As much as I try to be kind in my reviews of papers, every now and again I have to nag. A favorite gripe is that people do not seem to think about the differences between site scale and laboratory scales – or, the dreamland scales of a PhD dissertation. Once upon a time I did not think about the differences either. Here is a story:
In May, 1994 I was due to graduate but I had not yet finished my PhD dissertation. That was OK – I could graduate as long as I submitted the dissertation by the beginning of the next semester in August. But I wanted to feel like I was graduating properly, with the black gown, and funny hat, and the ceremony of my PhD research advisor, Prof. Richard E. Goodman, placing the blue and gold hood over my head up on the stage in front of hundreds of graduates and their families. It was important to me to feel like I deserved the fuss and bother. So, I worked to finish my draft for many long days and even all through the night to finish the draft on the morning of Graduation Day. While I was at the Graduation ceremony, a good friend photocopied my thesis and placed copies in the mail boxes of my three committee members – Prof. Goodman, Prof. Tor Brekke, and Prof. David L. Jones.
Within a week or so, I got the comments back. Tor Brekke had a few practical criticisms expressed in his characteristic cryptic Norwegian style. Dick Goodman, wrote many comments and a poem* and a very ego-shattering request that I try to write my dissertation so that it become “magnificent”. Yes, really, “magnificent”. That is not a word I have ever heard of again as related to academic writings. Certainly not mine, anyway. In the end Dick was satisfied with the final version, though it is not magnificent.
Davy Jones wrote only one comment on my draft: “Is a pebbly mudstone a bimrock?”
At first I was soooo pleased. Only one comment from the usually critical Davy!. Once I had pondered Davy Jones’ comment I realized that what he asked me was extremely insightful. A pebbly mudstone is indeed a bimrock at the scale of a lab specimen because the blocks (the pebbles) are geotechnically significant at that scale, But they are not significant at the scale of a TBM (Tunnel boring Machine)! The pebbles make no difference at all to the mechanical behavior of the rock as far a TBM is concerned – at that site scale a pebbly mudstone is just matrix.
Based on Davy Jones’ one simple question. I ended up extensively re-writing my thesis to reflect my further thinking about scale independence, block-matrix thresholds, and all that other stuff which still trips people up in their research and writings about bimrocks.
Davy Jones died In 2007. He was called “Dr. Franciscan” and was one of the pioneers in tectonics, micro-plate accretions, California geology and melange research. He was also a renown vintner with a vineyard called “Lava Cap”, being underlain by the Mehrten Formation, a volcaniclastic rock formed in the Sierra Nevada foothills of northern California. The Mehrten is a volcanic bimrock formed of tuff with blocks up to 1 to 2 meters in size. It is fitting that Davy Jones was connected to bimrocks via his prize-winning wines on Mehrten bimterroir.
Anyway: here are some things to think about.
Do not constrain your scale of interest to lab scale bimrocks. Rock mechanics is a servant to rock engineering, where problems need to be solved at site scales (tunnels, landslides, outcrop scales! ). Findings from lab studies of bimrocks only apply to site scale bimrocks if the bim materials have block size distributions that are scale independent, And what does that mean? Scale independence means that the block-size distribution curves (or particle-size distributions) look the same, regardless of the dimensions of blocks. In many melanges, in fact in many comminuted rocks/soils, the block sizes range over orders of magnitude, and block size distributions are fractal, or scale-independent. Don’t take my word for it: read all about it in Medley and Lindquist, 1995, and Medley and Zekkos, 2011.
Nowadays there is much fruitful work with virtual bimrocks, computer bim models. Often these virtual bimrocks have mono-sized blocks, which may not actually be “blocks”. Indeed, using the “rule” that the block/matrix threshold size is about 5% of the characteristic dimension of your problem – (say the diameter of the model specimen) – then everything below that threshold is actually “matrix”. (Nowadays it seems to be a rule, but in 1994 it seemed like common sense based on my scale-independent studies.)
Say we have a pebbly mudstone, where the pebbles are (conventionally) between 4 mm and 64 mm. What is the critical characteristic dimension (Lc) of a site such that the pebble size is right at the block/matrix threshold of 5% of Lc? Easy enough: 20 times 64 mm, or about 1.3 m. So if you have a project where you are concerned about the bimrock nature of pebbly mudstone in an outcrop 5 m high you do not have to fret yourself: its just matrix! If you have spent a lot of time in the lab developing relationships between VBP and bimrock strength, you have not wasted your time. At the scale of the outcrop you have lab results for the strength of your matrix.
This matter of the relevance of scale comes up all the time with SRMs (Soil Rock Mixtures). SRMS are generally called that in China for colluvial/diluvial soils and have blocks generally below 1 m in size. There is a now immense literature focused on SRMS which are also called, incorrectly, “bimrocks”. Really they are not bimrocks, but bimsoils up to the site scale of about 20 m. That is a substantial scale of course. But now I am off on my preachy hobby horse about SRMs…
*And the poem that Dick Goodman wrote to me? See the next post.