Table Of ContentSustainable Masonry
Series Editor
Noël Challamel
Sustainable Masonry
Stability and Behavior of Structures
Thierry Ciblac
Jean-Claude Morel
Firstpublished2014inGreatBritainandtheUnitedStatesbyISTELtdandJohnWiley&Sons,Inc.
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Contents
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
PART1.TECHNOLOGIESANDCONSTRUCTIONPROCESS . . . . . . . . 1
CHAPTER1.INTRODUCTIONTOSUSTAINABLEMASONRY . . . . . . . 3
1.1.Definitionsofsustainablemasonry . . . . . . . . . . . . . . . . . 3
1.1.1.Sustainableconstructions . . . . . . . . . . . . . . . . . . . . 3
1.1.2.Masonrystructures . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.Challengesofsustainabledevelopmentinconstruction . . . . . 5
1.2.1.Socio-economicaspects . . . . . . . . . . . . . . . . . . . . . 5
1.2.2.Environmentalimpact . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3.Sustainability. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.4.Recyclingandreuse. . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.Past(civilengineeringandarchitecture),present
andfuture(designtools)practices . . . . . . . . . . . . . . . . . . . . 7
1.3.1.Architecturalheritage. . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2.Culturalheritage. . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3.Rehabilitation,strengthening . . . . . . . . . . . . . . . . . . 8
1.3.4.Newconstructions. . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.Durability,deformationandpossiblemovement . . . . . . . . . 10
1.5.Importanceofexpertise(complexityofcasesand
historyofthestructure,evolutionovertime) . . . . . . . . . . . . . . 11
1.6.Rationalizationandcalculationmethods. . . . . . . . . . . . . . 12
1.7.Presentationoftheoutlineofthisbook. . . . . . . . . . . . . . . 13
1.8.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
vi SustainableMasonry
CHAPTER2.EARTHANDSTONEMATERIALS . . . . . . . . . . . . . . . 17
2.1.Stone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1.Geologicalconsiderations . . . . . . . . . . . . . . . . . . . . 17
2.1.2.Stonesupply . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.3.Rheologyandmechanicalstrength. . . . . . . . . . . . . . . 19
2.2.Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1.Geologicalandgeotechnicalconsiderations . . . . . . . . . 26
2.2.2.Supplyofearth. . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.3.Manufacturingofmaterialbycompaction(dry) . . . . . . . 27
2.2.4.Implementationofearthinplasticstate(wet). . . . . . . . . 38
2.2.5.Physicochemicalconsiderations. . . . . . . . . . . . . . . . . 43
2.3.Measurementofdrydensity . . . . . . . . . . . . . . . . . . . . . 43
2.3.1.Hydrostaticweighing. . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2.Gammadensitometerweighing. . . . . . . . . . . . . . . . . 46
2.4.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
CHAPTER3.BLOCKS:THEELEMENTSOFMASONRY . . . . . . . . . . 49
3.1Compressionofblocksofuncutstone,drystonemasonry. . . . 49
3.1.1.Cylindricalsampleswithdryjoints. . . . . . . . . . . . . . . 49
3.1.2.Compressionofroughblocks . . . . . . . . . . . . . . . . . . 50
3.2.Shearstrengthofrubblestones. . . . . . . . . . . . . . . . . . . . 51
3.2.1.Sheartestsofonebedofstoneonanother. . . . . . . . . . . 52
3.2.2.Sheartestsonrubblestone(uncut)onan
inclinedplane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.3.Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.Compressionofearthblocks . . . . . . . . . . . . . . . . . . . . . 55
3.3.1.Compressivestrengthtestsofclaybricksand
concretemasonryunits. . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.2.Testondirectlyflatearthblock. . . . . . . . . . . . . . . . . 57
3.3.3.TestdevelopedunderRILEM. . . . . . . . . . . . . . . . . . 58
3.3.4.Indirecttests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.5.Featuresofthecompressivestrengthofearthblocks . . . . 60
3.3.6.Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
CHAPTER4.ARRANGEMENTOFBLOCKS. . . . . . . . . . . . . . . . . . 69
4.1.Dryassembling,ortheartofarrangingirregular
blockstomakeawall. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1.1.Theareaofinfluenceofadrystoneretainingwall . . . . . 69
4.1.2.Qualityofthematerial . . . . . . . . . . . . . . . . . . . . . . 70
Contents vii
4.1.3.Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.1.4.Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.Mortarsofearthblocksandrubblestonemasonry. . . . . . . . 74
4.2.1.Measurementsinthefreshstate. . . . . . . . . . . . . . . . . 76
4.2.2.Dryingshrinkagemeasurements . . . . . . . . . . . . . . . . 83
4.2.3.Testsonhardenedmortars. . . . . . . . . . . . . . . . . . . . 84
4.3.Masonryofearthblocks. . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.Stoneblocksandmortars. . . . . . . . . . . . . . . . . . . . . . . 85
4.5.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
PART2.GRAPHICSTATICS . . . . . . . . . . . . . . . . . . . . . . . . . . 91
CHAPTER5.THEFOUNDATIONSOFGRAPHICSTATICS . . . . . . . . . 93
5.1.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2.Conceptsandprinciplesofstatics. . . . . . . . . . . . . . . . . . 94
5.2.1.Hypothesesandbasicconcepts . . . . . . . . . . . . . . . . . 94
5.2.2.Theprincipleoftheparallelogramofforces . . . . . . . . . 103
5.2.3.Theprincipleofequilibriumanditsconsequences . . . . . 104
5.2.4.Theprincipleofreciprocalactions
(oractionandreaction) . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.3.Layoutplanandforceplan. . . . . . . . . . . . . . . . . . . . . . 110
5.3.1.Layoutplan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.3.2.Forceplan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
CHAPTER6.REDUCTIONANDEQUILIBRIUMOFASYSTEMOF
FORCESINAPLANE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1.Goalsforthereductionofasystemofforces . . . . . . . . . . . 115
6.2.Concurrentforcesintheplane. . . . . . . . . . . . . . . . . . . . 116
6.2.1.Reductionofconcurrentforces . . . . . . . . . . . . . . . . . 116
6.2.2.Equilibriumconditionofnconcurrentforces. . . . . . . . . 119
6.2.3.Decompositionofaforceintoseveral
concurrentforces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2.4.Theoremofthreeforces . . . . . . . . . . . . . . . . . . . . . 124
6.3.Arbitraryforcesinaplane . . . . . . . . . . . . . . . . . . . . . . 125
6.3.1.Methodofsuccessiveapplicationsofthetheorem
oftheparallelogramofforces. . . . . . . . . . . . . . . . . . . . . . 125
6.3.2.Resultantcouple. . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.3.3.Equilibriumconditionofnarbitraryforces. . . . . . . . . . 128
6.4.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
viii SustainableMasonry
CHAPTER7.FUNICULARPOLYGONS. . . . . . . . . . . . . . . . . . . . . 131
7.1.Reductionofasystemofparallelforces . . . . . . . . . . . . . . 131
7.1.1.Reductionbyaddingtwodirectlyopposingforces. . . . . . 131
7.1.2.Reductionbydecompositionofforcesusingapoleand
constructionofthefunicularpolygon . . . . . . . . . . . . . . . . . 133
7.2.Funicularpolygonofasystemofnarbitraryforces . . . . . . . 137
7.3.Propertiesoffunicularpolygons. . . . . . . . . . . . . . . . . . . 141
7.3.1.Funicularpolygonsofsubsystemsofforces . . . . . . . . . 141
7.3.2.Funicularpolygonthroughtwoapriorifixedpoints . . . . 142
7.3.3.Relationshipbetweenfunicularpolygons
constructedfromtwodistinctpoles . . . . . . . . . . . . . . . . . . 144
7.4.Applyingthepropertiesoffunicularpolygons . . . . . . . . . . 148
7.4.1.Relationshipsbetweenatensedcableand
compressedarc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.4.2.Conditiononthemagnitudeofforces . . . . . . . . . . . . . 150
7.4.3.Passageofafunicularthroughthreepoints. . . . . . . . . . 152
7.5.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
CHAPTER8.PROJECTIVEPROPERTIESANDDUALITY. . . . . . . . . . 155
8.1.Projectivepropertiesandgraphicstatics . . . . . . . . . . . . . . 155
8.1.1.TheDesarguestheoremandequilibriumof
threeforces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.1.2.Steiner’stheoremandequilibriumofnforces . . . . . . . . 161
8.1.3.Scopeofgeometricpropertiesinconstructions
usinggraphicstatics . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.2.Reciprocalfiguresandprojectionsofpolyhedra . . . . . . . . . 165
8.2.1.Reciprocalplanefigures . . . . . . . . . . . . . . . . . . . . . 165
8.2.2.Reciprocalfiguresseenasprojectionsofpolyhedra. . . . . 169
8.3.Dualityingraphicstatics . . . . . . . . . . . . . . . . . . . . . . . 176
8.3.1.Interpretationofreciprocalfiguresinthecaseof
reticulatedstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.3.2.Reciprocalfiguresandfunicularpolygons . . . . . . . . . . 178
8.3.3.Applicationinthesearchfortensileplanar
structureshapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.3.4.Searchforsupportreactionsofasolid. . . . . . . . . . . . . 184
8.3.5.Applicationtothecalculationofreticulated
structuresloadedatthenodes. . . . . . . . . . . . . . . . . . . . . . 187
8.4.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Contents ix
PART3.YIELDDESIGNAPPLIEDTOMASONRY. . . . . . . . . . . . . . 191
CHAPTER9.PRINCIPLESOFYIELDDESIGN . . . . . . . . . . . . . . . . 193
9.1.Objectiveandpositionoftheyielddesignproblem . . . . . . . 193
9.2.Potentialstabilityandpotentiallybearableloads . . . . . . . . . 194
9.2.1.Notionofpotentialstability,domainof
potentiallybearableloadsandextremeloads. . . . . . . . . . . . . 194
9.2.2.Potentiallybearableloadsinareticulatedstructure . . . . . 196
9.3.SearchfordomainKofpotentiallybearableloads. . . . . . . . 198
9.3.1.Staticapproachfromtheinside. . . . . . . . . . . . . . . . . 198
9.3.2.Staticapproachfromtheoutside . . . . . . . . . . . . . . . . 199
9.3.3.Kinematicapproachfromtheoutside . . . . . . . . . . . . . 200
9.4.Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
CHAPTER10.STABILITYOFCURVILINEARMASONRY. . . . . . . . . . 203
10.1.Yielddesignappliedtoplanarcurvilinearmasonry. . . . . . . 203
10.1.1.Geometricdefinitionofplanarcurvilinearmasonry. . . . 204
10.1.2.Strengthcriteria . . . . . . . . . . . . . . . . . . . . . . . . . 207
10.1.3.Strengthcriteriaexpressedintermsof
generalizedstresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
10.1.4.Yielddesignandlimitanalysis . . . . . . . . . . . . . . . . 217
10.2.Lineofthrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
10.2.1.Definitionofalineofthrust . . . . . . . . . . . . . . . . . . 220
10.2.2.Systemswithonesupport:exampleofcorbelled
stacksundertheirownweight . . . . . . . . . . . . . . . . . . . . . 223
10.2.3.Systemswithtwosupports:exampleofthe
semi-circulararchunderitsownweight . . . . . . . . . . . . . . . 227
10.2.4.Extremelinesofthrust,jointsand
associatedmechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . 234
10.2.5.Minimumthicknessandgeometricfactorofsafety . . . . 236
10.2.6.Dimensionalsimilitude. . . . . . . . . . . . . . . . . . . . . 237
10.3.Constructionoflinesofthrustingraphicstatics. . . . . . . . . 241
10.3.1.Constructionoflinesofthrustusing
funicularpolygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
10.3.2.Parametricstudyofthesemi-circular
archandpointedarchesundertheirownweight. . . . . . . . . . . 248
10.3.3.Caseofanearthquake:quasi-staticapproach. . . . . . . . 252
10.3.4.Pseudo3Dstudyofarchesordomes. . . . . . . . . . . . . 252
x SustainableMasonry
10.4.Numericalmethodsfortheconstructionoflinesofthrust. . . 253
10.4.1.Forcenetworkmethod. . . . . . . . . . . . . . . . . . . . . . 253
10.4.2.Complexsystems. . . . . . . . . . . . . . . . . . . . . . . . . 256
10.5.Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
CHAPTER11.HOMOGENIZATIONANDYIELD DESIGN
OFMASONRY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
11.1.2Dunderstandingofmasonrywalls. . . . . . . . . . . . . . . . 262
11.2.2DmodeldevelopedbyDeBuhanandDeFelice . . . . . . . 264
11.3.Applicationtostructuresunderplanestress . . . . . . . . . . . 268
11.4.Applicationtostructuresunderplanestrain . . . . . . . . . . . 271
11.4.1.Retainingwalls. . . . . . . . . . . . . . . . . . . . . . . . . . 271
11.4.2.Masonrydams . . . . . . . . . . . . . . . . . . . . . . . . . . 272
11.4.3.Mixedrockfillandmasonrydams. . . . . . . . . . . . . . . 273
11.5.Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
11.6.Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
CONCLUSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
Preface
This book is the result of the meeting of two complementary approaches
tothesamesubject:masonry.ThefirstistheapproachdevelopedbyThierry
Ciblac at the Ecole Nationale Supérieure d’Architecture de Paris la Villette
(National School of Architecture of Paris La Villette), which revisits
historical design methods using digital tools. The second consists of studies
led by Jean-Claude Morel at the Ecole Nationale des Travaux Publics de
l’Etat (National Civil Engineering School), which are based on experiments
with masonry structures of earth materials. The convergence of these two
approachesoccursthroughthecommonuseofthetheoryofyielddesign.
This book was written to promote understanding of the mechanical
stability of masonry structures in a contemporary context and to introduce it
to the readers. This approach will allow contractors to carry out diagnostics
onexistingheritageandtodesignnewstructures.
The challenges presented by sustainability criteria have provided – or
restored – respectability to masonry constructions using earth materials. The
latest research in this area has been formalized by putting it into perspective
with historical approaches. This is done with the dual purpose of making
design methods used for old structures (mostly from the eighteenth century)
more accessible and providing “simple” tools for understanding their
behavior. In particular, developments relative to graphic statics, take on new
educationalanddemonstrativevalueswiththeuseofdigitaltools.
WewishtothankNoëlChallamelforproposingtheideaforthisbook,for
hisdetailedproof-readingofthemanuscriptandforhisvaluableadvice.
