Evaluating the Damage Content of Karbandi Using Frequency Domain Analysis (Case Study: Timche Haj-Mohammad-Qoli of Tabriz Historic Bazaar)

8 In this study, an alternate method to evaluate structural systems, especially those with historical 9 importance has introduced by applying Fourier Transform (FT) to the damage ratio of time history 10 outcome in the frequency domain. The concept of damage content (DC) regarding the mechanical 11 characteristics of the used material, including plastic strain, failure plane, and ultimate load-bearing 12 capacity, along with drift value, record selection criteria, and architectural aspects, have employed. Due to 13 its valuable aesthetic and architectural view, Timche Haj-Mohammad-Qoli of Tabriz Historic Bazaar, one 14 of the traditional covered spaces with the complicated configuration of spatial masonry intersecting 15 arches, selected for further assessment in the current research program. The required experimental samples 16 for obtaining the mechanical properties and relevant geometrical measurements to prepare the numerical 17 model of the structure obtained. The strong ground motions according to seismological and geological 18 characteristics of the construction site selected. The records with different durations were merged by 19 Fourier Transform (FT) and Damage Content (DC) analysis. According to the outcomes, the damage state 20 of the structure due to the imposed strong motion at every stage of the lateral loading from the failure 21 initiation to the final collapse was traceable. As a straightforward outcome, the vulnerability of the near-22


Introduction
Several historical and ancient masonry buildings are belonging to the vast circle of arches and vaults.
Aesthetic, slenderness, and load-bearing capability make these structures attractive for manipulation in the construction industry of monumental structures both in past and present (Sarhangi, 1999;Sevim et al., 2011;Sadeghi et al., 2019).However, numerous vulnerability points of these structures, to a large extent because of the limited load-bearing capacity of the masonry elements, make them laid open to natural hazards (D'Ayala and Speranza, 2003;Lourenço and Roque, 2006;Pasticier et al., 2008;Asteris et al., 2014;Asteris et al., 2019).Severe damages and failures caused by earthquakes demonstrate that masonry structures, including masonry arches and vaults on the top, are one of the most vulnerable elements in historical monuments (Lagomarsino and Podestà, 2004;Dogangun and Sezen, 2012;Formisano and Marzo, 2017;Cusano et al., 2019).Iran is a host country for numerous masonry structures that demonstrated the vulnerability of masonry arches to strong ground motions in numerous earthquakes consist of but not limited to the Tabas earthquake of 1978, the Manjil earthquake of 1990, the Ahar-Varzeghan earthquake of 2012, and the Sarpol-e Zahab earthquake of 2018.
The typologies of the heritage buildings are usually capable of resisting the gravity loads.However, they are weak to resist the seismic forces, and in some cases, vehemently ruined due to severe earthquakes.As a result, the seismic events gave a strong motivation towards understanding and interpreting the seismic response of masonry structures to different structural typologies (Bell, 1903;IASS, 1984;Nooshin, 1998), especially those exposed to high seismic hazards or unfavorable soil properties (Motro, 2009).Several studies devoted to analyzing historical masonry structures, such as churches, monuments, bazaars, and palaces (Haj Gasemi, 2004;Stach, 2010;Ahmadi, 2014;Kawaguchi, 2016;Aghabeigi et al., 2020). of historical masonries.Binda and Saisi (2005) indicated the importance of on-site observations and experimental investigations to achieve the reliable structural information on masonry buildings, such as geometry, structural details, crack patterns, etc.In another study performed by Lagomarsino et al. (2004), the importance of modeling strategies to assess the seismic response of masonry structures utilizing macro elements instead of conventional evaluation of structural behavior suggested.Doglioni et al. (1994) used the simplified techniques of kinematic mechanism to assess the seismic response of the churches.Lourenço (2002) showed even if the definition of the parameters to model a non-linear numerical simulation subjected to difficulties in many cases, it is advantageous to compare the other modeling methods to assess the seismic behavior of historic structures.More in advance during the past decade, investigations on three-dimensional simulations of geometrically complex structures performed to evaluate the seismic behavior of historical buildings (Casarin and Modena, 2008;Boscato et al., 2014;Castellazzi et al., 2018;Mendes et al., 2020).As yet, modeling strategies using numerical techniques, such as discrete element method (DEM) and finite element method (FEM) by considering non-linear material properties becomes a standard procedure in simulation of full-scale structures (Roca, 2001;Rots, 2001;Ramos and Lourenço, 2004).Most of the historical monuments and ancient buildings made of masonry elements, including but not limited to clay bricks, stones, raw clays, etc. Advances in using numerical methods to ease the calculation process in the design of structural elements demonstrate the complexity of considering the masonry elements presence.Because of the unpredictable post-failure behavior of these elements and their utilization inside the old-fashioned buildings, the procedure becomes even more difficult than anticipations.Hence, many researchers used FEM to predict the behavioral content of masonries in historical buildings (Chiarugi et al., 1993;Croci, 1995;Roca et al., 2010;Atamturktur and Laman, 2012).The complicated geometric shape of many historical buildings constrains the modeling procedure even in FEM software, in which the meshing is affected by numerous parameters, including convergence and unity problems.To solve this, new methods of modeling named simplified micromodeling and macro-modeling with more simple geometry were used by the researchers (Betti and Galano, 2012;Vicente et al., 2018;Ahani et al., 2019).Predicting the behavioral content of masonries due to the material diversity and load-displacement indices confronted with sensible errors.Hence, numerous behavioral contents were introduced by researchers to provide a better perspective on the behavior of masonry elements, many of which are also approved by prominent standards and design codes (FEMA 308, 1999;Eurocode 8, 2005).This is while many design codes and standards remained silent about the behavioral content of the masonry elements (ICC, 2003;Issue No. 120, 2003;ACI530, 2011;Standard 2800Standard , 2015)).Concrete damage plasticity as an empirical method was used in many experimentally and numerically performed research studies (Wang and Hsu 2001;Majewski, 2003).The accuracy of this method compared to the other approaches like concrete smeared crack and Drucker-pruger has more appropriate convergence.Hence, this method is introduced by Eurocode 2 (2005) to anticipate the postfailure behavior of concrete elements.Timche Haj-Mohammad-Qoli of Tabriz Historic Bazaar as a Cultural Heritage by further evaluation of its structural morphology and damage content considered the study case of this research.The basic steps for evaluating masonry buildings are to achieve adequate knowledge about the structure, materials, and the consecutive use of the obtained data for seismic evaluation purposes.To debrief, the historical and architectural description of the Tabriz bazaar and Timche Haj-Mohammad-Qoli, an on-site observation to identify the current status of the structure and its seismic assessment with the aid of Nonlinear Time History Analysis (NTHA) and Fourier Analysis (FA) have performed in the current research.The assessment of masonry structure performed in two states of subjecting to gravity loads, and gravity and seismic loads.
While limited standards provided protocols for testing and getting specimen samples from the historical structures (ASCE/SEI 31-03, 2003;ASCE/SEI 41-06, 2007), most of many (ATC-40, 1996;FEMA 306, 1998;ACI 201.1R-08, 2008) introduced the destructive tests for modern structures that were not applicable for historical masonries.Thus, the provided methods may not satisfy the required limits of historical monuments, and therefore while the destructive tests may have limited eligibilities (Standards for the Treatment of Historic Properties with Guidelines for Preserving, Rehabilitating, Restoring & Reconstructing Historic Buildings, 1995;36 CFR 68, 2012) and the outcomes of NDT tests may not comprehensively reliable for the long-lasted human heritages a thorough numerical evaluation shall be employed.In addition to the difficulty of finding the failure amount and location, determining them may of high value for the historical structures since the financial worthiness of these cultural heritages is incomparable with typical engineering structures.In this regard, many studies have evaluated the failure parameters of historical masonries (Zampieri et al., 2016;Zampieri et al., 2017;Zampieri et al., 2018;Galassi et al., 2018;Chen et al., 2019).According to carried out studies and the provided principles of the regulations and standards, the failure parameters were categorized as but not limited to soil settlements or support movements (FEMA 172, 1992;FEMA 274, 1997;Portioli and Cascini, 2017;Galassi et al., 2018;Zampieri et al., 2018), failure due to ground motion excitations (FEMA 172, 1992;Eurocode 8, 2005;ASCE/SEI 41-06, 2007;Severini et al., 2018;Carozzi et al., 2018;Zampieri et al., 2019), weathering (FEMA 172, 1992;FEMA 274, 1997;Boughton and Falconer, 2001;ASCE/SEI 41-06, 2007;Sarhosis et al., 2016;Solan et al., 2020), scouring (Scozzese et al., 2019;Solan et al., 2019;Solan et al., 2020), etc.
Concerning the mentioned implementation, an effective and economical method for evaluating these types of structures would gain attention by many researchers.
In the current study, with the assistance of Nonlinear Time History Analysis (NTHA) and Furrier Analysis (FA), the seismic assessments for evaluating the performance of a building in the loading period of the structure and the selected earthquake records by combining the responses of them and utilizing the Damage Content (DC) parameter to view the circumstance of the structure in every step of the seismic loading have been introduced.The introduced method cooperating with Incremental Dynamic Analysis (IDA) may provide more precise information about the lateral behavior of any other kinds of structures at every stage of surveying.Historical monuments located in seismically active places are the most vulnerable heritages of the commonwealths (Cavalagli et al., 2017;Pellegrini et al., 2018;Severini et al., 2018;Öztürk et al., 2019;Zampieri et al., 2019).Since the Middle East is the host for considerable numbers of historical monuments, especially masonry space domes, this study is involved with the seismic assessment of the Timche Haj-Mohammad-Qoli of Tabriz Historic Bazaar, which is considered a world heritage by UNESCO.

Masonry Space Structures
Jamshid Al-Kashani, the famous mathematician and astronomer in the early 15 th Century to design the Ulug Beg observatory with larger spans, provided a specific definition of arches and vaults, and gather related knowledge in a book named Meftah Al-Hesab (Al-Kashani, 1427).From his viewpoint, the arch is a curved shape that has been used for the spanning of the gap and has a considerable depth.He redefined Chefd 1 and Azj 2 architectural terminologies.The final chapter of the study was devoted to Chefd and its definitions.There is also valuable information regarding the drawing arches and length of spans they can bear.Graham Bell introduced the tetrahedral space frame as an appropriate form for three-dimensional 1 -Arch in Middle Eastern term 2 -Vault in Middle Eastern term (derived from Persian word means curved branch) structures, which was a significant breakthrough for space structures (Bell, 1903).After the invention of new types of space structures, the definition of space structure improved.IASS Committee defined the space frame as a structural system, assembled of linear elements so arranged that the loads are transferred in a three-dimensional manner.The constituent elements may be two-dimensional in some cases.
Macroscopically, a space frame often takes the form of a flat or curved surface (IASS, 1984).The formal definition for space structures has been given by Nooshin (1998), in which the term space structure refers to a structural system that involves three dimensions.According to these definitions, equal presence in three dimensions is the most outstanding feature of the space structures.This definition resides considerable extent of the historical structures in the circle of space structures.Masonry domes such as Karbandi should consider a space structure as an instance of this definition.Before introducing steel as a load-bearing element in engineering, masonries were the dominant materials for structural uses, especially in ancient civilizations like Iran, which contains numerous masterworks like bazaar complexes, mosques, bridges, etc., the monuments have erected by masonries.

Karbandi
Based on the precision, Al-Kashani defined 5 types of Chefds, the first of which is a circle divided into six parts that can cover spans with a 5.2 m length.The second type also has a circular shape divided into eight equal sections.The angle between these sections is 45°.The Chefd can bear the loads of spans with a length of 5.2 m to 15.6 m.The third type is obtained by dividing the span radius into 8 parts that lead to getting the center points of the bottom and top arches (Memarian et al., 2014).This type of arch is suitable to use in spans of more than 10.4 m lengths.The definition of Chefd type four and five would also be traced in Meftah Al-Hesab (Al-Kashani, 1427), correspondingly.The climax of composition in aesthetic and structural applicability could be reflected in the Chefd type five, in which to get the vault, two lines are directed to the span Pakar 1 .According to Papadopoulo and Jazanī (1989), Karbandi derived from rolling squares inscribed in a circle.Sharbaf (2006), along with Pirnia and Bozorgmehri (2006), categorized Karbandi into general Shaghooli 1 and Sarseft 2 types with the shape of hexadecagon and other geometrical shapes in a simple form or made from the intersection of two shapes.Lu and Steinhardt (2007) introduced Karbandi as an advanced architectural approach of transferring loads resulted from the premier knowledge of geometry and mathematics of its founders.Theoretical geometry mainly focuses on lines surfaces area of threedimensional objects, and the essence of practical geometry is to implement the science of geometry in wood, metal, brick, and other tangible things (Papadopoulo and Jazanī, 1989).Garofalo ( 2016 the geometrical pattern of one or multiple Chefds in harmony and aspect of subtlety, the outcomes of which would have a structural performance and application to the users.Examples of Karbandis consist of the Mausoleum of Baba Tahir (Hamadan, Iran), Mir-i-Arab Madrasa (Bukhara, Uzbekistan), Haidarzadeh Museum of Coin and Anthropology (Tabriz, Azerbaijan), etc. Karbandis widely used in the entrances, arcades, and intersections of historical Bazaars.Tabriz historical bazaar is one of the most landmark bazaars with numerous Karbandis in its different parts.The continuity of using Karbandi is highly demanded in contemporary Islamic Architecture but requires a precise understanding of geometrical and structural aspects of ancient Karbandis to achieve a modern design and construction strategy to meet new requirements.

Timche Haj-Mohammad-Qoli
The building of Timche Haj-Mohammad-Qoli dates back to the early Qajar dynasty (the 1810s).The architectural evaluation of the type and design of the vaults aesthetically concurred with that of the infrastructure fundamentals of that period.Although the design principles and rationale may root back to the basis of Karbandi, astronomical requirements, space creation, and the philosophy of using Chefd as an accurate object of arch creation are also plays a crucial role, the further details of which have been formerly discussed.

Location
Tabriz Historic Bazaar Complex consists of numerous masonry space structures and various fundamental features of masonry structural systems.These features include architectural and structural morphologies, force flow and force management in the masonries, and perception of the collaboration among structural elements.Timche 1 Haj-Mohammad-Qoli, with 11.5 meters diameter, is one of the covered spaces masterpieces of Tabriz bazaar with a sophisticated configuration of spatial masonry intersecting arches and selected for further evaluations in the current study.The Bazaar has various Timches and Rastehs 2 , which have covered with different masonry curved surfaces such as dome, vault, and Karbandi.The

Structural Evaluation
The structural evaluations of any system may consist of both non-destructive and destructive tests and there would be difficulties in performing destructive tests according to the historical value of the Timche.
Thus, up to the greatest extent, the assessments conducted to the non-destructive tests.The geometrical faces, spans length, arches dimensions, dome height, and the other requirements regarding the architectural principles were measured.The visual inspections determined the material properties used within the masonry consisted of clay brick and lime mortar.While getting direct samples from the masonry was ineligible, a request for acquiring unit and joint samples was officially submitted to the Cultural Heritage, Handicrafts, and Tourism Organization of East Azerbaijan.The bureau yielded limited numbers of masonry units extracted from the Timche and the lime mortar combination used inside the building, which is not presented due to passive defense factors.To obtain the characteristics of the materials, masonry prisms were constructed in the laboratory according to the instructions of the American Society for Testing and Materials (ASTM).

Material Properties
Determining the tensile behavior of masonry prisms regarding the principles of both ASTM E518/E518M-10 (2010) and ASTM E519/E519M-10 (2010) standards are viable.Although, since ASTM E519/E519M-10 ( 2010) is not applicable for lime mortars, the tensile and bending characteristics of the studied materials regarding the principles of ASTM E518/E518M-10 (2010) have determined.The compressive behavior of the studied materials has performed according to ASTM C1314-07 (2007).In Table 1 and    Table 2, details of the experimental outcomes of the studied samples have presented for flexural bond strength and compressive strength, respectively.In Figure 4, laboratory tests for determining the compressive strength and flexural bond strength of two specimens have been brought.Due to the erosion, weathering, corrosion, etc., factors, and the historical content of the perusing structure, the accuracy of the excerpted outcomes from experimentally evaluated specimens may be affected.Albeit, since the precision of any other non-destructive tests including but not limited to Schmidt hammer test, ultraviolet test, ultrasonic test, or the imposed damage from destructive tests like coring could not be acceptable, the prepared and tested samples regarding the principles of ASTM E518/E518M-10 (2010), were still advantageous.Therefore, they selected the criteria for evaluating the results.The experimental  The mechanical properties of the materials utilized within the masonry structure of the Karbandi, referring to the outcomes provided in Table 1 and Table 2 demonstrates diminutive deviations.Therefore, there is a feasibility to adopt failure criterions in numerical simulation.Thus, Concrete Damage Plasticity (CDP) criterion for the masonry material was implemented in numerical analysis.The stress-strain curve for the employed material has been illustrated in Figure 5.The epicentral distance and high unorthodox values in the velocity time history were considered the signs of only-pulsed records in various research studies (Baker, 2008;Panella et al., 2017;Kohrangi et al., 2019).In this study, the most prevailing selection method has been used, in which the epicentral distances lesser than 10 kilometers were considered only-pulsed records.Eventually, 20 records of strong ground

CDP Tensile Behaviour
Tensile Curve motions, half of which are only-pulsed, were selected for the current study.Since all the befallen severe earthquakes in Tabriz were belonged to the era when no measuring devices and no information about the site records exists, the relevant data was collected from the Pacific Earthquake Engineering (PEER) database.It is essential to mention 16 of the selected records are conjugated, which means the record data is extracted from two different stations to resemble the near-field and the far-field effects of the selected records.The characteristics of selected records for both near-field and far-field ground motions have shown in Table 3. normalize earthquake records for nonlinear dynamic analysis by scaling PGA of the ground motion to 1.0 332 g and applying the modification factor to them that obtained from comparing the convoluted response spectrum of the selected records to the standard design spectrum in the determined range of Time period for the studied structures.In this study, the records according to the principles of BHRC (2015) have been scaled and implemented in numerical modeling using ABAQUS FEM software.After the record normalization, the stress and strain outputs of the Karbandi subjected to the near and far-field records have been extracted and brought for further consideration, as explained in the Time History Analysis section.

The Failure Criterion
The failure mechanism in skeleton structures, took place when the formation of plastic hinges makes the whole structure or some parts of it unstable, referring to the principles of structural mechanics.Since masonry structures are continuous nonhomogeneous elements with low integrity, the determination of failure mechanism for them is more complicated than that of one-dimensional elements.According to the experimental and numerical outcomes of many pieces of research (Andreaus, 1996;Noor-E-Khuda et al., 2016;Bui et al., 2019), the ultimate failure of the masonry elements took place in a plane or planes of crack formation where some part of the masonry become unstable.Hence, it can assume that the failure of the Timche occurs following the formation of the first plane of failure, which leads to formation of a mechanism in some or all sections of it.The failure of masonry elements is the ultimate plastic strain of masonry prisms in compression and flexure extracted from experimental results.According to CDP criterion, the plastic strain respected to masonry failure in compression and tension was considered to be 0.00389 and 0.00032, respectively.These amounts were used for resembling the compressive and tensile behavior of masonry elements in numerical simulations.The corresponding failure drift in Nonlinear static analysis was considered to be the failure drift of the structure, in which it was comprehensively collapsed, and the analogous Damage Content (DC) of it was deemed equal to one.The zero point of the Damage Content (DC) is initiated when the plastic behavior of the structure corresponds to the yield point of the bilinear pushover curve of the Timche.The failure content of the Timche shall subsequently evaluate for the near-field and the far-field earthquakes.

Numerical Analysis
Due to structural complexity and controversial time costs of micro-modeling, numerical modeling of the masonry dome could reside in borderlines of macro-modeling strategy.In most cases because of the far beyond complexity and/or time-consuming procedure of the other methods, the macro-modeling approach was considered more efficacious since it can distinguish the response of large-scale structural elements and building systems with ease (Lourenço et al., 1995;Baloevic et al., 2016;Pantò et al., 2016).With regard to its acceptable accuracy, the CDP criterion was used for simulating the post-failure behavior of the masonry, the related parameters of which adjusted referring to Section 4.1(Material Properties).Static General analysis to determine the effects of the gravity loads (linear static analysis), Nonlinear Implicit analysis for the nonlinear pushover, and Nonlinear Explicit analysis for the nonlinear time history evaluations were employed through the related modules of ABAQUS FEM software.According to provided principles in Section 4.3 (Failure Criterion) and mechanical concepts, nonlinear pushover analysis was employed to get the bilinear curve and utilize in nonlinear dynamic analysis.The results obtained from the aforementioned curves, more specifically the displacement values related to the equivalent yielding and ultimate load-bearing points, were used in every stage of the dynamic appraisal deformation curves and obtaining the final DC value of the studied earthquake records.Due to the complexity of the masonry, the double-precision analyzing approach was employed to perform the explicit analysis.All components of the model were discretized using 4-node 3D linear tetrahedron elements (C3D4).The numerical model consisted of 23961 meshes.The graphical scheme of the FEM model has shown in Figure 6 Places where arch pillars posed on the earth considered as fixed supported boundary conditions.The masonry material used for dome, according to experimentally assessed masonry units and mortar samples (Section 4.1), was assumed to have an Elasticity modulus of 2690MPa, and Poisson's ratio of 0.15.For further details of calculating masonry parameters, Eurocode 6 (2005), Kaushik et al. ( 2007), and Kmiecik and Kamiński (2011) are to be referred.The models were subjected to 8000 N/m 2 vertical loads, which derived from the structure's self-weight (the dome thickness is 0.15 m), and the roof loads consist of precipitation and human loads.

Linear Static Analysis
The dome behavior, natural period, and its reaction to the vertical loads were investigated by using linear static analysis.The linear static analysis was carried out by considering the self-weight of the overall structure and rain and snow loads.Analysis results were surveyed in terms of maximum stress variation and the stress flow of the dome.Stress distribution due to gravity loads in the masonry space dome demonstrates that the maximum values of compressive and tensile stresses in both surfaces of the elements were taking place at the eight main load-bearing pillars of the Timche, which has displayed in Figure 7.
The stress flow in Timche to a better understanding of the structure mechanism have presented in Figure 8.According to the figure, it can be deduced the force flow transmits from minor arches to the main vaults and from them to the load-bearing pillars.Results also depict while the compressive stresses are dominant in the majority of members, tension stresses are negligible.Therefore, dominated stress distribution among the members indicates, despite the level of scientific knowledge during the building era, the structure was constructed skillfully.The structure period was obtained by Modal Analysis.The frequency range to perform the analysis by assuming the first natural period of the structure was assigned between 0.5 Hz and 20 Hz.The first frequency of the Timche was around 6.15 Hz that respects 0.163 Sec to the primary period of the  4, all the 411 information related to the initial 10 mode shapes of the Karbandi has been brought.412

414
Due to symmetry in the shape of the Karbandi, the concatenating lateral mode shapes in frequency 415 analysis were identical.The same observations have been sighted and traced in higher modes.416

Nonlinear Pushover Analysis
A linearized pushover curve could render an approximation to the yield and collapse point of the Karbandi.To this purpose, considering the plastic strain of the masonry, up to the point the first plane of failure was came into view the displacement-controlled lateral loads applied to the structure.In this regard, the ultimate strain extracted from the CDP criterion that considered the final failure point of the masonry could also be considered the point of failure in the formation of the failure plane.The bilinear curve shows the capacity of the Karbandi under the lateral load and corresponding displacement subjected to that.Since the probability of the failure in both directions was assumable, the pushover curve and related bilinear curve in both directions were extracted.Resultantly the curve with a lesser maximum failure load was considered the ultimate failure curve of the structure.In Figure 10 linearized pushover curve of the Timche in two perpendicular directions has been illustrated.In Figure 11, the formation of the failure plane concerning the attributed plastic strain in nonlinear pushover analysis for the idealized directions has presented.Due to lesser load-bearing parameters in presented results, direction 1 should be considered as the critical direction.In Table 5, by assuming the yield and failure points the simplified bilinear curves and corresponding load-bearing strength of the structure has brought.

Time History Analysis
The mixed average and envelope response spectrum curves presented in Figure 12 compare the standard design spectrum of BHRC ( 2015), referring to the selected records.According to the scaling principles proffered by BHRC (2015), the mixed response spectrum of the records between 0.2T and 1.5T, in which T is the natural period of the structure, may not be less than the 90% of the standard spectrum or modification coefficient.Since the scaling procedure for determining the modification coefficient are almost the same, further principles can also be traced from ASCE/SEI 7-10 (2013) and Eurocode 8 (2005).
Through the numerical time history analysis, the rest of required data for extraction of the DC value of studied records were obtained.The plastic strain at the final stage of loading for the studied records has been illustrated in Figure 13.The records with corresponding critical displacement in the crown of the Timche, referring to their significance and controversy for unexpected deformation have chosen for more assiduous assessment.
From the selected records three belong to the only-pulsed category (DCO, EWO, and KYO) and one to the non-pulse records (DCN), which is the most critical record in that class.The displacement of the control point and related Energy curve of the studied structure for three near field and one far field earthquake has been presented in Figure 14.

Damage Content
As previously explained, the damaged content was computed according to provided principles in Section 5 (Numerical Analysis).Resultantly the DC at each stage of earthquake application with considering the

Dissipation Energy for DCN Strong Motion
Strain Energy Kinetic Energy corresponding displacement, the final failure of which is assuming according to the formation of analogous plastic strain failure plane, obtained and for perpendicular directions in both far-field and nearfield earthquakes respectively presented in Figure 15 and Figure 16.The failure in these assessments was assigned when the DC reaches 1. Prior to the eventuation of the strong ground motion, failure in the perpendicular directions of the Timche axis was taken into place for the DCN in the far-field plus the DCO, EWO, KPO, KYO, and WPO in nearfield earthquake cases.Failures in the X axis (1 st direction) in most of the cases precede the Y axis (2 nd direction) and exist in all the cases that happened in both axes.In Figure 17, the crown drift of the Karbandi for X, Y, and vertical directions subjected to the near-field and far-field ground motions have been depicted.Vertical Driection-Near-field direction have had critical drift values.In Figure 18, the strain and kinetic energy differences for the studied records have been shown.than that of the far-field IFFT curves.Considering all the above-mentioned facts, the results emphasize the importance of the near-field records due to the incurred damage.According to the outcomes, the studied structure for a hundred-second lasting far-field earthquake in 50% of the cases may survive with severe damages; however, for the same near-field earthquake cannot survive for more than 40 seconds.In other words, if a near-field earthquake for the studied Timche has applied most probably before 0.4 of the earthquake occurrence time, the failure and collapse of the structure may take place.

Conclusion
The study relates to employ an alternative approach in evaluating historical structural systems using FFT, nonlinear static analysis, and nonlinear dynamic analysis.Accordingly, the structural system of Timche documents and resources), and current structural stance have been evaluated.The damage content (DC) concept regarding the mechanical characteristics of the used material, including plastic strain, failure plane, and ultimate load-bearing capacity, along with drift value, record selection criteria, and architectural aspects, has been employed.The present system undertakes the vertically applied gravity loads and transfers the force flow with convenience.However, the performed pushover analysis demonstrates the vulnerability of the structure to the lateral loads due to the limited drift content of the structural system.At last, a unified structural response in the frequency domain by merging the inversed damage content curves have obtained since the damage content of the structure in various records may alter, and differences in earthquake durations hinder the possibility of combining the structural response in the time domain.The residual outcome reversed to the time domain to make them structurally discussable.
The most landmarks results of the study, according to the aforementioned abbreviation, are as follows: -The idea of Karbandi from architectural feature, at least could be traced back to the early 15th century, when eminent mathematician Ghiyath Al-Din Jamshid Masud Al-Kashani, to establish the fundaments of arches with longer spans redefined and categorized the ancient science of the vaults and arches construction.The newly acquired science was used to build the observatory of Ulug Beg, which afterward became one of the extraordinary astronomical science discovery places of that era.The byproduct of this breakthrough led to employing geometrical patterns to utilize in places that requires long spans and broader spaces like mosques and covered bazaars, more specifically in cold habitats.The esthetical reflection of this achievement inspired the widespread use of Karbandi for ornamental purposes.
-The historical structure of the Timche was designed in a way to retain all the possible privileges of the compressive strength of masonry units in a manner that the least tensile strength due to the gravity loads impose to the structure.The system has a proper reaction to the lateral loads in the incipient stages of lateral deformation.However, imposing further lateral deformation exposes the masonry to the failure.
-An alternative method of evaluating structural systems, especially for those with higher sensitivity in their façade or other featural aspects due to their historical importance, aesthetical attraction, etc., with applying Fourier Transform to the damage ratio of time history outcome in the frequency domain has been introduced.The behavior of the vulnerable structures due to earthquake excitations by employing the introduced method along with IDA analysis may most properly determine the failure points of the structural system; hence, the required augmentation, including retrofitting, rehabilitation, and strengthening, with the least interception to the mechanical characteristics of the system, could be employed.
-As expected, the obtained DC from the far-field earthquakes has a lesser ratio comparing to the nearfield earthquakes.It is assumable due to their velocity contents, which most probably affect the structures with short period, the near-field strong ground motions for the low-rise structures have more significant repercussions.According to the results, 3 out of 10 far-field records cause failure in the structure, including one that took place in the perpendicular directions, whereas 7 out of 10 near-field earthquakes lead to the collapse-correspondent failure in the Timche, with five occurred in perpendicular directions.
Regarding the outcomes, a near-field earthquake may finally lead to the structural collapse during the initial stages (not more than 40% of the earthquake duration), whilst after the eventuation of a far-field earthquake, there is a 20% hope that the structure survives with a close to collapse and severely damaged remnants.
-The reliability of the median curve for unpredictable events such as earthquakes shall be more than that of the mean curve since the inverse median curve statistically represents more than 50% of the studied records, whilst the mean curve mathematically is the average value of the DC for the same records and cannot provide that assurance.On average the DC value for the median curve in the far-field and nearfield earthquakes is around 15.7% and 14.9% more than its peer amounts in the mean curves, respectively.

Data Availability
Since some outcomes of this study didn't publish in any other Journal, all data, models, and the results that support the findings of this study are available from the corresponding author upon reasonable request. -

Figure 1 :
Figure 1: Redefined and introduced 5 widespread Chefd types according to the mathematical calculations of Al-Kashani.All of the ancient arch types were reordered and mathematically reconsidered, for the possibility of utilization, in the upcoming future of that era.The obtained results were assembled in the book named Key to Arithmetic.
) introduced Karbandi as a kind of arched shape roofing based on Islamic star patterns.In brief, Karbandi is employing 1 -Plummet in Middle Eastern term (derived from Azerbaijani word) 2 -Out of plumb in Middle Eastern term (derived from Persian word) 1 -Covered trade places 2 -Covered trade passages arched shape foremost has been made by using Karbandi.In Figure2, the location and section cuts of the sophisticated Karbandi of the Timche Haj-Mohammad-Qoli presented.It has been located in the southern part of the Historical Bazar.The main part of the Timche is located at the northeast corner of the Bazar Complex.It has accessibilities from four sides.Appropriate connectivity with neighbor elements, especially in the east-west axis, makes the strong bond with Bazar texture.This Timche has been built based on orderly and comprehensive geometry and symmetrical shape on the north-south and west-east axis.

Figure 2 :
Figure 2: Timche Haj-Mohammad-Goli of Tabriz Historical Bazaar (a) Geographical location of the site; (b) 2D plan view and cross sectional views

Figure 3 :
Figure 3: The structural and architectural appearance of the Timche Haj-Mohammad-Qoli's Karbandi; (a) The hidden ribbed arches outside of the building increasing the load-bearing capacity of the Karbandi; (b) A final feature of Karbandi in which two results and research outcomes of the compressive strength for masonry are in good agreement.The same condition also observed in the ultimate strain obtained from indirect tensile tests and extracted values from the studies.By taking this into account, the obtained values from the lab utilized for numerical modeling of the material behavior.

Figure 5 :
Figure 5: The employed Stress-Strain curve for masonry material regarding the CDP model and the experimental results in compressive and tensile masonry prism specimens4.2Record Selection Criteria

Figure 7 :
Figure 7: Distribution of compressive and tensile stresses by employing Tresca criterion and maximum principal stress in gravity direction.

Figure 8 :
Figure 8: Stress flow within the main load-bearing elements of the Timche by considering 3D and gravity directions.The stress flow concentration in the corners of the Timche to convey the final flow to the endpoints in the gravity direction is considerable.
scheme of the first 10 mode shapes of the Karbandi has been presented in Figure9.In Table4, all the 411

Figure 10 :
Figure 10: Bilinear Curve of the studied Dome in the perpendicular Directions

Figure 11 :
Figure 11: Formation of failure planes in perpendicular directions due to nonlinear pushover analysis considering the attributed failure parameters

Figure 12 :Figure 13 :
Figure 12: The mixed average and envelope response spectrum of the near-filed and far-field records compared with the standard design spectrum of BHRC (2015)

Figure 14 :
Figure 14: The recorded displacement of the control point (crown of the Karbandi) (Left Column) and corresponding Dissipation (Strain and Kinetic) Energy (Right Column) for DCO, EWO, and KYO (near-field records) and DCN (far-field record)

Figure 15 :
Figure 15: DC value of far-field ground motionsin perpendicular directions

Figure 17 :
Figure 17: Drift value of the Timche in X, Y, and Vertical directions due to the employed earthquake records

Table 1 :
Laboratory performed tests to determine the flexural bond strength of the studied samples according to ASTM * It is a third-point loading method that was discussed in ASTM E518 with further details.** Coefficient of Variation.

Table 2 :
Laboratory performed tests to determine the compressive strength of the studied samples according to ASTM C1314-07 ** Coefficient of Variation.

Table 3
Ground motion records Name, Year, Station, Abbreviation and PGA 328

Table 4
The modal analysis results for the Timche Haj-Mohammad-Qoli including Circular Frequencies and Mode Types 413