[S-CG44] Rheology, fracture and friction in Earth and planetary sciences

[SCG44-P13] Time Response - material Uniformity - informativeness in Fracture phenomena

*Mitsuhiro Hirano¹, Hiroyuki Nagahama¹ (1.tohoku university)

Keywords:Fracture, Earthquake, Power law

Fracture phenomena have various power laws associated with their time response, material uniformity, and informativeness. Viscoelastic behavior with damage evolution (temporal power law in Secant modulus) is equivalent to an input-output relationship with a scaling law, which is accompanied by temporal fractal (power law of time and relaxation time). The shape parameter of the Weibull distribution, which is a probability distribution of fracture strength indicates the uniformity of the material and is also related to the b-value of the Gutenberg-Richter relation, which reflects the heterogeneity of the medium. Furthermore, the relaxation time distributions of the input-output relationship and the Gutenberg-Richter relation have been reconsidered from a probability distribution (q-exponential distribution family), where the information density for the probability parameter varies with the real number q. However, the connection between time response, uniformity in the material, and informativeness with respect to fracture phenomena has been unclear. In this presentation, based on the theoretical relationships for exponents of the power law reported in previous studies, we construct the relationship equations for exponents related to time response, material uniformity, and informativeness and discuss their relationship. Based on the obtained relational equations, the shape parameter of the Weibull distribution as the material uniformity decreases as the exponent for time response increases. This suggests that the scaling law of the input-output relationship reflects the hierarchical composition in the material. On the other hand, as the real number (q) related to information density for probability parameters increases, the exponent for the time response decreases, and the shape parameter of the Weibull distribution as the uniformity of the material increases. This implies that the information density for the probability parameter reflects the manifestation of the probability parameter in the relaxation time distribution, depending on the uniformity (non-hierarchy) of the material. Through the obtained relational equation, the range of possible values for the exponent of the time response, the shape parameter of the Weibull distribution as the uniformity of the material, and the real number (q) determining the information density of the probability parameter is generally harmonic, but we consider that the material chemical background and the need for correction should be discussed. Furthermore, the b value of the Gutenberg-Richter rule and the real number (q) that determines the information density of the probability parameter, which have been reported in previous studies, are also discussed in combination with this presentation.