Application of computational limit analysis to soil-structure interaction in masonry arch bridges

223 Pages·2015·36.96 MB·English

UNIVERSITY OF SHEFFIELD
Application of computational
limit analysis to soil-structure
interaction in masonry arch
bridges
by
Dong Nguyen
t 11 His Huhmittcd in partial fulfillment for the
drgrC'C' of Doctor of Philosophy
in the
'partmcnt of Civil and Stru tural Engineering
De 200
' Illb l'
IMAGING SERVICES NORTH
Boston Spa, Wetherby
West Yorkshire, LS23 7BQ
www.bl.uk
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Declaration of Authorship
I, Dong Nguyen, declare that this thesis entitled, . Application of computational
limit analysis to soil-structure interaction in Masonry arch bridges' and the work
presented in it are my own. I confirm that:
• This work was done wholly or mainly while in candidature for a research
degree at this University.
• Where any part of this thesis has previously been submittt'<i for a degree or
any other qualification at this University or any other institution, this has
been clearly stated.
• Where I have consulted the published work of others, this is always clearly
attributed.
• Where I have quoted from the work of others, the source is always given.
With the exception of such quotations, this thesis is entirely my own work.
• I have acknowledged all main sources of help.
• Where the thesis is based on work done by myself jointly with others, I have
made clear exactly what was done by others and what I have contributed
myself.
Signed:
Date:
Abstract
For the assessment of Masonry Arch Bridges (MAB), many structural and mate
rial models have been applied, ranging from sophisticated non-linear finite element
analysis models to much simpler rigid-block limit analysis models. i.e. clastic and
plastic methods respectively. The application of clastic analysis to MAB suffers
many drawbacks since it requires full mechanical characterization of ancient ma
sonry structures. The mechanical characterization of ancient masonry is difficult
since these structures have typically undergone a century or more of environmental
d('t('rioration and in many cases have been already subject('d to extensive modifica
tion. Also, sophisticated material models generally require specialized parameters
that are hard to assess, particularly if non-destructive tests are useoxi. In these cases
practicing enginccrs typically favour simpler material models, involving fewer pa
ramett'rs. Thus non-linear fillite element methods or other sophisticatlxi models
may not be a good choice for the assessment of MAB, whil(' simplified approaches
for example ba.. . ed on limit analysis principles are likely to be more appropriate. In
this research. a holistic computational limit analysis procedure is presented which
involves modelling both soil and masonry components explicitly. Masonry bridge
parts are discretized using rigid blocks whilst the soil fill is discretized using de
formable triangular clements and modelled a.'i a Mohr-Coulomb material with a
tension ('ut-off. Lower and upper bound estimates of the collapse load arc obtaineoxi.
R('sults a1'(' compared with those from recently p('rformed bridge tests carried out
in collaboration with the University of Salford. A key projelt fiuding is that the
use of peak soil strength parameters in limit analysis models is inappropriate when
the soil is modelled explicitly. However, use of mobilized strengths appears to be a
promising way forward, yielding much closer correlation with experimental data.
Acknowledgements
I would like to express my deep gratitude to Dr Matthew Gilbert and Dr Colin
Smith for their helpful advice, support and encouragement during the course of
this work.
I would like to acknowledge the financial support received from the Engineering
and Physical Sciences Research Council (EPSRC) and the University of Sheffield.
I would also like to express my gratitude to my wife Ha for everything she has
done. She has made me a father of two lovely children and my love for her can
not be expressed in words.
I would like to say thank to members of the CLADU research group at thc Uni
versity for tlwir willingness to help me and for fruitful discussions about a range
of topics.
iii
Contents
Declaration of Authorship i
Abstract ii
Acknowledgements iii
List of Figures ix
List of Tables xiv
Abbreviations xvi
1 Introduction 1
1.1 Background . . . . . . . . . 1
1.2 Objectives and methodology 3
1.3 Thesis layout . . . . . . . . 4
2 Literature review 6
2.1 Introduction.......................... 6
2.2 Bridge bearing capacity analysis and assessment methods . 8
2.3 Strengthening tcchniques for bridges .......... . 12
2.4 Load tests on full scale masonry arch bridges, to collapse 13
2.5 Theory of plasticity: historical remarks 14
2.6 Limit analysis: basic theory . 18
2.7 Computational limit analysis ... . 20
2.7.1 Introduction ........ . 20
2.7.2 Mathematical optimization. 20
2.8 Application of computational limit analysis. 23
iv
Contents v
2.8.1 Application to masonry structures. 23
2.8.2 Application in geomechanics ... 26
2.8.3 Computational mechanics issues . 29
2.9 Structural layout optimization . . . . . . 31
2.9.1 Introduction ........... . 31
2.9.2 Layout optimization of gridlike structures 33
2.9.3 Discontinuity layout optimization ..... 35
3 Numerical limit analysis model of masonry-soil interaction 38
3.1 Preface.................. 38
3.2 Model of masonry clements ..... . 38
3.2.1 Static (equilibrium) formulation 44
3.2.2 Kinematic formulation . . . . . 45
3.2.3 Extension of masonry model for crushing failure 46
3.3 Formulation of strengthening clement . 47
3.4 Model of soil. . . . . . . . . . . . . . . 49
3.4.1 Static (equilibrium) formulation 49
3.4.2 Kinematic formulation . 57
3.5 Model of soil-masonry interface 64
3.5.1 Static formulation ... 64
3.5.2 Kinematic formulation . 65
3.6 Solution ............ . 67
3.6.1 Static (equilibrium) formulation 67
3.6.2 Kinematic formulation ..... 68
3.7 Layout optimization of grid-like structure: mathematical formulation 69
3.7.1 Formulation of the problem of identifying optimal arrange-
ments of reinforcement in masonry structures ... 70
3.8 Comparison and validation . . . . . . . . . . . . . . . . . . 71
3.8.1 Strip footing bearing capacity on single layered soil 71
3.8.2 Strip footing bearing capacity on two layered soil . 77
3.8.3 Comparison between constant strain clement and linear strain
clement for the upper-bound solution ....... . 78
3.8.4 Simple retaining wall problem . . . . . . . . . . . . 81
3.8.5 Adaptive pieces wise linearized of the yield surface 83
3.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4 Application of numerical limit analysis model to soil-structure
interaction problems 86
4.1 Introduction............... 86
4.2 Analysis of a brickwork retaining wall. 88
Contents vi
4.3 Prestwood bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4 Load test to collapse of back-filled brickwork masonry arch bridges
at Salford University . . 96
4.4.1 Bridge geometry .. . 97
4.4.2 Materials ...... . 98
4.4.3 Finite element meshes .100
4.4.4 Bridge analyses .102
4.5 Conclusions ......... . · 112
5 Mobilized strength limit analysis of masonry arch bridges 121
5.1 Introduction................... · 121
5.2 Simple mobilized strength analysis ......... . · 123
5.2.1 The influence of mohili7.ed soil strength . . . . · 123
5.2.2 Simple model for mobilized strength analysis. · 125
5.3 Mobilized strength limit analysis: MSLA . . . . . . . · 128
5.3.1 Foundation settlement on a clay . . . . . . . . · 130
5.3.2 Load test to collapse of back-filled brickwork masonry arch
bridges at Salford University. . 134
5.4 Conclusions . . . . . . . . . . . . . . . 141
6 Discussion 149
6.1 Introduction........... . 149
6.2 The mesh dependency problem . 150
6.3 The 'locking' problem. . . . . . . 151
6.4 Potential application of layout optimization to the design of strength-
ening existing structures . . . . . . 152
6.5 Discontinuity layout optimization . . . . . . . . . . . . . . . . . . . 154
7 Conclusions and recommendations 157
7.1 Introduction ............................... 157
7.2 Measuring the success of the project ................ 158
7.2.1 Objective 1: development of a finite element limit analysis
model for combined soil and masonry problems, and initial
verification of this through application to a number of stan-
dard benchmark problems. . . . . . . . . . . . . . . . . . . . 158
7.2.2 Objective 2: more in-depth verification of the model through
application of this to a number of full scale bridge tests. .. 158
7.2.3 Objective 3: implementation of enhancements to the model
as proves necessary. . . . . . . . . . . . . . . . . . . . . . . . 159
Contents VB
7.2.4 Objective 4: consideration of other potential applications of
the developed numerical model. . 159
7.2.5 Concluding remarks ....................... 160
7.3 Recommendation for further work ................... 160
7.3.1 On the development of computational limit analysis and de-
sign synthesis .......................... 160
7.3.2 On the development of finite element limit analysis models
for the assessment of masonry arch bridges. . 161
7.3.3 On the strengthening of masonry arch bridges ........ 162
A Mathematical programming 176
A.l Linear programming and duality concept · 177
B Finite element limit analysis - computer code 179
B.1 Object-oriented programming . . . . . . . . · 179
B.2 Classes and objects ............. . · 180
B.3 The finite element limit analysis framework. · 180
C Simple model of concrete and steel beams 184
C.1 Two block cantilever beam analysis · 184
C.2 Concrete beam analysis. 185
C.3 Steel beam analysis . . . . . . . . . · 186
D Load test to collapse of back-filled brickwork masonry arch bridges
at Salford University 188
D.1 Introduction. . . . . . . . . 189
D.1.1 Terms of reference . 189
D.1.2 Test rig ...... . 189
D.1.3 Bridge and backfill geometry. . 189
D.2 Materials ... . 191
D.2.1 Bricks . . . . . . . . 191
D.2.2 Mortar. . . . . . . . 191
D.2.3 Crushed limestone · 191
D.2.4 Clay ... . · 192
D.3 Construction .. . · 194
D.3.1 Abutments · 194
D.3.2 Centering . · 194
Contents viii
D.3.3 Arch Barrel . . . . . . · 194
D.3.4 Tank construction ... · 194
D.3.5 Wall friction reduction · 195
D.3.6 Removal of centering · 196
D.4 Instrumentation .... · 196
D.4.1 Deflection . . . · 196
D.4.2 Earth pressures · 196
D.4.3 Imaging .... · 198
D.5 Loading Arrangement. · 198
D.6 Test Procedure ... · 199
D.6.1 Phase I test . .200
D.6.2 Phase II tests .200
E DLO: Visualization of failure mechanisms 201
E.1 Solid identification procedure ...... . · 201
E.2 On the calculation of solid absolute displacement .203