Dear Hachimi,

According to me, the value of Cs is always 0.2 to 0.3 times of Cc for natural clay soils based on the Modified Cam Clay model. 

Please refer B M Das textbook for further clarification.

Thank you.  

Usually Cc is grater than Cs. Since the soil in your case  has a critical swelling potential (liquidity limit estimated at 141%, the result may be different. However, confirm the results by at least three or more trials.

I have not encounter with this type of soil in which Cs is higher than Cc.

It looks very strange for me, however you should consider the mineralogy of that special soil.

To answer this question, just to analyze the mechanisms behind the virgin compression line and swell line.

During consolidation test(i.e., the loading process), the load acting on the soil sample will gradually increase. As a result, we will get a smooth consolidation curve, and the straight-line portion is the virgin compression line. However, for the virgin compression line, it should be noted that both plastic strain and elastic strain occurred during the consolidation test.

Correspondingly, if we stop increasing the load acting on the soil and gradually release the load (i.e., the unloading process). The permanent deformation cannot be recovered (because it is a type of plastic strain). However, the elastic component will be recovered. Hence, we get the swelling line, and swelling line will be different from the virgin compression line. At same time, the recovered deformation will be less than that developed during loading process. Therefore, the swelling line will be flatter than virgin compression line. Corresponding, Cs (negative slope of swelling line) will be less than the Cc (negative slope of virgin compression line).

I think the initial sttelements that you have recorded and calculated your Cs from them might be due to the movements of your porous stone or you might have not proper contact between your soil and the loading plate.

The other reason might be that you are dealing with a collapsible soil and you have a lot of immediate settlements.

Overall, the swelling index cannot be higher than the compression index, if that happens this means your soil would recover more stains than it experienced which is physically impossible.

I think you'd better repeat the test and make sure your setup is perfect, then calculate the Cs from the unloading portion of your e-logp plot.

I think the best comment on this just as explained by the previous comment.

I would have to agree with Liang Cui and Mohammad Shahsavari above.

A more reliable determination would be to perform a reload loop after unloading. Alternatively, the unload portion can be used as this is the actual swelling phase, as opposed to the reload phase which has been analysed here.

It is possible that the soil has undergone disturbance leading to volumetric increase, and that the initial loading deformation is due to this rather than any in situ behaviour.

Looking back at this today - is there a possibility of lack of contact between the sample and platen at the beginning of the test? Leading to a jump in displacement which is really just a closing of a gap during the initial load stage rather than soil behaviour.