Dear Nick,

Do you suggest that the rock engineering community should move towards numerical modeling of discrete nature?

Best

Sohrab

I believe the logical answer is yes - for smaller-scale excavations. Much more is learned. With large scale, where equivalent continuum may be needed, the shear strength (and deformation modulus) input needs to be corrected to much sounder principles: do not add 'c' and sigma tan(phi), make modulus depth-dependent.

I believe that the condition of the inner and outer layers of the rock should be taken into account in the discussion of plastic dependence.

Professor! I guess your point of view is undestandable if it comes from one who has performed 'plastic zone' studies - or seen those of your students? But please consider this alternative point of view. A well investigated 600m deep tunnel with three to four joint sets. We were able to input JRC, JCS, block size etc for UDEC-BB studies of the bolt forces. I suspect Phase 2/RS 2/GSI/H-B and all the GSI-using equations would have shown 'plastic zone' penetration into your referred outer and inner layers, since I have seen so many examples of such in the case of much, much shallower tunnels. The UDEC model on the other hand showed a rapid increase in joint shearing, deformation, joint apertures (hydraulic and mean mechanical, as modelled with BB) as the tunnel walls were reached. The EDZ (where we could just about see stress and deformation and shearing on joints was 1 to 1.5 tunnel diameters - sometimes - when with water inflow it can be more. We refer to EDZ 1 (delta stress) and EDZ 2 (delta joint movements), or EDZ 2w a bit increased if with water inflow. (EDZ 3 from blast damage is not modelled - but could be crudely if adding some cracking). From a rock mechanics (not smeared plastic) point of view, it was just a case of moderate deformation (max 10mm for the 8m diameter TBM tunnel simulation) and limited joint shearing and aperture changes. Bolting was designed from the Q-system, using suitably high stress/strength ratios. There was never any discussion of 'plastic' behaviour, because we are rock mechanics people, not continuum modellers. There are two different worlds in our profession it seems. And what if we are to consider the starting point for pre- or post-injection? Estimates of possible joint apertures, perhaps 0.1-0.2 mm are useful. How do 'plastic zone' studies help there? So please consider the potential advantages of more mechanics oriented analyses. I have reproduced these almost 30 years-old (!) UDEC-BB models as the last figure of a 2020 TUST article on joint over-closure.

Furthermore, it should be noted that the 2D / 3D analyzes in the context of the equivalent continuous / continuous medium in the case of deep tunnel in discrete / good rock determine an unreasonable effect: small variations in convergence (2-5cm) determine exceptional loads on the lining, hence the need to install exaggerated supports. The higher the modulus of the rock and the rock mass, the more evident the phenomenon is, as the liner shells no longer interact with the rock, but passively undergo the movements of the rock.

Unfortunately, in the infrastructure field these concepts are difficult to understand, especially in the context of clients, where the more colorful graphics and hundreds of pages of reports are made, the better it is for them, when most cases could be solved by looking at the Panet number or with a convergence-confinement sheet. They need pages and colors to demonstrate a work, to protect themselves from the bad final quality of the execution (and why they don't check during executions?), from the lack of choice of the real solutions that make the project feasible. As well as the idea that by lowering the parameters of the rock mass the project becomes more conservative (perhaps without adequate investigations ..), increasing even more the plastic areas mentioned in the previous messages

Strong opinions, but often shared by others in the last two decades when there has been a 'dilution' of actual rock mechanics by the 'colourful appendices' reporting. Even 3d-wedge analyses have been part of this process, with their lack of tangential stress, and therefore lack of the actual effects of roughness - not to mention the usual lack of length statistics, so grossly exaggerated wedges, and therefore unrealistically conservative bolting. Was actual rock mechanics supposed to be easy (just looking at a picture and guessing a number, and entering into software due to impossibly algebraic equations?)

Dear Dr. Nick,

Your interlocutor is obvious (I guess it is Dr. Evert Hoek !). Please forward your oppositions about GSI, H-B criterion, Rocscience software directly to him. Why you are wasting your time with young "numerical modellers" of rock mechanics community. They are the end users not the first developers.

Despite some of the wording used by some of the participants in this debate, for all of us that are involved in this field and industry, is important to understand the appropriateness and limitations of ALL methods that are applied in rock engineering design. Continuum, discontinuum, key block analysis etc. all of these are methods that have been/are used and the important thing is to understand when each is applicable and corresponds well to our site specific conditions. Since all of us understand that the results of an analysis rely heavily on our inputs, and since the GIGO principle applies (Garbage In Garbage Out), we need to clearly define our problem, understand the boundary conditions and nature of the material and then apply the appropriate method. Otherwise, we will be moving on a path that follows the concept "Oh but the numerical program gave me this..." without any engineering judgement and results irrelevant to reality.

Nishkarsha! You are a bit too strong of an optimist about the practicality of your

ideal. I understand the desire, but have to caution about not being disappointed when the true scope is understood. We have to simplify - but not too much!