Scalable BIM based open workflow for structural analysis of masonry building aggregates

Computers and Structures 297 (2024) 107321 Available online 27 February 2024 0045-7949/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Scalable BIM based open workflow for structural analysis of masonry building aggregates Maria Laura Leonardi * , Jos´ e Granja , Daniel V. Oliveira , Miguel Azenha University of Minho, ISISE, ARISE, Department of Civil Engineering, Guimar˜ aes, Portugal ARTICLE INFO Keywords: Built heritage HBIM Finite Element Method (FEM) Historic centres Seismic analysis OpenSees Interoperability OpenBIM ABSTRACT Masonry building aggregates are complex historical structures comprising interconnected buildings. The safety of each building depends not only on its structural integrity but also on the interactions with neighbouring structures and their collective performance. The structural assessment of such complex constructions can benefit from BIM methodology. The latter eases modelling complicated solid geometries and assigning mechanical properties information essential for developing a reliable finite element model. Thus far, BIM to finite element analysis procedures applied to historic constructions have remained laborious, semi-automatic, and based on proprietary software. This paper introduces an open-source automated solid finite element analysis method using OpenBIM data (IFC). The tool implemented automatically creates tetrahedron mesh and assigns mechanical properties, self-weights, and fixities at the structure’s base. The methodology is applied to an actual masonry building aggregate to validate its capability of working with complex geometries and scalability. 1. Introduction Masonry aggregates are unique historical unreinforced masonry structures that consist of assemblies of buildings, mainly residential, whose structural behavior is unitary. The presence of these constructions creates a recurring pattern within the landscape and significantly influences the morphology of historic centres [1,2]. Although their cultural value is currently universally recognized, their state of preservation is often poor and somehow unsuitable for a contemporary lifestyle [3,4]. A significant concern is the high vulnerability of masonry aggregates to natural hazards, particularly earthquakes [5]. After analysing postseismic scenarios, the scientific community has delineated two distinct seismic mechanisms exhibited by unreinforced masonry buildings and by extension, masonry building aggregates: out-of-plane and in-plane. In out-of-plane mechanisms, portions of masonry walls (or entire walls) rotate perpendicularly to their plane, leading to the collapse of significant parts of the building. Conversely, in in-plane mechanisms, cracks are formed in the plane of walls. Out-of-plane mechanisms occur even during mild earthquakes, mainly when the structure exhibits deficient connections between adjacent walls or between walls and floors. On the contrary, in-plane mechanisms occur during stronger earthquakes and depend mainly on the masonry’s shear resistance [1]. The current guidelines offer simplified methods to assess the seismic behaviour of masonry building aggregates, with a primary emphasis on out-of-plane ‘local’ failure, while neglecting their overall performance [6,7]. In addition to the mechanisms typical of masonry buildings in general, aggregates introduce specific mechanisms, such as beatings of the floor of a building to the adjacent one. Based on these considerations, the existing guidelines facilitate the identification of vulnerable areas within the aggregate, enabling timely consolidation interventions in critical locations. The most challenging aspect to achieve at present is the determination of the “aggregate effect,” which represents the variation in local responses arising from the composite nature of the construction. However, the proper assessment of this effect necessitates the utilization of global models [8]. The use of global models is considered as the most detailed level of analysis applicable for this type of construction, as defined in the guidelines, where it is stated that local analyses applied to small portions of the aggregate, without adequate modelling or with an approximate modelling of the interaction with adjacent building bodies, generally assume a conventional meaning and in some cases are even impracticable due to the uncertainty in the estimation of the variables to be adopted [7]. Structural engineering includes two ways of performing seismic analysis using global models: static and dynamic. Dynamic analyses * Corresponding author. E-mail address: [email protected] (M.L. Leonardi). Contents lists available at ScienceDirect Computers and Structures journal homepage: www.elsevier.com/locate/compstruc https://doi.org/10.1016/j.compstruc.2024.107321 Received 6 September 2023; Accepted 13 February 2024 Computers and Structures 297 (2024) 107321 2 enable a more representative simulation of the seismic behaviour of buildings, as they simulate the structure’s dynamic response when a dynamic load is applied. Another option is to perform static analyses by applying horizontal loads simulating an earthquake and verifying the building’s global capacity to withstand the horizontal load. The first procedure evaluates the building’s dynamic response to a specific seismic load. In contrast, the second method estimates the overall structural capacity under horizontal loads [9,10]. As per the Italian Building Code [11], which serves as a primary international reference for evaluating the structural behavior of unreinforced masonry structures, the utilization of global models is permissible only when there exists a satisfactory level of understanding regarding the assessed structure. This is because the reliability of global models strictly depends on the reliability of the input data [11]. For this reason, the structural model is the final step in a complex process involving experts from different fields. To identify the most appropriate modelling assumptions, historical analysis, in-situ surveys, inspections, and building monitoring must be carried out [12]. This process currently requires considerable time and economic resources. If this is already a major problem for individual buildings, it is even more so for complex structures such as masonry aggregates. For this reason, an optimal system for data and process management is required. Aside from the need for deep knowledge of the building, when it comes to historical constructions, global analysis presents significant computational costs, mainly due to the material and geometrical nonlinearity of traditional masonry structures. Furthermore, a thorough knowledge of the building is necessary to obtain reliable results. In order to decrease the computational costs, simplified models have been defined, such as the equivalent frame method [13]. However, the use of solid finite element models is recognised as more representative of masonry’s structural behaviour. Indeed, in the case of the equivalent frame, the structure is studied by considering pre-defined in-plane failure modes, neglecting possible out-of-plane collapses of the masonry. On the other hand, finite element analysis relies on the principles of continuum mechanics and mathematical modelling to simulate and understand the behaviour of structures under various conditions, and, even if not explicitly, it catches both in-plane and out-of-plane failure modes. Finally, masonry is a heterogeneous material consisting of units (bricks or stones) bound by joints (dry or with mortar) [14,15]. This feature can be included in the structural model in two different ways. Either the units and joints are modelled explicitly (micro modelling), or homogenised mechanical parameters represent the unit-joints ensemble (macro modelling). Various studies have made it possible to obtain these parameters, and the mechanical characteristics of various types of masonry are present in the Italian standards [11,16,17]. In the literature, both static and dynamic analyses have been found applied to masonry aggregates. Most of the contributions are done using the equivalent frame method, and just a few employ the finite element analysis. Examples of equivalent frame modelling are found in [19–21] and are intended to calibrate large-scale methods such as the ’vulnerability index’. The vulnerability index is still one of the most widely used methods for a fast large scale seismic assessment of masonry aggregates. Although it does not numerically evaluate the aggregate’s behaviour to seismic excitations, it aids in identifying the most vulnerable units within a whole aggregate. References to this method are available in [22] and [23], as well as in [24], where potential integration into BIM/GIS methodologies is discussed. In other contributions, equivalent frame models have been calibrated for analysing a single aggregate unit, creating boundary conditions that can represent the presence of adjacent units [25,26]. However, these applications consider only simple one-line aggregates and neglect material nonlinearity. Finally, in [27], the equivalent frame is compared with solid finite element models. In this scenario, it is affirmed that finite element analyses prove more suitable since they can effectively account for both in-plane and out-of-plane mechanisms, rendering them more reliable. Moreover, the equivalent frame involves breaking down masonry into regular panels, aligning with the simulated failure modes. This task can become complex (or even impossible) in masonry aggregates due to geometric irregularities. Finally, another application of finite elements to masonry aggregates is found in [28], where an entire aggregate was modelled, even if only walls were modelled (neglecting the presence of the floors) due to modeling complexity and computational costs. In the Architecture, Engineering and Construction (AEC) industry, the information management processes changed dramatically with the advent of Building Information Modeling (BIM). This methodology has been already applied to historical construction, referred to by the acronym of HBIM, which stands for Historic BIM [29]. Several HBIM uses have been proposed in the literature, validating the convenience of applying this method to historical construction [30,31]. Applications of interest to this field include damage mapping [32,33], health monitoring [34], and structural simulations [35–37]. In addition, the possibility of integrating energy analysis and different disciplines has been already stated [38,39], as well as the possibility of establishing a connection between the HBIM model and additional information stored as different datatypes [40]. Integrating various aspects of rehabilitation, including energy efficiency and structural restoration, is crucial in historical constructions, given that masonry walls serve dual purposes as both structural elements and envelope components. Moreover, ongoing studies are dedicated to enhancing the modelling process itself through the integration of advanced surveying systems, notably laser scanning [41,42]. Advanced acquisition systems offer the advantage of capturing complex geometry that can exert a significant influence on the structural response of historical buildings. As a result, workflows have been proposed to suitably derive the structural model from point cloud data [43–46]. Conversely, other contributions use the capabilities of BIM to associate the modelled geometries with parameters, including those of mechanical properties. These frameworks propose using the point cloud to model the building in BIM and then transition to finite element models [35,47,37], or to use the initial point cloud to create two distinct models: a BIM model and a more simplified structural model, without direct interoperability between BIM and structural model [48,36]. The primary challenge associated with the above-mentioned frameworks is their labour-intensive nature, as they are not fully automated processes, due to the absence of plug-ins to allow conversion from solid BIM representation to solid finite element meshing. These processes lack scalability and moreover rely on specific proprietary software. Consequently, those seeking to employ a particular methodology are required to obtain licenses, which can incur additional costs. In contrast, vendor-neutral processes allow the benefits of BIM processes to be extended by making them more accessible. The current terminology for this approach is openBIM [49], which relies on the Industry Foundation Classes (IFC) [50] format as the basis for exchanging data in the openBIM framework. IFC is an open and neutral data format standard designed for the exchange and sharing of information within the building and infrastructure industries [51]. Extending the openBIM approach to historical constructions presents a relevant challenge since IFC has not been structured adequately to describe such building typology. The suggestion to incorporate additional classes into the IFC schema has been made to improve its compatibility with the structural analysis of historical buildings [52,53]. Unfortunately, these classes are not currently acknowledged by either BIM or structural analysis software, rendering them unusable for this purpose. This paper proposes an original openHBIM method for the global analysis of masonry aggregates, with the scope of facilitate the use of solid finite element modeling (with macro modeling of the material). In line with what has been said up to now, it is assumed that the integration of the HBIM methodology in the structural analysis of masonry aggregates can lead to better data management, integration with all phases of the structural analysis itself and with any other disciplines involved in M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 3 the rehabilitation project. The proposed approach involves employing a code developed by the authors to export the IFC model to the ’OpenSees’ finite element calculation framework [54]. The code generates a mesh of tetrahedron elements and directly retrieves the mechanical properties from the parameters contained in the HBIM model. This methodology enables users to create their calculation models in any BIM software, export them to IFC, and conduct static and dynamic analyses. The model information is inputted into the BIM environment, adhering to the ’Level Of Information Need’ specified by the authors [55]. Moreover, the OpenSees calculation framework is an open framework, ensuring the methodology’s complete independence from proprietary software. The finite element model underwent testing through gravity and eigenvalue analysis, using an aggregate with complex geometries as a case study. The model holds the potential for both static and dynamic nonlinear analyses, due to the model content and mesh refinement. However, nonlinear analysis would add extra complexity that would deviate from the main purpose of this paper, which is to present the developed algorithm in detail. Nevertheless, performing nonlinear analysis is definitely a next step of research for harvesting the true potential of this tool. The article is organized as follows. Section 2 provides a comprehensive overview of the proposed methodology. Section 3 demonstrates the application of the methodology through a case study. Section 4 showcases the results obtained from the application. Section 5 presents the conclusions drawn from the study. 2. Scope and methodology 2.1. Masonry aggregates Masonry aggregates are the traditional housing constructions in many European centres. These were raised using masonry made of local stone/brick for the vertical elements and timber slabs and roofs. These structures exhibit diverse plan and elevation configurations, influenced by factors like historical changes, site morphology, and construction periods. These configurations can range from irregular layouts that follow the terrain’s morphology to more regular grid patterns. Various historical stages, such as the Middle Ages, Renaissance, Baroque, and 19th century, have contributed to the evolution of these aggregates. For example, Renaissance and Baroque periods saw the growth of aggregates with more regular plans, while the 19th century brought disruptive changes due to the creation of large roads [56–58]. Additionally, the introduction of new construction techniques like reinforced concrete led to the replacement of original roofs, introducing new vulnerabilities [1]. In contrast to monumental constructions, traditional residential buildings were not always built with the same level of attention to detail. This resulted in poor-quality wall cross-sections, especially in certain locations. Moreover, the successive construction phases introduced complexities in the configuration, including uneven floors, misaligned openings, and inadequate connections between cross walls. Structurally, these building compounds are particularly vulnerable to out-of-plane failure mechanisms, as the connections between orthogonal walls and between horizontal and vertical elements are not always adequate [59]. 2.2. Proposed approach The purpose of this contribution is to provide a systematic method for the comprehensive analysis of masonry aggregates. The integration with the HBIM methodology is included to increase the feasibility of a quick and cost-effective creation of complex models. Based on the construction characteristics of masonry aggregates, it is decided to employ solid FEM, bringing the potential of capturing other failure modes, aside from the prescribed ones. The accessibility of the methodology is guaranteed by proposing a methodology that does not rely on proprietary software. Aligned with an openBIM approach, it was decided to choose to use the IFC schema as our input model. In Section 3, the case study is modeled using Revit software (version 23.0.11.19) and then exported to IFC using the software’s built-in IFC interpreter [60]. Any BIM modelling software can generate an IFC model based on the requirements outlined in this article (Section 2.3). Interoperability between IFC and FEM was accomplished by Fig. 1. General workflow for the methodology. The workflow number refers to the detailed description of the algorithm in section 2.5. M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 4 developing a Python code, which was made available online for users and developers [61]. The proposed process starts from the BIM model and enables static and dynamic analysis in OpenSees. Due to the complexity of the geometry usually characterizing masonry aggregates, it is decided to use tetrahedra elements. The mechanical characteristics of the materials are associated with the elements directly in the BIM model and are read along with the geometry by the computational solver. Since OpenSees does not have an official open graphical interface, the results are displayed using the open FEM meshing software Gmsh [62–64]. Fig. 1 illustrates the overall workflow of the proposed methodology. By utilizing the Python code developed with its requisite dependencies, a seamless transition from an IFC model to the outcomes of the structural analysis can be achieved automatically. The ’IfcOpenShell’ and ’OpenCascade’ libraries enable access to the geometries and mechanical properties of the IFC model, respectively. The geometries undergo meshing using the Gmsh Python API, while the resulting mesh and mechanical properties are integrated into OpenSees for conducting the analyses. Finally, the analysis results are presented in the Gmsh GUI for visualization. 2.3. Modelling requirements The modeling requirements were established in accordance with the ’Level Of Information Need’ schema outlined in EN17412-1. According to this standard, for each design stage, it is essential to define geometric requirements, alphanumerical information (non-graphical data associated with the geometry), and documentation, if applicable. Refer to [55] for a detailed description of this schema. In the definition of the modelling requirements, BIM is leveraged as a collaborative platform for integrating diverse disciplines, enabling the creation of a federate multidisciplinary model from which generating Fig. 2. Federate multidisciplinary model compared to the discipline structural analysis model. Fig. 3. Common typologies of construction elements in masonry aggregates. M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 5 multiple exports into IFC format tailored to specific disciplines. As can be seen from Fig. 2, the passage from an architectural model to a structural model consists of only exporting the structural elements and neglecting the non-structural ones. In this case, the use of solid FEM modelling allows for the creation of an analytical model that is more straightforward without needing adjustments when switching from solid to oneor two-dimensional elements. This approach will not hinder the use of the complete model for other purposes. The objects of the structural breakdown were defined after a typological study based on the work of Giuffre [65], as follows: (1) structural wall, (2) partition, (3) foundation, (4) floor, (5) roof, and (6) openings (windows and doors). The following “IfcBuildingElement” are required to represent the different objects previously mentioned: “IfcWall” for Structural Walls and Partitions, “IfcFooting” for the foundations, “IfcBeam” for the main beams and secondary beams of roofs and floors, “IfcSlab” for the planking on top of the beams or reinforced concrete slabs, “IfcDoor” and “IfcWindow” for the openings. Each IFC object belongs to a specific “IfcBuildingElementType”. Fig. 3 shows common typologies of structural elements in masonry aggregates. Coherently with the type of modelling chosen (macro modelling), it is not necessary to geometrically model units and mortar. Therefore, walls are to be modelled as continuous prisms, to which different mechanical property values are assigned, corresponding to different wall types. The floors, usually in timber, should be modelled as a set of rafters topped by a timber plank that redistributes the weights (as shown in Fig. 2), and if present, the main beam as shown in Fig. 3 (Type B). Similarly, for wooden roofs, modeling the joists is also critical. For one pitch roof, the direction of the joists can be the same of the slope (Fig. 2) or perpendicular to it (Fig. 3, Roof B1). More complex roofs are characterized by two layers of joists perpendicular to each other (Fig. 3, Roof B2), or by the presence of two pitches and one main beam (Fig. 3, Roof C). When present, it is fundamental to model concrete roofs, since those are often recent additions which often cause local mechanisms in the aggregate. As show in Fig. 3 (Roof D), these can be modelled as simple slabs. Vertical partition elements, while not having a main structural function, contribute to the overall behaviour of the structure. These can be brick walls as in Fig. 2 or timber post/lintel structures (Fig. 3, Table 1 Detail of the elements in the breakdown. Elements Detail Structural Wall Continuous object of thickness equal to the resistant section of the masonry. The basic shape is a parallelepiped, which is modified by the presence of beams entering the wall thickness and stone lintels. Opening It consists of a void representing a hole in the wall and a solid representative of the lintel. Foundations Continuous object slightly thicker than the wall above. Floor Discontinuous object consisting of rectangular-section beams topped by two slabs representing respectively planking and tiling. Roof Discontinuous object consisting of rectangular-section beams topped by two slabs representing respectively planking and roof covering layer. Partition Continuous or discontinuous object (based on the type). Fig. 4. Association of the material properties to the elements in IFC. The material properties define the IfcMaterial, which can be associated with an Element or an ElementType. M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 6 Partitions B). Doors and windows can present different variations, but only the difference between arches and lintels has been considered at this stage. Finally, information about the foundations is difficult to encounter, but foundations can be assumed as a downward continuation of the walls, with a thicker cross-section. Regarding geometric requirements, ’Details’ and ’Dimensionality’ are established for each object, which are the relevant criteria for this application. All objects have 3D dimensionality, while the detail is established in Table 1. This is aligned with the choice of solid modeling and allows interoperability with different BIM uses. Regarding ’alphanumerical information,’ this application requires mechanical characterization of structural materials and connection types between timber and walls. The following paragraphs, and Fig. 4 explain the IFC schema and how these properties are assigned to elements in the model. The IFC schema is structured hierarchically and organized into classes that define various entities. Within this schema, ’IfcBuildingElement’ is a subclass of ’IfcObjectDefinition’ and a superclass to entities such as IfcWall, IfcSlab, IfcRoof, IfcBeam, IfcFooting, IfcWindow, and IfcDoor — classes utilized by the authors to model structural elements. On the other hand, ’IfcMaterial’ is a subclass of ’IfcMaterialDefinition’, and it is employed, in this application, for modelling structural materials. Mechanical properties of materials and pertinent characteristics of structural elements, like wall-timber connections, are represented as ’IfcProperties,’ a subclass of ’IfcPropertyDefinition.’ These properties are organized into groups called ’IfcPropertySets,’ another subclass of ’IfcPropertyDefinition.’ Each ’IfcProperty’ is associated with an ’IfcBuildingElement’ or an ’IfcMaterial’ via the class ’IfcRelDefinesByProperty,’ a subclass of ’IfcRelationship.’ Specifically, mechanical pro perties are ’IfcProperties’ associated with their respective ’IfcMaterial’. The type of wall-to-beam connections, on the other hand, is modelled with a parameter that is associated with the beams. The IFC schema inherently offers various ’IfcPropertySets’ containing ’IfcProperties’ for diverse applications. In this context, two ’IfcPropertySets’—’IfcMaterialCommon’ and ’IfcMaterialMechanical’—co ntain specific mechanical properties. ’IfcMaterialCommon’ includes the property ’MassDensity,’ while ’IfcMaterialMechanical’ encompasses ’YoungModulus,’ ’ShearModulus,’ and ’PoissonRatio.’ In Finite Element Method (FEM) modelling, ’ShearModulus’ and ’PoissonRatio’ are often correlated. The BIM modeller can choose either, depending on available data, such as in situ tests on masonry. When modelling features beyond the basic IFC schema, one can introduce new ’IfcPropertySets’ with customized ’IfcProperties.’ For instance, for the scope of the project, the authors introduced ’Pset_MaterialHistoricMasonry,’ accommodating parameters outlined in the NTC [11] not covered by the IfcPropertySets. Similarly, a new ’IfcPropertySet’ called ’IfcConnection’ was defined for structural information, describing connections between walls and beams. Within this property set, the ’Connection’ property can assume values like ’null,’ ’unstrengthen,’ or ’perfect.’ Based on this property associated with beams, the decision to export the beam is determined respectively, if the connection is ’null’ or ’perfect.’ For intermediate situations (unstrengthen), efforts are underway to automate, in this IFC to FEA framework, the implementation of nonlinear springs associated with this non-perfect connection (see [66] for detailed information). Finally, the association of an ’IfcBuildingElement’ with an ’IfcMaterial’ can occur in two distinct ways: through ’IfcBuildingElementType’ or directly through ’IfcBuildingElement’ itself. The former is applicable when identical walls, for example, are modelled using a wall type (’IfcBuildingElementType’) to which various instances (’IfcBuildingElement’) are linked. In the latter case, a unique wall with a specific material not belonging to any ’IfcBuildingElementType’ is represented. In both scenarios, the ’IfcMaterial’ is associated with either the ’IfcBuildingElement’ or the ’IfcBuildingElementType’ through the relation ’IfcRelAssociatedMaterial,’ a subclass of ’IfcRelationship.’ Moreover, depending on the object type, the material is associated with the object in either ’layers’ or ’profiles.’ For instance, a wall may have several layers with different materials, while a beam may feature one or more resistant sections. In addition to defining modeling requirements, exchange requirements are also established to determine the most suitable Model View Definition. Currently, there are two options available: ’Reference View’ and ’Design Transfer View.’ The former is mainly intended to validate the model’s accuracy, particularly for identifying and resolving geometrical conflicts between the elements (known as clash detection). Conversely, the latter is specifically designed for sharing useful data across different domains (for example: sharing the geometry from the architectural to the structural model). This holds significant importance, as the selection of one Model View Definition over another influences the way geometries are depicted within the IFC format. All structural elements are represented in 3D. In IFC, the ’IfcShapeRepresentation’ class attributes a geometry representation to an ’IfcBuildingElement’, and it is inherited from ’IfcProduct’. The IFC Fig. 5. Types of representation used for masonry aggregate walls available in different MVD. M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 7 standard presents a range of Representation Types, and not all of them are adequate for the scope of this research. For instance, a solid can be represented through tessellation, but this representation only creates the illusion of a solid, as it is just a surface. On the contrary, actual solids representations are the following: (1) SweptSolid. It is created by moving a two-dimensional shape, known as a profile, along a specified path in space. Tapered sweeps are referred to as AdvancedSweptSolid. (2) CSG (Constructive Solid Geometry). A solid is created from a Boolean operation between primitive solids. (3) Clipping. A solid is created by removing portions of an initial solid from a clipping region. (4) BRep. A solid is created as a collection of faces, edges, and vertices, which are used to define the boundaries and topology of the object. (5) Advanced BRep. A BRep supporting NURBS. In the context of masonry aggregates, exporting a model using the ’Reference View’ reveals that the complex geometries lead to the creation of a Tessellation. Conversely, the ’Design Transfer’ approach offers a broader range of options and ensures the export of solid geometry Fig. 6. Algorithm retrieving alphanumerical information. M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 8 (Fig. 5). This observation provides additional justification for designating the Design Transfer View as a necessary exchange requirement. 2.4. Developed algorithm The interoperability framework has been developed leveraging the capabilities of the following libraries: (a) IfcOpenShell (IfcOpenShell [67], (b) PythonOCC [68], (c) Gmsh [64], (d) Gmsh2OpenSees [63], and (e) OpenSeesPy [69]. Fig. 6 to Fig. 10 show the details of the code and can be traced back to the generic workflow in Fig. 1. The first algorithm can be divided into three parts, indicated on the left side of Fig. 6: 1) Input; 2) Material collection; 3) Material data collection. (1) The ‘Input’ consists of a for loop which retrieves all the IfcElements (beams, floors, walls, opening, and slabs) present in the IFC model (Fig. 6a). (2) The ‘Material collection’ consists of retrieving the material linked to the element collected. If the material is associated with the element (instance), it is directly linked through a “Relating material” (Fig. 6 – c). Alternatively, if the material is associated with the element type, the element is linked through a different association: the Relating type (Fig. 6 - b). The developed algorithm can obtain the “Relating material” in both cases. An element or element type can have many ‘Relating material’ to different ‘IfcMaterial’. In particular, based on the construction element, a ‘relating material’ can be either a ‘material layer set’ or a ‘material profile set’ (see also Fig. 4). For example, in the case of a wall, it can be composed of one or many material layers. Conversely, a beam can have one or more material profiles. The developed algorithm investigates whether the material is stored in layers or profiles. Based on this, it retrieves the relevant IfcClasses: IfcMaterialLayer (Fig. 6 – d) or IfcMaterialProfile (Fig. 6 – e). Finaly, collects the corresponding IfcMaterial. (3) The ‘Material data Collection’ retrieves the mechanical properties associated to the materials and stores them into a Python ‘dictionary’. A dictionary in Python is a collection of key-value pairs, allowing efficient retrieval and storage of data. In this dictionary, the first key is the name of the material, which is an attribute of the class ‘IfcMaterial’ (Fig. 6 – f). As shown in Fig. 4, each mechanical property needed for the analysis shall be stored in IFC as a ‘Property’ in a ‘Property Set’. The algorithm uses a for loop to access each property in the correspondent Property Set (Fig. 6 – g) and extract the name and the value of the property, which saves them as ’key’ and ’value’ in the dictionary, respectively. The ‘Output’ of this algorithm consists essentially of this python dictionary. As seen in the example (Fig. 6 – l), for each object (a structural material) there are several properties (MaterialName, YoungModulus, PoissonRation, MassDensity) to which it is associated a value (Masonry4, 400, 0.2, 2100). The second algorithm (Fig. 8) converts the IFC file to a STEP file, allowing interoperability between IFC and the meshing generator. Even though the IFC to STEP conversion process can be automated through the utilization of the Python module ’IfcConvert’ (IfcOpenShell [67], a tailored function was developed to keep track of the materials associated with the shapes, preserving the alphanumeric information from the passage from the IFC to the STEP file. The second algorithm is organized in two parts, as follows: 1) Input, 2) Create Manifold Solid BRep. (1) The input collects all IfcElements and with a ‘for’ loop (Fig. 8 – a) for each individual IfcElement their object type names (Relating type) (Fig. 8 – b) are compared with each material name in the previously generated dictionary (Fig. 8 – c). If the object type name contains a material name, it is assigned as a variable in Python, referred to as ‘label’. (2) In part 2 of the algorithm, the geometry of each IFC element is obtained in B-Rep format, using the ’Open Cascade’ geometry Fig. 7. Conversion of compound of faces into a solid. M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 9 kernel (Fig. 8 – d). To carry out a solid analysis, volumes must be as ‘TopoDS Solid’, converted in STEP as ‘manifold solid B-Rep’. It has been noted that when complex solids are modelled in IFC as IfcAdvancedBRep, this causes them to break into individual faces during STEP conversion. In that case, the shape is represented as a compound of faces (named TopoDS Compound). To guarantee preserving a solid representation of the objects, the developed algorithm checks when this happens, and generates the solid from the envelope of compound faces (Fig. 8 – e). This conversion process consists of three steps (Fig. 7): identification of children entities, sewing and solid generation. The first step is identifying the geometric entities which are in the TopoDS Compound, which are recognized by Open Cascade as the ‘children’ of the TopoDS Compound. Then, these shapes are joined together using the sewing function, in such a way that Open Cascade kernel recognizes them as a unique coherent shape. Finally, from this shape is generated a solid, of which the sewed shape is the envelope. The solids are associated to the ‘label’ generated in the initial phase of the algorithm, ensuring the preservation of material-related geometry (Fig. 8 – f). Finally, this solid geometry is stored in a STEP file, maintaining the label information associated with the geometry (Fig. 8 – g). The third algorithm (Fig. 9) is structured into four parts: 1) Input, 2) Physical Groups, and 3) Boundary Conditions. (1) In the ‘Input’, the STEP file is imported in Gmsh, using the Gmsh Python API, and it is used to generate a Gmsh geometry file (Fig. 9 Fig. 8. STEP conversion. M.L. Leonardi et al. Computers and Structures 297 (2024) 107321 16 CRediT authorship contribution statement Maria Laura Leonardi: Conceptualization, Funding acquisition, Investigation, Methodology, Writing – original draft, Writing – review & editing. Jos´ e Granja: Investigation, Methodology, Resources, Writing – review & editing. Daniel V. Oliveira: Investigation, Methodology, Resources, Supervision, Writing – review & editing. Miguel Azenha: Investigation, Methodology, Resources, Supervision, Writing – review & editing. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgements This work was partly financed by FCT / MCTES through national funds (PIDDAC) under the R&D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE), under reference UIDB / 04029/2020, and under the Associate Laboratory Advanced Production and Intelligent Systems ARISE under reference LA/P/0112/2020. This work is financed by national funds through FCT - Foundation for Science and Technology, under grant agreement 2022.10204.BD attributed to the 1 st author. References [1] Carocci CF. Small centres damaged by 2009 L’Aquila earthquake: On site analyses of historical masonry aggregates. Bull Earthq Eng 2012;10(1):45–71. https://doi. org/10.1007/s10518-011-9284-0. [2] Tocci C, Carocci CF. 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