## 1 Introduction
\[T=2\pi\sqrt{\frac{m}{k}} \tag{1}\]  
Lateral stiffness (\(k\)) is known to depend on geometric parameters, such as the dimensions or second moment of area (\(I\)) of the section of the resisting elements and the elastic modulus of the materials used in structural elements [14]. Therefore, when the total mass is known, from the natural period, structural stiffness can be directly linked with E and thus the material defined unequivocally. Analytical procedures exist that estimate the value of the fundamental period of a masonry structure using a specific formula for each structural type [15]. These formulae usually imply testing structures against dynamic loads such as earthquakes. They have been developed from empirical studies and represent an easy way of approximating the fundamental period according to existing data. This method is particularly useful when simplified seismic calculation procedures are applied, because, when the period of the vibration mode considered is lower than the maximum period that marks the plateau of the elastic response spectrum, a more refined estimate is no longer necessary, as the spectral ordinate is independent in simplified methods. This empirical value is included in national seismic regulations. However, despite the widespread use of this type of structure across the world, only Spain, France, Dominican Republic, Cuba, Peru, Romania and Albania include a specific formula in their building codes to calculate the fundamental period (IAEE, 2004) of most masonry wall constructions and which attempts to condense different structural configurations into a single expression adapted to each territory's individual conditions and construction methods. The formula varies from one set of regulations to another, i.e., from one country to another. Equation (2) shows the formula used in Spain (code for seismic design (NCSE, 2002)) and France (code de l'environnement), where \(T_{F}\) corresponds to the natural period, \(H\) is the height of the wall, and \(L\) is its length:  
\[T_{F}=\ \frac{0.06H\sqrt{\frac{H}{2L+H}}}{\sqrt{L}} \tag{2}\]  
In its attempt to afford generalisation, given the \(H\) and \(L\) variables used and the fact that it is an empirical formula, the range of results obtained may vary and disperse greatly from real values. These differences are more significant in historical masonry structures that have special or unique properties and characteristics or structural configurations. One must also remember that the main purpose of seismic standards is to calculate new construction structures and therefore the range of application differs significantly from the assessment of historical masonry. Consequently, applying this simple procedure may be somewhat inaccurate as a way of validating structural behaviour, especially due to the uncertainties raised by the type of construction materials used and the state of preservation. Therefore, given the complexity involved in ascertaining the mechanical properties of such structures in a deterministic way, probabilistic methods are called for, based on measuring a representative sample of the main existing typology and adjusting simplified empirical formulae to estimate the natural period of a building easily using basic data, such as its height or the number of storeys. In order to reduce the uncertainty and dispersion of results that can occur when adjusting the results of analytical procedures, several tests have been developed to provide information on the mechanical properties of masonry. Some of these are destructive testing (DT) or minor destructive testing (MDT), which can be performed both on site [16; 17] and in the lab [18]. These destructive tests, such as the diagonal compression test, drilling by Gucci penetrometer (PNT-G), single and double flat jack tests or twin panel testing (TPT), provide real data about compressive strength, elastic limit and ultimate strength.