22 November, 2023 13 min reading
Based on the dissertation by: Demiana Tse, M.Sc. in advanced masters in Structural Analysis of Monuments and Historical Constructions.


The main aim of this thesis, by the author Demiana Tse is to evaluate the structural response of the Torre de la Vela, located within the Alhambra, under blast and impact loading.


The Alhambra and the Torre De La Vela


The Alhambra is located in the South of Spain, in the city of Granada. The site stands on the al-Sabika hill, beside the river Darro. The Alhambra is composed of three main areas: the military zone (or Alcazaba), the palatine (or imperial) city, and the medina (or the residential, administrative, and religious area).

Alhambra is a palatine city, the only preserved example of its kind from the Islamic period in the Iberian Peninsula. It is also the best example of Nasrid (the last Muslim dynasty in the Iberian Peninsula) due to its architecture and decorate elements.


The Alhambra was listed as a UNESCO World Heritage site in 1984 under three criteria:

  • It is a masterpiece of creative genius,
  • A unique testimony to cultural tradition,
  • Its accessibility,
  • An outstanding architectural ensemble showing a significant stage in human history.

Layout of the Alhambra and the Alcazaba
The Alhambra has three principal areas within its walls:

  • The Alcazaba, which is primarily reserved for military use; the palace and its surroundings, which functions as a royal residence with up to seven distinct palaces.
  • The Medina, which is a residential and artisan’s city, where administrative and commercial activities take place for the royal court.
  • The Generalife is typically included in the description of the Alhambra. The Generalife, separated and located to the east of the Alhambra, is a semiurban, semirural residence with palaces and terraced gardens.

The Alcazaba is the military area of the Alhambra, situated on the West of the al-Sabika hill, which is also the hill’s highest point.

The Torre de la Vela

The Torre de la Vela was the first structure in the Alcazaba to be constructed (1238). During the early stages of its construction, the tower could be used as a watchtower to defend the city.

After several different names, it was named Torre de la Vela, after the Christian conquest, because of the name of the first bell that was rung in the tower, called “La Vela.”

Some traumatic events have marked the Torre de la Vela over the years:

  • In 1522 and 1821, the tower and the complex as a whole suffered an earthquake.
  • In 1590, a gunpowder factory located directly below the tower exploded, leaving the
    tower significantly damaged.
  • In 1882, the tower was struck by lightning.

The bell gable, and its bell on the west side of the terrace, is one of the character-defining elements of the tower. The bell gable itself had to be rebuilt in 1882 following the aforementioned lightning strike.


  • The highest tower in the Alhambra, measures 26.8 m in height.
  • Its square plan measures 16.0 m on either side.
  • The tower is four stories in height, where the thickness of the walls decreases with each increasing storey.
  • Two entrances exist in the Torre de la Vela. The main entrance to the building is located on the second floor of the tower, on the south side. Another entrance is located on the south side of the third floor.
  • The staircase, which is present on Levels 2, 3, and 4, is located in the south-east corner of the building, and is isolated from the building by a mortar wall.
  • Almost all the arches in the Torre de la Vela are semicircular, but the central voussoir converges to a point lower than the centre of the curve, making these arches identical to the Moorish arch.
  • On the exterior of the building, the Torre de la Vela is connected to various other elements in the Alcazaba. The Alcazaba wall is connected on the building’s east side, while a bridge is directly adjacent to the building’s south side.
  • The 3rd floor entrance is located at the top of this bridge, while the 2nd floor entrance is located underneath. The south-east corner of the building is below ground.
  • The entire Level 1 is effectively below ground.

Past Interventions and Construction Techniques


In the Alhambra, traditional masonry materials and techniques were employed.

The towers, gates, and walls of the fortified city have mostly been constructed from rammed earth and brick masonry. As the external walls of the towers were typically constructed of rammed earth, the visible locations of brick masonry indicate locations of possible reconstructed portions.

With respect to past interventions of the Torre de la Vela, some parts of the building have been rebuilt. Additionally, arches on the second and third floors have been filled over the years, which resulted in the loss of the original configuration of the building.

In the Torre de la Vela, two main construction techniques can be found, which are:
a) Tapial calicostrado (very similar to traditional rammed earth masonry)
b) Brick masonry

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The vulnerability of masonry envelopes under blast loading is critical due to the potential loss of lives. Blasts near or inside a building can damage and destroy parts of the building and can produce both local and global responses related to different failure modes within structural members.

Blast Loading


Explosions or blasts are defined as sudden releases of energy, where gas expands and increases in volume rapidly. The nature of explosions can be:

  • Physical: energy is released from e.g. catastrophic failure of a cylinder of compressed air, when two liquids are mixed at different temperatures, or during volcanic eruptions.
  • Chemical: energy is released from the rapid oxidation of carbon and hydrogen atoms.
  • Nuclear: energy is released from the formation of different atomic nuclei and the redistribution of the protons and neutrons within the interacting nuclei.


Scaling Laws
Scaling laws allow for parametric correlations between a given explosion and a standard charge of the same substance.

Equivalent TNT
All blast parameters are dependent on the magnitude of the explosion, measured by the amount of energy released, otherwise known as the explosive yield. The generally accepted reference standard for the explosive yield is the energy released in equivalent mass of TNT.

The proposed workflow is a parametric modeling approach based on flow-based programming and generative algorithms.

Explosive devices can be categorized in four sizes:

  • Small explosions (up to 5 kg of TNT);
  • Medium explosions (up to 20 kg of TNT);
  • Large explosions (up to 100 kg of TNT);
  • Very large explosions (up to 2500 kg of TNT).

External Blast Loading

External explosions are classified based on the relative position and angle of the source of the explosion, and the structure subjected to the blast load:

  • Free-air burst
  • Airburst
  • Surface burst.

Internal Blast Loading

Internal explosions occur when each surface is subjected to the shock waves caused by the reflections of multiple surfaces.

  • Fully vented explosion
  • Partially confined explosion
  • Fully confined explosions

Impact Loading


Impact loading falls under the “dynamic loads” category. When an object in motion hits a structure, the response will depend on the velocity and the material properties of both the structure and the object in motion.

Classifications of Impact Loading

Impact loads can be classified in two ways:

By their intensity and duration:

  • Particle impact
  • Rigid body impact
  • Transverse impact on flexible bodies


By the dissipative mechanism

  • Hard impact
  • Soft impact

History of Military Weapons

The Alhambra has been used as a fortress or stronghold in many different centuries. From sieges to military bases, a large variety of military weapons could have caused structural damage to the building over the centuries.

Gunpowder was first invented in China during the 9th century and spread throughout most of Eurasia by the end of the 13th century. Black powder was the type of gunpowder employed in all firearms until other types of smokeless propellants were invented in the late 1800s.

Black powder is the combination of three main ingredients:

  • Saltpetre
  • Charcoal
  • Sulphur

However, the proportions of this mixture have been modified and refined over the years.
Eventually, the recipe for black powder was refined to proportions of 75-15-10 by weight.

Gunpowder storage was an important aspect to consider as it is highly sensitive to flames, sparks, and moisture.

Following a modern-day investigation Reza et al. (2013) determined that 1 kg of black powder is the equivalent of approximately 0.60 kg of TNT.


The earliest known examples of cannons are from the Song dynasty in China, around the 12th century.

Cannons were particularly important during the Granada War. Between 1482 and 1491, the Catholic Monarchs Isabella I of Castile and Ferdinand II of Aragon led a joint project against the Nasrid dynasty’s Emirate of Granada. A notable facet of this war was the use of bombards and cannons, which resulted in shortening the sieges in the war. As stated by Cook (1993):

“Gunpowder firepower and artillery siege operations won the Granadan war, and other factors in the Spanish victory were actually secondary and derivative.”

Notably, a replica of the culverin extraordinary was made in 2003. This replica achieved a muzzle velocity of 408 m/s with a range of over 450 m when fired at point-blank.

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  • The numerical model of the Torre de la Vela was implemented in the software Abaqus CAE.
  • The geometry and material properties for this model were based on work done by Vuoto (2020).
  • The geometry of the tower was provided in AutoCAD 3D format and was imported into Abaqus to create the mesh and to conduct the analysis

Masonry Structures Under Blast Loading


Abaqus/Explicit is a finite element software within the Abaqus/CAE modelling environment that is efficient in analyzing large models subjected to short dynamic response times.
Concrete Damage Plasticity

The Concrete Damage Plasticity (CDP) model, which is available in the Abaqus software, is a modification of the Drucker-Prager model made by Lubliner et al. (1989) and Lee and Fenves

To use this constitutive model in Abaqus, the following parameters are required:

  • Density,
  • Young’s modulus,
  • Compressive strength,
  • Fracture energy in compression,
  • Tensile strength,
  • Fracture energy in tension.

Material Behaviour at High Strain Rates

The type of load applied on a structure can significantly affect its response.

Contact Interactions

The Mohr-Coulomb was adopted here to model the sliding failure on the frictional interfaces between the individual blocks.


Torre de la Vela

Finite Element Mesh

The geometrical model in Abaqus was discretized into a Finite Element mesh. As the computational effort increases significantly with the number of elements, different structural sections were assigned varying element sizes to keep the number of elements reasonable while maintaining the accuracy of the geometry.

Material Properties and Material Model

The values for the material properties were obtained from previous work on the Torre de la Vela conducted by Vuoto (2020).

The dynamic increase factors were calculated using Equation 36 through Equation 39 while assuming a strain rate of 100 s-1.

Model Validation

The validation of model created in Abaqus involved:

  • Checking the mass of the model against the model in AutoCAD,
  • Conducting an eigenvalue analysis to validate the model against the existing Diana model provided by Vuoto (2020),
  • A linear static analysis using the self-weight of the structure was performed to compare the mass of the model in Abaqus with the mass of the AutoCAD model obtained using hand calculations,
  • the linear static analysis also enabled the detection of any potential errors in the structural model.


1 – External Blast Loading

  • The loading scenario studied in this analysis corresponded to four barrels of black powder (around 110 kg TNT). This assumption is based on the number of barrels that could be transported at the same moment for storage.
  • The position of the explosives was selected based on the possible route of transportation from the outside of the building to the inside for storage purposes. Thus, the explosive was placed at 4 m from the entrance on Level 3, on the south side of the building.

The blast loading in this problem was defined as pressure profiles. The profiles acting on the surfaces were calculated based on the position and mass of the explosive.

2- Internal Blast Loading

  • The loading scenario in this analysis corresponded to a quarter barrel of black powder (6.8 kg TNT).
  • This explosive was placed in the North room on Level 2, close to the exterior wall. This location was assumed as an appropriate location for the storage of gunpowder, as the room is on the same level as one of the entrances.

The model of the Torre de la Vela was simplified to a single floor for the internal blast loading scenario to reduce the computation time of the analysis and because the damage is expected to be contained locally.

The location of the explosive in the North room of the building can be seen in red dot in Figure 65.


1- 16th and 17th Century Cannonballs

  • The loading scenario studied in this analysis corresponded to a cannon ball for the culverin cannon, found in sixteenth-century Spanish artillery.
  • The fourth level on the South façade was selected as the location where the impactor would strike. The size of the impactor is negligible compared to the thickness of the wall and, therefore, only the upper portion was modelled as a local response was expected.

Three different models were created: a continuum model with and without removal of damaged elements (Figure 80a), and a contact model (Figure 80b).

The impactor was modelled as a soft body, at an initial distance of 0.02 m from the wall to reduce computational time (Figure 80c).

  • The interaction between the impactor and the wall was defined by general contact, using hard contact as the normal behaviour contact property.
  • Separation was allowed after contact.
  • The translational velocity of the impactor was defined using a predefined field in the load module in Abaqus.
  • For the continuum element model, the mesh was refined around the location of impact.

Hypothetical Impactor

The impactor did not cause any damage to the model. For this reason, a hypothetical impactor was modelled to analyse how the continuum model using Abaqus feature involving the removal of damaged elements would behave under impact loading.


The structural analysis of the Torre de la Vela under blast loading was conducted for an exterior blast scenario and an interior blast scenario.

  • Initially, 110 kg of TNT was applied to the exterior entrance of the tower. Under these loading conditions, the building was determined to have suffered a small level of damage, according to the damage index based on the failure volume.
  • A simplified model of the South façade of the tower was created using contact elements to better understand the displacement occurring around the door opening, The displacements around the door using the contact model approach was very similar to those obtained in the whole building model. However, the stress and strain distributions on the façade varied between the contact model and the whole building model.
  • Another simplified model of the South façade of the tower was created using only continuum elements, with the removal of damaged elements feature in Abaqus activated. This resulted in a large portion of damaged elements being removed around the door opening, corresponding to the location where high levels of displacement were
    previously seen.
  • For the interior blast, only a single level of the Torre de la Vela was modelled. An explosive device of 6.8 kg of TNT was placed in an interior room of the tower. This analysis concluded that a total failure of an interior wall next to the position of the explosive device would occur. However, the remaining structural elements would have small or medium damage due to the blast. These findings led to further investigations of the single interior wall which failed under blast loading.
  • Initially, 110 kg of TNT was applied to the exterior entrance of the tower. Under these loading conditions, the building was determined to have suffered a small level of damage, according to the damage index based on the failure volume.
  • During the analysis of a single interior wall under blast loading, three methods of characterizing damage were assessed, and their mesh dependency was compared. For all methods, the models with a larger mesh size exhibited less damage than those with a more refined mesh.
  • The methods to characterize failure due to the displacement of the wall and failure due to the rotation of the support of the wall were both considered to be very meshdependent.
  • The damage index based on the failure volume was determined to be mesh- independent, based on the results obtained from applying blast loading on a single interior wall in the building. However, when using the damage index based on the failure volume, caution should be exercised as this method does not account for localized failure of structural elements, but rather the global behaviour of the structure.
  • The results using the Abaqus feature of removing elements when the damage exceeded a given threshold was compared to the results obtained from viewing the Concrete Tension Damage. Both methods resulted in very similar damage patterns, with the removal of damaged elements method indicating greater damage patterns.

A historical cannonball dating from the 16th and 17th centuries was modelled as an impactor on the Torre de la Vela. For this analysis, three models of a wall section of the tower were created:

  • A continuum model,
  • A continuum model with removal of damaged elements,
  • A contact model.

For all these models, no damage was caused by the impactor.

  • Differences in displacement between the continuum models and the contact model existed and were likely a result of the energy dissipation in the structure following impact.
  • To better understand the damage in the continuum model caused by an impactor, a larger hypothetical impactor was modelled. This resulted in localized damage on the surface of the wall, where the diameter of the damage was slightly greater than the diameter of the impactor, and the depth of the damage corresponded to the size of the mesh elements.


Some recommendations for future works on the numerical analysis of the Torre de la Vela under blast and impact loading:

  • The analysis of the structural response of the building subjected to internal blast loading should be done for the whole structure.
  • The global response of the whole structure subjected to both external and internal blast loading should be investigated using the removal of damaged elements.
  • A damage level threshold for rammed earth under compression should be investigated.