Nonlinear Seismic Assessment of a Historic Rubble Masonry Building via Simplified and Advanced Computational Approaches

Abstract

This research presents a comprehensive nonlinear quasi-static seismic assessment of an unreinforced rubble masonry building, Bytown Museum in Ottawa, Canada, using discontinuum-based analyses. In the proposed modeling approach, non-uniform geometrical properties of rubble masonry walls are replicated via a group of rigid polyhedral blocks interacting along their boundaries based on the discrete element method (DEM). Once the adopted modeling strategy is validated, the nonlinear quasi-static analysis of the South and North façades of the Bytown Museum is performed. Special attention is given to the irregular block generation within the discontinuum analysis framework, where discrete element models are generated from high-resolution site recording data, representing the masonry morphology at a high level of detail. Then, the predicted collapse mechanisms from advanced computational models are further utilized to generate pre-defined macro-blocks in kinematic limit analyses, providing a simple alternative solution for seismic assessment. The results reveal the significant effect of openings and the construction technique (morphology) in unreinforced rubble masonry buildings that can play an important role in the structural capacity and behavior. Moreover, it is noted that DEM-based solutions provide lower seismic capacity compared to kinematic limit analyses. Finally, a noticeable sensitivity to the input parameters in the discrete element models is noted; therefore, characterization of material properties is necessary for reliable predictions.

1. Introduction

The vast majority of historic masonry buildings were constructed using traditional techniques such as dry-joint or mortared unreinforced masonry (URM). The typical mechanical properties of URM constructions demonstrate relatively weak tensile strength (roughly 0.05–0.1 times its compression capacity). This salient feature of masonry causes cracking failures to be predominantly localized at the mortar joints. The cracking in masonry structures can be caused by: settlement, seismic activity, deterioration, and external loading, all of which threaten the conservation of the historic masonry buildings. These phenomena can be investigated via numerical modeling techniques (simplified or advanced approaches) or macro-block analysis based on virtual work principles.

Computational modeling of historic masonry buildings provides a better understanding of their structural mechanics, capacity, and failure mechanisms and is often utilized for structural analysis or performance assessments. The primary options for URM computational modeling can be described as macro, simplified-micro, and detailed micro-modeling. In the literature, macro modeling is also referred to as continuum-based analysis, and micro-modeling approaches are also called discontinuum-based analysis. The former approach is formulated based on the continuous finite element method (FEM), where the masonry is discretized as a fictitious homogeneous isotropic/orthotropic continuous medium with no local distinction between masonry units and joints [1,2]. In the macro-modeling approach, the damage is smeared out through the continuum unless a special crack localization algorithm is adopted [3,4]. Macro-models require less computational power; hence, they are commonly used in practice to analyze and design masonry buildings and in research for analyzing complex and large-scale masonry structures [5,6,7,8].

Simplified and detailed micro-modeling approaches offer a higher level of detail in representing masonry texture and behavior, although they have higher computational costs. In detailed micro-models, the masonry units, mortar, and unit-mortar interfaces are explicitly considered, where the units and mortar joints are represented as continuum blocks, and the unit–mortar interfaces are simulated using interface elements. This detailed representation of masonry allows for analysis of the local behavior, and failure can predominantly develop at the weak-mortar joints and/or unit–mortar interfaces. On the other hand, in simplified micro-models, masonry units are expanded by up to half of the thickness of the mortar joint, and the unit–mortar interfaces are considered to be zero-thickness interfaces [9,10]. This approach reduces the number of input parameters and computational power compared to the detailed micro-models.

Throughout this research, the discrete element method (DEM) is utilized to simulate the rubble masonry walls, which falls into the category of discontinuum-based analysis. The applied modeling strategy follows the simplified micro-modeling technique within the DEM framework. In DEM, the discontinuous nature of masonry is represented as the system of individual blocks that can be rigid or deformable [11,12]. The mechanical interaction between the adjacent blocks is described by point contacts, where orthogonal springs with frictional elements are defined. For the last several decades, discrete element models have been utilized in the analysis of various masonry structures ranging from small to large-scale with different levels of complexity [13,14,15,16,17,18]. It provides a substantial advantage compared to continuum-based solutions since the discontinuous description of the structure makes it possible to implement highly irregular geometrical features and existing cracks/openings in the numerical model [19,20].

It is important to note that, in any modeling strategy, the accuracy of numerical predictions relies heavily on the quality of imported geometrical data of the analyzed structure. Although various researchers proposed several workflows to import vision-based data into the continuum-based modeling techniques (e.g., Cloud-to-BIM [21]), a limited number of studies exist for the discontinuum type of analysis. Therefore, this research implements photogrammetric data in DEM to accurately represent rubble masonry walls and to predict their seismic capacity and associated collapse mechanism. DEM results are further utilized in the macro-block generation to perform kinematic limit analysis, which will provide a basis for preliminary engineering assessments. Hence, a novel data-driven discontinuum analysis approach is presented within the DEM framework to simulate the structural response of rubble masonry façades subjected to lateral forces.

The manuscript is organized as follows. First, a brief overview of the Bytown Museum is given (Section 2). In Section 3, the computational procedure of DEM and the adopted modeling strategy, referred to as Discrete Rigid Block Analysis (D-RBA), is presented. After presenting the validation of the proposed modeling approach in Section 4, the methodology used to numerically represent the rubble masonry from photogrammetric data is presented in Section 5. Section 6 discusses the in-plane pushover analyses carried out using DEM and compares the DEM results with the kinematic limit analyses. Finally, Section 7 offers concluding remarks on the findings of the study.

2. Bytown Museum

The Bytown Museum (former Commissariat Building) is an unreinforced masonry structure that was built with irregular limestone units (referred to as rubble masonry) and low-strength lime-based mortar joints (Figure 1). It is located in downtown Ottawa, adjacent to the Rideau Canal, between the Parliament buildings and the Fairmont Chateau Laurier. The Commissariat Building was a military storage facility established along the Rideau Canal. The three-story structure was constructed in 1827 by the Royal Engineering Corps using limestone masonry quarried nearby and is now Ottawa’s oldest stone masonry building. The building is 10.4 × 22.3 m² in plan and 12.2 m in height from the ground level to the peak of the roof. The thickness of the exterior masonry walls varies around 0.6 m, and several windows and bay doors are located at each level. The openings range from approximately 2 m² to 7 m². The elevations feature symmetrical and balanced compositions due to the rectangular shape and simple construction. The interior structure is composed of wood beams and columns and a simple truss system forming the gambrel roof, topped with cedar shingles. Throughout this research, an ideal material condition using a strong unit–weak mortar joint combination is adopted to develop the discrete element model. Moreover, no rubble stone core or second wythe of an irregular masonry wall is used in the computational models.

3. Brief Overview of Discrete Rigid Block Analysis (D-RBA)

This section briefly describes the employed modeling strategy based on DEM, developed by Cundall [22,23,24]. The proposed modeling approach, called the Discrete Rigid Block Analysis (D-RBA), considers the irregular and discontinuous nature of rubble masonry constructions as a system of rigid blocks that can mechanically interact with each other along their contact surfaces. Equations of motion are solved via the explicit finite difference method to predict block movements in a time marching scheme. Masonry units are represented via rigid polyhedral blocks, expanded by one half-thickness of the mortar joints on all sides, and the mortar joints are represented as zero thickness interfaces. Therefore, deformations are lumped at the joints without considering any deformations or stress concentrations that may develop within the block domain itself. This representation of masonry demands less computational power and reduces the required number of input parameters (also called simplified micro-modeling [10]).

The inter-block action/reaction forces are computed based on the point contact approach, illustrated in Figure 2. Throughout this research, only initially recognized point contacts, determined based on the common-plane concept [23], are used during the analysis. Once the contact plane is set by maximizing the gap or minimizing the overlap between the blocks, the contact normal is obtained, and point contacts (also called sub-contacts) are defined [25]. Essentially, two types of point contacts, vertex-to-face and edge-to-edge, are sufficient to assess all types of interactions [26]. At each point contact, orthogonal springs in the normal ($k_n$) and shear ($k_s$) directions are defined, governing the elastic behavior at the joints. The same contact stiffness is used both for compression and tension. Moreover, an identical constitutive model is utilized for both shear springs. In D-RBA, contact stiffness should represent the deformability of the masonry composite, which can be estimated using the Young’s and shear moduli of the material discussed in Section 6.3. Note that the soft-contact hypothesis is followed, which allows overlapping between adjacent blocks controlled by the assigned contact stiffness. Contact stresses are computed based on the relative point contact displacements in the normal ($u_n$) and shear ($u_{s,i}$) directions at each active contact point. In other words, the normal (∆${\sigma }_n$) and shear (∆${\tau }_{s,i}$) contact stress increments are obtained as a function of $∆u_n$ and $∆u_{s,i}$, respectively. In this study, recently implemented fracture-energy-based contact models are adopted for each point contact, incorporating the mode-I ($G_f^I$), mode-II ($G_f^{II}$), and compression ($G_C$) fracture energies (Figure 2) [27,28,29,30]. The tension capacity is limited by setting a tensile strength ($f_t$), while the Coulomb–Slip joint model is used for shear strength, requiring cohesion ($c$) and friction angle ($\varphi$), which are shown in the shear behavior plot in Figure 2. The calculated stress increments (∆${\sigma }_n$=$k_n∆u_n$, ∆${\tau }_{s,i}$=$k_s∆u_{s,i}$) are then added to the old contact stresses (computed in the previous time step). A contact stress update algorithm is employed to correct (if applicable) the new normal and shear stresses based on the given contact constitutive laws.

As mentioned earlier, the block movements are calculated by solving the equations of motions for the new translational (${\dot{u}}^{t+}$) and rotational (${\omega }^{t+}$) velocities that are obtained for block center of mass, given in Equation (1), where the time step ($∆t$) is evaluated at the mid-time intervals ($t^{+}=t+∆t/2$, $t^{-}=t-∆t/2$):

$$\begin{gathered} {\dot{u}}_i^{t+}={\dot{u}}_i^{t-}+\frac{∆t}{m}\left(\Sigma F_i^t-F_d\right); F_d=\lambda \left|F_i^t\right|sgn({\dot{u}}^{t-}) \\ {\omega }_i^{t+}={\omega }_i^{t-}+\frac{∆t}{I}\left(\Sigma M_i^t-M_d\right); M_d=\lambda \left|M_i^t\right|sgn({\mathsf{\omega }}^{t-}) \end{gathered}$$

(1)

where $m$, $I$, $\Sigma F_i$ and $\Sigma M_i$ are the block mass, the moment of inertia, the unbalanced force vector (sum of the contact forces, self-weight, and applied forces), and the unbalanced moment vector (sum of moments produced by contact and applied forces), respectively. Once the new velocities are obtained, the block positions are updated, and the new contact forces are computed. It is worth noting that the contact stresses are multiplied with the associated contact area to obtain contact forces utilized in equations of motion. Cundall’s local damping formulation is adopted to obtain quasi-static solutions, including a non-dimensional force-based damping constant, $\lambda$ (default value is 0.8) [31]. Note that the presented damping force/moment ($F_d$ and $M_d$ in Equation (1)) are proportional to the magnitude of the unbalanced force/moment opposing to the motion depending on the velocity vector ($sgn\left(\xi \right)=1, if \xi \ge 0, sgn\left(\xi \right)=-1, if \xi <0$).

Hence, block movements and interactions are computed via a dynamic solution scheme, and the numerical stability is ensured during the analysis by adopting a sufficiently small time step. The critical value ($∆t_c$), serving as the upper-bound for $∆t$, is computed utilizing the minimum block mass and the maximum contact stiffness defined in the system ($∆t_c=0.2\sqrt{m_{min}/k_{n,max}}$). The presented computational procedure of DEM is performed using a commercial three-dimensional discrete element code, 3DEC, developed by Itasca [32]. Furthermore, the adopted contact models are compiled as a DLL (dynamic link library) into 3DEC via the user-defined contact constitutive model option. In the following section, the validation of the D-RBA is presented.

4. Validation Study

In this section, the employed modeling strategy is validated against the recent experimental findings presented by Vasconcelos and Lourenço [33]. The benchmark study investigated the in-plane structural behavior of rubble masonry walls built with stone units and lime mortar under lateral loading. The tested masonry wall panels had dimensions of 1.2 × 1.0 × 0.2 m (height × length × thickness). The readers are referred to the reference study for more information about the test setup and experimental campaign [33].

The masonry wall panels built for the benchmark study are replicated using Rhino6, generating curves, surfaces, and solids using non-uniform rational basis splines [34]. The actual masonry morphology is developed in Rhino6 using joined line segments and extruded closed planar curves, such that it could be used in 3DEC, as shown in Figure 3. Furthermore, the material and contact properties are taken from the relevant literature studies [35,36,37], and are provided in

Table 1. Contact properties defined in the discrete element model.

$\mathit{\rho } \left(\mathit{k}\mathit{g}/{\mathit{m}}^3\right)$	${\mathit{k}}_{\mathit{n}}, {\mathit{k}}_{\mathit{s}} \left(\mathit{G}\mathit{P}\mathit{a}/\mathit{m}\right)$	${\mathit{f}}_{\mathit{t}},\mathit{c} \left(\mathit{M}\mathit{P}\mathit{a}\right)$	${\mathit{\varphi }}_{0, \mathit{r}\mathit{e}\mathit{s}} (°)$
$2000$	$20$$, 0.4k_n$	$0.1$$, 2f_t$	$22$$, 22$
$f_c \left(MPa\right)$	$G_f^I \left(N/m\right)$	$G_f^{II} \left(N/m\right)$	$G_c \left(N/m\right)$
6.1	10	100	9000

.

First, the self-weight and the vertical pressure (0.5 MPa) are applied, and the computational model is brought into equilibrium under these dead loads. Then, the lateral loading is imposed in a displacement-controlled manner by prescribing a displacement rate at a rigid loading beam at the top of the wall in the lateral direction. During the analysis, reaction forces developing between the supporting block and bottom course of the masonry panel are recorded. The results indicate that the proposed discontinuum-based approach provides accurate predictions capturing the ultimate load with a 2–5% difference compared to experiments, as shown in Figure 4. In addition, a good match is obtained regarding force–displacement response and the crack pattern, in which certain variations should be expected since the experimental envelopes were obtained from cyclic testing. In contrast, computational models are subjected to monotonic loading. Due to the irregular and asymmetric morphology of the rubble masonry panels, the left-to-right and right-to-left force-displacement curves are different (Figure 4). It should be noted that the force–displacement curves associated with DEM are obtained from two separate analyses, where each model is subjected to only one loading direction.

Different collapse mechanisms are obtained depending on the loading direction in line with the benchmark study. The cracks are localized and propagated through the weak mortar joints, where both tensile and shear failures are noted during the analysis, presented in Figure 5.

In the next section, the validated modeling strategy is applied to assess the seismic behavior of the rubble masonry façades.

5. From Vision-Based Data to D-RBA

The discrete element model of the Bytown Museum represents the morphology of the masonry to a high level of detail using geometric and visual data acquired via site recording methods. Site recording data, including high-resolution digital images and digital reference points of the Bytown Museum, were captured using a Sony Alpha A7RIV camera with a 24–70 mm lens, a Mavic 2 Pro drone, and Leica TS11 total station. The data were processed using Agisoft’s Metashape software to generate high-resolution orthometric images of each façade presented in Figure 6.

To generate discrete rigid blocks in 3DEC, each façade orthophoto is traced in Rhino6 using joined line segments. The employed discrete element code is limited to convex blocks only to accurately generate joint planes between rigid blocks. As such, any internal angle should be less than or equal to 180°, as illustrated in Figure 7. This geometric constraint resulted in some minor simplification of the joint patterns and block shapes from the actual morphology of the rubble masonry walls represented by the orthophoto, shown in Figure 8a. As mentioned earlier, based on the simplified micro-modeling approach, the joints are traced to describe the geometry of the masonry units, assuming that the units are expanded to include half the depth of the surrounding mortar joints. Furthermore, the rubble masonry texture of visually obstructed areas of the façade is assumed by following the average rubble block size and shapes. The North and South façades of the Bytown Museum comprise a total number of rigid polyhedral blocks, 2450 and 2398, as depicted in Figure 8b,c.

6. In-Plane Pushover Analysis of Bytown Museum

In this section, the seismic capacity and failure mechanisms of the North and South façades of the Bytown Museum are analyzed using the DEM-based model. The obtained results are utilized in a simplified analysis based on the upper bound theorem of limit state analysis. Furthermore, sensitivity analysis is used to illustrate the effect of several input parameters.

6.1. Discontinuum-Based Nonlinear Quasi-Static Analysis of the Bytown Building

The quasi-static nonlinear analyses are performed by adopting mass-proportional lateral forces in a gradually increasing fashion in the discrete element model by imposing a uniform acceleration field in the lateral direction. The displacements at the top left/right corners (depending on the loading direction) are monitored during the analysis and utilized in the force–displacement curves. The material and contact properties are determined based on the similar studies presented in the literature (e.g., [14,29,38,39,40]), given in

Table 2. Contact properties used in D-RBA.

$\rho (\mathit{k}\mathit{g}/{\mathit{m}}^3)$	${\mathit{k}}_{\mathit{n}},{\mathit{k}}_{\mathit{s}} (\mathbf{GPa}/\mathbf{m})$	${\mathit{f}}_{\mathit{t}},\mathit{c}, {\mathit{f}}_{\mathit{c}} \left(\mathbf{MPa}\right)$	${\mathit{\varphi }}_0,{\mathit{\varphi }}_{\mathit{r}\mathit{e}\mathit{s}} (°)$	${\mathit{G}}_{\mathit{f}}^{\mathit{I}},{\mathit{G}}_{\mathit{f}}^{\mathit{I}\mathit{I}}, {\mathit{G}}_{\mathit{c}} (\mathbf{N}/\mathbf{m})$
2000	$10, 0.4k_n$	0.1, 0.15, 1.9	35, 35	1.5, 15, 3035

. Moreover, the fracture energy values are computed following the suggested ductility index values in [41,42]. Specifically, the ductility index for tension $d_{u,t}$ (the ratio between the fracture energy and tensile strength, $G_f^I/f_t$) is taken as 0.15, whereas $G_f^{II}$ is estimated as 10 $G_f^I$ [42]. Furthermore, compressive fracture energy is computed considering the ductility of 1.6 (i.e., $d_{u,c}=G_c/f_c$), given in [41].

The results reveal that the North and South façades have distinct seismic capacities and failure modes that are also influenced by the loading direction. Note that applied lateral force vectors are denoted based on their directions, such as left-to-right (L-R) and right-to-length (R-L). As shown in Figure 9a, the North façade demonstrates 20% higher seismic capacity than the South façade for both L-R and R-L directions. The outcomes of this analysis highlight that the percentage, location, and proportions of opening in unreinforced rubble masonry walls have a considerable effect on the capacity and structural behavior presented in Figure 9b–e. Although the South and North facades have a close opening percentage (21% and 17%, respectively), the location of the opening is entirely different compared to one another, which drastically varies the in-plane response of the structure. The large rectangular openings in the South façade negatively influence its seismic capacity, as seen in Figure 9a. It is also important to note that a minor difference in seismic capacity is observed in both façades due to asymmetric and irregular morphology of wall cross-sections, causing slightly different crack patterns.

In all nonlinear quasi-static analyses, the initial damage is observed at the contact surface between the masonry walls and the rigid foundation block due to high flexural tensile stresses developing at the bottom section of the numerical model. This phenomenon can be observed in the force–displacement curves as the primary stiffness change in the structure (Figure 9a), followed by a gradual stiffness degradation due to successive joint opening and sliding failures until reaching the kinematic mechanism. The position of hinges, developing successively during the analyses, can be detected under the imposed incremental loading. These locations are utilized later to represent the façade as a rigid macro-block system. It is worth noting that the cracks concentrate at the corners where the openings exist and propagate diagonally through the weak mortar joints, as shown in Figure 9b–e. Toe crushing is noted at the bottom left or right corner (depending on the loading direction, see Figure 9b–e), where the compression forces are concentrated due to lateral deformation. Recall that, throughout this study, tensile and shear failures are lumped at the joints without considering cracking in masonry units due to the strong-unit weak-joint action assumption.

6.2. A Simplified Approach: Kinematic Limit Analysis

In this section, collapse mechanisms obtained from the D-RBA are used to guide the development of a model that uses rigid macro-blocks, considering Heyman’s material model for masonry (i.e., no tensile strength, no sliding failure, and infinite compression strength [43]). It is worth highlighting that, in line with the present study, different computational techniques (e.g., continuous displacement for fracture (CFD) and piecewise rigid displacements (PRD) methods) have been recently proposed to detect the rigid macro-block mechanisms in URM buildings within the limit analysis framework by other researchers [44,45]. Different from these developments, the proposed approach depicts the failure mechanism from D-RBA solely relying on DEM. The readers can find further discussion/application of limit state analysis using Heyman’s material model in the references ([46,47,48,49] among others).

As mentioned, when the masonry consists of weak mortar joints and no reinforcement are used, the collapse mechanism can be predicted via a pre-defined system of rigid macro-blocks interconnected through the instantaneous point of rotations (also referred to as hinges) [50]. Then, the lateral load multiplier (α) is computed using the virtual work principle, which can be written in a compact format as follows:

$$\begin{gathered} {\displaystyle \sum }_{i=1}^n\left(H_i{y}_i+W_i{x}_i\right){\theta }_k=0 \\ {H}_i=\alpha W_i \end{gathered}$$

(2)

where $W_i$ and $H_i$ represent the self-weight of the pre-defined macro-block and the horizontal seismic force (proportional to $W_i$ with a multiplier, $\alpha$). Additionally, the distance components of the vertical and horizontal forces from the instantaneous center of rotation are denoted by $x_i$ and $y_i$, respectively, with the associated virtual rotation, ${\theta }_k$. In Figure 10, the DEM-guided macro-blocks are presented for both façades. The collapse mechanism of the South façade consists of five macro-blocks, whereas the North façade has only one macro-block (Figure 10). Once the macro-block(s) are determined, the principle of virtual work is applied to compute the maximum acceleration that triggers the defined mechanism. The advanced discontinuum-based analysis, adopting the material and contact properties given earlier in Table 2, and the simplified solutions are compared in

Table 3. Comparison of D-RBA and Kinematic Limit Analysis (acceleration (g)).

	$\mathbf{D}-\mathbf{RBA} \left({\mathit{a}}_{\mathit{D}-\mathit{R}\mathit{B}\mathit{A}}\right)$	$\mathbf{Kinematic} \mathbf{Limit} \mathbf{Analysis} \left(\mathit{\alpha }\right)$	Difference $\left|\left(\frac{{\mathit{a}}_{\mathit{D}-\mathit{R}\mathit{B}\mathit{A}}-\mathit{\alpha }}{\mathit{\alpha }}\right)\mathit{\times }100\right|$
South Façade	0.31	0.39	20
North Façade	0.36	0.50	28

. The kinematic limit analyses result in higher seismic capacity, up to 30%, compared to the results obtained from the proposed discrete element models. This variation stems from differences in the assumptions of material constitutive law in D-RBA and kinematic limit analyses, in which the former approach has limited compression strength and finite stiffness, whereas the latter considers rigid macro-blocks with infinite compression strength.

6.3. Parametric Analysis and Comparison of D-RBA vs. Kinematic Limit Analysis

Sensitivity analyses are performed for contact stiffness (i.e., $k_n$: 10⁹, 10¹⁰, and 10¹¹ GPa/m) and masonry compressive strength (i.e., $f_c$: 1.9 and 3.8 MPa [51,52,53]) to better understand their effect on the in-plane seismic capacity.

The contact stiffness can also be predicted in D-RBA as the ratio of masonry elastic modulus and average vertical spacing in the discrete rigid block system (i.e., $k_n=E/h$). Therefore, the adopted contact stiffness values for the sensitivity analyses approximately correspond to the elastic modulus of masonry ranging from 0.2 to 20 GPa, which covers the experimental findings presented in the literature [52,53]. The results indicate the noticeable influence of both parameters (i.e., $k_n$ and $f_c$) on the in-plane seismic capacity, as shown in Figure 11. As noted earlier, the reference values of $k_n$ (10 GPa/m) and $f_c$ (1.9 MPa) consistently provide lower values for ultimate lateral acceleration for the North and South façades.

A good agreement is found between the discrete rigid block and kinematic limit analyses for the South façade, presented in Figure 11. Especially for higher values of contact stiffness ($k_n$ > 10 GPa/m), the seismic capacity obtained from D-RBA gets close to the kinematic limit analysis. This trend is in line with the material model assumption in limit analysis, which considers infinite compression strength and a rigid macro-block system. However, when two computational approaches are compared, a relatively large difference is observed for the North façade. This difference is attributed to the complex and progressive damage developing during failure affected by the smaller and more widely spaced openings in the structure. Therefore, the initial fracture pattern of the façade is utilized for limit analysis, which consists of a single macro-block, illustrated in Figure 10. Hence, the DEM-guided macro-block represents the initial failure mechanism and does not include the extensive cracking that develops in the piers during the progressive collapse mechanism.

7. Conclusions

This research investigates the seismic behavior and capacity of an old rubble masonry building constructed almost two centuries ago. A discontinuum-based modeling strategy, referred to as discrete rigid block analysis (D-RBA), is used in the seismic analysis of the Bytown building, where vision-based data are utilized to represent the construction details. The proposed vision-based computational modeling strategy provides high accuracy in the representation of wall morphology and, therefore, offers a better understanding of the effect of construction techniques in historic buildings. The outcomes of this study highlight the importance of opening layout (size and location) in unreinforced rubble masonry buildings affecting structural capacity and collapse mechanism. In this regard, according to the results of the analyses, the South façade of the Bytown building demonstrated 20% less in-plane seismic capacity than the North façade, which is attributed to its large and concentrated openings.

A simplified solution based on the kinematic limit analysis is proposed, where the pre-defined macro-blocks are taken from the D-RBA. It is shown that the kinematic macro-block approach can provide an alternative solution with reasonable accuracy for the preliminary seismic assessment. In future studies, we will further explore other components of the building, including the east and west façades, and include the timber floors to simulate the diaphragm action.