# Detecting Criticality by Exploring the Acoustic Activity in Terms of the \"Natural-Time\" Concept
## 3 Analysis of the Acoustic Activity by Means of the \(F\)-Function in the Natural Time Domain
### Shear of Mutually Interconnected Marble Blocks  
In this section data obtained from a structural experimental protocol during which complex structures consisting of two blocks of Dionysos marble, mutually interconnected by means of an \"1\" shaped titanium connector, were subjected to pure shear. The titanium connector is placed in grooves carved onto the marble blocks and is then completely covered with cementitious material (Figure 11a). A detailed description of the geometry of the structures (specimens) is given by [PERSON] et al. [46]. The loading scheme intended to impose a system of forces on one of the two blocks so that it moves parallel to the other (rigidly clamped) block in order for the \"1\" connector to be under pure shear. Displacement-control loading mode was adopted at a constant rate equal to 0.2 mm/min. Eight sensors were used for detecting and recording the AE data. For the typical test studied here, catastrophic fracture (of the moving block) occurred when the force applied attained a maximum value of 27.5 kN. During the whole loading process \(N=1092\) acoustic events were recorded. The temporal evolution of their amplitude is shown in Figure 11b, together with the respective evolution of the load imposed.  
For the calculation of the \(F\)-function \(n=30\) consecutive interevent time intervals were used. The evolution of the \(F\)-function in terms of conventional time is shown in Figure 12a, again, together with the evolution of the load applied. The sharp increase of the \(F\)-function is detected at the instant with \(\tau\approx 860\) s when the load attained a value of 27.2 kN, i.e., at about 99% of the respective maximum value reached during this experiment. In the previous time interval, i.e., for \(\tau<860\) s, the \(F\)-function exhibits progressively increasing values with a series of local peaks, which are attributed to locally intense acoustic activity due to the formation of many microcracks at the interface between the titanium connector and the cementitious material and to friction between the two marble blocks and, also, between the marble blocks and the cementitious material.  
Figure 10: The evolution in the Natural Time domain of the \(F\)-function and of the load imposed for the CSR marble specimen.  
Figure 11: (a) Sketch of the mutually interconnected marble blocks. The red arrows indicate the direction of the imposed force. (b) The temporal evolution of the amplitudes of the acoustic events recorded in juxtaposition to the force imposed.  
Figure 12: (a) The temporal evolution of the \(F\)-function and the load imposed. (b) The respective evolution in the Natural Time domain for the mutually interconnected marble blocks under shear.  
The evolution of the \(F\)-function in the Natural Time domain is shown in Figure 12b in juxtaposition to the respective one of the imposed loads (also, in Natural Time terms). The existence of a power law governing the evolution of the \(F(\chi)\) function is now observed when the applied load approaches its maximum value, and the catastrophic fracture is impending. The validity of the power law lasts from \(\chi=0.91\) until \(\chi=0.97\). By proper fitting, the exponent \(m\) for the specific experiment was found equal to 21.5. This high value is well explained by the fact that a great number of acoustic events are produced in a quite short period of time, for the reasons mentioned above.