30 Oct 2008 R.Perucchio 1
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
CONCRETE VAULTING INIMPERIAL ROME
A Structural Analysis of the GreatHall of Trajan’s Markets
Prof. Renato Perucchio University of Rochester - Department of Mechanical Engineering
Cornell University - Civil and Environmental EngineeringCivil Infrastructure Seminar - 30 October 2008
30 Oct 2008 R.Perucchio 2
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Prof. Cairoli F. Giuliani, “La Sapienza”• Dott. Lucrezia Ungaro e Massimo Vitti,
Museo dei Fori Imperiali• Prof. Alessandro Samuelli Ferretti,
“La Sapienza”• Philip Brune, University of Rochester
Acknowledgements
30 Oct 2008 R.Perucchio 3
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
•The Monuments•Opus Caementicium•Collapse Mechanism•The Vault of the Great Hall•The Vault of the Frigidarium
Outline
30 Oct 2008 R.Perucchio 4
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
PONT DU GARD - Nîmes (19 BC ?)
OPUS QUADRATUM
30 Oct 2008 R.Perucchio 5
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Sanctuary Fortuna Primigenia Praeneste (80 BC ?)
OPUS CAEMENTICIUM
30 Oct 2008 R.Perucchio 6
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Sanctuary Fortuna Primigenia Praeneste (80 BC ?)
OPUS CAEMENTICIUM
30 Oct 2008 R.Perucchio 7
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Markets ofTrajans -
Grande Aula(Great Hall)
(AD 107-110)
30 Oct 2008 R.Perucchio 8
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Markets ofTrajans -
Grande Aula
30 Oct 2008 R.Perucchio 10
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula -Contrasting Arches
30 Oct 2008 R.Perucchio 11
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Baths of Diocletian (AD 298-305)
30 Oct 2008 R.Perucchio 12
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Baths of Diocletian - Frigidarium
30 Oct 2008 R.Perucchio 13
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Frigidarium -Interior
30 Oct 2008 R.Perucchio 15
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Frigidarium - Contrasting Arches
30 Oct 2008 R.Perucchio 16
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
FrigidariumGrande Aula
Dimensions in meters
comparativegeometrical models
30 Oct 2008 R.Perucchio 17
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Dimensions in meters
comparativegeometrical models
FrigidariumGrande Aula
30 Oct 2008 R.Perucchio 18
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
vault longitudinal axis
Frigidarium/Grande AulaStructural Skeleton
contrasting walls
contrasting arches
30 Oct 2008 R.Perucchio 19
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Roman Concrete (opus caementicium)LIME + POZZOLAN + WATER + AGGREGATE• Burning travertine (limestone) ==> QUICKLIME (calx)• Volcanic ash ==> POZZOLAN (pulvis puteolanus)• tuf, travertine, basalt, or brick fragments ==>
AGGREGATE (caementa)
PREPARATION• Slaked lime and pozzolan are mixed with water to form
mortar (excellent cementing agent).• Layer of aggregate is placed over mortar in a wooden
form.• Mortar is tamped into form.• Concrete hardens and form is removed.
30 Oct 2008 R.Perucchio 20
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Mechanical Properties
opuscaementicium 0,45 6,0 3000 1,5
Strength intension[MPa]
Strength incompres.[MPa]
Moduluselasticity[MPa]
Density[t/m3]
pozzolanicconcrete 4,0 65,0 34000 2,3
Experimental data• for opus caementicium by A. Samuelli Ferretti (analysis of Basilica ofMaxentius)• for modern pozzolanic concrete with light aggregate from TokioUniversity database.
30 Oct 2008 R.Perucchio 21
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Roman Concrete (opus caementicium)ADVANTAGES• Good strength in compression.• Lighter than stone or brick.• Can be formed into complex 3D shapes (domes, vaults).• Less expensive than stone or brick.• Can be used under water (hydraulic cement).
OUTSTANDING STRUCTURAL MATERIAL
DISADVANTAGES• Small strength in tension (but not zero).• Requires (long) curing time.• Must be protected from atmospheric agents (brick or tile facing).• Domes and vaults require complex and expensive frameworks.
30 Oct 2008 R.Perucchio 22
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Opus Caementicium - FrameworksFrigidarium
Grande Aula
30 Oct 2008 R.Perucchio 23
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
accurate CADreconstruction
Finite Elementmodels
Static anddynamicanalysis,deformationsand stresses
Structural Analysis - Grande Aula
30 Oct 2008 R.Perucchio 24
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Structural Analysis - Frigidarium
30 Oct 2008 R.Perucchio 25
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Model assumes identical linear elastic behavior incompression and tension
Appropriate for STATIC ANALYSIS:-- can predict the onset of critical stress state-- but cannot follow the evolution of critical state to
collapse
Limited applicability for DYNAMIC ANALYSIS:-- applicable to modal extraction (natural
frequencies)-- not applicable to advanced earthquake analysis
Not applicable for VISCOPLASTIC ANALYSIS-- cannot model mortar before curing-- cannot analyze stress state during construction
Opus Caementicium - Material Characterization
30 Oct 2008 R.Perucchio 26
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Elastic deformation of concretevault under gravitational load
Infinitesimal deformations(mm over 10m span)
Opus Caementicium - Cross Vaulting Carried by PiersCollapse Mechanism
30 Oct 2008 R.Perucchio 27
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
compression
tension
Bending deformation at thecrown of the vault
Extrados in compression
Tension at the intrados
Opus Caementicium - Cross Vaulting Carried by PiersCollapse Mechanism
30 Oct 2008 R.Perucchio 28
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Relative motion of the supporting blocks(travertine) increases downwarddeformations and tensions at the crown
Opus Caementicium - Cross Vaulting Carried by PiersCollapse Mechanism
30 Oct 2008 R.Perucchio 29
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
concrete block
fracture plane
highest tension
Tensions (or compressions)higher than concrete ultimatestress will fracture the material
Fracture due to tensile stresspropagates on planeorthogonal to the direction ofhighest tension
Presence and orientation oflarge aggregate affects crackpropagation (direction and rateof growth)
Opus Caementicium - Cross Vaulting Carried by PiersCollapse Mechanism
30 Oct 2008 R.Perucchio 30
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Fractures weaken the structure byreducing the load paths, changingthe static and dynamic behavior
Functionality may be compromised
Fractures may lead to catastrophiccollapse
Since macroscopic fractures aredetectable to the naked eye, theymay provide feedback to thestructural designer
The mechanics of fracture in opuscaementicium is unknown
Hadrian’s Villa - Small Baths
Opus Caementicium - Cross Vaulting Carried by PiersCollapse Mechanism
30 Oct 2008 R.Perucchio 31
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
monolitic vaultstructural skeleton (contrastingwalls
contrasting archessupporting blocks(travertine)
Grande Aula - Structural System
30 Oct 2008 R.Perucchio 32
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula - Finite Element Models
30 Oct 2008 R.Perucchio 33
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Tensions at theintrados of the vaultcrown
Grande Aula - Fracture of the Vault
• Support conditions(blocks) affecttractions
a) Sliding of blocks
b) Blocks rigidlyconnected
30 Oct 2008 R.Perucchio 34
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula - Fracture of the VaultTensile stresses at theintrados of the vault crown
High tensile stresses maycause a longitudinal crack atthe intrados of the crown
30 Oct 2008 R.Perucchio 35
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Excellent correlationsbetween tensile stresses(model) and repaired cracks(reality)
Grande Aula -present restoredstate - 2007
Similar fracture patterns onthe lateral vaults
Grande Aula - Fracture of the Vault
Grande Aula-as revealedin 1926 -1934
30 Oct 2008 R.Perucchio 36
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
+-
• Contrasting arch does not affect stresses (tensions) at thecrown of the vault (under static loading)
Grande Aula - Contrasting Arches
• Removing the arch has only a local effect on stressdistribution
30 Oct 2008 R.Perucchio 37
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Contrasting Arch vs Shear Wall
30 Oct 2008 R.Perucchio 38
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• The expected function of the contrasting arch is to preventthe wall - and the vault - from rotating outward
Grande Aula - Contrasting Arches
• Under gravitational load the vault rotates inward andpulls down the arch (no contrasting action!)
Expected lateral force from vault Actual force transmitted by vault
30 Oct 2008 R.Perucchio 39
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula - Contrasting Arches
Grande Aula:stato attuale(2005)
Computed stress fields show high tensile stresses at the attachments of the arch
Fractures at the arch springing and evidence of major reconstruction are visible onthe actual arches
30 Oct 2008 R.Perucchio 40
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula - Motions of the Blocks
• Relative motions of the supporting blocks affect stressesat the crown in a critical manner
Blocks rigidly connected Blocks free to move
30 Oct 2008 R.Perucchio 41
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula - Motions of the Blocks
• Evidence suggests that clamps wereintended to prevent the inwardrotation of the blocks
• Signs of dovetail clamps (Roman?) on all blocks• Blocks are damaged near clamps’ placement
30 Oct 2008 R.Perucchio 42
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula - Conclusions• The Grande Aula is an early cross-vault design in
opus caementicium derived from previous buildingpractices (with different materials?)
• This design is not adequate (produces structuralfailures) for larger scale cross-vaults (such as theFrigidarium)
• The analysis and the correction of the structuraldeficiencies revealed by the Grande Aula providedthe basis for a new (and mature) cross-vaultingdesign (Frigidarium)
30 Oct 2008 R.Perucchio 43
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Grande Aula - Conclusions
Flavian amphitheater - Rome
30 Oct 2008 R.Perucchio 45
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Frigidarium - Contrasting Arches
position of arch inGrande Aula position of arch in
Frigidarium
Contrasting arch positioned closer to impost of crossvault, on top of shear wall
30 Oct 2008 R.Perucchio 46
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Basilica of Maxentius
Frigidarium - Supporting Blocks
position of arch inFrigidarium
Blocks fully embedded (and constrained) in theshear wall
position of blocksin Grande Aula
30 Oct 2008 R.Perucchio 47
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Frigidarium - Vault ExtradosGable extrados follows the contour of the vaultintrados with substantial weight reduction
vault extradosFrigidarium
vault extradosGrande Aula
30 Oct 2008 R.Perucchio 48
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Frigidarium - Finite Element Models
30 Oct 2008 R.Perucchio 49
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• The thickness of the vault is unknown. Models useeither 1.8m (3 bipedales bricks) or 1.2m (2 bipedales).
Frigidarium - Finite Element Models
30 Oct 2008 R.Perucchio 50
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
3 bipedale thick:
• Non uniform downward deformation along the crown
Frigidarium - Deformed Shape
• Max. deformation = 8 mm.
30 Oct 2008 R.Perucchio 51
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Max. principal stresses at the intrados (3 bip. thick)Frigidarium - Stresses
• Max. tensile stresses below 0.2 MPa (fracture at 0.45MPa)
30 Oct 2008 R.Perucchio 52
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Max principal stresses at the intradosFrigidarium - Vault Thickness
3 bipedale thick
2 bipedale thick
• Max. stressesreduced by 15%
30 Oct 2008 R.Perucchio 53
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Finite Element model with shear wall but withoutcontrasting arch
Frigidarium - Contrasting Arches
30 Oct 2008 R.Perucchio 54
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Max. principal stresses at the intrados (3 bipedale thick)Frigidarium - Contrasting Arches
With contrasting arches
Withoutcontrastingarches
Max. stresses 30%higher ( lowerthan 0.26MPa)
30 Oct 2008 R.Perucchio 55
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Finite Element model without contrasting (shear) wallsFrigidarium - Contrasting Walls
• Uniform deformationat the crown (32 mm.!)
• With walls andcontrasting archesmax. defor. = 8 mm.
30 Oct 2008 R.Perucchio 56
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Max principal streses without contrasting wallsFrigidarium - Contrasting Walls
• Tensile stresses (max. 1.8 Mpa) above fracture level.VAULT COLLAPSE!
30 Oct 2008 R.Perucchio 57
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Contrasting arches have structural role (30% lower tensilestresses at the intrados)
Frigidarium - Summary
In the Grande Aula the contribution of thearches is irrelevant
WITHARCHES
WITHOUTARCHES
30 Oct 2008 R.Perucchio 58
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• Blocks cannot develop relative motions because they arefully constrained within the opus caementicium wall
Frigidarium - Summary
• In the Grande Aula the relative motion of the blocks affectsthe stresses in the vault in a critical manner.
• Vault stresses are not affected by motions of the blocks
30 Oct 2008 R.Perucchio 59
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
• The lowering of the contrasting arches allows reshapingthe vault extrados
Frigidarium - Summary
• The removal of material (concrete) from the extradosreduces the static load on the vault
30 Oct 2008 R.Perucchio 60
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Conclusions• The structural design of the vault of the Frigidarium
evolved from the design of the Grande Aula.
• The genealogy is evident in the use of contrastingwalls, contrasting arches, and supporting blocks.
• The evolutionary character is shown by therepositioning of the arches, the constraining of theblocks, and the higher elevation of the contrastingwalls.
• The success of this new design (structurally andfunctionally intact after 17 centuries) indicates the levelof maturity achieved by Roman structural engineering.
30 Oct 2008 R.Perucchio 61
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
ROMAN STRUCTURES
• 3-week summer program in Italy since 2003open to all undergraduates
• Engineering and social structures in ImperialRome
U Rochester Programs
30 Oct 2008 R.Perucchio 62
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
ARCHITECTURE ENGINEERING ANDARCHAEOLOGY : From Antiquity to the Pre-IndustrialWorld
• Undergraduate (major/minor)interdisciplinaryprogram
• Mech.Eng.+Art History+Rel. & Classics+History(20-30 faculty)
• Signature program (UR 2007 strategic plan)
• Inaugurated Fall 2008
U Rochester Programs
30 Oct 2008 R.Perucchio 64
PROGRAM IN ARCHAEOLOGY ENGINEERING AND ARCHITECTURE
Roman Structures 2006