It is true that the strength of rock increases with the increase in confining pressure and will continue to do so. During multi-stage tri-axial testing, it is often observed that the rock sample is broken but due to the confinement the rock mass cannot move and hence, the broken rock start to take more load. The limit of confining is often restricted by the maximum confining pressure the compressor can provide and the design of hoek cell. When experimenting, it should also be kept in mind to prevent the sleeve from damage as it will otherwise contaminate the sample being tested. lowering the platens with gradual increase in confining pressure will ultimately lead to puncture of the sleeve as the rock (when retrieved) are often in powdered form. Hope this helps.

Thanks @Harshit Agrawal. This information is really helpful for me. You said the limitation of the compressor or hoek cell. This is the limitation of manmade machine. But what happens if it is possible to increase the confinement as per our desires. I would like to know what is the maximum strength of the rock under confinement. Is there any mathematical expression by which we can predict it?

Limitations in terms of machine capacities both Hoek cell and compressor. Apparently when you keep moving the ramp down to increase the load, the rock breaks and its not the strength of rock that you measure, as the rock is already crushed.

For the 3D stress state, the tensile strength is determined at different stress ratios. GENERALIZED COMPRESSION, GENERALIZED EXTENSION, GENERALIZED SHEAR. Study the LODE-NADAI criterion -

the limit of triaxial strength is presented as the functions from the main tensions σ1, σ3 and from the Lode-Nadai μσ parameter