Weak electric signals termed as "Pressure Stimulated Currents, PSC" are generated and detected while cement based materials are found under mechanical load, related to the creation of cracks and the consequent evolution of cracks' network in the bulk of the specimen. During the experiment a set of cement mortar beams of rectangular cross-section were subjected to Three-Point Bending (3PB). For each one of the specimens an abrupt mechanical load step was applied, increased from the low load level (Lo) to a high final value (Lh), where Lh was different for each specimen and it was maintained constant for long time. The temporal behavior of the recorded PSC show that during the load increase a spike-like PSC emission was recorded and consequently a relaxation of the PSC, after reaching its final value, follows. The relaxation process of the PSC was studied using non-extensive statistical physics (NESP) based on Tsallis entropy equation. The behavior of the Tsallis q parameter was studied in relaxation PSCs in order to investigate its potential use as an index for monitoring the crack evolution process with a potential use in non-destructive laboratory testing of cement-based specimens of unknown internal damage level. The dependence of the q-parameter on the Lh (when Lh < 0.8Lf), where Lf represents the 3PB strength of the specimen, shows an increase on the q value when the specimens are subjected to gradually higher bending loadings and reaches a maximum value close to 1.4 when the applied Lh becomes higher than 0.8Lf. While the applied Lh becomes higher than 0.9Lf the value of the q-parameter gradually decreases. This analysis of the experimental data manifests that the value of the entropic index q obtains a characteristic decrease while reaching the ultimate strength of the specimen, and thus could be used as a forerunner of the expected failure.