Just before I wrote this message, former prime minister Shinzo Abe was shot dead in a crude act of violence. A depressing blow to us all. In Japan we are becoming sadly accustomed to grim occurrences of this sort.
　The appearance of Bulletin No. 16 gives a span of fifteen complete years to look back on, and the shock left behind by the former prime minister’s terrible end leads me to think back over them. One thing that occurs to me is that in these 15 years of writing these Messages, I have never spoken yet of how much I owe to Professor Minoru Matsuo. He was another figure who departed from us too soon, before his time and still in the prime of his vigor.
　When he died in 2015, Matsuo was 78. In July that year, a request came for me to write his obituary in Soils and Foundations, the journal of the Japanese Geotechnical Society. What I wrote there was accurate and as it was written only eight years ago it is still easy enough to find for anyone wishing to look it up. I hope some readers will. But it was limited to one page, and my deeper feelings had to be left out.

　Matsuo had originally been preparing for a graduation thesis at Kyoto University under Professor Sakuro Murayama. But as circumstances turned out, he had to tie up his preparations hurriedly at the planning stage (under Professor Yoshimi Nagao) and then take a year off from university to go to the Himalayas with the Academic Alpine Club of Kyoto as leader of an AACK Bhutan Academic Exploration Expedition. When he returned from that time out to join Nagao Sensei’s graduate school class, it happened to be just when I was moving up to graduate school after my fourth undergraduate year. And that chance brought us together. It would have been around 1970.

　The Akaike Information Criterion (AIC) for the minimization of information loss was first unveiled at an international conference in 1973 as an extension of methods for the estimation of maximal likelihoods. But the first opportunity I had myself of hearing Hirotsugu Akaike in person lecturing on AIC was at Kyoto University in 1975. Assuming ten points of data in the coordinate space defined by axes x and y, if a ninth power equation is construed for this system it is possible to obtain a fit for all the data, but in reality, no one would ever do that. Normally, we make do with y = a₀ + a₁x or, at most, y = a₀ + a₁x + a₂x². The reason for stopping here is because of a minimization norm (the AIC) leading us to select the expression we estimate as most likely to match the principle of parsimony (or minimum required effort). Matsuo and I later made use of this new type of information quantity criterion to develop a model of effective stress distributions for the undrained shear strength of a clay soil, which we presented in 1977 at a conference in Tokyo of the International Society for Soil Mechanics and Geotechnical Engineering. But to be honest, neither of us would have said at the time that this research left a particularly deep impression on us. I also gave other presentations at that Tokyo ISSMGE conference, but I have long since forgotten what they were about.

　What did have an eye-opening impact, however, was an encounter with the Rosenblueth Method (1975). Matsuo Sensei’s specialty field, however you look at it, was the area of reliability in geotechnical design. Reliability design is not inherently a difficult subject to talk about, but the calculations for it are formidable. Essentially, if you take a probability variable X, reliability design can be thought of as a problem of finding probability distributions for Y in some relation Y = f(X). Generally, the mean values and dispersions for Y would need to be found from a Taylor series of mean values and dispersions of f(X) around mean X (the first order second moment method). But let us think, for example, of the case of a circular arc slip analysis φu = 0 where X is the undrained shear strength of a clay soil and Y is a required safety factor. As is well known, the whole point of a circular slip analysis is to find the maximum slip surface arc radius compatible with a minimum of assured safety. In terms of plasticity theory, this is the equivalent of an upper limit problem: without this limit arc value for assured safety, a circular slip analysis cannot be mechanically sound. As for performing the calculation, after an arduous series of trial-and-error attempts, the analyst finally closes in onto one X = x value from which the safety factor requirement Y = y can be determined. But in this stage of the process, everything is indeterminate. There is no way of formalizing f(X) analytically in advance, or of finding first- and second-order derivatives that will lead to the solution. And for all the talk of “Monte Carlo simulations”, there are plenty of circular slip analyses that do not lead to realizable outcomes. As an alternative to this hit and miss approach, the Rosenblueth Method replaces all of the probability distributions of serial probability variable X with just 2 points of scatter data and then conducts just two circular slip analyses on these to obtain the corresponding probability distributions for safety factor Y. For closer details, go to the references indicated below. By multiplying the data points for the probability distribution and so on, there are also further ways of enhancing the accuracy, but there is no need to go here into matters of that kind.

　Up until that time, Professor Matsuo had always worn an embarrassed look when talking about the crudeness of these “reliability analyses” that seemed to lack (indeed, still do usually lack) any rational criterion of arc radius for the required minimum of safety. But from then on, it was a joy to see his years of accumulated frustration progressively brightening and turning sunny. I never ceased to be surprised by the quickness of his insights. But I also remember him as a dogged worker who tolerated no compromises where academic excellence was on the line and who cherished his life as a true scholar.

　Let me end with some lighter memories overheard from other colleagues. When Professor Nakano was promoted to professor, he shocked everyone by coming out with the remark, “Asaoka Sensei has never touched real clay, you know.” Another memory is of Professor Kodaka, now head of the Academic Support Center at Meijo University, being troubled while performing his water penetration tests in a sandy soil up to the point of soil failure in case the ordinary water he used from the mains supply would cause “air bubbles to pop up everywhere and create problems.” Kodaka was serious and not a drinker, but Asaoka, the only person there who drank like a fish every evening, would say, “What’s wrong with that? It is one way to turn water into beer.” I remember Professor Noda, too, saying point blank at a department meeting – maybe around the time he was promoted to assistant professor – “From the time I was a student, I was always the one who made Professor Asaoka’s exams, and then had to mark them as well.” Well, what can I reply? Nothing. All of those stories were true. And they all also applied about as much to Matsuo as they did to Asaoka. Of course, Matsuo went on later to become President of the University, and there was no way they could have let Asaoka do that. But apart from that, in the rest of our doings and dealings with our students, we were pretty much alike. What memories. Those were the days.

Reference 1. Emilio Rosenblueth. “Point estimates for probability moments”. Proc. Nat. Acad. Sci. U.S.A. Vol. 72, No. 10, pp. 3812-3814, October 1975.
Reference 2. Akira Asaoka and Minoru Matsuo. “A simplified procedure for probability based φu = 0 stability analysis”. Soils and Foundations. Vol. 23, No. 1, pp. 8-18, March 1983.

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