## 1 Introduction  
A broad variety of experimental techniques has been developed during the last years in order to collect experimental data that could be valuable in the direction of getting deeper insight into the damage mechanisms, which are activated while cementitious building materials are loaded at levels that approach the critical ones, namely, the loads that cause fracture. Among these techniques, the one based on the study of the acoustic emissions (AE) is the technique most broadly used worldwide [1; 2]. The AE technique is nowadays the most firmly founded structural health monitoring tool concerning its natural principles. It permits real time monitoring of damage evolution within the mass of loaded materials and structures by detecting the acoustic signals that are emitted as a result of the activation of various mechanisms (like micro-cracking), which release mechanical energy in the form of elastic waves. Among the simplest parameters, used to study the acoustic activity, is the number of the acoustic signals (either cumulative or not), which are detected and recorded (hits per second). This is a time-dependent function, since micro-cracking becomes gradually more intense as the externally applied load increases approaching the load that will cause macroscopic fracture of the specimen or the structure [3; 4; 5; 6]. In this study, the temporal evolution of the acoustic activity is analyzed with the aid of a recently introduced alternative approach, which is based on the F-function [7; 8]. Compared to the traditional method of studying the acoustic activity (namely, using directly the \"number-of-hits-per-second\"), the F-function is proven advantageous since it enlightens with finer resolution the temporal evolution of the acoustic activity, especially during the very last loading steps before macroscopic fracture. In order for the F-function to be determined and plotted, advantage is taken of the interevent time intervals (\(\xi\tau_{i}\)) of a sufficient number n of successive acoustic hits or events. Any specific value of the F-function is the inverse of the average value of the n interevent time intervals. The next value of the F-function is calculated by \"sliding\" the \"window\" of the n acoustic signals by one acoustic signal. It can be said, thus, that the F-function represents the average frequency of generation of acoustic hits (or events) from the onset of the loading procedure until the fracture instant. The values of the F-function are \"paired\" to an average time instant, which is calculated as the mean value (\(\tau\)) of the time instants at which each one of the n members of the specific \"window\" were generated (detected). Concerning the numerical value of the parameter n, its choice is, more or less, empirical and depends, mainly, on the overall number N of hits (or events) recorded during the overall duration of the experiment. Usually, n varies between 2% and 10% of N. The study of the acoustic activity by means of the F-function has been already adopted by many researchers worldwide (see indicatively refs. [9; 10; 11; 12]). Very recently the evolution of the F-function was considered in the domain of the Natural Time, \(\chi\)[13] (instead of the conventional time domain, t), taking advantage of experimental data obtained from a protocol with marble specimens of various geometries subjected to various loading schemes. The concept of Natural Time (NT) was introduced in 2001 by [PERSON] et al. [14; 15], who suggested that analyzing time series in the NT domain permits the study of the dynamic evolution of complex systems offering valuable insight concerning the proximity to the critical stage, i.e., the stage of impending catastrophic events [16; 17].