Extended Abstract Constructive and Structural Behaviour of Tiled Vaults Jorge Miguel Marques dos Santos Supervisors Professor Dr. António Manuel Candeias de Sousa Gago Lieutenant Colonel Engineer João Carlos Martins Rei Military Academy & Instituto Superior Técnico, Universidade de Lisboa October 2014 Abstract Masonry is one of the oldest construction techniques. The sustainability, durability, economy and simplicity of the process has contributed towards the widespread use of this composite material. Therefore, nowadays there is a great number of masonry structures, in which the arched structures have a significant role, for allowing to overcome spans using a material with low tensile strength. With the growing interest in the conservation of heritage buildings, it has become necessary to study a specific type of vault in Portugal called “abobadilha”. These are sustainable pavements and ceilings characteristics of the nineteenth and twentieth centuries buildings in the regions of Alentejo and Algarve. This dissertation studies the constructive process of the abobadilha alentejana, as well as the analysis of two different types of this vaults: the barrel vault and the cloister vault. When it comes to structural analysis, numerical models were used to analyse the response of the system when non-symmetric load was applied. Due to masonry behaviour, the Discrete Element Method was applied. It allows the usage of a non-linear behaviour model and can perform the full simulation of the structures behaviour since the load is applied until the structure collapse. An experimental full-scale model was also created, with the objective of comparing the numerical and experimental results. The results showed that, similar to arches, these structures have a low bearing capacity when subjected to non-symmetric loads, and also it was possible to conclude that the filling of the extrados leads to a large increase in bearing capacity. Keywords: Structural Analysis, Masonry, Vault, Tiled Vault, Discrete Element Method 1. Introduction Due the constructive characteristics of masonry (simplicity, economy, durability, sustainability, good acoustic and thermal properties), this technique has been widely used and there presently exists a vast quantity of construction. However, despite the large variety of masonry buildings, a common element to most of these is the arch, and consequently domes and vaults. Despite the masonry’s low tensile strength the introduction of these elements has enabled large spans to be crossed and this explains their widespread use in masonry buildings. There are a lot of existing brick vaults in Portugal, of which the abobadilha alentejana is particularly notable. These are structures that are typically used in the regions of Alentejo and Algarve, and have similar characteristics to others in Mediterranean, European and African regions, like the Spanish bóvedas tabicadas, the French voûtes à la Roussillon and the Italian volte in folio or la volterrana. “Abobadilhas” distinguishes itself from the ordinary vaults. These vaults are used with ceramic elements that run along the surface of the vault (Figure 1.1a), in opposition to the ordinary vaults where the bricks are placed perpendicularly to the arched surface (Figure 1.1b). (a) “Abobadilha” (b) Vault Figure 1.1 – Distinction between “abobadilha” and vault 1 Therefore, due to the large number of these type of structures, the growing interest in conserving historical heritage, as well as, the need to rehabilitate these vaults, it becomes quite clear that a study regarding the materials, construction techniques and structural behaviour must be done. Given this, the study focuses on the tiled vaults describing these vaults origins and evolution, its geometry, typologies, construction techniques (without formwork), aiming to contribute towards shedding light to the knowledge of this element widespread through many countries. The structural behaviour of this system is also analysed with three-dimensional discrete element models, using the software 3DEC in order to simulate its structural performance. In this paper an experimental model to assess the strength and to obtain numerical data for the calibration of numerical results was also used. 2. Origin and Evolution of Vaults The vault comes from the widespread use of the arch, which was invented in Mesopotamia and Egypt around 6000 years ago [1]. These civilizations were the first to master brick manufacturing, as a result, they were the first ones to build vaults using this material. The first example of these, built around 5000 years ago were barrel vaults [2]. There is varying opinion within the scientific community about the evolution of the tiled vaults among the countries of Southern Europe. The main assumption is that it was a result of slow but progressive evolution to which several civilizations contributed, such as the Byzantines (masters of construction without formwork), the Romans, and the Arabs, which possibly implemented these vaults in the Iberian Peninsula, given that the oldest date back to the end of the twelfth and start of the thirteenth century [3, 4]. Initially, in the fourteenth and fifteenth centuries, this technique was widely used to fill the spaces between the cross-ribs in gothic vaults, later evolving to the groin vaults greatly used in the modern age [5, 6]. In the sixteenth and seventeenth centuries there was a raise in the worldwide usage of this structural and constructive system, which was valued due to the fact that this system is easily assembled, has high resistance, and low self-weight leading to lower horizontal thrust on supports. After the industrial revolution, in the nineteenth century, the technique used to construct the tiled vaults was combined with steel frames, leading to the constructive method of “abobadilha” between iron beams characteristic of the nineteenth and twentieth centuries architecture [7]. Lastly, in the last few years the tiled vaults have been used by contemporary architects like Guastavino, Gaudí e Le Corbusier, who adapted them to modern requirements, a token to the technique’s simplicity and versatility [3]. 3. The tiled vault There is a large variety of brick vaults in Alentejo and Algarve, which are not only sustainable structural solutions for pavements and ceilings, but also have a good acoustic and thermal performance [8, 9]. These structures can consist of a single brick layer or multi-layered [8]. The most prevalent tiled vaults are “barrel vaults” (Figura 3.1a), “groin vaults” (Figure 3.1b) and “cloister vaults” (Figure 3.1c). (a) Barrel vault (b) Groin vault (c) Cloister vault Figure 3.1 – Types of tiled vaults 2 3.1. Geometry aspects The generating lines that tiled vaults follow are [9]: circular, continuous or elliptic lines. In the case of ! ! the circular tiled vaults, the rise is generally less than half the span (L), being between � and �. ! ! Sometimes these vaults were designed from a succession of circular arches. Finally, the elliptic lines are also a common geometric design, matches the largest axis with the span and the smallest with the rise. Another important characteristic of this kind of structures is the double curvature that is the result of the intersection of two torus. For this reason the central keystone is higher than the keystone of the lateral arches. This is always used whenever the length of the “abobadilha” is more than two metres, improving its stability despite its increased constructive complexity [9]. Table 3.1 shows the rises that are normally used depending on “abobadilha” layout sizes. Figure 3.2 illustrates the rise, which makes the vault have double curvature. Table 3.1 – Rises in the haunch area [9] Span [m] Length [m] Rise [mm] 3,5 3,5 15 5,0 5,0 35 to 40 5,0 10 40 to 50 8,0 8,0 50 to 55 8,0 10 50 to 55 Figure 3.2 – The presence of double curvature 3.2. Materials These vaults are usually built with solid clay bricks, usually with 300x150x35 mm3. In terms of the mortar, it is usually a mixture of limestone and plaster (without sand) in a 3:1 ratio. The plaster is used so that the mortar hardens almost instantly, which enables the constructive process without formwork [9]. 3.3. Rules of design Similar to other arched brick structures, the traditional design rules of this kind of vaults are essentially based on empiric and geometric proportions rules. Thus some of the rules are the following: a) Filling height According to Fidalgo [9], in tiled vaults the filling should be made up to 1/3rd of the height of the rise, preventing any of the haunches from detaching, improving the vaults´s structural behaviour. b) Rise Masons have concluded that flatter outlines lead to a more stable structure, for this reason tiled vaults usually have these given rises: 3 Table 3.2 – Tiled vaults’s rise [9] Span size [m] Rise [% of the span] until 4,0 15 to 20 From 4,0 to 6,0 25 to 30 From0 6,0 to 10,0 35 c) Stiffeners With the goal of improving the structural behaviour of the vaults, reinforcement elements like braces and bearing walls are often used. The braces (Figure 3.3a) have a length of 0,30 or 0,45 m, and are separated by 2,5 to 4,0 m [10]. The walls themselves are only used in larger vaults, and as the filling have the goal of preventing haunches displacement. In terms of the cloister vaults, the bearing walls are placed in both directions, and on the four corners blocks are placed in order to avoid corner “uplift” when a load on the vault is applied (Figure 3.3b). (a) Barrel vault (b) Cloister vault [9] Figure 3.3 – Stiffeners on tiled vaults 3.4. Construction Techniques The first step in the execution of this kind of vaults it’s the layout on surrounding walls, followed by the execution of hollows ensuring an adequate connection between the walls and the vault (Figure 3.4a).