a comprehensive structural study of the basilica of pilar in … · 2014. 5. 20. · figure 6:...

A comprehensive structural study of the Basilica of Pilar in Zaragoza (Spain)

L. E. Romera, S. Hernández & J. M. Reinosa School of Civil Engineering, University of Coruña, Spain

Abstract

The Basilica of Pilar, located in the city of Zaragoza, is one of the best known Spanish cathedrals. Several domes of this church contain frescoes authored by Francisco de Goya, and some of them have suffered damage in the past decades due to various pathologies, in particular the frescoes of dome Regina Martirum are being restored at the present time. A set of structural models was developed and validated with the aim of simulating the current structural state, their security level and the relationship between the structural behaviour and the damage observed. The numerical models have been formulated applying the FEM in linear and non-linear theory, considering the constructive process and the reinforcement works added to the structure along with their history.

1 The building and their history

The Basilica of Pilar is one of the most important worship places in Spain. The actual temple is a large and complex brick masonry construction, with rectangular plan and measures about 100 m. long and 70 m. wide. Their construction was long in the time and difficult [1]. In the current site, more than a thousand years ago, a small Visighotic chapel had been built; later on became a Romanesque church with cloister that will suffer posteriorly a Gothic enlargement. Nevertheless, all the aforementioned constructions were of small size compared with the huge extension which took place in XVII century when the project of a baroque church was set up by the Spanish architect Ventura Rodríguez. The central dome rises by the middle of XIX century, and the towers of Ebro river facade are erected in 1940. Figure 1 presents a sketch describing the position of each building along the history, and Figure 2 shows plans and several views of the actual temple.

© 2005 WIT Press WIT Transactions on The Built Environment, Vol 83, www.witpress.com, ISSN 1743-3509 (on-line)

Structural Studies, Repairs and Maintenance of Heritage Architecture IX 103

Figure 1: Evolution of worship site.

a) Plan and front section for the elliptical dome of existing temple

b) External views.

c) Some interior views

Figure 2: The Basilica of Pilar in Zaragoza.


104 Structural Studies, Repairs and Maintenance of Heritage Architecture IX

The temple is composed of three longitudinal naves. The central one contains the main dome of circular plan and double shell, and two more domes of elliptical shape. The two lateral naves have eight more revolution domes located at a second level, and surrounding the complex there is a system of chapels and rooms with up to eleven more domes at a third lower level. Four towers of more than 90 m height mark the corners of the building.

2 Historical structural pathologies and past repairing works

In year 1796 the first references appear verifying problems about fissures in arches, tambours and vaults, especially in elliptical domes. In year 1907 after the completion of the southern towers symptoms of general ruin come into view; in year 1927 cracks of relevant size could be seen in arches; pillars were out of their vertical orientation and important relative displacements were observed in the Regina Martirum dome. Therefore, an ambitious programme of repairing works was approved under the direction of an architect, Teodoro Ríos in that year. The rehabilitation task continued until the Spanish civil war started in year 1936 and after finishing it resumed again to end on year 1940 (Figure 3). The most important features of the restoration (Figure 4) can be summarized as follows. ─ An extensive injection of cement grouting in the soil, and foundation

improvement with RC beams linking steel caissons at pillars foundation. ─ Temporary support and steel reinforcement of central arches and pillars. ─ External reinforcement of several tambours by reinforced concrete. ─ Installation of inclined supports in tambours under the central and the

elliptical domes, connecting them with external buttress.

Figure 3: Outside views at year 1939.

A few years ago other structural pathologies, of a smaller entity that the aforementioned, but significant due the affection of frescoes authored by one of the most brilliant Spanish painters, Francisco de Goya, was observed: ― Presence of humidity, small fissures and lost of material in frescoes of Regina

Martirum dome (Figure 5) and San José dome. ― Cracks in several arches near the Santiago apostle chapel. ― Deterioration of masonry towers, especially in towers of square facade.



Figure 4: Foundation reinforcements, steel bonds of tambours and discharge arches.

To determine if the damage of frescoes could be due to structural pathologies, and if this was the case, to outline the necessary actions to correct them, an extensive numerical study was carried out [2, 3]. Finite elements models were used to simulate the temple global structural behaviour and the local one of Regina Martirum dome.

Figure 5: Frescoes of Regina Martirum dome and fissures detail.

3 Methodology: CAD and visualization

The approach used in the study is described in the flowchart of figure 6. Due to geometrical complexity and the significant structural dimensions, first of all a detailed 3-D digital model of the complete church was generated by using information from blueprints and in situ measurement and observations. The development of this geometrical model (Figure 7) allowed to better understand the architectural composition and to realize also the construction connectivity between the components of the temple. Only the temple parts without structural significance were not included in this model. Starting from the geometrical model the visualization model (Figure 8) and several structural models were developed.



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Figure 6: Flowchart of methodology.

Figure 7: Geometrical model.

Figure 8: Visualization model.

4 Structural models

Two types of F.E. models have been developed: global models considering the whole temple and local models to study in detail the behaviour of Regina Martirum dome, and several classes of structural analysis have been applied in the study. To carry out them the codes Cosmos/m v.2.8 [4] and Msc.Marc2003 [5] have been used, combining several types of finite elements depending of the architectural parts of the construction. Hexahedral and tetrahedron elements were used for modelling arches, pillars, tambours, buttresses and soil foundation; whereas beam, bar and quadrilateral or triangular shell elements were selected for meshing domes, floors, walls and reinforcements structures. The first global model intended to represent the behaviour of the temple before the repairing works launched in year 1927. Therefore a finite element mesh including not only the construction but also a volume of the surrounding soil was created, as presented in Figure 9. The comparison between the results obtained with this model and the existing descriptions of past pathologies allowed us to check the validity of the structural model and the hypothesis made



to develop them. After verifying the year 1927 model, a new one representing the current state of the temple was generated (Figure 10). The results obtained with the actual state model, with soil properties enhanced due to reinforcement of foundations, are almost identical to those obtained with fixed basement. Thereby, this last solution was used and the soil was eliminated in the current state model. The only temple parts not included, due to their null resistant function, are the cover system and the chapiters of domes and towers.

Figure 9: Details, 3-D view and plan of year 1927 structural model.

Figure 10: Reinforcement details and 3-D view of actual state model.

For each model a first version of linear solids and shell elements with 4 or 3 nodes, and a second version of quadratic solids and shells with 6 to 9 nodes were carried out. The latter mesh is composed by 82000 elements and 140000 nodes. The loads were assumed to be static and were composed of: gravity loads including dead load due to cover systems and chapiters; uniform thermal load with ∆T = ±15ºC in the whole temple; and finally a thermal gradient in the Regina Martirum dome, produced by a temperature difference of ±15ºC between the inner and the outer face of shell elements that model the chapel.

4.1 Material properties and models

Initially a linear analysis was carried out considering for each linear elastic material the isotropic parameters indicates in table 1. In the year 1927 model two different hypotheses about the soil mechanical properties distribution were carried out to take in account the possible deterioration in the sedimentary soil



near the riverside. Regarding to the principal masonry pillars, with cross section dimensions about 6 m. x 6 m., one material with a reduced elasticity modulus was considered in several analyses in order to simulate the existence of a filled nucleus surrounded by masonry. After linear analysis, two nonlinear material models were considered (Figure 11). In both the brick masonry was simulated as an isotropic material, with brittle behaviour in tension and linear in compression (model 1), or considering moreover the possibility of plastic behaviour in compression (model 2) using an elastoplastic Mohr-Coulomb linear model [6, 7].

Table 1: Linear properties.

E (KPa) ν γ (KNs2/m3)Masonry 4.5 · 106 0.1 1.8 Soil 1 2.5 · 106 0.3 - Soil 2 1.0 · 105 0.3 - Pillars 2.25 · 106 0.1 1.8 Concrete 3.0 · 107 0.2 2.4 Steel 2.1 · 108 0.3 7.85

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E Elasticity modulus ν Poisson coefficient γ Density Es Discharge modulus εap Crushing deformation σcr Cracking stress σres Residual stress σc Yielding stress

Model 1 Model 2

Figure 11: Nonlinear material models.

Material model 1 was programmed inside the Cosmos/m code, and was applied to the global temple model only for solid elements with a smear-crack approximation. In each iteration and for every Gauss point, the possibility of cracking perpendicular to the principal tension stress was checked out. Material model 2 was applied in the local analysis of Regina Martirum dome. Regarding the material parameters used in both models, a typical range of values for brick masonry obtained from bibliography was considered and a parameter variation study of results concerning them was done.

4.2 Constructive process effects

It is necessary to highlight the importance in stress results obtained if an evolutionary model considering several constructive stages is included in the numerical simulation, even with linear material models [8]. Globally, stresses



decrease in towers and superior parts, especially in the most slender like domes, and they are increased in central pillars and arches. A probably procedure for temple construction could consists on four stages, without temporally scaffolding: step 1 (pillars and arches), step 2 (tambours and perimeter walls), step 3 (vaults and domes), and step 4 (towers in three new stages). In such case stresses decrease approximately 50 % in tambours, domes, vaults and towers, and are increased in the arches in more than 70 %.

5 Numerical results

Regarding the year 1927 model, considering linear material and a uniform soil of type 1, principal stresses field reaches maximum values of 900 KPa for tensile stresses, and 2400 KPa for compressive stresses (Figure 12). Both values overcome the allowable range for masonry.

Figure 12: Vertical displacement (m) (left), and principal tensile stresses (right) (KPa).

The main cause of these significant values is the excessive weight coming from the central dome. Principal tensile stresses distribution agrees with the description of structural damages in that time, with maximum values in arches and vaults surrounding the central dome. However there is no evidence of important tensile stresses in elliptic domes tambours, in contradiction with historical reports stating that these tambours had important cracking. Figure 13 shows the cracking results obtained with non linear analysis using material model 1, with σcr = 150 Kpa, σres = 0.1σcr, Es = 0.1 E, and a retention shear factor of 0.01 for open cracks. The cracks begins in arches and progress fundamentally by the tambours of the elliptic domes, due to the transversal rotation that imposes them the excessive weight of central tambour and dome. With regards to the historical pathologies in the Regina Martirum dome a distribution of tensile stresses with maximum values up to 1300 KPa were obtained (Figure 14), located in a position quite similar to the real crack, if 1/6 of soil volume have poor soil properties. For the actual state model, the sequential application of the repairing additions has allowed to check their relative effect, being this especially



significant in the case of foundation works and steel lining of pillars and arches. Considering linear material properties and all the rehabilitation works applied, the maximum principal stresses in masonry decreases to 102 KPa for tensile stresses in arches keystone, and to 1123 KPa for compression stresses in pillars. In the Regina Martirum dome, principal membrane stresses are shown in Figure 15; adding the bending effects, stresses values are increased up to 281 Kpa and 911 Kpa respectively with these maximum values located in the top parts of dome area.

Figure 13: Percentage of integration points cracked in solid elements.

Figure 14: Model with two different soils and stresses in Regina Martirum

dome (KPa).

Figure 15: Principal membrane stresses in Regina Martirum dome (KPa).



Considering nonlinear material model 2, a local analysis of Regina Martirum dome modelled with solid elements has been carried out. The displacements obtained in the dome base from the global model have been imposed as constraints to the base dome in local model. Although a small error level may appear in dome analysis, the results are better than those with fixed base dome. To study the limit collapse behaviour, instead of increasing external loads above their real amount, a collapse mechanism was found by varying the material nonlinear parameters with current loads. Final values were: E = 4.5e6 KPa, ν = 0.1, γ = 1.8 T/m3, Es = E/8, εap = 0.004, σcr = 70 KPa, retention shear factor for open crack = 0.01, cohesive parameter c = 200 KPa, and internal friction angle φ = 40 º. Considering the cracking stress as variable the collapse takes place with a value of 70 KPa, lower but close to the most habitual value of 100 KPa.

Figure 16: Equivalent cracking deformation (left) and plastic areas (right).

6 Conclusions

The previous realization of a detailed geometrical model has allowed the generation of a complete F.E.M model with parametric meshing.

The study has permitted to reproduce numerically the temple historical pathologies, and to check out the efficiency of restoration works developed in the past by the architect D. Teodoro Ríos.

The use of linear models as previous step to nonlinear analysis, allows obtaining approaches that facilitate the comprehension of structural behaviour, with lesser cost and complexity.

Numerical models shown that the current structural situation of Regina Martirum dome is satisfactory and there is no risk of pathologies. Globally the temple structural situation is good, except in the southern towers, due to environment deterioration of brick masonry.

The obtained results are based on simplified material models and theoretical values for material parameters. Thus, it will be convenient to test material specimen to determine real properties of masonry and its spatial distribution.



Acknowledgements

Thanks are due to A. Sánchez, I. Valcarce, J. Cascales and P. Loscos, former research assistants of the U. of Coruña, for their contribution to this study.

References

[1] T. Ríos Usón y T. Ríos Solá, El Pilar de Zaragoza, CAI ed., pp.185-212, (1983).

[2] S. Hernández, L.E. Romera. Computer Modelling of the Basílica of Pilar In Zaragoza (Spain), C.A. Brebbia ed. Structural Studies, Repairs and Maintenance of Heritage Architecture VIII, (2003).

[3] L. Romera, S. Hernández y J.M. Reinosa. Análisis del comportamiento structural de la Basílica del Pilar de Zaragoza, Métodos Computacionais em Enghenaria V, APMTAC (2004).

[4] COSMOS/M v.2.8. Finite Element Analysis System: I) User Guide, IV) Advanced Modules. Structural Research & Analysis Corp., (2003).

[5] MSC.MARC 2003. Vol. A Theory and User Information, (2003). [6] P.B. Lourenço, Experimental and numerical issues in the modelling of the

mechanical behaviour of masonry. P. Roca, J.L. González, E. Oñate and P.B. Lourenço eds. Structural analysis of historical constructions II. Possibilities of num. and exp. tech., CIMNE, pp. 57-92, (1998).

[7] Structural repair and maintenance of historical buildings. C.A. Brebbia (ed.), Computational Mechanics Publications, (1989).

[8] Computational Modelling of Masonry, Brickwork and Blockwork Structures. J.W. Bull (ed), Saxe-Coburg Publications, (2001).



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