Visco-elasticity can lead to strain-rate dependent apparent modulus change. Is this fully explaining the observations that the modulus is a function of strain-rate in rock dynamics? Are there other physical mechnisms that might lead to this?
Or a somehow related question, does strain-rate dependent modulus lead to strain-rate dependent elastic energy? I understand that this is not the case if viscoelasticity is the only mechnism for such dependency.
Thanks!
In oil & gas prospection and petrophysics, I guess this is not the case, Dr. Niu Zihua
Please, here there is one reference: Rocks are very important for oil & gas
Article An experimental investigation of dynamic elastic moduli and ...
Hi Niu Zihua , with your question you are opening a can of worms. You ask specifically about strain-rate dependence of elastic moduli of rocks.
In rocks, you have another mechanism that will create an apparent strain-rate dependence of observed moduli, given by poro-elasticity. In a poro-elastic medium, e.g., a rock filled with a fluid, at low strain rates the fluid inside the pore space can flow as a the rock is deformed, whereas at high strain rates (and low permeability of the rock) the pore fluids can not flow as the rock is deformed and pore pressure cannot equilibrate. You can see how this would lead to a different BULK elastic behaviour of the rock, depending on strain rate.
Additionally, you can have a strain-magnitude dependence of elastic moduli, i.e. a non-linear elastic medium. Since measurements of elastic moduli via high-frequency (Hz to kHz) elastic waves typically have much smaller strain magnitudes than measurements of elastic moduli measured under quasi-static deformation, non-linear elasticity may also manifest in a similar manner visco-elasticity (i.e., showing a strain-rate dependence of elastic moduli).
Lastly, there are researchers who state that for most experiments under quasi-static conditions, the strain magnitudes are such that non-elastic deformation occurs (e.g., by breaking of grain-to-grain bounds without complete failure of the rock). This behaviour would be well described by a visco-elastic model.
On question I would have for you, is why you care about the question you pose? In applied geosciences there are many "engineering" solutions, such as application of a dynamic-to-static modulus correlation to account for the effect that dynamic moduli are often larger than static moduli, without understanding the exact mechanism why this is the case.
Good luck with your research in a very interesting (and complex) question!
Jorg
Dear Jorg Herwanger ,
Thanks for your very extensive answers to my question! I asked this question because I am seeking an explanation to the recent observation in the field of "non-classical nonlinear elasticity", or more specifically the so called "slow dynamics". The modulus/wave velocity reaches a new stationary value under cyclic dynamic perturbations. And the new stationary value seems to be rate/frequency dependent.
Such observation is, to my understanding, cannot be explained by viscoelasticity. But if the elastic modulus itself is a function of strain-rate, or, from thermodynamic point of view, the internal energy of rocks has some rate-dependency, such rate-dependent "slow dynamic" behavior might be explained.
Thanks,
Zihua
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