Foundation Settlement Analysis of Fort Sumter National Monument: Model Development and Predictive Assessment

Engineering Structures 65 (2014) 1–12

Contents lists available at ScienceDirect

Engineering Structures

journal homepage: www.elsevier.com/locate/engstruct

Foundation settlement analysis of Fort Sumter National Monument: Model development and predictive assessment

a a, b a c Saurabh Prabhu , Sez Atamturktur ⇑, Denis Brosnan , Peter Messier , Rick Dorrance a Glenn Department of Civil Engineering, Clemson University, Clemson, SC 29634-0911, United States b Department of Materials Science and Engineering, Clemson University, Clemson, SC, United States c Fort Sumter National Monument, National Park Services, Charleston, SC, United States article info abstract

Article history: This study investigates the mechanisms by which a masonry vaulted structure responds to settlement of Received 16 January 2013 supports considering a wide range of possible settlement scenarios through a numerical model substan- Revised 4 November 2013 tiated with experimental evidence and on-site evaluations. The simulation based investigation of settle- Accepted 27 January 2014 ment induced damage is completed on the Fort Sumter, SC, where the numerical model is developed Available online 26 February 2014 through a multi-faceted approach utilizing ﬁeld investigations including material testing of specimens, three-dimensional laser scanning of fort’s geometry, and dynamic measurements of relative movement Keywords: between adjacent structural components. The poorly known model input parameters are substantiated Coastal fortiﬁcation with comparisons against measured dynamic characteristics of the fort, and the remaining uncertainties Brick masonry Historic monument in the input parameters are propagated to the model output to obtain a probabilistic evaluation of the Nondestructive and semi-destructive fort’s behavior under various settlement scenarios. evaluation Ó 2014 Elsevier Ltd. All rights reserved. Ambient vibration testing Finite element analysis Model calibration Substructuring

1. Introduction For many existing structures, the settlement magnitudes and types that form hinges in the structure and lead to cracking are dif- Differential settlements occur when soil conditions below the ficult to determine through analytical, closed-form-solutions, gi- foundation are inhomogeneous or the load distribution at the ven the structure’s complex geometric configuration and material soil–structure interface is non-uniform. The subsequent angular behavior. Empirical approaches published in literature regarding distortions and tilting of the superstructure disturbs the structure’s the determination of critical settlements have many limitations intended geometry, resulting in the development of tensile stres- such as isolation of settlement-induced damage from other sources ses. These tensile stresses can lead to cracking if the magnitude and lack of exhaustive, quantitative analyses [1–4]. On the other of the tensile stress exceeds the rather small tensile capacity of ma- hand, numerical simulations are identified as effective tools for sonry. Thus, a relatively small magnitude of settlement can lead to analyzing the behavior of masonry structures under any settle- cracking of the masonry assembly. These cracks, if uncontrolled, ment severity and configuration [5–8]. can ultimately lead to sudden hinge formations due to the brittle The major challenge in developing numerical models for his- nature of historic unreinforced masonry, which in turn can result toric masonry is the assignment of accurate input parameters, such in structural instability. Little is known however, about the early as geometry, material properties and boundary conditions [9,10]. warning signs of settlement induced damage to historic masonry This challenge is further magnified in the case of historic monu- structures, which typically are a complex system of arches, vaults, ments that have irregular geometric features with permanent piers and walls. If such warning signs are known, infrastructure deformations, high spatial variability of material properties, and managers could identify when support settlement are the cause uncertain interactions between adjacent components and between of structural distress and take precautionary actions to prevent po- the structure and ground [10–12]. To ensure model predictions are tential structural instability. representative of the actual structural behavior, on-site data must be incorporated to mitigate potential uncertainties and errors in Corresponding author. Tel.: +1 (864) 656 3003; fax: +1 (864) 656 2670. model input parameters [13,14,25]. Accordingly, using a numerical ⇑ E-mail address: [email protected] (S. Atamturktur). approach integrated with experiments, this manuscript presents a http://dx.doi.org/10.1016/j.engstruct.2014.01.041 0141-0296/Ó 2014 Elsevier Ltd. All rights reserved. 2 S. Prabhu et al. / Engineering Structures 65 (2014) 1–12

The walls of the fort, except for the gorge wall, are made up of a series of structures called casemates which once held two tiers of arched gunrooms. The perimeter of the fort is encased by a scarp wall, which has gun embrasures on four sides to allow cannons to fire. Typical of third system coastal fortifications, the barrel vaulted casemates, which hold the cannons, are built adjacent to, but, detached from the scarp wall. This construction detail sepa- rates the scarp wall and the casemate as independent structural entities and keeps any external damage by cannonballs isolated to the scarp wall [16]. During the Civil War, Fort Sumter was bombarded from virtu- ally all sides and left in a state of ‘‘practical demolition’’ [60] (Fig. 2a). After the war, three barbette platforms and 11 lower-tier gunrooms were reconstructed. Originally over 50 ft. tall, the fort’s walls have been reduced to one tier of casemates (Fig. 2b). In 1948, Fort Sumter was declared a national monument and has since been maintained by the National Park Service. Fig. 1. Roof plan marking the six casemates to be modeled and the locations of the core sampling points (plan drawing courtesy of National Park Service). 3. Site inspection and evaluation: Data collection for model development probabilistic evaluation of the settlement-induced damage to an unreinforced masonry vaulted casemate of Fort Sumter under the This section discusses the field inspections of the present condi- incremental development of a wide range of possible settlement tion of Fort Sumter, including (i) physical tests on material sam- scenarios. ples, (ii) three-dimensional laser scanning of the fort’s geometry This manuscript is organized as follows. Section 2 provides a and (iii) ambient vibration testing of the casemates. brief history and reviews the structural characteristics of Fort Sum- ter while Section 3 details the field investigations that support the 3.1. Coring samples and material testing development of the numerical models. The development of the three-dimensional nonlinear FE model of the casemate is discussed Although the construction drawings of the fort indicate the fort in Section 4, followed by a discussion on the calibration of the was originally designed with brick masonry all throughout the imprecisely known parameters of this model against in situ vibra- walls (see U.S. National Archives, Drawer 66, Sheet 1), on-site eval- tion measurements in Section 5. Section 6 presents the simulated uations and cored samples reveal a construction of masonry walls response of the vaulted casemates for various support settlement with concrete infill (Fig. 3). Therefore, the brick walls of Fort Sum- while, quantitative and qualitative assessments under the simu- ter are heterogonous in nature, not only in the use of masonry lated support settlement scenarios are provided in Section 7. Final- units and mortar joints, but also in the inner morphology of the ly, Section 8 investigates the effect of uncertainties in the model structural system with lower strength filler material or cavities. input parameters remaining after calibration followed by a sum- To reflect this heterogeneity, three distinct regions with individual mary of the manuscript and concluding remarks. material properties are identified in the numerical model: (i) the masonry walls and piers, (ii) the barrel vault of the casemate 2. Fort Sumter National Monument: History and structural and, (iii) the tabby concrete infill in the scarp wall and piers system (Fig. 3). An independent parameter value is assigned for the vault to reflect the differences in the joint orientation. The construction of Fort Sumter began in 1829 with local sand Most masonry mortar used at Fort Sumter is constituted of nat- being used to create a two-acre island. Ten thousand tons of gran- ural cement (also known as Rosendale cement), lime and sand [17]. ite and over sixty thousand tons of other assorted rocks were used Rosendale cement is a binder generally producing lower strength to provide a foundation [15]. By 1860, the pentagonal-shaped fort mortar than Portland cement–sand mortars [18]. The concrete had 5 ft. thick, 50 ft. tall brick walls, enclosing a parade ground of infill of the fort can be best described as ‘‘tabby concrete’’ – a con- approximately an acre (Fig. 1). The nearly four million bricks used crete-like compound generally composed of quicklime (obtained in the construction of the walls were manufactured locally. The by burning oyster shells) and aggregate (composed primarily of mortar used was a mixture of local sand, cement from New York oyster shells and sand with some brick pieces) [19]. To determine and limestone from burnt oyster shells [15]. characteristics of brick and mortar used during the construction, a

Fig. 2. (a) Photo taken on August, 1863 showing the ﬁrst breech in Fort Sumter walls (original photograph by G.S. Cook) and (b) photo taken in August, 2011 showing the current condition of Fort Sumter casemates. S. Prabhu et al. / Engineering Structures 65 (2014) 1–12 3

Fig. 3. Solid model of the casemate showing the different material assignments and the location of the scarp wall interface modeled with contact elements.

305 355 152 mm block sample is collected from the site and Â Â tested in the laboratory (Fig. 4a and b); while the characteristics of the concrete infill are determined from the cored specimens. Two samples, cut from the block specimen collected on site (Sample A and Sample B as shown in Fig. 5), are tested to obtain both compressive and tensile material properties. During compression experiments, Sample A is tested for compressive strength in the direction normal to the bed-joint (Fig. 5a), while Sample B is tested for compressive strength in the direction parallel to the bed-joint (Fig. 5b). The compressive strength of the brick and mor- Fig. 5. (a) Sample A crushed in the compression test; (b) Sample B crushed in the tar assembly is determined using 50 mm cube specimens accord- compression test; (c) stress strain curves for Sample A and Sample B from the compression test. The slope of the elastic region is taken as the elastic modulus. ing to ASTM C109/109M-11a. The modulus of elasticity is calculated as the slope of the elastic region of the stress–strain curves as shown in Fig. 5c. For both samples, averaged modulus calculated by cutting the specimen into cylinders and measuring of elasticity of 3.57 GPa and compressive strength of 20.7 MPa the weight-to-volume ratio. The densities of brick and mortar that are obtained. The mean values for modulus of elasticity are consid- are measured as 1490 kg/m3 and 1670 kg/m3, respectively. A volu- ered as prior information for the calibration of the numerical mod- metric average yields a density of 1500 kg/m3 for the masonry el against experimentally obtained vibration measurements assembly. (discussed later in Section 5.2). Diametral tests on three core samples of tabby concrete, shown Three point flexural tests conducted on samples cut from the in Fig. 4d, provide a compressive modulus of elasticity of 530 MPa block specimen (Fig. 6) yield the tensile strength of mortar and and average tensile and compressive strength of 0.53 MPa and brick as 0.65 MPa and 2.37 MPa, respectively. The final tensile 6.37 MPa, respectively. The density of the tabby concrete infill is strength is calculated as a volumetric average of the mortar joints measured from the core samples as 1600 kg/m3. The material and brick units and set to 2.07 MPa. Moreover, bulk densities are properties used in the FE model are summarized in Table 1. Note

Fig. 4. (a) Block specimen from the remains of the fort; (b) block specimen segmented into smaller samples for testing; (c) coring of the wall in progress; (d) an intact core sample of tabby concrete inﬁll. 4 S. Prabhu et al. / Engineering Structures 65 (2014) 1–12

Fig. 6. Samples cut from the block specimen for 3-point ﬂexural test and corresponding stress–strain curves. that values of the modulus of elasticity of the masonry are ﬁne- tuned as described in Section 5.2.

3.2. Laser scanning and geometric model development

Masonry construction must carry loads in a compressive manner requiring curved elements to span distances, such as arches Fig. 7. (a) Polygonal mesh of Casemate 4 generated in Polyworks V11; (b) and vaults, and thus result in complex geometries. Over the life wireframe of Casemate 4 generated in Rhino v5.0. of the structure, the geometry is further complicated by the accu- mulation of structural degradation, such as permanent deformations, crack formation, and support movements. While geometric FE model outputs of interest. The scan data was collected from mul- features must be simplified to reduce computational demands, it tiple setups of the scanner in and around the casemates. To main- is crucial to preserve the structural properties (such as cross sec- tain the integrity of the overall models created from multiple tional area and moment of inertia) for achieving high-fidelity scanner setups, a high accuracy control survey was performed to numerical models [20]. For this purpose, laser scanning has been provide control points for the scanner. The control points were successfully applied to three-dimensional surveying of several ma- established with procedures that insured gross and systematic er- sonry structures such as, masonry arch bridges [21–23] and ma- rors were accounted for such that random errors were minimized sonry vaulted monuments [24]. in order to achieve a relative positional accuracy of ±1 mm. This en- To obtain the geometry of Fort Sumter in its present form, a sured that the individual scan setups meshed together accurately. high-resolution three-dimensional laser scan of the fort is per- The laser scan data, obtained in the form of a point cloud is formed [22]. The Trimble CX laser scanner uses proprietary technol- post-processed using Polyworks v.11 geometric modeling systems. ogy that combines time-of-flight methodology for long range Using triangulated irregular network generation, surfaces (trian- distance discrimination and phase shift methodology for high short gles) are created between adjacent points in the point cloud. Dur- range accuracy. This combined methodology provides high resolu- ing triangulation, the maximum dihedral angle is kept at 45° and tion positional measurements of the object’s surface at the rate of maximum edge length is left unconstrained. The surfaces are then 54,000 points per second from distances in the order of up to decimated by a factor of 80%. Finally, wireframe models are created 50 m and measures the return time for the reflection from the ob- from the casemate polygon mesh using RhinoV5 including impor- ject. Assuming the pulse travels with a constant speed, the distance tant geometric features such as cracks and indentations. Fig. 7 between the laser scanner and the object can be calculated in a shows the polygonal mesh and the corresponding wireframe mod- straightforward manner [26]. This distance combined with the el for Casemate 4. simultaneously measured horizontal and vertical angles provides high accuracy positions of the collected points. The Trimble CX 3.3. Ambient vibration testing scanner has a positioning accuracy of 4.5 mm at 30 m and a distance measurement accuracy of 1.2 mm at 30 m. Also, the scanner Ambient vibration tests are performed on the casemate with a corrects for temperature and humidity. For the distances within total of 41 measurement points located on the piers, arches and the casemate, the expected positional accuracy is ±3 mm or better vault (Fig. 8). Twenty measurement points are located on the piers which is insignificant enough to cause a substantial change in the to measure horizontal acceleration response, while 9 measurement points on the three arches and 12 measurement points on the vault measure vertical acceleration response. The measurement loca- Table 1 tions are chosen after a careful study of the mode-shapes from a Material properties of the masonry and tabby concrete. preliminary modal analysis performed on the FE model of the case- Elastic Tensile Compressive Density mate. From this preliminary model, it is observed that for the first 3 modulus strength strength (MPa) (kg/m ) 10 modes of the casemate, the most dominant modal displace- (GPa) (MPa) ments are the vertical deflections of the vault and arches and the Masonry of piers 3.1 20.7 2.07 1500 horizontal deflections of the piers. The sensor locations are chosen Masonry of vault 1.58 20.7 2.07 1500 accordingly to capture these displacements with sufficient spatial Tabby concrete 0.53 6.37 0.53 1600 resolution to prevent spatial aliasing. S. Prabhu et al. / Engineering Structures 65 (2014) 1–12 5

Fig. 9. Sub-structured FE model of Casemate 4 with springs used to represent the Fig. 8. The experimental set-up showing accelerometers mounted on the vaults and foundation. The meshed region is the casemate itself adjoined by superelements of piers. the neighboring casemates.

PCB 393B04 seismic accelerometers are deployed to record 30 min vibration responses due to ambient excitation forces (see 4.1. Generation of the finite element model [27] for a discussion on ambient vibration testing of historic masonry monuments). The PCB 393B04 seismic accelerometers have The geometry of the FE model is built in ANSYS 13.0 according a sensitivity of 1000 mV/g, measurement range of ±5 g and a fre- to the wireframe model generated in Rhino 5.0 (Fig. 9) (recall Sec- quency range of 0.06–450 Hz. The high sensitivity is ideal for mea- tion 3.2). When necessary, property-preserving approximations suring low-amplitude ambient vibrations for an operational modal are made to eliminate difficulties in geometric modeling and mesh test. A baseband frequency range of 0–1.6 kHz is used with a sam- discretization. A predefined 8-noded solid isoparametric SOLID65 pling frequency of 819.2 Hz. Thus, a total of 1,474,560 samples are element in ANSYS 13.0 is implemented. SOLID65 element faithfully collected over the measurement duration. The sampling frequency represents typical masonry failure, characterized by cracking in is down-sampled to 160 Hz to reduce the size of the data vectors. tension and crushing in compression. SOLID65 element accounts Using Enhanced Frequency Domain Decomposition system identi- for cracking through a smeared crack analogy and crushing fication method [28–29], two modes are extracted from the raw through a plasticity algorithm in three orthogonal directions data at 27.48 Hz and 45.2 Hz with a MAC rejection level of 0.8. according to Willam–Warnke failure criterion [30,31]. SOLID65 The identified natural frequencies and the corresponding modes element allows the input of open and closed crack shear transfer shapes are given later in Table 2. coefficients ranging from 0 to 1, where 0 represents a smooth crack (no shear transfer at the crack surface) and 1 represents a perfectly rough crack (complete shear transfer at the crack surface) [32]. In 4. Development of the structural finite element model this study, shear transfer coefficients are prescribed as 0.2 for open cracks and 0.6 for closed cracks, respectively [33,34]. This section discusses the development of the structural finite According to construction drawings, the initial construction of element model, including (i) generation of the model, (ii) verifica- Fort Sumter included a narrow gap between the scarp wall and tion of the mesh size and (iii) implementation of substructuring casemate (Fig. 10). This gap has been closed due in part to perma- techniques to represent the adjacent components. nent deformations and in part to the reconstruction of the fort. Currently, the interface between these two structural systems Table 2 exhibits a contact of unknown nature with highly uncertain force Comparison of measured and simulated modes with respective MAC values. transfer characteristics. In the FE model, this interface is modeled Mode 1 (MAC = 0.86) using contact elements on one surface (contact surface, CONTA174 in ANSYS) and target elements on the other surface (target surface, 27.48 Hz 29.9 Hz TARGE170 in ANSYS) forming a contact–target pair (as indicated in Fig. 3) [35]. In these contact–target pairs, the nature of the force transfer is dictated by normal and tangential contact stiffnesses. Herein, normal contact stiffness, which controls the penetration, is assumed identical to the stiffness of the masonry beneath the contact surface. The sliding behavior between the scarp wall and piers is a complex combination of interlocking, friction and possible cohesion, which are difficult to measure without destructive tests. The combined tangential force transfer, that governs the slid- Mode 2 (MAC = 0.6) ing behavior at the interface, can be idealized by a friction coeffi- 45.2 Hz 42.8 Hz cient applied to the contact elements, which represents the tangential stiffness at the interface. This friction coefficient is, thus, a homogenized idealization of the sliding resistance at the scarp wall interface and must, therefore, be inferred via calibration measurements collected on site, as it will be discussed in Section 5.1. The foundations, which are excluded from the model, provide a semi-rigid support to the casemate which can be idealized by a system of identical but independent, closely spaced vertical and horizontal linear springs (COMBIN14 in ANSYS) distributed 6 S. Prabhu et al. / Engineering Structures 65 (2014) 1–12

Fig. 10. Casemate used for connectivity tests showing the outline of the scarp wall interface (a) in elevation and (b) in section. throughout the base of the casemate forming a Winkler foundation [36–38] (as indicated in Fig. 9). The springs are of course, fictitious and thus, the spring stiffness’s are uncertain quantities requiring calibration to experimental measurements as it will be explained later in Section 5.2. The resulting model is thus nonlinear, incorporating (i) the material non-linearity (concrete material model), (ii) geometric non-linearity (P–D effects) and (iii) non-linear boundary conditions (contact elements). Thus, the FE model requires an iterative solver. Herein, the Newton–Raphson equilibrium iteration scheme [39] is used to update the tangent matrix and the restoring force vectors corresponding to the element internal forces. In solving the nonlinear equations, considerable use has been made of the Clemson University high performance computing capability, Pal- metto Cluster. Fig. 11. Mesh refinement study showing the change in the first four natural frequencies as a function of the element size. 4.2. Determining the optimal mesh size

To ensure numerical solutions accuracy and prevent errors from superelements are coupled to the structure of interest, i.e., Case- compensating during calibration, a mesh size that strikes a balance mate 4, to form the complete system [48]. Note that the loads ap- between computational time and numerical precision is sought. plied to Casemate 4 are also applied respectively to the adjacent First, a reference solution is defined using a generalized Richardson casemates and are transferred through the interface degree-of- extrapolation [40]. This reference solution at element size Dx = 0, freedoms via a reduced superelement load vector. Herein, a fixed- i.e. a model with infinite elements, theoretically yields the exact interface CMS is employed, where the eigenvalue problem for the solution. The maximum element edge length, Dx of the solid tetra- component is solved by restraining each of the interface degrees hedral element is varied between 0.18 m to 0.26 m in steps of of freedom, as it is computationally less expensive due to the smal- 0.01 m. Solution convergence as the maximum element edge ler size of the eigenvalue problem. length is reduced is checked for the first four free-free natural fre- Substructuring is computationally advantageous over the com- quencies. Fig. 11 shows that employing a mesh size of 0.23 m mon approach of including adjacent structural components for yields a numerical uncertainty below 4% of the reference solution, each axis of symmetry [10,49]. Note that the use of a substructur- less than the experimental variability that can be attributed to ing technique for Casemate 4 results in an approximate threefold temperature and moisture variations commonly observed in ma- reduction in the number of degrees-of-freedom that would be sonry and concrete construction (i.e., 5–6%) [41–42]. Herein, a solved and stored if the adjacent casemates were also modeled. maximum element edge length of 0.23 m is implemented, which yields a model with 87,555 elements and 131,232 nodes with three 5. Calibration of the structural finite element model translational degrees of freedom. This section reviews the calibration activities that include (i) 4.3. Substructuring of the un-modeled adjacent casemates back-calculation of the unknown friction coefficient of the contact elements used to represent the interface between the casemate To represent lateral restraints from the un-modeled adjacent and scarp walls and (ii) inference of the imprecisely known spring casemates, the structure is partitioned into substructures through constants model input parameters. Component Mode Synthesis (CMS) [43–47]. The method consists of first reducing the order of the components of lesser interest, 5.1. Back-calculating the friction coefficient through load path analysis i.e. the adjacent casemates, down to their interface degrees of freedom, generating what are referred to as superelements. Sub- Recall Section 4.1, where a fictitious friction coefficient is de- structuring must therefore be applied after an appropriate mesh fined to represent the highly uncertain force transfer at the size is selected (recall Section 4.2). Next, these reduced order interface between the casemate and scarp wall. This coefficient, S. Prabhu et al. / Engineering Structures 65 (2014) 1–12 7

are calculated for six levels of impact force increasing from 2.6 kN to 8.8 kN. For all force levels, the average relative displacement ratio is obtained to be 3.8, considering both south and north sides of the casemate. The friction coefficient l, in the FE model shown earlier in Fig. 9, is back-calculated such that the relative displacement ratio in the FE model is equal to 3.8. This back-calculation is completed considering two surface interaction models that differ in the treatment of separation between surfaces. In Fig. 13, by interpolating between data points, a coefficient of 1.14 is obtained as an average of the two surface interaction models and the impact force levels. This value is used for the fictitious friction coefficient for the CON- TACT174 elements in the FE model to approximate the connectiv- Fig. 12. Test set-up on the north pier of Casemate 4 showing two adjacent ity and interlocking behavior between the scarp wall and casemate accelerometers mounted parallel to the scarp wall interface with one accelerometer (as indicated earlier in Fig. 3). on the pier and one on the scarp wall. being highly dependent upon the present condition of connectivity 5.2. Calibrating the uncertain parameters of the finite element model and interlocking between these two structural components, is back-calculated from available on-site measurements. As sug- Despite of the concerted efforts made to collect on-site informa- gested by [50], structural connectivity can be inferred by measur- tion regarding the present condition of the fort, uncertainties re- ing the vibrations transferred between adjacent structural main in (i) the material property values and (ii) the spring components. If the scarp wall and casemates are in full contact constant that represents the support at the base of the structure. resulting in a complete force transfer (i.e. no sliding), the displace- It is of value to reduce the uncertainty in these input parameters ments parallel to the interface must be continuous (i.e. the dis- by systematically comparing the numerical model predictions of placement of the scarp wall and the casemate within the global mechanical behavior of the casemate against those that immediate vicinity of the cold-joint must be nearly identical). are measured on site, a process commonly known as model calibra- Therefore, the measured relative dynamic displacements of these tion [13,25,55] (see [12] for a thorough overview of model calibra- two adjacent structural systems can be used to estimate the friction as applied to masonry monuments). tion coefficient. With the modal parameters of the fort identified in Section 3.3, A hammer impact test is performed [51,52], in which two accel- uncertain FE model input parameters can be calibrated. Since com- erometers, one on the casemate pier and one on the scarp wall, are putation of modal parameters is deeply rooted in the linearity mounted parallel to the interface and a hammer strike is applied assumption, only parameters affecting the linear response can be parallel to the interface (Fig. 12). PCB 393B04 accelerometers with calibrated, namely the elastic modulus of the materials and spring a frequency range of 0.06–450 Hz ± 5% and weight of 50 gm each constants representing the boundary conditions. The elastic modu- are used to measure the vibration response of the fort. B&K 8210 lus of walls and piers (h1), the elastic modulus of the vaults (h2) (re- modal sledge hammer with a 5.44 kg (12 lb) head and a maximum call Fig. 3) and stiffness of the springs at the supports (h3) (recall force range of 22.2 kN (5000 lbf) is used to excite the structure. Fig. 9) are imprecisely known input parameters in the FE model. First, the low frequency noise in the acceleration time history mea- Through a fully Bayesian implementation of the statistical infer- surements are filtered with a high-pass Butterworth filter with a ence procedure proposed by [56], these three model input param- frequency cutoff of 20 Hz [53]. Next, the acceleration response is eters are inferred by exploiting the availability of known modal converted to displacement using cumulative trapezoidal numerical parameters (see [57] for the derivations of the statistical inference time integration with a time step size of 0.002 s [54]. The cutoff approach and [10] for a discussion on the implementation of this frequency of 20 Hz that yields displacement response with a procedure on a masonry monument). zero-mean is applied after studying a range of cut-off frequencies. For the material properties (h1 and h2), in the absence of a suf- From displacement time histories, the ratios of the maximum dis- ficiently large number of material tests, prior distributions are de- placements of the casemate and scarp walls are calculated. To cap- fined to be uniform distributions. The bounding limits of the ture the potentially nonlinear behavior of the interface, these ratios uniform distribution are determined such that the predicted

Fig. 13. Plot showing the relative displacement ratio using (a) standard surface interaction model and (b) no-separation surface interaction model for different values of applied force and l. 8 S. Prabhu et al. / Engineering Structures 65 (2014) 1–12

Fig. 14. The ﬁrst six natural frequencies obtained from the FE model plotted against logarithmically varied foundation spring stiffness. natural modal parameters envelop the experimentally measured modal parameters; thus for h1 a range of 3–4 GPa and for h2 a range Fig. 15. Posterior distribution of input parameters (h1 is the elastic modulus of of 1.5–2.5 GPa are considered. The bounding limits of h2 are consid- walls and piers, h2 is the elastic modulus vaults and h3 is the foundation spring ered to be lower than those of h1 due to the vertical orientation of stiffness). the joints in the vaults.

The range for the spring constant h3 is defined to ensure a semi- rigid connection through a parametric analysis of the first six nat- (MAC) that represents the degree of linear correspondence be- ural frequencies, in which the stiffness of the linear springs is log- tween two mode shape vectors [58]. MAC lies between zero and arithmically varied to find the stiffness values at which the unity, where a higher MAC value indicates better agreement. Be- foundation becomes effectively pinned (lower bound) and effec- tween the experiments and the calibrated numerical model, a tively rigid (upper bound) (Fig. 14). According to Fig. 14, the prior MAC value of 0.86 for the first mode and 0.60 for the second mode distribution of the spring constant is set to be uniform between 10 is observed for the experimental and simulated mode shapes. and 103 MN/m. The domain defined by the prior distributions of the three cali- 6. Support settlement analysis of Fort Sumter bration parameters is explored via Markov Chain Monte Carlo (MCMC) sampling. A total of 20,000 MCMC accepted runs are ob- Seven possible settlement configurations are simulated, each tained to generate the posterior distributions for the calibration with a maximum magnitude of 100 mm in the vertical direction parameters. These posterior distributions yield the likely values as shown in Fig. 16. Aside from the settlement of the supports, for the three uncertain model input parameters that improve the the self-weight of the casemate itself is also considered in the sim- agreement between the two experimentally measured and pre- ulation. The configurations are designed accounting for the two dicted natural frequencies (see Fig. 15). adjacent casemates on the two sides of Casemate 4. The settlement The values corresponding to the peak of the probability distri- configurations are generated as bi-variate quadratic curves using butions shown in Fig. 15 are used as the calibrated input parame- the MATLAB procedure polyfitn [59] and are designed to encom- ters, which correspond to an elastic modulus of 3.1 GPa for the pass global settlement of the three casemates as well as local set- walls and piers (h1), 1.58 GPa for the elastic modulus of the vault tlement of the piers and walls. The settlement configurations are 7 (h2), and a support spring stiffness of 6 10 N/m (h3). The correla- grouped as sagging configurations (1, 2 and 3), pier settlement Â tion between the first two experimental modes and the corre- (4) and tilting settlements (5, 6 and 7). As the settlement is incre- sponding model predictions obtained with these calibrated input mented, cracks begin to develop in the casemate. The pattern of the parameters is given in Table 2. cracking is observed to be dependent upon the settlement config- The calibrated model yields a first natural frequency, which is uration and magnitude: 8.8% higher and a second natural frequency, which is 5.3% lower Sagging settlement: Configuration 1 simulates the unsymmetri- than the experimentally obtained natural frequencies. While com- cal sagging under the north side of the scarp wall. The cracks begin paring the agreement between experiments and model predic- forming at the bottom of the scarp wall on the intact side and grad- tions, another commonly used metric is modal assurance criteria ually progress upwards. At around 50 mm of settlement, a crack

Fig. 16. Seven settlement configurations used for FE simulations. S. Prabhu et al. / Engineering Structures 65 (2014) 1–12 9 which initiates at the base of the scarp wall on the intact side pro- pier itself that settles less among the two endures more cracking gresses diagonally across the scarp wall and fully forms a diagonal than that which settles more. crack (indicated with a dotted line in Fig. 17). While such a settle- Tilting settlements: Configuration 5 represents inward tilting of ment results in substantial cracking within the scarp wall, owing to the foundation towards the west. According to the model predic- the cold joint between the scarp wall and the rest of the casemate, tions, cracking is predicted at the springing of the arch above the the vault, arches and the inner piers are not significantly affected. inner piers of the casemate (indicated as a and b). Cracking is ini- Configuration 2 simulates the sagging under the entire north side tiated at the outer tips of the base of the north- and south-piers at a of the casemate. Beginning at the scarp wall, heavy cracking is ob- settlement magnitude of approximately 10 mm while cracking at served on the less settled side of the casemate. At approximately the outer edge of the base of the scarp wall is initiated at approx- 50 mm of settlement, a complete diagonal crack is formed on the imately 20 mm. These cracks gradually progress upwards and scarp wall (indicated by a dotted line in Fig. 17). Cracking is also reach the springing point of the arch (indicated as a and b) at a initiated at the springing of the arch on the south side at a magnitude of 50 mm. Configuration 6 simulates outward tilting 50 mm settlement magnitude. Configuration 3 simulates symmet- of the foundation towards the east. Cracking is predicted at the rical sagging of the ground, which results in symmetrical cracking springing point of the arches above the inner piers on the side of of the arches (indicated as a and b in Fig. 17). At approximately the scarp wall. At a settlement magnitude of 15 mm, cracking at 60 mm settlement, a load bearing arch is formed within the scarp the inner tips of the base of the piers is first observed, with the in- wall to span across the regions of settlement (as indicated by a dot- ner edge of the base of the scarp wall beginning to crack at around ted line in Fig. 17) in agreement with an earlier simulation based a 40 mm of settlement. Cracks in the piers and scarp wall progress study by [5]. upwards and reach the springing point of the arch at approxi- Settlement of piers: Under configuration 4, which simulates set- mately 60 mm of settlement. Settlement in configuration 6, which tlement under the north-pier, cracking begins first at the base of represents the outward tilting of the foundation towards the east, the scarp wall on the south side and the south-pier at a settlement is less structurally critical compared to configuration 5 primarily magnitude of 10 mm. The configuration also leads to cracks at the due to the highly stiff scarp wall resisting the thrust of the vault. springing of the arch (indicated as b in Fig. 17) at a settlement Finally, configuration 7 simulates tilting of the foundation towards magnitude of approximately 60 mm. Extensive cracking and for- the north in the longitudinal direction of the right face. The south mation of a hinge are also observed within the vault (indicated pier of the casemate is heavily cracked due to the horizontal thrust as a in Fig. 17). It can be concluded that when one of the piers set- exerted by the vault. Diagonal cracking, initiated in the scarp wall tles more than the other, unsymmetrical cracking of the vault oc- originating from the base on the south side runs completely across curs on the side of the pier that exhibits more settling. Also, the the scarp wall at a 50 mm settlement (indicated by a dotted line).

Fig. 17. Crack plots of the casemate under 100 mm settlement of the seven conﬁgurations. 10 S. Prabhu et al. / Engineering Structures 65 (2014) 1–12

When the discontinuities are formed in the vaults and arches in the form of hinges, an instability condition is assumed. Although, further cracking may be allowed past the assumed instability condition, cracking of vaults and arches is treated as a critical condition as structural collapse is imminent at any value of further settlement. Fig. 19 indicates the settlement magnitudes at which the abovementioned damage classifications occur. The instability condition, as defined herein, is not experienced under configurations 1 and 6 up until a 100 mm settlement magnitude. The assumed instability conditions are experienced under configurations 2, 3, 4 and 5 between 60 and 80 mm settlements.

8. Remaining uncertainties Fig. 18. Total principal strain plotted as a function of settlement magnitude. This section evaluates the effects of the remaining uncertainties in the maximum principal stresses for two support settlement sce- Cracking at the springing point of the north arch is initiated at a narios that produce highest principal strains at 100 mm settle- 50 mm of settlement (indicated as b in Fig. 17), while cracking of ment: Configurations 3 and 2 (as seen from Fig. 18). Uncertainty the vault on the south side is initiated at 80 mm (indicated as a in the model predictions of the maximum principal strain is as- in Fig. 17). The cracks in the vault form a hinge rapidly through sessed by performing a parametric analysis within mean ±2X std. the length of the vault at a 90 mm settlement. deviation (recall Fig. 15). Parameter values are evaluated according Results presented in this section reveal that the mechanism, in to a three-level full factorial design of experiments, which yields 27 which the fort withstands the support settlement, differs signifi- cases. For the two critical settlement configurations (configura- cantly for different settlement configurations. Therefore, visual tions 2 and 3), Fig. 20 shows mean values of the maximum princi- observations of crack patterns can be used to diagnose potential pal strain obtained from the 27 cases along with the 95% settlement configurations. However, it must be noted that not confidence intervals. The maximum principal strain predictions every cracking in the structure can be attributed to settlement. show significantly high uncertainty of up to 24.9% of the mean Cracking may occur due to temperature and moisture expansion, for configuration 2 and 22.09% for configuration 3. This assessment seismic and high wind activity, forces from adjacent buildings, shows the high dependency of the non-linear analysis of maximum chemical and biological processes, freeze–thaw cycles, etc. principal strain on the linear input parameters and highlights the importance of model calibration exercised discussed earlier in Section 5. 7. Qualitative classification of settlement-induced damage

When cracking occurs within an element, the strain in the 9. Conclusions direction normal to the cracked element edge increases significantly. Total strain is, thus, proportional to the number of cracks This manuscript investigates settlement-induced damage pat- and their widths. Therefore, the degree of settlement induced dam- terns specifically focusing on Fort Sumter, SC, a historic 19th cen- age can be quantified using the total principal strain in the entire tury island fort, through a numerical analysis substantiated with structure. Fig. 18 plots the total principal strain as a function of experiments and field investigations. The FE model of one of the the settlement magnitude. It can be deduced that configuration fort’s casemate is built that allows cracking of the masonry mate- 3, which is the symmetric sagging under the casemate is the most rial when the failure criterion is exceeded. The input parameters of damaged case in terms of the intensity of crack formation, while the model are determined following on-site experiments and mod- configuration 5 which is the outwards tilting of the casemate is el calibration. the least damaged in the same sense. Seven settlement configurations are simulated to include global Focusing on the damage patterns discussed in Section 7, a qual- settlements as well as localized settlements under the piers and itative damage classification scheme is devised. Minor smeared walls. The cracking behavior is observed at each step as the settle- cracking limited to walls and/or piers is classified as slight damage, ment magnitude is increased up to 100 mm in increments of while the initiation of large cracks or discontinuities in walls and 2.5 mm. The formation and progression of cracks are observed to piers is classified as moderate damage. Severe damage is reported be unique to the settlement configurations. Therefore, by visual when through cracks are completely formed in the walls and piers. investigations of early warning signs in form of cracks, the

Fig. 19. Qualitative structural damage matrix showing damage levels based on crack locations and magnitudes. S. Prabhu et al. / Engineering Structures 65 (2014) 1–12 11

Fig. 20. Mean and 95% confidence intervals of the maximum principal stress in the FE model from the parametric analysis of material uncertainty for settlement (a) configuration 2 and (b) configuration 3. stewards of historic monuments can draw conclusions regarding Benjamin Rennison for the development of the wireframe models the settlement configuration causing damage to the structure. It and Peter Messier for collection of the laser-scan data. Additional must be noted, however, that cracks in an existing structure are thanks to Mr. Godfrey Kimball of Clemson University for his edito- not formed due to settlement alone. rial assistance. Thanks to Will Alexander, an undergraduate Crea- Unsymmetrical sagging types of settlements are characterized tive Inquiry student of Clemson University for his valuable by diagonal cracking of the scarp wall originating from the bottom contributions in reviewing the archival documents. on the less-settled side. Symmetric sagging under the casemate, however, forms cracks that originate from the bottom of the scarp References wall from both sides and converge at the center forming an arch that spans the length of the casemate and bears the loads of the [1] Grant R, Christian JT, Vanmarcke EH. Differential settlement of buildings. J Geotech Eng Div 1974;100(9):973–91. wall above. Cracks due to stress concentrations are seen for most [2] Polshin D, Tokar R. Maximum allowable non-uniform settlement of structures. settlement configurations at the intersection of the structural In: Proc fourth international conference on soil mechanics and foundation members such as the springing of the arches and vaults. Cracking engineering; 1957. p. 402–5. of the vault is observed in configurations that involve differential [3] Skempton AW, MacDonald DH. The allowable settlements of buildings. ICE Proc Eng Div 1956:727–68. settlements of the piers. Cracks once formed in the vaults, progress [4] Walhls H. Tolerable settlement of buildings. ASCE J Geotech Geoenviron Eng rapidly without warning as the settlement increases. Thus, crack- 1981;107:1489–504. ing of the vault should be taken as a structural stability concern. [5] Augarde CE. Numerical modeling of tunneling process for assessment of damage to structures. PhD thesis. University of Oxford; 1997. Structural damage is quantified by the total principal strain in [6] Potts D, Addenbrooke T. A structure’s influence on tunneling induced ground the casemate as it approximately reflects the number of cracks movements. Proc Inst Civ Eng Geotech Eng 1997;125(2):109–25. and the crack widths. Symmetrical sagging is found to be the set- [7] Burd H, Houlsby G, Augarde C, Liu G. Prediction of tunnel-induced settlement damage to masonry structures. OUEL report 2162/98. Department of tlement scenario that amounts to the most crack damage. A qual- Engineering Science, Oxford University; 1998. itative damage classification system is devised on the basis of crack [8] Rots J. Settlement damage predictions for masonry. Maintenance and propagation and location that indicates the level of damage restrengthening of materials and structures – brick and brickwork. In: Proc int workshop on urban heritage and building maintenance; 2000. p. 47–62. encountered as the settlement magnitude increases. The damage [9] Roca P. Structural analysis of historical constructions: possibilities of levels range from slight damage signifying minor cracking in walls numerical and experimental techniques. International Center for Numerical and piers to instability conditions when cracks occur in the hori- Methods in Engineering; 1997. [10] Atamturktur S, Hemez FM, Laman JA. Uncertainty quantification in model zontal members i.e. vaults and arches. verification and validation as applied to large scale historic masonry Finally, the dependency of the results on the homogenized in- monuments. Eng Struct 2012;43:221–34. put parameters is found to be significant, suggesting the impor- [11] Lourenço PB. Computations on historic masonry structures. Prog Struct Eng tance of using combined nondestructive evaluation and Mater 2002;4(3):301–19. [12] Lourenço PB. Recommendations for restoration of ancient buildings and the calibration techniques to obtain accurate model input parameters. survival of a masonry chimney. Constr Build Mater 2006;20(4):239–51. In future studies, the settlement analysis must be performed by [13] De Sortis A, Antonacci E, Vestroni F. Dynamic identification of a masonry also incorporating foundation soil properties and the soil–structure building using forced vibration tests. J Eng Struct 2005;27(2):155–65. [14] De Stefano A. Structural identification and health monitoring on the historical interactions that will alleviate the simplifications assumed in this architectural heritage. Key Eng Mater 2007;347:37–54. study for the spring foundations that were assumed linear and iso- [15] Hunter AF, Symonds CL. A year on a monitor and the destruction of Fort tropic. Such a study can also assess the effect of the fort on its foun- Sumter. Colombia, SC: University of South Carolina Press; 1991. [16] Johnson J. The defense of Charleston Harbor: including Fort Sumter and the dation to infer the possible settlements to be expected in the adjacent Islands 1863–1865. Whitefish, MT, USA: Kessinger Publishing; 2006. future. Both a sound numerical model of the fort, discussed in this [17] Brosnan DA, Sanders JP, Hart SA. Application of thermal analysis in manuscript, as well as a dependable numerical model of the soil preservation and restoration of historic masonry materials. J Therm Anal Calorim 2011;106(1):109–15. will be required for coupling of these two fields. [18] Treussart CL, Courtois C, Petot JC. Essays on hydraulic and common mortars and on limeburning; 1838. Acknowledgements [19] Clark TE. Falling to pieces: the preservation of ruins in coastal Georgia. PhD thesis. USA: University of Georgia; 2006. [20] Atamturktur S, Sevim B. Seismic performance assessment of masonry tile This work is funded by the National Park Service, South Atlantic domes through non-linear finite element analysis. J Perform Constr Facil Cooperative Ecosystems Studies Unit (Contract Number: 142091). 2011;26(4):410–23. [21] Arias P, Armesto J, Di-Capua D, González-Drigo R, Lorenzo H, Pérez-Gracia V. Many thanks, to Fort Sumter National Monument personnel for Digital photogrammetry, GPR and computational analysis of structural their cooperation and helpfulness during site visits to the fort, damages in a mediaeval bridge. Eng Fail Anal 2007;14(8):1444–57. 12 S. Prabhu et al. / Engineering Structures 65 (2014) 1–12

[22] Armesto J, Roca-Pardiñas J, Lorenzo H, Arias P. Modelling masonry arches [39] Bathe KJ. Finite element procedures. New Jersey: Prentice Hall; 1996. shape using terrestrial laser scanning data and nonparametric methods. Eng [40] Roache P. Perspective: a method for uniform reporting of grid refinement Struct 2010;32(2):607–15. studies. Trans Am Soc Mech Eng J Fluids Eng 1994;116:405. [23] Drosopoulos G, Stavroulakis G, Massalas C. Influence of the geometry and the [41] Sohn H. Effects of environmental and operational variability on structural abutments movement on the collapse of stone arch bridges. Constr Build health monitoring. Philos Trans R Soc London Ser A 1851;2007(365):539–60. Mater 2008;22(3):200–10. [42] Ramos LF. Damage identification on masonry structures based on vibration [24] Schueremans L, Van Genechten B. The use of 3D-laser scanning in assessing signatures. PhD thesis. Guimaraes, Portugal: University of Minho; 2007. the safety of masonry vaults—a case study on the church of Saint-Jacobs. Opt [43] Craig RR. Methods of component mode synthesis. Shock Vib Dig 1977;9(11): Lasers Eng 2009;47(3):329–35. 3–10. [25] Gentile C, Saisi A. Ambient vibration testing of historic masonry towers for [44] Ali S, Moore I, Page A. Substructuring technique in nonlinear analysis of brick structural identification and damage assessment. Constr Build Mater masonry subjected to concentrated load. Comput Struct 1987;27(3):417–25. 2007;21(6):1311–21. [45] Craig RR. Coupling of substructures for dynamic analyses: an overview. In: [26] Riveiro B, Caamaño J, Arias P, Sanz E. Photogrammetric 3D modelling and 41st AIAA/ASMA/ASCE/AHS/ASC structures, structural dynamics and materials mechanical analysis of masonry arches: an approach based on a discontinuous conference, AIAA; 2000. p. 2000–1573. model of voussoirs. Autom Constr 2011;20(4):380–8. [46] Craig RR, Bampton MCC. Coupling of substructures for dynamic analyses. AIAA [27] Atamturktur S, Pavic A, Reynolds P, Boothby T. Full-scale modal testing of J 1968;6(7):1313–9. vaulted gothic churches: lessons learned. Exp Tech 2009;33(4):65–74. [47] Craig RR. Substructure methods in vibration. J Mech Des 1995;117:207–13. [28] Brincker R, Zhang L, Andersen P. Output-only modal analysis by frequency [48] Tran DM. Component mode synthesis methods using partial interface modes: domain decomposition. In: Proc international seminar on modal analysis, KU application to tuned and mistuned structures with cyclic symmetry. Comput Leuven; 2001. p. 717–24. Struct 2009;87(17):1141–53. [29] Gade S, Møller N, Herlufsen H, Konstantin-Hansen H. Frequency domain [49] Erdogmus E. Structural appraisal of the Florentine Gothic construction system. techniques for operational modal analysis. In: Proc 1st IOMAC PhD thesis. State College, PA: The Pennsylvania State University; 2004. conference, Copenhagen, Denmark; April 26–27, 2001. [50] Atamturktur S, Bornn L, Hemez F. Damage detection in masonry vaults by [30] Willam K, Warnke E. Constitutive model for the triaxial behavior of concrete. time-domain vibration measurements. Eng Struct 2009;33:2472–84. International association of bridge and structural engineers. In: Seminar on [51] Ewins DJ. Modal testing: theory, practice and application. Hertfordshire, concrete structure subjected to triaxial stresses, paper III-1, Bergamo, Italy, UK: Research Studies Press, Ltd.; 2000. May. IABSE Proc 19; 1975. [52] Avitabile P. Experimental modal analysis. J Sound Vib 2011;35(1):20–31. [31] Fanning P. Nonlinear models of reinforced and post-tensioned concrete beams. [53] Parks TW, Burrus CS. Digital filter design. New York: Wiley-Interscience; 1987. Electron J Struct Eng 2001;1:111–9. [54] Han S, Lee J. Analysis of errors in the conversion of acceleration into [32] Kohnke P. ANSYS theory reference. ANSYS; 1999. displacement. In: Proc 19th IMAC; 2001. [33] Queiroz F, Vellasco P, Nethercot D. Finite element modelling of composite [55] Atamturktur S, Fanning P, Boothby T. Traditional and operational modal beams with full and partial shear connection. J Constr Steel Res testing of masonry vaults. Proc ICE Eng Comput Mech 2010;163(3):213–23. 2007;63(4):505–21. [56] Kennedy MC, O’Hagan A. Bayesian calibration of computer models. J R Stat Soc [34] Cubel F, Mas A, Vercher J, Gil E. Design and construction recommendations for 2001;63(3):425–64. brick enclosures with continuous air chamber. Constr Build Mater 2012;36: [57] Higdon D, Gattiker J, Williams B, Rightley M. Computer model calibration 151–64. using high-dimensional output. J Am Stat Assoc 2008;103(482):570–83. [35] ANSYS. Element library. ANSYS element reference; 2001. [58] Allemang RJ. The modal assurance criterion–twenty years of use and abuse. J [36] Winkler E. Die Lehre Von Der Elasticitaet und Festigkeit. UMI; 1992. Sound Vib 2003;37(8):14–23. [37] Brown CB, Tilton JR, Laurent JM. Beam-plate system on Winkler foundation. J [59] D’Errico J. PolyfitN function. Mathworks Central Repository; 2006. Eng Mech Div 1977;103(4):589–600. [60] National Park Service. Fort Sumter: Anvil of War: Fort Sumter National [38] Dutta SC, Roy R. A critical review on idealization and modeling for interaction Monument, South Carolina. Division of Publications; 1984. among soil–foundation–structure system. J Comput Struct 2002;80(20): 1579–94.