The influence of the stress state type and scale factor on the relationship between the acoustic quality factor and the residual strength of gypsum rocks in fatigue tests

• Rock residual strength σrσr and quality factor Q are connected with each other.
• In compressive stress state σr(Q)σr(Q) can be approximated by a logarithmic function.
• In tensile stress state σr(Q)σr(Q) can be approximated by an exponential function.
• The scale factor does not affect the relationship σr(Q)σr(Q) in rock under uniaxial tension.
• The scale factor does affect the relationship σr(Q)σr(Q) in rock under uniaxial compression.

The purpose of this study is to establish the influence of the stress state type and the sample sizes on the interrelationship between the acoustic quality factor Q   and residual strength σrσr in the gypsum-containing rock of the Novomoskovskoye deposit (Russia) in mechanical fatigue tests. The aforementioned relationship for residual strength under uniaxial compression can be approximated to satisfactory accuracy by a logarithmic function and for the residual tensile strength by an exponential function. Cylindrical samples with a diameter of ∅∅30 and ∅∅80 mm and aspect ratio 1:2 during compression, and with a ratio of height to diameter equal to 1 in tension were tested. For these dimensions, the size effect does not influence the interdependency σr(Q)σr(Q) under uniaxial tension, but does have an influence under uniaxial compression.