Research On The Elastic Constitutive Model And Wave Propagation Properties Of Rocks With Distributed Fractures

In this paper, a new heterogeneous anisotropic constitutive model of fractured media was presented, and the properties of elastic waves excited from a two-dimensional (2D) point source propagation in 2D fractured rocks were investigated by the pseudo-spectral method (PSM). The main work and achievements are summarized as follow:Hudson's crack model and Liu's fracture model were introduced. The anisotropic properties of rocks with dry and water-filled parallel fractures were discussed.The PSM was extended to heterogeneous anisotropic medium and a program for 2D elastic waves propagation was written in Fortran. The stable condition of PSM for 2D anisotropic media was introduced and discussed.The propagations of elastic waves, excited by point sources in homogeneous isotropic/anisotropic rocks, were simulated. The effects of parallel aligned opening or water-filled fractures on waves propagation were investigated. The results shows that: 1) the existence of anisotropic properties of fractured rocks leads to waves conversion and the wave fronts become wider. 2) the effects on waves conversion are stronger in rocks with dry fractures than that in rocks with water-filled fractures, and S-waves attenuate more rapidly in rocks with water-filled fractures. 3) the explosive point source which locates in anisotropic media can excites not only P-waves but also S-waves. 4) the properties of waves propagation were discussed and compared for several point sources with different source functions.The effects of different geometric interfaces on waves propagation in anisotropic rocks were simulated. Three structures, including the corner structure, the straight structure and the multi-stripe structure, were discussed. The results show that: 1) the effects of interface on waves scattering are stronger in the structure with the interface perpendicular to the direction of fracture normal than that in the structure with the interface parallel to the direction of fracture normal. 2) when the interface is perpendicular to the direction of fracture normal, the amplitude of reflected waves and converted S-waves are higher and there are the sub-P- and sub-S-wave.3) When the elastic waves propagating in the multi-stripe model, wavesforms become complex due to multiple scattering on interfaces.To model the elastic properties of rocks with distribution fractures, a new heterogeneous anisotropic constitutive model was presented. In this model, the autocorrelation function is used to describe the spatial distribution of crack number density. The macro-mechanicalproperties (the elastic constants) of the fractured rocks can be connected with the micro-parameter of crack (crack number density). As examples, heterogeneous anisotropic fractured rocks of which the autocorrelation functions of crack number density can be described as 2-dimensional exponential ellipsoidal or Gaussian function were simulated especially. The results show that: 1) the random distribution characters could be different for different elastic constants under the same random distribution of crack number density. 2) the exponential ellipsoidal heterogeneous anisotropic random fractured model could be a suitable model for the multi-scaled and self-similar heterogeneous media. 3) on the other hand, the Gaussian heterogeneous anisotropic random fractured model might be a suitable model for the single-scaled and smooth heterogeneous media.The propagation of elastic waves, excited by an explosive point source in exponential ellipsoidal and Gaussian heterogeneous anisotropic random fractured rocks, were simulated. The effects of heterogeneous anisotropic random fractured rocks with different autocorrelation length and different autocorrelation function were discussed. The results show that: l)the scattering effects become weaker when the autocorrelation length becomes larger. 2) the exponential ellipsoidal random fractured rock has different scattering effects on waves in different coordinates direction, and 3).the Gaussian random fractured rocks has the same...