Hi Abolfazl,

Regarding your question, I can say that scale dependency is an important and well-known issue in rock engineering.

Indeed, in the design of large excavations (both on the surface or underground) in jointed rocks, ignoring scale dependency may results in catastrophes.

Please check the following references:

"Practical rock engineering" by Prof. Evert Hoek, https://www.rocscience.com/learning/hoek-s-corner/books

and

"Ground behaviour and rock mass composition in underground excavations" by Dr Arild Palmstrom. You may find a free version of the article here: http://www.rockmass.net/

Please also check Dr Nick Barton's publications.

https://www.researchgate.net/profile/Nick_Barton5

I think, depending on the type and size of project one may ignore scale dependency. I can illustrate a few examples here:

For instance, in the analysis of brittle failure of rocks, normally scale dependency is ignored and the UCS of intact rock is used to predict and assess the depth of spalling. This is because it is assumed that brittle failure occurs in competent rock masses and a small sample can be a good representative of the entire mass.

The other example is the design of rock fragmentation in D&B operations in both underground or surface mines. To the best of my knowledge, the UCS of intact rocks is widely used for such design and analysis. But here the reason is that the dynamic geotechnical parameters of rock mass should be considered in the analysis of the dynamic breakage of rocks. Since such data are not normally available, the static counterpart parameters of intact rock which are much higher than the ones related to the jointed rock mass are used. This may somehow account for the difference between the dynamic and static parameters of the rock mass.

Overall, I think, considering scale dependency in design and analysis depend on the type and the size of the geotechnical problem. Of course, the mode of instability should always be considered as an important factor.

If you are thinking about performing numerical modelling, for any sort of stability analyses, perhaps a safe option could be to utilise UDEC/3DEC. Then the geo-mechanical parameters of intact rock can be used as the required input parameters for the intact blocks in the DEM simulation. By including discontinuities in the analysis and properly defining their spatial distribution and mechanical parameters, your model will replicate the behaviour of the jointed rock mass.

Regards,

Ebrahim

Dear colleagues

Thanks so much for sharing your thoughts.

As I said considering scale effect is a common practice in underground openings with sufficiently large cross section and many surface structures such as in slope stability.

What I am really interested in is "Geomechanics in Petroleum Engineering". An important factor in scaling lab results is the size of say for example the tunnel in relation to the size of joints spacing. If the tunnel has a diameter of 5 meters and the joint sets are spaced for example 8 meters, then scaling effects seem to be minimal. In OIL INDUSTRY the main structure is a well which has a diameter of less than 25 cm in the considered section. Cored plugs are provided from the well path in this section . Those core are of sizes of relatively comparable to the well size. Therefore, the need to upscaling is of question here.

I would be grateful if you could give your thoughts on this particular matter.

Many thanks for your invaluable comments.

Many good answers - but back to the scale of Abolfazl's question. Already the surrounding diameter(s) around the wellbore have increased the scale by an order of magnitude in relation to the cored plugs, and it is in the early phase of scaling that we see the biggest scale effects. The P-wave velocity, with appropriate stress-dependence in relation to depth, will show a reduced magnitude from plug size to 2-3 wellbore diameter sizes, due e.g. to JCS and JRC scale effects, if/because, jointing/bedding may be involved (i.e. down-hole velocity relative to lab plug). Modulus can be scaled via Vp, using the increased Vp at depth, which however brings the surround rock mass (20-30 inches scale?) closer to the confined plug modulus. So maybe strength falls faster than modulus with plug-to-surrounds scaling, due to the effect of confinement. UDEC-BB can give some indicators of the scaling using the Ln/Lo (small) block-size scaling. But suggest JCS replaced by confined strength due to the depth and absence of weathering.

Dear Abolfazal,

You can also follow this link:

https://www.researchgate.net/post/How_we_can_scale_the_result_of_experimental_tests_to_field_for_simulating_in_large_scale

Regards,

Dear Dr. Barton,

Thanks for your invaluable answer.

In all other underground rock mechanics applications the rock mass can be appropriately defined using your excellent Q-system, the same goes for surface applications using the Q-slope. These rating systems give a very good concept of the rock mass strength we are dealing with. However, they cannot be easily applied to wellbores due to much more limited available data. I would love to see a "Q-well" system. It would make petroleum geomechanics much much easier.

Back to your answer, I would be grateful if you could elaborate more on the using P-wave velocities in scaling lab results.

One thing I should mention is that I think a part of the difference in core plug P-wave velocity and down-hole P-wave velocity is due to the variation of sonic velocity with frequency. Sonic velocity measurements made under laboratory conditions are usually made at 1 MHz because the core plugs are small and the high frequency has a short enough wavelength to fully penetrate the sample. On the other hand, down-hole sonic velocity measurements are made with a low frequency (typically 5 to 35 KHz under normal reservoir conditions). I believe there are some relations to convert high frequency data to the equivalent low frequency (logging tool) values.

You can also follow this link:

www.sciencedirect.com/science/journal/03767361

Good points about the potential influence of high-contra-lower frequency in such sonic lab contra sonic down-hole. My suggestion that (static) deformation modulus scaling could be derived by using the down-hole scale of velocity measurement was not supposed to include scaling of other properties.

No - not yet a 'Q-well' system, i.e. at smaller scale. Nevertheless, Q H2O for predicting permeability based on near-borehole permeability testing does seem to work (...Jr/Ja are changed to Ja/Jr, and a depth correction is also applied). This can be considered a 'well-scale' property as so much of a permeability test result is determined by what happens in the first few diameters where there is most head-loss. Re modulus 'scaling' (using the larger scale Vp) See: Near‑surface gradients of rock quality, deformation modulus, Vp and Qp to 1 km depth. First Break, NB, 2007 for : Emass ≈ Qp ≈ 10E(Vp – 2.5 + log σc)/ 3 GPa.

I recommend Nick's answer

Best Regards