Soil Mechanics

Philosophy of Soil Mechanics

Posted in Critical State Soil Mechanics, On Paradigm Shifts, Scholasticism by Paul Joseph on February 23, 2017

There is a branch of philosophy called “philosophy of science.” In case you are bored, you should try a course in it–it is well worth it. I recap below, key understandings from philosophy of science, specifi­cally targeting them to soil mechanics in general and critical state soil mechanics (CSSM) in particular. If you can’t take a college course in the philosophy of science, I strongly recommend this audio course–it is very good! I was lucky enough to be able to borrow it from my local library. It isn’t easy I have to say–I had to listen to it three times be­fore I felt I understood its key points.

FALSIFIABLE: The first question to ask when presented with a the­ory is this: does it have a falsifiable hypothesis. If it does, then the concept or theory is scientific. In the 1950’s the world famous phi­losopher of science Karl Popper defined a scientific theory to be a theory founded on a falsifiable hypothesis, a definition which since then has been taken for granted.

IF a theory does not have a falsifiable hypothesis, then like it or not, the theory is not scientific. A theory without a hypothesis is like a fortress without a well; a theory without a falsifiable hypothesis is a fortress whose well will soon run dry. Remarkably, even today, more than half a century later, most academics in soil mechanics seem unaware of the implications of this statement, and one finds expensive books written on theories that cannot be falsified,such as this one!

Andrew Schofield and I have been in communication for the last decade and I have learned much from him as a result. I first met him in the Summer of 1986 at the Cambridge Centrifuge Laboratory, and hold him in high esteem. I read his 2005 book (Schofield, 2005) and strongly recommend that everyone read it. You can read my review of this book, including my detailed critique of CSSM here. Recently (2013), after some discussion between us, Andrew Schofield wrote me that the falsifiable hypothesis for elasto-plastic soil mechanics is that soils can be modeled as metals (molten). If so, then this hypothesis has indeed been falsified–it can be readily shown NOT to match commonly available empirical data on ordinary soils.

The basis of this hypothesis is the Drucker-Prager criterion first proposed in 1952 by the two mathematicians Daniel C. Drucker and William Prager in a short eight page note in a journal of mathematics (see Drucker and Prager, 1952). This failure criterion was for materials idealized as having no structure. In their note Drucker and Prager also showed how to use their theory to calculate the critical height of a vertical cut in clay, using plane and log spiral failure surfaces. Roscoe, Schofield, and Wroth in the soil mechanics department of Cambridge University enthusiastically embraced Drucker and Prager’s approach.

This ability to readily falsify the hypothesis that soils can be mod­eled as materials with no structure and implicitly constituted of iso­tropic point particles was identified as soon as the theory was first adapted for soils in the 50’s and 60’s. Alan Bishop of Imperial Col­lege used to routinely demonstrate that CSSM and elasto-plasticity theory did not stand up when applied to real soils (Niechcial, 2002). The reason for this (as you will see below) is because Drucker and Prager criterion as applied to soils are at root, scholastic–not taking into account the fundamental, empirical fact that soils are particulate materials (not point particles) with particles that have explicitly aniso­tropic properties (not isotropic). Drucker and Prager’s (and An­drew Schofield’s) premise that soils can be modeled as metals (molten) with implicit isotropic point particles is not found true, ex­cept as a very crude approximation–a scholastic idealization. Sir Alec Skempton, the “founding father” of British soil mechanics, attributed the scholastic nature of CSSM to Roscoe, of whom he said: “… he did little field work and was, I believe, never involved in a practical engi­neering job.” (Niechcial, 2002).

Most papers on CSSM models follow along in this scholastic ap­proach–when they prove their model, use a “simple clay,” i.e., a pure CH material. They run a few tests on normally consolidated samples or samples at a low OCR to get a simple stress-strain curve with no strain-softening. The sample chosen is usually an “insensitive” clay, i.e., a clay that exhibits no stress-strain softening. This simple stress-strain curve is then shown to be matched by the model.

But falsifiable does not mean seeking “confirmation.” I can run a thousand tests that create simple stress-strain curves with little to no strain-softening, and show that my model matches the empirical evi­dence (the test data). However this is not an attempt at falsification–rather it is the opposite–an attempt at confirmation.

Scientific theories are not tested this way–rather, falsification means to try every which way to break the model and to see where it fails. A true attempt at falsifying the theory would be to model realis­tic stress-strain curves that show strain-softening, to match the accom­panying pore-pressure (or void-ratio) changes. The test would be on a soil with a wide range of grain sizes–not an insensitive clay that is al­most guaranteed to generate a simple stress-strain curve.

Attempts have been made using CSSM based elasto-plastic soil models to match complex stress-strain curves from real soils (those with a mixture of grain sizes) and the results have been abysmal–a complete failure to match strain-softening curves beyond peak strength. So yes, CSSM theory has indeed been falsified, other than for the simplest stress-strain curves from soils (CH and also, CL soils) that do indeed resemble soft metals.

Further, most CSSM models violate the laws of thermodynamics (a big no-no in and of itself). Later on, you in this chapter you will read about hyperplasticity–a theory that does not violate these laws. However, hyperplasticity is based on a non-falsifiable ­hypothesis–the Ziegler Orthogonality Condition.

We know that a theory that is either falsified or which is not falsi­fiable is not a scientific theory. A theory that is not scientific, but which is presented as if it is, meets the standard definition of a pseu­doscience (see Hansson, 1996). Metals based theories of plasticity as applied to soils being either already falsified, or based on non-­falsifiable theory, but yet which are taught as if they are scientific, count as pseudoscience. More on this later in this chapter.

SIMPLE: A second test to apply when comparing two theories is Oc­cam’s razor – which theory is simpler while yet explaining all the facts? By any measure, DSSM is very simple – in fact one mathemati­cian I presented it to called it … yes you got it…”very simple.” It needs simple hypotheses (Poisson process, simple friction, dynamical sys­tem) based on transparent underlying physical phenomenon and one equation to directly formulate the numerical model. Truly, as New­ton said some five hundred years ago, Nature is simple, and always consonant to itself.

Note: It is very important to note that this simplicity results primarily be­cause we do not consider inertial effects of individual particles, i.e., effects of the mass of individual particles as they collide against each other during defor­mation. This is simply because strain-rates in traditional soil mechanics prob­lems are small enough to where we can ignore these effects. Once you consider grain inertial effects, the complexity goes up by an order of magnitude at least. In 1997 as part of my “wild hunt” for evidence that I was dealing with a dy­namical system, I came across a paper in the journal Nature that modeled particles in a fluidized bed furnace, an environment where the velocities are very high and the particulate densities very low, so that the particles are sus­pended in gas or fluid and where consequently, inertial effects play a role along with temperature and aerodynamic effects. The paper described the resultant chaotic dynamics that occur. The mathematics was extremely complicated, but yet the paper gave me a huge sense of relief–I knew now for sure, that at least at very high velocities and very low densities, chaotic behavior existed in particulates and that there were other fields that considered this as nothing new. I no longer have that Nature paper, but you can find similar papers quite easily on the internet–see for example this one.

PARSIMONIOUS: Good theories are also parsimonious theories–they should require a minimum of words and equations to explain them. The DSSM model is based on a hypothesis that is six words long (a Poisson process drives soil behavior), is expressed by one set of equations that explains all the known behaviors of soil including the log-linear consolidation curve. This contrasts with CSSM that needs upwards of 50 equations and many strange, artificial properties, and which takes the log-linear consolidation curve, a fundamental and basic relationship in soil mechanics, to be a given.

EXPLAIN: A third test of a theory is its explanatory power. We saw that DSSM theory explains things previously mysterious – for exam­ple why in one-dimensional consolidation, void ratio must vary lin­early with the log of the effective vertical stress or why  should be approximately constant for a wide range of soils. I am not aware that CSSM has explained anything per se. CSSM is at best, only a de­scriptive theory – for ­example, it simply takes the linear relationship between void-ratio and the log of the effective vertical stress as a given.

PREDICT: A fourth test to apply to a theory is how many new and surprising things does it predict? As we saw Chapter 4 of the DSSM book pre­dicts on the basis of entropic principles what the distributions of in­terparticle contact areas should look like at the initial condition and at the steady-state. I am not aware that CSSM makes any predictions, novel or otherwise. In fact, soil mechanics, being dominated to date by CSSM, is a stark contrast to subjects like physics.

In physics, theories exist that are powerful enough to make pre­dictions with. Hence in physics, theory based predictions usually lead experimental verification. Recall the recent discovery of the Higgs Boson–a multi-billion dollar search that was driven by a predic­tion made almost half a century ago based on theory! In stark con­trast, in soil mechanics, the reverse is the case. For example prior to the advent of DSSM, no theory predicted the experimental findings by Mesri that  is approximately constant or that the EOP curve obtained from static incremental one-dimensional loading is unique. Till the advent of DSSM, there was no theory to explain Mesri’s ex­perimental obervations even ex post facto. DSSM shows why these two relationships must hold (see Chapter 7 of the DSSM book) .

MATCH: A fifth (and essential) test is to see how well does the model that derives from the theory fit the actual data. Recall from Chapter 1 of the book  that our motto is: test predictions with experiments! Remember ­Richard Feynman and his eloquent statement: “You may have the most beautiful and elegant theory in the world, but if the model that re­sults from it does not fit the data–then your theory is simply wrong!” Of course, CSSM is notorious for the tremendously poor fits it provides to stress-strain and void-ratio strain curves with strain-softening. CSSM seems to fall into a limbo of being neither right or wrong. It brings to mind the story told of another Nobel Prize winning physicist, Wolfgang Pauli, who when presented by his friend with a theory remarked: “Das ist nicht nur nicht richtig, es ist nicht einmal falsch!” (“This isn’t right. This isn’t even wrong!”).

Any mismatch should not be excused away. Recall from Chapter 3 of the book that the DSSM parameters were obtained from sets of stress-strain curves that went far past failure including those points measured long after failure planes had developed in the sample. Re­call also that the fits were very good for the entire curve, right to the end, well past the point when failure planes developed. Recall also that what this means is that the DSSM equations are tracking condi­tions on the dominant failure plane, past failure, past the develop­ment of failure planes, and is able to do it very well (witness the high chi values). This contrasts with CSSM that is quite unable to track conditions once failure planes develop. In fact, the development of failure planes is given as the chief reason (excuse) why CSSM based models are unable to track conditions post failure.

Imre Lakatos, a noted philosopher of science coined the term “degenerate research program” for theories where excuses are used to justify an inability of theory to match empirical data. Lakatos was commenting in general about scientific programs and probably did not even know that a field like soil mechanics existed, which makes his comments all the more powerful. DSSM needs no excuses as it is able to track conditions post failure plane development. CSSM on the other hand qualifies as a “degenerate theory” given its need for excuses about its inability to match the empirical evidence (test data).

TRANSPARENT (PORTABLE): Good theories have a transparent physical basis–for example, when using DSSM, the underlying physi­cal phenomenon (Poisson process, simple friction, dynamical system) are clear, always present, and easy to understand. The more basic the underlying phenomena that drive the model, the more “portable” the model is–by this I mean, the easier it is to explain the model to someone in a different field, but who is aware of the fundamental physical principles that the model rests on–in this case, basic friction, Poisson processes, and dynamical systems theory. For example, I was able to explain the DSSM model quite comprehensively to an Electri­cal engineer, in less than an hour!

This contrasts with CSSM where one requires a lot of arcane spe­cialized knowledge and background to figure out what is going on in the first place. The CSSM models are complex and not portable–in the midst of all the equations, one loses sight of the physical basis of many of the idealizations that CSSM makes. And if one works on something else for say a year and then returns to it, it is hard to figure out once again some of the arcane CSSM models with their relatively arbitrary assumptions, and naive and questionable idealizations.

One example of such naive and questionable idealizations is a key assumption made by many CSSM models, namely that pure hydro­static stress results in no shear strains. This is absurdly wrong – a soil structure can be analogized (thought of) as a “house of cards” much like what we used to build when we were little children. Applying pure hydrostatic stress to a house of cards will cause shear deforma­tion, and the structure to collapse. Even small children know this intuitively.

Truly, any version of CSSM that assumes pure hydrostatic stress causes no shear strains is indeed a house of cards, fundamentally flawed from the very get-go! Such models indicate their authors do not have a physical feel for the nature of soil and soil structure. Andrew Schofield has told me many times that try hard though he did, he was never able to put soils into pure hydrostatic compression. You can read about it in Schofield (2005) also.

The reason such a flawed, artificial assumption is made is that numerical instabilities occur in elasto-plastic finite element models if it is assumed that pure hydrostatic forces also cause shear strains. It seems to me this assumption of zero shear strain under pure hydro­static compression is an example of the dangerous idealizations that I mentioned earlier. If you do a FEM analysis, please do confirm that your model does not make this assumption. If you find it does, dump the model ASAP!1 In a court case it is easy for a lawyer to convey to a jury made up of non-technical people, the error in assuming zero shear strains under pure hydrostatic stress, using the “house of cards” analogy above. This can work to your advantage/disadvantage de­pending on which side of the case you are on.

Models that make artificial assumptions which do not match un­derlying physical phenomena often can be traced to academics who have not physically interacted soils since they left graduate school, and who consequently lack a physical feel for soils. As I wrote in a footnote in Chapter 2, I believe that one obtains this “physical feel” in a quite literal sense only after one has extensively interacted physi­cally with the object of ones ­introspection, using one’s hands and not by merely doing “analysis” or “design.” One cannot expect elasto-plas­tic theories derived originally for metals that implicitly assume the material being modeled to be made of isotropic point particles, to provide good results when applied to materials composed of irregular, finite-sized particles, with inherent anisotropic properties.

Note: In 1980, one of the first questions I asked my soil mechanics professor S. V. Ramaswamy was why soils were being treated as metals. I had just turned 20, and by this time, my brother and I had been tuning two-stroke motorcycles for racing, for several years. At that time in India, motorized metal grinders were not cheap and so we had to use ordinary metal hand files to raise or lower the two-stroke intake, transfer and exhaust ports. The experi­ence of grinding cast iron manually was for me, simply put, a huge shock. Only when I took 8 hours to lower the exhaust port by a mere 3 mm did I realize how hard a metal (then too a relatively soft metal like cast iron) really was. Only when I saw the fine iron powder, in which it was impossible to discern any different shapes of the iron powder particles without a microscope, did I realize what an atom must be. Hence when in undergraduate class, I was told soils were modeled at metals, I was instinctively and immediately taken aback–the idea struck me as simply absurd–hence my question. It was Professor Ramaswamy who told me that it was possibly because of his train­ing as a mechanical engineer, as well as the lack of any alternate theory, that made Roscoe amenable to suggestions of modeling soils as metals. Today, al­most thirty-five years later, I realize the importance of my experience filing metal with a hand file for eight hours. This is exactly why I admire Nietzche’s saying: The doer alone learnth. As with metals, so also with soils! Hands on contact is essential to obtain a physical feel for the object of study and to truly understand! Today, sadly, most academics lack this “physical,” hands on training, and hence are too quick to accept bizarre statements like: “soils are really metals in disguise.” Should you listen to my interview of Steve Poulos you will see how Cassagrande handled this issue. And as it hap­pened with Steve, so also it happened with me. A relatively recent New York Times non-fiction best-seller that captures this viewpoint is: Shopcraft as Soul­craft: An Inquiry into the Value of Work. I think this book is essential read­ing if you want to become really good in soil mechanics! Ramaswamy helped me understand what Roscoe and the “metal” people knew but which I didn’t then–that at very high stresses, metals indeed behave like “modeling clay.” But what I intuitively realized then and which Roscoe and his “metal” people did not seem to (or at least, to this date are not able to realize in their model) is that while metals are made up of isotropic chemical molecules, i.e., isotropic point particles, real soils are not so–they are not point particles and have very anisotropic shapes. This seemingly trivial difference is the heart of the matter, the very core of it. Models that do not account for this core property of soil grains are bound to fail, just as current “metal” models of soils have failed. This is because anisotropic grains created structure that resembles a “house of cards.” And it is this structure that controls behavior. Metal based theories of soil do not capture the behavior of card like structure resulting from this core property of grains–that they are anisotropic at the particle level. Conse­quently, such metal plasticity based models are fundamentally broken at their very center. Attempts to directly model such card like structure will result in extremely complicated mathematics. DSSM on the other hand doesn’t need to model this structure directly because the net effect of this structure is a friction based Poisson process. This, DSSM models directly.

There is a long tradition in the general sciences (other than soil mechanics) of theories that come and do a poor job of things. As I noted before, a famous philosopher of science, Imre Lakatos, coined the phrase “degenerate research program” to describe such theories. According to Lakatos, a degenerating research program is a scientific enterprise that started out with great promise, showing impressive results in a limited domain. Researchers then apply the program more generally. At this point, if they succeed, the program gains more followers and expands and is not degenerate. However, on the other hand, if researchers encounter important anomalies that consistently resist explanation with the new concepts, then the program will stag­nate. It will be characterized by a lack of growth, or growth of a pro­tective belt of auxiliary hypotheses.

Lakatos was almost certainly completely unaware of the existence of a subject called soil mechanics. Nonetheless, it seems to me that CSSM, with its protective belt of auxiliary hypotheses (excuses) such as failure planes or non-uniform particles or anisotropy or lack of shear under pure hydrostatic stress, or local non-linearity of very early stress-strain behavior, etc., etc. to explain away poor fits to real data, qualifies itself as one of ­Lakatos’s degenerate research programs. Worse, his comments on pseudoscience seem also ­applicable to CSSM.

You have reached the end of the course. One last assignment though! … stop for a minute … visualize the Poisson process of soil deformation … then from understanding (and not because you sim­ply memorized it), write out the single set of three equations that di­rectly describe how the deformation occurs. Well done! You have fully, and comprehensively described the fundamental mechanism of soil deformation.

Now step back in your mind and compare what you just did to the over 50 equations that it takes to define CSSM. Recall too that the CSSM model provides very poor fits to the test data, and that we really have no physical understanding of what the central, falsifiable hypothesis of CSSM is. Recall also, that CSSM is not able to derive that most fundamental relationship in soil-mechnics–the linear rela­tionship between void-ratio and vertical stress in one-dimensional consolidation. Nor can it explain why  is approximately con­stant nor why the EOP curve obtained from static incremental one-dimensional loading is unique.but simply takes these as given. Recall that CSSM makes no new, novel predictions. Which model do you now believe? I personally believe that CSSM is a failed and broken theory–a dead end, a red-herring in the history of soil mechanics.

The question then arises–why has the soils community stuck with CSSM for so long? The reasons are two. First, till now, there has been no alternate theory. This reminds me of the well known story where a policeman saw a man searching for something under a lamppost. “What have you lost?” the policeman asked. ” My keys,” said the man. The policeman then helped the man look. After searching for a while he asked the man: “Where exactly did you drop them?” “Over there,” responded the man, pointing towards a dark street a good distance away. The policeman asked exasperatedly “Why are you looking here if you lost your keys over there?” The man replied “Because the light is so much brighter here.”

So too with CSSM; absent any alternative, the soils community had no choice. Hopefully, the advent of DSSM provides an alterna­tive, and now the search can proceed where the keys really are!

The second reason for CSSM is that, yes, crudely, very very crudely, a fine grained, homogenous material, lacking in structure, somewhat does resemble a soft metal. As I mentioned above, I first heard this in the Spring of 1980 from my undergraduate soil mechan­ics teacher–Prof. S. V. Ramaswamy. He was the first to suggest to me that perhaps Roscoe naturally analogized soils with metals because he was a Mechanical engineer by training. In the 1950’s, when CSSM was birthed, most triaxial tests were on fine grained clays, remoulded and reconsolidated isotropically. Such tests generate simple stress-strain-volume curves and scarcely exhibited strain-softening; indeed their behavior can be crudely approximated by a metals theory of plasticity.

DruckerPragervon Mises were all applied mathematicians who worked on modeling solid materials, particularly metals in plastic yielding (analogous in their plastic state to a molten metal). In the late 50’s, the Cold War was being waged in earnest and metals based elasto-plastic models were applied initially to problems in the aero­space industry and later to problems relating to underground nu­clear shelters. Aeronautical engineers were using finite-element analyses on air-frames and there was much talk in engineering circles of this (then) new technique–use of FEM methods and elasto-plastic models to analyze a multitude of engineering problems. For a history of the development of Finite Elements, see Clough and Wilson (1999).

In my opinion, it is no coincidence that Kenneth Roscoe (1914–1970) who trained as a Mechanical engineer, was the first to approxi­mate soil plasticity as metal plasticity. It would have been natural and instinctive for him to be receptive to the idea of soil plasticity as anal­ogous to metal plasticity–an approximation that today, on detailed examination and application, we find holds up only very crudely. Note: this analogy with metals probably holds up best for soils that are pure “fatty” clays (CH). The reason I use the word “pure” is that once you exceed 5% particles larger than clay-size, then it is these larger particles that control behavior. In short, as the percentage of soil greater than clay-size increases, behavior becomes more complex–this is why CSSM models do a very poor job of predicting behavior as the sand content goes up.

As the years went by, soil-fabric level structural effects came into play, either through soils with non-symmetric grain-shapes or larger sized particles, or as a result of an anisotropic fabric obtained through Ko consolidation. Samples began to exhibit strain-softening and very quickly it was realized that CSSM as it was then, provided very poor fits. The band-aid was to add another two dozen or so equations to attempt to address these issues, resulting in some of the murkiest and ugliest mathematics that it has been my karmic misfortune to have had to read. Mathematics like this impresses only “newbies”2 or non-mathematicians! To the formally trained mathematician on the contrary, mathematics of this ugliness has always been a fairly reliable indicator of something being fundamentally broken in the basic approach!

Almost all elasto-plastic models including the various flavors of CAM clay violate basic thermodynamic principles. To correct this a recent (largely since 2000) development in geomechanics has been “hyper-plasticity” with models that satisfy the First and Second Laws of thermodynamics. Hyper-plasticity though is flawed by a fundamen­tal assumption–Ziegler’s Orthogonality Condition (ZOC). ZOC as­sumes a very strong and restrictive version of the Second Law of Thermodynamics–one that is rejected by many as overly restrictive, and if applying at all, then applying only to a narrow subset of materi­als. Further, ZOC remains unproven and it is highly unlikely that anisotropic particles would meet the conditions required of ZOC. Worse, it is a principle which is not testable simply because to date, no one has been able to conceive of an experiment with which to test it.

A recent book (Dawid, R., 2013) discusses string theory in the context of falsifiablity. To date, string theory has not been empiri­cally confirmed, raising the question–is it really science? The world of physics is split into two camps. Thus one camp holds that string theory is to be understood to be a candidate for a final theory, a theory that at a fundamental level accounts for all observable phys­ical phenomena. However most scientific observers fall into the second camp–one that denies any claims of string theory being a final theory, a claim they feel is an indication of the over-optimistic mindset prevalent among string physicists. It remains a philosophi­cal question if a final theory claim makes epistemological sense and if so, whether this spills over to non-final theories such as the ZOC.

In short the fundamental principle on which hyper-plasticicty rests on today cannot be falsified, and as best we know from Karl Pop­per’s work in the 1950’s, a theory that cannot be falsified does not count as scientific. Nonetheless, in (expensive) text books, ­hyper-plasticity is presented as if it is scientific. Many researchers in the general sciences accept Hansson’s (1996) definition for what counts as pseudoscience: “An activity or a teaching has to satisfy the following two criteria: (1) it is not scientific, and (2) its major propo­nents try to create the impression that it is scientific. ” By this stan­dard, it seems to me that hyper-plasticity counts fully as a pseudo-science3.

However, regardless of whether or not hyper-plasticity is a pseudo­science or whether or not the laws of thermodynamics can be met or whether or not ZOC can be proven, the fact remains is that we are still dealing with metal plasticity as applied to soils, i.e., the same old metal-plasticity in new thermodynamically viable bottles! Conse­quently, hyper-plasticity continues to have the same fundamental problem of being unable to match soils that are constituted of non-anisotropic particles because like all current elasto-plstic theories it implicitly assumes that soil particles are point particles. They are not! Soil particles (for anyone who has actually handled real soils) have mass, anisotropic shapes and other anisotropic particle level proper­ties. In other words, in addition to the soil fabric’s “bedding plane anisotropy”, there is the question of particle level anisotropy. Plastic­ity theories with their inbuilt, implicit assumption of point particles (isotropic), are fatally flawed at their very core, regardless of whether or not they meet the laws of thermodynamics.

This can be seen by studying almost any book or paper on elasto-plastic soil models–the scope of the proof is meagre–the attempts are not at falsification using “complex” stress-strain curves that exhibit strain-softening, but rather, are mere demonstrations of confirma­tion using simple stress-strain curves from insensitive soils, typically pure CH or CL-CH soils. As we saw earlier, this is most certainly not the way that theories are validated!

DSSM does not need to make any of the numerous assumptions made by CSSM and elasto-plasticity. In fact, DSSM stands in strong contrast with pseudoscientific soils plasticity theories, as it is falsifi­able at many levels as described in the main body of this course. Hence, DSSM could have been falsified at any of the following points listed ­below–the fact that it wasn’t means that as of now, like any valid scientific theory, it remains to be falsified. Note: any current scientific theory is not true in an absolute sense. All a scientific the­ory says is effectively…” here is our best falsifiable hypothesis that ac­counts for the empirical evidence–so far, no one has been able do disprove it.” This does not mean that at some point in the future some one will not be able to falsify it. When this happens, the theory, like any other scientific theory, has to be either abandoned or modi­fied (while yet retaining falsifiability) to account for the new informa­tion that falsified it originally.

Hence DSSM could have been falsified in the claims made in Chapter 2–that soil shear is a dynamical system, or in Chapter3–that its underlying basis is a Poisson process resting on simple friction or in Chapter 4–that the logarithm of the ratio of peak shear to confining stress varies linearly with the logarithm of OCR and that stress-strain curves normalize or in Chapter 5–that strain-rate effects depend crucially on the dependence on strain-rate of the coefficients of friction at inter-particle contacts, or in Chapter 6–that if DSSM were falsifiable, it would not be able to predict (as it did) the linear relationship in one dimensional consolidation be­tween the void-ratio and the log of the effective vertical stress, or in Chapter 7–that the EOP curve under static loading is unique and that  is indeed approximately constant for a wide range of soils.

The fact that it is falsifiable at these points, but has yet not falsi­fied, indicate that currently, DSSM is a scientific (falsifiable) princi­ple that to date has stood the test of falsifiability. As noted above, this does not mean the theory is complete or even true–no scientific the­ory is really true–all we can say is that to date, it has not been falsi­fied. Also, no scientific theory is complete–one can always drive down to a level where unknowns remain–in our case, the fundamen­tal nature of simple friction remains to be clearly understood even today.

I recently had to review two complex elasto-plastic models, rather well known to those in the field but which I shall not name, one from the US, the other from the UK, and found each to be riven through and through with thumb rules, dangerous idealizations, and un­proven assumptions. Curious about this, I checked out several other models published recently and found that they all had a common feature–the core equations they use for the plastic model, generally some variant of the original Cam clay model with a slight modifica­tion or two. Some appear to have been pulled out of a magician’s hat, coming complete with magical constants, magical starting equations, and magical beliefs.

Thirty years ago in graduate school, I too was very enamored of elasto-plastic models. My views have changed since then as a result of knowledge gained from experience, study, and introspection. To­day I see elasto-plastic soil models as “emperors with no clothes,” just waiting to be challenged in order to be exposed as being nothing but glorified, pseudoscientific thumb-rules or highly theoretic equations that by themselves have not been proven to match the empirical evi­dence, i.e., test data from a wide range of soils. At the heart of each model is a varied combination of approximations, thumb rules, and dangerously idealized assumptions, most, individually unverified over a wide range of soils. If you believe any of these models, do contact me–as they say here in the US to indicate a gullible person: “I’ve got a bridge to sell you.”

Long story short, CSSM is a broken and failed theory, and ac­cording to me, nothing but pseudoscience. If you want me to decon­struct any CSSM model to make this point clear email me using the website for the book information on your model of choice and I shall do so in a post on this site on Deconstructing Elasto-Plastic Soil MEchanics.. I believe the concepts behind these CSSM models are dangerously idealized understandings of soils that originate from academics who have not physically handled for years and with their fingers (I mean this literally), a wide variety of soils and so have never developed a physical feel for soils.

This physical feel can be only developed by years of actually han­dling in ones fingers, a wide variety of soils. Such experience does not come from mere “consulting” or doing “geotechnical design.” Rather it involves physical, intimate, direct, “hands-on” contact with soils, an approach that usually takes at least three to five years of continuous work directly performing field and laboratory tests on soils. Sadly to­day, most academics lack this kind of intense “hands-on” intimate, physical contact with soils, as a result of which some of them create theories that are naive–at best simplistic, at worst, dangerous. Idealizing soil as a metal is one such theory–naive, simplistic, and dangerous!

Note: Should you listen to my interview of Steve Poulos, you will hear that Cassagrande required each of his instructors to ob­tain this hands-on experience by spending at least four years in the Harvard laboratory, running experiments themselves. Little did I know why, but this is the same route that Steve made me follow at GEI–spending about two years in the lab, in addition to the prior three years I had worked in a soils laboratory at a different company!

To repeat, thirty years ago, in my graduate school days, I too strongly believed in CSSM and elasto-plastic soil mechanics. Today however I have come to understand them to be but dead ends. The belief that soils are “really metals” is one that is scholasticism–and to continue to hold it in the face of evidence to the contrary is to be but a scholastic, i.e., someone who adheres to tradition and logic (Aristotelian) and who pays little heed to the (readily avail­able) empirical evidence. I will not be surprised if DSSM replaces CSSM within a generation. As Max Planck famously observed: “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”

Much work remains to be done with DSSM starting with inde­pendent validation of the theory. Additionally, the entire field of soil dynamics remains to be investigated in the light of DSSM. I also be­lieve that concepts from particulate discrete element modelling (see O’Sullivan, 2011 for an overview) complement DSSM and should be leveraged. Hopefully, now that you are have an understanding of DSSM, you will be able to take up this work. Remember this quote, thought to be by Einstein: “If you can’t explain it simply, you don’t understand it well enough.4” So, do not build overly elaborate ­theories–paradoxically, it is far easier to create overly complex theo­ries than simpler theories because usually over complex theories are not fundamental. Consequently, they rarely meet the acid test of a wide range of empirical data. Metals based soil theories are a ­classic example of this.

We started this self-study course with a few words – you will see these again below – but now, hopefully, their meaning is not only clear, but also, self evident!

SOIL DEFORMATION IS A POISSON PROCESS.

Notes

1. As Soon As Possible

2. American slang for someone who is very new to a field

3. The classic book on pseudoscience is Gardner (1957).

4. Einstein: the life and times (1971) pp. 418 by Ronald W. Clark: Louis de Broglie did attribute a similar statement to Einstein. To de Broglie, Ein­stein revealed an instinctive reason for his inability to accept the purely statistical interpretation of wave mechanics. It was a reason which linked him with the physicist Rutherford, who used to state that “it should be possible to explain the laws of physics to a barmaid.” (note: I have met barmaids (so called) who are geniuses–old Ruthie was prob­ably just another old sexist pig.) Einstein, having a final discussion with de Broglie on the platform of the Gare du Nord in Paris, whence they had traveled from Brussels to attend the Fresnel centenary celebrations, said “that all physical theories, their mathematical expressions apart ought to lend themselves to so simple a description ‘that even a child could understand them.’

Advertisements

Deconstructing Elasto-Plastic Soil Mechanics

Posted in Critical State Soil Mechanics, On Paradigm Shifts, Scholasticism by Paul Joseph on February 23, 2017

In the mid-nineties, Bob Whitman, my professor at MIT (and whom I fondly recall as the Clown Prince of soil mechanics), retired, and to celebrate his retirement, MIT threw a party. One of the founding members of critical state soil mechanics, let us call him AS, came all the way from England, to attend. There, he met Steve Poulos and ­Gonzalo Castro and the resulting interaction has gone down in history.

On a piece of paper, Steve drew a canonical set of strain-softening stress-strain curves (both shear and normal stresses) for an undrained triaxial test, taken all the way to the steady-state. They then readily identified (as anyone who understands the steady-state condition can) the start of the steady-state condition on these curves–the point in the two curves where changes stop happening. They then asked AS to locate the critical-state on the curves. AS hemmed and hawed and though Steve and Gonzalo pushed him somewhat hard to do so, he refused to identify any point on the curve that he would say repre­sented the critical-state.

I then recalled that in 2007 I had much the same experience with AS–I had emailed him asking him to locate for me the point on Fig­ure 8.18 (pp. 157) of the book Critical State Soil Mechanics, where the soil was at a critical-state but not (per him) at the steady-state. To my dismay, confirming what I had been told earlier, he refused to give a simple answer to my simple question. Instead, he danced all around it, talking about deep philosophical issues, but in the end, again, fail­ing to do something that should be simple–identify a point on the curve where one can make a simple statement along the lines: “At this point, the soil sample is at the critical state.” Truly, emperors, surpris­ingly often, wear no clothes, and it truly amazes me that “sheep pro­fessors (sheeple)” who slavishly believe in the “­critical-state” have not asked their “guru” this basic question.

So there you have it–there is nothing critical about the critical state–it does not really exist, and a founding member, is well known to have been unable to identify it on a set of standard, stress-strain curves. Now, if you continue to believe in the critical-state after read­ing this appendix, do show the world (or simply email me) a set of like curves, with the critical-state point clearly marked. If that isn’t a simple, basic, and reasonable thing to ask then I don’t know what is.

In my graduate school days I strongly believed in CSSM and elasto-plastic soil mechanics. Today however I have come to under­stand both to be but dead ends. I am not alone in believing this. In 1999, at Imperial College, London, during a debate held as part of the “Geotechnics in the New Millennium Symposium,” the following motion was passed at a debate on the future of soil mechanics: “…that this house believes continuum models are past their sell-by date…” (O’Sullivan, 2011, pp. 504). In short it has long been under­stood by many researchers that the main continuum model of that time, i.e., elasto-plastic CSSM, is but a dead end. Fifty years after their inception, the concepts of the critical state and elasto-plastic soil mechanics are viewed with suspicion by seasoned engineers, and as this appendix demonstrates, this is rightly so.

The key problem with CSSM and elasto-plastic soil models is they can readily shown to be false–they can be readily shown NOT to match commonly available empirical data on ordinary soils. This in­ability was identified as soon as the theory was first proposed–Alan Bishop of Imperial College used to routinely demonstrate that CSSM theory did not stand up when applied to real soils (Niechcial, 2002). The reason for this (as you will see below) is because CSSM and elasto-plasticity as applied to soils are at root, ­scholastic–not taking into account the fundamental fact that soils are particulate materials and so cannot be modeled as metals (molten), except as a very crude approximation. The basis of this hypothesis is the Drucker-Prager cri­terion first proposed in 1952 by two mathematicians, Daniel C. Drucker and William Prager (Drucker and Prager, 1952) for idealized materials with no structure (roughly, molten metals). In their short eight page note, Drucker and Prager also demonstrated how to use their approach to calculate the critical height of a vertical bank with using either plane or log spiral failure surfaces; this approach was ex­tended by Roscoe and others in the soil mechanics department of Cambridge University.

Sir Alec Skempton, the “founding father” of British soil mechan­ics, attributed the scholastic nature of CSSM to Roscoe, of whom he said: “…he did little field work and was, I believe, never involved in a practical engineering job.” (Niechcial, 2002). If anything, this seems far more true of both Drucker and Prager, being as they were, math­ematicians. Their model assumed no structure–and soils are funda­mentally governed by soil structure, the result of their finite particulate nature with anisotropic fabric and grain properties that fundamentally control behavior, properties that violate the basic as­sumptions made by Drucker and Prager.

To repeat, the key problem with CSSM and elasto-plastic soil models is simply put–these models can be routinely falsified–they do not match test data for a wide variety of soils. The key reason is that the fundamental assumptions of elasto-plastic CSSM lie a theory of plasticity developed for materials win no inherent structure, a the­ory that does not account for the particulate nature and anisotropic fabric and grain properties of real soils. In 1980 on first encountering this concept of modeling soils as metals, I asked my undergraduate soil mechanics teacher–Prof. S. V. Ramaswamy, how on earth could this be.1 He suggested to me that Roscoe thought of modeling soils as metals because he was a Mechanical engineer by training. I now have come to hold that the belief that soils are “…really metals” is scholasti­cism; to continue to hold it in the face of evidence to the contrary is to be but a scholastic. CSSM models that attempt to do so, are ex­traordinarily ugly in their mathematics, and murky in the extreme.

Yes, very crudely, very, very crudely, a fine grained, homogenous material, lacking in structure, may be idealized as a molten metal, implicitly composed of point particles. This analogy with molten met­als probably holds up best for soils that are pure “fatty” clays (USCS-CH). The reason I use the word “pure” is that once you exceed 5% particles larger than clay-size, then it is these larger particles, which cannot be modeled as “point particles,” that begin to control behav­ior. As the percentage of soil greater than clay-size increases, behavior becomes more complex, which is why elasto-plastic models do a very poor job of predicting the behavior of sands. In other words, the the­ory has been falsified.

Further, elasto-plastic models including the various flavors of CAM clay violate basic thermodynamic principles. To correct this a recent (largely since 2000) development in geomechanics has been “hyper-plasticity” with models that satisfy the First and Second Laws of thermodynamics. Hyper-plasticity though is flawed by a fundamen­tal ­assumption–Ziegler’s Orthogonality Condition (ZOC). ZOC as­sumes a very strong and restrictive version of the Second Law of Thermodynamics–one that is rejected by many as overly restrictive, and if applying at all, then applying only to a narrow subset of materi­als. Further, ZOC remains unproven and it is highly unlikely that anisotropic particles would meet the conditions required of ZOC. Worse, it is a principle which is not testable simply because to date, no one has been able to conceive of an experiment with which to test it.

The fundamental principle on which hyper-plasticicty rests on to­day cannot be falsified, and we know from Karl Popper’s work in the 1950’s that a theory that cannot be falsified does not count as scien­tific. Nonetheless, in (expensive) text books, hyper-plasticity is pre­sented as if it is scientific. Many researchers in the general sciences accept Hansson’s (1996) definition for what counts as pseudoscience: “An activity or a teaching has to satisfy the following two criteria: (1) it is not scientific, and (2) its major proponents try to create the im­pression that it is scientific. ” By this standard, it seems to me that CSSM (and not just hyper-plasticity) also counts fully as a pseudo-science2.

The key reason why I consider elasto-plastic soil models to have failed is simple and straightforward–for all the mathematics, these models fail to match readily available empirical evidence, specifically, the stress-strain and pore pressure/void ratio data available from basic triaxial tests on a wide variety of soil types. Further, they are (again, despite the complex mathematics) at base, fundamentally unscien­tific. At their core, you will find what are essentially naive idealiza­tions implicitly bringing along with them numerous inbuilt assumptions and approximations, or thumb rules/heuristics, whose rigorous basis is unknown and which does not apply to all soils, but only to those for which the thumb rules in question were developed. You will find highly theoretical equations, purportedly derived rigor­ously from fundamentals, but which have not been validated at the equation level (far less than model level) and contain in them numer­ous untested assumptions. Some of these key thumb rules and ideal­izations are often naive and ­dangerous–idealizations and approximations of soil behavior that result from a lack of a physical (I mean the word literally!) feel for soils.

One of the most egregious of these idealizations, one that is as naive as it is dangerous, is the assumption made by many models that pure hydrostatic stresses result only in hydrostatic deformation–a con­venience assumption made to handle numerical instabilities that can arise otherwise in numerical analyses. Soil structure can be usefully analogized to a house built of playing cards. And this assumption of zero shear strains on application of hydrostatic stress to a real soil is a house of cards! Even a child knows that if you apply even a slight compression load to a house of cards you are going to get a collapse of structure somewhere, resulting in large shear deformations.

A mathematical model is like a bicycle chain–it is only as strong as its weakest link. Sometimes you see bizarrely complicated models which however, make critical mistakes at key points, rendering them fundamentally flawed. These mistakes can be either in formulation or in application.

A typical elasto-plastic model divides into an elastic component and a plastic component. Elastic behavior is modeled using standard elastic constants while the plastic behavior is modeled using a series of “stress surfaces” linked together by a “hardening rule.” The model follows either an associated or a non-associated flow rule. For materi­als that compress in shear an associated flow rule is reasonable but for those that dilate during shear a non-associated flow rule is needed. Non-associated flow rules need at least two different surfaces to de­scribe plastic behavior. In the case of an associated flow rule, these two surfaces coincide. A yield surface controls whether plastic defor­mation occurs and a plastic potential controls the direct of the plastic strain increment on yield. Failure is modeled by a failure surface. In other words, there are numerous complex surfaces and rules, and more often than not, no common lab tests models the relevant field conditions. Consequently, idealizations, approximations and judg­ments abound, and the end result reminds one of a Rube-Goldberg contraption.

Another idealization is the “associated flow rule”, an assumption made to conveniently reduce complexity. The associated flow rule as­sumes, purely for reasons of convenience, that at the current stress-state, strain increment vectors are normal to the yield surface. There is no validation of this rule, made purely to make the mathematics less ugly than it already is, and it may or may not be safe–we just don’t know yet.

Then there is the thumb-rule of isotropic yield surfaces made by many CSSM elasto-plastic models. Soils in-situ are fundamentally anisotropic, both in terms of fabric and grain shape; isotropic yield surfaces completely ignore this. Assumptions of isotropic yield sur­faces result in crude approximations of reality. Additionally, this thumb-rule can be dangerous. For example, if you use standard triax­ial test data to create this isotropic yield surface, then you will severely underestimate shear deformations. To be conservative, an isotropic yield surface should use Ko consolidated direct simple shear test data, but these tests are rarely run being expensive.

Coupled with this is the troubling lack of either explanations for known soil behavior such as why stress-strain curves normalize for example, and further, a lack of any novel predictions that derive from these elasto-plastic models in particular, and CSSM in general. This is why I believe CSSM and its resulting models to be nothing but pseu­doscience. In fact, you can read for yourself, Imre Lakatos, the noted philosopher of science, discuss pseudoscience here. Lakatos probably did not even know a subject like soil mechanics existed, but yet, when you read his comments on pseudoscience, it seems he is talking about CSSM and elasto-plastic soil models.

If you enter the key words “elasto-plastic soil models” in a search engine, you will come up with dozens of hits each pointing to a differ­ent model. Yes, elasto-plastic CSSM models are a dime a dozen–a re­flection of the fact that no rigorous science underlies them–only thumb rules or highly esoteric equations, some combination of which individual authors decide, “works.” In other words, each model is fundamentally idiosyncratic.

Idiosyncratic though these models may be, one thing common to all of them is that on studying them, one gets a sense that the person behind the model last touched a real soil with their hands, back in graduate school soil mechanics lab. Their knowledge is but scholastic; as a result, so too is their resulting model. Validation always seems to be a small handful (around three) of stress-strain curves that appear to match the model and you will almost never see matches for pore-pressure of void-ratio.

This kind of careful selection of tests that match a model is called “conformal” testing, and if an undergraduate came to me with such “proof” I would use it as a teaching opportunity. But if a professor came to me with such “proof” I would, if I could, fire him on the spot! Hypothesis testing requires “falsification” testing, i.e., attempts to show how the hypothesis behind the model can be proven wrong, and not “conformation” testing and the fact that senior professors in soil mechanics do not appear to know this and allow their peers to use or get away with such shoddy research, indicates to me that the intellectual standards are among academics in soil mechanics is very low–the bar needs to be raised! It astonishes me that five hundred years after Galileo demonstrated the fallacy of scholasticism, we still have academics who are but scholastic s, sitting atop ivory towers, and counting angels on pinheads!

But more important than giving you specific examples of why par­ticular elasto-plastic models are broken, my fundamental purpose in this Appendix is to give you the tools whereby you yourself can inde­pendently examine any elasto-plastic CSSM model and likewise de­construct it to its underlying thumb rules or dangerous idealizations.

To this end, I hope to deconstruct at least four models–two will be those “old chestnuts” as they say, CAM clay and modified CAM clay models, while the remaining two will be of your own choosing. With the deconstruction of these four, hopefully you will get the hang of things and be able to proceed to deconstruct any other such model that you choose. If you want me to do more, of course, do let me know which ones, and I shall add their deconstruction to this Appendix.

As they say in the US, you can use all the lipstick you want on a pig, but in the end, you still have a pig. In this case, no amount of “mathematical lipstick” disguises the fact we are dealing with a mix­ture of dangerous thumb rules, idealizations, and approximations. It is a theory that has failed to make any predictions, novel or other­wise. Far less, it has not explained many basic known facts of soil be­havior such as why stress-strain curves normalize, or why e varies linearly with the log of the vertical effective stress in one-­dimensional compression, or why Ca/Cc is approximately constant, or why the EOP curve from static loading is unique. DSSM has explained these basic known facts.

In short, CSSM and elasto-plastic soil mechanics together consti­tute a broken, failed theory. The only reason we know of CSSM today in the 21st century is because Andrew Schofield, a Roscoe loyalist (Niechcial 2002) and charismatic teacher, inculcated a number of like loyalists in this scholastic model from his soap-box in Cambridge University. These have gone out into the world and spread this “kool-aid” to unsuspecting youths all around the world, creating a CSSM/elasto-plastic soil mechanics cult. As with any cult, it foundational principles can be readily shown to be wrong, i.e., falsified.

Let us proceed with the deconstruction.

APPROACH TO DECONSTRUCTION

Rather than deconstruct each model one by one–a tedious and repe­titious ­undertaking–let us instead construct a framework that de­scribes any elasto-plastic model. Then, in the light of this framework, let us do the deconstruction.

Thus every elasto-plastic model that exhibits hardening (as a soil does), has four components. These are the components that describe i) elastic deformation ii) the criteria for yielding iii) how plastic defor­mation takes place (the flow rule) and iv) hardening, i.e., how the yield criterion changes with plastic strain.

Recall that in Chapter 5 of the book Dynamical Systems Based Soil Mechanics, Graham-Eagle and I showed that for soil shear, the intrinsically non-linear stress-strain curve is nearly linear at small strains. The reason for this is that at small strains the underly­ing physical behavior as described by the governing equations is ap­proximately linear even though the equations themselves are non-linear. It is so often the case that non-linear processes behave near linearly at small values of the independent variable, that it is one of the first things that mathematicians automatically and immedi­ately look for because it greatly simplifies analyses for cases where the value of the independent variable is small. The analysis in Chapter 5 showed that the equations describing soil shear were close to linear at strains as high as 0.5%.

Atkinson (1993) and Hicher (1996) among others report that elastic behavior occurs only up to very small strains, in the order of 0.00001% or less. Beyond this, even though the stress-strain curves appear linear, the damage to the soil structure that has already oc­curred ensures that the soil will not return to its original state on un­loading, i.e., even in this early region of the curve, plastic deformation has begun. Recall the analogy to the house of cards that I keep on and on about!3

These considerations lead us to state that the linear nature of the early part of a stress-strain curve does not mean behavior is elastic. Rather it is the expected linear behavior at small strain of the same mechanism of non-linear plastic deformation that governs the entire remaining stress-strain curve–the mechanism of particles moving into the ­steady-state flow structure at random shear strains. The physical mechanism operative in this early linear region of the curve is the same as that operative in the non-linear region, i.e., simple friction and a Poisson driven process.

This contrasts with elastic theory which, being based on solid ma­terials and not particulate materials, holds that the reasons for elastic behavior are due to intra-molecular deformations of the solid mate­rial (in the case of soils, the soil grains). But soils are not metals and the linear behavior is not governed by intra-molecular considerations of soil grains, but instead due to the same simple friction that governs the entire deformation process. We are not talking about cemented soils so neither are grains rigidly bonded to each other to allow for metal like elastic behavior. Elastic theory applied to soils became pop­ular I think more due to the simplicity of the concept, erroneous though the underlying physical premise is.

Elasto-plastic soil models make much use of the deformation in the elastic regime, small though it is, to determine the elastic stresses and strains, and particularly to calculate pore-pressures, which ac­counts for the very poor predictions that CSSM models make for de­termining pore-pressure changes. Standard equations of an elastic solid are generally used, and again, I think that this much effort spent for deformations in the “elastic regime,” which is probably less than 0.5% of the total range of interest, is not a particularly useful exer­cise. Hence, in the deconstruction of the CSSM models, I ignore the elastic components of the model, considering them to be distractions from the main event–plastic deformation. Nonetheless, the fact re­mains that elasto-plastic models calculate the bulk of their stresses based on this flawed assumption of elasticity.

For each of the four models I propose to deconstruct, I will fill up the table below, describing for each model, how the three compo­nents relate to plastic deformation. Once the table is filled in, we will do a “meta-analysis.” Now this is a term that isn’t used often in soil mechanics, but it is a very powerful concept, used extensively in gen­eral scientific research. It means, rather than simply consider the spe­cifics of the model, we go one level higher, to the “meta” level where we analyze the analysis. This approach makes things clearer and we will use it to discuss the models in question. This “meta-analysis” ap­proach is powerful because once we have a new model to analyze, all we have to do is to place it in the context of the meta-level to see if if it has already been analyzed at the meta level, either by you or by someone else, for example, me in this Appendix. You will see, for all their diversity and number, these elasto-plastic models all map to the same meta-concepts.

DeconstructingElastoPlasticSoilMechanics.png

For me there are only two questions that I feel I need to ask, at this meta-level–1) is the equation in question a thumb-rule. If so, then that’s it, we are dealing with a glorified heuristic that almost always applies only to a narrow range of soil types and 2) does the model make any dangerous idealizations and/or approximations. If so, we are dealing not just with a glorified heuristic, but with a dangerous, glorified heuristic! The other issue to examine is how well has the complete model been tested, and against what kind of soils.

Let us proceed to the table! As you can see, the structure of the table is fairly basic–the name of the model followed by three columns that breakdown the model into how it handles the three plastic com­ponents listed above. Then there is another column that lists how the model handles pure hydrostatic stresses, and a final column that cat­egorizes the model as either a heuristic or an idealization, or a combi­nation thereof. If it assumes zero shear strain under pure hydrostatic stresses in addition to thumb rules or idealizations then we classify it as “dangerous.” I color code the cells–orange if it contains a thumb rule or heuristic, purple if it is an idealization, green if it is realistic. and red if it is dangerous!

THE DECONSTRUCTION

Here are the steps to follow for your model of choice:

  1. Identify the four components–discard the elastic component from consideration even though in all likelihood, the model in question derives the bulk of its stresses from this (non-existant) elastic regime.
  2. Determine for the remaining three components if they are idealiza­tions or thumb rules. In case of idealizations, is there any test data that directly bears on the idealization in question (and not the model as a whole).
  3. Determine if the model assumes zero shear strain for hydrostatic compression.
  4. Fill up the table and classify the model as idealized or heuristic. If the answer to step 3) above is yes, then mark the model as DAN­GEROUS. Color code the cells accordingly.

Once you build this table and do your meta-analyses (or maybe before you do this even?) you should check how the model has been vali­dated by the author(s). Strange though this may seem to you, you should immediately discount any finite element analysis with the model that compares its results with those of an instrumented field trial. Why? Because, with results already known, it is easy to make the model produce the required output. This is what Lambe (1973) called a Type C prediction, a prediction made after the results are known, and considered the “lowest quality” prediction.

In the US, analysts who make “after the fact” predictions are re­ferred to as “Monday morning quarterbacks.” Sitting in the comfort of their armchairs on Monday morning, they analyze the weekly Sun­day night’s football game and tell us how the quarterback (team cap­tain) should have really handled the plays and how they themselves could have done it so much better! Likewise with Finite Element Anaylsis of soil structures using CSSM and elasto-plastic models: in the real world, the way such analyses are typically done is as follows: a young Ph.D is given the task and she or he works under a senior en­gineer. The two work together, till the results match what the senior engineer was expecting based on experience. In other words, here too, we have what implicitly is a Type C “Monday morning quarter­back” analysis.

What you should really look before doing a complex analysis is the underlying constitutive model–how well does it predict stress-strain and void-ratio strain for standard shear tests–for example, for good old “triaxial tests.” Pay particular attention to three things. First, how many tests were compared against. If less than 10, then you can safely dump the model immediately–if you do not, then you will de­serve whatever befalls you from using such a “lightly verified model.”

Second, look at the stress-strain curves being modeled–do they include strain-softening or do they simply use test data from “insensi­tive clays,” i.e., clays that do not show much strain-softening, but which have simple stress-strain curves. If you find this to be the case, again, you can discard the model as being insufficiently validated. The third key factor to observe is to what strain has the prediction been taken–if the model cannot demonstrated close matches till at least 20%, then the model has failed–excuses such as shear bands preventing comparisons are just that–excuses.

Imre Lakatos, the noted philosopher of science coined the term “degenerate research program” for theories where excuses are used to justify an inability of theory to match empirical data. Lakatos was commenting in general about scientific programs and probably did not even know that a field like soil mechanics existed, which makes his comments all the more powerful. DSSM needs no excuses as it is able to track conditions post failure plane development. CSSM on the other hand qualifies as a “degenerate theory” given its need for excuses about its inability to match the empirical data., and Imre Lakatos would smile knowingly on hearing these excuses.

A fourth key factor is this–whose test data is it? If it is test data run by the very people who are proving out their model, then view it very skeptically. As Andrew Schofield told me in 2007, “…one can torture a triaxial sample in a cell until it tells you what you want to hear!.”

Fifth, examine for undrained tests how well the model matches the pore-pressures; for drained tests examine how well the model matches void-ratio versus strain curves. Do good matches of pore-pressure or void-ratio changes come at the expense of matches for the stress-strain curves? If the model doesn’t match the pore-pressure or void-ratio as well as the stress-strain data, again, dump it!

Finally, when comparing the model predictions to test data, check to see that you are given the chi values and that you are not being asked to believe good old “chi by eye,” i.e., blithe verbal assurances that “…the fit was good.” If it is a case of “chi by eye,” then you know what to do. As that classic book “Numerical recipes in C” (Press et. al. 1992) puts it … those that practice and accept chi-by-eye deserve the treatment they get.

You will find that in general, elasto-plastic CSSM based soil mod­els perform very poorly with soils that exhibit strain-softening and void-ratio/pore-pressure changes with strain. This is but an expected outcome given the theoretical origins of this class of model–the bi­zarre idealization that all soils are really metals!

To repeat, I find the concepts behind these CSSM models to be dangerously idealized understandings of soils that originate from aca­demics who have not physically handled for years and with their fin­gers (I mean this literally), a wide variety of soils and so have never developed a physical feel for soils. This physical feel can be only devel­oped by years of actually handling in ones fingers, a wide variety of soils. Such experience does not come from mere “consulting” or do­ing “geotechnical design.” Rather it involves physical, intimate, di­rect, “hands-on” contact with soils, an approach that usually takes at least three years of continuous work directly performing field and laboratory tests on soils. Sadly today, most academics lack this kind of intense “hands-on” intimate, physical contact with soils, as a result of which some of them create theories that are naive–at best simplistic, at worst, dangerous. Idealizing soil as a metal is one such theory–na­ive, simplistic, and dangerous!

Note: Should you listen to my interview of Steve Poulos, you will hear that Cassagrande required each of his instructors to obtain this hands-on experience by spending at least four years in the Harvard soil mechanics laboratory, running experiments themselves. Little did I know why, but this is the same route that Steve made me follow at GEI–spending about two years in the lab, in addition to the prior three years I had worked in a soils laboratory at a different company!

Long story short, CSSM, elasto-plastic soil mechanics, and any soils model that idealizes soils as made up of point particles (Mohr-Coulumb failure surface) are dead–the theory is a broken and failed theory. Again, the belief that soils are really metals in “disguise” is ­bizarre–it is scholasticism to continue to hold it in the face of empirical evidence to the contrary. Here is a classic quote from that world famous soil mechanist Fried­rich Wilhelm Nietzsche  about the death of CSSM: “After the Criti­cal State was dead, its shadow was still shown for years in a cave–a tremendous, gruesome shadow. Elasto-plastic soil shear theory is dead; but given the way of men, there may still be caves for decades of years in which its shadow will be shown.”

CONCLUSION

What we have done in this Appendix is create a framework with which to quickly classify any elasto-plastic soil shear model by determining:

  1. a) if its components are based on thumb rules or alternately, on un­verified idealizations with built in assumptions that render them invalid. Recall for example, the associated flow rule and isotropic yield surfaces–arbitrary assumptions made purely for ­convenience that are used in many elasto-plastic CSSM models, and which vio­late fundamental thermodynamics. Also, these individual compo­nents remain unvalidated with test data. The fact remains, that the components that make up the model are not justifiable other than for a lack of a better approach (till the advent of DSSM).
  2. b) whether the model makes any dangerous idealizations regarding its behavior under pure hydrostatic stress, and
  3. c) how the model as a whole has been validated against shear test data.

This framework is just a start; email me at pjoseph@soilmechanics.us to let me know how we can improve it or if you would like me to de­construct a model of your choice.

Note: the more accurate predictions, ones I actually think may be use­ful, first calibrate their model parameters using actual field measure­ments made during the initial embankment construction (see for example the analyses in the report by the US Highways Administra­tion, 1984). So yes, basically they curve fitted their simplistic model to the field data, but nonetheless, this calibration to actual field val­ues has a long history in geotechnical engineering and is an approach I consider to be realistic and commendable (see for example, Peck, 1969). Such an approach though almost mandates simple theoretical models–it is hardly possible to theoretically justify calibrating numer­ous parameters of a complex model to field data. That being said, it is often of little other than academic value to use such an approach of field calibration–most times the reason for doing the analysis in the first place is to predict deformations so that one can optimize the design! However, there does seem to be a place though for a hybrid approach–an initial estimate based on laboratory tests (that don’t re­ally directly apply to the problem in terms of stress/strain paths), fol­lowed up with more refined estimates based on actual field data obtained in the early stages of construction. Just don’t get grandiose ideas that good predictions mean that your model is theoretically correct.

Notes

  1. Note:In 1980, one of the first questions I asked my soil mechanics professor S. V. Ramaswamy was why soils were being treated as basically, molten metals. I had just turned 20, and by this time, my brother and I had been tuning two-stroke motorcycles for racing, for several years. At that time in India, motorized metal grinders were not cheap and so we had to use ordinary metal hand files to raise or lower the two-stroke intake, transfer and exhaust ports. The experience of grinding cast iron manually was for me, simply put, a huge shock. Only when I took 8 hours to lower the exhaust port by 3 mm did I realize how hard a metal (then too a relatively soft metal like cast iron) really was . Only when I saw the fine iron powder, in which it was impossible to discern any different shapes of the iron powder particles without a microscope, did I realize what an atom must be. Hence when in undergraduate class, I was told soils were modeled at metals, I was instinctively and immediately taken aback–the idea struck me as simply absurd–hence my question. It was Professor Ramaswamy who told me that it was possibly because of his training as a mechanical engineer, as well as the lack of any alternate theory, that made Roscoe amenable to suggestions of modeling soils as metals. Today, almost thirty-five years later, I realize the importance of my experience filing metal with a hand file for eight hours. This is exactly why I admire Nietzche’s saying: The doer alone learnth. As with metals, so also with soils! Hands on contact is essential to obtain a physical feel for the object of study and to truly understand! Today, sadly, most academics lack this “physical,” hands on training, and hence are too quick to accept statements like: “soils are really metals in disguise.” Should you listen to the interview with Steve Poulos (Appendix 4) you will see how Cassagrande handled this issue. And as it happened with Steve, so also it happened with me. A book that captures this view was a relatively recent New York Times non-fiction best-seller. I consider it essential reading if you want to become really good at your profession, what­ever it may be. The book is called Shopcraft as Soulcraft: An Inquiry into the Value of Work. I think this book is essential reading if you want to become really good in soil mechanics! Today, over three decades later, I now realize that what Roscoe and the “metal” people knew but which I didn’t then, was that at very high stresses, metals indeed behave like “modeling clay.” But what I intuitively realized then and which Roscoe and his “metal” people did not seem to (or at least, to this date are not able to realize in their model) is that while metals are made up of isotropic chemical molecules, i.e., isotropic point particles, real soils are not so–they are not point particles and have very anisotropic shapes. This seemingly trivial difference is the heart of the matter, the very core of it. Models that do not account for this core property of soil grains are bound to fail, just as current “metal” models of soils have failed. This is because anisotropic grains create structure that resembles a “house of cards.” Anisotropic grains also have irregular shapes by definition/And it is this structure and grain shape that con­trols behavior. Metal based theories of soil do not capture this card like structure or the irregular shape properties resulting from the core property of grains–that they are anisotropic at the particle level. Consequently, such metal plasticity based models are fundamentally broken at their very core. The center of the theory does not hold, and so things fall apart! Attempts to directly model such card like structure will result in extremely complicated mathematics. DSSM on the other hand doesn’t need to model this structure explicitly because the net effect of this structure and grain level anisotropy is implicitly incorporated into a friction based Poisson process. This, DSSM models directly. 
  2. The classic book on pseudoscience is Gardner (1957). 
  3. There is a special test that I had to do for six months straight till I was almost insane from boredom, called the Resonant Column Soil Shear test. In this test you send small amplitude shear waves of various frequencies up through a cylindrical sample and measure changes. For this loading, deformations are very small, and the soil grains in general, hardly move–rather, they adjust in place. Here perhaps, elasticity does indeed apply. 
  4. (Roscoe and Schofield, 1963) 
  5. (Roscoe and Burland, 1968) 

Interview with Dr. Steve J. Poulos

Posted in On Paradigm Shifts by Paul Joseph on February 23, 2017

Dr. Steve J. Poulos, Professor of Soil Mechanics at Harvard University under Arthur Cassagrande, and the first person to formally de¬fine the steady state condition, graciously agreed to my interviewing him. I interviewed him on March 1, 2014 between 10:00 and 11:00 AM at his house in Lexington, MA, USA.

StevePoulos.jpg

After the interview I suddenly noticed that on the table next to Steve was James Gleick’s book Chaos. In the early 90’s this book had been on the New York Times best seller list in the non-fiction cate¬gory, for several months. It was serendipity pure and simple because it was this book that had caused me to realize that soil deformation must be a dynamical system! I asked Steve if I could photograph him holding the book and he kindly agreed.

Steve has minored in mathematics and so I had naturally thought he was already aware of “dynamical systems” and that this was why he’d used the term “steady state” to describe the end condition of shear. Should you listen to the interview you will hear that I ask him if when he was at Harvard, he’d heard the term “steady-state” or knew of the field of “dynamical systems.” I have asked these questions of him three times at least, starting in 1995, and each time his answer has been consistently the same, and so I have to believe him. This is why I think that he is a true “shaman” which in my book, is the high¬est tribute I can give someone.

Why did I ask Steve this question in 1995? Because in 1995, I had read Al Gore’s classic book “Earth in the Balance.” (IMO, Al Gore ranks intellectually with the Founding ¬Fathers of the US.) In Gore’s book for the first time, I saw the term “steady state” used in connec¬tion with something other than soil mechanics–Gore had used the term in connection with global climatic systems. I was amazed! I had thought that the “steady state” was a term that applied narrowly to soils, but here was Al Gore using it to refer to climate!

I looked at the back of the book and found that Gore had refer¬enced James Gleick’s book “Chaos–Making a New Science.” I imme¬diately got Gleick’s book from the library and to my astonishment learned from it that “steady states” were to be found everywhere in nature and that there was an entire sub-field of mathematics called dynamical systems theory that was devoted solely to studying systems that had steady states. I immediately realized that soils must behave as a dynamical system and sought to prove it. I tried for two years but had no success. Little did I know that I had started on a journey which would take about twenty years to complete. (Had I known it would take this long, I would probably have given up on the spot!) Yes, this online course represents a distillation of twenty years of deep introspection on soil behavior, much of which time was spent in fruit¬less dead ends.

I felt like a paleontologist who had stumbled on the fossilized toe of a creature (s)he knew would revolutionize her/his field, but who lacked the resources and knowledge to extract it from the ground. I started with a simple linear model (what you get when you take out the exponentials from the non-linear model). I gave it my best for two years, but after filling up three notebooks with mathematical explorations (basically junk) had got nowhere. Note: One very important thing that I learned was that thermodynamically, soil deformation is a dissipative process and that there are proofs to show that all thermodynamic dissipative systems must have steady-states (see for example, Nicolis and Prigogine, 1977). Indeed, were soil deformation not to possess a steady-state, it would violate the fundamental laws of thermodynamics, falsifying them and forcing a reconsideration of the entire field of thermodynamics. This is very unlikely to be the case. This is why I am a bit fed up with naive understandings of the steady-state condition in soil, the most common one being that only soils with “needle or plate like” particles can “align” to a steady-state. These understandings are naive–the steady-state is a statistically constant structure, and even an assemblage of perfectly spherical ball-bearings made of steel and produced to extremely narrow tolerances, can reach steady-state conditions. So please (puh-leeze?!), before you email me that steady-states in soils are only to be found in clays with needle or plate-like structures, first introspect on what a “statistically constant structure” means; next attempt to visualize in your minds eye, a collection of steel ball-bearings, reaching a steady-state.

Back to my search though. It was Christmas of 1999 and I was visiting my sister in Texas. There sitting at her kitchen table, I opened my notebook and tried my quest again. My brother-in-law, a PhD in Electrical Engineering, and a few years older than me asked me what I was doing. I told him what I was attempting, (trying not to be condescending!) and not expecting he would understand! It turns out that electrical engineers are very familiar with dynamical systems; I soon discovered that my brother-in-law had forgotten far more about dynamical systems than I knew at that time. In the span of just half an hour he was easily able to figure out what my goal was! Note: this is the power of a model that is rooted in basic science–it does not take much to educate someone in a different field, about it. I did not realize this, except in hindsight, thinking about this experience with my brother-in-law. My brother-in-law told me that he knew a famous applied mathematician and that he would take me to meet him.

About a year later, my brother-in-law introduced me to this famous applied mathematician who was actually a Professor of Electrical Engineering no less! He heard me out in great detail–again, the power of a theory based on fundamental science is that it can be easily communicated to those in other fields and so it wasn’t hard for me to describe my thinking (such as it was at that point) to him. After he heard me out, he asked several questions and then said that he thought I had a good case. He warned me though that if the system was non-linear, it would take me 10 years to figure out the model.

By now, discouraged, I had stopped working on the linear model for a year, but meeting with the applied mathematician and hearing his encouraging answers, I came back to the problem and finally, I “bit the non-linear bullet.”
Note: the lesson I learned from this is that when you are stuck on a problem, then, try to get another person to help–the new information you get from them invariably takes you out of any rut you may have backed yourself into. Fifteen years later, when figuring out how to apply my model to finite element analysis (FEA), I got stuck again … but this time instead of waiting for years, after going nowhere for a few months, I asked my friends for input. They had none. So I widened my circle and asked the author of a well known (I consider it a classic) book on FEA. He didn’t quite understand what I was up to, but one of his remarks to me made me realize that I should be searching for a square stiffness matrix. With this jolt of information from the outside, I was able to climb out of the rut I had dug myself into, and within a few months was able to solve my problem. In hindsight, this may seem obvious. But then again, everything is obvious in hindsight and as the Nobel prize winning neuroscientist Roger Sperry used to say: “nothing is easier than yesterday’s solutions.”

Back to my search … sure enough it turned out that this mathematician was about right–in the end it took me about ten years as he had predicted–three years exploring the linear model (a dead end no doubt, but extremely educative in value nonetheless) and the next seven or eight years with the non-linear model. During these years I slowly accumulated the tools and knowledge I needed to “extract” my find. I felt as though I was in a pitch dark room filled with furniture, trying to find my way to the door at the opposite end from where I was, and stumbling and falling over and over again in the darkness, banging and hurting my shins and head against the sharp, hard edges and pointy corners of the furniture.

Then one day, January 6, 2006, while in the shower, I “found the light switch” in my dark room and turned it on, and lo, the way was clear! In short, suddenly that day, the thinking from the years of introspection suddenly came together and “clicked.” The result was the phenomenological dynamical systems model, described here in Chapter 21.
Once you have a quest you are passionate about, no matter how dumb or ignorant you may be at the start, no matter that others tell you that you are a fool, remember what the poet William Blake said: “if a fool were to follow their folly, (s)he shall become wise!” Stumbling in that dark room for years, “following my folly,” slowly but surely made me wiser in soil mechanics. As Nietzsche famously said: “The doer alone learneth!” All told, it had taken me just over 10 years. And my own experience has confirmed all of what these wise people, through the centuries, have been telling us.

For example, because of this experience I fully agree with Einstein–far more important than knowledge or answers are imagination and questions. In school many of my classmates were people who knew their text books inside-out, but who could not, for the life of them, extend this information to anything outside the text book because they lacked that quality which I count as far more important than intelligence or even knowledge –of course I am talking about “imagination.” A person may have the biggest brain in the history of the human race, and may know all the textbooks cover to cover, but if (s)he lacks imagination then (s)he lacks the ability to ask new questions, will not be open to new possibilities, and the likelihood (s)he will make breakthrough discoveries is…yes, you guessed it … ZERO! Conversely, if one has imagination, is open to new possibilities, then regardless of “brain size,” with enough effort, breakthroughs are indeed possible.

In philosophy of science, there is a key finding by that tragic philosopher Edward Constant, known as “presumptive anomaly.” Briefly put, Constant suggested that new discoveries are made because the discover finds something interesting used in some field, that should work in his or her own field but finds that anomalously it is not used. Her/his presumption that it will work in her/his field is strong enough that (s)he then puts in the effort and makes it happen! Hence, Frank Whittle is thought to have got the idea of the airplane jet engine based on his learning about the steamship turbine of the 1900s. Likewise, supposedly, Frank Williams (yes, another Frank!) the famed F1 car designer, when boarding a plane suddenly realized that if he inverted the wing shape of a plane and used it on a car, he could get tremendous down-force. He did this, and his cars were unbeatable until such wing shapes were banned! Long story short–if you want to make breakthrough discoveries, look for “presumptive anomalies.”

As with jet engines and F1 cars, so also for soils! It would have been anomalous if, possessing a steady-state, soil behavior was not a dynamical system. For me, the easiest way to find such anomalies is to read widely–no, not newspapers, magazines, text books, nor even journals (and no, sorry, I do not count watching documentaries as “reading”). I mean reading books, then too, non-fiction books, of all kinds (I also get the same benefit from listening to them on tape or CD or MP3 player when commuting). Speaking for myself (you could well differ in what works for you, after all Williams found his anomaly when boarding a plane), I find the long and immersive experience of reading a non-fiction book as necessary to find lasting, fruitful presumptive anomalies. And even if a book leads to no presumptive anomaly, I find it gives often gives me new information, fertile ground for new associations and new ways of looking at old problems! I owe a huge debt to my mother and father, for encouraging in me a deep and abiding love for reading such books, and I read them continuously because I enjoy doing so. I try to average at least one non-fiction book a week and if I do not read at least 30 such books in a year I feel I am slacking.

In fact, I think that reading non-fiction books is a “secret” and powerful weapon, a secret that lies “hidden” in plain sight, available for all to use, but which in actuality, very few do. If I had one piece of advice it would be this: read books–ideally, non-fiction books outside of your field. Should you read only the journals or books belonging to your field then rest assured that you are highly likely to be one of T. S. Kuhn’s “foot soldiers of science,” i.e., someone destined to only incrementally extend existing discoveries and not someone who will create new, deep understandings triggered by resolving presumptive anomalies discovered in the course of reading books outside of one’s field. By reading Al Gore’s book, I for one discovered one such presumptive anomaly, one that resulted in the creation of DSSM. This method of discovering and resolving presumptive anomalies in one’s field and thereby making deep discoveries is simple, but requires sincere effort.

Now say, that based on your extensive reading on other fields, you’ve identified a presumptive anomaly in your own field, worked on it for several years, and finally, after much effort, have successfully resolved it. You may then think, as I did, that you are done–that researchers in your field are going to welcome your findings and that all you need do is to write up your results in a paper and send it off to a top journal for publication .

Far from it! In fact, your work is just be-ginning, as I learned the hard way! Typically, resolving a “presumptive anomaly” results in significant disruption of existing practice. And the more disruptive your finding, the more it is likely to meet obstruction by the experts and other vested interests in the current paradigm. An essential (if difficult) book to read on this topic is T. S. Kuhn’s “The Structure of Scientific Revolutions.” Almost everyone who in the process of resolving a presumptive anomaly creates thereby a new paradigm runs immediately into a head on confrontation with the existing establishment in their field.

Edward Constant in his book The Origins of the Turbojet Revolution (a fascinating book, a must read!) reveals how, for example, Frank Whittle was asked to take his idea to leading aeronautical engine experts in the world, (experts in internal combustion engines, i.e., the then current paradigm). These experts (mostly academics) scoffed Frank’s idea of the turbojet, with one such pundit proclaiming dismissively to Frank that his engine would not have the power to “…pull the skin off a rice pudding.” The stresses resulting from these obstructionists led to Frank Whittle’s 1940 “nervous breakdown,” the first of three that he would have in the years to come! F1 racing car designer Frank Williams did not have to face this issue as he controlled his own company, had his own source of funds, and consequently could do as he pleased.

As Edward Constant points out in his book, when you have a NEW paradigm, the LAST person to take it to for validation is an expert in the CURRENT paradigm. The reason the is quite simple–practitioners seek to protect their investment (normally substantial) in the current paradigm and so they have a bias against new paradigms. Such a bias may be conscious or unconscious, and regardless of all the solemn talk about “the need for out-of-the-box thinking.”

I was lucky. In 2008 I was fortunate to present my first paper to Joe Labuz, then editor of ASCE’s Journal of Geotechnical and Geoenvironmental Engineering. Joe had the technical knowledge and self-confidence to override a negative recommendation from one of his reviewers, realizing that this reviewer knew nothing about dynamical systems theory.

Joe also took me up on a suggestion I made to him to have the paper reviewed by a professor of applied mathematics. I made this suggestion because I knew that most soil mechanics people would know nothing about dynamical systems theory. The review by the mathematician that Joe found would turn out to be worth ten times its weight in gold.
This anonymous mathematician validated my model, but said that while two hundred years ago such a model might suffice, today the bar was higher–that what I had was really a phenomenological model (I didn’t understand what “phenomenological” meant when I first saw this term in the review), and that I really needed to find the physical basis of my phenomenological model.

For this review, I owe Joe Labuz a big thank you because prior to Joe’s feedback I had been quite unaware of either what a phenomenological model was or the need to drive a phenomenological model down to its underlying physical basis, obvious though it now all seems in hindsight (again, hindsight makes all things seem “obvious”). Sure enough, even though initially I was convinced it would be impossible for me to find the physical basis of my model, two years later, because I had been primed for it by Joe’s feedback, the physical basis presented itself to me.

Beyond this specific review by this mathematician, I am deeply grateful that the first editor to review my paper was Joe Labuz (who didn’t know me from Adam), a person who had the technical strength, confidence, and open-mindedness needed to properly evaluate new ideas. I was to later find that these properties are not commonly to be found in the same individual; such individuals are the striking exception, not the rule!
Like Joe Labuz, Peter Clayton at Geotechnique, Chandrakant Desai and Musharraf Zaman at the International Journal of Geomechanics were three other technically very strong, self-confident editors, able to override less than skillful assessments from one or two of their reviewers.

Some of these reviewers, apart from an expected lack of knowledge of dynamical system theory occasionally betrayed what struck me as a surprising and completely unexpected lack of understanding of the basis of the scientific method (i.e., that in science, the only thing that counts is whether predictions from theory match experimental data and that one’s own subjective opinions, i.e., biases, play little to no role). A few reviewers also seemed surprisingly ignorant of basic calculus and probability theory (for example one reviewer did not even know the chain rule!)

Strangely, this seemed particularly true of some of the assessors at Geotechnique and the ASCE’s Journal of Geotechnical and Geoenvironmental Engineering. And unfortunately for me, due to a change, these journals were now piloted by editors (Alexander Puzrin and Patrick Fox respectively) who seemed to lack the technical confidence needed to make their own independent decisions regardless of what their assessors said. Bureaucrat gate-keepers, both failed the acid test of a new idea.

In general, the reaction from the older academic community, with the exception of a few “stalwarts,” has been one of “silence.” The history of science shows that this reaction, unfortunately, is to be expected. As Max Planck said wryly: “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”

Sad but true! Nonetheless, I find Planck to be unduly pessimistic–he did not have the tools we have today to track changes in opinion. In my case, the usage logs for this site, and the email questions I receive reveal that the interest in DSSM is very strong, and as old Max correctly said, is primarily to be found in the next generation. For example, graduate students send me numerous emails, representative ones of which I have posted directly on this site, emails that show that they are keenly aware of what is going on! Kudos to them!
So though Max Planck was correct in that the next generation, having little vested in the existing/old paradigm is open to a new paradigm(in fact, they often feel sealed out of the existing paradigm and so actively seek out new ones), the process of change is continuous and does not wait for the older generation to completely disappear.

The web logs also indicate something unexpected–that yes, the Cold War still rages on, but silently, at the “grass-roots” level, and with a new wrinkle. Thus, on average, for the year 2014, every month, after accounting for bots, spiders, and other non-human agents, the web logs for this site indicate that about 1,500 unique users visited the site. Between them, every month, they averaged a total of about 6,500 visits, in the course of which they downloaded on average a total of 24,000 pages. More precisely, for all of 2014, a total of 18,352 visitors made 79,631 visits and downloaded 284,542 pages. Note: This indeed is the revolutionary power of the internet–that in one year, I, who have never once taught a single classroom based soil mechanics class (or any class for that matter), can suddenly reach out and teach far more students in one year than most people do in their lifetime in a classroom setting. Life is indeed strange.

But it is the distribution of visitors across countries startles me and leads me to the conclusion that a new Cold War, not that much different than the old one, is waging silently, at the grass-roots level, revealing its outlines in cyberspace, and defining what the 21st century is going to look like. Thus, the country with the most visitors and pages downloaded is the US–on average, the number of visitors from the US and the pages they download equals the sum of all the other visitors from the other countries and the pages that they download … but for one country–China! China is second in terms of the number of visitors and pages downloaded. In fact the enthusiasm from China is HUGE–one user even translated my table of contents to modern Chinese on his own and kindly sent it to me to use. And use it I did! Third in terms of usage are, cumulatively, the countries of the former Soviet Union–Ukraine first, followed by the Russian Federation.

Then come countries from the EU: Netherlands, Germany, France, and so on … strangely the UK hardly figures–I now think that sadly, the UK is no longer a “power house” in terms of new ideas in soil mechanics. Lost in dreams of the glories of yesteryear, it betrays no curiosity about new developments in other countries. Brazil and India also show very low usage. I understand why it is so for Brazil, after all, English is not their main language. However college education in India is exclusively in English and in modern India, English is often a first language (yes, first language) for many, myself included. I am beginning to think that India is perhaps at root, hostile to innovation and new ideas, a result maybe, of a residual caste system based mentality by which innovation is ever a threat.

So basically, the logs appear to tell me that the 21st century is going to be a struggle for dominance in the world of ideas between the US, China, and the countries of the former Soviet Union! Being brought up under old school rules of “cricket” all I have to say is: “may the best side win.” And hopefully, they will treat the rest of us with kindness.
Back to Steve Poulos though. I think it is a real tragedy that he has not been recognized for his seminal contribution to soil mechanics. But he is not alone–I believe Golamreza Mesri at the University of Illinois at Urbana-Champaign deserves formal recognition for his discovery that the ratio is nearly constant, and that the EOP curve under static loading is unique (see Chapter 7 of this course to see how both these conclusions can be reached from first principles using DSSM theory). Many people, long since forgotten, have been awarded Terzaghi and Rankine lectureships for reasons that, unlike the case of the Nobel prize, are murky and hard to figure out, captured by a generic “…contributions to the field.”

I was taught by no less than four Terzaghi lecturers, including one who was also a Rankine lecturer. These were intense semester-long interactions in small size classes in Graduate school, but today, almost 30 years later, despite being familiar with the important research in soil mechanics, I am yet to figure out what exactly is the specific innovation that each of these so called “Terzaghi lecturers” contributed. They were very charismatic people though with strong personalities and the ability to “meet and greet,” with a huge network of devoted former students and associated with them, a “cult of personality”. Stepping back, these “personality cults” strike me as so imma-ture, so “boy” (“boi?”) like, and really, so immature, they disgust me!

I recently had to interact with a Rankine lecturer, a professor at an esteemed college no less, who amazingly did not know that i) a key requirement for a theory to be scientific was for it to have a falsifiable hypothesis, ii) to teach a theory that was not scientific (lacks a falsifiable hypothesis) as though it were scientific, makes the teaching meet the definition of pseudoscience and c) a common meaning of the word “scholastic” is to “adhere to tradition and logic (Aristotelian) and to pay little heed to the empirical evidence.” Naively he seemed to think it was confined to mean “…someone with no practical work experience.”

This is why I now believe that the Terzaghi and Rankine lectureship awards are but the result of the smooth and seamless operation of incestuous “old boy/girl networks.” These networks are not “conspiracies,” but rather, a natural outgrowth of the system as it currently is. This is why I have now come to believe historians when they say, that we must wait till 50 years after the events have occurred and the dust has settled, before we can decide questions of true merit. Surely, then, Steve Poulos and Golamreza Mesri will be given the kudos they so richly deserve.

Because of this “old boy/girl network” based identification of awardees, the Terzaghi or Rankine lectureship is given for the reasons that are opaquely worded as “…contributions to the field”–the real contribution is unclear in most cases. It is precisely to guard against this kind of loss of credibility that the Nobel Prize specifically targets a specific achievement–for ex. the discovery of the structure of DNA–and consequently, the Nobel Committee can confidently award a 34 year old youngster the Nobel Prize for a discovery he made when he was 25. I am talking of course about young James Watson who at 25 made the key discovery that would win him the Nobel prize ten years later.

So if one were to take Golamreza Mesri for example, he would have earned his award about ten years after his discoveries in the mid-eighties. His award should have read…” for discovering that the ratio is approximately constant and that the EOP curve obtained from static, incremental, one-dimensional loading is unique.” Likewise Steve Poulos formally presented the steady state in courses at Harvard University starting in 1971 and ideally he should have got his award in the early 80’s. For Steve the reason for his award would read something like…” for formally describing the steady-state condition in soils and its impact on soil behavior.” Not in either case, the opaque “…for contributions to the field.” Even statements like “…for contributions to the development of the piezometer” (for example) do not quite cut it–exactly what contributions are we talking about?

Both Golamreza’s and Steve’s theories meet that acid test of a scientific theory–they are falsifiable hypotheses that yet remain unfalsified. As detailed in the Conclusion, with its many findings, DSSM is also strongly falsifiable, but yet remains unfalsified. By contrast, metal theories of plasticity as applied to soils can be easily, routinely falsified–simply apply the model to any real soil with a variety of grain-sizes, and Ko consolidated. Yet proponents of metals based theories do not seek to falsify but rather to confirm their theory by modeling only “simple clays” with “simple” stress-strain curves.

I can run thousands of tests on a fat clay, isotropically and normally consolidated to test my model, but this is “conformal” testing, not falsification testing! This kind of conformance testing is not the way to attempt to falsify a hypothesis and if an undergraduate were to come to me with this kind of validation, I would use it as a “teaching moment” on how science is properly done. But for seasoned professors to use conformance testing is, simply put, unpardonable! In short, metals theory of plasticity as applied to soils is a broken theory, readily falsified with stress-strain data from real soils. Yet, no one seems to call to account those that push these flawed, broken, and failed theories!

Experience has taught me that the best way to judge someone’s geotechnical merit is to ignore the number of publications they have, ignore their degrees, ignore their titles, their prizes … ignore everything about them, including how they smell, look, feel, talk, or (horror of horrors) whether they kick their dog when alone at home. They may even look green, drive what looks like a flying saucer, and appear to be from Mars. Ignore all this! Instead, simply ask them to tell you in one sentence restricted to twenty-five words or less (ideally ten words or less), what their most important contribution to soil mechanics has been.

Judge their soil mechanics merit accordingly. You will find that many of these so called Terzaghi and Rankine lecturers will simply disappear, while people like Mesri and Poulos will come to the fore. Note: The fewer the words, the more powerful the finding–Watson’s discovery (“discovered the structure of DNA”) takes just five words; Poulos’s (“formalized the steady-state condition”) takes just four!

NOTE: I am happy to report that six months after I posted this, in September 2014, the ASCE suddenly presented Mesri with his long overdue Terzaghi Award. Nonetheless, note how the citation remains as always, opaque and does not mention his key contributions, ones that will last for the foreseeable future–finding that the ratio of creep rate to compressibility index is approximately constant and that the EOP curve obtained from static, incremental, one-dimensional loading is unique. Why might this be the case? Because to specify his key contributions would but highlight the fact that almost every other Terazaghi Award winner, has made NO such fundamental contribution, the four such awardees who taught me for example. Anyway, perhaps the less said the better. Now, its Steve Poulos’s turn.

Looking back on my own personal journey in soil mechanics, it seems nothing but the same old story–The Three Metamorphoses of the Spirit–that Nietzsche powerfully described in his classic Thus Spake Zarathustra. Thus with Ramaswamy, and at Purdue and MIT, I was like a camel, loading myself, in my case, with knowledge. After the fiasco at MIT I rushed in the desert.  At GEI, thanks to the nurturing kindness of Gonzalo Castro and Steve Poulos, I turned into a lion. Then, for the next ten years I fought with the great dragon: “‘Thou-shalt,’ is the great dragon called. But the spirit of the lion saith, ‘I will’.” And then, in the course of this struggle, I became like a child in soil mechanics: “Innocence is the child, and forgetfulness, a new beginning, a game, a self-rolling wheel, a first movement, a holy Yea.”

I wonder how many of you will understand how exactly Nietzsche described this, my long (three decades) journey in soil mechanics–I myself understood it only recently, several years after it was all done.

Anyway, that’s it folks! As always, I love hearing from you, so do email me on my book page at Taylor and Francis (CRC Press/Balkema) your thoughts/opinions; rest assured I shall reply so long as I am physically able to.

Notes
1. For those with some background in neuroscience, it may be of interest to know that when I formulated the equations for the phenomenological model, my thinking till then had been predominantly in terms of visual images–grains tumbling and rearranging under the action of small force vectors that I pictured in my mind. In late 2006, I sent the equations for the phenomenological model to my undergraduate professor, Prof. S. V. Ramaswamy, who had introduced me to soils in 1980. He then asked me what the equations signified. It was only when he asked that I “translated” the equations into words for the first time, even to myself (“the rate of change of p’ and q is proportional… etc.”). In other words, the verbal description in ordinary English statements and words came only about six months after I had first described the mechanism mathematically. Now both mathematics and the higher stages of visual imagery involve the PFC and right hemisphere, and my solving the problem without using language, must imply it was largely a PFC and right brain hemisphere activity. I hypothesize now that the left hemisphere, with significant parts of it used up by the Wernicke and Broca areas that deal with language, may actually be handicapped in terms of introspective problem solving, and that contrary to common thinking, the right hemisphere may be actually more powerful in solving deep problems using imagery together with the mathematical functionality of the PFC. In short, the basis of so called “creativity” or “intuition” (commonly associated with the right hemisphere) may but be but genuine, logical understandings that are only not expressible in conventional language. Looking back, the three hardest problems that I have solved in my life have all been solved outside of language. Perhaps in this case the three notebooks I filled up with “junk mathematical explorations” were not a waste at all but rather drove the mathematics past the intermediary barrier of language, right down to the actual mechanisms being modeled? Perhaps this deep immersion even though in what turned out to be dead ends made my brain more powerful in its approach to the basic problem as now language became “superficial” allowing my brain to discard “mere words” and to tackle the problem directly? An interesting book that I highly recommend reading is “The Autistic Brain” by Temple Grandin. She posits there are two types of thinkers–most people are top down thinkers (proceed from concepts, to the underlying details) while those on the autistic spectrum are bottom up thinkers–(-proceed from details to then build concepts). I am a “bottom up” thinker. Likewise in each group she posits three kinds of ways of thinking–one that primarily uses word facts, one that uses images and one that uses patterns. Many people are “word facts” thinkers and so do well when learning from standard text books. These people tend to do well in school. Others, including me, are image and pattern based thinkers, and don’t do so well in traditional school. I learned this only when I was 55 and wish I knew it when I was 5–it would have saved me a *whole lot of grief* in school! I also only recently discovered that I am probably on this autistic spectrum–luckily for me at the productive (Asperger’s) end of it, what Temple Grandin calls a “happy Aspy.” She claims that many of the computer scientists she meets in Silicon Valley are “happy Aspys.” Reading her book explained to me a lot about my own life, both past and present, both good and bad.