Soil Mechanics

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) 
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