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

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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

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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).

Figure 3.1 – Types of tiled vaults

(a) Barrel vault (b) Groin vault (c) Cloister vault

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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 !

!𝐿 and !

!𝐿.

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:

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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). Usually the tiled vaults are constructed starting from the outside towards the center given that each row is closed nearly at the center (Figure 3.4b) [9].

(a) Hollows in the support walls (b) Layout sequence [9]

Figure 3.4 – Construction technique

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4. Structural behaviour modelling Given the non-linear behaviour of masonry structures and their low tensile strength, limited shear strength and the discontinuity between the elements, the definition of a structural model is a complex task. There are several possible approaches that can be followed when are studding the behaviour of these structures behaviour. Two of the most suitable are the non-linear finite element models and the discrete element models.

In this study the Discrete Element Method (DEM) was chosen because of the advantages it has when analysing masonry structures. Firstly, because it does not require a thorough mechanical characterisation of the materials, and secondly, because the DEM allows substantial displacement and rotation between elements (including their separation), an aspect that is of major importance when simulating the collapse mechanism of these structures.

4.1. Description of the models used

In this paper, several discrete element models were developed, such as barrel and cloister vaults models. These models are presented below:

(a) Model 1.1 (b) Model 2.2 (c) Model 3.2

(d) Model 4.2 (e) Model 5.2

(f) Model 6.2 (g) Model 7

Figure 4.1 – 3DEC models of the vaults

The structures were modelled using the 3DEC software [11], considering rigid blocks connected by deformable joints. This is beacuse the “abobadilhas” are, under normal conditions, conditioned by the behaviour (strength and strain) of the joints. The dimensions of the blocks in the three dimensional discrete element models are the same of the real ones, which have the dimensions of 300x150x35 mm3, and a density of 1680 kg/m3. The Mohr-Coulomb’s shear behavioural model was used in the

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joints between the blocks. Thus, it was admitted a linear elastic behaviour with unlimited compressive stress strength and tensile strength of 0.20 MPa in the normal direction at the contact. On the shear model was considered a cohesion of 0.20 MPa and a 35º frictional angle. In model 1.1, zero tensile strength was assumed with the propose of assess the influence of the tensile stress of the mortar.

Results

Before showing the results, it is important to highlight that the analysis had the aim of obtaining an estimate of the strength of these two types of “abobadilhas” (barrel and cloister vaults). The loads considered in the analyses include, as dead load, the self-weight (volumetric weight 𝛾!= 16.80 kN/m3) and as filling only in model 3.2 (𝛾! =24 kN/m3), and, as live load, a linear load was applied along the “abobadilhas”. Given that, this last load is applied along the entire model length on the models 1.1, 2.2, 3.2 and 4.2, and only in a one meter lane on the others cases. The Figure 4.2 shows the above-mentioned load. Because the live load is applied on an extension on the barrel vaults and on another different on the cloister vaults, in order to compare the behaviour of these vaults, it was considered a new type of barrel vault (model 7 – Figure 4.3).

(a) Barrel vault (b) Cloister vault

Figure 4.2 – Load Configuration

Figure 4.3 – Detail of the linear load used in model 7

The results of the Discrete Element Method (DEM) are analysed below.

Firstly, the behaviour of the models 1.1 and 1.2 were analysed. These models refer to barrel vaults with a rise of 0.60 m, considering different values for the tensile strength on the joints. So, in Figure 4.4 one can clearly shown the favourable effect of the mortar tensile strength, trough the increase of the ultimate load in the model where the tensile strength of the joints is considered (model 1.2).

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Figure 4.4 – Ultimate load as a function of its position (model 1.1 vs. model 1.2)

It is clear, from Figure 4.4, that most of the ultimate loads were lower than 1.0 kN/m, which means that load carrying capacity of these structures is quite low. It occurs because the fact that the models had a thickness/radius ratio very close to the minimum admissible.

In terms of the horizontal thrust, by analysing for example model 1.2, it is clear that its distribution for the barrel vault is practically constant along the edges (Figure 4.5). Furthermore, the load that refers to the self-weight (PP) of the structure is the one that transmits the less thrust to the walls. This is different to the results shown when the load is applied in the middle of the span, being this the case that leads to the greater thrust (Figure 4.6).

Figure 4.5 – Distribution of the thrust on edge 1

Figure 4.6 – Horizontal thrust on edge 1 (as a function of its position, model 1.2)

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As expected, the barrel vault had a similar collapse mechanism to the one of an arch, which consists of the formation of hinge rotations. On Figure 4.7a, one can see the hinge formation due to symmetrical loading. On the other hand, on Figure 4.7b it is possible to see a collapse mechanism involving four non-symmetrical hinge rotations due to asymmetric loading.

(a) Symmetric load– five joints

(b) asymmetric load – four joints

Figure 4.7 – Collapse mechanisms of barrel vaults

In terms of the effect of the filling and of the supporting transversal walls, there was an increase in the load carrying capacity of the models, especially when supporting transversal walls were used (model 4.2 – Figure 4.8). In fact, the existence of these stiffeners elements leads to greater voussoir compression, as well as a restriction of horizontal displacements near the haunches, which results in a substantial increase in the model stability [12].

Figure 4.8 – Ultimate load as a function of its position (models 2.2, 3.2 e 4.2) – influence of the stiffeners

Similar to the study made on barrel vaults, the ultimate load of models 5.2 and 6.2 (cloister vaults) were also analysed. In these models three different load positions were used, at mid-span (½ span), at one third of the span (1/3 span), and close to the support. All these positions can be seen in Figure 4.9.

(a) Load at 1/2 span (y=0.000) (b) Load at 1/3 span (y=0.358) (c) Load near the edge 1 (y=0.781)

Figure 4.9 – Position and configuration of the loads

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Through this analysis one can conclude that the model with a rise of de 0.40 m is more strength when the load is located at the edge of the “abobadilha” (load position y=0.000), as can be seen in Figure 4.10.

Figure 4.10 – Ultimate load of the models 5.2 and 6.2

As for thrust distribution on the cloister vault supports (Figures 4.11 and 4.12), there is a decrease near to the edges, evident in all load cases, even when only the dead load was applied. This results show that there is no thrust concentration near the curved surface edges of these vaults.

Figure 4.11 – Distribution of the thrust on the edge parallel to the applied load

Figure 4.12 – Distribution of the thrust on the edge perpendicular to the applied load

Lastly, comparing both types of “abobadilhas” (barrel vault – model 7 and cloister vault – model 5.2) it is possible to understand that, independent of its position, the ultimate load of the cloister vault is considerably larger than that of the barrel vault (Figure 4.13). On the other hand, in both cases, the situation where the load position is more onerous is when it is placed at 1/3 of the span (y = 0.358).

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Figure 4.13 – Ultimate loads of models 5.2 and 7

Finally, the collapse mechanism of the cloister vault presents a more local character, which leads, at a later stage, to the global collapse of the structure. The Figure 4.14 shows the collapse mechanism for each of the load cases analysed, where the local collapse mechanism is clearly shown. As well as this aspect, there is also the particularity (highlighted with a circle in the figure below) where the side opposite to the load moves outwards.

Load at 1/2 span Load at 1/3 span Load close to edge 1

Figure 4.14 – Collapse mechanism of the models 5.2 and 7

5. Conclusions The constructive technique of the abobadilhas is the result of a result of a slow but progressive evolution process, to which several civilizations contributed, such as the Byzantines (masters of construction without formwork), the Romans, and the Arabs, who probably implemented these vaults in the Iberian Peninsula.

This technique uses traditional materials such as brick and mortar, and does not require complex tasks or equipment, just some specialised labour. Some of the more relevant aspects are:

• Brick on flat placement;

• Use of a mortar based on lime/cement and gypsum so as to harden rapidly;

• Process does not require formwork;

• Complex geometry due to its double curvature.

To be able to build the “abobadilha” without formwork, the first step is to mark the layout on the surrounding walls, followed by opening the respective spaces in these walls. Only after this has been done is the brick layered, which usually are placed using two sides. It is also important to highlight that the process always start from the outside and works towards the insides, only starting a new row after the previous has been completed.

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In terms of the characteristics, as well as the previously mentioned aspects, the tiled vault is extremely durable and versatile, economic and light. This kind of vault require fewer materials and are lighter, they have lesser self-weight and as a result a reduced ceiling height. They also have less labour and material requirements as there is no need for formwork.

In terms of the structural performance of this technique, when the “abobadilhas” don’t have any filling, they have less bearing capacity. The benefic effect of including filling is because of the result of the compression of the “abobadilha” brick rows, as well as the restriction of their horizontal displacement.

The barrel vault, as expected, has a similar behaviour to the arch. When compared the effect of the use of a load bearing wall to filling, it is clear that the use of the walls leads to a much greater increase of load capacity, indicating how effective it is as a reinforcement technique.

Comparing the cloister and barrel vault, it is clear that the bearing capacity of the cloister vault is superior to the barrel vault, with a decrease in thrust at the corners of the intersections of the curved surfaces.

Lastly, when comparing both of the model’s collapse mechanisms, the cloister vault has more local characteristics which only at a later stage leads to the global collapse of the structure. The barrel vault collapse mechanism is, on the other hand, more similar to that of an arch, when consists of the formation of rotation joints.

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