1 Introduction

Historical structures are cultural heritage constituents that convey the traces and characteristic features of civilizations to the present days [1, 2]. One of these structures, which are among the monumental artefacts, are historical bridges. Although the main purpose of bridge construction is to provide transportation, they are generally designed as piece of art. Many of these bridges vary depending on a number of factors such as material usage, design, architectural texture, inscriptions, traditional preferences [3,4,5]. Historical bridges built with stone materials and bearing the traces of their civilization are extremely important [6, 7]. Such architectural structures, which cannot be transported, should be preserved in the same location in the form of an open-air museum.

Masonry arch bridges are one of the most important historical bridge types. The arch form has facilitated the passage of wide openings and is therefore the most preferred form. In today's societies, cultural and socio-economic differences add originality and aesthetics to arch bridges [8,9,10]. However, due to its geometrical design, it is exposed to pressure. The basic building material is generally stone. Over time, deformations have been observed in bridge elements and arch forms depending on many parameters [11,12,13]. Historical bridges were damaged due to various effects in light and heavy direction depending on the progress of time. A number of parameters need to be known when determining the cause of the damage. These parameters include the history of the building, cracks, the type of materials used and the mechanical and chemical properties of these materials, their strength against lateral and vertical loads, the structure of the floor on which they are built, and error of construction [14].

To protect historical buildings, 3D photogrammetric documentation of these structures, detailed determination of geometric and material properties and performing computer-aided structural analysis using appropriate modelling techniques are very important. Calculations for determining behavior provide the basic information needed to select restoration, repair and strengthening techniques suitable for historical buildings. The existing methods used to perform the analyzes have several advantages and disadvantages depending on the approaches and assumptions used [15,16,17]. In historical buildings, it is necessary to interpret the behavior occurring accurately and precisely. Therefore, it is necessary to know the contents of the materials that make up the structure and the resistance of these materials under certain loads. These bridges usually consist of foundation, side wall, arch and back filling material. The materials forming the masonry structures are generally natural stone and brick. Both materials are brittle. Just like concrete, they exhibit behavior against pressure. Since mortar and masonry structures do not contain reinforcement in their components, they cannot show ductile behavior like reinforced concrete elements. Just like in reinforced concrete structures, vertical loads affect the floors to the arches, from there to the vertical bearing masonry walls and finally to the foundation. Only the moment of inertia due to lateral loads has a strong effect on masonry structures. The horizontal moment of inertia affects these loads, which exhibit rigid behavior despite the impact, on the walls with vertical bearing. However, these loads act on vertical carriers as shear and bending [18]. In masonry structures exposed to the effect of lateral loads, cracks occur in critical areas such as vertical bearing and floor joints, and this process puts the structure in the process of collapse.

There are many well-detailed studies in the literature on the structural behavior of masonry bridges. Some of these studies can be summarized as follows. Fanning and Boothby [19] used the test results of existing masonry arch bridges to determine appropriate material properties. After that, solid finite elements were used for 3D numerical analysis of bridges. The 18-span Tanaro Bridge in Italy, built in 1866 studied by Brencich and Sabia [20]. The dynamic properties of the bridge have been determined. Sevim et al. [21] conducted a study with operational modal analysis on linear seismic analysis of two historic masonry arch bridges. The 3D static non-linear behavior of masonry arch bridges analyzed by Milani and Lourenço [22]. Castellazzi et al. [23] experimentally examined the train bridge consisting of 15 openings and developed the finite element model. They decided that the bridge could be strengthened for the purpose of structural improvement. Numerous articles have been published on laser scanning measurement and three-dimensional (3D) modelling methods. Most of these articles are about the protection of cultural heritage and include different purpose structures such as historical buildings and archaeological sites and museums [24]. Dynamic evaluation of an existing three-span masonry arch bridge was studied by Pelà et al. [25]. The seismic capacity of the masonry bridge was determined by pushover and time history analyzes. Korkmaz et al. [26] have presented an analysis of the Timisvat stone arch bridge in Turkey's Rize under different lateral loads. The behavior of arch and stone bridges under different static loads evaluated by Rafiee and Vinches [27]. Altunışık et al. [28] investigated the effect of arch thickness variable on structural behavior. Stavroulaki et al. [13] are studied to prepare a realistic geometric model for 3D structural analysis of a stone arch bridge using Ground Penetrating Radar (GPR) and terrestrial photogrammetry. A hybrid method with macro and micro combination is used in the model. The effects of uncertainty in material parameters on the stochastic response in a historical masonry bridge exposed to random ground motion investigated by Hacıefendioğlu et al. [6]. The analyzes were carried out on the finite element mesh prepared by the macro modelling method of the historical masonry bridge system. Karaton et al. [29] investigated the non-linear seismic specifications of the historic twelfth century Malabadi bridge for different earthquake loads. Three different seismic load levels were selected for earthquake loading. The historical Dilovası Sultan Süleyman Bridge in Kocaeli was studied by Çakır [30]. To determine the structural behavior of the bridge, modal and response spectrum analyzes were determined using the finite element method. Drygala et al. [31] performed a seismic response analysis of a historic masonry arch viaduct located in Krakow, Southern Poland. The viaduct was modelled with ABAQUS [32] structural software program using 3D finite element model (FEM). Incremental dynamic analysis of two old railway bridges between Tehran and Kum was performed by Jahangiri al. [33] using several earthquake ground motion records. Bautista-De Castro et al. [34] proposed a multidisciplinary approach to study the reinforced concrete Bôco Bridge in Portugal, combining terrestrial laser scanner, ambient vibration testing and minor destructive testing. Caddemi et al. [35] proposed an original Discrete Macro Element Method (DMEM) that simulates masonry structures and masonry bridges with a lower computational load compared to conventional nonlinear FEM analyzes. Di Sarno et al. [36] focused on the structural performance of existing masonry and reinforced concrete bridges investigated following the 2016 Central Italian earthquakes. Analyzes have been made on bridge models to understand the true transverse failure mechanism. A macro model consisting of 3D finite elements was improved using TNO DIANA structural software. A multidisciplinary approach to determining the earthquake resistance of historical colossal defense structures presented by Dall'Asta et al. [37]. For this purpose, geometric analysis using modern tools such as laser scanning and related point cloud processing has been used to describe the exterior and interior geometry of the large structure and to verify existing historical information. Hokelekli and Yılmaz [38] studied the in-plane and non-linear structural responses of the sidewalls of a historical masonry bridge. To this end, in 1787 the structure was built in Bartin said Turkey's history is selected masonry arch bridges. 3D finite element model and nonlinear seismic analysis of the bridge were made with ABAQUS structural software. Zhao et al. [39] proposed a two-step numerical modelling method to accomplish the difficulty in defining masonry material anisotropy and to analyze the bearing capacity of masonry arch bridges. In this modelling strategy, the masonry is selected to be a two-stage material consist of stone blocks and mortar joints. Kujawa et al. [40] prepared a study on modeling a historic church using FEM, whose geometry is based on laser scans. The aim of the study is to investigate the crushing and cracking reasons of masonry fragments. For this purpose, the FEM model of the building was prepared in ABAQUS. The homogenization procedure was applied to provide the material parameters used in the modelling. In recent years, many studies have been carried out on imaging, material characterization, modeling and seismic performance of historical bridges [41,42,43,44,45,46,47]. By the technological innovations, many kinds of structures could be digitally measured easily and with high accuracy. And also, many effective structural analysis programs have been developed. Therefore, it is seen that increased interdisciplinary studies that deal with these two features together and that could be benefit various engineering applications and the assessment of historical heritage [48,49,50].

The aim of this study is to present an effective, reliable, and fast multidisciplinary approach for the analysis of historical masonry bridges. The aforementioned approach is presented as an example for the behavior of the recently restored historical Ayvalıkemer (Sillyon) masonry arch bridge under possible loadings. Terrestrial laser scanning (TLS) was used to determine the bridge geometry with high accuracy. The point cloud data obtained from TLS was simplified and a three-dimensional CAD based solid model of the structure was created. This solid body has been formed the basis of the macro model for structural analysis. The macro modelling technique is an analysis method that well represents the behavior of large-scale masonry structures. According to this technique, masonry unit and mortar are modeled as a whole. Macro modelling technique is widely used in modelling structures such as towers, mosques, churches and bridges with complex geometric features [6, 34, 35, 39].

Thus, an analysis was carried out which presents the structural behavior of a historical bridge with high accuracy and reliability. It is thought that this proposed approach facilitates, accelerates the modelling steps, and in this sense brings innovation to the literature. In addition, no analytical studies on the assessment of the Sillyon bridge have been found in the literature.

2 Sillyon bridge

Ayvalıkemer (Sillyon) bridge is located within the borders of Yanköy Village, Serik District of Antalya Province in Turkey. It is located on Koducak stream, which passes about 1 km south west of Sillyon antique city. There is no inscription on the Sillyon Bridge indicating the date of construction or repair. No archive record was found about its history. Considering the architectural features of the bridge, large block stones used in its construction, round arches, its proximity to the ancient city of Sillyon, and similar bridges in its immediate environment, it can be dated to the Roman period, to the second century. It has a length of 37 m. It has a deck width of 4.7 m. It has three arches and the middle arch is larger than the other two. The floor covering and railing of the bridge has not survived to the present day. Due to the stone foundation being below the water level, material losses have been occurred on the stone surface depending on the streams and the alluviums carried. Color change and complete extinction were observed in some parts. In summary, the bridge elements (e.g., spandrel walls, two flood splitters, stone foundation and three arches) have partially survived by preserving its original qualities apart from partial material losses (Fig. 1a) [51]. In addition, the Western Mediterranean geography, which includes the ancient city of Sillyon and its bridge, witnessed many earthquakes in history and the historical buildings were exposed to destructive damage [52,53,54,55]. As a result, it was restored in 2018 by the General Directorate of Highways in accordance with the original (Fig. 1b).

Fig. 1
figure 1

Sillyon Bridge a before and b after restoration (downstream direction)

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3 Material and methods

3.1 Methodology, terrestrial laser scanning technologies and data set

The Methodology carried out in this study is summarized in Fig. 2. There are two different methods to create the analysis model, preferably first, the "CAD based solid model" has been created, and then meshing this single solid by the macro modelling technique is prepared.

Fig. 2
figure 2

Methodology of TLS based structural analysis

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Digital photogrammetry and terrestrial laser scanning (TLS) method are among the best measurement methods for historical buildings due to their high spatial resolution capabilities. In particular, TLS method has replaced traditional measurement methods recently. It is one of the best examples of technological advances in terms of geomatic methods to measure the 3D geometry of objects without direct contact with objects [56]. It facilitates the modelling of sections (e.g., vaults, bridge legs) that are difficult to reach. With this method, millions of points are obtained with high precision and accuracy [57]. In the literature, there are many studies on the use of terrestrial laser scanners in historical construction and bridge measurements [11, 56,57,58,59,60].

In this study, FARO Focus3D X130 laser scanner was used. Under normal light and reflection conditions, it has a sensitivity of 2 mm and can measure between 0.6 and 130 m. The scanner has the ability to rotate in the direction of 300° vertical axis and 360° horizontal axis. The weight of the scanner is 5.2 kg. It has a color resolution of 70 megapixels and can obtain 976,000-point data per second [61]. In this study, the distances between the measurement stations and the bridge are generally kept as low as possible within the range of 5–8 m and the angular resolution of the scanning process is determined as 0.08°. Point clouds contain many data other than bridge details. For this reason, unneeded points in the scanning data are removed before creating a 3D point cloud. After removing the data, the point clouds obtained from different stations were combined in a common coordinate system to obtain a single 3D point cloud of the entire bridge. High resolution orthophotos were prepared using the combined three-dimensional and color scanning data obtained. 3D models of historical buildings will be an important reference data for restoration works. If these historical buildings are damaged or destroyed due to any situation, they serve as archives in digital environment. In addition, when the point clouds created by TLS method are transformed into solid models, they also contribute to analysis on historical buildings.

3.2 Macro modelling method

When modelling historical masonry structures, two basic assumptions are taken into account: macro modelling and micro modelling. In the micro modelling method, stone or brick, which is the carrier structural material, is modelled separately, and the mortar providing binding effect is modelled separately [62, 63]. This modelling is divided into two as detailed and simplified among themselves. In the macro modelling method, modelling is done by accepting the structural materials as a single material, not separate (Fig. 3a–c).

Fig. 3
figure 3

Modelling techniques in masonry walls a detailed micro modelling b simplified micro modelling c macro modelling [64] d Homogenization by unit cell method

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Macro modelling technique is preferred in the analysis of large structures, since a finite number of finite elements is required than the number of nodes and elements used in micro modelling techniques [65]. This approach is generally used in the modelling of walls, feet, buttresses, arches and vaults of complex system masonry structures. However, in this approach, no detailed information can be obtained about crack geometry, spread and collapse behavior. In this approach, the material is considered composite. Stone or brick and mortar are homogenized and transformed into a single material feature [66]. It is based on modelling the masonry structure with a homogeneous anisotropic environment without any discrimination and difference between stone, brick and mortar. At the same time, using the composite material theory, homogenization is performed by accepting that the masonry unit has a homogeneous and isotropic material feature [67]. Lourenço et al. [68] performed numerical modelling of masonry units with a homogenization method called "Unit cell method" (Fig. 3d).When a simple cell taken from the masonry wall is examined, it is used in the material parameters taking into account the participation rates of mortar and brick and can be considered as a single material. Lourenço [68] proposes Eq. (1) for the calculation of other material parameters, especially the elasticity module for brick and mortar. In this study, Eq. (1) is used to define the linear initial part of the behavior:

$$E_{{{\text{wa}}}} = \frac{{t_{{\text{s}}} + t_{{\text{m}}} }}{{\frac{{t_{{\text{s}}} }}{{E_{{\text{s}}} }} + \frac{{t_{{\text{m}}} }}{{E_{{\text{m}}} }}}}\delta_{{{\text{w}}}}$$
(1)

here; Ewa is the average modulus of elasticity for the composite material obtained, tm is the mortar thickness, ts is the brick thickness, Em is the modulus of elasticity of the mortar, Es is the modulus of elasticity of the brick. δw is a coefficient ranging from 0 to 1, which indicates the effectiveness of the bond between brick and mortar, and can be accepted as 0.5 for an average structure.

The Concrete Damage Plasticity (CDP) material model, which has been widely used in recent years for the stress–strain behavior of brittle materials, is also used in this study to express the nonlinear part of the behavior [69,70,71]. Compressive stress–strain behavior of the material and uniaxial tensile stress–strain behavior is defined by the relations [72, 73] shown in Eqs. (2,3):

$$\sigma_{{\text{c}}} = f_{{{\text{co}}}} \frac{{n\left( {\frac{{\varepsilon_{{\text{c}}} }}{{\varepsilon_{{{\text{co}}}} }}} \right)}}{{\left( {n - 1} \right) + \left( {\frac{{\varepsilon_{{\text{c}}} }}{{\varepsilon_{{{\text{co}}}} }}} \right)^{n} }}\quad \varepsilon_{{{\text{co}}}} = 2.7 \times 10^{ - 4} \left( {\sqrt[4]{{f_{{{\text{co}}}} }}} \right)\quad n = 0.4 \times 10^{ - 3} f_{{{\text{co}}}} + 1\;({\text{MPa}})$$
(2)
$$\sigma_{{\text{t}}} = f_{{{\text{to}}}} \left( {\frac{{\varepsilon_{{{\text{to}}}} }}{{\varepsilon_{{\text{t}}} }}} \right)^{{\left( {0.4} \right)}} \quad \varepsilon_{{{\text{to}}}} = \frac{{f_{{{\text{to}}}} }}{{E_{{\text{c}}} }}$$
(3)

In Eq. (2), fco and εco denotes compressive strength and strain at maximum stress. fc and εc are compressive stresses and strains at any point on the stress–strain curve. The steepness of this curve is controlled by the empirical coefficient “n”. σt and εt in Eq. (3) are the tensile stresses of material and the strains corresponding to these stresses, respectively. fto is the tensile strength, εto is the unit strain corresponding to fto and Ec is the elasticity modulus of the material.

There are several methods used to determine the material properties of masonry stonewalls. One of these methods is given in EUROCODE-6 [74]. Here, a common and equivalent material property can be determined by considering the geometrical and material properties of the different materials working together. The strength of the composite material consisting of natural stone and mortar in EUROCODE-6 is as given in Eq. (4):

$$f_{{{\text{co}}}} = K \times f_{{{\text{stone}}}}^{0.7} \times f_{{{\text{mortar}}}}^{0.3} $$
(4)

here; K value is determined according to EUROCODE 6—Table 3.3, for the dimensioned natural stone type and Group-1 ground class, 0.45 value is selected from the table. The tensile strength of the masonry wall is mostly related to the strength of the mortar material, which has less value than the stone parts. For this reason, to define the upper limit of the tensile stress in the masonry wall, the minimum tensile strength of the mortar can be used as fto value.

In the analysis of historical structures, four different methods can be used, such as static analysis under vertical and horizontal loads, free vibration analysis (modal analysis), behavior spectrum analysis and analysis in the time domain. Correct interpretation of the analyzes made is critical in the renovation or strengthening phase of the building. Strengthening and renewal required in the structure are applied depending on these interpretations.

4 Findings

4.1 CAD based solid model preparation using point cloud data and macro modelling

After the restoration works of the bridge were completed, the point cloud and orthophoto image were produced by the terrestrial laser scanning method. Point cloud file has been transferred to ReCap 2020 software [75] (Fig. 4). First, in the point cloud file, arches, handrails, foundations, folds and points deemed necessary from all surfaces were determined separately from the upstream and downstream sides to model the structure exactly. In AutoCAD 2020 software [76], a solid model was produced using some tools (e.g., 3DPoly, Surface, Loft, Patch, Sculpt) (Fig. 5).

Fig.4
figure 4

Point clouds obtained by terrestrial laser scanning (upstream and downstream direction)

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Fig. 5
figure 5

Solid model production steps and perspective view of solid model in AutoCAD

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Thus, the entire bridge as a single solid piece can be exported to the finite element analysis program. The finite element model and its mesh pattern of the bridge prepared using the macro modelling technique are shown in Fig. 6. In the modelling, it was assumed that the foundation on which the bridge is located is totally rigid.

Fig. 6
figure 6

Perspective view of the finite element model

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4.2 Material and load types for macro modelling

In this study, Concrete Damaged Plasticity (CDP) material model was used to describe the inelastic behavior of homogenized structure [69, 70]. The tension meridians of the failure surface of the CDP, which is developed with the modification of the Drucker Prager model, are reduced with the K coefficient, and the linear meridians are transformed into parabola with the eccentricity (e) parameter. Dilation angle (β) is obtained from the angle between mises equivalent effective stress and the hydrostatic axis. fb0/fc0 is the ratio of the biaxial compressive strength of the material to the uniaxial compressive strength. The CDP parameters considered for the whole structure are assumed as; β, 36; e, 0.1; fb0/fc0, 1.16 and K, 0.667 respectively [71].

During the restoration study, material tests were performed on the travertine stone that forms the historical bridge (Table 1). The "Denizli, Kocabağ" travertine, which is compatible with the original material properties, was decided to use in the restoration. In this study, the modulus of elasticity required for the linear part of the analysis is considered as the arithmetic mean of the vertical and horizontal test results. The Poisson ratio of travertine stone was taken into consideration as 0.3 in accordance with the article prepared by Çelik and Çobanoğlu [77].

Table 1 Mechanical properties of materials
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“Master Emaco S285 TIX” repairing mortar was used as a binder between stones in restoration. Only one elasticity module is needed for the macro model of the composite bridge. To obtain this value, taking into account the common effect of the bonding material and stones, the expression of Lourenço given in Eq. (1) has been used. The average modulus of elasticity (Ewa) value obtained for the wholestone wall pattern with an average edge length of 300 mm and a joint spacing of 10 mm is shown in Table 1. The tensile strength (fto) of the whole masonry structure was considered as 0.15 MPa, because of the mortar bond strength is weaker than the tensile strength of travertine stone. The material models and damage parameters considered to represent the compressive and tensile behavior of the homogenized material of the masonry bridge are shown in Fig. 7.

Fig. 7
figure 7

Material models and damage parameters for CDP [72, 73]

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In the static analysis, besides self-weight (G) load, 150 kg/m2 live load (Q) and 500 kg/m2 flood load (W) acting from the upstream direction of the bridge were taken into account. If these loading conditions are converted to SI unit system, 0.001471 N/mm2 as live load (Q) and 0.049033 N/mm2 as flood load (W) are obtained. The parapet walls that do not contribute to bridge strength are considered only as distributed load in modelling (Fig. 8). The parapet load, which was calculated as 450 kg/m, was applied as a distributed load on the upstream and downstream sides.

Fig. 8
figure 8

Parapet load distribution in finite element model

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4.3 Structural analysis using macro modelling

For the analysis, nonlinear explicit dynamic solution method was used. Explicit solution method was preferred in order not to encounter numerical instabilities and convergence problems caused by brittle damage and sudden stiffness losses seen in nonlinear models. In the model, homogenized stone and mortar structure represented with C3D8R (8-node brick elements with reduced integration) solid elements using macro modeling method.

Totally, eight analyzes were performed on the macro model of the historical bridge. These are; dead load analysis (G), live load analysis (Q), upstream direction flood load analysis (W), free vibration analysis (S) for the first fifty modes, horizontal X direction spectrum analysis (SPECX), horizontal Y direction spectrum analysis (SPECY), vertical Z direction spectrum analysis (SPECZ) and spectrum analysis (SPECXYZ) in all XYZ directions simultaneously. The loading combinations considered for these analyzes are given in Table 2.

Table 2 Load combinations considered in macro modelling
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4.3.1 Static analysis for vertical and horizontal loads

The static analysis of the Ayvalıkemer (Sillyon) bridge for vertical and horizontal loads is important in terms of obtaining the stress distribution under the dead and moving loads and determining the damage zones that may occur. This loading, which does not take into account horizontal loads such as earthquake and wind, is actually the usual loading condition of the building and is expected to be carried without any problem. In static analysis, the weight of the building as dead loads, and the loads that may occur during the transition over the structure as live loads are considered. Because of these loads, the analysis results of the stress and displacement obtained are shown in the Fig. 9.

Fig. 9
figure 9

Principal normal stresses and vertical displacements under static loads

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4.3.2 Free vibration analysis (modal analysis)

Modal analysis has been performed to determine the dynamic characterization of the Ayvalıkemer (Sillyon) bridge and to provide the sub-data needed by the response spectrum analysis. In this analysis; free vibration periods, mode shapes and mass participation rates of the building are determined. The contribution of each free vibration mode of the structure to the behavior of the building system is obtained separately. Response spectrum analysis is done by combining the contribution of each mode (mode superposition method) so that the dynamic behavior of the structure is determined [78].

In this study, the free vibration characteristics of the Ayvalıkemer (Sillyon) bridge structure have been tried to be determined analytically. A suitable number of mode shape vectors should be taken into account for the response spectrum analysis of the structure. For this purpose, it has been understood that it will be sufficient to determine the first 50 modes of the building according to the mass participation rates in the global directions. The free vibration characteristics of the structure are presented in Table 3 and the related 1–5th and 50th mode shape vectors are presented in Fig. 10.

Table 3 Modal periods and frequencies of the structure (mode 1–50)
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Fig. 10
figure 10

Mode shape vectors of various modes

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4.3.3 Response spectrum analysis

Maximum value of parameters such as stress and displacement is required in the design of structural systems. Therefore, using the spectrum of the earthquake motion, the most unfavorable values are directly obtained without the need for numerical analysis that is long and complex. Since the spectral curves give only the greatest values and are not sufficient in determining the contributions of various modes for a given moment, some mathematical approaches have been developed for the calculation. One of these approaches is the Complete Quadratic Combination (CQC) method.

Response spectrum analysis was performed in global directions with macromodelling of the Ayvalıkemer (Sillyon) bridge structure. For this purpose, bridge coordinates were treated to interactive Web App (AFAD Turkey Earthquake Hazard Maps) to determine the seismicity of the bridge area. With the data obtained here, the formulas in Turkish Building Earthquake Code 2018 [79] were used to create the earthquake spectrum curves. The resulting horizontal and vertical elastic design spectrum curves are shown in Fig. 11. To be used in obtaining curves; damping ratio, 0.05; local ground class, ZE; short period map spectral acceleration coefficient (Ss), 0.519; map spectral acceleration coefficient for 1.0 s period (S1), 0.138; short period design spectral acceleration coefficient (SDS), 0.8665; the design spectral acceleration coefficient for 1.0 s period (SD1), 0.53240, was taken into account.

Fig. 11
figure 11

Horizontal and vertical elastic design spectrum curves for the region

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In the response spectrum analysis, four different load combinations were considered shown as in Table 2. With these combinations, the maximum stress and displacement values that can occur in the structure as a result of the loading acting separately in the global X, Y, Z directions and simultaneously in these three directions were obtained (Fig. 12).

Fig. 12
figure 12

Principal normal stress and displacement values for various load combinations

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5 Conclusions

Origin of the stone used in Ayvalıkemer (Sillyon) historical bridge is travertine stone. A preliminary investigation was carried out on which quarry would be extracted from the nearby area, and it was determined that the stone could be obtained from the Kocabaş quarry of Denizli in Turkey. After the supply of the material to be used, the renovation project was prepared and the works were completed by preserving the original structure. At the end of the restoration work, the final version of the bridge was scanned and archived by the TLS (Terrestrial Laser Scanning) method.

In this study, it has been understood that the point cloud obtained as a result of terrestrial laser scanning technique provides a very fast and highly accurate data for determining the structural geometry that will support the structural analysis. A computer-aided solid element model of the building was created using the point cloud data. Following the completion of the modelling, load and material assumptions were made and static and dynamic analyzes of the structure were carried out, respectively.

The analysis of restored Ayvalıkemer (Sillyon) historical bridge was performed by using macro modelling technique. Analytical study was carried out on a solid model of the structure. It has been seen that the principal normal stress and displacement values determined in the analyzes remained in the initial elastic part of the material defined for the whole masonry structure (Figs. 7, 9, 10, 11, 12, Table 1). Therefore, despite the preparation of a numerical model including the inelastic material behavior by the CDP, no damage result in the form of crushing or cracking was obtained under the considered loadings at the components of the historical bridge. The greatest compressive stress was calculated as 3.168 MPa as a result of G + SPECXYZ response spectrum analysis performed for all global directions (Fig. 11). It has been determined that this stress does not exceed the compressive strength of both mortar and travertine stone and can safely carry the loads on the bridge, which is closed to vehicle traffic. It has been observed that the point cloud obtained by TLS method is very useful for modelling and analytical studies that will be carried out for historical buildings.