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There is a wealth of experimental evidence that, in a wide variety ofnatural stones, repetition of uniaxial compression loading cycles produces aprogressive permanent contraction εv in the load direction, which represents asignificant indicator of damage progress. Self-similarity arguments are applied toanalyze possible forms for kinetic equations of fatigue-damage evolution, correlatingfor fixed test parameters (frequency, temperature, load intervals etc.) the damageindicator “εv” with the number “n” of damaging actions, i.e. each complete loading-unloading cycle. Two distinct phases are predicted by simply using dimensionalanalysis arguments, provided that “n” is considered a dimensional parameter andfurther invariance with respect to supplementary groups of similarity transformations isassumed. The first phase is indicated by a pseudo-linear dependence of εv upon thelogarithm of n. The second phase, prior to failure, is instead characterized by a power-law relationship εv vs. n. These two phases of the material behavior have distinctpeculiarities at both the mesoscopic and microscopic level. Interpolating curvesobtained from these deductions are in excellent agreement with experimental results.