Correlation between Shear Wave Velocity and Porosity in Porous Solids and Rocks

The shear wave velocity dependence on porosity was modelled using percolation theory model for the shear modulus porosity dependence. The obtained model is not a power law dependence (no simple scaling with porosity), but a more complex equation. Control parameters of this equation are shear wave velocity of bulk solid, percolation threshold of the material and the characteristic power law exponent for shear modulus porosity dependence. This model is suitable for all porous materials, mortars and porous rocks filled with liquid or gas. In the case of pores filled with gas the model can be further simplified: The term for the ratio of the gas density to the density of solid material can be omitted in the denominator (the ratio is usually in the range of (10？4, 10？3) for all solids). This simplified equation was then tested on the experimental data set for porous ZnO filled with air. Due to lack of reasonable data the scientists are encouraged to test the validity of proposed model using their experimental data. 1. Introduction The porous materials are usually prepared by various powder metallurgy methods from powders, which composition, particle size, and shape can vary significantly. During the powder consolidation different porosity can be achieved by varying of the technological parameters: such as temperature, external pressure, or time. Compacting starts from just touching powder particles and goes to the lower porosity by the creation and growth of the necks between particles. The subsequent closure of the pore channels leads to the elimination of the pores. Three various porosity ranges can be usually identified, for example, for sintered iron the following porosity ranges can be observed ([1] and references therein):(i)porosity <3%: fully isolated pores of nearly spherical or elliptical shape,(ii)porosity >20%: fully interconnected pores of complex shape, and(iii) porosity between 3% and 20%: both isolated and interconnected pores are present in various amounts. This indicates that the powder consolidation is in general a connectivity problem, which is studied by the percolation theory [2]. According to the percolation theory a critical volume fraction exists, called a percolation threshold, at which a solid phase forms a continual network spanning across the whole system. Below this threshold it is just a pile of powders or mud of powders mixed with liquid. At and above the percolation threshold the geometrical, physical, and mechanical properties of the system behave in the form of the power law dependence for , where is the porosity within the