NEW TOOLS FOR MODELLING SOIL-FILLED MASONRY ARCH BRIDGES By Michał Pytlos

158 Pages·2016·43.77 MB·English

NEW TOOLS FOR MODELLING SOIL-FILLED
MASONRY ARCH BRIDGES
By
Michał Pytlos
Supervisors:
Dr Colin Smith
Professor Matthew Gilbert
A thesis submitted in partial fulfilment of the requirements for the
degree of Doctor of Philosophy
The University of Sheffield
Department of Civil and Structural Engineering
October 2015
Abstract
This study is concerned with the development of new numerical and physical tools suit-
able for modelling soil-filled masonry arch bridges. Firstly, a novel modelling approach is
presented which makes use of the Box2D rigid body physics engine, widely used in the
computer games industry. A description of the simulation method implemented in Box2D
is provided and it is shown that this tool is capable of accurately simulating disc and block
interaction dynamics, and can successfully capture the critical state response of granular
media. Four Box2D based computer programs, constituting a ‘virtual laboratory’, are pre-
sented and are shown to be capable of accurately simulating load tests to failure on both
bare and soil-filled masonry arches. It is also demonstrated that the macro-scale properties
of a virtual soil material, modelled as an assembly of randomly shaped polygons, are inde-
pendent of the simulated scenario. Practical issues associated with the use of Box2D as a
modellingtoolareconsideredandadvantagescomparedwiththetraditionaldistinctelement
methodarediscussed. Secondly,aninnovativeexperimentalfacilitydevelopedbytheauthor
and suitable for testing medium-scale sand-filled masonry arch bridges is described. The
testfacilityfeaturesanovelsandconveyanceandpouringsystemwhichprovidesverygood
controloverbackfillpropertiesandsignificantlyspeedsupthedepositionprocess. Initialtest
results from the test facility are described and recommendations for future work are made.
i
Acknowledgements
Firstly, I would like to acknowledge my supervisory team of Dr Colin Smith and Professor
MatthewGilbert. ColinandMatthewhavealwaysbeengenerouswiththeirtime,fullofideas
and provided support and inspiration when it was needed.
IwouldliketothankthetechnicalstafffromtheDepartmentofCivilandStructuralEngineer-
ing for their hard work in the development process of the experimental facility. In particular,
I wish to acknowledge Dr Paul Bentley for his help in the development of the sand con-
veyance and pouring system and wiring of the instrumentation, Kieran Nash for fabricating
the voussoirs, Chris Todd for help with the Kelsey actuator, Mark Foster, Alex Cargill and
David Callaghan for their substantial help throughout the whole development process and
Paul Blackbourn and Paul Osborne for their technical advice. Special thanks go to Martin
Taylor for his participation in the crucial process of fine-tuning of the sand conveyance and
pouring system, his enthusiasm and technical knowledge were of enormous help.
I would like to thank Sebastian Buccello, Richard Osborne and Nadine Fecht for their help
in conducting the laboratory test.
I am grateful to the EPSRC for funding my PhD research for three years.
Finally, I would like to thank my family, and in particular my parents and my sister Marysia,
for all their love and support over the years.
ii
Contents
1. Introduction 1
1.1. Aims and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Background 3
2.1. Structural behaviour of masonry arch bridges . . . . . . . . . . . . . . . . . . 3
2.1.1. Typical structural details . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2. Arch barrel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.3. Spandrel walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.4. Backfill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2. Methods of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1. MEXE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2. Rigid-block analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3. Other limit analysis methods . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.4. Elasto-plastic finite element . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.5. Distinct element method . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.6. Assessment in practice . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.7. Limitations of current methods of analysis . . . . . . . . . . . . . . . . 16
2.3. Physical modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1. Full scale tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2. Model scale tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3. Centrifuge tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4. Knowledge gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3. Box2D physics engine 21
3.1. Method description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1. A bigger picture: physics engines . . . . . . . . . . . . . . . . . . . . . 21
3.1.2. Rigid body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.3. Unconstrained motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.4. Contact model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.5. Constrained motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.6. Position error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.7. Comparison with the distinct element method . . . . . . . . . . . . . . 30
3.1.8. Comparison with Contact Dynamics . . . . . . . . . . . . . . . . . . . 33
3.2. Modelling with Box2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1. Modelling and processing the simulation output . . . . . . . . . . . . . 34
iii
3.2.2. Simulation accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3. Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1. Disk on incline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2. Biaxial compression of hexagonally packed discs . . . . . . . . . . . . 39
3.3.3. Block on incline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.4. Multiple blocks on incline . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.5. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4. Modelling soil using Box2D physics engine 49
4.1. Soil model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.1. Micro-scale soil properties. . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.2. Adopted soil model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2. Biaxial compression test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1. Simulation accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.2. Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.3. Confining stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.4. Biaxial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5. Modelling masonry arch bridges using Box2D physics engine 57
5.1. Masonry model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2. Bare arch test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2.1. Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2.2. Accuracy settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.3. A technique to decrease simulation runtime . . . . . . . . . . . . . . . 61
5.2.4. Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3. Simplified backfilled masonry arch test . . . . . . . . . . . . . . . . . . . . . . 66
5.3.1. Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.2. Backfill model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3.3. Example test with dense backfill . . . . . . . . . . . . . . . . . . . . . 67
5.3.4. Example test with loose backfill . . . . . . . . . . . . . . . . . . . . . . 75
5.3.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.4. Full backfilled masonry arch test . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4.1. Test description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4.2. Example test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.4.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.5.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.5.2. Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5.3. Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
iv
6. New facility for testing of soil-filled masonry arch bridges 90
6.1. Design specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.1.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.1.2. Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.1.3. Model size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.1.4. Automation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2. Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2.1. Arch model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2.2. Backfill material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2.3. Test chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2.4. Loading system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2.5. Sand conveyance and pouring system . . . . . . . . . . . . . . . . . . 100
6.2.6. Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.2.7. Friction between the glass walls and the sand mass . . . . . . . . . . 112
6.3. Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.3.1. Bare arch tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.3.2. Backfilled arch tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7. Conclusions 121
7.1. New numerical modelling tool . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2. New physical modelling tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8. Recommendations for further work 125
8.1. Box2D based numerical modelling . . . . . . . . . . . . . . . . . . . . . . . . 125
8.2. Test facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.2.1. Further development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.2.2. Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
9. References 129
Appendices 136
A. Method statement for static load tests to failure on medium-scale models of
masonry arch bridges backfilled with sand
B. Test rig design drawings
C. Developed source code
v
1. Introduction
Thereareover70,000highwayandrailwaymasonryarchspansintheUK.Themainperiod
ofarchbuildinginthiscountrylastedfromthesecondhalfofthe18th tothebeginningofthe
20th century when canal, railway and road infrastructures were subject to rapid expansion.
There are relatively few masonry arch bridges built nowadays but the existing stock forms a
vital part of the UK’s national infrastructure.
Overthecenturiesmasonryarchbridgeshaveproventobeextremelyversatileandsus-
tainable structures, with many of them far surpassing the original design assumptions, both
in terms of lifespan and in terms of load capacity. Yet, in order to cope with material dete-
rioration and ever increasing demands on performance, the existing stock requires careful
management. Specifically, considering the continuing crucial role of masonry arch bridges
intheUK’stransportnetworks,thelargenumberofspansstillinservice,andthelimitedbud-
getsavailableforrepairandmaintenance,itisveryimportantthatengineershaveaccessto
reliable assessment methods, capable of identifying which bridges require attention.
Masonry arch bridges have been the subject of research for well over two centuries,
yet their behaviour is still not fully understood. In particular soil-arch interaction, three-
dimensional effects and behaviour under cyclic loading require further investigation. The
presentresearchisconcernedwiththefirstoftheseissues,soil-archinteractionunderquasi-
static loading conditions.
1.1. Aims and objectives
Theoverallaimofthepresentworkistodevelopnewphysicalandnumericalmodellingtools
which facilitate in-depth study of the behaviour of soil-filled masonry arch bridges. In order
to achieve this aim the following objectives were set:
(i) Todevelopalaboratorytestrigcapableofmodellingquarterscalemodelsof3mspan
bridges being simultaneously tested at the University of Salford. The rig should allow
collectionofhighqualitydataonsoilkinematicsandsoilpressures,providerepeatable
test results and allow the density of the (frictional) backfill materials employed to be
varied.
(ii) To develop a numerical tool for the analysis of masonry arch bridges capable of mod-
elling frictional backfill materials directly, offering the benefits associated with the well
known distinct element method but without its main drawbacks.
(iii) To evaluate the performance of the newly developed tools from (i) and (ii) when used
to model soil-filled masonry arch bridges.
1
1.2. Thesis structure
Chapter 2 provides background information that led to the stated aims and the objectives.
The structural behaviour of masonry arch bridges is discussed, a short review of the cur-
rent methods of analysis is given and the relevant physical studies conducted to date are
summarized.
Chapters 3, 4 and 5 are concerned with a novel numerical tool for modelling masonry
archbridgesbackfilledwithfrictionalsoil. Chapter3providesadescriptionofthesimulation
method and discusses the practical side of modelling. Results from a series of validation
problems are also presented. Chapter 4 discusses modelling of soil. The adopted soil
model is presented and results from two biaxial compression tests, designed to determine
the macro-scale properties of virtual soil materials, are presented and discussed. Chapter
5 discusses modelling of bare and backfilled masonry arch bridges. Results from a series
of tests designed to allow validation against limit analysis software programs are presented
and the concept of a virtual laboratory is discussed. Techniques to determine the required
accuracy settings, decrease runtime of simulations and determine the minimum required
number of soil particles in the backfilled arch model are proposed and tested.
Chapter 6 presents the developed innovative facility for testing of sand-filled medium-
scale models of masonry arch bridges. Results from a series of bare arch tests exploring
the influence of compressive strength of joints on the behaviour of the arch are discussed.
Sample results from a backfilled arch test are also presented.
Chapter7summarizestheoutcomesandthekeyfindingsfromtheresearchpresented.
Therecommendationsforfurtherworkon,andwith,thetoolsdevelopedaregiveninChapter
8.
2
2. Background
2.1. Structural behaviour of masonry arch bridges
2.1.1. Typical structural details
An overview of a single span square masonry arch bridge is shown in Figure 2.1. Due
to the terrain conditions specific to a given site as well as the lack of design codes and
material standards at the time of construction, UK masonry arch bridges vary considerably
in shape, structural details and materials. From a statistical point of view the majority of
railway masonry arch bridges are of brickwork with segmental profiles and consist of single
or multiple spans below 10 metres (Page, 1993).
Figure 2.1.: General arrangement of a masonry arch bridge (after Hughes and Blackler
(1997))
2.1.2. Arch barrel
The arch barrel is the main load bearing element of a masonry arch bridge. It is usually
built either of stone or brickwork; the possible shapes include semicircle, circular segment,
pointed arch, parabola, ellipse and a combination of a number of circular segments.
Stone barrels typically consist of a single ring. Stone units can be either square and
dressed (ashlar) or irregular in shape and size (rubble). The latter material often gives a
varying arch thickness.
3
Brickworkarchbarrelsusuallyconsistofmultipleconcentricrings. Typicalbondingstyles
are shown in Figure 2.2. Bridges in the UK were usually built using the stretcher bonding
style (Melbourne et al., 2007).
Figure 2.2.: Typical bonding styles (after Melbourne and Gilbert (1995))
Material
Masonry is essentially a collection of stiff and strong units bonded with a relatively weak
and soft material. Due to its composite nature, it exhibits a complex anisotropic behaviour.
Masonryisstrongincompressionandweak(withabrittleresponse)intension. Inshearing,
once the bond between the mortar and the units is broken, it exhibits a frictional response.
Line of thrust
In masonry structures the internal forces are often visualized using a line of thrust, defined
astheeccentricityofthecompressiveforce(eccentricity=moment/axialforce). Ifthelineof
thrust lies entirely within the masonry, the forces can be transmitted purely by compressive
action. It cannot pass outside the cross section as this would mean that tensile forces are
being developed. Assuming infinite compressive strength of the masonry, the limit occurs
when the thrust line just touches the external surface of the masonry; the force is then
transmitted at a strip of an infinitesimal width and the rest of the cross section is at zero
stress. At this point a hinge is formed, allowing plastic bending of the structure. Figure 2.3
illustratestheconceptofthelineofthrustinanarch. Ithastobenotedthatmasonryarches
are statically indeterminate structures and the actual line of thrust can be determined only
at the point of failure.
4