

three on each inside surface. On a given side, there is one rosette at the enter, and two

rosettes placed 85mm fiom the ends of the specimen.

To distribute the load, Plaster of Paris was laid to a width of 150mm on the top

and bottom of the specimen. There was a small taper on either side of the plaster, so

when the load was distributed in the analysis, it was treated as a stnp 16Smm wide.


Figure 4.11 Line Load Test of Specimen LD100F1 under the Baldwin Testing Machine

Figure 4.12 Line Load Test of Specimen LD 1 OOF6 under the Baldwin Testing Machine


The results of the h e load tests consist of the foiiowing:

- Moment-Cwvatture plot for each specimen, taken at the side of the specimen, as weli as

the tophottom of the specimen.

- Plot of Moment versus change in strain for both the longitudiial and circumferential

strain gauges.

- Modulus of Rupture

F i we must find the rnornent-curvature plots which will then be cornpared to the

analysis. Only the load-deflection curves resuited directly fkom the line load tests. These

are displayed in figures 4.13 and 4.14. Two cornrnents should be made with respect to

these figures. Fust of dl, increasing the percentage of fibres from 1% to 6% increased the

moment capacity of the section by 74%. Secondly, the figures clearly show a considerable

increase in ductility for the specimens with 6% fibres.

5 ,

O 5 10 15 20 25 r)

Change In Radius (mm)

Figure 4.13 Load-Deflection Curve for Specimen LD lûûFl Under a L i e Load

To convert the deflections to cuwature, the foiiowing equation fom FluggeI6 is

used:


Figure 4.14 Load-Deflection Curve for Specimen LD IOOF6 Under a Line Load

Equation (4-2) is based on a deflection pattern corresponding to the following:

These equations are based on the coordinate system as defined in Figure 4.1 S. We biow

&om theory that the cylinder will deform into an ellipse under the line load. This is further

borne out fiom observation during testing. Therefore, m=2. Furthemore, there is no

defonnation dong the length of the cylinder, so the sine tem must equal 1. To do this,

1 Recognizing that curvature, K = 4 , I D , then equation 4.1 can be rewritten as,

where K = cunrature at any point w = displacement a point where curvature is caiculated rn = 2 since the cyünder deforms into an ellipse Tm = the radius of the cytinder measured to the center of the thickness D = flexural stifthess of the shell, D = €t3 1 12(1- v2 )

This equation is valid as long as the cylinder continues to defom in the shape of an ellipse.

As a sirnplifjing assumption, the cylinder is assumed to deform in the shape of an ellipse

t hroughout testing.


Figure 15 Coorduiate system used in the analysis of the cylinder under a Luie load.

We also know how the moment in a Iinear elastic cylinder will Vary as a fùnction of

load. Using the superposition of three load cases1', the formulas presented in Figure 4.16

can be denved. Notice that while the maximum moment at the top is at location A, the

specimens cracked at location B instead. Evidently, the plaster on the top of the cylinder

helped resist load- Therefore, when calculating moment at the top and bottom, the

moment at B is used. When calculating moment at the side, the moment at C is used-

Because the section at C is subjected to compression forces, this increases the moment

carrying capacity of the section. In other words, while the moment at the side is larger in

magnitude, because of the beneficial effects of the compression force, initial cracking may

occur at the top or on the side. To illustrate this difnculty, dunng the testing of specimen

LDlOOFl, the first crack occurred at the top, whereas dunng the testing of specimen

LD 1 OOF6, the first crack occurred at the side.

w Figure 4.16 Moment Relations for a cylinder under a line load

Behaviour of Fibre Reinforcecl Concrete 44

The fonnufas presented in Figure 4.16 are used to convert load to moment at the

side and at the top of the specimens. The validity of these formulas degrade as the shape

of the cylinder becomes less elliptical, however they are assumed adequate for the

complete load history. Figures 4.17 to 4.18 display the momentnirvature diagnms

derived f?om the Ioad-dispIacement diagrams in the manner described above.

Curvature (raâllrm)

Figure 4.17 Moment-Curvature Plots for Specimen LD lOOFl 450,

Figure 4.18 Moment-Curvature Plots for S pecimen LD 1 OOF6

Behaviour of Fibre Reinforcecl Concrete 45

To calculate the moddus of rupture, the moment when the specimen first ctacked

must be defined. To do so, we look at the plot of hwp strain at the side of the specimen

versus moment at the side. Oniy the Uiitiai portions of these curves are displayed in

Figures 4.19 and 4.20. The first crack in specimen LDlOOFl is clearly at 243kNmm. The

first crack in specimen LD100F6 is not as clearly defined, but close inspection suggests

that the first significant deviation nom iinearity occurs at 245LNmm. The modulus of

rupture is caiculated using the standard formula, as 5-SMPa for both specimens.

-250 J

Moment at Side (kHnm)

Figure 4.19 Hoop and Longitudinal Strah for Specimen LI3 100F1

4.3.3 M i e l h g the Implosion Specimens U i e r O Iine Lwd Using Respome-2000

Using the above concrete properties, the implosion specimens were modelled using

Response-2000. Once again, the primary purpose of Response-2000 was to discover

what area of the steel fibres was effectively acting as continuous steel reinforcing bars.

The properties of the steel fibres are the same as those described in section 4 - 2 3 Table

4.4 shows the properties of both the steel fibres and the concrete matrix which were input

to Response-2000. The specimen with 6% reinforcement cracked on the side of the

specimen, and so an axial load of W/2 is included in that analysis, where W is the total


load. The specirnen with 1% reinforcement cnisked on the top of the specimen, 8Omm

fiom the center of the line load, and consequently no axial load w u included.

Moment 1 skie (kNmm)

Figure 4.20 Hoop and Longitudinal Strain for Specimen LD100F6

Table 4.4 Properties used in Response-2000 for Line Load Test

Figures 4.21 and 4.22 compare experimentai results and predicted responses fkom

Response-2000. Again, the close correlation shows that the fibres can be accurately

modeiied using continuous reinforcement.


Figure 4.21 Comparison of Responses of Specimen LD 100F6

Figure 4.22 Comparison of Responses of Specimen LD 100F 1

4.2.4 Correlation of R e d & with Pt-ogrm Tempesl

To produa the charts in Figures 4.21 and 4.22, we made assumptions with

regards to the moment-load relation, and the curvature-displacement relation, which

Behaviour of Fibre Reuiforced Concrete 48

dowed correlation with a sectional analysis program. To ver@ the validity of doing so, it

is usefùl to incorporate our assumptions into a non-linear h e analysis package to

detennine whether we can re-produce the experimentd load-deformation plot. Program

Tempest, a fiame analysis program developed specificaily for concrete, was used to model

both specirnens LD IOOF6 and LD 1 OOFl.

To formulate the model, the cylinder was discretited into 24 line elements forming

a ring of radius 296mm, with a width of 740mm as shown in figure 4.23. The ring was

reinforced with smeared steel in six Iayers uniformly distributed through the 19mm depth

of the ring. Ail of the properties of the concrete and steel were identicai to those used for

Response-2000 as displayed in Table 4.7 except for E, and the concrete stiaiess.

Tempest does not have an option for +, and so its reinforcement model requires that the

stress in the steel remains constant at 200MPa and the steel never ruptures. Also, whereas

Response-2000 uses €0 to evaluate the initiai concrete stifhess, Tempest requires an initial

value for the Young's Modulus of the concrete. A value of 2f& was chosen. The

supports at the bottom resist movement both horizontally and vertically.

Figtcre 4.23 Tempest Model

Two types of loading were used for each specimen, A and B. Loading A consisted in a

distributed load over elements 6 and 7. Loading B consistai in identicai prescribed

displacements for nodes 6, 7, and 8. In other words, loading B forces elements 6 and 7 to

maintain their onginai shape, whereas loading A permits the shape to change. The actual

situation is intemediate between these two cases. Furthemore, loading B provides much

better post-peak response for specimen LD lOOFl than does loading A. The resulting

responses are shown in Figures 4.24 and 4.25. The predicted load-deflection curves fiom


Tempest are in excellent agreement with the experimental results. This strongly suggests

that both the moment-load relation and the curvature-displacement relations in*ally

ïbdirl Orpl-ment at SMe (mm)

Figure 4.24 Comparison of Load-Displacement Response for Specimen LD100F6

O 2 4 6 8 10

FWld Orplacement 1 Top/-tt (mm)

Figure 4.25 Comparison of Load-Displacement Response for Specimen LD 1 OOFl


Modelling the Fibre Reinforced Concrete Subsequent

Analyses

This section summarizes the results of the previous two sections. Some attempt is

made to understand these results, and then properties are listeci which wül be used to

represent the fibre reidorced concrete in the implosion analyses of the next chapter.

4.4.1 Under-ng the Behaviour of Fibre Reinforced Concreie

The behaviour of individual steel fibres has already been introduced in section

4.1.2, and in Figure 4.6. Once the shape of the fibre response cürve is known, the oniy

remaining concern is to determine how many fibres are effective in the concrete m a s

Table 4.5 sumrnürizes the percentage of steel fibres required to mode1 the experimentai

response of both the slabs and the Line load specimens. This table plainly shows that

having a fibre volume of 6% of the concrete volume does not mean that the section has

6% of effective wntinuous reinforcement. This section tries to explain the results

presented in table 4.5 through a consideration of fibre orientation, bailing, and the

distribution of fibres in the specimen.

Table 4.5 Percentage of Steel Modeled in each Specimen

1 effective percentage of reinforcement in the hoop d i e d o n

Fikt consider the effcct of orientation. m e r testing, two of the slabs and part of

two implosion specimens were crumbled to give an estimate of the overall orientation of

the fibres. The cnimbled slabs were H6%-A and L6%-A; the crumbled implosion

specimens were specimens LD250F6 and LD100F6. As the samples were crumbled,

Behaviour of Fibre Relliforced Concrete 5 1

fibres were exposed, and the onentation of each individual fibre was measured using a

protractor.

To accwnt for the vaqing onentation of fibres, consider fibre (i) displayed in

Figure 4.26. The force-displacement relation for this fibre is as foiîows:

F=AEAiL (4-9)

However, as the concrete elongates by A, the fibre elongates by only ACUSO. Sùnilarly,

the component of the force Fr onented in the x-direction is F~COS~. Therefore, the

contribution of force fkom the fibre to the concrete in the x-direction is actudly,

F~=(AEAIL)COS~~, (4- 1 0)

which essentially means that the effective area of fibres contributing to the section is

reduced by a factor of cos2@.

Fi're 4.26 Fibres distributeci in the concrete mas

To find the effective area reduction, we use the fibre orientations measured with a

protractor. Ifwe have numerous fibres oriented at different angles, gr, then the ratio of the

effective reinforcement ratio to the total reinforcement ratio will be as follows,

Pen - -- COS* el + C O S ~ e2 + C O S ~ e3 +....+ C O S ~ en . (4-11) Ptot n

Behaviour of Fibre Reinforced Concrete 52 - -

In this manner, the ratio p, /p,can be calculateci for each of the samples where fibre

orientation was maisured. The ratios are presented in Table 4.6.

Toble 4.6 Ratio p, I p,

Sample Ratio p d k ~6%-A' ~6%-B'

~ 0 2 5 0 ~ 6 ~ 0.57 Li31 0 0 ~ 6 ~ 1 0.56

'Rati! represents fibres oriented dong ! he length of the slab 2 Ratio represents fibres oriented in the hoop direction

First consider the two slabs. Slab H6%-A is meant to model fibres cast in the

hoop direction of the implosion specimens, and slab L6%-A is meant to model fibres cast

in the longitudinal direction. The effective area of steel given by table 4.6 nom slab L6%-

B is 64% of that fkom slab H6%-A Similady, from table 4.5, we notice that the effective

area of steel given by Response-2000 using slab L6% is 54% of that fiom H6%.

Therefore, a wnsideration of fibre orientation explains the reduction in steel area fiom the

hoop direction to the longitudinal direction of the implosion specimens within reasonable

error.

Next consider specimens LD250F6 and LD100F6. Table 4.6 predicts that the

reduction in steel area due to the unfavourable orientation of steel fibres would be 0.58.

Meanwhile, the reduction fiom Response-2000 given in table 4.5 for specimen LD lOOFl

is 0.64% 1 1% = 0.64. Therefore, a consideration of fibre orientation predicts the

reduction to within 9?4 error. However, we might then expect that the reduction in steel

area for specimen LD100F6 would be 0.58 also. The actud reduction is 1.79% / 6% =

0.30. This is considerably more than arpected. To explain this, we consider balling.

Balling occun when there is a luge amount of fibres in the concrete, and rather

than acting independently, the fibres clump together in a mass. This reduces the effective

area of the steel. When the specimens were broken up, it was observed that the specimens

with 6% fibres contained considerable balling, whereas there was no balling in the


specimens with 1% fibres. Therefore, both balhg and unfavourable fibre orientation

d u c e the effective steel area of specirnens with 6% fibres.

One question remains to be answered with respect to table 4.5. Both slabs Hl96

and L1% give anornalous results. This is because the slabs are 140mm wide, whereas the

implosion specimens are 740mrn wide, and slabs Hl% and L1% have oniy 1% fibres as

opposed to 6%. Clearly, this will result in a much less uniform distribution of fibres, and

there is a greater chance that whatever section cracks first will either be under-reinforced

or over-reinforced.

4.4.2 Implosion Specimen Proprhes usedfor Subsepent Analyses

A complete Iist of propedes used in the subsequent analyses an display& in table

4.7. The concrete properties and the sectional properties were described in detail in

chapter 3. The steel properties were detined in this chapter. Values for Es, f-, and f*

were based on puii-out tests of fibres embedded in concrete as discussed in section 4.2.3,

and in Figure 4.6. The value of is baxd on the Response-2000 analyses ofspecirnens

under a line load as indicated in table 4.4. The percentage of reinforcement in the hoop

direction was taken fiom table 4.5 as 0.64% for spe-ens with 1% fibres, and as 1.79%

for specimens with 6% fibres. The ratio of steel in the longitudinal direction to steel in the

hoop direction was taken as 0.98% / 1.80% = 0.54 fi-om table 4.5. Therefore, the

percentage of reuiforcement in the longitudinal direction was 0.64% x 0.54 = 0.35% for

specirnens with 1% fibres, and 1.79% x 0.54 = 0.97% for specimens with 6% fibres.

Behaviour of Fibre Reidorced Concrete 54

Table 4.7 Properties Used for Subsequent Implosion Analyses

20dy required by the RASP analysis; both longitudinal steel and hoop steel were defined in two layers, one 4.75m fiom the top, and one 14.25m.m fiom the top.

Analysis of the Implosion

Problem

Various methods exist which attempt to predict the implosion of cylinders under

hydrostatic pressure. This section presents the methods that are most cornmonly used.

First, the theory behind elastic buckling of cytnders is presented, which will act as

background material for the remainder of the methods. Once this is done, the elastic

buckling analysis is revised to account for material nonlinearity using a plasticity reduction

factor. The next method, created by Olav 01sen2, acmunts for material nonlinearity, but

also initial out-of-roundness which is ignored by the previous approach. Olsen's method

is the method currently used to investigate the implosion of the very large cylindrical

structures beneath offshore platforms. Finally, a finite element model, RASP, can be used

both to investigate implosion, and also to verifj. that the pressures recorded would not

cause failure at the ends of the cylinder.

Analysis of the Implosion Problem 56

5.1 Elastic Anaiysis

5.1. i First-Oràèr ïkory

Before investigating buckling theory, it is usefil to describe linear elastic

deformation behaviour of a perféctly circular cylinder. As will be s h o w in chapter 6 of

this report, some of the specimens defonned in an almost linear marner, and so it is

instructive to know the failure pressure of these specimens as calculated on the basis of

linear theory.

First, consider a thin cyiiider of infinite length. The first-order hoop stress and

decrëase in radius of the cylinder are simply, -

where a h = Grst-order hoop stress h = thickness p = pressure fo = outer radius r, = mean radius

% w '= 'decrease in radius

Using these equations, and knowing the concrete strength, a quick estimate of the

implosion pressure can be made as Ph, =Cc hlr,. However, the thickness of the

cylinders cannot really be ignored, and so this equation is modified according to ~arne',

where Pm = implosion pressure.

The prediaions fiom equations (5-3) are presented in table 5.1, accompanied by an

estimate of the radial displacements due to the expenmental implosion pressure using

equation (5-2).


Table 5-1 Implosion Pressure and Displacements of Elastic Infinitely Long Cyiinder

Because the specimens used for this study were not of infinite length, but had simply

supported ends, we might expect this to change the prediaed implosion pressure.

However, the resulting change is less than 0.2% and can be ignored.

Since most of the specimens failed near the ends, there was 2 concern that cracks

may have developed there before implosion due to high tensile stresses nom the

longitudinal bending moments. The expression for the maximum longitudinal bending

moment can be denved fiom the general theory ofcylindrid shellsl' as follows,

where Mx = longitudinal bending moment fi = scaling factor

fi is composed of a series of sines, cosines, and hyperbolic sines and cosines which Vary

dong the length of the cylinder. The maximum values of Mx are presented in table 5.2.

Table 5.2 Maximum Values of Mx

The table also presents the tensile stress at failure. Since the maximum permissible

stress before the onset of cracking is SSMPa, the table suggests that al1 of the specimens

would fail prematurely. In each case, the pressure when cracks begin is 90psi. The RASP

Anaiysis of the Implosion Problem 58 - - -- -

analysis presented in section 5.4, and various observations show that cracks do not

develop, and that the elastic analysis overestimates the tensile stresses.

51.2 E W c Buckling Theory

Now that the linear elastic deformation of the cylinders has been discussed,

consider buckiing theory. Buckhg theory for cyiinders foiiows the same principles as

buckling theory for a column. Therefore, the two theories are developed in parailel below.

Step 1 : Formulate Digerential Equations Step 1 : Fonnulate Differential Equations

for the disturbed equilibrium state- for the disturbed equilibrium state.

M=P(d+e-w) (5-5) M=Mo -pr,(w-w,) (5-6)

Step 2: Use the appropriate elastic law Step 2: Use the appropriate elastic law

to formulate a linear differential equation to formulate a linear differential equation


Step 3: Solve the Différentiai Equation. Step 3 : Solve the DEerential Equation.

let k = JW, then let k = d m , then

Taking the second derivative at FL

should make this expression equal O

(since moment at fne end =O).

Therefore, ws(kL) = 0 , whose lowest

root occurs when kL = ~r / 2. If - ~ J F ï Ë ï = n / î , then

(5- 12)

Taking the first derivative at 8 = R 1 2

should make this expression equal O.

Therefore, sin(kz / 2) = 0, whose

lowest root occurs when k=2. If

1 + p r g 1 ~ = 4 , t h e n

w here p, = critical buckling pressure for thin cylinden a, = critical buckhg stress D = flexural stiffiess of the shell, D = E h3 / 1 2(1- v2 )

By replacing f c with equation (5-16) in Lame's equation, we get the implosion pressure

for long cylinders, for which the UD ratio is very large. For very short cylinders, just as

for stub columns, material failure govems, and equation (5-3) is used by itself.

Furthemore, just as there is a transition curve for columns with a moderate

slendemess ratio, there is also a transition curve for cyliider with a moderate L/D ratio.

The curve is derived fkom D o M ~ ~ ~ ' s equation,

This, too, can be substituted into Lame's equation to find the implosion pressure.

There is also a more gened fonn of Donnell's equation which should be included

here for completeness. Whereas the original derivation for long cylinders only considered

circumfmntial deformation into an huo-lobed ellipse, Domeii's equation considers

Analvsis of the Im~losion Problem 60

circumferentiai defonnation into any number of lobes, as well as longitudinal deformation

into any number of lobes. Therefore the secondsrder differential equation (5-1 1) is

replaced by an eight order dserential eq~ation'~. The solution is as foliows,

mL p z - '%

where m = mode shape number in the hoop direction; may be a decimal value n = mode shape number in the longituduial direction

This equation has a limitation. It does not apply to the case when m=2, which

corresponds to an elliptical shape like that used in the derivation of the elastic buckling

capacity above. In other words, (5-18) gives incorrect results for long cylinders.

Equation (5- 17) is a simplification of (5-1 8) for the case when Z> 100.

Equations (5-15), (5-16), (5-17), (5-18) are plotted in figure 5. i for the geometry

and matenal characteristics of the five specimens used in this report. Because Z varies

fiom 68 to 400, (5-17) can be used instead of the more complicated (5-18) for the

transition curve. Figure 5.1 is completely analogous to columns c w e s .

What is important to realize about these curves is what is rnissing nom them. First

of ail, they do not account for the unique non-linear behaviour of concrete. Secondly,

they do not account for initial out-of-roundness. Thirdly, they only represent an end

condition which is simply supported. Finally, the curves do not account for refircement.

Notice dso that in each case, the implosion specimens have UDo ratios which do not

appear on the graph. Thedore, based on elastic buckling theory, the specimens ali fail

due to a material failun based on Lame's equation. However, it was obsetved that the

specimens failed by bucWing Elastic buckling theory predicts very high implosion

pressures. The next section uses a plasticity reduction factor to reduce the implosion

pressures.

Analvsis of the Implosion Problem 61

Figure 5.1 Implosion Pressure Calculated From Buckling Theory for each Specimen

where DO = outer diameter

5.2 Plasticity Reduction Factor

There are two methods used to incorporate a plasticity reduction factor uito the

buckling analysis. The fist method uses the mathematical theory of inelastic stability to

generate an equation for calculating the plasticity reduction factorlg. The second method

is a curve fit used by Haynes and ~ o r d b ~ ' .

5.2.1 IneIastic Stabiliry Theory

Based on inelastic stability theory, the following equation cm be derived for a

cylinder of moderate length,

where Et = tangent stifniess

Analvsis of the Implosion Problem 62

Es = secant stifltiiess v, = elastic Poisson's ratio v, = plastic Poisson's ratio; assumed equal to v.

Tu demonstrate how to apply this equation, a solution will be caiculated for specimen

LD250F1. First, in order to calculate Et or E, the stress-strain curve must be known.

From a mathematical curve fit to the data resulting fiom a standard cylinder test, the

following equations were derived in terms of strain,

o = -0.252~' t 0.439e3 - 4.81 9e2 + 27-1 59s (5-24)

Using equations (5-24) to (5-27), q can be deterrnined as follows:

1. A value for E is guessed.

2. al, Et, and E, are calculated fiom equations (5-24) to (5-27).

3. Using 6 and E, q can be calculated fiom equation (5-22).

4. a- is calculateci with no plasticity reduction factor fiom (5-17) or (5-18). Then =

W C r -

5. Guess a new value for E, and repeat steps 2 to 4 until al = az. When these values

converge, then q is correct, and 0 2 is the critical buckling stress.

Figure 5.2 Graphical solution of q using Inelastic Stability Theory


This method is shown graphically in figure 5.2. From the graph, q4.3 77, aa=33.6h4Pa,

and Pb = 2.029MPa = 294psi. The expenmental implosion pressure for this specimen was

209psi. Therefore, this method for calculating the critical implosion pressure can seriwsly

overest imat e failure pressures.

5.2.2 H m e s And Nordby

The second method of detennining the plasticity redudion fiidor is to use a m e

fit as suggested by Haynes and ~ordby' . They derived a curve for q based on

expenmental data f?om plain concrete cylinders. The curves from Haynes and Nordby are

dependent on the ratio of WC, which they define as Yeo. For the implosion specimens,

this value ranged fkom 727 to 1ûûO with an average of 866. Because the upper limit on

this ratio defined by Haynes and Nordby was 667, then a airve had t o be extrapolateci to a

ratio of 866. This curve is labelled ai in figure 5.3.

Figure 5.3 Graphical solution of q using the Haynes and Nordby Curve Fit

Using Haynes and Nordby's cutve fit, q can be detennined as follows:

1. A value for ql is guessed.

2. O- is calculated with no plasticity reduction factor fkom (5-17) or (5-18). Then a* =

q lacr.


3. Based on the ratio of 02/f C, figure 5.3 can be used to fïnd a new q2. Altematively,

equation (5-27), which was derived fiom figure 5.3, can be used to calculate 12.

m = 9 . 2 l 5 3 ( o ~ f c)' - 29.348(m~f c ) ~ + 3 5 . 0 3 5 ( a ~ f cl2 - I9.MS(an/f c) + 4.2232

(5-27)

4. Repeat steps 2 to 3 until the critical buckling stress converges.

This rnethod is shown graphically in figure 5.3 for specirnen LD2SOF 1. From the graph,

q=0-248, so mQ=22.1MPa, and Ph = 1.381MPa = 2OOpsi- This is very close to the

experimental implosion pressure of 209psi.

There is a problem with the paper by Haynes and Nordby. They indicated that

reinforcement should only be considered when the wall stresses are less than O.Sf c. This

was not true for the implosion specimens investigated in this report. Furthemore, their

paper indicated that embedded steel reinforcement can actually reduce the implosion

strength of cylinders when the steel percentage is less than 2%. As was indicated in

chapter 4 of this report, the effective steel percentages in t h e implosion specimens were

0.64% and 1.79% for the specimens with 1% fibres and 6% fibres tespectiveiy.

Therefore, the paper by Haynes and Nordby would suggest that the fieel fibres should

have had no effect on the implosion strength of these specimens. Table 5.3 compares the

implosion pressures caiculated using Haynes and Nordby's method with experimental

results. One calculation is done accounting for steel, and one is done neglecting the efftct

of steel. The calculation which accounts for steel p e d t s an hcrease in w d thickness

fiom transfonned sections (using a steel stiffiess of 200000MPa) as recommended by

Haynes and Nordby if the wall stress is less than 0.5f c (which is not true in ttùs instance).

Table 5.3 Cornparison of Haynes and Nordby's Prediction to Experimental Results

Specimen exp.) steel) steel) steel) %Errer steel) %Emr LD250F6 193.7 0.238 16 168 -1 3.3 125 -35.5


Table 5.3 demonstrates the importance that s t d h u on the implosion strengh.

Both specimens with a length-to-diameter ratio of 1.75 had approxhately the sarne

concrete arength, yet the cylinder with 6% fibres had an experimental implosion strength

28% higher than the cylinder with 1% fibres. Aiso, the caidations which incorporate

steel were a significant improvement over those which did not incorporate steel.

Haynes and Nordby's assertion that steel reinforcement has little effect on

implosion strength was b a d on a series of six test$. Two of the tests involved 69mm

thick concrete spheres without any reinforcement, and the remaining four tests involved

concrete spheres with a neel reinforcing cage placed 1Omm fkom the inside of the sphere.

The spheres were mmposed of two concrete halves, bonded together by epoqr.

The failure of the reinforced spheres occurred in iwo phases. First, in-plane

cracking occurred parailel with the reinforcing cage, because there was v e y small spacing

between the reinforcement, and consequently poor bond between the steel and the

concrete. Using fibres, this is not a problem, because even if the surfiace layer of concrete

delaminates as did occur with the slabs disaissed in chapter 4, there are stüi fibres

embedded within the concrete away €rom the sunace layer, which can continue to resist

load.

In the second phase, there was a compression induced shear failure of the wall at

the epoxy joint. The steel was not designed to resist shear, and so it naturally did not

improve the implosion strength. Furihemore, the failure occurred at the epoxy joint,

which makes the strength of the epoxy suspicious. The cyliiden tested for this report

failed by implosion due to bending, and so the fibres do play an integral role in resisting

this failure.

Haynes and Nordby's design method did supply excellent predictions of implosion

strength when steel was incorporated into their mode1 using transformeci sections.

However, their restrictions which say that steel should not be considered when the wall

stresses are greater than 0.5f c, or when sted Y less than 2% of the concrete area, do not

appear to be vaiid.


Olsen's Method

Olsen's Method has t h e strong advantages over the methods using a plasiicity

reduction fictor. First, and most importantly, Olsen's method incorporates out-of-

roundness into the formulation. According to Haynes and Nordby, if ZX00 (modenite

cylinder size), then out-of-roundness does not need to be considered. Second, Olsen's

method uses a sectional analysis procedure which duectly includes reinforcement

distributeci in any manner through the section Thirdly, Olsen's method gives a simple

procedure based on sheii theory for dealing with end conditions different fiom simple

supports. Haynes and Nordby use an empirical factor.

5.3.1 Description of the 19 78 Method

Olsen's method is primarily a design method. The original method described in

Olav Olsen's paper in 1978~ was defined by equations (5-28) and (5-29)

Mi <Ma (5-28)

M. = pr,P(wo + w) (5 -29)

where w = radial displacement wo = initiai radial eccentricity p = pressure fo = outside radius M. = extemal moment produced by the hydrostatic pressure, p Mi = intemal moment resistance of the cylinder B = factor accounting for the effects of the end caps

Olsen's method is based on the idea that implosion wi1l occur before a shaft can

reach stress levels calwlated on the basis of first-order theory. In other words, assuming

that the shaft defonns in a cylindrical shape d l produce an u n d e design. In reality, the

shaft is not perfectly round initially, and sa therc are not only first-order hoop stresses, but

also hoop moments fiom the start. As the pressure increases, the out-of-roundness

increases, which in tum increases the hoop moments in the shaft. These second-order

hoop moments increase the compressive stresses beyond the first-order hoop stresses

which precipitates an early failure. Specüically, failure occurs when the extemal hoop

Analvsis of the Implosion Probtem 67

moments d e h e d by equation (5-29) exceed the interna1 moment capacity of the SM

dehed by a sectional andysis.

Notice the similarity between equation (5-29) and (5-6). The big dinerence

between the two equations is that Olsen's equation contains a term WQ to deal with out-of-

roundness. In order to apply Olsen's method, we must first define some of the terms.

To £ind w, a principle sirnilar to that used for bearns is useci. Just as for a beam

under a uniform load, the displacement is related to the curvature by w = K L ~ 18 ; for a

cylinder under a hydrostatic presstire, w = w12 1 x 2 , where L = 2mm Im, and m is the

number of lobes. In other words, maximum displacement in the cylinder is related to

maximum curvature by equation (5-30).

where K = change in cuwature

The locations where both w and K are caiculated are shown in figure 5.4 for various mode

shapes.

Tu find wo, Olsen give two approximations in equation (5-3 1).

Mi is calculated using sectional analysis procedures, and can either be done by hand, or by

computer for more accurate results.

p is intended to account for a reduction in the hoop stress pfa because of shell

action. In other words, equation (5-29) assumes that the pressure is wholly resisted by

stresses in the hoop direction. This is only true of an infinitely long cylinder. However,

for a cylinder of finite length, the pressure is resisted by a combination of hoop stresses

and stresses dong the length o f the shell produced by end restraint, and Dnal loads.

Therefore, the hoop stresses are less. One way to aceount for the reduction of hoop

stresses is to realize that the radial displacements also will be reduced by shell action. In

other words, the radial displacement predicted on the basis of an infinitely long cylinder,

using equation (5-30), is reduced by the following ratio,


where w- = maximum radial displacemefit ûf the actual cyhder w , = maximum radial displacement of an infinite cyiinder

Figure 5.4 Location of maximum w and 4 for various mode shapes

Equation (5-32) is the equation used by Olsen in his 1978 paper. To evaluate this

ratio, the generai theory of sheUs is implemented"! The coordinate system is shown figure

5.5. The theory is based on the following assumptions with respect to loading and

displacement patterns,

nltx p, = p, cosmt) sin- L

(5-3 4)

Anaiysis of the Implosion Problem 69

W can be evaluated in terms of p, using three simultaneous equations. These equations

apply to a sirnply supported cylinder only.

(5 -40) where

p,, Pr are pressures in the longitudianl, circuderential, and radial directions respectively.

u, V, w are the displacements in longitudinal, circuderential, and radial directions respectively .

U, V, W, p, are unknowns

Figure 5.5 Coordinate system used in the analysis of the cylinder


W can be evaluated in t a m s of p, for the actuai length, and for an innnite length (Ml).

The ratio of these two numbers is equal to B. To solve for the implosion strength using Olsen's methoci, we use the following

procedure:

1. We assume values for p, and m. For long cylinders m is near 2, and for moderate

cylinder lengths, m is near 3.

2. The axial load applied to the section is pro per unit width. Using this axial load, a

sectional analysis is performed for the section The geomew, ranforcement, and matenal

properties for the section must agnx with those of the cylinder.

3. Fmd the Mi+ a i m e from the sectional analysis.

4. Using various values of curvature, w can be calculated fiom equation (5-30) for a

&en m. We know p and wo already, so M. can be calculated fiom equation (5-29).

5. Plot both M. and Mi as a fùnction of curvature. When M. everywhere exceeds Mi, then

the assumed value of p is too high. Iterate seps 2 to 4 using smaller values of p u n d M.

is everywhere on the verge of exceeding Mi.

6. This process is repeated far different m values, until the minimum implosion capacity,

Pi,, is found.

O 50 100 150 200 250

Cutvlure (irdlkm)

Figure 5.6 Graphical Representation of Olsen's Method


The above p r d u r e is illustrateci in figure 5.6 for specimen LD250F1. The highest

possible value of axial load was 0.440 kN/m width. This corresponds to a pressure of

209psi. A value of rn qua1 to 2.6 was most critical.

5.3.2 Revisions to OIsen 's Method

There have been various revisions to Olsen's method since it was first published in

1978. The fkst change involves equation (5-30). Equation (5-30) assumes that water

pressure is a consenrative load, which it is not. Water pressure always remains

perpendicular to the surface of the cylinder, and is therefore a Yoiiower ioad," or a non-

consecvative load. i fwe use a more ngorous equation, (4-2), then we find that

The other two changes involve the B factor. Equation (5-29) has been revised to

the following:

M. = Pra(,(P,w, + B,w) (542)

Equation (5-32) is meant to account for any differences bebveen the actual cylinder, and

an infinitely long circular shaft with uniform hydrostatic pressure dong its length. In most

practical situations, there are loads which vary with water depth, and axial loads and end

conditions which may not be simple supports. AU of these conditions require

modincations to equations (5-38) to (540), and there may not even be an elastic solution

available. Aiso, equation (5-34) for the radial load requires that the load Vary as a =sine

around the cucuderence. This is never tme of a hydrostatic pressure. Therefore,

designers arrived at a method which accounts for most practical situations to which actual

cytinders are subjected. in this method, 8, is defined as the following,

Equation (5-44) is identical to equation (5-14) for the buckling of long cylinders except

that it has been generaiized to account for mode shapes other than m=2. p, is found by


performing a finite ekment buckling analysis. In other words, a finite element model is

created incorporating the appropnate materiai properties, geometry, and arbitrary loading,

and then a buckling malysis is perfonned. p, is then the product of the load and the

eigenvalue fiom the buckling analysis.

To understimd where equation (543) cornes fiom, we notice that it is analogous

to equation (532). Neglecting eccentricity WC+, then M. = p,r,w,, and

Me = p,r, w ,, , so w , 1 W, = p, / p , . However, whereas w is calculated on

the basis of a pressure which varies as a wsine wave uound the cylinder, p is calculated

on the basis of a uniform pressure around a cylinder with a displacement pattern which

varies as a cosine. Therefore, the new method should be more accurate.

Notice that the eigenvalue corresponds to nothing more than buckling pressure

fI.om elastic theory. In other words, for our case, we can use either equation (5- 18) or (5-

17) more easily than we could do a finite element analysis. However, equation (5-18) and

(5-17) do not account for the axial load on the cylinder. A model was created in ANSYS

which checked the effect of the axial load on the eigenvaiue buckling strength of the

cylinder. Only specimen LDlOOFl was checked. There was a 5% increase in the

eigenvalue buckling strength of the cylinder due to the axial load. Table 5.4 compares the

ratio of p, l p, calculated using equation (5-44) and (5-18) with the ratio of

w,, I w, calculated using equations (5-33) through (540). Table 5.4 does not account

for the effect of the axial load.

Table 5.4 Cornparison of w ,, I w, with p, I p, Specimen m 1 w&i P ~ P ~ Diff(%)

1 m = 2.6' 1 0.75 0.69 8.5

5 1 m = ~ - 6 ~ 1 0.60 1 0.50 1 6.4 LOptkum m based on O l ~ n ' s method 20&wn m based on Elastic theory


Because the buckling analysis does not directly incorporate wa then a separate f3

factor has to account for it, narnely b, where

where Mc = intemal hoop moment in shaA when subjected to initial out-of-roundness, w=1 sinm4 w = initial radial displacement , 1 NI = first order hoop force, Prrn

To fïnd Br, we perform a static analysis of the same finite element mode1 of the cylinder for

which there is an initial radial displacement w=I sinrn4. (The initial radial displacement

can be simulated by appIyïng a first load stage for which a circumferential pressure varies

as a sine wave). After giving the cylinder an initial displacement, pressure is applied. Mi is

the intemal hoop moment in the cylinder when subjected to an initial displacement of

Isinm$, and a subsequent extemal pressure. In other words, we are finding Mi

n o m a f i with respect to initial displacement W, and hoop force NI, and then multiplying

the normalized Mi by the actual hoop stress N, and the actual initial displacement. For the

cylinders studied here, this is very similar to the method used to calculate B fiom the 1978

paper. The substantial difference is that now, while the displacement pattern varies as a

sine wave, the pressure is uniform. Recall that to calculate P origindy, the pressure also

varied as a sine wave.

5.3.3 Anaiysis Using Oken 's Method

Table 5.5 presents the results of various analyses using Olsen's Method. First the

original method taken directly from the 1978 paper is used. Next, the changes noted

above are taken into account in the Revised Method. Both equations (541) and (5-42)

were incorporated into the analysis, except that P, = P, for simplicity. B( was taken fiom

tabte 5.4. Because the initial out-of-roundness was measured for specimens LD175F6 and

LD100F1, then the actual value of wo could be incorporated into the analysis to compare

with the results using Olsen's assumption that w, = 0.015r l m . For LD175F6, the

actual value of wo was 1.27mm and Olsen's assumption yields a wo of 1.48mrn. For

LD 100F 1, the actual value of wo was 0.65mm and OIsen would assume a wo of 1.1 Imm.

Analysis of the Implosion Probtem 74

Finally, the revised version of Olsen's method generally uses an optimum value of m based

on the eigenvalue anaiysis, which is an elastic analysis. Up until now, the value of m used

was based on the optimum value of m using OIsen's method. Therefore, the last results

presented in table 5.5 use a value of m based on the elastic anaiysis to determine whether

the results significantly degrade. For this final analysis, values of Pr were again taken fkom

table 5.4.

Table 5.5 Resuits of Various Analyses Using Olsen's Method

Note: Pressures are in psi '0ptimum rn based on Olsen's Method 'optimum m based on Elastic Theory

Various conclusion can be drawn Born table 5.5. First, the revised method in al1

cases causes only a small change in the predicted implosion pressure. Second, by

inwrporating the actual value of the initial out-of-roundness, the results are improved.

Third, the difference between using the optimum value of rn fiom the elastic analysis as

opposed to the optimum value of m using Olsen's method is marginal.

5.4 RASP ANALYSIS

RASP is a non-linear finite element shell anaiysis program developed at the

University of Toronto specifically for c ~ n c r e t e ~ " ~ '. RASP uses nine-noded degenerated

quadratic isopararnetric layered she il elements. Its formulation is based on the modified

compression field theorp . Each of the specimens was modelled using RASP. The

purpose of these analyses was two-fold. First of al], the finite element models provided

yet one more method of analyzing the implosion problern. Second, there was a concern


that implosion might be preceded by cracking at the ends of the specimen, and so RASP

was used to investigate this.

5.4.1 RA SP m i y s i s of ImpIosion

Recall the derivation of the buckling formulae for a column based on elastic

principles in section 5.1. A colurnn was given an initial eccentricity, e, which under a load

P caused the colurnn to deform until the capacity of the column was reached. The

derivation was perfomed closed €0- but ifwe used a finite element package to model

the column, and the column was given an initial eccentricity, and the program couid

account for second-order effects, then the program would yield the same result as the

closed fonn solution. Also, whereas the closed fonn sohtion does not account for the

plastic, non-hear behaviour of a reinforced concrete colurnn, the appropriate finite

element package can do so.

The sarne p ~ c i p l e s as discussed for wlurnns can be applied to reinforcd concrete

cylinders. The concrete cylinder can be modelled by the finite element program RASP

with an initial out-of-roundess of the form w, sinm4. Pressure wi then be appiied to

the cylinder until the capacity of the cylinder is reached, and this will correspond to its

implosion capacity. Actually, this is very similar to Olsen's method- However, the finite

element method should be an improvement over Olsen's method because it d i redy

accounts for shell action, rather than using the P factor.

The most extensive investigation was performed on specirnen LD2SOF1 because

this specimen gave poor results using RASP. Rather than describe the meshes used in all

the models, only the meshes used for LD250F1 will be described in detail. Three meshes

were used to investigate the behaviour of specimen LD250FI. These meshes are labeiied

triai 1, triai 2, and trial 3 in figure 5.7.

Trial 1 assumed that the undeformed shape varied as l.27 sin254. Based on

Olsen's method, m-2.6, but using m=2.5 was easier to model. HaV of the length of the

cylinder was used for this model. The axial load was approximated by a series of

concentrated loads acting on elements 1 through 10. The magnitude of the axial load was

p(ic305' 12x296). The hydrostatic pressure was approximated as a distributed loading

IJNDEFORME D SHAPE

Tr ia l 1 ~ 2 . 5 mesh B

Mesh I/2 scale

465 -4

MESH A

Tr ia l 3

mes

MESH B

Meshes Used to Model Saecimen LD250F1 in RASP


over elements 1 through 40. Figure 5.7 shows that the u n d e f o d shape was modifieci.

This was done to reduce the unredistic stress concentrations at the indicated position.

Trial 2 assumed that the undeformed shape varied as 1.27sin20g. Because trial

1 predicted higher implosion pressures than experirnentally determined, we reduced m

fiom 2.5 to 2.0 in trial 2 to investigote the dierence. Trial 2 also used halfof the cylinder

and the sarne loading as used in trial 1.

Because trial 2 still predicted high implosion pressures, trial 3 used elements which

were one quarter the size of those used in trials 1 and 2- Large elements can potentially

make the mesh too s t q and increase the predicted failure loads. To accommodate the

smaller elements, only 118 of the cylinder was modelled for trial 3 as shown labelled mesh

A in figure 5.7. Trial 3 assumed that the undeformed shape varied as 1.27 sin2.04, like

trial 2. The same loads as used in trial 1 were used in trial 3.

In al1 cases, the models failed by bending in the cùcumferential diiection at the

middle of the specirnen where the circumferential stresses were greatest. When rn=2.5,

failure occurrd as the concrete crushed on the outside surf' of the cylimder at point A

shown in figure 5.7, whereas when m=2.0, failure occurred at point B in the figure.

Figure 5.8 shows the effect of the type of mesh on the response of the RASP

model. First consider trials 2 and 3 for which m=2.0. The mesh which representsl/8 of

the cylinder (mesh A) has a soAer response than the mesh which represents 112 of the

cylinder (mesh B). This was expected. However, the overall change in implosion pressure

was not large. Therefore, the accuracy of the coarser mesh is verified. Next, consider

trials 1 and 2 for which the value of rn changes. We would expect that the minimum

implosion pressure should occur at the optimum value for m. Olsen's method suggests

that the optimum m value is 2.6, and elastic theory suggests that the optimum m value is

2.4. Therefore, the model which uses m equal to 2.5 should yield a lower implosion

pressure. As expected, it does. A fourth trial was also used, which used a higher value of

the concrete peak strain, G,. Because the tests took more than two hours, it was suspected

that the specimens might creep. To model this, the value of E, was increased fiom

2.3Smm/m to 4.0mm/m. The value of 4 .0mdm is an approximation for cornparison

Analysis of the Implosion ProbIem 78

purposes. The change in E. substantiaily reduced the stifiess of the specimens, but the

capacity was approximately the same.

Maximum Uspiacement (mm)

Note: EO is the strain at the maximum compressive stress in d m .

Figure 5-8 Cornparison of meshes used to mode1 specimen LD250F1

The experimentally determineci failure pressure was 209psi at a maximum

displacement of 1.5mm. It can be seen that all of the predictions for implosion pressure in

figure 5.8 are unconservative by large margins. Furthemore, RASP permits

displacements larger than 1 . 5 m before failure. Olsen's method suggests that the

maximum displacement at failure should be 1 -35mm. Notice in figure 5.8 that if a

displacement of either 1.35rnm or 1 .Smm is assumed to cause failure, then the predicted

implosion pressures are irnproved. Furthemore, the next chapter shows that most of the

RASP predictions were too stiE This could be improved by two of the methods

described above. The mesh could be made finer, or the value of could be increased to

account for creep.

Table 5.6 compares the results of the ICASP analyses with experimental results.

LDlOOFl used a mesh sirnilar to Mesh A in figure 5.7, whereas the other specirnens used

a mesh similar to Mesh B due to more difficult geometry. Al1 of the models used

Analvsis of the Imolosion Problem 79 --

reinforcement and conmete properties identical to those disaisseci previously for Olsen's

method. For both specimens LDlOOFl and LD175F6, the value of wo was mwured prior

to testing, but for the remaining specimens, the value of wo was estimateci. Figure 5.9

compares the responses of each of the analyzed specimens.

D 0.2 0.4 0.6 0.8 1 1-2 1.4 1.6 1.8 2

Maximum Us placement (mm)

Figure 5-9 Surnmary of RASP analyses

Table 5.6 Cornparison of RASP Implosion Strength with Experimental Results

5.4.2 Cracking af the E d of the Spcimem

The elastic analysis predicted high tensile stresses in the longitudinal direction

60mm fiom the ends of each of the specimens, as shown in table 5.2. The RASP analyses

aüowed us to check the magnitude of these stresses, and to determine whether they could

cause cracking prior the implosion.


Figure 5.10 shows the maximum tensile stresses undergone by each of the

specimens. The tensile stresses were always within lOOmm of the end of the specimens.

Even in the worst case, the tensile stress never exceeded IMPa. The cracking stress is

SSMPa, so there was never any threat of cracking according to the RASP analysis.

Furthemore, no cracking was ever observed during testing. Had there been

cracking, there would have been substantial water Ieakage into the specimen which was

not observed. Also, when specimen LD 100F1 was removed ftom the vesse1 after the

aborted test, ody one crack was observed. This crack was oriented parailel to the le+

of the specimen, and was not caused by the tensile stresses investigated here.

Figure 5.10 Maximum tensile stresses predicted by RASP

Finally, the tensile strains measured in the longitudinal direction 35rnm nom the

end of the specimen never becarne large enough to cause cracking. This evidence will be

presented in the next chapter. Based on d l of this evidence, cracking did not occur at the

ends of the specimen before implosion too place.

Cornparison of Analysis with

Experimental Results

This section of the report compares the experimental results with the pressures,

displacements, strains, and failure modes predicted by the various analyses.

6.1 Pressure

The most important result is the implosion pressure fiom each test. The

experimental implosion pressures are presented in Table 6.1 dong with the best estimates

of the implosion pressure fiom the analysis methods presented in Chapter 5. None of the

methods are in ali cases conservative. Remarkably, the Haynes and Nordby curve fit gives

the best results. However, because Olsen's method is more grounded in sound

engineering p ~ c i p l e s , Olsen's method is the recommended method to calculate the

implosion pressure.

Cornparison of Analysis with Experimental Results 82

Table 6.1 Implosion Pressures

pressure 2 Assuming steel can be treated by using the transformai section o one using the revised method and w, = 0.01 5r l m

Various observations can be drawn from the comparisons made in Tabie 6.1. First

of aU, the calculations for the specimens with 6% fibres are always low relative to the

other predictions. This suggests that reducing the reinforcement ratio fiam 6% fibres to

oniy 1.8% continuous reinforcement in the hoop direction may have been inaccurate.

R e d that the reduction was based on the fiexural response of specimens LDlOOFl and

LDlOOF6 after the specimens had ctacked under a iine load. Clearly, this does not

represent the implosion situation where the specimens do not crack. We justified the

reduction by saying that bulking causes many of the fibres t o be i n e f f d v e in resisting

tension. However, the fibres are ail in compression dunng implosion, and bukng may not

cause as large a reduction when in compression as in tension. We still have confidence in

the reduction of the reinforcement ratio Erom 1% to 0.64% for specimens with 1% fibres

because this was justified by the unfavourable orientation of fibres, which definitely

occun. However, the reduction for the two specimens with 6% fibres may have been too

severe.

Secondly, the predictions for specimen LD lOOFl are also low relative to the other

predictions. As will be s h o w in section 6.2.6, while the optimum f ~ l u r e mode shape for

this specimen corresponds to m = 4.0, the displacement pattern observed durhg testing

more closely fits a shape corresponding to m = 3.0. The minimum failure pressure always

corresponds to the optimum mode shape, and any other mode shape will produce a higher


implosion capacity. This could explain why specimen LDlOOFl implodes at a higher

pressure than predicted.

Thirdly, al1 of the predictions should have been reduced to account for creep. This

was an oversight on the part of the author. Ail of the analyses used a value of based on

standard cylinder tests which last a few minutes. Because the implosion tests lasted

between one and a half to three hours, then a larger value of €0 should have been used.

Because a larger value of reduces stiffiiess, the displacements would increase, and the

extemal hoop moment would increase, which would m e r increase the hoop stresses,

and precipitate an earlier failure.

Finally, the second objective stated in the introduction to this study can be

answered looking at the experimental results by themselves. The second objective asked

whether there was a correlation between the implosion strength and either f, or length-to-

diameter ratio. Fust consider f ,, and specimens LD250F1 and LD250F6. They both have

the same proportions, except that LD250F6 has a wncrete strength of 25.OMPa, and

LD250F1 has a concrete strength of 35.4MPa. Also, LD250F6 has 6% fibres and

LDZSOFI has LYO fibres. Notwithstanding the lower amount of reuiforcement, specimen

LD250F1 has an 8% higher implosion capacity. Therefore, higher concrete strength

clearly increases implosion capacity.

Next, we try to ve* the importance of length-to-diameter ratio on implosion

capacity. Consider specimens LD 1 OOFl and LD250F 1. The specimens both have

approximately the same concrete strength and the same amount of fibres, but specimen

LD250F 1 has 2.5 times the length-to-diameter ratio of specimen LD 100F 1. Specirnen

LDlOOFl has a 35% higher implosion capacity. Similarly, specimen LD250F6 has f -43

t h e s the length-to-diarneter ratio of specimen LD l7SF6, but approximately the same

concrete strength and the same amount of fibres. Specimen LD l X F 6 hm a 12% higher

implosion capacity. Clearly then, implosion capacity is higher for lower values of length-

to-diameter ratio- In other words, this study verifies previous research which suggests

that implosion capacity is strongly iduenced by both concrete strength and length-to-

diarneter ratio.

Cornparison of Analysis with Experirnentai Results 84

6.2 Displacement and Strain

6.2. l General

The second most important renilt obtained fiom this study is the displacement

pattern undergone by the cylinden during testing. It is impossible to know this

displacement pattern acairately given the displacement measurements taken during

testing. The best tests recorded displacements only at the rnidspan of the specimen, and

only at four positions around the &cumfaencc. Four displacements cannot adequately

d e h e an eiiiptical shape, or a thne-lobed shape, or most other shapes. However, four

displacements can suggest what the cylinder is not. For exarnple, to deform as a circle, we

would expect that the four displacements should be the sarne. To deform as an ellipse,

displacements on opposite sides of the cylinder should be the same. To deform as a four-

lobed shape, again al1 displacements m u a be equal. If any of these patterns do not appear

fiom the data, then we can assume that the guessed shape was wrong. Udortunately, this

is not entirely true because the initial shape of the cylinder is unknown in most cases.

Therefore, ifthe initial shape of the cylinder is approximately three-lobed, and the cylinder

deforms into an ellipse, then displacements measured on opposite sides of the cyhder will

definitely not be the same. With these limitations in mind, an attempt has been made to

correlate the results fiom the RASP analysis with the experimentally measured

displacements.

For each specimen, a chart showing the experimentai pressur~displacement

history is prescnted dong with a similar history fiom RASP. In al1 cases, inward radial

displacement is positive, and outward radial displacement is negative. Also, the

circumferential strains fiom the tests are plotted against pressure for some of the

specimens, but are not compared to the RASP results. The RASP anaiysis assumed an

initial undeformed shape for the cylinder of the fonn w, sinm4. This shape is shown

accompanying each pressure-displacement chart to indicate the position of the

displacement transducers in relation to the assumed shape. Not only is the shape assumed,

but the position of the displacement transducea is selected in order to get the best fit.


For al1 b seeming arbitrariness, the investigation into displacements is still usenil.

Whiie we cannot know the displaced shape for certain, we can determine whether in f a a

the assumed shape is possible, which in turn adds to the validity of the analysis. Secondly,

by comparing the shape of the pressure-displacement curve, and the magnitude of the

displacements produced by RASP, some insight can be gained into how the RASP analysis

can be improved.

Longitudinal strains were also recorded during testing. These strains are plotted

against pressure, and shown in Appendix B. dong with those plots of cirCULIlferentia1

strain not referenced in the main text. The longitudinal strains principally define whether

the cyiinder is anywhere subjected to sufficient longitudinal moment to cause cracking

before implosion occurs. The results in Appendix B clearly show that this never happens.

6.2.2 Displacements for Specimen LD25ûF6

The displacements for the lefl side of specimen LD250F6 are shown in figure 6.1,

and the displacements for the right side are s h o w in figure 6.2. Three observations can

be drawn fiom the experirnental data itself First, the displacement is plainly nonlinear.

Second, the LVDTs on the right side of the specimen show a change in direction. In other

words, the displacement is initially inwards, and then the walls begin to move outwards at

a pressure of about 150psi. The outward movement progresses until failure. Thirdly, if

we look at the displacement pattern dong the length of the specimen in figure 6.3, we

notice that the displacement is consistent with a simply supporteci cylinder. It is difficult

to reconcile such a pattern with a fixeci end cylinder.

A number of conclusions can also be drawn fiom the correlation with the RASP

anaiysis. We have already shown that the implosion pressure predicted by RASP is larger

than the measured implosion pressure. However, the general shape of the pressure-

displacement curves predicted by RASP are very consistent with the experimental data.

Furthemore, RASP does predict that the displacements on the right side of the specimen

wiil change direction, except that RASP predicts the change at a later pressure than

actually recorded. Even the magnitude of the predicted displacements correlates weii with

test data.

Corn parison of Analysis with Experirnentd Results 86


Because there are only two displacement measurements around the circumference

of the specimen, it is impossible to prove that the predicted displaced shape of the cyiinder

is correct. However, the change in the direction of displacement before failure indicates

an implosion failure, which vaIidates Our results.

Figure 6.3 Displacement Pattern at Failure

The validity of the assumed shape is firther enhanceci when strain is considered.

Figure 6.4 shows the circumferential strains recorded on those gauges which s u ~ v e d the

testing procedure. The assumed undeformed shape suggests that circumferential gauge

line 1 should have higher curvature, and so be subjected to higher compression than gauge

lie 2. This is supported by the fact that the strain fiom MC14 is greater than the strain

fiom MC2-7.

6.2.3 Diqplacements for Specimen D O F I

As discussed in the previous chapter, the RASP prediction of implosion capacity

for specimen LD250F1 was worse than for any of the other specimens. Simiîarly, the

agreement between the experimental pressure-displacement curves and the analysis was

worse than for any of the other specimens. The reader should be rerninded f?om chapter 2

that the dispiacement measurements relied upon the tip of the dispiacement transducers

bearing against the wall of the specimen under a small amount of pretension, whereas for

the remaining three tests, the tip of the displacement transducers was epoxied to the walls

Cornparison of Analysis with Experirnental Results 89

of the specimens. Therefore, the measurernents for LD2SOFl are more Wcely to be in

error.

- -- - - - - -

Figure 6.4 Circumferential Strain for specimen LD250F6

Nevertheless, information can still be gained fiom these measurements. Figure 6.5

shows a cornparison between the RASP andysis and the experimentai results. First, it

should be said that both transducers C and D indicate that the walls of the specimen are

moving outwards fiom the begiming of the test. This again is consistent with an

implosion failure. This result is definitely not consistent with a straight compression

material failure where the whole ring would move inwards. Sirnilarly, RASP does predict

that part of the wall move outwards nom the beginning, but not at the locations of

transducer C or D. RASP predicts that the wall at transducers C and D begins to move

inwards, and then changes direction. However, the overall displacement pattern predicted

by RASP is consistent, in that transducer B displaces more than transducer A, and

transducer C displaces Iess thon transducer D. The pnmacy difference between the RASP

analysis and the experimental results is that RASP predicts much stiner behaviour than

actudy obsewed. The previous chapter suggested than a finer mesh, and increasing the

Cornparison of Anahsis with Ex~erimental Results 90

Comparison of Analysis with Experirnental Results 91

value of î. would decrease the sti£hess, and thm the results should improve. In summary,

while the stifhess is overestimated by RASP, the assumed shape is consistent with the

test, which helps to validate the results.

6.2.4 Diqlacements for Specimen LDl75FI

Figure 6.6 presents a cornparison of the RASP anaiysis to test results for specimen

LD175F1. This test, more even than the previous two tests, indicates that the assumed

displacement pattern is very consistent with w b t actually occumd. Even the magnitude

of the displacements predicted by RASP are reasonable. Still, the RASP predictions suffer

because they are too sta and the predicted implosion pressure is still too high.

6.2.5 Diphcements for Specimen LD175F6

Figure 6.7 presents a cornparisun of the RASP analysis to test results for specimen

LD175F6. Wdortunately, transducer A was destroyed dunng the test, and cannot be

wmpared to RASP. Still, what is imrnediately evident is that the RASP results are not too

s t i e and wincidentdly, this test had the best prediction of the implosion pressure out of

aU the tests. Again, whiie we cannot prove that the assumed shape was the sarne as what

actually occurred, we can Say that the assumed shape is consistent with results.

6.2.6 Displacements for Specimen LDlOOFI

Figure 6.8 presents a cornparison of the RASP analysis to test results for specimen

LD175F6. This test was unique in that the specimen was not failed, and so the descending

part of the curve is shown. This descending curve yields a number of observations. First,

there is a break in the descending curve at roughly 240psi for each displacement

transducer. This suggests that a crack had developed during the test, and then closed up,

increasing the stiffiiess of the specimen. A crack in the specimen proves that failure was

about to occur before the test stoppeci. When the specimen was removed fiom the vessel,

only one crack was obsaved. Figure 6.9 shows the 90mm crack oriented perpendicular to

the circurnferentid direction. The crack did not visibly penetrate the whole thickness of

the cylinder. The crack occurred midway between transducers C and D. It is cornforting

Corn parison of Analysis with Expenmental Results 93

Cornparison of Analysis with Expenmental Results 94

Comparison of Analysis with Experimentd Results 95 p p p p p

to know that this crack was caused by ciraiderenlai moments (those responsible for

implosion), rather than longitudinal moments.

Figure 6.9 Crack Observed in S pecimen LD 1 OOF 1 M e r Testing

Figure 6.8 yields a second observation- Transducers B, C, and D did not return to

a zero displacement. Rather, they ail showed a plastic defonnation of 0.30mm in the

cylinder wall. The consistency of this plastic deformation demonstrates the accuracy of

the displacernent transducers. Figure 6.8 shows that the nodinear range of transducers B

and C lasts roughiy 0.30mm, whereas the noniinear range of transducer D lasts roughly

0.70mm. Because the crack was near transducer D, then it coutd be that closing the crack

had more effect on transducer D.

Unlike the previous four specimens, the assumed displacement pattern does not

correlate with experimental results. The assumed shape was four-lobed, but if the

assumed shape is correct then al1 of the displacements should be the same, which does not

occur. The maximum and minimum displacements predicted by RASP are shown in figure

Cornparison of Analysis with Experimental Results 96 - - - - - --

6.8 in order to determine whether either the magnitude or shape of the pressure-

displacement curves suggested by RASP are accurate. The correlation is reasonably good.

Rather than a four-lobed shape, a three- lobed shape would agree much better with

the experirnental data. There was no mode1 in RASP used to determine the pressure-

displacement curve assuming a three-lobed shape, but figure 6.11 shows how it is at least

possible to reconcile the expenmental displacement pattem with a three-lobed shape. The

undeformed shape used in figure 6.1 1 is based upon mepsurements of the variation in

diameter of the specimen at midspan taken pnor to testing. Notice, to get the variation in

radius, the change in diameter was simply divided in hall: and so the undeformed shape

may not be strictly correct.

Figure 6.10 Displacements of LD 1 OOF 1 Figure 6.1 1 Displacements of

assumùig an initidy cimiiar shape LD lOOF 1 using the actual undeformed shape

(displacements are factored by 50) (displacements are factored by 50)

We can conclude from the above discussion that a four-lobed displacement pattern

is incompatible with the experirnentd displacements. However, a three-lobed

displacement pattern is conceivable, and maybe also an intermediate displacement pattern.

6.3 Failure Mode

6.3.1 Generaf

The failure mode was experïmentally detennined in two ways. Fust, the test was

recorded by a video m e r a from a viewport at the top of the pressure vessel, so that the


implosion itseifcould be watched. Second, pictures were taicen d e r the test to detennim

the magnitude of damage, and possbly where the failure occurred. The location of the

fdure, and the type of m u r e are compareci with that predicted by the analysis. There is

no discussion for specimen LD IOOF1 because that specimen was not tested to final Mure

in the hydrautic test facility.

Experimentaiiy, the implosion was in al1 cases accompanied by a loud noise and

vibrations which wuld be felt in rooms adjacent to the lab. The video carnera recorded

bubbles rising quickly tiom the specimen- The origin of the first bubbles could sometimes

be determined in order to predict where the fim cracking occufted.

The type of failure predicted by RASP is aiways crushing of the outer concrete

surface in the circumferential direction at the midspan of each specimen due to a

combination of axial compression and bending. The bending in tum is caused by

deformation of the specirnen into its optimum mode shape. Essentiaily, this is the process

of implosion. It is of course impossible to physically see whether the specirnen deforrns

into its optimum mode shape because the displacements are so small. However, exploring

the fdure is still a valuable exercise.

6.3.2 Failure Mode for Spcimen D250F6

The f ~ l u r e of specimen LD250F6 occurred at the top of the cylinder as shown in

figure 6.12. This is disconcerthg because all the analyses predict that displacements are at

a maximum at the center of the specimen, and so the circumferentiai stresses should also

be at a maximum at the center of the specimen, and failure should occur at the center.

However, according to figure 6.1, RASP predids that the dif5erence between the

displacement at the midspan, and at 400mm fiom the end is smali. Furthennore, figure 6.1

aiso shows that the displacement recorded at LVDT TOPMLFT, located 400mm fiom the

end is greater than at midspan. Therefore, it is no surprise that the top half of the cyhder

caused failure.

The reason why failure ocnirred at the top of the cylinder may be due a number of

causes. Maybe the top of the Sinder is slightly t h i ~ e r than the bonom of the specimen.

Maybe confinement played a role. The longitudinal stress distribution caused by the axial

Com~arison of Analvsis with Exnerimental Results 98

pressure is approximately unZorn at rnidspan, but due to bending at the ends, it is not

uniforrn near the end. Therefore, if there is any strength enhancement due to biaxial

eEects, these effkcts should be greater a midspan than at the ends, and so failure rnight

occur toward the end.

One other thing shouId be said about the failure of specimen LD250F6. The

specimen remained IargeIy intact because there is 6% fibres in the specirnen. The other

specimens did not remsin intact.

Figure 6.12 Failure of Specimen LD250F6


6.3.3 Faïiure Mode for Specimen LD250FI

The videotape recording the implosion of specimen LD250Fl showed that bubbles

rising fiom the end of the specimen preceded bubbles rising from the midspan of the

specimen. This suggests that failure first occurred at the ends of the specirnen which is

consistent with the failure mode recorded for specimen LD250F1.

The specimen afker failure is shown in figure 6.13. Clearly, having 6% fibres made

a larger difference in maintainhg the stmctural integnty of the specimen.

Figure 6.13 Failure o f Specimen LD250FZ

6-2.4 Fadure Mode for Specimerl LDI 75Ff

The videotape for specimen LD l75Fl was destroyed, and the remaining specimen

shown in figure 6.14 is so badly damaged that it is impossible to discern where failure was

initiateci.

Cornparison of Analysis with Experirnental Results 100

Figure 6-14 Failure of Specimen LD175FI

Figure 6- 15 Failure of Specimen LD l X F 6

Cornparison of Analysis with Experïmental Resuits 101

6-2.5 FaiZwe Mde for Spcimen L D I TSF6

As with specimen LD250F6, havùig 6% fibres meant that this specimen held

together better than the previous two specimens. However, the damage was greater than

for specimen LD250F6, owing perhaps to the higher imptosion pressure. Figure 6.15

shows that failure was again not at midspan.

Conclusions and Future

Work

This section of the repon is divided into two sections. The section responds

to the objectives stated in the introduction to this report, and ais0 reflects on what wuld

have been done to improve results. The second section offers suggestions as to how any

future implosion test programs on reinforcd concrete cyhders should be conducted.

7.1 Conclusions

1. The first objective of this report was to evaluate the feasibility of using steel fibre

reinforced concrete models to study the behaviour of heavily reinforced concrete offshore

structures. To this end, chapter three describeci the tests of ten slabs and of two implosion

specirnens which were tested under a Iine load. An attempt was made to mode1 the

discrete fibre reinforcement as continuous reinforcing bars which wuld be easily

incorporated into analysis methods. The properties of the fibres were determinecl fiom

previous research, and the equivalent area of continuous steel reidorcement was

calculated based on the slab tests and the line load tests,

One Iunitation of this approach to calculating the equivalent steel area is that it was

be based on tests of flexural behaviour. In other words, al1 of these specimens failed d e r 102

Conclusions and Future Work 103 -. - - - - - - -

cracking, when the fibres began to puii out. During implosion, the cylinders do not crack;

they fail by crushing. Modeling the fibres in a situation of flexure involving cracking may

not be applicable to a situation primarily of compression without cracking. The major

effect of this oversight would be in subsequent analyses involving the implosion specimens

containing 6% reinforcement.

In summary, while fibres can be used to accurately model heavily reuiforced

offshore structures, they make analysis dif£icult.

2. The second objective of this report was to verify the importame of length-to-diarneter

ratio and concrete ~trrngth on implosion capacity. Specimens with similar strength and a

sirnilar percentage of fibres but different geometries consistently showed that a smaller

iength-to-diameter ratio increases the implosion capacity. Sirnilarly, specirnens with

similar geometry, but different concrete strength show that increasing the concrete

strength does inaease the implosion capacity.

3. The third objective was to detennine the effect of reinforcement on implosion capacity.

Previous research makes two suggestions. First, for thin cylinders whose wall stresses at

implosion are greater than 0.5f,, it was suggested that it is not appropriate to include the

effects of reinforcement. Second, percentages of reinforcement less than 2% are stated

not to enhance implosion capacity, at least for thicker qlinders. The implosion specimens

studied for this report violated both these conditions. However, these sarne specimens

clearly show that higher levels of fibre reinforcement do improve implosion capacity.

Specimens with the same geometry, and similar concrete strength, but a different

percentage of fibres showed that increasing the percentage of fibres increases the

implosion capacity.

4. The final objective of this study was to analyze the implosion specimens using a variety

of models, and to determine which one was best. Three models described the behaviour

of the implosion specirnens with a reasonable degree of acairacy; the model by Haynes

and Nordby which incorporates an empirically derived plasticity reduction factor into the

Conclusions and Future Work 104

conventional buckling anaiysis; the model of Olsen basad on second-order moments nom

out-of-roundness; and the RASP finite element model. While Haynes and Nordby7s

method yields the best results Olsen's method is more desirable because it directly

incorporates both out-of-roundness and reinforcement,

A Iimitation of ail the analyses, but especiaily the RASP analysis, was that aeep

effects were not included. Because the tests lasted between one and a half to three hours,

creep likely would have affécted stfiess, which would have increased displacements, and

because the second-order moments increase with i n c r d displacement, the implosion

capacity wodd have been reduced. This wuld account for RASP's unconservative

results.

7.2 Future Work

This section presents various changes to the implosion test program describeci

herein which would improve any future study on implosion. The first major suggestion is

to use continuous reinforcing bars. A substantial portion of this report was spent

describing tests used to model the discrete fibre reinforcement as continuous bars, and

there is stiil uncertainty as to whether the model was correct.

The second major suggestion is to use better displacement monitoring. To ver@

the models, it is important that the deformed shape of the specimens is hown. This shape

is best defined using a test program similar to the one conducted by Haynes and ~unge',

and descnbed earlier in chapter 2. In that study, the cylinders were instrumented with a

central shaft with linear potentiorneters on anns at different elevations dong the length of

the cylinder which could be rotated around the entue circumference to obtain

displacement data. This accurately defines the shape of the cylinder, for which the four

displacement transducers used in this report were inadquate.

Finally, there are two considerations of which a researcher must be wary. First of

all, when dealing with continuous reinforcement, lamination oden becornes a problem70.

Second, because of the influence of creep on the results, the rate of loading is a critical

parameter.

References

Haynes, EH and Nordby, B-A, "Concrete Cylinder Structures under Hydrostatic Loading," American Concrete Institute Structural Journal, Vol. 73-7, No. 2, February 1976, pp. 87-96.

Olsen, O., "Implosion Anaiysis of Concrete Cylinders under Hydrostatic Pressure," Journal of the American Concrete hstitute, Vol. 75, No. 3, Match, 1978, pp. 82-85.

Aboussalah, M. and Chen, W.F., "Nonlinear Fite Element Analysis of Concrete Cylindrical Shells Subjected to Hydrostatic Pressure," Proceeding of the 2"' International Conference on Computer Methods in Water Resources. Marrakesh, Morocco, pp. 255-274.

Haynes, H,H, and Chen, W.F. and Chang, T.Y. and Suniki, H., 'Extemal Hydrostatic Pressure Loading of Concrete Cylinder Shells," American Society of Mechanical Engineering, Pap.no. 79-PVP- 1 25, June 1 979, l2pp.

Agnes, R and Jakobsen, B., "Implosion of Reinforced Concrete SheUs," International Association for Shell and Spatial Stmctures International Congress, V. 3, USSR Gosstroy, Moscow, pp 257-271.

Leick, RD. and Bode, J.H., "Implosion Strength of Cylindrical Concrete Shells: A Cornparison of Theoretical and Experimental Results." Journal of Petroleum Technology, Vol. 32, No. 1, January 1980, pp. 27-34.

Fumes, O. "Mode1 Tests of Concrete Capped Cylinders," Otfshore Stnrcfures: The Use of Physical M'miels in nieir Design, Construction Press, New York, 198 1, pp. 113-120.

Runge, KH. and Haynes, H-H., ''Experimental Implosion Study of Concrete Structures," Proceedings of the Eighth Congress of the Federation International de la Preconîrainte, London, May 1978.

Albertsen, N.D., "Behaviour of Steel Bar Reinforced Concrete Spheres Under Hydrostatic Loading," Technical Note No. N-1364, U.S. Naval Civil Engineering Laboratory, Port Heuneme, Dec. 1974,22 pp.

References 106

10. Koltuniuk, Roman, "Investigating the Muence of fIigh Water Pressure on Cracked Surfaces of Offshore Concrete Structures," M.ASc. thesis, Department of Civil Engineering, University of Toronto, 1990, 1 5 5pp.

11. Helmy, AIL, "Behaviour of Reinforced Concrete Cylinders Subjected to Extemal Hydrostatic Loading," M-&Sc. thesis, Department of Civil Engineering, University of Toronto, 1993, l69pp.

12. Helmy, ALI., "Behaviour of Offshore Reinforced Concrete Structures under Hydrostatic Pressure," Ph.D. thesis, Department of Civil Engineering, University of Toronto, 1997,2 17pp-

13. Neville, AM-, Properiies of Concrete, 3" dition, Longman Singapore Publishers, 1994, pp. 561.

14. AC1 Cornmittee 544, "Design Considerations for Steel Fibre Reinforced Concrete," AC1 544 AR-88, Amencan Concrete Institute, Detroit, 1994.

15. Chanvillard, G. and Aitcin, P., "Pull-Out Behaviour of Comgated Steel Fibres: Qualitative and Statistical Analysis," Advn. Cern. Bas. Mat., Elsevier Science Tnc., 1996, pp. 28-4 1.

16. Flugge, W., Stresses in Shells, Spnnger-Verlag, Berlin, 1973, pp. 217-219.

17. Roark, Raymond J., Ruwk 's Fomular for Shesr and S m , McGraw-Hill Book Company, New York, 1965, pp. 172-174.

18. Timoshenko, S.P., Theory of Pl'es and Shells, 1. edition, McGraw-Hill Book Company, New York, 1940,492 pp.

19. Gerard, George, Introduction to Stmcfural Stability Theory, McGraw-Hi11 Book Co., New York, 1962, pp. 129-134.

20. Polak, M.P., 'Woniinear Analysis of Reinforced Concrete SheUs," Ph-D. thesis, Department of Civil Engineering, University of Toronto, 1992, 388pp.

2 1. Seracino, R, "Towards Irnproving Nonlinear Analysis of Reinlorced Concrete Shelis," MASc. thesis, Department of Civü Engineering, University of Toronto, 1995, 177pp.

22. Vecchio, F.J. and Collins, M.P., "The Modified Compression Field Theory for ReUiforced Concrete Elements Subjected to Shear," Journal of the American Concrete Institute, Vol. 83, No. 2, March-Apnl 1986, pp. 2 19-23 1.

Appendix A Manual for the Hydraulic

Test Facility

This section of the report is intended as a manual for future students interested in

using the Hydraulic Test Facility. For someone interested only in understanding the

implosion tests, this section is not necessary reztding. Four aspects of the Hydraulic Test

Facility wiii be investigated: how to adapt specirnens to the features of the pressure

vessel; how to use the facility for a test; what happens during a test; and how to address

some common problems.

A. 1 How to Adapt Specimens to the Pressure Vesse1

There are three kinds of specimens which have been tested in the hydraulic test

fac*ty, and each d l be treated separately, in order of their complexity.

Type 1 : CIased 3pecimen.s without uny diplacement monitors, where on& the faihre

pressure is investigated. For example, Arlene Bristol in her B .&Sc. thesis imploded

several PVC pipes, which had fiat plates epoxied to the ends. The only consideration

necessary for this type of specimen is how to anchor it to the bottom of the pressure

Al

Manual for the Hydraulic Test Facility A2

vessel, because it will usudly float. For this purpose, there are holes in the plate on

which the specimen rem. Either ropes or cables can be passed through the holes to

anchor the specimen.

Type 2: Seded specimens, where there is a potential for water fe&ge. and wwhh

contain some dqdacement monitors. The implosion specimens were an example of

this Iand of specimen. Because water may leak into these specimens, two things are

necessary. First, a gasket was required between the ends of the implosion specimens,

and the steel hexagonal plate. Second, an outlet was made in the steel end plate to

allow water to leak out, as shown schematically in figure A 1. The outlet is connected

by a high pressure hose to a portal on the tank which leads to a drain. The hose is

shown in figure 2.8. Because there are cables leading fiom transducers and strain

gauges inside the tank, there must also be outlets for the cables to leave the specimen.

Two outlets shown in figure A 1 were designed in the steel end plate for this purpose.

The outlets are again connected by a high pressure hose to a portai on the tank which

leads to the outside of the pressure vessel. Also, because the specimen may float, it

must be anchored to the bottom of the tank.

Figure A. I Diagram of the steel end plate used for the implosion specimens

Type 3: (Ipnghi specimens, which are anchored to the plate ut the bot- of the

pressure vesei, and which contain a large mrrnber of diqpiacemenî monitors. An

example of this kind of specimen is the 1:13 scale mode1 of a Condeep pladom


storage ceiî tested by Amr Helrny, and show in figure k 2 . Threaded rods attach the

specimen to the plate at the bottom of the pressure vessel. These threaded rods

requin a specul tightening operation described later. A rubber gasket seals the

specimen fkom leakage. Both the threaded rods and the rubber gasket are in storage in

the pit under the pressure vessel.

Inlets are already drilled into the plate at the bottom of the vessel for drainage and

for any cables which must exit the tank. The same high pressure hoses used for the

implosion test shouid be used for drainage and for the cables- Do not use the hoses in

place already, since they leak

For details on how to instrument one of these specimens, refer to Am. Helmy's

Ph.D. thesis".

A.2 How to Use the Hydraulic Test Facility

This section is intended as a step-by-step guide, beginning with the initial set-up,

and ending with clean-up.

Step 1: Put the pnmary reservoir in place, and clean the dust out of the reservoir.

Then fil1 the reservoir. The prirnary reservoir is shown in figures A3 and A4. S k

hoses must be connected to the reservoir. Hose A is the outlet for water leaving the

reservoir during testing. Hose B is the inlet for water filling the reservoir. Hose C

retums water h m the b l e d valve and the relief valve on the lid of the specimen.

Hose D returns water ffom a pump relief valve. Hose E is a high pressure hose

connecteci to the directional valve. Finally, hose F cornes fiom the secondary pumps.

The purpose of al1 these valves will be explained later. For now, it is only important to

connect the hoses as shown in figures A.3 and A.4. The connections in the reservoir

are made so that only one hose can fit each comection. Close al1 valves leading fkom

the reservoir and attached to the different hoses now comected. To close the valves,

tum the handle so that it is perpendicular to the direction of the pipe.

Manual for the Hvdraulic Test Facilitv A4

Figure A.2 Upright Specimen in the Pressure Vessel (From Ref. 12)

sket

Open to ins


Figure A.3 Hoses Connected to the Pnmary Reservoir

Figure A.4 Front of the Primary Reservoir

Manual for the Hydraulic Test Faciiity A6

To tili the reservoir, open the valve on the water supply labelled G in figure k4.

The valve is open when the handle is parallel to the pipe. There is a float switch

attached to the reservoir. The water supply immediately shuts off when the water

reaches the level o f the float switch.

Step 2: Feed the cables for the pressure transducers, and the emergency stop mvitches

through the hole beneath the floor next t o the pressure vessel. A research technician

will likely do this.

Step 3: At some stage, but not necessarily at this time, the pump control unit will

have to be put in position, and the cables will have to be hooked up. This again will be

done by a research technician.

Step 4: Remove the Iid. Position the lid in a clear area atop three stub steel column

sections, spaced equally around the specimen. This will allow access underneath the

lid. Under the lid, there are four lights dangling tiom an aluminum plate. Currently,

al1 of the bulbs are finnly in their sockets. However, after a test, some of them are

knocked loose. Always check for loose bulbs before a test, and if necessary, remove

the plastic lid from the light with an Allen key, and return the bulb to its socket.

Step 5: Anchor the specimen to the plate at the bottom of the pressure vessel. For

specimens of type 1 o r 2 describeci in section A. 1, this can be done by stringing rope

or steel cable over the specimen, both of which are shown in figure 2.8. For the type 3

specimen, this step requires tightening of the threaded rods. The hydraulic wrench is

used for this operation because the oil pump has a gauge indicating hydraulic oil

pressure. The oil pressure which ensures that the threaded rods are adequately tight is

given by the followïng relation, which is explaineci in Appendk D of Amr Helmy's

Master's thesis", and plotted in figure AS,

P(pso = 0.1 1 08 - K - O:,,) - f(Yield) (A- 1)

Pm, = oil pressure @si)


K = 0.1 1 for dry threads and 0.23 for lubricated threads (dimensionless) @ = diameter of the threaded rods (in) fwew = yield stress (70000 psi assumed)

This relation tightens the rods to 75% of the yield force of the threaded rod (threaded

included), which is considered as tight as possible.

Figure A.5 Relation between oil pressure and rod size for different thread conditions (From Ref. 1 1)

The procedure for tightening requires that the oil pressure be set to about 500psi

below the required level, and that the rods be tightened in the sequence prescribed in

figure A6. Then the oil pressure is increased to the required level, and the wrench is

applied to d l nuts continuously without any special sequence. To untighten the

threaded rods aftenvards, the air wrench is quicker than the hydraulic wrench, but dso

louder.

hfanual for the Hvdraulic Test Facilitv A8

Figure A.6 Proposed sequence for fastening the specimen to the steel base plate

@rom Ref. 11)

Step 6: Fasten the high pressure hoses leading fkom the specimen to the outside of the

tank. This will likely invoive passing cables through the high pressure hoses, and then

passing cables through the portal leading to the outside of the tank. The drain portal is

labelled A in figure A7, the two cable portals are labelled B and C in figure A-7.

Step 7: Hook the cables t o the data acquisition system. This step may be postponed

until later if desired. The type of data acquisition system used will depend on which

one is preferred by the Research Engineer.

Step 8: Wash the inside of the tank with the hose ~ 0 ~ t X t e d to the tap adjacent t o the

top of the pressure vessel, Make sure that the tank drain at the bottom of the vessel is

open so that the dirty water can drain fiom the tank. The Tank Drain is labelled A in

figure A2. The valve is open when the handle is parailel to the pipe, and closed when

the handle is perpendicular to the pipe. Pay carefùl attention t o the three viewing

portals, especially the one in the lid. Any dust on the viewing ponals will obscure the

specimen during a test.


Figure A. 7 Portals used for drainage and as an outlet for cables fiom the specimen to the outside of the pressure vessel.

Step 9: Retum the lid to the pressure vessel. When the lid is still attached to the

Crane, very carefùlly attach the four cables from the lights inside the lid to the single

cable running up the inside of the pressure vessel. To make sure that this is the correct

cable, check that the other end of this cable has eight multi-coloured wires protmding

fiom it. When the lights are attached, lower the Iid into place until it is about to touch

down on the tank. To position the lid correctly, line up the 'N' label on the north side

of the vessel with the 'N' label on the lid. When the labels are lined up, place two

threaded rods into position to hold the lid in place. Next, place two threaded rods into

position on the east, south, and West sides of the lid. When al1 eight threaded rods are

in place, then lower the lid completely.

Step 10: Insert the remaining 80 rods. Don't fasten the nuts until al1 80 rods are in

place. In al1 likelihood, some of the rods will not fall into place, so after inserting al1


80 rods, the lid should be lifted one last time, and the rods will adjust themselves and

fa11 into place. Now fasten the nuts until they are hand-tight.

Sttp 11: Tighten the lid to the pressure vessel. This operation is similar to step 5.

Again the hydraulic wrench is used. The oil pressure is now given by a different

expression:

P(oii) = K - 67 - P(wate r)

= oil pressure (psi) K = 0.1 1 for dry threads and 0.23 for lubncated threads (dimensionless) P(- = water pressure in pressure vessel @si) It is conventional to use the maximum allowable water pressure of 275 psi even if the actual water pressure in the tank is expected to be less

The procedure for tightening is again similar to step 5. The required oil pressure level

given by the equation was taken to be 3000psi for the implosion tests, which was

sufficient for a water pressure of 280psi. Therefore, the oil pressure should fist be set

at 2500psi, and the rods should be tightened in the sequence prescribed in figure A8-

Then the oil pressure is increased to 3000psi, and the wrench is applied to al1 nuts

continuously without any special sequence. This operation requires about four hours.

To untighten the threaded rods atterwards, the air wrench is quicker than the hydraulic

wrench, but also louder.

Step 12: Begin filling the tank with water. This operation requires 14 hours. Fust

check that the tank drain is closed. The tank drain is labelled A in figure A2. The

valve is closed when the handle is perpendicular to the pipe. Nen, open the bleed

valve completely. The b l e d valve is labelled A in figure A.9. The bleed valve is used

to remove air fiom the vessel as it fills with water. Remove the blue plug Born the top

of the tank. This blue plug is labellecl B in figure A9, and may requin vice grips to

remove. Replace the blue plug with the pipe s h o w next to it in the figure (the pipe is

found in a box in the pit beneath the pressure vessel). Connect a hose, leading fiom

the water tap next to the top of the pressure vessel, to the pipe. Tum on the water tap

to begin filling the pressure vessel. M e r IS minutes, feel the air moving in front of the

Manuai for the Hydraulic Test Facility Al 1

bled valve to ensure that it is working. If the bled valve is not working, pressure will

build up inside the pressure vessel until the water pressure in the city water line is

reached, which is as much as 50psi.

Figure A.8 Proposed method for fastening vessel head to its shell (from Ref. I l )

Step 13: Hook up the interior lights. The power source for the lights is stored by the

lab technicians. The cable for the lights protmdes from a steel casing at the bottom of

the pressure vessel, and extends roughIy two feet fiom the pressure vessel. The cable

ends with 8 coloured wires combined into pairs. These wires must be C O M ~ C ~ ~ to the

grey box attached to the power source. Each pair of wires corresponds to a pair of

terminais on the box. The box should be elevated on a platform, and the box and the

cable fiom the box must be covered in thick polyethylene sheeting after the wires are

attached, to prevent accidental spillage fiom destroying them. The Iab technicians

know how the lights work.


To check the level to which the water rises in the pressure vessel, tum on the iights

periodically.

Figure A. 9 Top of Pressure Vesse1

Step 14: Hook the hose to the bleed valve. The bleed valve is labelled A in figure

Ag. The end of this hose should be connected to a needle connection adjacent to the

water reservoir. Remove the hose corn the needle connection and feel in fiont of the

hose to ensure that there is air movement. When the pressure vessel is Ml, water will

begin shooting out of this hose into the primary reservoir.

Step 15: Hook the hose to the relief valve labelled C in figure A.9. The relief valve

has a pressure indicator which can be used to roughly indicate water pressure inside

the vessel in the event that the pressure transducers are not working properly- When

the pressure inside the vessel reaches between 250 and 275psi, the maximum design

pressure of the vessel, the relief valve gradually lets water escape, thereby ensunng

that the design pressure is not exceeded.


Step 16: Hook water hose and air hose to the release valve, labelled D in figure Ag.

One end of the air hose should be c o ~ e c t e d to the nonle at the ypp of the release

valve shown in the figure, and the other end of the air hose must be comected to the

air supply in the pit below the pressure vessel. The second end of the water hose must

be connectai to the secondary reservoir also in the pit. There are two black knobs on

the release valve. Both of these knobs must be pulled out. The author is not entirely

certain what ttus valve does. The valve definitely removes air fiom the vessel, but it

may also be u s 4 for fatigue testing. Please refer to Amr's P~.D.'* thesis for an

improved explanation.

Step 17: Wait until the water in the tank is full, then turn off the water supply, close

the bleed valve, and replace the standpipe for the water supply with the blue plug. The

tank is f i I l when water begins to spurt fiom the hose connected to the bleed vaive. It

is very important to stop filling the tank as soon as the tank is full, because the opening

in the bleed valve is smaller than the opening for the water supply. Therefore, water

enters more quickly than it can leave, and pressure will build up in the pressure vessel

until is reaches the city water supply pressure of 50psi.

Step 18: Prepare the cornputer for testing. A research technician will likely help.

Step 19: Mount the video camera on the viewing pond on the Iid of the specimen.

There is an angle and a screw with a fly nnt on the pond for this purpose. They are

shown labelled E in figure k g . Conveniently, there is a smail portable TV with an

interna1 VCR which can be hooked to the video camera so that the specimen can be

seen throughout the test.

Step 20: Set out the kill switches for the pump. There are two kill switches with a

single button and a blinking red light. Pressing these switches wili instantly stop the

pump and halt the test in case of problems with the pressure vessel. Because these

Manual for the Kydraulic Test Facility A14

switches can potentially destroy test results, they must be placed in d e , conspicuous

places, where they are not likely to be bumped.

Step 21 : Pediorm the following check list before testing:

a. Check that the water outlet, for water leaving the specimen, is open. This

outlet is labelled B in figure A2. The valve is open when the handle is parallel to the

length of pipe.

b. Check the portals fiom which the displacement gauge cables extend- The b i d e

of these portals should be relatively dry. if they are not dry, it may indicate that water

is leaking into the specirnen more quickly than it can drain-

c. Check that al1 strain gauges and other displacement gauges are zeroed.

Step 22: Open ail four blue valves dong the line fiom the p n m q resewoir to the

pressure vessel- Do not start the pump until this is done, because if the pump does not

have any water in it when it starts, damage may occur.

Step 23: Tum on the pump. This is done using the pump control unit, generally

controlled by the lab technicians-

Step 24: The input flow indicator on the pump control unit must be set to zero after

the pump is turned on. The input flow indicator is shown in figure A 11. To do this,

four nuts labeled 4 B, C, (and D is not shown) on the flow meter in figure A. 10 must

be opened. When each nut is opened, a small spray of water will shoot out. Allow

this water to shoot out for about 15 seconds, or until there is no more air escaping.

Step 25: Begin the test, and press record on the VCR to record the test.

Step 26: After the test is completed, dean up al1 cables, remove the threaded rods

fiom the lid with the air wrench, remove the specimen fiom the tank, and dean up al1

debns at the bottom of the tank in preparation for the next researcher.


Figure A. IO The flow meter

Upper Pressure Lower Pressure Transducer Transducer

Figure A. II Schematic of the Pump control Unit

1 Centura Valve Indicator

EGl

M ~ P W P Frequency Control

O

Input Flow -

Secondaiy

"" Centura Dirccuonal

- .

Pump Control Wve Control

I E l Stop Start Key

00 C)


A.3 What Happens During a Test

This section descnies the cornponents of the pressure vessel, and how these

components fùnction. The system is entirely automated, but does allow some manual

ovemdes. The process will be describeci beginning fiom the primary reservoir, and ending

at the pressure vessel. For small specimens, like those used in the implosion tests, only

the primary reservoir is used. For larger specimens, when the specimen cracks, the pump

must supply a very large arnount of water to maintain the appropriate pressure inside the

pressure vessel. Therefore, the secondary reservoir rnust be used. A diagram showing the

entire process is shown in figure A 12. Reference will d so be made to Figure A. 1 1 which

is a schematic of the pump control unit.

A.3.1 Using the Primary Reservoir only

Step 1: First, Water begins flowing fiorn the prirnary reservoir (upper water

resewoir) labelled A in figure A12, and passes through two blue control valves

before it reaches the main electric pump labelled B in the figure.

Step 2: The main electric pump is controlled by the pump control unit in figure

A.11. To turn on the pump, a key is inserted, the start button is pushed, and the

fiequency dia1 is tumed until the pressure in the vessel begins to increase. An increase

in pressure is indicated by the displays for the upper pressure transducer and the lower

pressure transducer. For the implosion tests, these few elements were the only parts

of the pump control unit in use.

Step 3: Next, the water flows through the pump manifold, where it may pass through

the pump relief valve labelled C in figure A. 12. The pump relief valve is similar to

the relief valve descnbed in step 15 of section A.2. The valve contains a pressure

gauge, and if the pressure exceeds between 250 and 275psi, water gradually begins

leaking through the relief valve and dong the emergency return line until it reaches the

Hoin elcctrrc punp

Pressure gouge City r o t e r supply

Figue A. 12 Test Sequence (from Ref. 12)

Manual for the Hydraulic Test Facility Al8

primary reservoir where it began. This ensures that the maximum capacity of the

pressure vessel is not exceeded-

Step 4: The pump manifold also contains another outlet to a Centura Directional

Valve, Iabelied D in figure A12. The directional valve was not used during the

implosion tests. When the directional valve is partially open during a test, it can

divert a portion of water dong a high pressure retum Iine back to the primary

reservoir, By having the d'uectional valve partialîy open dunng a test, and then closing

the valve slowly, the pressure inside the vessel can be slowly increased in very small

increments without increasing the fiowrate through the pump. Because of the high

water demand near failure, the directional valve should be closed then.

The pump control unit controls the directional valve. The degree of openness is

indicated by a range fiom O to 90 degrees on the controt unit.

Step 5: Beyond the pump manifold, the water travels through a check valve labelled E

in figure A 12. The check valve permits water to move fiom the primary reservoir to

the pressure vessel, but not in the reverse direction.

Step 6: The water flows through two more blue control valves, until it passes through

the Venturi meter labelled F in Figure A 12, which measures the flowrate as indicated

on the pump control unit. After this, the water passes into the pressure vessel.

A. 3.2 Using the Secondary Resenoir

Step 7: M e n the water in the primary reservoir drops below a certain level, the

ultrasonic level meter, labelled If in figure k 4 , records this drop and activates the

second- t r a d e r pumps IabelIed H in figure k 1 2 . The two secondary transfer

pumps pump water fiom the secondary resmoir (iower water reservoir) to the

primary reservoir. The secondary transfer pumps can be partially controlled by the

pump control unit. They can be used simultaneously or altematively.


Step 8: The secondary reservoir is labelled G in the figure. If it is to be used, it must

be partially filleci with water before the test. The secondary rescrvoir should not be

niiiy filled since water from the release! valve on the top of the pressure vessel empties

to this reservoir during a test. Also, there are two valves, one downstream of the

secondary reservoir, and one upstream of the primary reservoir which must be opened.

Step 9: The Floating Valve Switch, rnounted 200mm nom the bottom of the upper

reservoir is open at the beginning of the test, and closes if the water level in the upper

reservoir drops below that level. This ensures that the Main pump does not dry out.

A.4 Trouble-Shooting This section of the report suggests solutions to various problems comrnonly

encountered during testing.

Interior Lighis Don't tum on: It is very likely that the bulb has fallen out of its

socket, o r disengaged slightly. Remove the plastic face plate with Allen wrenches, and

return the bulb to its socket.

Hy&aulic Wrench Reqirires More thun Four Hmrs to Tighten Threuded R d in

the Lid: The hydraulic pump does not have enough hydraulic fluid, and sorne rnust be

added.

m e Pump Starts, but Waiet Will Not Flow to the Pressure Vesel: The cause of

this problem has not yet been discovered, but the suspicion is that calcium is building up

inside the pump. The solution is sim~ly to increase the frguency of the pump until

enough pressure has built up in the line to remove any built-up calcium.

The Valve on the Tank Drain will not Close: There is debris in the valve. The

hole in the very bottom of the pressure vessel must be cleaned out.

The Steel Casing surrounding the Lights Cable. or the Pressure Tr(II1Sducer

Cable, is Leuking Severely: A Small leak is not a problem, so long as pressure can be

maintained inside the pressure vessel. If the leak is large enough so that pressure cannot

Manual for the Hydrauiic Test Facility A20

be maintained, then the first thing to try is to tighten the steel casing. Tightening the steel

casing squeezes the seal inside- However, tightening also twists the seal and may damage

the seal permanently, and this should only be done as a last reoort. if the leak persists,

then the seal inside the casing must be replaced. There are some spare seals, but they may

be difncult to locate. The best solution is to use a product fiom 3M called ~ c o t c h c a s t ~

2130 which can be molded into the form of a seal inside the casing. This product was very

successfirl in the past.

AS Options This section discusses some options available for use in conjunction with the

pressure vessel which have not yet been discusseâ.

Undenvafer Canrera: This Camera was used inside the upright specimen shown in

figure A2. It can also be conveniently mounted on the aluminum plate under the lid of the

pressure vessel. There is a m e r a control unit kept in storage by the research technicians.

Unfortunately, it has a number of problems currently. First, the plastic shield is cracked.

Nso, while an image does corne h m the camera, the carnera cannot be focused, zoomed,

tilted, or panned any longer. The shield can easily be fixed, but the other features may

require a return to the manufacturer.

Water Outflow Rate: The pump control unit has a disptay for the water outflow

rate. When water leaves the specimen through the specimen drain, it passes over a paddle

wheel, which signals an electric pulse whenever it tums. The outflow rate was calibrated

based on this electric pulse. This outflow rate can be incorporated into the data

acquisition synem to measure leakage fiom the specimen.

Appendix B Implosion Test Strain Results

This Appendix presents al1 of the circumferential and longitudinal strain gauge

results fiom the Implosion Tests.

Implosion Test Strain Results B2

B. 1 Specimen LD250F6

Strain (mlcro strdn)

Figure B. I Circumferential Strains fiom Specimen LD250F6

81r.ln (mlcro strdn)

- Ml -2 - U - 8

Figure B.2 Longitudinal Strains fiom Specimen LD250F6



Simin (micro strrin)

Figure B. 3 Circuderentiai Strains fkom Specimen LDZSOF 1

Strrln (mlcro strdn)

Figrre B.4 Longitudinal Strains from Specimen LDZSOFl

ImpIosion Test Strain Results B4

B.3 Specimen LD l75Fl

Strain (mkro s train)

Figure B. 5 Circumferential Strains fiom Specimen LD 175F 1

-200 -150 -100 SO O 50 100 150 aW

âtrain (m kro straln)

-6L1-2 - --- BL2-4 -m-6- - m-8 - - --------- m-12

Figure B. 6 Longitudinal Strains fiom S pecimen LD 1 75F 1

Implosion Test Strain Results BS

B.4 Specirnen LD175F6

Figure B. 7 Cirnimferential S trains fiom S pecimen LD 1 7SF6

Srdn (mkro strah)

[ 8L1-2 - BU-4 M 2 - 8 T L 1 - 1 0 -TU-12

Figure B. 8 Longitudinal S trains fiom Specirnen LD 1 TSF6


B .5 Specimen LD 100F 1

Strain (micro rtrain)

Figure B. 9 ~ircumfer&ntial Strains from Specimen LD 1 OOF 1

Strrin (micro strrin)

Figure B. 10 Longitudinal S trains fiom S pecimen LD 1 00F 1

implosion of steel fibre reinforced concrete …...abstract implosion of steel fibre reinforced...

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