Shear modulus, minerals

Another commonly used equation is the Hirsch predictive equation (Christensen et al. 2003). In this case, the dynamic modulus is determined with respect to voids in the mineral aggregate, voids filled with binder and dynamic shear modulus of bitumen. The equation developed is as follows ... 

A more simplified predictive model has been developed by Al-Khateeb et al. (2006), which, for the determination of dynamic modulus, uses only two parameters the voids in the mineral aggregate and the dynamic shear modulus of the binder. As concluded, the model is capable of predicting the dynamic modulus of an asphalt concrete at a broader range of temperatures and loading frequencies than the Hirsch model. It also has the advantage of estimating the dynamic modulus of an asphalt concrete with modified bitumen (Al-Khateeb et al. 2006). The mathematical formulation of the model developed is as follows ... 

Figure 21.6. Djmamic shear modulus G ) vs. frequency (u>) of untreated and grafted silica nanoparticles in mineral oil at 30°C...

Most seismological constraints on mantle composition are derived by comparison of values of seismic wave velocities inferred for particular regions within the Earth to the values measured in the laboratory for particular minerals or mineral assemblages, with such comparisons being made under comparable regimes of pressure (P) and temperature (T). The primary parameters of interest, then, are the compressional (or P-) wave velocities (Vp) and the shear (or S-) wave velocities (Ej). These wave velocities are simply related to the density (p) and to the two isotropic elastic moduli, the adiabatic bulk modulus (Ks)... 

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