Hi Ehtesham,

Like Jean Louis said, the solution is formulated for isotropic homogeneous rocks, so a highly fractured rock wouldn't match these conditions.

However, depending on the accuracy level you want to put in your calculation, you still can use it. For example, in a very simplified manner, I would use the Hoek Brown criterion (you can use RocData, which is free and very easy to use) to homogeneize the rock and get a equivalent young modulus (called Em), and use it in the kirsh solution.

Try to take a look at chapters 7.4 and 7.5 of Goodman's book (Introduction to Rock Mechanics), it will help you for sure.

Cheers

Thank you guys for your comments. I have viewed few publications that use these equations to define the stress state in fractured rock mass which was a bit confusing for me. Thank you for the references, they will surely help me.

Cheers

Hi Ehtesham,

As said before homogeneous isotropic linear elastic behavior (= HOOKE's law) is supposed by KIRSCH. Nevertheless you can get a first idea about the stress distribution around a circular hole (= tunnel or shaft) in JRM. The stress distribution is independent of E and nue. But if you want to guess the displacements at the surface of the circular hole, you have to take the deformation modulus of the JRM (not the modulus of elasticity, which might be different) and a rather low Poissons ratio. If the primary state of stress is such that it leads to pure compressive stress pathes in the secondary state of stress, the estimation is not to bad.

KIRSCH's equations were extended bei KASTNER (1971) who introduced a zone of plasticity. This can improve the simple analytical solution. It is always good to verify the results of numerical simulations.

Cheers

Thomas

Like others have said, the Kirsch equations are really only for isotropic media and a circular opening. Once the well bore wall is fractured, the equations break down. It is for these reasons that breakout width is not a reliable indicator for estimating SHmax magnitude. Similarly, the Kirsch equations are only useful for estimating fracture initiation pressures, and not what happens afterwards.

I really would not use the Kirsch equations for fractured media. There are too many other variations in stress that occur around fractures in elastic media, these will result in the Kirsch equations not giving any sort of useful estimate for stress disturbance around a borehole in fractured rock.

Thanks Thomas and Mark, your answers are really helpful