Shear stiffness Ks is an entirely different parameter to normal stiffness Kn, despite being given the same units such as MPa/mm or the equal GPa/m. Because Ks is doubly scale-dependent (peak shear strength and displacement to peak are involved), the ratio Kn/Ks is seldom as low as 10, may often be 50, and can be 100. It cannot be 1 as seen too often! Since normal closure of joints is limited maybe to tens of microns, at least to fractions of mm, it has to be much higher than Ks. So why does one see so many errors in the literature?
Joint stiffness tests are not an easy issue, especially the measurement of normal stiffness (kn). In addition, there is not much published data, and it is not easy to calibrate the models.
Sometimes, the "superpowers" of the numerical models make us forget the basics, and there are still many things we need to know about the basic behavior of rocks.
Mauro!
I partly agree, but the 'past must not be forgotten' here, and you and those modelling with DEM will find lots of data in Bandis et al. 1983 (more for normal stiffness) and in Bandis et al. 1981 (more for shear stiffness with scale effects). Also a lot of the BB-modelling back-ground in Barton, 1982. These two stiffnesses are programmed in UDEC-BB, once things like lab-scale JRC and JCS and actual block-size(s) are given - meaning the mean spacing of relevant cross-joints for each set modelled. With literally hundreds of such models performed in a huge variety of situations, one can feel some confidence in results which link well with empirical results
(Q-based deformation estimation). A key thing here is to not exaggerate the continuity of joint sets (either in UDEC-BB or UDEC-MC) - and to try to avoid the use of 'lazy' automatic joint generators, unless paying great attention to the latter (relative continuity of the different sets). Experienced geologists and engineering geologists can provide sketches of jointing that can be digitised - one day of extra work that can pay off, as so many unrealistically 'uniform' UDEC models and seen and published, missing all the advantages of such modelling capabilities.
Agree, shear stiffness of natural discontinuities is expected to be much smaller than normal stiffness, unfortunately this fact indeed has been dealt with crudely in many DEM modelling papers by just assigning equals values. I think this is an error and should be faced seriously, and this issue can be resolved through calibrating Kn and Ks (microparameters) separately against normal deformability tests ( Bandis et al., 1983 ) and direct shear tests.
I feel normal stiffness and shear stiffness can be evaluated for soils by conducting direct shear test with varying soil stiffness..
The discussion above was only adressing the shear and normal stiffness of rock joints - which we (who took part) know about. Soil is the domain of others!
Karthigeyan! We seem to be reading different 'answer' feeds? This started as a rock mechanics discussion - up until you added comments re soil?
Hi Nick,
Following this discussion with interest... I have also witnessed a number of papers using an extremely high kn/ks ratios and am keen to understand the implications of this further. The simplest example to try and model to understand the kn & ks input parameters and calibrate their behaviour in DEM software is surely to simulate a lab scale direct shear test at a sensible normal load and compare with empirical data.
I've just set about doing this to try and further understand the implementation of UDEC-BB, and there is in fact an example of this exact problem in the UDEC manual. However I note that even in this example of implementing UDEC-BB, the input properties of kn & ks are set to be equal (40 GPa/m), and the results give a shear stress vs. shear displacement curve that is perfectly reasonable and I imagine very closely resembles empirical data, i.e. resultant shear stiffness is an order of magnitude lower. Am I missing something fundamental here?
Thanks,
James
Dr. Barton could write something about it, if that's how compliant it is for 2D modeling, I imagine it will be much more complicated for 3D modeling (3DEC). I'm confused.
Unfortunately Itasca sometimes appear less concerned with real Kn and Ks values, but rather that their models should run fast. Ks as high as 40GPa/m or 40 MPa/mm (easier to think of experimentally) is very unlikely unless under very very high normal stress, and then joints would be 'closed' so Kn extrememly high. Very low realistic Ks values - after all ks is a completely different mechanism to kn - are to be expected as ks is doubly scale-dependent, while kn is not in principle - if sampling is careful, and interlock is ensured - not easy in a big shear box sometimes. We who have pioneered the non-linear BB modelling are concerned with the differentiation of Kn and ks (10:1, even 50:1? see Barton, 2006, Ch. 16) - which happens automatically in UDEC-BB - because we may be modelling M-H coupled behaviour and mechanical (mean E) and hydraulic (e) apertures are to be differentiated.
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