Numerical safety assessment of earthen structures in La Alhambra, Granada, Spain
The main aim of this thesis, by the author Annalaura Vuoto is to obtain a better understanding of the structural and seismic behaviour of the rammed earth structures within the Alhambra in order to assess their safety, focusing on the Torre de la Vela.
The Alhambra is a UNESCO World Heritage Site from 1984 and one of Spain’s major attractions. It bears exceptional testimony to the Muslim Spain of Al-Andalus between the 13th and 15th centuries. Its architecture reflects the Islamic culture of the Middle Ages through its proportional system, area compartmentalization, no exteriorization, and the typical acclimatized design, while its decorative aspects constitute the best example of Nasrid art. It is highly enriched by the symbolic value of the different areas of the complex, which, since the 13th century, have been mostly preserved in their original way.
It is located in the city of Granada, in the South of Spain and it is the main enclave of a complex territorial structure, which reveals its importance due to the domain over the city. Granada matches the historic model of the hilltop city, surrounded by mountains and irrigated by the Darro and Genil rivers.
Seismic hazard and historical seismicity
Spain, in general terms, is not characterized by high seismic hazard. Andalucía is the area with the highest seismic hazard of the peninsula.
The coasts of Málaga, Granada and western Almeria are indicated as the most dangerous seismic zones. The areas of greater activity are precisely the coasts of Adra (Almería) and the Granada basin. Andalucía is therefore the region with the highest number of earthquakes in Spain. Approximately half of the earthquakes yearly recorded in Spain occur in Andalucía, to provide some examples (according to the National Geographic Institute):
⦁ 1527 out of 3792 in 2007;
⦁ 1110 out of 2543 in 2006;
⦁ 1565 out of 2933 in 2005.
The oldest known earthquake affecting the area of Granada, causing extended damage also in the Alhambra, is the one occurred in 1431, characterized by a macro-seismic intensity of VIII-IX (EMS98).
The strongest was the earthquake of 1884 in Arenas del Rey, which reached an intensity of IX-X (EMS98), producing 839 deaths.
Geology and stability assessment of the Alhambra hill
The Alhambra was constructed on top the al-Sabika hill, on a conglomeratic sequence that constitutes the so called formación Alhambra (Alhambra formation). The hill dominates a plain, surrounded by mountains, where most of the city of Granada extends. From a geological point of view, this plain is known as Cuenca de Granada (Granada basin). This depression (Figure 5, center) is located in the central sector of the Betic Cordillera, and is one of the most seismically active zones in the Iberian Peninsula.
As part of a study carried out by Justo et al. regarding the slope stabilization at the Alhambra, several tests were performed, which allowed to reconstruct the stratigraphy of the Alhambra conglomerate. Two boreholes – depicted in Figure 6 (right) – were drilled at the top of San Pedro escarpment. Pressuremeter down-hole and cross-hole, penetration, permeability, and subsequent laboratory tests were carried out.
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According to the tests, the main difference between the different conglomerate layers is related to maximum particle size, core recovery, and stiffness as measured in the pressuremeter and geophysical tests. No clear differences in color were found. The following layers (Figure 7) appear from top to bottom in the geological profile:
1. Dense conglomerate, with 100 mm maximum particle size and core recovery 100%, of brown to pale grey silty matrix;
2. Very dense conglomerate, with a maximum particle size of 5–8 cm and core recovery of 100%, of brown to reddish silty to clayey matrix;
3. Moderately dense conglomerate, with core recovery of 60%, of brown to pale grey silty matrix;
4. Very dense, gravelly, and sandy conglomerate, of brown to pale grey silty fine matrix and variable permeability;
4.a One meter thick clay layers, interspersed in layer 4. Core recovery of 100%.
Evolution of the Alhambra from the Nasrid Kingdom of Granada to the 20th century
The fortress of the Alhambra was built on a pre-existing structure, dating back to the Umayyad caliphate as stated, although a Roman or Visigothic origin is also admitted. The first information about Alhambra dates back to 889, when the Qalat al-Hambra (the red castle) is mentioned for the first time. It is described as a castle of modest importance in the context of the internal uprisings that took place in the last years of the Umayyad emirate.
Torre de la Vela
The construction of the tower began during the Sultanate of Muhammad I, in 1238. It was the first structure of the Alcazaba to be built.
The tower has four storeys and a terrace. The base is surrounded by a barbican and a passable moat (Calle-Foso) that connected the original entrance to the Alcazaba with the Torre de las Armas, the building of the stables, and the Puerta de las Armas. Nowadays, it is not allowed to walk through the moat and the current entrance is located at the second floor, from which the terrace can be reached after 52 stairs. The staircase was renovated after the Christian conquest and is much wider than the original one.
Until the 16th century, the terrace was made up of battlements, defensive elements which were lost in time as a result of several disasters affecting the tower, namely: the earthquake in 1522; a gunpowder explosion in the Darro valley in 1590 that left the tower significantly damaged; and a lightning strike that destroyed the bell gable in 1882.
CURRENT STATE ASSESSMENT
Geometrical description of Torre de la Vela
Located in the Western border of the Alcazaba fortress, the Torre de la Vela is its highest tower, with a height of 26,80 m. It is a squared tower with 16 m side plan. It is divided into four floors and a terrace top floor with the bell gable.
A detailed geometrical description of the tower is provided by Pavón and Gómez Moreno.
The ground floor of the tower is a sort of single nave dungeon with rectangular plan. The three upper floors show the same layout, with a squared central area enclosed by two naves on the four sides. As it is visible in the cross section depicted in Figure 27, the tower has a central room, two narrow spaces on both sides, and two additional slightly larger rooms at the edges. The width of the two outermost rooms increases from the second to the last floor plan, as the outer wall decreases in thickness, from 4,60 m on the ground floor to 1,62 m on the last floor.
A fixed scheme for the structural elements, which is repeated in all the floors, was adopted. The layout assumed for the 3D model was defined as follows and is shown in Figure 30. From the inside:
1 – Central square open with a variable number of arches;
2 – External square, which defines the inner narrow nave, open with a variable number of arches;
3 – Walls bracing the corners of the outermost nave. According to the available description, these walls were originally arches, some of which closed. In uncertainty, they have been modelled as walls without openings;
4 – Vaults of variable typology according to the description above;
5 – Vaults’ infill;
6 – External walls.
Construction techniques and structural characterization
The defensive structures of the Alhambra are built with materials and techniques proper of the traditional masonry constructions. Rammed earth and brick masonry are widely used for towers, gates and city walls. Originally, the external walls of the towers were built in rammed earth, so that it is possible to locate the reconstructed parts, usually realized in brick masonry, with a simple visual inspection.
The Torre de la Vela’s outer shell is made of tapial calicostrado, showing some reconstructed areas made of clay brick masonry. The inner structural elements, pillars, arches and vaults, are made of well-baked irregular clay bricks assembled with mortar joints up to 3 cm thick. The employed mortar is loose and made of earth, clay and lime, except for the one used in the vaults which is a hard gypsum mortar. Plasterwork, when present, is made of lime mortar.
Given the impossibility of carrying out a visual inspection in Torre de la Vela, the distribution of the materials shown in Figure 32 is assumed, based on available references and information collected for other towers of the Alcazaba dating back to the same period, and several pictures.
For the characterization of the materials, reference is made to the study of the Torre del Homenaje carried out by Villegas, which in turn refers to different sources, both experimental and normative. The Torre del Homenaje and the Torre de la Vela date back to the same period and their constructive system are similar. Therefore, it is considered plausible to use the same characterization.
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Based on the available information, it is not possible to carry out an accurate damage assessment for the tower. The following pictures are the most recent available ones, and show a significant crack pattern affecting the external walls. The most damaged façades seem to be the East and the North ones.
In the East façade, the cracks (highlighted in red in Figure 36, left) are located in the upper part, both in the original rammed earth part and in the reconstructed brick masonry one. The entire upper part of the façade is reconstructed in brick masonry, as well as the SE corner of the tower (Figure 36, right). The cracks mainly affect the area of the façade where the windows are located. An extended vertical crack is at the connection between the two different materials.
In the North façade, the crack pattern (highlighted in red in Figure 37, left) is also characterized by vertical cracks: one is located in the upper center of the façade in the area of the window, a second one appears in the NW corner, and seems to be corresponding to the connection between two different materials, being apparently only the upper part of the corner made of brick masonry. Extended longitudinal cracks are located in the center of the façade and start from the middle reaching the ground floor. Horizontal cracks appear at the fourth floor level, again apparently in the area (highlighted in orange in Figure 37, left) of the connection between the different materials.
The movement and tilt of the towers on the northern side of the al-Sabika were monitored from January 1989 until October 1994. In the Torre de la Vela cyclic vertical motion was found, as visible from the recording of the vertical displacements in Figure 38, with resultant settlement of less than 1 mm.
The numerical model of the Torre de la Vela was implemented in the software DIANA FEA. The model was prepared using literature data both in terms of geometry and mechanical properties of materials. The geometrical model was realized using AutoCAD 3D software, it was then imported into DIANA, where the mesh was processed and the structural analyses were carried out.
The geometry of the Torre de la Vela was simplified as shown in Figure 30 using several categories of elements, in order to have a better control during the discretization of the mesh in DIANA. The geometrical model imported in DIANA is shown in Figure 39.
The structural analysis of masonry buildings characterized by a large number of units and joints, as the Torre de la Vela is, can be carried out only considering a macro-mechanical based finite element model.
In this work, Total Strain-Based Crack Model (TSBC) with a rotating crack formulation was chosen among the different material models provided by DIANA.
4. Mesh definition
When designing the mesh, a fair compromise between accuracy and computational efforts should be given, especially when non-linear static or dynamic analyses are performed. This approach was followed for the model of the Torre de la Vela, characterized by a significant number of elements. The mesh size was assigned as function of the size of the element, with different size set from 0,5 m in the thick external walls to the 0,2 m in the vaults (Figure 42).
The used mesher type is quadratic/hexagonal, except for some of the vaults for which the triangle/tetrahedron fitted better.
Linear Static analysis
A linear static analysis was carried out taking into account the elastic mechanical properties of the materials and the self-weight in order to detect any errors in the structural model.
An eigenvalue analysis was run as a further check of the model, to see if the values obtained for the frequencies were plausible.
Incremental vertical analysis
An incremental vertical analysis was performed in order to understand the behavior of the building under its self-weight. Due to the characteristic of the tower, remarkably massive, it was considered not significant to perform the analysis until reaching the peak value of the vertical load, so a vertical load up to the double of the self-weight was applied.
Incremental horizontal analysis
The response of the tower under seismic action was assessed by carrying out a pushover analysis with a load profile proportional to the mass. Pushover analysis is a non-linear static analysis performed using horizontal forces to simulate the seismic action.
An incremental-iterative method is used assuming constant gravity loads and monotonically increasing the horizontal load. Pushover analysis allows to estimate the collapse mechanisms of the structure, to evaluate the distribution of damage, to assess the structural performance of existing buildings and their capacity in order to compare it with the seismic demand.
In this work three pushover analysis were carried out:
1 – In –X direction including the bell gable;
2 – In –X direction discarding the bell gable;
3 – In –Y direction.
Simplification of the structural model
On the one hand, the analyses carried out showed that the structural response of the tower is mainly depended by the outer walls, to which most of the mass is attributed.
On the other hand, the geometry of the inside of the tower is quite complex and includes many elements.
This increases computational time and leads to problems in performing non-linear analyses to achieve convergence of the numerical solution. For these reasons it was considered to evaluate the structural response of the tower using a simplified model that includes only the outer walls (Figure 70), so as to evaluate the influence of the inner part on the overall behavior.
This work has attempted to increase the level of knowledge related to the Torre de la Vela and to systematically collect available information from multiple sources, and the most significant data related to the geographical, historical, architectural context have been selected and reported identifying those that may be useful for subsequent safety analysis.
Particular attention has been paid to the geometry of the tower, with the aim of obtaining a geometrical model that responds to historical drawings and information from the literature. The employed materials have been analysed on the basis of available experimental works, and the traditional construction techniques that characterize the rammed earth buildings of the Alhambra have been studied and described.
A set of analyses was carried out to understand the structural response of the building subject to gravitational and seismic loads.
In a first phase, a linear static analysis and a modal analysis were carried out to verify that the numerical model was well executed and did not present inconsistencies, which would have been problematic for the subsequent analysis.
In a second phase, several non-linear analyses were performed:
⦁ An incremental analysis for gravitational loads was carried out also simulating the construction phases of the different levels of the tower, with the aim of evaluating the behaviour of the structure subject to its own weight, since its main structural elements are very massive.
⦁ Then, several pushover analyses were performed in order to evaluate the seismic response of the building and assess its safety level.
⦁ Lastly, some considerations regarding the possible simplification of the numerical model were made, with the aim of reducing computational time and simplifying the geometry. To this end, the structural behaviour of a model that only includes the external walls was analysed, the results of the analysis were compared with those of the full model in terms of capacity and structural response. The hypothesis of using a simplified model seems to be plausible according to the results of the analysis, considering the possibility of preparing and using an intermediate model.
The following recommendations are suggested:
⦁ The geometry of the tower has to be validated with a geometrical survey, since the historical drawings are dated, and certainly the internal configuration of the tower has undergone changes over time.
⦁ The numerical model must be validated through the use of experimental data, a campaign of NDT tests is recommended and would allow to update the mechanical properties assigned to the materials.
⦁ In the safety evaluation of the building and in the structural analyses, some factors neglected in this work should be taken into account, such as the interaction between the structure and the subsoil and the reconstruction interventions of the façades made with brick masonry. On these factors could in fact depend the state of damage that characterizes the structure at present, and which has not been captured by the performed analyses.
⦁ A simplified model could be used to carry out further analyses aimed at understanding the overall response of the structure, in order to reduce modelling and computation times and have the possibility to perform dynamic analyses, notoriously more complex and time demanding than those carried out up to now.