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.’

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) 

A review of Prof. A. Schofield’s book

Posted in Critical State Soil Mechanics by Paul Joseph on October 22, 2007

NOTE: I wrote the review you see below, in 2007.  At that time I naively did not realize that the concepts in this book would be used to inform text books on geotechnical engineering, and realized this only when I was recently asked to evaluate a proposal for one such text book.  This led me to finally appreciate the dangerous nature of the understanding on liquefaction Andrew Schofield proposes.  As a result of this new appreciation, today I consider this book to be both dangerous and scholastic, and feel strongly that I have to make this corrective comment.  Andrew Schofield claims that soils on the contractive side of the steady-state line do not liquefy.  This is wrong!  It derives from the scholastic assumption that particles are isotropic; isotropic particles on the contractive side exhibit stress-strain curves that rise to a maximum and stay there.  Real soils are not made of isotropic particles and so, on the contractive side, such particles exhibit stress-strain curves that rise to a peak, then decrease to their steady-state value.  Such soils can absolutely liquefy!  For more details read Section 4 below, on liquefaction, which remains largely as I wrote it in 2007. Further, as I point out below, I understand CAM clay, which is the basis of this book, as to be but an exercise in scholasticism.  Soils cannot be treated as metals made up implicitly of isotropic point particles. Any model based on the Drucker and Prager failure criterion makes this underlying assumption that does not apply to real soils.  Rather, soils are constituted of finite particles that have anisotropic properties and these govern behavior.  Consequently models based theories that implicitly (or explicitly) assume isotropic point particles routinely fail to match readily available data from real soils, i.e., such theories can be routinely falsified.  This inability to match real data was known almost as soon as the elasto-plastic critical state based model was first introduced.  Paul G. Joseph, Tuesday, August 10, 2015.

Disturbed soil properties and geotechnical design

A.N. Schofield, Thomas Telford, London, 2006, 216 pages

Und wenn du lange in einen Abgrund blickst, blickt der Abgrund auch in dich hinein.

[And when you look long into the abyss, the abyss also looks into you.]

– Friedrich Nietzsche (Jenseits von Gut und Böse [Beyond Good and Evil])

INTRODUCTION:

Long story short—buy this book and master it, for this little book is a rarity in its field and worth every cent of its price. It is an important book, a snapshot of the current state of soil shear as viewed by one of the founders of Critical State based soil mechanics, and taken from the perspective of the Cambridge, England, school of soil mechanics . It is essential reading for anyone who thinks they have something to say about soil shear. Should you master it, whether you agree with its concepts or not, you will be very knowledgeable about soil shear. The book is not a textbook, and is much the better for it. It is the only one of its kind in geotechnical engineering that I am aware of; it stands in welcome contrast to the pile of mediocre textbooks available at twice its price.

A good book reads the reader and not only does this book read the reader, it reaches out further and reads both the profession and, its author. Hence the quote from Nietzsche above as it seemed to have the needed gravitas as opposed to the simple “a good book reads the reader.” Once you read this book, you will realize the gaps in your education, the gaps in the profession here in the US, the gaps in the profession in the UK, and the gaps in the book.

My review consists of four parts—this introduction, comments on the book in general, discussion of the specific points made, and a conclusion.  I have tried to make it “modular” so that each part (and sub-part) is self-contained–if you are pressed for time you can skip a part and jump to the next.  You can even jump straight to the conclusion should you be very pressed for time!

In the first line of the Tao Te Ching Lao Tzu famously said that “The way that can be written is not the way,” and I find him to be exactly right.  Consequently, I will revise this review as and when I am presented with new information or insights.  I encourage you to stop by at least once a year to read my latest version.  I also enjoy and learn from your comments, so please do post a response to my write up–what you like about it, what you disagree with, as well as anything else you would like to add.  Should you think your colleagues will find this review of interest, please forward it on to them.

[NOTE 1: if you came here only for my critique of critical state soil mechanics you can go to the conclusion without loss of continuity.]

[NOTE 2: The opinions expressed here are mine and mine alone.]

COMMENTS ON THE BOOK IN GENERAL

One drawback about this book is the figures, some of which are less than clear to me. For example, the frontispiece and figure 55 are key figures, but were confusing to me. References to figures scattered throughout the book force one to scurry from figure to figure and page to page, all to understand a single paragraph.

The other cavil is that Schofield is in general gives short shrift to both Terzaghi and Harvard. In this sense, the book reads Schofield. Thus while it is true that Terzaghi may have been wrong regarding cohesion, it nonetheless does not diminish his achievement of discovering the effective stress principle and formulating a mathematical model of pore pressure dissipation. Harvard also gets short shrift but the book presents only a partial picture of the activities at Harvard with no mention made of important concepts from Harvard such as the steady-state condition and it being the reason for Casagrande’s recommendation regarding liquefaction that is posited as wrong on the back cover of the book.

As someone long used to the KISS (Keep it Simple and Stupid) style of writing often used in the corporate world, I did not find this book an easy read and often wished that it used the KISS approach. I read only about three pages a day, but made sure I knew which parts of the three pages I understood and which I did not. There is still much in this book that I do not understand and which I suspect to understand requires me to fundamentally shift my interests.  In this way, the book read me, exposing large gaps, selectivity, and bias, in my knowledge of soil mechanics in general and of shear strength in particular.

These are but minor cavils and more than balanced by the points made and by the interesting quotes from still very important original works by Coloumb, Rankine, Terzaghi etc. Rather than review the book chapter by chapter, I have identified what to me were important themes that thread through the book and have commented on these.

Prof. Schofield was kind enough to answer numerous questions from me by e-mail and this review contains some of this information. As Prof. Schofield recommends, first read the book with a “credulous mind.” He says that his earlier book—Critical State Soil Mechanics (CSSM)—is “widely quoted, but little understood.” I hope I do not make that mistake in this review, but if I do, I do so in the sense of Blake’s “If the fool would persist in his (or her!) folly, he (or she!) would become wise.”

DISCUSSION OF IMPORTANT THEMES

1. Isotropy, shear planes and stress paths vs. tensors and the implications thereof

Some themes run throughout the book; isotropic continuum vs. shear planes; stress paths vs. tensor representations of stresses.  Per critical state soil mechanics, the aggregated grains that are shearing and which are of interest are always isotropic, with grains of all shapes and sizes distributed randomly and having no distinct geometrical patterns be they on the wet or dry side of critical. Grains form a three-dimensional skeletal structure with lines of highly loaded grains that buckle as the loads change. The grains move into new three-dimensional structures. Aggregates are elastically loaded and unloaded and deform plastically. As a whole, the aggregate behaves as an elasto-plastic material.

On the wet side of critical, a volume of soil reaches the critical state without formation of a shear plane. On the dry side, though, a shear plane forms. Hence samples initially on the wet side of critical fail in a sort of bulging manner with no definite failure plane, whereas those on the dry side develop failure planes.

In the lab, once a sample fails with a shear plane, per Schofield’s approach, the sample is no longer in a known state in terms of measurements of strains with sliding occurring on a plane between two rigid blocks. In the field, failures on the dry side as in the case of over-compacted soil can cause dangerous instabilities, whereas soils that are on the wet-side are ductile and fail in a stable manner. Analyses in the lab or in the field that use stress-paths as is commonly done in the US are not correct as on the wet side, one is not dealing with a distinct plane of failure, but with a volume of failure. Tensor analysis of volumes of soils is required, but since this approach appears more “complicated” than the stress-path approach, engineers (especially in the US) do not use it.

Implications of the importance given to the failure plane by Schofield are of great significance I briefly explore how it relates to the steady state shear strength. There are three differences between the critical state and the steady state. One is that the steady state has a requirement that the deformation explicitly occur at a constant velocity. Fair enough, but since the critical state implicitly occurs also at effectively a constant velocity—the quasi-static velocity—it meets this requirement of the steady state. So does the critical state correspond to the steady state with deformation at quasi-static velocity?

Not quite, we have the second and third differences. First, that shown in Fig. 8.18 of CSSM where soil strength decays below that shown to be the critical state and second, that at the steady state, there is an explicitly oriented structure as opposed to the implied random structure of the critical state.

According to Schofield, Figure 8.18 distinguishes between two different ideas. The first is the idea of a test path of successive states that lead to the critical state that obtains for an initial single volume of aggregated grains which becomes three distinct bodies; two blocks that are in sliding contact but not yielding because they are being unloaded and a third thin smear of CS paste in which all displacement becomes localized on the slip surface.

This distinguishes against the second idea—that of residual strength on a slip surface where the relative displacement has a slip length longer than the length of many typical grains, with particle alignment in the direction of slip. The basis of the critical state concept is the concept of isotropic aggregates, continuing to remain isotropic during shear even if the thin smear is a layer that is only 15 or 20 grains thick after failure, i.e. there is no particle alignment in the direction of slip. Fig 8.18 shows the resulting contrast. The path shown to the critical state is the behavior of the ideal theoretical model following the ideal test path to the critical state. Real test data may not follow this test path, leading instead to concepts such as the steady state, with its associated rotation and alignment of soil grains, which the critical state model does not represent.

Per Schofield, tests he ran at Manchester on a model of a trench cut into a large sample of stiff fissured clay showed that the little block of clay that had slipped had a slip surface with a thin smear that was a slickenside. However, it was clear that “the clay first deformed as a rubble of blocks and then as these moved their faces had slipped against each other and a continuous surface had formed with many smooth bumps as it passed over the separate blocks in the sliding faces.” Per Schofield, “…the residual strength is something for an engineer to have in mind in site investigation. If there is evidence that at some past time there were large displacements of many feet on an old slip surface and it is found now to be a slick surface then the strength must be expected to be much less than CS.”  He tells me that a horizontal, think layer of Kaolinite clay within limestone or chalk will allow the blocks of rock above and below it to have very large relative displacements on a slip plane.

Were Schofield right in that particle alignment plays no role in shear, then he has a point. I feel though that it probably does play a role, that conditions in failure are not as unknown as Schofield makes them out to be, and that consequently, the steady state is a robust “real life” concept as opposed to the more theoretical but more developed critical state concept.

2. Use of plasticity theory in soil shear theory

Another theme that runs through the book is that of “plasticity.” The book has a chapter on the plastic design of structures, and in Schofield’s book concepts of plasticity app directly apply to a structure such as a dam made of compacted soil. A comparison is made of the Empire State building, vs. the Murrah and the World Trade Center (WTC) buildings. At the time Schofield wrote the book, the prevalent theory on how the World Trade Towers had failed emphasised the high temperature of the fire and supposed that the connections between the horizontal, wide, open floors and the outside tubular wall of windows and columns gave way suddenly and the floors “pancaked” on one an other and that both the WTC and the Murrah building were not designed to fail “plastically”.

Schofield notes that fire at the top of a WTC tower did not heat lower floors.  People were still escaping down “cool” stairwells at the time of the final “pancake” collapse.  He also considers that failure of US educators to teach student engineers the lessons learned from World War II in bomb damaged UK, had the result that the WTC and the Murrah building were not designed with floor-to-column connections allowing sufficiently large lateral displacement.  Ductile connections are essential for such structures to fail plastically.  Experts now think the WTC failed plastically initially allowing many to escape, but that ultimately it underwent a brittle failure. This though does not nullify, but rather supports Schofield’s larger point that buildings should be designed to fail plastically.

Schofield extends the soft plastic yielding of structures to soil and recommends that soils be brought to a ductile state where they will yield in a stable manner. Using the analogy of the blocks of stone used to build Kings College chapel in Cambridge, he points out that masonry recover any energy used for dilation. He describes work done at Cambridge by numerous researchers using the Cam-clay model in which the work input by the movement of forces on the specimen boundaries plus or minus changes in the stored elastic energy in the aggregate of grains, is dissipated in friction.

In using theories of plasticity and flow rules upon which to describe and quantify soil shear, Schofield puts soil shear firmly on a “scientific” footing, points to the future, and offers a welcome contrast to empirical, thumb-rule driven approaches such as SHANSEP.  However, plasticity theory treats soil as a “paste” and so is unable to provide insight into soil structure and changes in soil structure with shear.

3. Terzaghi’s Error

The back of the book states that Harvard soil mechanics teaching contained two errors. The first of these was that Terzaghi was wrong to assert that soil has true cohesion and friction. i.e. that soil strength came from “pure” cohesion and friction. A major thread running through this book is how and why Terzaghi was wrong. For Schofield, Taylor’s discovery with sands holds equally for clays–soil strength is due to interlocking structure plus friction. Terzaghi thought that surface chemistry of fine clay mineral grains and dissolved salts in pore water was the basis of adhesion between grains i.e. of true cohesion.

Schofield’s claim that Terzaghi was wrong rests on two main points–one that Hvorselv’s data that Terzaghi used as a basis for his claim, plots a line that ends where it intersects the critical state line. Hvorslev had no data to the right of this line, but Terzaghi and Hvorslev extended their interpretation of this line without any limit, into this region where he had no data points (normalized confining stress > 0.6 in Fig. 27.) Second, any true cohesion would exist on both the wet side and dry side of the critical state line, or not exist at all, and soil states on the wet side of critical show no sign of cohesion. In short, the apparent cohesion measured on samples on the dry side of critical is the result of interlocking and is not true cohesion. Engineers should not rely on it in their designs.

Underlying Schofield’s premise regarding the lack of true cohesion is a far deeper principle with important implications. This principle is that the movement of soil aggregates is due to grain-to-grain contact and not due to surface chemistry i.e. viscous layers on the surfaces of soil grains sliding past each other. This in turn means that the movement of importance in soil shear is of the type driven by changes in shear and effective confining stresses and not by viscous effects of surface chemistry and that viscous effects of the surface chemistry such as strain rate dependence and creep are of small importance.

Hence, per this view, there is no need to give strain rate undue weight–and the steady state’s requirement of explicitly specifying the deformation rate is of secondary importance as the only rate that is important is the quasi-static rate. Research at Harvard by one of Casagrande’s students indicated that the dependence on strain rate of the steady state strength, while it did exist, was small. In addition, as explained later on, the emphasis of the Soviet Union’s centrifuge studies on creep, took its soil mechanics in a different direction to the soil mechanics based on grain movement due to shear and effective stress changes.

While Schofield has a point that the geotechnical engineer should not rely on cohesion for his designs, one wonders with another reviewer, if given the fact that the bulk of the tests done at Cambridge were on kaolin, a clay with relatively low surface chemistry, whether the results would be different if highly plastic clays such as smectites had been tested. In short, while it may be correct that surface chemistry plays a small role at the stress levels encountered in geotechnical design problems and that one should not use it in design, in reality it probably exists and play a small role as revealed through the slight dependence of the stress-strain curves on strain rates, and by soil creep.

4. Liquefaction

The second error in the teaching of soil mechanics at Harvard according to Schofield is that Casagrande was wrong to assert that contractive soil liquefies. Strangely, the unabridged Oxford English Dictionary does not have a meaning for “liquefaction” in the context of soil mechanics and earthquakes. Perhaps if it did, a lot of the confusion and misunderstanding in this area would just simply go away.  It turns out, for reasons explained below, that Cassagrande remains correct–and that Schofield is dangerously wrong–soils on the contractive side of the steady-state line do indeed liquify! (Note: Schofield and others use the term “wet side” and “dry side” to indicate soils states on either side of the steady-state line.  Steve Poulos does not like these terms at all, as they don’t describe behavior, i.e., he prefers instead the terms “contractive” and “dilative” to “wet side” and “dry side” respectively, as they describe the actual soil behavior.)

Liquefaction for Schofield consists of two types—Hazen’s and Herrick’s. Per the Harvard school of thought, there are five terms that are related, overlap, and which need to be clearly distinguished from each other. These terms are “liquefaction”, the “z-condition”, “deformation during cyclic loading”, “sand blows”, and “quicksand”.

Off these, “Harvard terms”, the “liquefaction” term is the one that Casagrande had in mind when he said that that if a soil state moved to the contractive (wet) side of the critical or steady state line, then it was at risk of liquefying. Liquefaction per the Harvard definition is a stability failure due to undrained shear of highly contractive, fully saturated masses of soil, where the driving shear stresses are greater than the undrained steady state shear strengths such that failure involves acceleration of the mass and its subsequent coming to rest as the driving stresses are reduced and the inertia of the accelerated mass is overcome by the undrained steady state shear strength. As so defined, it corresponds to Hazen’s liquefaction.

Per the Harvard approach, soils that show a peak with subsequent decrease of their shear strength are candidates for liquefaction, if they were loaded to a meta-stable condition (in-situ static shear stresses were between peak and steady state values.)  Strain caused by an earthquake would cause strengths to first increase, but then post peak, they would decrease, a result of soil particles aligning in the direction of the shear.  Once they decrease, post-peak, below the in-situ static shear stress,  there would be failure (liquefaction) with the soil failing in a process that Casagrande called a “chain-reaction” that starts locally and then spreads.

Per Schofield though, Casagrande’s “chain reaction” with its particle realignment, flow structure, and decay of shear strength to steady state values does not occur.  He says that he could not trigger Casagrande’s chain reaction in his testing when he searched for this (on the wet side.)  A stress path for disturbed-soil paste  can never lead to Casagrande’s “chain reaction” if the soil particles are such that, shear strengths uniformly increase to their steady state values. This is the case for soils made up of “bulky grains” or grains that resemble “point particles” such as the clays that formed the bulk of the soils that Andrew used.  Consequently, though there may be deformation due to yielding, there would not be a stability failure as the driving stresses in-situ prior to the event would be lower than the critical state shear strength that the system would reach during and after the earthquake.  For soils with platy or elongated grains though, the situation is different and here after peaking, soil strengths decrease to their steady state value.  Here, one should indeed see the “chain reaction” and a liquefaction failure, if the soil had been initially subject to a shear stress value that was between the peak and the steady state shear stress values.

As Steve Poulos wrote me:  “The contractive sands and clays that lead to flow failures (liquefaction) have a peak and a drop down to the steady state strength. The reason that the drop occurs is that the peak is formed as the undisturbed structure is modified by the shear loading until it breaks down and the strength drops as the strains increase, until the steady state strength is reached.”

So I asked Schofield and he clarified: ” The Critical State point of view gives simple equations of the mechanics of an isotropic aggregate that dissipates work as it deforms in shear but continues to remain isotropic. My ideal aggregate has the behavior that Taylor observed. It contracts or dilates depending on whether it is on the wet or the dry side of the Critical State…The Original Cam Clay (OCC) equations provide a full prediction of the stress strain path resulting from loading or unloading; it applies when grains form aggregates that are isotropic. I do not doubt that other soil grains may align themselves to form an aggregate with transverse isotropy.”

In a nutshell, the Critical State concept applies to an idealized aggregate, not a real soil, and this idealized aggregate contracts or dilates depending if it is on the dry side or wet side of the Critical State.  The book though does not emphasized the “idealized” nature of the soil to which the critical state concept applies and as a result, wrongly indicates that one does not need to study the risk of liquefaction if one is meta-stable on the contractive (wet) side.  So I asked Schofield: what about “real life” soils?  Schofield answered indicating that first one had to understand the behavior of idealized aggregates before one could really understand “real life” soils.

Casagrande’s “chain reaction” can indeed be systematically triggered in a triaxial test.  I will never forget an experience I had in the early 90’s, standing with Gonzalo Castro next to a triaxial test under “meta-stable” conditions, along with the lab director Gregory Thomas who was running the test.  The sample had been loaded undrained to a shear stress approximately half way between its maximum shear strength and its steady state shear strength (i.e. it was “meta-stable.”)  The undrained sample was then “tickled” by subjecting it to very small cyclic strains.  As expected, when the cumulative strain reached a “triggering” value corresponding approximately to the post-peak  shear strain at which the available shear strength was less than the imposed shear stress, the sample failed catastrophically, and with a loud noise like a bomb going off, as the dead-weight crashed down and slammed into the floor.

I was so startled that I  raised my hands and ducked under a nearby heavy laboratory workbench to protect myself against what I thought had surely been an explosion of the lab’s huge air-pressure cylinder.  Castro being the kind hearted man he is pretended not to notice either my antics, nor the fact that in my subsequent embarrassment, I had blushed a deep red.   The “chain reaction” does exist and can be readily reproduced on samples consolidated to the contractive aka “wet” side–there is no magic about it, and the test method has been published.

When I described this test to Schofield, he said that “failure appears most sudden when the unloading path lets elastic strain energy in a specimen flow into some localized damage mechanism and allows sudden displacement of a loading platen. I have never seen grains being re-oriented as a ‘chain-reaction’ propagated through an aggregate.”  I for one do not believe that a non-brittle solid such as the triaxial sample of sandy clay, can store this much elastic energy to the point that it behaves like a crystalline solid that “shatters.”  I do not understand why Andrew feels that this is a case of storing “elastic energy.”  We continue to discuss this by e-mail, but here is a classic case where one must test to validate ones thinking, and where we can continue to go in circles, if appropriate tests are not run.  Also, in case you were wondering, the loading equipment used was made of very heavy and rigid steel, i.e., did not store any “internal elastic energy,” and was used routinely to test similar samples.

The best way to study this (Steve Poulos wrote me) is  “…if he prepares a contractive specimen of sand, an undrained triaxial test is okay. Best to make the specimen highly contractive and use strain control. Load control will cause a failure after peak (liquefaction) is reached and nothing will be recordable during the large strain portion of the test.”  The sand should be made of particles that are neither “bulky” nor approximately “point particles” else one won’t see a peak in the curve.

Schofield also says that in the disturbed soil from which he made centrifuge models it was impossible to follow stress paths that brought soil paste to a state of perfectly spherical compression without shear stresses.  This is very interesting–the fact he could not find it is really a blow against elasto-plastic theories because such these theories imply such a state exists, and separate out the effects of shear and confining stress with one occurring independent of the other.  This is fundamentally a wrong assumption–soil structure can be usefully analogized to a “house of cards” such as the ones we used to build as children; the slightest compression on such structures results in immediate shear deformation, as any child can attest.

The book describes the failure of an early concrete drilling platform in the Norwegian Frigg offshore oil field.  This platform stood on a slab that did not have the skirt of sheet piles that later became a standard feature.  In the earlier design, for one platform, the designer in an attempt at preventing possible liquefaction moved the soil state to the dry side of critical.  This ultimately caused the platform to fail. This example needs to clarify two important concepts. First, that moving the soil state to the dry side of critical did not absolve the designer from also investigating other modes of failure such as the “pumping action” that subsequently caused the failure in this case. Second, that had he been on the wet side of critical, Casagrande would have told him that if in-situ driving stresses were less than the corresponding steady state undrained shear strength, then, the worst damage that an earthquake could cause would be significant deformation but not liquefaction.

As is, this claim by Schofield that soils on the wet (contractive) side of the steady-state line cannot liquefy is very dangerous and a huge mistake in his book.

5. Model testing and the centrifuge

The book has a section on modeling using the centrifuge that ties together major themes in the book—the use of plastic design in geotechnical engineering, model analysis and the role of surface chemistry. It presents interesting information about centrifuge research in the former Soviet Union along with the general concept of the use of the centrifuge by engineers to experience failure of their own designs in an orderly way, to the betterment of their own design skills.

As he recently put it to me:  “In the Soviet view TOTAL stresses on soil cause VISCOUS creep time effects. Their Academician Vyalov modeled such changes using a power law with an exponent that was found by experiment. His analysis was applied to both permafrost and to the centrifuge data of tests with primary consolidation. I have read about “models of models”, not about centrifuge testing of permafrost models. I believe that when training of Soviet civil engineers taught about TOTAL stress that intended to prepare them to work on new military construction and new East/West transport routes in frozen regions. In contrast, our training of civil engineers in Harvard prepared them to work in the un-frozen zones with soils that are left after an Ice Age. It made sense for Harvard soil mechanics to concentrate on effective stress and neglect creep while Moscow soil mechanics taught total stress analysis.”

Schofield presents interesting case studies of work done by his centrifuge group on the modeling and failure analysis of levees on the Mississippi river, the Teton dam, and a North Sea oil platform. Information in the book on geotechnical related centrifuge development at Cambridge University and companies that Schofield set up to further centrifuge research show the impressive amount of effort he personally put into developing the use of the centrifuge to study geotechnical issues.


CONCLUSION

[Note: to fully understand what follows you should be familiar with the views of the philosopher of science Paul Feyerabend]

1. Parochialism in soil mechanics

In the mid-eighties at MIT, the basic and advanced graduate courses on soil mechanics, taught by a “Terzaghi lecturer,” centered on the empirical, thumb-rule riven SHANSEP concept, with not a single mention of either Critical State or Steady State soil mechanics. The course on soil dynamics, taught by another “Terzaghi lecturer” said nothing about the different schools of thought on liquefaction. This though both Poulos and Castro who together represent the Harvard University approach to soil mechanics post-Casagrande, consulted a scant eight miles away.

A meme in soil mechanics is parochialism in the worst, most blinkered, sense of the word, a practice seemingly initiated by the “Founding Father” himself—Karl Terzaghi (then at Harvard)—who (with the assistance of Peck, his junior colleague) tried to prevent and then delay the publication of the theory of interlocking and friction in sands proposed by Taylor at MIT.  The impact of this action is still felt today, as we shall see later in this article, in MIT’ and Cambridge University, with both ignoring the important Steady State concept from Harvard.

Schofield’s book at least mentions the Harvard school of thought. though it does not do it full justice. It studiously avoids mention of that key concept, central to the Harvard approach–the steady state condition. In this way, Schofield is also parochial. I wrote to Schofield asking him about “this fly in the ointment.” He replied that he was indeed parochial in the sense of the word given in most dictionaries–“taking care of one’s parish.”

This is true, and perhaps the word I am looking for is “partisanship.”  However, the end result is the same as one of the meanings of the word in the unabridged Oxford English Dictionary, where it is defined as “/esp./ confinement of one’s interests to the local sphere; lack of global perspective; narrowness of view; petty provincialism.”

In the end, it is disappointing that each school appears to puff themselves with pride and preaches their “own true religion.”

2. Empiricism in soil mechanics

To his credit, Schofield’s approach, based on the concept of work done on the soil and the energy it dissipates, is rational and based on general mechanics. It leverages and extends standard concepts of plasticity that would be familiar to structural engineers, places soil strength in a rational framework, and shuns the thumb-rule driven empiricism  to which soil mechanics, at MIT for example, has atrophied.

Ironically, it was at MIT that Taylor pioneered a rational approach to soil shear. Roscoe, Schofield, and others at Cambridge then applied these concepts to clays and sands whereas Taylor’s successors at MIT, unfortunately, were only able to follow an empirical, thumb-rule based approach, thus allowing Cambridge University to lead in fundamental research on soil shear.

Bob Whitman wrote me saying “I’m all for fundamental understandings (and steady-state soil mechanics is one such), but a good blend of fundamentals and empiricism can be very useful for practical work.”

True.

And this would be a perfect approach at a trade or vocational school.

Richard Goodman wrote me that he had once queried Harry Seed about pursuing a more “fundamental” research program.  Seed replied to him that “the implicit message of Hooke’s law is empiricism.”  The point is taken, but one could just as easily substitute “gravity” in place of Hooke’s law.

So is empiricism the implicit message of gravity?  The answer of course is that our current inability to explain gravity currently drives a vast amount of fundamental research and that at root, empiricism speaks of an inability to reach to the fundamental cause of the observed behavior. Science has rightly held crude “trade-school”/”thumb-rule” based empirical approaches a distant second to more rigorous empirical or theoretical approaches.  (One cannot but recall Leibniz, attempting to distinguish human intelligence from animal knowledge:  “And men, in so far as they are empiricists, that is to say in three-fourths of their actions, only act like brutes.”)

Whitman did not address my earlier comments on parochialism at MIT. Nor did he reply to my follow up e-mail asking why, if he thought steady-state soil mechanics was a “fundamental understanding”, it was not taught at MIT. (Bob Whitman was no parochialist–quite the contrary,  I personally heard him during a graduate school luncheon request that the steady state concept be taught, only to be turned down; the person in question trotted out an old “war story” of how someone at Harvard had said of someone at MIT that “the man was an idiot” and that this was why he felt no obligation to teach Harvard’s steady state concept.  I think this was but a handy, if dramatic, excuse: the real reason, much more mundane, down to earth, practical, and universal, I discuss later.)

I think that MIT’s  crude parochialism and it’s intellectually lazy trade-school empiricism speaks of an approach that is, in the final analysis, not worthy of emulation.  Its legacy may be the stagnation in research on soil shear in the US during this period.

But enough of blinkered  parochialism!  Enough of timorous, trade school empiricism!  Enough of pretentious posturing!  In short, enough of “my little distraction.”  Let us instead put aside this sad shambles and move on, to discuss real soil mechanics.

Schofield, though consciously parochial, does not appear to be a true empiricist.  He bases his approach on theory to the point that at times he appears (is?) scholastic,  seeming to shy away from the useful empiricism of Francis Bacon’s Novum Organum i.e. he seems to place the experimental validation of the critical state based model a distant second to theory; that as he once wrote me,  “…you can torture a sample in a triaxial cell to get whatever result you want.”

Neuroscience tells us that our brain, is not as perfect as it is made out to be–that it’s construction was dictated by evolutionary needs with a “deliberative system” overlaid on an ancestral, reflexive/emotional system.  To paraphrase Hume, our brains are not thinking machines that feel, but rather, are the reverse–feeling machines that think.  Consequently, our thinking is biased, colored by our emotions, and we very easily construct theories that we wish were true i.e. Bacon’s point in Novum Organum has a physiological basis and so he (Bacon) will remain relevant so long as our brains are physically the way they are.  We can discuss soil mechanics theories till the cows come home (or as Schofield put it to me: “till Herrick brings home the Bacon”), but the fact of the matter remains that the proof of the pudding  is in the testing (to paraphrase Bacon).

Remember the learned “Divines” before Galileo who would look at you gravely in the eye and tell you very sagely that it was obvious that heavier objects fell faster than lighter ones.  Or recall the physicists of the nineteenth century who would also tell you that if you moved in the direction of light, that your velocity relative to light would increase.  It took the experiments of Galileo and Michelson-Morley to prove that intuition is often wrong.  Bacon: “I contrive that the office of sense shall only be to judge of the experiment, and that the experiment itself shall judge of the thing.”

I repeatedly pushed Schofield over the last few years as to why he did not believe in the concept of the steady state, but was not able to get a clear answer.  In the end it appeared to me that as in other things, our beliefs are at root psychological, which is why (again) Bacon’s contribution in Organum is so important–believe what we may, the proof of our beliefs is in the test data.

It continues to amaze me how even today, five hundred years after Bacon, my interactions with senior professors in soil mechanics from all over the world reveals an appalling ignorance of Bacon’s fundamental, foundational concept of science–a simple concept that every school child should be taught if we wish to educate them well.  And reviewers too, who should know far better.  Sometimes a reviewer of one of my papers will reject it, saying he/she does not believe in the steady-state concept!  They ignore results in the same paper that shows that the steady-state driven hypothesis was validated by the experimental data.  Probably these reviewers also believe that heavier objects fall faster than lighter ones, and that the earth is flat!  At any rate, they should be reminded of the basics of science–again, something a school child should know–that one’s beliefs come a distant second (if at all), to “hypothesis/validation of hypothesis by testing,” the foundational principle of science.

The other thing that also is astonishing is that in soil mechanics when a researcher presents his or her model, they compare it against their own test data!!  This is a very low bar indeed and I am surprised these papers even see the light of day–they should be rejected on the spot!  Such comparisons are definitely not “acid tests” and I consider these comparisons third rate.  After 50 years or more of shear strength testing of soils, stress-strain data are far from rare, even data from true-triaxial testing are freely available.  Models should be compared against data from tests conducted by those not responsible for creating the model and who are NOT co-authors of the paper in which the model is being tested, unless of course the data in question is of a very specialized kind involving new kinds of tests.  In my papers I take great pains to test my model against data obtained by others and then too, I look specifically for data examined by rival theories.  This allows for a direct comparison of the two theories.

This is the reason why I chose to model the Plant data–it was the data set used in Roscoe, Schofield, and Wroth’s paper on the critical state.  I also used Gilbert’s data which Roscoe, Schofield, and Wroth also analyzed, but found the data to not be sufficiently rigorous for quantitative modeling–Gilbert only recorded an average of 12 points per curve, which was insufficiently rigorous to define large portions of the curves.

(Note: contrary to what some reviewers think, you cannot join two measured points by a “smooth curve” and use data points from this interpolated curve as input to your model.  Such an approach speaks of a basic lack of knowledge of the underlying mathematics.)

Hence when Andrew wrote me that one could get any data one wanted from a triaxial test (the exact reason why a modeller should not use her own data), I was able to tell Andrew that I used data from his own paper.

And one more thing…when testing a model against data one should validate with a lot of tests…lots both in number and kind.  A minimum of a 100 tests, drained, undrained, normally and over-consolidated, triaxial, true-triaxial etc.  and on clays, silts, and sands, are called for in my opinion.  I have seen some papers (one by a so called “Rankine prize winner”) where the model is considered to be validated with comparisons done against as few as three tests on a single clay!  Absurd!

3. The critical state and elasto-plastic models

The thrust of Schofield’s book is largely pedagogical.  Consequently, his coverage of modeling does not go beyond the pedagogically useful CAM clay model, and he does not address controversial issues that surround the critical state concept.  These include questions such as why, despite their unwieldy complexity, the latest models based on the critical state fail to provide good matches with stress-strain-void ratio curves obtained from tests on soils such as sands and moderately to highly over consolidated clays.  Can a theory founded on an idealized isotropic aggregate, apply to real soils?  Recall that most real soils show a peak when contractive samples on the wet side are tested, and that this is not possible with an idealized isotropic aggregate.

No real soil is isotropic to the point that it continues to deform isotropically during shear!  No real soil is isotropic to the point that under pure hydrostatic compression it does not show shear deformation!

Andrew curbed my naivety with this reply: “The word “real” has the sense of the realm of control in which a sovereign exerts power or the land and property that people sell. That corresponds to the land for a few hundred miles around Harvard. However there are granular aggregations that exist on the sea-bed, or are hypothesized to exist in space before star-dust forms a new star, to which it may not make “real” sense to apply un-diluted Harvard soil mechanics.”

Karl Popper, a philosopher of science, came up with the criterion that to qualify as scientific, a theory should be falsifiable.  Is the critical state concept, to the extent it depends on an idealized aggregate, falsifiable?  Does it fail Popper’s test?  Any deviation from theoretically expected behavior can be disqualified by the ad-hoc reasoning that the test was on a real soil–not the idealized material that the Critical State theory is built upon i.e. isn’t the critical state concept not falsifiable and so not qualify as scientific?

I put the question to Andrew, and here is his reply:

“…There are logical mathematical arguments that tell us that we can only say that a homogeneous isotropic material has a property such as stiffness or strength if we can measure it and ascribe a value to it that is independent of our choice of reference axes. So invariance under transformation of axes can provide us with a test of truth or falsity of any claim about a theory…”

In this limited sense, I concede the point.   It is a point about homogeneous isotropic material.  No real soil behaves as such.

One should make claims about hypothetical materials with the care of a person walking a tightrope stretched high across an abyss else one may fall into statements that cannot be falsified i.e.  fall out of science, and into the absurdity of scholasticism.

Half a century of research later, the question of the endogenous/micro-structural basis of critical state based models remains.  Can a theory originating from a metals theory of elasto-plasticity be used to model soil behavior? Does soil really resemble metal? Is soil really elastic? If so, why do I get permanent shear strain when I apply the slightest ISOTROPIC compression to a sample of loose or medium dense sand?  Can a structure that is much like a “house of cards” be elastic?  Elasticity is only a good APPROXIMATION, one that only works with dense sands and clays and then too at very low strains.

Recall also Schofield’s  inability, despite a “determined attempt,” to  follow stress paths that brought soil paste to a state of perfectly spherical compression without shear stresses, a state that should readily exist per elasto-plastic theory. (The yield surface of the original Cam-Clay model was a logarithmic arc.  This was changed to a ellipse in the Modified Cam Clay model.  The reason for this change is that the plastic strain increment vector, which is normal to the yield surface,  now becomes horizontal for the largest mean effective stress i.e. no incremental deviatoric plastic strain occurs for a change in mean effective confining stress.  This makes it “numerically stable.”  However the problem is that real soils do show plastic shear strains when subject to pure hydrostatic stresses, as evidenced from Andrew’s search above, and also from common intuitions as to how complex structures would behave.)

Likewise recall that plasticity theory has no option but to treat soil as a “paste” and thereby is not able to provide insight into soil structure and changes in soil structure with shear.

When in the 8th grade, I remember distinctly being taught about the religions of the world.  The teacher then came to the original form of Buddhism as preached by Gautama Siddhartha Buddha and today called,  “Theravada” Buddhism.  The Buddha did not mention nor need the concept of God, and my teacher called the religion “a fortress without a well.”  Being young and impressionable this phrase struck me with force and I remember it to this day.  So also with elasto-plastic theories based on the concept of the critical-state.  The approach that they use does not have a clear, simple, transparent underlying organizing principle that can describe the shear process in a few easy to understand words and so sometimes seems to me to be “a fortress without a well.”

Roscoe was a mechanical engineer by training and his introduction to soils occurred when bravely tunneling out of a German Nazi prisoner of war camp.  Andrew Schofield was mentored by Prof. Baker, one of the great structural engineers whose courses and whose approach to steel structures were based heavily on the theory of plasticity.  Given the dearth of any alternate theory, it makes sense then that they applied elasto-plastic theory then available for metals, to soils.

However, this smacks 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.”

This is not to disparage Roscoe et al.  Rather, this is how such things often happen in science and technology: there was not alternate theory ; one had to be pragmatic and use what was available.

Today elasto-plastic models are “a dime a dozen,” with each model claiming superiority in a niche area, but each uniformly doing a poor job of accurately predicting stress-strain curves over a wide range of soil types and soil conditions.  Here too Popper’s falsifiability criteria cannot be applied because the elasto-plastic theoreticians explain away their inability to fit the stress-strain curve post-shear failure in the case of brittle materials that develop distinct failure planes by saying that once localized deformation develops, models that determine their parameters based on the assumption of homogeneity of deformation for the entire stress-strain curve are invalid.

In short it means that we do not know if overall, their approach is right or wrong as their theory is falsifiable only up to shear plane development i.e. once a shear plane develops  it does not qualify as a testable theory i.e. is not scientific.  (Note though that the dynamical systems based approach provides close fits post failure, indicating that the generation of a failure plane does not significantly disrupt the underlying failure mechanism and that this hypothesis used by critical state theory to explain away poor fits post failure is but an excuse.)

I am reminded of Wolfgang Pauli (who seemed to be channeling Popper) who on reading a paper submitted by a physicist colleague, said:  “This isn’t right.  It isn’t even wrong.”

The best that one can say about the critical state and elasto-plastic theory based on the critical state is that it is a “heuristic,” useful in engineering.  But outside of the world of soil-mechanics, in the more rigorous world of science, it would qualify as a “just so story.”

Perhaps this is the reason why soil-mechanicians so easily forget their “Bacon” as mentioned earlier–we are educated and work largely on the basis of heuristic models which in turn makes it so easy and natural for us to “explain away” differences between test data and theoretical model/hypothesis.  The critical-state/elasto-plastic approach is largely unconstrained theory driven by more theory and not theory driven and constrained by real test data.  They should recall the late Richard Feynman (who was really only channeling Bacon) when he said: “It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.”

Over the years I have slowly but steadily come to believe that the critical-state and the elasto-plastic approach will eventually be seen to have been red-herrings–dead ends in soil shear modeling, or as Bacon would put it, “idols of the (soil-mechanics research) marketplace.”  It will take new paradigms and a new generation of researchers for this recognition to occur.  Recall Max Planck’s words on new paradims!  A new generation is least vested in old models–they have yet to build their careers based on any paradigm and so are more easily able to choose.  For the previous generation (myself included) to move to a new paradigm requires “switching boats in mid-stream” which is almost always much harder than simply remaining in one’s old boat!

Already one sees signs of this with the numerous “niche” critical-state models, all tremendously complex and providing poor matches other than their particular niche application.  By contrast,  the concept of the steady-state places soil shear squarely within a powerful mathematical framework–dynamical systems theory–and with a clear, transparent, physical basis, and which provides close matches with but 2 equations.  If you are a young professor seeking to build a research reputation, take note and do not paint yourself into a corner.

The critical-state based approach shows many signs of becoming what Imre Lakatos called a “degenerating research program.”  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,  and if they succeed, the program gains more followers and expands.  If on the other hand, 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 (such as failure planes or non-uniform particles or anisotropy or lack of shear under pure hydrostatic stress being the reasons for poor fits to real data) behind which researchers will attempt to shield the theoretical core from falsification.

Let me end this section with a quote (with apologies to Nietzsche): “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.”

4. Schizophrenia, “exceptionalism”,  and complexity in soil shear research

Current research on soil shear has a “schizophrenic” feel to it.   On the one hand are crude, empirical, thumb-rule riven approaches, such as MIT’s , and on the other are approaches where Ph.D’s count angels on the point of a pin and create models (usually some variation of the elasto-plastic model) with over sixty equations, each equation dependent on the previous and each subject to simplifying assumptions.  (The assumptions are often subtle and hidden, seemingly even to the model’s creator who proceeds, blithely oblivious.)

In most of these papers authors apply their model to data from their own tests.  As mentioned above, Andrew once wrote me, a specimen in a triaxial cell, can be tortured to produce any result you want.  After over fifty years of research into soil shear, with most tests run on standard, run-of-the-mill triaxial or true-triaxial tests surely the bar has to be raised.  In my opinion, researchers who fit models to their own data should not be allowed to publish the results of their fits.  Rather, they should demonstrate the validity of their hypothesis by applying their model to data collected independently by others, and preferably, from tests run before their hypothesized model was even conceived of.

These papers also usually omit to provide  “chi” or “goodness of fit” values when comparing predicted vs. observed curves.  The authors of the classic text “Numerical Recipes in C” caustically refer to this approach as “chi by eye” and say that “…its practitioners usually get the treatment they deserve.”

Except that is in soil mechanics where the bar is set much lower and researchers are allowed to get away with statements like: “the fit was good.”

Two other (somewhat minor) examples of this kind of egregious “soil mechanics exceptionalism” are the use of the universal mathematical constant “e” as the symbol for the void ratio and the use of  the prime symbol ‘, the universal symbol for the first derivative, as the symbol for effective stress.

Dick Goodman wrote me: “…in Erdbaumechanik, (1925) Terzaghi used the Greek letter epsillon(ε) for the  pore number (Porenziffern), which was  identified as “the quotient of the volume of voids to the volume of grains”.  I looked into Terzaghi’s 1929 book , Ingenieurgeologie (engineering geology) with Redlich and Kampe, (1929)  and found he was now using “e” for void ratio.   Since in clays he saw this as measure of the distance between particles, I thought he might have selected “e” to represent a special kind of distance  – –  the word “entfernung” comes to mind.  It means “distance”.   But I have no information to suggest that this is the origin of the symbol.  Of course, he might just have tired of using a Greek symbol and replaced it with the Latin “e”.”

As any scientist will tell you, the number e is one of the most important numbers in mathematics, and is sometimes called Euler’s number.  It is an irrational number whose first few digits are: 2.7182818284590452353602874713527… (and forever more).

But the key “exceptionalism” is this:  “critical states” are defined in science as states at which a phase boundary ceases to exist. There are multiple types of critical points such as vapor-liquid critical points and liquid-liquid critical points but the only field that I am aware of which (mis)uses this term for a non phase boundary transition is soil-mechanics.

The critical state condition in soils is a stark case of exceptionalism–there is nothing critical about the critical state in soils!  One does not find such a condition anywhere else in nature–a stark contrast with the ubiquitous steady state condition.  I have repeatedly asked Andrew about this, but he has given me no answer. (Note: an author of a noted text book on critical state soil mechanics wrote me that the sense in which he now uses the term “critical state” is the same as Poulos’s definition of the “steady state”.  Such use of nomenclature is to me a grave error–the term “steady state” is rigorously defined not just in soil-mechanics but in numerous other fields and to misuse an old term and use it in a new sense in soil  mechanics would be another grievous example of the aforementioned “exceptionalism.”)

The “steady state” is indeed ubiquitous in nature.  They can be found everywhere and at all distance scales: in the beating of the heart; in one’s eye; in the formation of an infant in the womb; in the shape of shells; at the heart of tornadoes and hurricanes; the Great Red Spot on Jupiter; in galaxies–where ever you turn you find steady states.  (A good book describing examples of the steady state condition is the New York Times best seller “Chaos” by James Gleick.)

Indeed it would be very odd and anomalous were soils under shear not to exhibit a steady state–it would qualify as what that tragic philosopher of science Edward Constant would call a “presumptive anomaly” because a soil under shear is nothing but an “open” (energy coming from outside the system) “dissipative” (energy dissipated through processes such as friction) thermodynamic system.  Open, dissipative systems fall into a general class called “non-conservative” systems that have been extensively studied by physicists.  All non-conservative systems must involve a “contraction of phase space” with “attractors (steady states) and consequently, that is exactly what one must find in a soil being sheared if one is not to contravene the laws of physics.  Unless of course we want to exceptionalize soils even out of the realm of the laws of physics…to where? into the supernatural?  Michael Jackson’s Thriller?…or perhaps we could, like MIT, wallow in Leibniz’s pigpen of trade school empiricism?

Back to the bloated 60+ equation  elasto-plastic, “state-of-the-art” models of soil shear.  Complex models impress only novices.  Seasoned innovators know that Nature (of which soil mechanics is a part!) is not schizophrenic and that she acts in radically simple, economical, and elegant ways.  As Newton believed and said numerous times in one form or the other: “Nature is exceedingly simple and conformable to herself.”

Consider our own throat,  which nature uses for the essential tasks of eating, breathing and vocalizing.  This kind of radical simplicity and radical economy is beyond the ability of all but a few to conceive of, and then too perhaps only after much introspection.  But that is no reason why nature should not be radically simple and economical.  As Albert Einstein said, “Nature did not deem it her business to make the discover of her laws easy for us.”

Complex models usually are indicative of an approach that is basically flawed and schizophrenia indicates that things as a whole are not wired together right.  Complex models, paradoxically, are not that hard to create.  It is radically simple and economical models that explain observed behavior that are hard to create, hard for our minds to conceive of.  Very hard.  Again, Mr. Einstein: “Nature rarely surrenders one of her magnificent secrets!”

I have observed that if there is little or nothing to be said, or if the point is not “robust”, then the person often couches what they have to say in complex, difficult to understand wording or mathematics.  Nietzsche got it exactly right:  “Being deep and appearing deep–Whoever knows he is deep strives for clarity; whoever would like to appear deep to the crowd strives for obscurity.  For the crowd considers anything deep if only it cannot see to the bottom: the crowd is so timid and afraid of going into the water.”

Beneath all the various stress-strain-void ratio curves lies a simple explanation.  It is indicative of how puny the “great human mind” really is that we have taken so long to find it.

5. Secret Knowledge

Senior geotechnical engineers on hearing about the steady state concept react with surprise.  “I have been practicing for 25 years but haven’t heard of this.” they say.  Why is this knowledge “secret.”  In truth, it is not “secret” so much as “hidden.”

Secret/hidden knowledge like this exists in literally hundreds of fields as diverse as real estate, finance, human spirituality and so on, protected by vested interests who would rather not publicize certain knowledge.  A technical word used by people who study this fascinating phenomenon is “information asymmetry” where, in the absence of a free flow of information, institutions or organizations which control access to information, can “hide” information that they felt didn’t contribute to their own best interests. Thus a powerful theory from Harvard was not appetizing to certain universities seeking to “take the lead.”

The impact of this has been a blight in soil shear knowledge and research.  Schools that consider themselves among the best seem to be completely ignorant of the steady state condition.  Ph.D dissertations done at these schools and which focus on shear strength do not even mention the steady state in their literature review.

An additional result of this parochialism, is a great trans-Atlantic divide in the teaching and research on soil shear.  Schools in the US tend to follow the mathematically impoverished, thumb-rule driven, trade school MIT approach with no good theoretical soil model being taught and with the emphasis on soil behavior.  Schools in the UK and Europe on the other hand have a far more theoretical and mathematical approach driven largely by critical state based models, and with no real constraint from empirical data.

But with the advent of the internet, information asymmetry is steadily decreasing as the ability to distribute information becomes democratized and any old Joe (Paul Joe??) can quite effectively communicate to the targets of the information asymmetry using mechanisms such as this very blog…, and that too, for free.  Sure, this facility is often misused and “mavericks and unsound thinkers” abound–you will have to decide on your own the trustworthiness of the information presented here.

So how do you know I am not an “unsound thinker?”  As Gautama Siddhartha Buddha put it 2,500 years ago: “Believe nothing, O bhikku (learned monk), just because you have been told it, or it is commonly believed, or because it is traditional or because you yourselves have imagined it. Do not believe what your teacher tells you merely out of respect for the teacher. But whatsoever, after due examination and analysis, you find to be conducive to the good, the benefit, the welfare of all beings – that doctrine believe and cling to and take as your guide.”  Today he would probably have added a few choice words on Bacon.

6. Which model will “win?”

Jim Graham, a researcher from Canada of elasto-plastic models has provided input to my research on a dynamical systems based model.  While he agreed with me that the Cam Clay was an idealized model for isotropic clay with low surface energies, and that consequently he has taught Cam Clay only as an idealized component of elasto-plastic soil mechanics, he disagreed in that real clays were different.  He said that my comments on elasto-plastic approaches to soil shear constitute “blue snow” (only negative hypotheses can be proven) and that newer elasto-plasticity frameworks that account for anisotropic elasticity and other physical processes etc. are the only way to make sense of what is going on when dealing with unsaturation, temperature effects, chemistry, and viscosity/strain rate effects.

Perhaps.  But to me it seems that these issues are best addressed at the root–at the level of the micro-structure.  It is here that temperature, pore fluid viscosity and saturation interact with the material friction of the particles and with soil-structure changes .  Again, the proof of the pudding is in the testing and not in trading opinions over each other.

The obvious question is which model is going to “win”–the critical state or the steady state?  The answer of course is that science has tools (some for centuries) with which to decide the better of two rival theories.  These include tests to determine which theory is:  a) simpler (“Occam’s razor”) b) a better fit (measured quantitatively) to experimental data (Bacon) c) more falsifiable (Popper), d) more complete (has an endogenous explanation), e) has greater explanatory power (explains for example why the e-log p’ curve in 1-D consolidation is linear) and f) fits in with fundamental concepts from the basic sciences.

Einstein when asked which theories are most likely to survive the test of time answered: “A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability.” (He went on to say that on this basis, he would bet on the first and second laws of thermodynamics.)

Usually though it takes a new generation before a paradigm shift in theory becomes widely accepted.  As Max Planck said: “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.”  What happens also is that the current generation is very vested in the existing paradigm and simply cannot afford to simply dump a life time of research and beliefs, without putting up a good fight.  The next generation though has little vested in either of two competing paradigms and so is likely to consider rival theories, free from any “emotional baggage” and to choose what they see is the most promising approach.

There is nothing special in soil mechanics having two competing soil shear theories–what is special is how one theory has been kept tightly under wraps.  Ultimately, with the Internet fostering the free flow of information, “information asymmetry” of all kinds will reduce and slowly but steadily wither away;  the standard tools of science will sort things out without any “Sturm und Drang.”  One should remember that if one does not understand the theory, but if it none the less makes predictions that conform closely with experiment, then the problem may not lie with the theory, but rather with the particular person’s inability to understand it.

One major hindrance to progress in research in soil shear is that over 60 years after World War II, a time when soil mechanics developed momentum, we are still missing a free and universally available data set on soil shear, that researchers all over the world can use to test their constitutive models against.  In 1992, the NSF, under a visionary director (Dr. C. J. Astill) funded an ambitious program called VELACS, with duplicate tests run in independent soils laboratories on the East and West Coast of the US and following previously agreed upon test standards.  You can find more details here.  The VELACS data set is freely available and has played a fundamental role in my own papers.

If we could do it in 1992, we surely can do it two decades later when test equipment, procedure, and communications (email/internet) have all become so much more sophisticated and ubiquitous.  We cannot claim that the “old timers” knew how to test better than we do today, and that so, we can no longer do this.  Some of the best test data I have seen in over three decades was obtained by a 22 year old graduate student who built and used a true-triaxial machine for the testing.  When I ran a soils laboratory, I worked closely with an “old timer,” and I can assure you, “old timers” come with their own set of issues and with rigid opinions as to how things should be done.  I firmly believe that it is very difficult to outdo a modern automated testing system that requires minimal “art” on the part of the tester, in order to produce good data.  The days of manually recording a dozen or so data points should be well behind us.

In short, it beggars common sense that standardized, publicly available datasets developed along the lines of VELACS are not available, and that we proceed on an amateurish, ad-hoc basis.  I wrote to Richard Fragaszy, Program Director of Geomechanics and Geomaterials at the NSF to ask if they would fund the creation of such datasets.

Richard said most researchers believe that there were an abundance of high quality laboratory data sets available to validate numerical models, that many would say that additional tests would only be of minimal benefit, and that the difference with VELACS was that VELACS added centrifuge modeling of full-scale problems, not additional laboratory element tests.  He made a valuable suggestion: instead of individual tests on soil elements a better comparison with VELACS would be centrifuge model tests of foundations systems, excavations, embankments, etc.

Based again on his extensive experience with the geotechnical research community, he still did not have a good feeling as to how such a test program might review.  He anticipated the argument that there were enough high quality centrifuge tests already to do what I proposed without needing to do new tests, and that the proposal would have to make a strong argument for new tests.  He suggested that I give some thought to using existing data from appropriate tests.  He added that he was not saying this was better, but rather that I should be open to the idea and be able to defend either use of old data or justification for new data.

I am open to using old (existing) data—in fact I agree completely with Richard’s thinking that simply running additional tests that simply repeat what was done before would be a complete waste of tax payer money that could be put to better use elsewhere.  However, where are these publicly available data sets?  I asked Richard.  He replied that I could do a search on the NSF web site for funded awards that have centrifuge tests included.  Since our taxpayer money funded the creation of these data, they would be available to the public for the incremental cost of providing it.  Richard also pointed me to the NEES Project Warehouse.

I searched both the NSF Funded Awards and the NEES Project Warehouse, using the key word “centrifuge” and in the “Engineering – Civil” field of application.  The search returned 86 distinct centrifuge test programs that had been funded by the NSF over the last 40 years.  Of these 86, I found none that modeled a non-dynamic loading of an excavation or embankment.  If my finding bears up to a more detailed and thorough investigation, it sounds to me that a good case can be made to ask the NSF to fund a program for this purpose.

So in the end I did not find the centrifuge tests I was looking for.  I know that these data exist (in the UK for example) but they seem closely held, gathering dust on some academic’s shelf somewhere.  Also, I do know that there is real data from an instrumented embankment that was part of a research program done in the US in the 1970’s.  Should you know of any such data, do email me with the details and we can strive to release it to the public.

I proposed to Richard that were such data available, we could put it up on a website using a “wiki” format.  Researchers who had a constitutive model that they had published in an international peer reviewed journal would be eligible to use the data, provided they described in their section of the wiki transparently, exactly, and in gory detail, how they used their model so that any one who chose to, could independently confirm that the values reported were correct.

With an approach like this, the community can directly compare different models, and quickly “separate the wheat from the chaff.”  The approach is voluntary in that if your model does not appear to provide good fits, you simply do not contribute to the wiki.  Once I suggested this to Richard, it dawned on me that one reason why this seemingly commonsense approach has not happened in 60 years is perhaps this is actually the LAST thing that some may want to happen–empirical evidence that their model is wrong!.  I for one would rather know that my model was wrong, then to live with the uncertainty of not knowing how accurate it really was.

7. Wrap-up

In the end, for me, this wonderful book by Schofield read the author, the current state of the soil mechanics research profession both in the US and in the UK, and the national agencies that fund highly empirical research that does not fit into a general framework of science.  Everything reads everything else and in the end, I suppose, this review also reads me (“Wer mit Ungeheuern kaempft, mag zusehn, dass er nicht dabei zum Ungeheuer wird“).

Ultimately, Schofield’s book raises two fundamental issues that need resolution. First, how important is surface chemistry in soil shear—the book says it is not of primary importance, and I would agree (while guiltily doffing my cap to Bacon!). Second, do soil grains move into a steady state structure or are they randomly oriented? If the former, you have steady state soil mechanics, residual strengths and the approach to liquefaction as prescribed by Harvard; if the latter, you have critical state soil mechanics and the approach discussed in this book.

I came away amazed that 40 years after the Harvard soil mechanics department shut down, its concepts are still powerfully relevant–a reflection that, all said and done, thanks to overt parochialism, research in soil shear has essentially stagnated.

Another prime cause of this stagnation is the way the highest honors appear to be awarded in soil-mechanics–for example the Terzaghi award.  Unlike the Nobel prize which can be awarded to (say) James Watson for a specific discovery he made when he was 23, the Terzaghi award is given every two years for an opaque “outstanding contributions to knowledge in the fields of soil mechanics, subsurface and earthwork engineering, and subsurface and earthwork construction.”  I believe that this allows for the smooth and seamless operation of an old boy network.  The committee appointed to select the awardee usually lacks the technical depth to identify, rank, and reward deserving innovators, but instead appear to select the awardee from a list submitted by members in a process open to hidden influence.  Further, the selection of awardees by and large tends to be nationalist and in this additional sense, blinkered, and parochial.

Specific discoveries/innovations are more to be prized than opaque “contributions” (which is the reason why the Nobel is awarded this way) and you will, in the case of the Terzaghi award, be hard pressed to find what specific discovery or innovation awardees have  made to our understanding of soils.  Deserving innovators are ignored–can someone tell me why Steve J. Poulos is yet to be honored for his seminal 1981 paper “The Steady State of Deformation” or Gonzalo Castro for important work on liquefaction?  Or G. Mesri for seminal work on creep and consolidation? In my opinion, the opacity of the reasons behind the award has allowed the award to be made in the past to a petty parochialist, a timorous trade-school empiricist, a pretentious junior author of a text book, and combinations thereof, whose specific innovations are unknown at worst and murky at best.

Along these lines, when someone tells me they have written N papers where N is often over 100, I ask them, what their most important finding has been from among these N papers.  Surprisingly often (initially my question was asked in all innocence), the result is a lot of sputtering and stammering followed by a haughty “you will have to read them to find out!”  Yes, indeed.  Any when I do read them I find that they usually consist of “filigree on top of filigree” in short–no major finding or advance.  Sometimes though they tell me frankly and clearly what it is and I am able to place them accordingly.  Either way, I quickly know their true “soil mechanics merit.”

So the next time someone tries to impress you with their awards or with their “chairs” or with the number of papers they have published, ask them a simple question–tell me in one sentence of less than twentyfive words, what has been your most important finding?  Judge their “soil mechanics merit” accordingly, keeping this quote from Albert Einstein (my last quote from him, I promise!) in mind:  “I have little patience with scientists who take a board of wood, look for its thinnest part, and drill a great number of holes where drilling is easy.” Misguided though I believe the critical state and elasto-plastic concepts to be, Andrew Schofield deserves kudos and respect for drilling most useful holes where the wood is thickest.

In the early 20th century Karl Terzaghi created a narrow bridge connecting science to soil-mechanics.  Since then this narrow bridge has been submerged by mindless trade school empiricism, crude parochialism, and Aristotelian scholasticism.  As a result, it seems to me that today soil-mechanics has become an isolated island separated from a continent of general, applicable, scientific knowledge.  It is high time we uncover a connection to the main land by a wholesale (not retail) import of elementary science and scientific thinking into the subject.  Schofield’s concluding call for more research in the fundamentals of soil shear is apt; it is up to current researchers to take up the challenge.

If you think that you know about soil shear then you should be knowledgeable about the critical state condition, the steady state condition, and the concepts presented in this book.  Should this describe you then do write to me with your thoughts on soil shear and this review–I would like very much to hear from you.  But should  this not describe you, then be warned!  You walk on thin ice!  You rush where angels fear to tread!