Hoek & Brown model using strain softening

Hi everyone. How can use the model Hoek & Brown in version 7 to simulate strain softening in the rock mass (using tables to mb,s,a)? I try to simlate the example in paper “Guidelines for numerical modelling of rock support for mines” of Lorig and Varona (2013), where I must calculate critical strain. I understand that IMASS is better, but I dont have CPPUDM option for the moment. Thanks in advance.

One option could be to linearise your H-B input properties to equivalent M-C properties at a suitable sigma_3 for your problem, and implement with a strain-softening/hardening M-C constitutive model?

As you’ve suggested, you’d need to calculate the critical plastic strains as per Lorig & Varona (2013) (or I believe Oliveira & Diederichs (2017) present similar critical strain equations but based on crack initiation and deformation modulus) and then implement your c, phi, (tensile and dilation) values as tables relating to those relevant critical strains.

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With the Hoek-Brown (HB) constitutive model you can specify the HB softening parameters directly via property commands and tables (x-y pairs of plastic strain and property value). For example, below is the start of a simple model illustrating how you specify these.

; Example of strain-softening HB model property specification
model new
model large-strain off
zone create brick size 1 1 1
zone cmodel assign hoek-brown
zone property dens 2500 bulk=1.19e10 shear=1.1e10
zone property constant-sci=110e6 constant-mb=11.46 ...
              constant-s=0.062 constant-a=0.501 ...
              table-sci 1 table-mb 2 table-s 3 table-a 4
table '1' add 0 110e6 1e-3 50e6 1e-2 50e6
table '2' add 0 11.46 1e-3 0.481 1e-2 0.481
table '3' add 0 0.062 1e-3 0.0002 1e-2 0.0002
table '4' add 0 0.501 1e-3 0.530 1e-2 0.530
; End of model example

Note that the const-* properties aren’t technically necessary, but the current version of FLAC3D (7.00.147) has a bug that makes this necessary (for const-sci). This will be fixed in the next sub-version release.

It’s important to appreciate that the softening (or hardening) properties kick-in with (i.e., are defined relative to) the onset of plastic strain and then change linearly between the plastic strain values specified in the tables. In the above example, the HB “a” value is initially 0.0501 at peak strength and then changes to a residual value of 0.530 by a plastic strain of 1e-3, remaining constant up to a plastic strain of 1e-2. You can have many x-y pairs to define the stress-strain path characteristic of your material. You can see the concept in the following diagram.

Also, if localization (e.g., shear bands) is evident in the model, then the critical strain needs to be scaled to account for the zone size (e.g., based on the cube root of zone volume) as discussed in the paper you referenced (Lorig and Varona, 2013). The HB constitutive model property, length-calibration, can be used to account for zone size automatically. The default value is 0.0, whereby the model does not perform length calibration to account for zone size. If the length-calibration property is 1.0, then a zone size scaling factor of 1/(zone volume)^(1/3) is applied; but it can be any other non-zero float value (e.g., 0.1, 2) to apply different factors to the length-calibration zone scaling.

Learn more about the Hoek-Brown constitutive model and the available softening properties (table-*).


Thank you so much David. I had doubts in this case about the length calibration parameter that have this constitutive model, but you clarify me with your answer. Cheers

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Hi Guys!

Thank you for bringing this topic up. I’m implementing this for a back analysis that I’m doing as a part of my MSC thesis. I’ve got Lorig & Varona (2013) paper, and I’m using the one suggested equation for getting and supporting my e_crit choice. The paper says this latter is taken from Professor Brown’s caving study, which I have too. Unfortunately, I haven’t been able to see the mentioned expression in the quoted study explicitly. So, Does anyone know from where this expression originally comes up? Or have you seen similar equations that can refer them to me?.

Thank you in advance!.

Hi David!

Thank you for such a clear explanation of the code’s application. It has helped me a lot!. Are the plots from a specific publication? Might you share the reference?


Hi Andres,

The plots are based on an unpublished Itasca report titled “GUIDELINES FOR MINE TUNNEL SUPPORT DESIGN (REVISION 1)”, January 2011, ICG09-2456-9-25R1, 284 pages. The report authors were Andrew Corkum[3], Loren Lorig[1], David O. DeGagné[1] and Jarek Jakubec[2].

[1] Itasca Consulting Group, Inc.
[2] SRK Consulting Ltd.
[3] BGC Engineering Inc.

We also use these figure in our Software Introductory Training courses for the Introduction to Constitutive Models section.

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Hi David,
Is it possible for me to get access to this publication I am very much interested.

Thank you.

Hi @ddegagne ,
I have a question about the Hoek-Brown model with hardening / softening.
I often use tables to vary linearly the HB parameters in a range of possible plastic strains using one of the two history parameters provide by FLAC for such model. The problem is the calibration of the hardening / softening behavior. In general, the hardening/ softening parameter refers to the rock mass already scaled with the GSI but for calibration I have generally only tx tests done on intact rock. Intact rock is equivalent to GSI=100 (neglecting the effect of the Disturbance Factor) so, the calibration could be performed setting GSI=100 and setting the variation of the HB parameters to obtain a good fit with sperimentale results. The question is: passing from the intact rock to the actual rock (with a specific GSI), are the ranges of variation of the hardening / softening parameter (e.g. shear plastic strain) still valid or they should be scaled? In my opinion they should be scaled, but how? In fact, the GSI is a parameter to scale the yielding surface considering the blockiness but there is no a general scaling correlation for the plastic strain.
In the IMASS model this aspect is solved introducing the critical plastic strain which is dependent on GSI. However, as the blockiness of the rock increases with the deviatoric stress, should the critical strain be updated during the analysis or not?
Moreover, setting GSI=100 in the IMASS critical plastic strain equation leads to eps_c_p = 0 while from the tx tests on intact rock, the plastic strain to drop to zero cohesion is greater than zero.
Thank you in advance.



Hi David,

Thank you for your answer back to this; I appreciate it. Hopefully, you can publish it one day, as I think it would be very insightful for many of us.

I am looking into seeing of this document can be made public.