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significant structures of the past

HISTORICSTRUCTURES

Dr. Sez Atamturktur serves as anassistant professor in the GlennDepartment of Civil Engineeringat Clemson University. Priorto joining Clemson University,she served as LV technical staffmember at Los Alamos NationalLaboratory. Dr. Atamturktur maybe reached at sez@clemson.eduand further information about

her work can be found atwww.cuideas.org.

Saurabh Prabhu is a graduatestudent in the Glenn Departmentof Civil Engineering at ClemsonUniversity. Mr. Prabhu may bereached at saurabp@clemson.edu.

By Sez Atamturktur, Ph.D. andSaurabh Prabhu

Simulation-Based

Structural Analysis of

Fort Sumter Considering

Foundation Settlement

Modeling of Historic Structures

With the invention ofmid-19thcentury naval

weaponry, coastal forti-fications in the United

States were rendered obsolete as they losttheir functional use of defense. More than100 coastal forts, now over a century old,are considered national heritage structuresto be preserved for future generations.

Many of these brick masonry forts haveincurred structural damage during bom-bardments, and further accumulateddamage due to the harsh environmentsin which they were constructed.Tere exist no guidelines, however, to

assist stewards in the safeguarding of thesehistorically significant masonry fortifica-tions. Terefore, a structural engineer musteither rely on modern rules of materialstrength and structural behavior, or try to under-stand the failure mechanisms of the unreinforced

masonry on a more

fundamental level.An understandingof unreinforcedmasonry can beachieved through

a combination of experimental and numericalstudies by gaining insights into macro-levelstrength-deformation behavior and micro-leveldefects and crack growth of masonry structures.While uncertainties and errors inevitably arise inthe development of such numerical models, experi-ments can ultimately reduce such uncertainties anderrors in predictions.

Fort Sumter National Monument

Fort Sumter, in Charleston harbor, SC, is a 19thcentury brick masonry coastal fortification.Declared a national monument in 1948, it isbest known as the site where the first shots of theAmerican Civil War were fired in 1861. Accordingto archival documents, construction began in1829 with the foundation, a man-made islandfilled with nearly ten thousand tons of graniteand over sixty thousand tons of assorted rocksand aggregate. By 1860, the pentagonal-shaped

structure (Figure 1a) rose nearly 50 feet high,with three tiers built with locally made bricksand Rosendale mortar. After several devastat-ing bombardments between 1861 and 1865 andreconstruction efforts lasting into the early 20th

century, only the lower first tier of the originalfort stands with major portions reconstructed.Te walls are made up of barrel vaulted casemates(Figures 1band 1c) that once held guns and artil-lery. Each casemate has a gun embrasure openingin the exterior scarp wall allowing artillery to firefrom the fort in all directions. Te scarp wall,is adjacent to the casemate piers and vault, but

the masonry is not continuous at the interface,thus forming a cold joint. Tis design is typicalof Tird System coastal fortifications in North

America, as it served as a method of isolatingthe impact damage from enemy artillery on theouter walls.In this article, we investigate the behavior of

this structure under various foundation settle-ment scenarios.

Finite Element Model

Development

Finite element (FE) analysis is a widely acceptedmethod for analyzing historic masonry structuresdue to its ability to model complex geometric

3-dimensional shapes and resolve nonlinear andanisotropic material behavior.In the nonlinear analysis of masonry behavior,

to represent an appropriate failure criterion formasonry, the elastic modulus, cracking strengthand crushing strength of the homogenizedassembly must be defined. Tis modeling step istypically when the majority of uncertainties areintroduced, due in part to our lack of knowledge(known as epistemic uncertainty) and in part tothe natural variability of the material (known asaleatory uncertainty). Any laboratory tests or onsite evaluations of material characteristics would

help reduce the epistemic uncertainties, while thealeatoric uncertainty (such as the spatial variabil-ity of masonry) inevitably remains in the modelpredictions.During our studies on Fort Sumter, a prism

sample along with 2.5-inch diameter coredsamples were obtained on site (Figure 2, page

28). Te compressive strength and modulus ofelasticity were determined according to ASMstandard tests parallel and perpendicular to themortar bed joints. Te tensile strengths of thebrick and mortar samples are determined viathree-point flexural tests. Te tensile capacity

Figure 1: Te current state of Fort Sumter National Monument:(a) aerial view, (b) barrel vaulted casemates, and (c) degradationof brick and mortar piers.

continued on page 28

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of the brick-mortar assembly is taken as thevolumetric average of a representative cell.Te properties of the tabby concrete infill aredetermined via diametral tests on the coredsamples. Lastly, the densities of the materials

are measured by taking a ratio of weight tovolume of the specimen.Historic masonry monuments are typically

a complex network of curved elements suchas arches, vaults, domes, and buttresses withstraight elements such as piers and walls. Somestructural elements may also contain decora-tive moldings, surface texture or damage suchas minor chipping, etc., making it difficult toreproduce the geometry in a numerical model.Such details can unnecessarily increase themodel complexity and, thus, the computa-tional demand. Te fundamental principle

in geometric modeling must be preservingthe structurally important geometric features,such as cross sectional area, center of gravity,moment of inertia, etc.Over the past 150 years, Fort Sumters

infrastructure has undergone significantand permanent deformations, material deg-radation, and discontinuities due to crackformations. In our study, terrestrial 3-Dlaser scanning with a rimble CX scanner

was implemented to digitally reproduce theforts geometry.A 3-D non-linear FE solid model of one ofthe casemates was developed using ANSYS13.0. Te model geometry was constructedfrom the wireframe models developed usingthe laser scan, and initial material proper-ties were assigned according to the materialtests. In analyzing masonry with the finiteelement approach, the geometric model wasmeshed with specialized elements designedfor brittle materials accounting for crack-ing and crushing according to a predefinedfailure criterion. Te size of the mesh wasdetermined based on the trade-off betweennumerical accuracy and run times. A mesh

size of 0.2 meters typically yields a numeri-cal uncertainty below the variability in thestructures expected response due to envi-ronmental factors (5-6%).In our study, the discontinuous interface

between the scarp wall and vaulted portionof the casemate (Figure 3) was treated as acontact surface and approximated by a fric-tion coefficient. Te coefficient was calibratedaccording to an experimentally measured ratioof displacements on the two sides of the inter-face when an instrumented hammer was usedto impact one side.he casemate foundation was modeled

assuming a linear relationship betweenthe pressure on the foundation and thedeflection, i.e. a Winkler type foundation.hus, a series of vertical and horizontal

linear springs was distributed throughoutthe base of the casemate. he stiffness ofthe springs represented the foundationstiffness, which required calibration to theexperimental data.When developing finite element modelsof large masonry monuments, it is oftennecessary to isolate a portion of the struc-ture. Such an approach, although necessaryto keep the problem to a manageable size,results in unknown restraining forcesbetween the structure of interest and com-ponents that are excluded from the model.o account for these unknown forces, themost computationally efficient approach issubstructuring, which entails approximat-ing the force-displacement relationship ofthe adjacent components through a smallnumber of elements located at the interface.Tese elements are known as superelements,and they significantly reduce computa-tional demands. While modeling one ofthe casemates of Fort Sumter, the adjacentcasemates are represented with superele-ments, effectively reducing the problem toone third (Figure 4).

Calibration of Material

Properties

Calibration refers to the systematic adjust-ment of model input parameters to matchthe solution with experimental observa-tions. Non-destructive vibration tests were

performed to extract the natural frequenciesof the casemate, such that the model inputparameters can be fine-tuned by comparingthe predicted natural frequencies with actualmeasurements. Accelerometers were used tomeasure 30 minutes of ambient vibrationson 41 points on the casemate. Te vibrationresponse of the casemate, recorded in thetime-domain, was post-processed to extractthe first two natural frequencies at 27.48Hertz and 45.2 Hertz.Natural frequencies are linear properties of

the global behavior of the system and, thus,

were used to calibrate material parameters thatdefine linear behavior and boundary condi-tions. For the FE model of the casemate, threeinput parameters were selected for calibration:the elastic modulus of both the barrel vaultand the walls and piers, and the stiffness ofthe foundation springs. Te calibrated inputparameters were obtained such that the FEmodel reproduced the measured natural fre-quencies with 10% accuracy.

Support Settlement Analysis

Four settlement scenarios were consideredwith smoothly varying profiles including sag-ging settlements, pier settlements and tiltingof the ground. Each settlement scenario issimulated with a maximum magnitude of100 mm in increments of 2.5 mm.Scenario 1 (Figure 5) simulated an unsym-

metrical sagging in the north-south direction,including both the scarp wall and piers. Withthis scenario, a significant through crack origi-nating at the base of the scarp wall on thesouth side ran diagonally across the scarpwall. Also, severe cracking at the springing

Figure 2: Coring of material samples revealed thatalthough the construction drawings indicate abrick wall across the width, the construction of the

fort is composite with tabby concrete infill.

Figure 3: Te discontinuity between the scarp walland barrel vaulted casemate isolates the structuraldamage to the scarp wall to prevent the casemate

from collapsing in the event of an attack.

Figure 4: Te finite element model of the casemate isbuilt recognizing the elastic constraints of the adjacentcasemates as well as the unmodeled foundation.

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of the arch on the south-side was observed.Scenario 2 simulated symmetrical saggingunder the casemate in the north-south direc-tion. Tis scenario resulted in a crack thatbegan at the base of the scarp wall at bothends and converged in the center, forming aload bearing arch.Scenario 3 simulated the settlement of the

north piers. Differential settlement of a pier

caused an unsymmetrical cracking of the vaultclose to the pier that has settled, while the pierthat has settled less experienced more damage.Scenario 4 constituted the tilting of the

casemate in the north-south direction. Tisscenario resulted in heavy cracking of thesouth pier, diagonal cracks in the scarp walland a rapidly developing through crack in the

vault. Cracking in the vault must be treatedas an instability condition as the progressionof cracks once initiated in these members wasrather rapid (Figure 6).

Summary

Te computer simulation indicated thatunsymmetrical sagging types of settlements

were characterized by diagonal cracking ofthe scarp wall, originating from the bottomon the less-settled side. Symmetric saggingunder the casemate, however, formed cracksthat originate from the bottom of the scarpwall from both sides and converge at thecenter forming an arch that spans the lengthof the casemate and bears the loads of the wallabove. Cracks due to stress concentrations

were seen for most settlement configurationsat the intersection of structural members,such as the springing of the arches and vaults.Cracking of the vault was observed in configu-

rations that involve differential settlements ofthe piers. Cracks, once formed in the vaults,progressed rapidly without warning as settle-ment increased. Tus, cracking of the actualvault should be taken as a structural stabilityconcern. Te formation and progression ofcracks were observed to be unique to eachsettlement configuration.

By utilizing visual investigations of thesepeculiar early warning signs in the form ofcracks, the stewards of this historic monu-

ment can use these computer simulations tohelp draw conclusions whether settlementmay be causing damage to the structure.Tis of course assumes that the cracks arenot due to external loads, which too canbe incorporated into the numerical model,making simulations a useful tool for historicstructural assessment.

Figure 5: Te four settlement scenariosconsidered in the analysis.

Figure 6: Crack development under the settlementscenarios shown in Figure 5.

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