Pont du Gard

Presented by Group 4: Cassandra Pruefer, Steven Kreeley, Robert Capece, Jesse Chladil, Grigorios Papadourakis

What and Where Is It?

• Roman aqueduct built in 1st Century A.D.

• Located in southern France

• Once supplied water to the city of Nimes from a spring in Uzes

• Spans the Gardon River

Strength and Serviceability • Many structural modifications

throughout history either reinforced or impaired the Pont du Gard

• Built in 3 years (very fast for the time) and with no mortar

• Restored as a monument in 1855

• Despite renovations, the Pont du Gard still continues to tilt upstream

• Three tiers of arches made of unreinforced masonry (yellow limestone)

• Pier thickness: Arch span = 1:5

• Arches purposely varied to prevent subsidence

• Aqueduct in form of specus to allow for ease of water flow and alleviate water pressure on the top tier

Structural Form

Dimension 1st Tier 2nd Tier 3rd Tier

Length (ft) 456.0 797.2 885.8

Height (ft) 71.8 64.0 24.3

Width (ft) 20.9 15.0 10.0

Number of Arches 6 11 35

Average Arch Span (ft) 65.6 65.6 15.7

Average Tier Width (ft) 14.9 14.9 10.2

Width of Voussoirs (ft) 5.2 5.0

Foundation

• Pont du Gard was built directly into surrounding rock on either side of river

• While no subsurface information could be found with respect to the Pont du Gard, it is inferred that the foundation rests on bedrock

Load Carrying Mechanism/Load Path

• Major structural element is the arch, transforms vertical loads into both horizontal AND vertical loads

• Any force applied to the top of the arch will follow the curvature of its components to maximize compression, minimize tension, and remain intact through self-weight.

• Components of an arch: keystone, voussoirs and two springers

• Load path process repeats from tier to tier

• Top is lightest; bottom is heaviest (designed this way for load carrying purposes)

Geometric Model • Helped conceptualize the Pont du Gard’s structural form and aid

construction of the physical model

• Main issue- incongruous dimensions between multiple sources • Eventually idealized based on common sense and culmination of many sources

• Idealization and simplification regarding the location of structure on the hillside

Simulation Model (Preliminary Analysis) • Both shell and solid elements were compared to determine which should be used in the

construction of the simulation model

• Solid elements chosen since load could effectively be applied to an area as opposed to linearly distributed load for shell elements

• Determined that the solid elements accurately modeled the deformation of an arch under load

Solid Elements

Shell Elements

Simulation Model (Simplifications and Idealizations) • Assumed fixed supports on the foundation in order to restrict lateral movement and rotation

• Portion of structure spanning river chosen for the model due to unknown information about the hillside, redundancy in structure, and capability of software

• Surrounding sides of chosen portion lined with area springs to account for arches on either side

Construction of the Simulation Model • 3 tiers = 3 layers in AutoCAD → imported into SAP 2000 → thin-shells made via Poly-Area →

divided into mesh → extruded to solids

• Fixed supports assigned to bottom joints on the first arcade

• Area springs attached to east-west ends to simulate lateral pressure from other arches and surrounding mountains

• Solid surface pressure option chosen to apply wind, pedestrian, water, and earthquake loads

Area Springs Fixed Support

Load Cases/Combinations

• Dead load of structure, wind load, pedestrian live load, weight of water determined

• Nimes, France used as location for climate (rain, snow, ice, floods negligible)

• ASCE 7 used for wind load since Eurocode lacked information (southern California winds used due to similarity)

Load Cases/Combinations Combinations employed ASCE 7- 05 Factored Loads for Strength Design • Case 1: 1.4 (Dead) • Case 2: 1.2(Dead) + 1.6(Pedestrian) • Case 2a with water load: 1.2(Dead) + 1.6(Pedestrian) + 1.6(Water) • Case 3: 1.2(Dead) + 0.8(Wind) • Case 4: 1.2(Dead) + 1.6(Wind) + 1.0(Pedestrian) • Case 4a with water load: 1.2(Dead) + 1.6(Wind) + 1.0(Pedestrian) +

1.0(Water) • Case 5: 0.9(Dead) + 1.6(Wind) • Case 6: 1.2(Dead) + 1.0(Earthquake) + 1.0(Live) • Case 7: 0.9(Dead) + 1.0(Earthquake)

Simulation Model Analysis

• The analysis of the original structure yielded three results for each load case: • Stress Contour Diagram

• Deformation Diagram

• Displacement/Stress Value Tables

• The majority of the structure accurately exhibited compression

• Localized tension “hotspots” appeared underneath the supports of the middle arcade • Attributed to the boundary conditions, complexity of the model, and

inexperience with the modeling software

Analysis Results

Deformation Diagram for Pedestrian Load

Analysis Results

S33 Stress Contour Diagram for Pedestrian Load

Analysis Results Element Stress Table

Joint Displacement Table

Structure Redesign • Overall dimensions and properties of structure kept the same…but extruded at half thickness

• Purpose was to show if Romans could have used less material while still keeping the same structural properties

• Structure did not fail- expected, all stresses and deformations were greater

WHOLE HALF

Physical Model • Represents scaled conceptualization

• Simulates load carrying mechanisms mentioned in Load Carrying Mechanism/Load Path slide

Physical Model • Based largely off simulation model, dimensions used from geometric model

• Scale of 1:10 used to ensure that model would not exceed 3 feet

• Physical model also includes boundary conditions to represent area springs and fixed supports

Conclusion

• Realization that the structure is greatly overdesigned; stresses less than 1500 psi

• Structure could have been built with less material

• Importance of creating several models in order to understand the structure’s response to loads

• Modeling process requires many idealizations and simplifications; is an art form, not a science

• Possible future analysis: comparison of materials, comparison between shell and solid, comparison of different finite element analysis software

Questions?