It is a matter of habit. Some researchers use specific volume (v) instead of void ratio (e). E.g. Atkinson prefers specific volume whereas Jefferies and Been use void ratio.

In my opinion there is no difference apart from that one should be careful when applying constants characterising the configuration of NCL or CSL (i.e. the gradient and the value of v or e at p'=1kPa). These constants should conform the formulation of the model of a soil in which they are used. And the numeric values would be different dependent on the formulation.

Depend on how you understand it. It does not matter so much. the important thing is the result trend and not the magnitude, Magnitude can be refine later.

both can be used , it doesn't affect. however, the use of the specific volume is more common.

In a natural soil, the various elements (air, water, grains) are arranged in a dispersed order and according to an arrangement related to both the conditions and the subsequent history undergone. We will distinguish:

** the volumes occupied by each component respectively Vs for grains, Vw for water, Go for air with

V = Vs + Vw + Va the total volume and Vv = Vw + Va void volume;

** the masses of grains ms, water mw (the mass of air is zero: weighed in the air);

** the weights of ps grains and water pw.

Given that the aim of the CSSM is to explain the soil behaviour, using specific volume gives you a direct correlation to volumetric strain. Unfortunately, tradition means that specific volume (a direct correlation with water content) is more well known and widelly used. Using e or v will yield the same result and the comment made by Krzysztof Sternik reagrding parameters is important.

Void ratio can theoretically become zero (when the volume of voids become zero), while specific volume is always >=1 - for certain calculations it can be an advantage with a property than cannot be zero and therefore specific volume could be more convenient.

The reason is the one described by Pedro Miguel Vaz Ferreira above. The specific volume is linked to total volumes and definition of volumetric strain is then straightforward. No effect on the CSSM parameters, other than that

Sometimes e=0, no void space and specific volume is always >=1, so it is recommended to use specific ratio than e... I think

In Physics any specific property is defined when we divide one property by another one, for example, the specific volume can be defined as the volume (V) occupied by a specific substance divided by its mass (m), which is equal to the inverse of the density. Another example of a specific property is density, also many times known as specific mass (mass per unit volume). The void ratio is the ratio of the volume of pores to the volume of solids. If you replace this definition in the equation v=1+e, you will also have a reason between two properties (volumes), i.e., the ratio between the total volume and the volume of solids. Thus, observe that there is difference between the definition of specific volume and the result of 1+e!