Dear Mr . Goswami,

you could drill a hole in your core sample, insert something like a thin water pipeline and increase the water pressure until your specimen fails. Additionally you need to seal the opening of the pipeline. It's like a small borehole packer test.

You could combine this technique with an oedometer or triaxial cell.

Or you could frac a block sample with a cylindrical hole if you are able to take such a specimen.

Best Regards

Hi Goswami

See the following, It can perhaps help you.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.622.8345&rep=rep1&type=pdf

Thank you 

Dear Mr . Goswami,

this publication could be very interesting for the solution of your question:

Wang, H., Xu, W., Jia, C., Cai, M., and Meng, Q. (2016). "Experimental Research on Permeability Evolution with Microcrack Development in Sandstone under Different Fluid Pressures." J. Geotech. Geoenviron. Eng., 10.1061/(ASCE)GT.1943-5606.0001462