Initially thanks to a shared acquaintance with Professor Yamaguchi Hakuju at Tokyo Institute of Technology，I have had friendly relations with Professor (hon. c.) Kusakabe Osamu going back a good 45 years. When he was young, Professor Kusakabe had the opportunity of learning almost all there was to know about the centrifugal loading model experiments performed in the soil mechanics laboratory at the University of Cambridge. This covered everything from the principles underlying centrifugal modeling, through the deliberate reconstitution of a saturated clay foundation with a consolidation history, to the aptest techniques for measuring pore water pressure during a centrifugal loading experiment in progress. Kusakabe is still remembered in Japan as the man who set “Foundation Studies with Physical Modeling” on its feet. Last autumn (2023), with a year’s delay, it was a pleasure to hear him go back over the gist of his 2022 Schofield Lecture, originally presented in Korea: “Development and Challenges of Physical Modeling ― Japanese Contributions.” And on top of that, in April this year (2024), it was a privilege to hear his review of his own 45 years personal research history. Later, reading back at leisure through the many achievements included in those fruitful years of activity, I couldn’t help feeling some emotion. In contrast to the straight experimental path followed by Professor Kusakabe, I have rather parted company with broader theory to engage in more bounded areas of numerical replication and analysis for particular instances of elastoplastic soil modeling. In the space of a page or so here, let me look back through memories of my own to account for what this “divergence of ways” comes to signify for me in the span of a long research career.
We are used to hearing how numerical analysis and modeling experiments stand in a complementary relationship to each other. But in fact, in the particular case of geotechnology, the two approaches have seldom been viewed in this kind of harmony. The emotion, if anything, comes from the disconcerting reflection that, for all the similarities in our research objectives over the past 40 or 50 years, we have only lately come to agree that, far from complementarity, most of this time has been spent in conflict and competition.
The Cam-clay model, as originally devised at the University of Cambridge, does no more than describe the loading behavior of artificially remolded clay samples in a state of normal consolidation (on the“Super loading surface”). For this reason, the creators of the model, being fully aware of the limitations implied, hardly ever used it to obtain estimates of actual elastoplastic deformations found in real foundations. Yet long after the first introduction of the model in Japan, this crucial restriction was still poorly understood. The difference in practice, compared with the cautiousness of the model’s originators, can be seen in the way it was used by some Japanese researchers to predict consolidation deformation on either side of a “uniformly distributed” embankment load ― whatever that is meant to mean ― on a clayey soil foundation. Following the death of K. H. Roscoe in 1970, A. N. Schofield and others identified a steeply inclined critical state line in centrifugal modeling test results which Asaoka regards as marking a limit for this Cam-clay model. This accords with the opinion of H. B. Poorooshasb, another of the originators of the Cam-clay model, that trust is not to be placed in calculations based only on constitutive equations, not to mention Schofield’s own assertion that “Geotechnical centrifuge development can correct soil mechanics errors.”
In stability problems occurring with centrifugal load tests in shallow foundation models, Professor Kusakabe’s regular practice was to assume a failure mechanism at the calculated upper bound of stability and relate this to the collapse mechanism observed in the testing. Restating this in the terms of numerical geotechnical analysis, it is equivalent to arriving at a bearing capacity analysis for a saturated foundation by way of a soil-water coupled rigid plasticity analysis mounted on an upper bound theorem. Considering also the great lengths of time it took (up to around 1986 or 1987) to adapt the two methods sufficiently to be able to handle actual problems of this intricate sort, it comes as a surprise to see how very similar the development paths turned out. Chronologically, as can be seen from Kusakabe’s degree dissertations, it was numerical analysis that for a long time rather played second fiddle to advances in modeling tests. There may be some people ready to assert that numerical analysts were achieving successes with multidimensional elastoplastic compression problems. But the rough and ready, if not ramshackle nature of these “successes” is a point that I have insisted on too often in the past to want to backtrack on it seriously now. The plain fact is, these achievements were sloppy and not at all what was needed for dealing with real analysis issues.
At this point it is also worth recalling the attacks unleashed on both model experimentalists and numerical analysts by that grand old authority Karl von Terzaghi. For him, they are mad researchers who set out from conclusions based on pure theory, or from “small scale tests on materials with very little if any resemblance to real soils,” yet feel no qualms in generalizing from results like these. Elsewhere, he urges that “One of the principal goals of instruction in soil mechanics should be to discourage this prevailing tendency to unwarranted generalization, to expose it for the excess that it is, and put a stop to it.” Or again: “The attempt to identify all of the myriads of relations linking the minute details of loading test results to the altogether larger subsidence movements observed at the layered foundation level is an impossible and unprofitable undertaking.”
As a corrective, the problem of how to compare modeling test results with behaviors of naturally deposited (and in that sense, undisturbed) site foundations, was also becoming a major issue in centrifugal load testing by around 1988. Tangible progress in this area by Kusakabe and his associates began to be seen in achievements from around 2001. Here, too, comparing the progress achieved in elastoplastic numerical estimates for various elementary external disturbance scenarios, the integrals for the equations of motion (i.e., the finite deformation estimates) in naturally deposited overconsolidated cases were showing a close fit with real results by 2000 or so, evidence that numerical analysis and test modeling, far from really being complementary methods, appeared to be running in competition. That, at any rate, was the early impression.
Around the year 2000 in elastoplastic soil mechanics, structure sensitivity and soil disturbance were coming to be seen as issues for clayey soils and much the same points could be made for compaction states in sand. Theoretically, this was clear, but in the general practice of numerical analysis in geotechnical engineering, there was, and still is, an idea that “sand liquefaction cannot be measured with tools meant for compaction but requires a separate scale of its own.” In that sense, we are still far from a world in which geotechnical theory, embodied in software like GEOASIA, can be said to have reached universal diffusion. And much as we may think that theory is theory, for many years it was widely but mistakenly believed that “a foundation liquefied and subsequently recompacted does not liquefy again (!?).” It is only recently that the true view has circulated that “the reason that makes re-liquefaction such a ubiquitous phenomenon is that “induced anisotropy in sand is a response that propagates rapidly.” Not long ago, this would have been denied on “theoretical” grounds. All the same, even in a world of such complex phenomena, each day adds its grains of wisdom, allowing the theory and practice of numerical analysis to evolve. The same must be true in the area of modeling experiments, giving us all the more reason to avoid spreading non sequiturs of the sort: “Liquefaction can be calculated but compaction cannot; therefore, no logical chain can lead from a liquefied and reconsolidated state to renewed liquefaction.”
From quoting Terzaghi, my own argument has turned too polemic. I had better stop here, then, but let me end by breaking one more lance with the recently popular V&V (Verification and Validation) mode of argument: demonstrating something first and then comparing how it works out.
As a way of vouching for the reliability and adequacy of a method, V&V is reminiscent of procedural concepts developed for the fields of mechanics and particle physics. For numerical analysis findings, too, there seem to be increasing numbers of situations in which an aligned “comparison” has to be made with starting and resulting positions in modeling tests. It goes without saying that comparisons of this kind are important, but it also has to be said that the original purpose of numerical analysis was to maintain alignment between the two background theories of mechanics and mathematics. When it comes to ensuring the reliability and limitations of arguments, surely the first step in any V&V procedure should be strict logical demonstration. Here my deepest respect goes to the researchers who first created the Cam-clay model at the University of Cambridge, but were wisely modest enough “not to use it” in that bare form. We can all learn from that.

Note 1) Professor Kusakabe’s account of his career history has now appeared in the invited paper series “A Review of the Author’s own Seminal Contributions” in Soils and Foundations 64 (2024) under the title “Foundation Studies with Physical Modeling.” I recommend the reading of this to all readers.

Note 2) In the early years ― perhaps around 1994―, I recall receiving phone calls from Professor Schofield in person sounding out my interest in buying an improved version of the Cambridge centrifugal testing apparatus. He even went as far as to say that since his daughter worked for a large Japanese bank, wouldn’t it be a good thing for me to buy this equipment from England? As it turned out, however, the small French factory that was manufacturing it presently went into insolvency to my great relief. I am not a baseball prodigy like Shohei Otani, able to pitch and bat with equal accuracy, and if I try to do two things at once I am likely to fail in both.

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 Akira Asaoka
Senior research advisor, the Association for the Development of Earthquake Protection (reg. foundation)　　
Emeritus professor, Nagoya University