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Analysis of Cylindrical Masonry Shell in St. Jacob`s Church in Dolenja Trebuša, Slovenia—Case Study

Analysis of Cylindrical Masonry Shell in St. Jacob`s Church in Dolenja Trebuša, Slovenia—Case Study buildings Article Analysis of Cylindrical Masonry Shell in St. Jacob‘s Church in Dolenja Trebuša, Slovenia—Case Study 1 , 2 1 Mojmir Uranjek *, Tadej Lorenci and Matjaž Skrinar Chair of Structural Mechanics, Faculty of Civil Engineering, Transportation Engineering and Arhitecture University of Maribor, Maribor 2000, Slovenia; matjaz.skrinar@um.si Department of Health and Safety, Abrasiv Muta, Muta 2366, Slovenia; tadej.lorenci@gmail.com * Correspondence: mojmir.uranjek@um.si; Tel.: +386-2-22-94-357 Received: 9 April 2019; Accepted: 18 May 2019; Published: 22 May 2019 Abstract: This paper focuses on identifying key reasons for the damage of the cylindrical masonry shell structure in St. Jacob‘s church in Dolenja Trebuša, Slovenia. Typical damage patterns which can be formed in shell structures and may a ect the load bearing capacity are outlined. Several stress states (membrane, bending and also combined stress state) that can occur in the shell structure are described. Load cases such as the vertical displacement of the support structure, temperature loading, weight of maintenance team and also seismic loading are taken into account in order to identify the actual cause for the registered crack pattern in the shell structure. Analysis of the shell structure is performed using the SAP2000 structural software. Based on the obtained results, which highlighted key reasons for registered damage, the monitoring of cracks is recommended in the first phase, and, in continuation, the most appropriate repair and strengthening measures are proposed. Keywords: masonry shell; cracks in shells; static analysis; strengthening 1. Introduction Motivation for this work is the fact that masonry shell structures as a part of historical buildings such as churches, monasteries and castles are present in a relatively large number not just in Slovenia but also worldwide. Over the years, due to various reasons (change in magnitude and distribution of loading, earthquake loading, foundation settlements, etc.) these structures can be damaged. Consequently, inner forces are redistributed and in many cases the static system is changed. Nevertheless, most of these structures maintain their function also afterwards [1]. In the case of reconstruction, the load bearing capacity of the shell structure should be checked in accordance with current regulations and, if necessary, appropriate measures have to be undertaken. In this paper, computational analysis of the actual shell structure is demonstrated. By using the results of this analysis, causes for damage are identified and possible rehabilitation and consolidation measures are proposed. 2. Stresses and Typical Damage Patterns of Masonry Shells To describe the geometry of the shell, the spatial position of the midsurface and the thickness of the shell at each point have to be known. The analysis of shell structures is usually performed using two theories: Membrane theory, which is usually valid for lager part of the shell and bending theory, which includes the e ect of bending [2]. In areas where due to local disturbances (supports, point loads, changes of curvature or thickness) the ideal membrane stress state is no longer valid (Figure 1), the membrane theory should be supplemented by the bending theory. Buildings 2019, 9, 127; doi:10.3390/buildings9050127 www.mdpi.com/journal/buildings Buildings 2018, 8, x FOR PEER REVIEW 2 of 11 Buildings 2019, 9, 127 2 of 11 Figure 1. Critical parts of the shell where the bending stress state can be formed (adapted after [3]). Figure 1. Critical parts of the shell where the bending stress state can be formed (adapted after [3]). For shell structures in historical buildings in most cases the membrane theory has to be For shell structures in historical buildings in most cases the membrane theory has to be supplemented by the bending theory. As the result of the simultaneous e ect of membrane forces N , supplemented by the bending theory. As the result of the simultaneous effect of membrane forces Nx, N N and bending moments M , M M the stresses which occur in the shell can be written as: y , xy x y , xy Ny, Nxy and bending moments Mx, My, Mxy the stresses which occur in the shell can be written as: N 12M z x x = (1) = − (1) N 12M z y y = (2) t 12 (2) = − N 12M z xy xy = (3) xy (3) The first terms in the above expressions = represent − the membrane stress while the second terms, the bending stress. The distribution of stresses  ,  and  within the shell thickness is linear. x y xy Perpendicular shear stresses  in  as a consequence of shear forces have a parabolic distribution, The first terms in the aboxz ve expre yz ssions represent the membrane stress while the second terms, but their values are generally small in comparison with other stress components and can usually the bending stress. The distribution of stresses σx, σy and τxy within the shell thickness is linear. be neglected. Perpendicular shear stresses τxz in τyz as a consequence of shear forces have a parabolic distribution, Damage of shells, often in the form of cracks, occurs due to various reasons: Foundation but their values are generally small in comparison with other stress components and can usually be settlement, horizontal displacements of supporting walls, material deficiencies and degradation or neglected. local overloading as well as their combinations. Some typical crack configurations due to various Damage of shells, often in the form of cracks, occurs due to various reasons: Foundation reasons in the case of barrel vault are shown in Figure 2. settlement, horizontal displacements of supporting walls, material deficiencies and degradation or local overloading as well as their combinations. Some typical crack configurations due to various reasons in the case of barrel vault are shown in Figure 2. (a) (b) (c) Figure 2. Some typical crack configurations for barrel vault [4]. Figure 2. Some typical crack configurations for barrel vault [4]. (d) (e) (f) Figure 2. Some typical crack configurations for barrel vault [4]. Buildings 2019, 9, 127 3 of 11 Buildings 2018, 8, x FOR PEER REVIEW 3 of 11 3. Analysis of Masonry Shell in St. Jacobs Church 3. Analysis of Masonry Shell in St. Jacobs Church 3.1. Characteristics of the 2004 Earthquake 3.1. Characteristics of the 2004 Earthquake Generally, Slovenia is a territory with almost regular (moderate) seismic activities. On an average Generally, Slovenia is a territory with almost regular (moderate) seismic activities. On an day, an earthquake with a magnitude higher than 1 is normally detected. Further, Dolenja Trebuša lies in average day, an earthquake with a magnitude higher than 1 is normally detected. Further, Dolenja a region with some more than average seismic activities. Nevertheless, although this area is not one of Trebuša lies in a region with some more than average seismic activities. Nevertheless, although this the most seismically exposed parts of our country; it still lies quite close to the region, which was severely area is not one of the most seismically exposed parts of our country; it still lies quite close to the damaged by the 1976 earthquake (with the magnitude of 6.5 the strongest earthquake that has been region, which was severely damaged by the 1976 earthquake (with the magnitude of 6.5 the strongest recorded in Slovenia so far). The considered 2004 earthquake occurred on 12 July 2004 with an epicenter earthquake that has been recorded in Slovenia so far). The considered 2004 earthquake occurred on to the northwest of Dolenja Trebuša (areal distance was about 35 km). It occurred on the same place of 12 July 2004 with an epicenter to the northwest of Dolenja Trebuša (areal distance was about 35 km). the 1998 earthquake (which had the magnitude of 5.7). Both these earthquakes are listed among the three It occurred on the same place of the 1998 earthquake (which had the magnitude of 5.7). Both these last severe earthquakes that were recorded in Slovenia. Although most of the damage resulting from the earthquakes are listed among the three last severe earthquakes that were recorded in Slovenia. 2004 earthquake occurred in the vicinity of Bovec mainly due to local geological conditions, other areas Although most of the damage resulting from the 2004 earthquake occurred in the vicinity of Bovec such as Dolenja Trebuša were also affected. The 2004 earthquake caused material damage primarily on mainly due to local geological conditions, other areas such as Dolenja Trebuša were also affected. The old 2e 0r 04 b u earthqua ildings, ke whcau ichsed in th m is atreri egal ion dam hav ag e e a pri verma y lo riw ly e on ar to hlq de ua r k be ui re ldi sis ngs tan , cwh e. N ich am in elthis y, thregi e bu oin ldhav inge sta o ck con vs ery istslm ow ain earthqua ly of old ke sto resi ne sta ma nce. son rNa y hmel ousy, es tw he ith bui on ldi e o ng r tw stoc o s k toco rensists ys builma t lair nl ge y ly of frol om d stone two-lema af m sonry asonry houses with one or two storeys built largely from two-leaf masonry with two-leaf stone masonry with with two-leaf stone masonry with weak lime mortar and wooden floors [5]. weak lime mortar and wooden floors [5]. 3.2. Structural Characteristics and Damage of Analyzed Masonry Shell 3.2. Structural Characteristics and Damage of Analyzed Masonry Shell For the analysis, a barrel vault in St. Jacob Church in Dolenja Trebuša in Slovenia was chosen. The Church was built in 1786 and retrofitted in 2013 in order to simultaneously rehabilitate and For the analysis, a barrel vault in St. Jacob Church in Dolenja Trebuša in Slovenia was chosen. strThe engthen Churc its h str was uctur buie lt after in 178 the 6 an earthquake d retrofitted in 2004. in 201In 3 in spite order of the to si rmul enovation taneously in 2013, rehabcracks ilitate ain ndthe consider strengt ed hen vaul its tstruc reopened. ture afte The r the stone earth masonry quake in barr 2004 el . In vault spite is o built f the out reno of vat limestone ion in 201 and 3, cracks leech istone n the in considered vault reopened. The stone masonry barrel vault is built out of limestone and leech stone lime mortar. Geometry and materials of the vault are shown in Figure 3. The length of the vault is in lime mortar. Geometry and materials of the vault are shown in Figure 3. The length of the vault is 10 m (above the nave) with a span of 7.75 m. The thickness of the vault is changing from 30 cm at the 10 m (above the nave) with a span of 7.75 m. The thickness of the vault is changing from 30 cm at the base and to 8 cm at the top. base and to 8 cm at the top. (a) (b) Figure 3. Analysed stone masonry barrel vault from bottom (a) and top (b). Buildings 2018, 8, x FOR PEER REVIEW 4 of 11 Buildings 2018, 8, x FOR PEER REVIEW 4 of 11 Buildings 2019, 9, 127 4 of 11 Figure 3. Analysed stone masonry barrel vault from bottom (a) and top (b). Figure 3. Analysed stone masonry barrel vault from bottom (a) and top (b). Before rehabilitation and strengthening of the church in 2013, numerous cracks in the walls and Before rehabilitation and strengthening of the church in 2013, numerous cracks in the walls and Before rehabilitation and strengthening of the church in 2013, numerous cracks in the walls and vaults were listed. In the middle area of the analysed vault there was a crack running along the entire vaults were listed. In the middle area of the analysed vault there was a crack running along the entire vaults were listed. In the middle area of the analysed vault there was a crack running along the entire length of the nave, which continued through the supporting arch and presbytery vault with length of length of the nave, which continued through the supporting arch and presbytery vault with length length of the nave, which continued through the supporting arch and presbytery vault with length 13.5 m and thickness of 1.0 mm. Other cracks were also present on the vaults, especially in the area of of 13.5 m and thickness of 1.0 mm. Other cracks were also present on the vaults, especially in the area of 13.5 m and thickness of 1.0 mm. Other cracks were also present on the vaults, especially in the area the transverse vaults although of smaller width and length (Figure 4). of the transverse vaults although of smaller width and length (Figure 4). of the transverse vaults although of smaller width and length (Figure 4). Figure 4. Registered crack pattern of analysed barrel vault before rehabilitation in 2013 [6]. Figure 4. Registered crack pattern of analysed barrel vault before rehabilitation in 2013 [6]. Figure 4. Registered crack pattern of analysed barrel vault before rehabilitation in 2013 [6]. The cracks although to a lesser extent, reopened in the same places after the repair works in 2013 The cracks although to a lesser extent, reopened in the same places after the repair works in 2013 The cracks although to a lesser extent, reopened in the same places after the repair works in 2013 (Figure 5). (Figure 5). (Figure 5). (a) (b) (a) (b) Figure 5. Reopened crack in the analysed shell (a) and in wall near transverse vault (b). Figure 5. Reopened crack in the analysed shell (a) and in wall near transverse vault (b). Figure 5. Reopened crack in the analysed shell (a) and in wall near transverse vault (b). 3.3. Static Analysis of Masonry Shell 3.3.Static Analysis of Masonry Shell 3.3.Static Analysis of Masonry Shell The stone masonry barrel vault was analysed by using the SAP2000 software [7]. A combination The stone masonry barrel vault was analysed by using the SAP2000 software [7]. A combination The stone masonry barrel vault was analysed by using the SAP2000 software [7]. A combination of three and four-node shell finite elements combined with linear finite elements was used in the of three and four-node shell finite elements combined with linear finite elements was used in the of three and four-node shell finite elements combined with linear finite elements was used in the model. The structure was modelled with varying thickness according to actual geometry. Supports model. The structure was modelled with varying thickness according to actual geometry. Supports model. The structure was modelled with varying thickness according to actual geometry. Supports (main arch, closed arches at the side, supporting wall) were modelled using linear finite elements of (main arch, closed arches at the side, supporting wall) were modelled using linear finite elements of (main arch, closed arches at the side, supporting wall) were modelled using linear finite elements of the corresponding cross section. The barrel vault was modelled with 2211 shell and 436 linear finite the corresponding cross section. The barrel vault was modelled with2211 shell and 436 linear finite the corresponding cross section. The barrel vault was modelled with2211 shell and 436 linear finite Buildings 2019, 9, 127 5 of 11 Buildings 2018, 8, x FOR PEER REVIEW 5 of 11 elements interconnected in 2499 nodes. Horizontal steel ties were modelled as linear elements with elements interconnected in 2499 nodes. Horizontal steel ties were modelled as linear elements with circular cross section of  32–45 mm (Figure 6). circular cross section of  32-45 mm (Figure 6). (a) (b) Figu Figure re 6. 6. 3 3D D F FE E mo model del ((a a) ) and and cro cross ss sectio section n ((b b) sh ) showing owing chan changing ging thick thickness ness of a of analysed nalysed ba barr rrel el vault vault. . When the registered crack pattern is compared with possible crack configurations shown in When the registered crack pattern is compared with possible crack configurations shown in Figure 2, several actions can be identified as the potential cause of such damage. The longitudinal Figure 2, several actions can be identified as the potential cause of such damage. The longitudinal crack at the bottom middle part of the shell may thus be caused either by simultaneous horizontal crack at the bottom middle part of the shell may thus be caused either by simultaneous horizontal divergent displacement of supporting walls (Figure 2 top left), di erential settlement of foundations divergent displacement of supporting walls (Figure 2 top left), differential settlement of foundations (Figure 2 bottom left) or point load in the central part of the shell (Figure 2 bottom right). (Figure 2 bottom left) or point load in the central part of the shell (Figure 2 bottom right). Since the increase of the structures weight was eliminated as a possible cause for the registered Since the increase of the structures weight was eliminated as a possible cause for the registered crack pattern, other possible causes were analysed in the numerical analysis: Self weight of structure crack pattern, other possible causes were analysed in the numerical analysis: Self weight of structure and rubble layer, di erential settlement of foundations, seismic loading, maintenance loading and and rubble layer, differential settlement of foundations, seismic loading, maintenance loading and temperature di erence (Figures 7 and 8). temperature difference (Figures 7 and 8). The implementation of non-linear behaviour would be the most appropriate approach for the analysis of the considered shell. However, we were not involved in any material properties acquisition (all the mechanical parameters were taken from the Technical Report, [6]) for the analysed shell. Furthermore, our analyses were not part of any ocial study, and were thus not financially supported. Therefore, the decision was met to perform only linear elastic analyses, which nevertheless provided satisfactory results and enabled the identification of possible causes for the damage. Five load combinations were considered altogether: Load case »1«: Self weight and rubble layer: X X 1.35  (a) G + 1.35  G Load case »2«: Self weight, rubble layer, vertical displacement of outer supports on one side by D = 0.5 cm: X X X 1.35  G + 1.35  G + 1.5  D N z Load case »3«: Self weight, rubble layer, maintenance team: X X X 1.35  G + 1.35  G + 1.5  Q N V (b) Buildings 2018, 8, x FOR PEER REVIEW 5 of 11 elements interconnected in 2499 nodes. Horizontal steel ties were modelled as linear elements with circular cross section of  32-45 mm (Figure 6). (a) Buildings 2019, 9, 127 6 of 11 (b) Figure 6. 3D FE model (a) and cross section (b) showing changing thickness of analysed barrel vault. Load case »4«: Self weight, rubble layer, horizontal displacement of all supports on one side by D = When 0.5 cm: the registered crack pattern is compared with possible crack configurations shown in X X X 1.35  G + 1.35  G + 1.5  D Figure 2, several actions can be identified as the potential cause of such damage. The longitudinal N y crack at the bottom middle part of the shell may thus be caused either by simultaneous horizontal Load case »5«: Self weight, rubble layer, temperature di erence: divergent displacement of supporting walls (Figure 2 top left), differential settlement of foundations X X X (Figure 2 bottom left) or point load in the central part of the shell (Figure 2 bottom right). 1.35  G + 1.35  G + 1.5  D N T Since the increase of the structures weight was eliminated as a possible cause for the registered crack pattern, other possible causes were analysed in the numerical analysis: Self weight of structure and rubble The discr layer, ete rdifferential esults’ values settlement are presented of foundations, for seven points seismic visible loading, in Figur maintenance e 9. loading and temperature difference (Fiures 7 and 8). (a) Buildings 2018, 8, x FOR PEER REVIEW 6 of 11 (b) Figure 7. Load case simulating vertical displacement of outer supports on one side (a) and horizontal Figure 7. Load case simulating vertical displacement of outer supports on one side (a) and horizontal displacement of all supports on one side (b). displacement of all supports on one side (b). (a) (b) Figure 8. Load case simulating maintenance team (a) and temperature di erence (b). Figure 8. Load case simulating maintenance team (a) and temperature difference (b). The implementation of non-linear behaviour would be the most appropriate approach for the analysis of the considered shell. However, we were not involved in any material properties acquisition (all the mechanical parameters were taken from the Technical Report, [6]) for the analysed shell. Furthermore, our analyses were not part of any official study, and were thus not financially supported. Therefore, the decision was met to perform only linear elastic analyses, which nevertheless provided satisfactory results and enabled the identification of possible causes for the damage. Five load combinations were considered altogether:  Load case »1«: Self weight and rubble layer: 1.35 ∗ + 1.35 ∗  Load case »2«: Self weight, rubble layer, vertical displacement of outer supports on one side byΔz=-0.5 cm: 1.35 ∗ + 1.35 ∗ + 1.5 ∗  Load case »3«: Self weight, rubble layer, maintenance team: 1.35 ∗ + 1.35 ∗ + 1.5 ∗  Load case »4«: Self weight, rubble layer, horizontal displacement of all supports on one side byΔy=0.5 cm: 1.35 ∗ + 1.35 ∗ + 1.5 ∗  Load case »5«: Self weight, rubble layer, temperature difference: 1.35 ∗ + 1.35 ∗ + 1.5 ∗ The discrete results’ values are presented for seven points visible in Figure 9. Buildings 2019, 9, 127 7 of 11 Buildings 2018, 8, x FOR PEER REVIEW 7 of 11 Figure 9. Selected points corresponding to stress values given in Table 1. Figure 9. Selected points corresponding to stress values given in Table 1. The The distribution distribution of of str stresses esses acr acro oss ss the the shell shell thickness thickness is is linear linear. . In In the the eval evaluation uation of of r results, esults, values values obtained obtained in in the the upper upper (external) (external) and and b bottom ottom part part of of the the shell shell wer were e consider considere ed. d. By By taking taking into into account account the the values values o of f z z = = t / t/2 2and and zz = = -t / t/2 2for for the the upper upper and and bottom bottom part o part of f the the shel shell,lr , espectively respectively we we o obtain: btain: F 6M 11 11 = (4 (4) ) = − 11up t t F 6M 11 11 = + (5) 11bot (5) = t + F 6M 22 22 = (6) 22up = − (6) F 6M 22 22 = + (7) 22bot t t where designations »up« in »bot« stand for stresses on the upper and bottom part of the shell. According = + (7) to Eurocode 6 for masonry structures, the actual compressive stress ( ) and tensile stress ( ) should be c t smaller than the design compressive (f ) and/or design tensile strength (f ) of the material, respectively. cd td where designations »up« in »bot« stand for stresses on the upper and bottom part of the shell. Values of the characteristic compressive (f ) and tensile strength (f ) were taken from the Technical c t According to Eurocode 6 for masonry structures, the actual compressive stress (σc) and tensile stress Report, reference No. 6 and were obtained from investigations of similarly built stone masonry walls (σt) should be smaller than the design compressive (fcd) and/or design tensile strength (ftd) of the and vaults studied both in situ and in the laboratory of ZRMK. Design values are obtained by dividing material, respectively. Values of the characteristic compressive (fc) and tensile strength (ft) were taken the characteristic compressive (f ) and tensile strength (f ) of the material with the material safety factor c t from the Technical Report, reference No. 6 and were obtained from investigations of similarly built , as given by the code: stone masonry walls and vaults studied both in situ and in the laboratory of ZRMK. Design values f f c t are obtained by dividing the characteristic compressive (fc) and tensile strength (ft) of the material < ,  < (8) c t M M with the material safety factor ΥM, as given by the code: The material safety factor is assessed as = 2.0. Calculated stresses should be smaller than M M permissible values. In the case of tension we obtain: < , < (8) 0.08 < f = = = 0.04 MPa = 40 kN/m (9) td The material safety factor γM is assessed as γM =2.0. Calculated stresses should be smaller than permissible values. In the case of tension we obtain: And in the case of compression: 0.08 < = = = 0.04 = 40 / (9) c 0.5 2 < f = = = 0.25 MPa = 250 kN/m . c cd And in the case of compression: The results obtained in selected points are summarised in Table 1. < = = = 0.25 = 250 / . The results obtained in selected points are summarised in Table 1. Buildings 2019, 9, 127 8 of 11 Table 1. Evaluated discrete stress values in seven points for load cases considered. Point 157 200 269 955 1174 1293 1301 [kN/m ] 41.28 36.73 52.70 33.07 33.53 71.39 68.44 11top Buildings 2018, 8, x FOR PEER REVIEW 8 of 11 LC1  [kN/m ] 44.92 7.10 97.54 1.48 2.49 26.30 30.91 11bot [kN/m ] 119.26 124.74 12.98 147.14 156.93 177.86 179.27 22top Table 1. Evaluated discrete stress values in seven points for load cases considered. [kN/m ] 181.40 -28.88 -259.61 64.44 86.14 61.21 61.43 22bot Point 157 200 269 955 1174 1293 1301 [kN/m ] 120.11 265.17 567.59 120.82 13.75 180.22 177.48 11top σ11top [kN/m ] −41.28 −36.73 52.70 −33.07 −33.53 −71.39 −68.44 LC2  [kN/m ] 50.19 513.14 447.47 29.13 86.94 85.03 83.61 11bot σ11bot [kN/m ] 44.92 7.10 −97.54 1.48 −2.49 −26.30 −30.91 LC1 2 [kN/m ] 240.61 344.94 321.98 158.93 334.60 531.38 560.17 22top σ22top [kN/m ] −119.26 124.74 −12.98 −147.14 −156.93 −177.86 −179.27 [kN/m ] 282.48 113.76 886.58 257.32 47.17 164.13 199.86 σ22bot [kN/m ] −181.40 -28.88 -259.61 −64.44 −86.14 −61.21 −61.43 22bot 2 2 σ11top [kN/m ] −120.11 −265.17 567.59 120.82 13.75 −180.22 −177.48 [kN/m ] 75.67 66.08 91.63 44.53 136.14 354.65 158.88 11top σ11bot [kN/m ] 50.19 513.14 −447.47 29.13 86.94 85.03 83.61 LC3  [kN/m ] 82.37 12.28 161.91 17.07 50.18 148.84 42.61 11bot LC2 σ22top [kN/m ] −240.61 344.94 321.98 −158.93 −334.60 −531.38 −560.17 [kN/m ] 204.97 196.11 32.57 209.95 363.76 608.23 436.52 22top σ22bot [kN/m ] −282.48 113.76 −886.58 −257.32 −47.17 164.13 199.86 [kN/m ] 305.60 48.38 431.64 167.37 86.61 174.44 17.66 22bot σ11top [kN/m ] −75.67 −66.08 91.63 −44.53 −136.14 −354.65 −158.88 63.50 66.64 82.45 60.25 57.92 112.90 107.81 [kN 2 /m ] 11top σ11bot [kN/m ] 82.37 12.28 −161.91 −17.07 50.18 148.84 −42.61 LC3 [kN/m ] 71.79 5.53 153.84 10.56 1.21 -38.65 46.36 LC4σ22top [kN/m ] −204.97 196.11 −32.57 −209.95 −363.76 −608.23 −436.52 11bot σ22bot [kN/m ] −305.60 −48.38 −431.64 −167.37 −86.61 174.44 17.66 [kN/m ] 212.72 186.28 39.18 269.19 277.32 301.05 302.35 22top σ11top [kN/m ] −63.50 −66.64 82.45 −60.25 −57.92 −112.90 −107.81 [kN/m ] 272.82 49.41 421.87 88.60 131.64 103.18 104.44 22bot σ11bot [kN/m ] 71.79 5.53 −153.84 10.56 1.21 -38.65 −46.36 LC4  [kN/m ] 84.97 103.62 42.07 72.93 67.18 123.88 118.42 11top σ22top [kN/m ] −212.72 186.28 −39.18 −269.19 −277.32 −301.05 −302.35 [kN/m ] 94.06 54.80 120.62 20.64 8.32 30.73 38.42 LC5 11bot σ22bot [kN/m ] −272.82 −49.41 −421.87 −88.60 −131.64 −103.18 −104.44 [kN 2 /m ] 228.95 167.47 67.97 265.28 269.97 296.05 297.56 σ11top [kN/ 22topm ] −84.97 −103.62 42.07 −72.93 −67.18 −123.88 −118.42 σ11bot [kN/m ] 94.0 6 268.14 54.80 3.97 −1 2404.63 0.62 20 91.91 .64 138.79 8.32 107.81 −30.73 109.23 −38.42 [kN/m ] 22bot LC5 σ22top [kN/m ] −228.95 167.47 −67.97 −265.28 −269.97 −296.05 −297.56 σ22bot [kN/m ] −268.14 −3.97 −404.63 −91.91 −138.79 −107.81 −109.23 In addition to the discrete stress values’ presentation in Table 1, the distribution of stresses for In addition to the discrete stress values’ presentation in Table 1, the distribution of stresses for load cases “2” and “3” is shown in Figures 10–13. load cases “2” and “3” is shown in Figures 10–13. Figure Figure 10. 10. Str Stesses resses σ11bot [ [kN kN/m /m ]]—load – load ca case se »2« »2«. . 11bot Buildings 2018, 8, x FOR PEER REVIEW 9 of 11 Buildings 2018, 8, x FOR PEER REVIEW 9 of 11 Buildings 2018, 8, x FOR PEER REVIEW 9 of 11 Buildings 2019, 9, 127 9 of 11 Figure 11. Stresses σ22bot [kN/m2]– load case »2«. Figure 11. Stresses σ22bot [kN/m ]– load case »2«. Figure 11. Stresses  [kN/m ]—load case »2«. Figure 11. Stresses σ22bot [kN/m ]– load case »2«. 22bot Figure 12. Stresses σ11bot [kN/m2 2]– load case »3«. Figure 12. Stresses σ11bot [kN/m ]– load case »3«. Figure 12. Stresses  [kN/m ]—load case »3«. 11bot Figure 12. Stresses σ11bot [kN/m ]– load case »3«. Figure 13. Stresses σ22bot [kN/m2]– load case »3«. Figure Figure 13. 13. Str Stesses resses σ22bot [ [kN kN/m /m ]]—load – load ca case se »3« »3«. . 22bot Figure 13. Stresses σ22bot [kN/m ]– load case »3«. Buildings 2019, 9, 127 10 of 11 4. Discussion of the Results As already stated, five load combinations were considered in order to find the most probable cause for the formation of the registered crack pattern. In load case »1« self weight and rubble layer was considered. Numerical results show that stresses are locally exceeded in areas where no actual damage was registered on the shell. On the other hand, calculated stresses in areas with cracks are within the permissible limits. However, it should be noted, that the cracks on the upper side of the shell are poorly visible due to the rubble layer and rough surface. In load case »2« vertical displacement (D = 0.5 cm) of outer supports on one side was considered which simulates di erential settlement of foundations. In this case, high tensile stresses occur in the top area of the shell (Figure 11), which may cause the recorded longitudinal crack. Di erential settlement of foundations can thus be one of possible causes for the registered crack pattern. However, the results of this load case otherwise show high stress levels also in other parts where no damage of the actual shell has been recorded. Load case “3” took into account the self weight of the structure, weight of the rubble layer and weight of the maintenance team. In this case, compressive stresses in the upper middle part (Figure 13) as well as tensile stresses in the lower middle part (Figure 12) of the analysed shell are exceeded, which coincides with the registered crack pattern. This loading combination can therefore be considered as the most possible cause for the formation of a longitudinal crack [8]. With load case “4” the impact of seismic loading on the analysed structure was examined. Results show that stresses in this case are not exceeded, and, consequently, the influence of the seismic load as a possible cause for the formation of longitudinal crack can be excluded. Results of load case “5” which took into account self weight of the structure, rubble layer and temperature change (D = 15 C) show that such loading combination is critical for collateral vaults but cannot be responsible for the registered longitudinal crack. The executed numerical analyses thus show that load cases “2” and “3” are the most likely ones to cause the registered crack pattern. The longitudinal crack in the middle area of the analysed shell most likely formed due to separated or combined e ect of maintenance team loading and di erential settlement of foundations. 5. Possible Repair and Strengthening Measures Based on the results of the analysis of the considered shell, it can be concluded that the cracks formed mainly due to direct loading of the middle upper part of the shell (simulation of maintenance works in load case “3”). Considering the fact that cracks reappeared in the same areas after repair works in 2013, it is recommended that monitoring of the shell be carried out with an emphasis on the longitudinal crack in the middle part of the shell. In the case that the widening of that crack continues, strengthening of the shell will be required. Strengthening could be done by applying reinforced concrete layer either using FRP (fiber reinforced polymer) or FRM (fiber reinforced mortar) on the critical area. However, if the monitoring does not confirm any propagation (widening and/or length extension) of cracks, strengthening considering unchanged loading condition is not necessary. Nevertheless, the problem in the case of loading of the shell during maintenance works should be solved for any potential future works as the numerical simulations show that the shell is locally overloaded even by weight of a single maintenance worker. A possible simple solution for this problem is a working platform not only for access of the maintenance team but generally also for any secure access to the area above the shell [8]. The weight of the platform could be partially carried by the existing wooden roof structure and mainly by the stronger stone-masonry walls of the church structure. 6. Conclusions The paper demonstrates the simulation modelling as a powerful tool in addressing problems of structures’ reconstructions. Although the implementation of non-linear behaviour would be the most Buildings 2019, 9, 127 11 of 11 appropriate or rather more common approach for the analysis of the considered shell, the analyses carried out in this work showed that it is possible to identify the causes for damage, even with the simple elastic material model, without performing more complex non-linear analyses. As found, the longitudinal crack in the middle area of the analysed shell most likely formed due to the separate or combined e ect of maintenance team loading and di erential settlement of foundations. However, none of these two most probable causes for the registered crack pattern were considered in the numerical analysis within the ocial rehabilitation project. Consequently, the main longitudinal crack re-opened after more or less cosmetic patching as a part of rehabilitation works. This shows that repair and/or strengthening measures of existing structures should be planned after a thorough analysis of all possible causes for the damage, since only by using such approach any further damage and propagation of cracks can be prevented. Registered damage of existing structures should thus not be addressed partially by merely cosmetic corrections such as patching of visible cracks, but firstly by performing numerical analysis aiming to identify the possible causes for damage, by monitoring of the structure if necessary and eventually by strengthening of critical parts or the structure as a whole. Author Contributions: Conceptualization, M.U.; Methodology, M.U. and M.S.; Software, T.L.; Validation, M.U. and M.S.; Formal Analysis, T.L.; Investigation, T.L.; Resources, M.U. and T.L.; Data Curation, M.U. and T.L.; Writing—Original Draft Preparation, M.U. and M.S.; Writing—Review and Editing, M.U. and M.S.; Visualization, M.U. and M.S.; Supervision, M.U. and M.S.; Project Administration, M.U. and M.S.; Writing—original draft, M.U. and M.S.; Writing—review & editing, M.U. and M.S. Funding: This research received no external funding. Acknowledgments: The authors wish to thank the firm GI ZRMK for providing insight into the technical report on reconstruction of the Church of St. Jakob in Dolenja Trebuša. Conflicts of Interest: The authors declare no conflict of interest. References 1. Holzer, S. Statische Beurteilung historischer Tragverke. Band 1-Mauerwerkskonstruktionen; Ernst & Sohn: Berlin, Germany, 2013. 2. Ugural, A.C. Stresses in plates and shells; McGraw-Hill: Boston, MA, UAS, 1999. 3. Peerdeman, B. Analysis of thin Concrete Shells Revisited: Opportunities due to Innovations in Materials and Analysis Methods. Master ’s Thesis, Delft University of Technology, Delft, The Netherlands, June 2008. 4. De Vent, I.A.E. Prototype of a diagnostic decision support tool for structural damage in masonry. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, June 2011. 5. Gostic, ˇ S.; Dolinšek, B. Lessons learned after 1998 and 2004 earthquake in Posocje ˇ region. In Proceedings of the 4th International i-Rec Conference Building Resilience, Christchurch, New Zealand, 30 April–2 May 2008; pp. 11–25. 6. Štampfl, A. Reconstruction of the Church of St. Jakob, Dolenja Trebuša; Technical Report; GI ZRMK: Ljubljana, Slovenia, December 2011. 7. Computers & Structures. CSI Analysis Reference Manual for SAP2000, ETABS, SAFE and CSiBridge, Berkeley. Available online: http://docs.csiamerica.com/manuals/misc/CSI%20Analysis%20Reference%20Manual% 202011-12.pdf (accessed on 10 December 2015). 8. Lorenci, T. Masonry shell structures in historical buildings. Maribor, 2016; p. 104. Available online: https://dk.um.si/IzpisGradiva.php?id=61543 (accessed on 12 December 2018). © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Buildings Multidisciplinary Digital Publishing Institute

Analysis of Cylindrical Masonry Shell in St. Jacob`s Church in Dolenja Trebuša, Slovenia—Case Study

Buildings , Volume 9 (5) – May 22, 2019

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buildings Article Analysis of Cylindrical Masonry Shell in St. Jacob‘s Church in Dolenja Trebuša, Slovenia—Case Study 1 , 2 1 Mojmir Uranjek *, Tadej Lorenci and Matjaž Skrinar Chair of Structural Mechanics, Faculty of Civil Engineering, Transportation Engineering and Arhitecture University of Maribor, Maribor 2000, Slovenia; matjaz.skrinar@um.si Department of Health and Safety, Abrasiv Muta, Muta 2366, Slovenia; tadej.lorenci@gmail.com * Correspondence: mojmir.uranjek@um.si; Tel.: +386-2-22-94-357 Received: 9 April 2019; Accepted: 18 May 2019; Published: 22 May 2019 Abstract: This paper focuses on identifying key reasons for the damage of the cylindrical masonry shell structure in St. Jacob‘s church in Dolenja Trebuša, Slovenia. Typical damage patterns which can be formed in shell structures and may a ect the load bearing capacity are outlined. Several stress states (membrane, bending and also combined stress state) that can occur in the shell structure are described. Load cases such as the vertical displacement of the support structure, temperature loading, weight of maintenance team and also seismic loading are taken into account in order to identify the actual cause for the registered crack pattern in the shell structure. Analysis of the shell structure is performed using the SAP2000 structural software. Based on the obtained results, which highlighted key reasons for registered damage, the monitoring of cracks is recommended in the first phase, and, in continuation, the most appropriate repair and strengthening measures are proposed. Keywords: masonry shell; cracks in shells; static analysis; strengthening 1. Introduction Motivation for this work is the fact that masonry shell structures as a part of historical buildings such as churches, monasteries and castles are present in a relatively large number not just in Slovenia but also worldwide. Over the years, due to various reasons (change in magnitude and distribution of loading, earthquake loading, foundation settlements, etc.) these structures can be damaged. Consequently, inner forces are redistributed and in many cases the static system is changed. Nevertheless, most of these structures maintain their function also afterwards [1]. In the case of reconstruction, the load bearing capacity of the shell structure should be checked in accordance with current regulations and, if necessary, appropriate measures have to be undertaken. In this paper, computational analysis of the actual shell structure is demonstrated. By using the results of this analysis, causes for damage are identified and possible rehabilitation and consolidation measures are proposed. 2. Stresses and Typical Damage Patterns of Masonry Shells To describe the geometry of the shell, the spatial position of the midsurface and the thickness of the shell at each point have to be known. The analysis of shell structures is usually performed using two theories: Membrane theory, which is usually valid for lager part of the shell and bending theory, which includes the e ect of bending [2]. In areas where due to local disturbances (supports, point loads, changes of curvature or thickness) the ideal membrane stress state is no longer valid (Figure 1), the membrane theory should be supplemented by the bending theory. Buildings 2019, 9, 127; doi:10.3390/buildings9050127 www.mdpi.com/journal/buildings Buildings 2018, 8, x FOR PEER REVIEW 2 of 11 Buildings 2019, 9, 127 2 of 11 Figure 1. Critical parts of the shell where the bending stress state can be formed (adapted after [3]). Figure 1. Critical parts of the shell where the bending stress state can be formed (adapted after [3]). For shell structures in historical buildings in most cases the membrane theory has to be For shell structures in historical buildings in most cases the membrane theory has to be supplemented by the bending theory. As the result of the simultaneous e ect of membrane forces N , supplemented by the bending theory. As the result of the simultaneous effect of membrane forces Nx, N N and bending moments M , M M the stresses which occur in the shell can be written as: y , xy x y , xy Ny, Nxy and bending moments Mx, My, Mxy the stresses which occur in the shell can be written as: N 12M z x x = (1) = − (1) N 12M z y y = (2) t 12 (2) = − N 12M z xy xy = (3) xy (3) The first terms in the above expressions = represent − the membrane stress while the second terms, the bending stress. The distribution of stresses  ,  and  within the shell thickness is linear. x y xy Perpendicular shear stresses  in  as a consequence of shear forces have a parabolic distribution, The first terms in the aboxz ve expre yz ssions represent the membrane stress while the second terms, but their values are generally small in comparison with other stress components and can usually the bending stress. The distribution of stresses σx, σy and τxy within the shell thickness is linear. be neglected. Perpendicular shear stresses τxz in τyz as a consequence of shear forces have a parabolic distribution, Damage of shells, often in the form of cracks, occurs due to various reasons: Foundation but their values are generally small in comparison with other stress components and can usually be settlement, horizontal displacements of supporting walls, material deficiencies and degradation or neglected. local overloading as well as their combinations. Some typical crack configurations due to various Damage of shells, often in the form of cracks, occurs due to various reasons: Foundation reasons in the case of barrel vault are shown in Figure 2. settlement, horizontal displacements of supporting walls, material deficiencies and degradation or local overloading as well as their combinations. Some typical crack configurations due to various reasons in the case of barrel vault are shown in Figure 2. (a) (b) (c) Figure 2. Some typical crack configurations for barrel vault [4]. Figure 2. Some typical crack configurations for barrel vault [4]. (d) (e) (f) Figure 2. Some typical crack configurations for barrel vault [4]. Buildings 2019, 9, 127 3 of 11 Buildings 2018, 8, x FOR PEER REVIEW 3 of 11 3. Analysis of Masonry Shell in St. Jacobs Church 3. Analysis of Masonry Shell in St. Jacobs Church 3.1. Characteristics of the 2004 Earthquake 3.1. Characteristics of the 2004 Earthquake Generally, Slovenia is a territory with almost regular (moderate) seismic activities. On an average Generally, Slovenia is a territory with almost regular (moderate) seismic activities. On an day, an earthquake with a magnitude higher than 1 is normally detected. Further, Dolenja Trebuša lies in average day, an earthquake with a magnitude higher than 1 is normally detected. Further, Dolenja a region with some more than average seismic activities. Nevertheless, although this area is not one of Trebuša lies in a region with some more than average seismic activities. Nevertheless, although this the most seismically exposed parts of our country; it still lies quite close to the region, which was severely area is not one of the most seismically exposed parts of our country; it still lies quite close to the damaged by the 1976 earthquake (with the magnitude of 6.5 the strongest earthquake that has been region, which was severely damaged by the 1976 earthquake (with the magnitude of 6.5 the strongest recorded in Slovenia so far). The considered 2004 earthquake occurred on 12 July 2004 with an epicenter earthquake that has been recorded in Slovenia so far). The considered 2004 earthquake occurred on to the northwest of Dolenja Trebuša (areal distance was about 35 km). It occurred on the same place of 12 July 2004 with an epicenter to the northwest of Dolenja Trebuša (areal distance was about 35 km). the 1998 earthquake (which had the magnitude of 5.7). Both these earthquakes are listed among the three It occurred on the same place of the 1998 earthquake (which had the magnitude of 5.7). Both these last severe earthquakes that were recorded in Slovenia. Although most of the damage resulting from the earthquakes are listed among the three last severe earthquakes that were recorded in Slovenia. 2004 earthquake occurred in the vicinity of Bovec mainly due to local geological conditions, other areas Although most of the damage resulting from the 2004 earthquake occurred in the vicinity of Bovec such as Dolenja Trebuša were also affected. The 2004 earthquake caused material damage primarily on mainly due to local geological conditions, other areas such as Dolenja Trebuša were also affected. The old 2e 0r 04 b u earthqua ildings, ke whcau ichsed in th m is atreri egal ion dam hav ag e e a pri verma y lo riw ly e on ar to hlq de ua r k be ui re ldi sis ngs tan , cwh e. N ich am in elthis y, thregi e bu oin ldhav inge sta o ck con vs ery istslm ow ain earthqua ly of old ke sto resi ne sta ma nce. son rNa y hmel ousy, es tw he ith bui on ldi e o ng r tw stoc o s k toco rensists ys builma t lair nl ge y ly of frol om d stone two-lema af m sonry asonry houses with one or two storeys built largely from two-leaf masonry with two-leaf stone masonry with with two-leaf stone masonry with weak lime mortar and wooden floors [5]. weak lime mortar and wooden floors [5]. 3.2. Structural Characteristics and Damage of Analyzed Masonry Shell 3.2. Structural Characteristics and Damage of Analyzed Masonry Shell For the analysis, a barrel vault in St. Jacob Church in Dolenja Trebuša in Slovenia was chosen. The Church was built in 1786 and retrofitted in 2013 in order to simultaneously rehabilitate and For the analysis, a barrel vault in St. Jacob Church in Dolenja Trebuša in Slovenia was chosen. strThe engthen Churc its h str was uctur buie lt after in 178 the 6 an earthquake d retrofitted in 2004. in 201In 3 in spite order of the to si rmul enovation taneously in 2013, rehabcracks ilitate ain ndthe consider strengt ed hen vaul its tstruc reopened. ture afte The r the stone earth masonry quake in barr 2004 el . In vault spite is o built f the out reno of vat limestone ion in 201 and 3, cracks leech istone n the in considered vault reopened. The stone masonry barrel vault is built out of limestone and leech stone lime mortar. Geometry and materials of the vault are shown in Figure 3. The length of the vault is in lime mortar. Geometry and materials of the vault are shown in Figure 3. The length of the vault is 10 m (above the nave) with a span of 7.75 m. The thickness of the vault is changing from 30 cm at the 10 m (above the nave) with a span of 7.75 m. The thickness of the vault is changing from 30 cm at the base and to 8 cm at the top. base and to 8 cm at the top. (a) (b) Figure 3. Analysed stone masonry barrel vault from bottom (a) and top (b). Buildings 2018, 8, x FOR PEER REVIEW 4 of 11 Buildings 2018, 8, x FOR PEER REVIEW 4 of 11 Buildings 2019, 9, 127 4 of 11 Figure 3. Analysed stone masonry barrel vault from bottom (a) and top (b). Figure 3. Analysed stone masonry barrel vault from bottom (a) and top (b). Before rehabilitation and strengthening of the church in 2013, numerous cracks in the walls and Before rehabilitation and strengthening of the church in 2013, numerous cracks in the walls and Before rehabilitation and strengthening of the church in 2013, numerous cracks in the walls and vaults were listed. In the middle area of the analysed vault there was a crack running along the entire vaults were listed. In the middle area of the analysed vault there was a crack running along the entire vaults were listed. In the middle area of the analysed vault there was a crack running along the entire length of the nave, which continued through the supporting arch and presbytery vault with length of length of the nave, which continued through the supporting arch and presbytery vault with length length of the nave, which continued through the supporting arch and presbytery vault with length 13.5 m and thickness of 1.0 mm. Other cracks were also present on the vaults, especially in the area of of 13.5 m and thickness of 1.0 mm. Other cracks were also present on the vaults, especially in the area of 13.5 m and thickness of 1.0 mm. Other cracks were also present on the vaults, especially in the area the transverse vaults although of smaller width and length (Figure 4). of the transverse vaults although of smaller width and length (Figure 4). of the transverse vaults although of smaller width and length (Figure 4). Figure 4. Registered crack pattern of analysed barrel vault before rehabilitation in 2013 [6]. Figure 4. Registered crack pattern of analysed barrel vault before rehabilitation in 2013 [6]. Figure 4. Registered crack pattern of analysed barrel vault before rehabilitation in 2013 [6]. The cracks although to a lesser extent, reopened in the same places after the repair works in 2013 The cracks although to a lesser extent, reopened in the same places after the repair works in 2013 The cracks although to a lesser extent, reopened in the same places after the repair works in 2013 (Figure 5). (Figure 5). (Figure 5). (a) (b) (a) (b) Figure 5. Reopened crack in the analysed shell (a) and in wall near transverse vault (b). Figure 5. Reopened crack in the analysed shell (a) and in wall near transverse vault (b). Figure 5. Reopened crack in the analysed shell (a) and in wall near transverse vault (b). 3.3. Static Analysis of Masonry Shell 3.3.Static Analysis of Masonry Shell 3.3.Static Analysis of Masonry Shell The stone masonry barrel vault was analysed by using the SAP2000 software [7]. A combination The stone masonry barrel vault was analysed by using the SAP2000 software [7]. A combination The stone masonry barrel vault was analysed by using the SAP2000 software [7]. A combination of three and four-node shell finite elements combined with linear finite elements was used in the of three and four-node shell finite elements combined with linear finite elements was used in the of three and four-node shell finite elements combined with linear finite elements was used in the model. The structure was modelled with varying thickness according to actual geometry. Supports model. The structure was modelled with varying thickness according to actual geometry. Supports model. The structure was modelled with varying thickness according to actual geometry. Supports (main arch, closed arches at the side, supporting wall) were modelled using linear finite elements of (main arch, closed arches at the side, supporting wall) were modelled using linear finite elements of (main arch, closed arches at the side, supporting wall) were modelled using linear finite elements of the corresponding cross section. The barrel vault was modelled with 2211 shell and 436 linear finite the corresponding cross section. The barrel vault was modelled with2211 shell and 436 linear finite the corresponding cross section. The barrel vault was modelled with2211 shell and 436 linear finite Buildings 2019, 9, 127 5 of 11 Buildings 2018, 8, x FOR PEER REVIEW 5 of 11 elements interconnected in 2499 nodes. Horizontal steel ties were modelled as linear elements with elements interconnected in 2499 nodes. Horizontal steel ties were modelled as linear elements with circular cross section of  32–45 mm (Figure 6). circular cross section of  32-45 mm (Figure 6). (a) (b) Figu Figure re 6. 6. 3 3D D F FE E mo model del ((a a) ) and and cro cross ss sectio section n ((b b) sh ) showing owing chan changing ging thick thickness ness of a of analysed nalysed ba barr rrel el vault vault. . When the registered crack pattern is compared with possible crack configurations shown in When the registered crack pattern is compared with possible crack configurations shown in Figure 2, several actions can be identified as the potential cause of such damage. The longitudinal Figure 2, several actions can be identified as the potential cause of such damage. The longitudinal crack at the bottom middle part of the shell may thus be caused either by simultaneous horizontal crack at the bottom middle part of the shell may thus be caused either by simultaneous horizontal divergent displacement of supporting walls (Figure 2 top left), di erential settlement of foundations divergent displacement of supporting walls (Figure 2 top left), differential settlement of foundations (Figure 2 bottom left) or point load in the central part of the shell (Figure 2 bottom right). (Figure 2 bottom left) or point load in the central part of the shell (Figure 2 bottom right). Since the increase of the structures weight was eliminated as a possible cause for the registered Since the increase of the structures weight was eliminated as a possible cause for the registered crack pattern, other possible causes were analysed in the numerical analysis: Self weight of structure crack pattern, other possible causes were analysed in the numerical analysis: Self weight of structure and rubble layer, di erential settlement of foundations, seismic loading, maintenance loading and and rubble layer, differential settlement of foundations, seismic loading, maintenance loading and temperature di erence (Figures 7 and 8). temperature difference (Figures 7 and 8). The implementation of non-linear behaviour would be the most appropriate approach for the analysis of the considered shell. However, we were not involved in any material properties acquisition (all the mechanical parameters were taken from the Technical Report, [6]) for the analysed shell. Furthermore, our analyses were not part of any ocial study, and were thus not financially supported. Therefore, the decision was met to perform only linear elastic analyses, which nevertheless provided satisfactory results and enabled the identification of possible causes for the damage. Five load combinations were considered altogether: Load case »1«: Self weight and rubble layer: X X 1.35  (a) G + 1.35  G Load case »2«: Self weight, rubble layer, vertical displacement of outer supports on one side by D = 0.5 cm: X X X 1.35  G + 1.35  G + 1.5  D N z Load case »3«: Self weight, rubble layer, maintenance team: X X X 1.35  G + 1.35  G + 1.5  Q N V (b) Buildings 2018, 8, x FOR PEER REVIEW 5 of 11 elements interconnected in 2499 nodes. Horizontal steel ties were modelled as linear elements with circular cross section of  32-45 mm (Figure 6). (a) Buildings 2019, 9, 127 6 of 11 (b) Figure 6. 3D FE model (a) and cross section (b) showing changing thickness of analysed barrel vault. Load case »4«: Self weight, rubble layer, horizontal displacement of all supports on one side by D = When 0.5 cm: the registered crack pattern is compared with possible crack configurations shown in X X X 1.35  G + 1.35  G + 1.5  D Figure 2, several actions can be identified as the potential cause of such damage. The longitudinal N y crack at the bottom middle part of the shell may thus be caused either by simultaneous horizontal Load case »5«: Self weight, rubble layer, temperature di erence: divergent displacement of supporting walls (Figure 2 top left), differential settlement of foundations X X X (Figure 2 bottom left) or point load in the central part of the shell (Figure 2 bottom right). 1.35  G + 1.35  G + 1.5  D N T Since the increase of the structures weight was eliminated as a possible cause for the registered crack pattern, other possible causes were analysed in the numerical analysis: Self weight of structure and rubble The discr layer, ete rdifferential esults’ values settlement are presented of foundations, for seven points seismic visible loading, in Figur maintenance e 9. loading and temperature difference (Fiures 7 and 8). (a) Buildings 2018, 8, x FOR PEER REVIEW 6 of 11 (b) Figure 7. Load case simulating vertical displacement of outer supports on one side (a) and horizontal Figure 7. Load case simulating vertical displacement of outer supports on one side (a) and horizontal displacement of all supports on one side (b). displacement of all supports on one side (b). (a) (b) Figure 8. Load case simulating maintenance team (a) and temperature di erence (b). Figure 8. Load case simulating maintenance team (a) and temperature difference (b). The implementation of non-linear behaviour would be the most appropriate approach for the analysis of the considered shell. However, we were not involved in any material properties acquisition (all the mechanical parameters were taken from the Technical Report, [6]) for the analysed shell. Furthermore, our analyses were not part of any official study, and were thus not financially supported. Therefore, the decision was met to perform only linear elastic analyses, which nevertheless provided satisfactory results and enabled the identification of possible causes for the damage. Five load combinations were considered altogether:  Load case »1«: Self weight and rubble layer: 1.35 ∗ + 1.35 ∗  Load case »2«: Self weight, rubble layer, vertical displacement of outer supports on one side byΔz=-0.5 cm: 1.35 ∗ + 1.35 ∗ + 1.5 ∗  Load case »3«: Self weight, rubble layer, maintenance team: 1.35 ∗ + 1.35 ∗ + 1.5 ∗  Load case »4«: Self weight, rubble layer, horizontal displacement of all supports on one side byΔy=0.5 cm: 1.35 ∗ + 1.35 ∗ + 1.5 ∗  Load case »5«: Self weight, rubble layer, temperature difference: 1.35 ∗ + 1.35 ∗ + 1.5 ∗ The discrete results’ values are presented for seven points visible in Figure 9. Buildings 2019, 9, 127 7 of 11 Buildings 2018, 8, x FOR PEER REVIEW 7 of 11 Figure 9. Selected points corresponding to stress values given in Table 1. Figure 9. Selected points corresponding to stress values given in Table 1. The The distribution distribution of of str stresses esses acr acro oss ss the the shell shell thickness thickness is is linear linear. . In In the the eval evaluation uation of of r results, esults, values values obtained obtained in in the the upper upper (external) (external) and and b bottom ottom part part of of the the shell shell wer were e consider considere ed. d. By By taking taking into into account account the the values values o of f z z = = t / t/2 2and and zz = = -t / t/2 2for for the the upper upper and and bottom bottom part o part of f the the shel shell,lr , espectively respectively we we o obtain: btain: F 6M 11 11 = (4 (4) ) = − 11up t t F 6M 11 11 = + (5) 11bot (5) = t + F 6M 22 22 = (6) 22up = − (6) F 6M 22 22 = + (7) 22bot t t where designations »up« in »bot« stand for stresses on the upper and bottom part of the shell. According = + (7) to Eurocode 6 for masonry structures, the actual compressive stress ( ) and tensile stress ( ) should be c t smaller than the design compressive (f ) and/or design tensile strength (f ) of the material, respectively. cd td where designations »up« in »bot« stand for stresses on the upper and bottom part of the shell. Values of the characteristic compressive (f ) and tensile strength (f ) were taken from the Technical c t According to Eurocode 6 for masonry structures, the actual compressive stress (σc) and tensile stress Report, reference No. 6 and were obtained from investigations of similarly built stone masonry walls (σt) should be smaller than the design compressive (fcd) and/or design tensile strength (ftd) of the and vaults studied both in situ and in the laboratory of ZRMK. Design values are obtained by dividing material, respectively. Values of the characteristic compressive (fc) and tensile strength (ft) were taken the characteristic compressive (f ) and tensile strength (f ) of the material with the material safety factor c t from the Technical Report, reference No. 6 and were obtained from investigations of similarly built , as given by the code: stone masonry walls and vaults studied both in situ and in the laboratory of ZRMK. Design values f f c t are obtained by dividing the characteristic compressive (fc) and tensile strength (ft) of the material < ,  < (8) c t M M with the material safety factor ΥM, as given by the code: The material safety factor is assessed as = 2.0. Calculated stresses should be smaller than M M permissible values. In the case of tension we obtain: < , < (8) 0.08 < f = = = 0.04 MPa = 40 kN/m (9) td The material safety factor γM is assessed as γM =2.0. Calculated stresses should be smaller than permissible values. In the case of tension we obtain: And in the case of compression: 0.08 < = = = 0.04 = 40 / (9) c 0.5 2 < f = = = 0.25 MPa = 250 kN/m . c cd And in the case of compression: The results obtained in selected points are summarised in Table 1. < = = = 0.25 = 250 / . The results obtained in selected points are summarised in Table 1. Buildings 2019, 9, 127 8 of 11 Table 1. Evaluated discrete stress values in seven points for load cases considered. Point 157 200 269 955 1174 1293 1301 [kN/m ] 41.28 36.73 52.70 33.07 33.53 71.39 68.44 11top Buildings 2018, 8, x FOR PEER REVIEW 8 of 11 LC1  [kN/m ] 44.92 7.10 97.54 1.48 2.49 26.30 30.91 11bot [kN/m ] 119.26 124.74 12.98 147.14 156.93 177.86 179.27 22top Table 1. Evaluated discrete stress values in seven points for load cases considered. [kN/m ] 181.40 -28.88 -259.61 64.44 86.14 61.21 61.43 22bot Point 157 200 269 955 1174 1293 1301 [kN/m ] 120.11 265.17 567.59 120.82 13.75 180.22 177.48 11top σ11top [kN/m ] −41.28 −36.73 52.70 −33.07 −33.53 −71.39 −68.44 LC2  [kN/m ] 50.19 513.14 447.47 29.13 86.94 85.03 83.61 11bot σ11bot [kN/m ] 44.92 7.10 −97.54 1.48 −2.49 −26.30 −30.91 LC1 2 [kN/m ] 240.61 344.94 321.98 158.93 334.60 531.38 560.17 22top σ22top [kN/m ] −119.26 124.74 −12.98 −147.14 −156.93 −177.86 −179.27 [kN/m ] 282.48 113.76 886.58 257.32 47.17 164.13 199.86 σ22bot [kN/m ] −181.40 -28.88 -259.61 −64.44 −86.14 −61.21 −61.43 22bot 2 2 σ11top [kN/m ] −120.11 −265.17 567.59 120.82 13.75 −180.22 −177.48 [kN/m ] 75.67 66.08 91.63 44.53 136.14 354.65 158.88 11top σ11bot [kN/m ] 50.19 513.14 −447.47 29.13 86.94 85.03 83.61 LC3  [kN/m ] 82.37 12.28 161.91 17.07 50.18 148.84 42.61 11bot LC2 σ22top [kN/m ] −240.61 344.94 321.98 −158.93 −334.60 −531.38 −560.17 [kN/m ] 204.97 196.11 32.57 209.95 363.76 608.23 436.52 22top σ22bot [kN/m ] −282.48 113.76 −886.58 −257.32 −47.17 164.13 199.86 [kN/m ] 305.60 48.38 431.64 167.37 86.61 174.44 17.66 22bot σ11top [kN/m ] −75.67 −66.08 91.63 −44.53 −136.14 −354.65 −158.88 63.50 66.64 82.45 60.25 57.92 112.90 107.81 [kN 2 /m ] 11top σ11bot [kN/m ] 82.37 12.28 −161.91 −17.07 50.18 148.84 −42.61 LC3 [kN/m ] 71.79 5.53 153.84 10.56 1.21 -38.65 46.36 LC4σ22top [kN/m ] −204.97 196.11 −32.57 −209.95 −363.76 −608.23 −436.52 11bot σ22bot [kN/m ] −305.60 −48.38 −431.64 −167.37 −86.61 174.44 17.66 [kN/m ] 212.72 186.28 39.18 269.19 277.32 301.05 302.35 22top σ11top [kN/m ] −63.50 −66.64 82.45 −60.25 −57.92 −112.90 −107.81 [kN/m ] 272.82 49.41 421.87 88.60 131.64 103.18 104.44 22bot σ11bot [kN/m ] 71.79 5.53 −153.84 10.56 1.21 -38.65 −46.36 LC4  [kN/m ] 84.97 103.62 42.07 72.93 67.18 123.88 118.42 11top σ22top [kN/m ] −212.72 186.28 −39.18 −269.19 −277.32 −301.05 −302.35 [kN/m ] 94.06 54.80 120.62 20.64 8.32 30.73 38.42 LC5 11bot σ22bot [kN/m ] −272.82 −49.41 −421.87 −88.60 −131.64 −103.18 −104.44 [kN 2 /m ] 228.95 167.47 67.97 265.28 269.97 296.05 297.56 σ11top [kN/ 22topm ] −84.97 −103.62 42.07 −72.93 −67.18 −123.88 −118.42 σ11bot [kN/m ] 94.0 6 268.14 54.80 3.97 −1 2404.63 0.62 20 91.91 .64 138.79 8.32 107.81 −30.73 109.23 −38.42 [kN/m ] 22bot LC5 σ22top [kN/m ] −228.95 167.47 −67.97 −265.28 −269.97 −296.05 −297.56 σ22bot [kN/m ] −268.14 −3.97 −404.63 −91.91 −138.79 −107.81 −109.23 In addition to the discrete stress values’ presentation in Table 1, the distribution of stresses for In addition to the discrete stress values’ presentation in Table 1, the distribution of stresses for load cases “2” and “3” is shown in Figures 10–13. load cases “2” and “3” is shown in Figures 10–13. Figure Figure 10. 10. Str Stesses resses σ11bot [ [kN kN/m /m ]]—load – load ca case se »2« »2«. . 11bot Buildings 2018, 8, x FOR PEER REVIEW 9 of 11 Buildings 2018, 8, x FOR PEER REVIEW 9 of 11 Buildings 2018, 8, x FOR PEER REVIEW 9 of 11 Buildings 2019, 9, 127 9 of 11 Figure 11. Stresses σ22bot [kN/m2]– load case »2«. Figure 11. Stresses σ22bot [kN/m ]– load case »2«. Figure 11. Stresses  [kN/m ]—load case »2«. Figure 11. Stresses σ22bot [kN/m ]– load case »2«. 22bot Figure 12. Stresses σ11bot [kN/m2 2]– load case »3«. Figure 12. Stresses σ11bot [kN/m ]– load case »3«. Figure 12. Stresses  [kN/m ]—load case »3«. 11bot Figure 12. Stresses σ11bot [kN/m ]– load case »3«. Figure 13. Stresses σ22bot [kN/m2]– load case »3«. Figure Figure 13. 13. Str Stesses resses σ22bot [ [kN kN/m /m ]]—load – load ca case se »3« »3«. . 22bot Figure 13. Stresses σ22bot [kN/m ]– load case »3«. Buildings 2019, 9, 127 10 of 11 4. Discussion of the Results As already stated, five load combinations were considered in order to find the most probable cause for the formation of the registered crack pattern. In load case »1« self weight and rubble layer was considered. Numerical results show that stresses are locally exceeded in areas where no actual damage was registered on the shell. On the other hand, calculated stresses in areas with cracks are within the permissible limits. However, it should be noted, that the cracks on the upper side of the shell are poorly visible due to the rubble layer and rough surface. In load case »2« vertical displacement (D = 0.5 cm) of outer supports on one side was considered which simulates di erential settlement of foundations. In this case, high tensile stresses occur in the top area of the shell (Figure 11), which may cause the recorded longitudinal crack. Di erential settlement of foundations can thus be one of possible causes for the registered crack pattern. However, the results of this load case otherwise show high stress levels also in other parts where no damage of the actual shell has been recorded. Load case “3” took into account the self weight of the structure, weight of the rubble layer and weight of the maintenance team. In this case, compressive stresses in the upper middle part (Figure 13) as well as tensile stresses in the lower middle part (Figure 12) of the analysed shell are exceeded, which coincides with the registered crack pattern. This loading combination can therefore be considered as the most possible cause for the formation of a longitudinal crack [8]. With load case “4” the impact of seismic loading on the analysed structure was examined. Results show that stresses in this case are not exceeded, and, consequently, the influence of the seismic load as a possible cause for the formation of longitudinal crack can be excluded. Results of load case “5” which took into account self weight of the structure, rubble layer and temperature change (D = 15 C) show that such loading combination is critical for collateral vaults but cannot be responsible for the registered longitudinal crack. The executed numerical analyses thus show that load cases “2” and “3” are the most likely ones to cause the registered crack pattern. The longitudinal crack in the middle area of the analysed shell most likely formed due to separated or combined e ect of maintenance team loading and di erential settlement of foundations. 5. Possible Repair and Strengthening Measures Based on the results of the analysis of the considered shell, it can be concluded that the cracks formed mainly due to direct loading of the middle upper part of the shell (simulation of maintenance works in load case “3”). Considering the fact that cracks reappeared in the same areas after repair works in 2013, it is recommended that monitoring of the shell be carried out with an emphasis on the longitudinal crack in the middle part of the shell. In the case that the widening of that crack continues, strengthening of the shell will be required. Strengthening could be done by applying reinforced concrete layer either using FRP (fiber reinforced polymer) or FRM (fiber reinforced mortar) on the critical area. However, if the monitoring does not confirm any propagation (widening and/or length extension) of cracks, strengthening considering unchanged loading condition is not necessary. Nevertheless, the problem in the case of loading of the shell during maintenance works should be solved for any potential future works as the numerical simulations show that the shell is locally overloaded even by weight of a single maintenance worker. A possible simple solution for this problem is a working platform not only for access of the maintenance team but generally also for any secure access to the area above the shell [8]. The weight of the platform could be partially carried by the existing wooden roof structure and mainly by the stronger stone-masonry walls of the church structure. 6. Conclusions The paper demonstrates the simulation modelling as a powerful tool in addressing problems of structures’ reconstructions. Although the implementation of non-linear behaviour would be the most Buildings 2019, 9, 127 11 of 11 appropriate or rather more common approach for the analysis of the considered shell, the analyses carried out in this work showed that it is possible to identify the causes for damage, even with the simple elastic material model, without performing more complex non-linear analyses. As found, the longitudinal crack in the middle area of the analysed shell most likely formed due to the separate or combined e ect of maintenance team loading and di erential settlement of foundations. However, none of these two most probable causes for the registered crack pattern were considered in the numerical analysis within the ocial rehabilitation project. Consequently, the main longitudinal crack re-opened after more or less cosmetic patching as a part of rehabilitation works. This shows that repair and/or strengthening measures of existing structures should be planned after a thorough analysis of all possible causes for the damage, since only by using such approach any further damage and propagation of cracks can be prevented. Registered damage of existing structures should thus not be addressed partially by merely cosmetic corrections such as patching of visible cracks, but firstly by performing numerical analysis aiming to identify the possible causes for damage, by monitoring of the structure if necessary and eventually by strengthening of critical parts or the structure as a whole. Author Contributions: Conceptualization, M.U.; Methodology, M.U. and M.S.; Software, T.L.; Validation, M.U. and M.S.; Formal Analysis, T.L.; Investigation, T.L.; Resources, M.U. and T.L.; Data Curation, M.U. and T.L.; Writing—Original Draft Preparation, M.U. and M.S.; Writing—Review and Editing, M.U. and M.S.; Visualization, M.U. and M.S.; Supervision, M.U. and M.S.; Project Administration, M.U. and M.S.; Writing—original draft, M.U. and M.S.; Writing—review & editing, M.U. and M.S. Funding: This research received no external funding. Acknowledgments: The authors wish to thank the firm GI ZRMK for providing insight into the technical report on reconstruction of the Church of St. Jakob in Dolenja Trebuša. Conflicts of Interest: The authors declare no conflict of interest. References 1. Holzer, S. Statische Beurteilung historischer Tragverke. Band 1-Mauerwerkskonstruktionen; Ernst & Sohn: Berlin, Germany, 2013. 2. Ugural, A.C. Stresses in plates and shells; McGraw-Hill: Boston, MA, UAS, 1999. 3. Peerdeman, B. Analysis of thin Concrete Shells Revisited: Opportunities due to Innovations in Materials and Analysis Methods. Master ’s Thesis, Delft University of Technology, Delft, The Netherlands, June 2008. 4. De Vent, I.A.E. Prototype of a diagnostic decision support tool for structural damage in masonry. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, June 2011. 5. Gostic, ˇ S.; Dolinšek, B. Lessons learned after 1998 and 2004 earthquake in Posocje ˇ region. In Proceedings of the 4th International i-Rec Conference Building Resilience, Christchurch, New Zealand, 30 April–2 May 2008; pp. 11–25. 6. Štampfl, A. Reconstruction of the Church of St. Jakob, Dolenja Trebuša; Technical Report; GI ZRMK: Ljubljana, Slovenia, December 2011. 7. Computers & Structures. CSI Analysis Reference Manual for SAP2000, ETABS, SAFE and CSiBridge, Berkeley. Available online: http://docs.csiamerica.com/manuals/misc/CSI%20Analysis%20Reference%20Manual% 202011-12.pdf (accessed on 10 December 2015). 8. Lorenci, T. Masonry shell structures in historical buildings. Maribor, 2016; p. 104. Available online: https://dk.um.si/IzpisGradiva.php?id=61543 (accessed on 12 December 2018). © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Journal

BuildingsMultidisciplinary Digital Publishing Institute

Published: May 22, 2019

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