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.’

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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) 

Time to end Scholasticism in Soil Mechanics. #2: Hypothesis A vs. Hypothesis B

Posted in Scholasticism by Paul Joseph on April 7, 2016

This is my second post on the subject of scholasticism in soil mechanics–unfortunately, scholasticism remains alive and well in soil mechanics.  Even 500 years after Galileo, Newton, and Bacon, some researchers/academics in soil mechanics still do not seem to “get” this basic/fundamental concept. It is high time that we put an end to scholasticism in soil mechanics, it is high time we raise the bar in terms of rigor of research in soil mechanics. (My first post on the subject of scholasticism is here.)

This second post on this topic concerns a “debate” that has been going on in soil mechanics these past four decades, one which has wasted a lot of time and energy for some researchers, needlessly confused other researchers, and in general has wasted space in the research literature, not counting numerous beautiful trees that have been felled to publish this needless debate.

The debate I mean is that of “Hypothesis A vs. Hypothesis B,”a debate  that has been going on, as I have said these past four decades, with neither side able to convince the other.  The reason that neither side is able to convince the other is because both sides are scholastic–stuck at the phenomenological level of the problem, a level where the root cause driving behavior cannot be found.  Both sides seemingly lacking the intellectual ability or desire to penetrate deeper to the underlying physical bases of the phenomena to do a root cause analysis.  Or worse, they may be unaware of a basic concept–that the full resolution of a problem requires a root cause analysis and that the root cause is typically to be found at the material/physical basis of the problem.

Because these researchers remain stuck at the superficial phenomenological level, the level of merely manifest phenomena, because they seem unable to go below this level, they have failed in their efforts to convince each other, and the “world” as a whole.  This is because, being stuck at the phenomenological level means that they can, according to their biases, select some manifest behaviors while ignoring others according to their particular likes and dislikes.  This innately predisposes them to avoid going to the nitty-gritty, i.e., the material bases where the root cause solution lies.

In short, my own root cause analysis of why neither side has prevailed is this–both sides are scholastic, because both sides selectively examine the available manifest phenomena selectively,  carefully picking and choosing only that empirical evidence (phenomenological) that supports their own hypothesis, while scrupulously ignoring other (also phenomenological) data.

Rigorous thinking and *really good engineers and scientists* seek root causes for behaviors–they try as soon as possible to go below mere manifest behavior (phenomena).  Once the physical root cause is identified, ambiguities are such as this one are usually permanently and incontrovertibly resolved.  In this debate of Hypothesis A vs. B, both sides studiously avoid a root cause analysis, one which by definition, must be at the physical basis.  Because to do so would force them to examine data that does not support their hypothesis.

In this case, not surprisingly, a root cause analysis reveals that both sides are both right and wrong–that  like the proverbial blind wise men and the elephant, each side has a part of the whole picture, and having only a part, comes up with bizarre understandings and claims, that, naturally fail to convince not just the “other side,” but, neutral observers who don’t give a damn which hypothesis governs, but just want to get their job done.  A root cause analysis of the underlying physical basis drives researchers relentlessly past mere Aristotelian logic, past personal biases, to a complete picture based on a ALL the empirically evidenced data.  To do otherwise is to be but a scholastic.

It is time we end this amateurish, scholastic research, emanating from both groups.

So on the one side we have Hypothesis A and the other Hypothesis B. According to Hypothesis A, creep compression strain due to viscous effects occurs only after the End of Primary consolidation (EOP), and that consequently the strain at EOP is the same in both thick layers in-situ and thin layers in the laboratory test. Hypothesis B, on the other hand, assumes that creep compression strain due to viscous effects occurs during both primary consolidation and secondary consolidation, and that consequently, the compressive strain at EOP for a given stress is also a function of strain rate, i.e., closely tied to the thickness of the consolidating layer.

Today the followers of Hypothesis A are by and large led by Mesri while those of Hypothesis B are led by Watabe and Leroueil. A recent discussion between the two (one which unfortunately I was not aware of till it was too late to join in) is this one: Discussions and Closures Discussion of “Settlement of the Kansai International Airport Islands” by G. Mesri and J. R. Funk.

As I mentioned earlier, both sides scrupulously stick to selected observed behavior, i.e., the manifest phenomena, and strictly avoid any root cause analyses for these observed phenomena.  To do so would be to resolve this debate and in the process reveal that both sides have but a partial glimpse of the truth.  To NOT do so, for both to talk past each other and to remain stuck in a debate that will last till the cows come home as they say.  Such an amateurish approach will continue to waste valuable time and energy, and to follow what is essentially an intellectually lacking approach to problem solving, one I have seen many times in various fields and where, until the root cause physical analysis is done, the problem, like this one, remains unresolved, permanently in play.  

It astonishes me that the bar in soil mechanics is so low among academics and researchers, who come across as intellectually bankrupt. When I was young an older gentleman warned me against doing a PhD.  

“Your mind will become warped” he said.  “You will start counting the number of angels that dance on pin heads.”

 And being young and filled with hubris I disbelieved him.  Now though, I think he was right as far as many PhD’s, at least in soil mechanics, are concerned.  Consider the present case: if Hypothesis A is correct, then what explains the lack of strain-rate dependent friction?  Have the Hypothesis A people found (and counted) angels dancing on interparticle contacts and holding oil cans with which to lubricate the contacts to reduce friction related strain-rate effects? (These must be angels that are “mechanics” on the side it seems.)  Or the Hypothesis B folks–have they found and counted angels also dancing on interparticle contacts but this time, armed with “sand paper” to roughen up the contacts (one assumes that these angels are “carpenters”)?

The strange thing is whether they realize it or not, both sides have indeed pointed to where the physical basis of the root cause lies.  Thus Mesri in his various writings has pointed out that Terzaghi held strongly that the root cause of viscous behavior lay in interparticle friction seated at the viscous layer.  Likewise Watabe and Leroueil have published a remarkable figure (also reproduced in the discussion above) that points to strain-rate behavior being dominated by viscous layer governed interparticle friction.

Now, before we dive in, let us step back and ask, what exactly is one-dimensional consolidation?  A little consideration shows that it is nothing but shear along the Ko line.  In other words, it is but a special case of shearing and the standard one dimensional consolidation lab test is really nothing but a shear test where the sample is always under a Ko condition.  

Strain rate effects in drained and undrained soil shear have been studied extensively and are well known to reside in interparticle friction and the viscous layer.  These strain-rate effects map (to the extent the data exist) reasonably straight-forwardly to one-dimensional consolidation tests–see this paper for example.  The net-net is that strain rate effects exist in both drained and undrained shear, and also, that they are very small.

At a consulting company I once worked at (GEI Consultants), one of its founders, Dr. Dan LaGatta, formerly from the soil mechanics department at Harvard University and a world expert on strain rate, told me of his thumb-rule for strain rate effects.  And though I personally detest thumb-rules, this one I have to say has its place.  He told me that extensive tests he ran at Harvard and at GEI showed that for most soils, an increase in strain rate by about three orders of magnitude of strain-rate typically results in approximately a 10% increase in both peak and steady-state strengths.  In short, strain-rate effects for most engineering problems can by and large be ignored.

Likewise with one-dimensional consolidation, i.e., shearing along the Ko line.  The root cause of strain-rate effects, as in the case of shear in a triaxial compression test or any shear test, is interparticle friction seated in the viscous layer.  Consequently as in other shear tests, here also, strain-rate driven changes here too are small and need not be considered except for very thick layers (10 meters or more?) of soft clays subject to extensive consolidation.

And this is why both sides are right and wrong and why they prefer instead to stick at an amateurish “manifest behavior/phenomena” level, where as a result of their cherry picking the phenomenological data, they remain unable to convince each other for four decades.  Each side has a partial hold on the truth (i.e., each side is partially also wrong), and so each holds that they are right while the other is wrong.

So Hypothesis A groupies are correct in their claim that the EOP line is unique and that the ratio of creep rate to compression index is constant for a given soil (and they are correct in that this is a law no less) and approximately constant for groups of soils (see here for why). But despite their being correct on these important matters, they are fundamentally wrong when say claim that creep compression strains due to viscous effects occur only after EOP.  In short, despite the correctness of their other, claims Hypothesis A is fundamentally wrong.

Likewise, Hypothesis B groupies are partially correct–they are correct in the core issue, i.e., correct to say that viscous effects occur DURING consolidation as well as after.  But they are wrong to say that this matters in the majority of geotechnical problems.  Standard methods (which implicitly assume the erroneous Hypothesis A) of calculating consolidation and creep settlements suffice for the vast majority of geotechnical projects.  This is because of various factors including, chiefly, the small effect of strain-rate during consolidation, sample disturbance in “undisturbed” samples taken from the ground by the average commercial drilling company, and the fact that the thick highly compressible layers that take decades to consolidate and where strain-rate effects might play a role in the design are encountered fairly rarely in real life.  It is only for this small minority of field situations that the isotache method together with high quality sampling has a role in design.

Both sides have a part of the truth; both sides stick to the phenomenal evidence; both sides drive their arguments based on their emotional biases; both sides amateurishly and with a complete lack of rigor seem to not understand the importance of a root cause analysis that fundamentally derives from the physical bases of the behavior observed.  Both sides, instead, amateurishly remain stuck at the superficial level of mere manifest phenomenal data.

In short, BOTH SIDES ARE BUT SCHOLASTIC–hewing to faulty (being partial) logic (Aristotelian), stuck at mere phenomenology, and blind to root cause, physically based empirically evidenced data.

The next time more squabbling on this topic is published, I plan to submit a discussion raising these issues to the authors in question.

Comments welcomed–email me at pjoseph@soilmechanics.us

 

Time to end Scholasticism in Soil Mechanics. : #1 “Hyperplasticity”

Posted in Scholasticism by Paul Joseph on April 7, 2016

500 years after Galileo, Newton, and Bacon, one would think that Aristotelian scholasticism is dead.

Not so apparently in soil mechanics, where some academics still don’t seem to “get” this basic/fundamental concept.

It is time to put an end to this.  To this end, see below my review of two recent books on  “hyperplasticity.”

Fingers crossed, but the “Leibnizian pigsty style of trade school heuristics” soil mechanics pioneered by MIT seems to be a thing of the past.  Now its time to take aim at scholasticism in soil mechanics. Towards ending this scholasticism, I plan to subject any future book I encounter in like vein, to the same, standard, 500 year old test–one that school children (at least in the US) are well aware of–that of empirical evidence.

Comments are welcomed.

1) http://www.amazon.com/Constitutive-Modelling-Geomechanics-Alexander-Puzrin/dp/3642273947/ref=sr_1_1?s=books&ie=UTF8&qid=1437136072&sr=1-1
2) http://www.amazon.com/Principles-Hyperplasticity-Approach-Plasticity-Thermodynamic/dp/184628239X/ref=sr_1_2?s=books&ie=UTF8&qid=1437136122&sr=1-2

For background information on this please read the following:
1) http://www.soilmechanics.us/dssm/soil-mechanics/appendix-3-deconstructing-elasto-plastic-cssm-models/
2) http://www.soilmechanics.us/dssm/soil-mechanics/chapter-9-conclusion/ and
3) https://soilmechanics.wordpress.com/