On the Poroelastic Biot Coefficient for a Granitic Rock

Round 1

Reviewer 1 Report

The ms. has many shortcomings, most of which can be addressed with a more complete discussion. The attached file contains a list of suggestions for improvement; those marked with * are the most critical.

Comments for author File: Comments.pdf

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 2 Report

The paper deals with the experimental determination of the poroelastic Biot coefficients for a granitic rock
(Lac du Bonnet granite).
The article is very well presented, the approach is rigourous and detailed.  
This article complements and and enhances the former works of very high scientific qualities of the Author.
Let us also emphasize the very instructive aspect of the article.
The article can be published as presented. 
There are however a few typos problems in the paper (in certain formulas, the characters are superposed).

I would nevertheless like to start a discussion with the author. This discussion is not intended to be
be inserted in the article. 
The questions I have are the followings:
-1)The isotropy and the homogeneity are hypotheses often made in geomechanics or mechanics. 
The author is well aware of this fact.The Biot coefficient is in this context a scalar.
If we are dealing with a strongly anisotropic materials, the Biot coefficient would have to be
a tensor ? no ?

-2) The Biot coefficient " reflects/define-by " a ratio between the bulk modulus of the porous structure/matrix and 
the bulk modulus of the  "pure"  solid constituting the rock matrix. 
If the bulk modulus of the solid (rock) is a function of the mineralogical 
composition (and its history at the geological scale), the bulk modulus of the porous matrix is also a function of the porosity. 
In general, the porosity is determined on a rock free of any mechanical stress (stress free). 
If the porous rock sample undergoes a loading, the porosity evolves and is therefore not
constant, which should be the case of the Biot coefficient ?
In other terms, even in poroelasticity (and finite deformation to introduce non-linearity) or in poro-plasticity,
the Biot coefficient would therefore not be constant and should be a 
function of the volume deformation eps_v alpha=alpha(eps_v) ?

-3)Suppose that the rock specimen has a porosity p=Vv/V. 
Vv is the TOTAL volume of ALL pores and V the volume of the specimen.
For a total volume of all pores Vv (volume of the voids) we can theorically determine an infinitly number of volume, 
shapes and distribution of single pore Vv_i: 
Vv=SUM_i (Vv_i)=SUM_i(Volume_Pore_i)
The number, space distribution, volume and shape of the pores will contribute substantially to the mechanical behavior 
of the porous matrix. 
For example, for two different porosity distributions, having the same value of TOTAL void volume at the Darcy scale, 
the bulk modulus of the matrix would be different?

-4) This leads to the question, raised and discussed by the author, not only of the relevant RVE 
but of the characteristics (features) at the micro-scale. 
The "Biot" formalism is at Darcy-scale (an "average" of the components at the micro scale).
It seems to the reviewer that from a mathematical point of view one can pose the 
hydro-mechanical problem at the micro scale (one or more pores)
and explicitly formulate the fluid (Navier-Stokes)/structure (solid) interaction. 
An upscaling would allow to have an explicit formulation of the Biot coefficient at the Darcy scale ? 

I would like to have the author's enlightened opinion on these few points, based on his undeniable expertise in 
this topics.

 

Author Response

Please see the attachment

Author Response File: Author Response.docx