CONCRETE VAULTING IN IMPERIAL ROME A …rlp/RomanStructuresPresentations/CornellOct... · 30 Oct 2008 R.Perucchio 1 ... • Prof. Cairoli F. Giuliani, ... Opus Caementicium - Cross

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



• 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



•The Monuments•Opus Caementicium•Collapse Mechanism•The Vault of the Great Hall•The Vault of the Frigidarium

Outline



PONT DU GARD - Nîmes (19 BC ?)

OPUS QUADRATUM



Sanctuary Fortuna Primigenia Praeneste (80 BC ?)

OPUS CAEMENTICIUM



Sanctuary Fortuna Primigenia Praeneste (80 BC ?)

OPUS CAEMENTICIUM



Markets ofTrajans -

Grande Aula(Great Hall)

(AD 107-110)



Markets ofTrajans -

Grande Aula



Grande Aula -Interior



Grande Aula -Contrasting Arches



Baths of Diocletian (AD 298-305)



Baths of Diocletian - Frigidarium



Frigidarium -Interior



Frigidarium - Vault



Frigidarium - Contrasting Arches



FrigidariumGrande Aula

Dimensions in meters

comparativegeometrical models



Dimensions in meters

comparativegeometrical models

FrigidariumGrande Aula



vault longitudinal axis

Frigidarium/Grande AulaStructural Skeleton

contrasting walls

contrasting arches



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.



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.



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.



Opus Caementicium - FrameworksFrigidarium

Grande Aula



accurate CADreconstruction

Finite Elementmodels

Static anddynamicanalysis,deformationsand stresses

Structural Analysis - Grande Aula



Structural Analysis - Frigidarium



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



Elastic deformation of concretevault under gravitational load

Infinitesimal deformations(mm over 10m span)

Opus Caementicium - Cross Vaulting Carried by PiersCollapse Mechanism



compression

tension

Bending deformation at thecrown of the vault

Extrados in compression

Tension at the intrados




Relative motion of the supporting blocks(travertine) increases downwarddeformations and tensions at the crown




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)




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




monolitic vaultstructural skeleton (contrastingwalls

contrasting archessupporting blocks(travertine)

Grande Aula - Structural System



Grande Aula - Finite Element Models



• Tensions at theintrados of the vaultcrown

Grande Aula - Fracture of the Vault

• Support conditions(blocks) affecttractions

a) Sliding of blocks

b) Blocks rigidlyconnected



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



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



+-

• 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



Contrasting Arch vs Shear Wall



• The expected function of the contrasting arch is to preventthe wall - and the vault - from rotating outward


• Under gravitational load the vault rotates inward andpulls down the arch (no contrasting action!)

Expected lateral force from vault Actual force transmitted by vault




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



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



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



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)



Grande Aula - Conclusions

Flavian amphitheater - Rome



Frigidarium




position of arch inGrande Aula position of arch in

Frigidarium

Contrasting arch positioned closer to impost of crossvault, on top of shear wall



Basilica of Maxentius

Frigidarium - Supporting Blocks

position of arch inFrigidarium

Blocks fully embedded (and constrained) in theshear wall

position of blocksin Grande Aula



Frigidarium - Vault ExtradosGable extrados follows the contour of the vaultintrados with substantial weight reduction

vault extradosFrigidarium

vault extradosGrande Aula



Frigidarium - Finite Element Models



• The thickness of the vault is unknown. Models useeither 1.8m (3 bipedales bricks) or 1.2m (2 bipedales).

Frigidarium - Finite Element Models



3 bipedale thick:

• Non uniform downward deformation along the crown

Frigidarium - Deformed Shape

• Max. deformation = 8 mm.



• Max. principal stresses at the intrados (3 bip. thick)Frigidarium - Stresses

• Max. tensile stresses below 0.2 MPa (fracture at 0.45MPa)



• Max principal stresses at the intradosFrigidarium - Vault Thickness

3 bipedale thick

2 bipedale thick

• Max. stressesreduced by 15%



• Finite Element model with shear wall but withoutcontrasting arch




• Max. principal stresses at the intrados (3 bipedale thick)Frigidarium - Contrasting Arches

With contrasting arches

Withoutcontrastingarches

Max. stresses 30%higher ( lowerthan 0.26MPa)



• Finite Element model without contrasting (shear) wallsFrigidarium - Contrasting Walls

• Uniform deformationat the crown (32 mm.!)

• With walls andcontrasting archesmax. defor. = 8 mm.



• Max principal streses without contrasting wallsFrigidarium - Contrasting Walls

• Tensile stresses (max. 1.8 Mpa) above fracture level.VAULT COLLAPSE!



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



• Blocks cannot develop relative motions because they arefully constrained within the opus caementicium wall


• 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



• The lowering of the contrasting arches allows reshapingthe vault extrados


• The removal of material (concrete) from the extradosreduces the static load on the vault



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.



ROMAN STRUCTURES

• 3-week summer program in Italy since 2003open to all undergraduates

• Engineering and social structures in ImperialRome

U Rochester Programs



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







Roman Structures 2006



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CONCRETE VAULTING IN IMPERIAL ROME A …rlp/RomanStructuresPresentations/CornellOct... · 30 Oct 2008 R.Perucchio 1 ... • Prof. Cairoli F. Giuliani, ... Opus Caementicium - Cross