**1. Introduction**

Acoustic emission (AE) is a method that has been used for a very long time in concrete engineering [1]. Acoustic emission measurements can be applied to recognize the early hydration of cement [2,3]. Most papers have focused on determining the destruction process (cracks, maximum load, and failure of reinforcement in cement composites) [4–40]. It was noticed that AE is an effective method in determining the critical stress fcr of cement composites corresponding to the first crack [4–6]. It is used for the accurate definition of the elastic range corresponding to Hooke's law [7,8]. The continuous AE evaluation in composites and acoustic emission AE events sum (sum AE) has been applied to determine the first crack [4,9,10], micro and macro-cracks, and their propagation in the fracture process in cement composites with [11,12] and without reinforcement [13,14].

The test results indicate that AE is a good method for crack formation monitoring in mechanically loaded traditional [15,16] and high strength [17,18] cement composites. It was demonstrated that this method is effective during compression [19,20] and bending tests [21,22].

Acoustic emission measurements also focus on the possibility of identifying crack orientation [23–25] q, thus enabling the recognition of cracks occurring as a result of compression, tensile, and shear stress.

AE is used to identify the destruction process of different materials (e.g., reinforced geopolymer mortars) [26]. The effectiveness of acoustic emission measurements in structures control was confirmed [27–29]. This method is used for example to monitor and control bridges condition [30,31]. The AE is still improved for the purpose of the identification of failure processes in different materials and structures [32–34].

Our previous own works have focused on the correlation between AE and the individual failure processes of each of the different composite components based on the sound spectrum [7,35,36]. The conclusions indicate that for the accurate recognition of composite failure processes, the AE recording should be expanded to include the analysis of each sound separately (also a single signal in a very small range of frequencies) and the analysis of the range of sounds corresponding to a given mechanical effect with the use of acoustic spectrum. It was noticed that the acoustic spectrum 2D and 3D should be correlated with the load-deflection curve and with other acoustic effects, which enables the identification of the failure process.

The presented paper confirms that there is a possibility of correlation between AE and the failure process in quasi-brittle cement composites. This correlation enables a determination of the stage of damage in cement composites, increasing the safety of using the composite and a decision whether or not the damaged composite can be repaired.

The main innovation of this research is the possibility of identifying AE micro events in the area preceding the occurrence of critical crack initiating the destruction process in cement composites. The main idea in this paper is the possibility of micro event recognition in the Hooke's law range, which enables the prediction of the destruction process.

The paper presents the results of our own studies on a selected paste sample in a four-point bending tensile test conducted at IPPT PAN in Warsaw, taking into consideration the current recommendations [37–41].

The results of tests carried out on a number of cement composites (cement paste, mortar, concrete, with and without dispersed reinforcement [40]) confirmed the general conclusions presented in the paper, indicating the possibility of their generalization.
