1.1 WHAT IS THIS BOOK ABOUT?
Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness for a generally short time but nevertheless long enough for liquefaction to be the cause of many failures, deaths and major financial losses. For example, the 1964 Niigata (Japan) earthquake caused more than $1 billion in damage and most of this damage was related to soil liquefaction. The Aberfan (Wales) colliery spoil slide was caused by liquefaction and killed 144 people (116 of whom were children) when it inundated a school. Liquefaction was involved in the abandonment of the Nerlerk (Canada) artificial island after more than
$100 million had been spent on its construction. Liquefaction at Lower San Fernando dam (California) required the immediate evacuation of 80,000 people living downstream of the dam. Liquefaction is an aspect of soil behaviour that occurs worldwide and is of considerable importance from both public safety and financial standpoints.
In terms of age of the subject, Ishihara in his Rankine Lecture (Ishihara, 1993) suggests that the term spontaneous liquefaction was coined by Terzaghi and Peck (1948).
The subject is much older than that, however. Dutch engineers have been engineering against liquefaction for centuries in their efforts to protect their country from the sea.
Koppejan et al. (1948) brought the problem of coastal flow slides to the soil mechanics fraternity at the 2nd International Conference in Rotterdam. In the last paragraph of their much-cited paper, they mention flow slides in the approach to a railway bridge near Weesp in 1918 triggered by vibrations from a passing train. They claim that this accident, with heavy casualties, was the immediate cause of the start of practical soil mechanics in the Netherlands.
At about the same time, Hazen (1918) reporting on the Calaveras Dam failure clearly recognized the phenomenon of liquefaction and the importance of pore pressures and effective stresses. If the files of the US Corp of Engineers are consulted one finds that Colonel Lyman densified fill for the Franklin Falls dam (part of the Merrimack Valley Flood Control scheme) in the late 1930s specifically to ensure stability of the dam from liquefaction based on the concept of critical void ratio given in Casagrande (1936).
Reading these files and reports is an enlightening experience as Casagrande discussed many topics relevant to the subject today, and Lyman’s report (1938) of the Corps’
engineering at Franklin Falls is a delight that historians of the subject will enjoy.
We will not attempt our own definition of liquefaction, or adopt anyone else’s, beyond the first sentence of this book. Once it is accepted that liquefaction is a constitutive behaviour subject to the laws of physics, it becomes necessary to describe the mechanics mathematically and the polemic is irrelevant.
Liquefaction evaluation is only considered worthwhile if it may change an engineering decision. Testing and analysis of liquefaction potential is only undertaken in practice in the context of a particular project. As will be seen later, liquefaction is an intrinsically
brittle process and the observational method must not be used. If liquefaction is a potential problem, it must be engineered away. Engineering to avoid liquefaction involves processes with often relatively high mobilization (start up) costs, but a low marginal cost of additional treatment. So if liquefaction may be a problem, then the construction costs to avoid it may show considerable independence from the potential degree of liquefaction or desired safety factor against liquefaction. Many practical problems simply become go/no-go decisions for near fixed price ground modification. In such situations, there is nothing to be gained from elaborate testing and analysis if it will not change the decision. As it turns out, many projects with possible liquefaction issues fall into this class.
One might mistakenly take such a decision-driven approach to be pragmatic and anti-theory. This is not the case and theory has a crucial role. More particularly, relevant theory must be much more than some vague liquefaction “concept” or definition. A full constitutive model is used to predict not just when liquefaction occurs but also the evolution of pore pressures and strains. It is self-evident that liquefaction, in all its forms, is simply another facet of the constitutive behaviour of soil and as such can only be properly understood within a background of constitutive theory. Why such an elaborate demand for theory? There are two reasons.
Firstly, the literature abounds with liquefaction concepts developed on the basis of incomplete information or poorly formed theory. How are these many concepts to be distinguished? Which concepts are erroneous if applied to other situations because they missed crucial factors? Which concepts assume one form of behaviour which, while a reasonable approximation within any given limited experience, wrongly predicts outside its experience base? Which concepts are reasonable representations of the micro-mechanical processes actually happening between the soil particles? Demanding a full constitutive model which works for all testable stress paths, while not guaranteeing future adequacy (and there is nothing that can give such assurance), does at least ensure as good a job as possible and eliminates ideas that are intrinsically wrong.
Secondly, it is a fact of life that civil engineering is an activity with little opportunity for full scale testing. Correspondingly, much experience is based on a few (relative to the total construction market) failures for which there is often limited and uncertain information. This necessity to deal with what might be called rare events distinguishes civil engineering from the many other branches of engineering in which it is feasible to test prototypes. Further, in geotechnical experience there are generally enough free (unknown) parameters to fit any theory to any failure case history. Correspondingly there is enormous potential for misleading theories to be perceived as credible by the incautious. Only by using theories whose adequacy is established outside the case history can the profession limit its potential for being misled. It is not an overstatement that the profession can be misled. One of the empirical graphs in common usage is a plot of residual shear strength after liquefaction against SPT blow count (N value), first proposed by Seed (1987). This graph has been reproduced many times with additional data since then but the graph is fundamentally wrong—it ignores the initial stress level on one axis but uses a pressure normalized penetration resistance on the other axis. The implied relationship for post-liquefaction strength is dimensionally inconsistent, and the chart cannot possibly be useful in a predictive sense.
In effect, the approach in this book demands that the profession’s view of liquefaction should pass what could be called a variation of the Turing test: “if it does not compute, then you have nothing”. Turing, 1912–1954, was a mathematician and logician who pioneered in computer theory and logical analyses of computer processes. Turing computability is the property of being calculable on a Turing machine, a theoretical computer that is not subject to malfunction or storage space limits, i.e. the ultimate PC.
There should be no interest in non-computable “concepts” and liquefaction dogma. The approach to liquefaction presented in this book meets this criterion of computability.
Surely, one might ask, if mechanics is so good then why not rely on it? The answer is that there are factors such as time, scale effects, pore water migration, strain localization, and soil variability that are routinely neglected in most theories, testing, and design methods but these factors are real and important. Emphasizing practical experience, properly set in a plasticity framework, develops an understanding of what is formally known as model uncertainty.
So what this book provides is a mathematically and physically consistent view of an important subject with a strong bias to real soils and decisions that must be faced in engineering practice. Because a lot of the material may seem intimidating, derivations are included in detail so that the origin of the equations is apparent. Samples of source code are available from a website so that the reader can see how complex looking differentials actually have pretty simple form. The source data are provided as downloadable files, so that this book can be used as a tutorial. The book is also quite a bit more than a compendium of papers and many ideas have evolved since first publication.
It is also worth noting what is not covered. Mainly, methods of analysis are not considered. This book will help the reader determine the cyclic strength of sands, but it does not cover how to get the imposed cyclic stresses. Analysis, particularly with general purpose finite element programs for transient problems, is a large subject in its own right.
1.2 WHY A CRITICAL STATE VIEW?
This book is sub-titled “A Critical State Approach” for a particular reason. Density affects the behaviour of all soils—crudely, dense soils are strong and dilatant, loose soils weak and compressible. Now, as any particular soil can exist across a wide range of densities it is unreasonable to treat any particular density as having its own properties.
Rather, a framework is needed that explains why a particular density behaves in a particular way. The aim is to separate the description of soil into true properties that are invariant with density (e.g. critical friction angle) and measures of the soils state (e.g.
current void ratio or density). Soil behaviour should then follow as a function of these properties and state.
The first theory offered that captured this ethos was what became known as critical state soil mechanics, popularized by Schofield and Wroth (1968) with the Cam Clay idealized theoretical model of soil. The name critical state derives from anchoring the theory to a particular condition of the soil, called the critical void ratio by Casagrande in 1936. The definition of the critical state will come later but for now just note that the critical state is the end state if the soils is deformed (sheared) continuously. The neat thing about the critical state, at least mathematically and philosophically, is that if the
Introduction 3
end-state is known it then becomes simple to construct well-behaved models. You always know where you are going.
The need to have a model comes back to the earlier statement paraphrasing Turing—if you cannot compute, you have nothing. Computing needs a model. These days there are a number of appropriate models to choose, but the choice is more a matter of detail than fundamental. Given the philosophical view that the model should explain the effect of density on soil behaviour, it turns out that (to date) only models incorporating critical state concepts are available. So, one way or another, things get anchored to a critical state view once the requirement is invoked for computable behaviour with density independent properties.
Before going much further, it is appropriate to acknowledge a related school of thinking. At about the same time as critical state soil mechanics was developing in England, workers in the USA, in particular Castro (1969) with guidance from Casagrande at Harvard, put forward the view that the critical state during rapid shearing was the end point and knowledge of this end point allowed the solution of most liquefaction problems. The critical state after rapid shearing was termed the steady state. On the face of it, this approach allowed exceedingly simple analysis of a complex problem—a post-liquefaction strength (the steady state) allows engineering of stability using straightforward undrained analysis.
Mathematically there is no difference between the definitions of steady and critical states and they are usually taken to be the same. So, does this book belong to the Steady State School? The answer is an emphatic no. The Steady State School does not provide a computable model or theory. In contrast, this book offers a computable constitutive model in accordance with established plasticity theory that gives the details of strains and pore pressures during liquefaction. Critical state theory, being formulated under the framework of theoretical plasticity, insists on consistent physics and mathematics.
However, it is also true that many of the ideas incorporated in critical state soil mechanics owe as much to Cambridge, Massachusetts as Cambridge, England. The similarities and differences will be discussed in Chapter 2 and 3, as these aspects are interesting both historically and intellectually.
The basic approach is to anchor everything to the state parameter, ψ, defined on Figure 1.1. The state parameter is simply the void ratio difference between the current state of the soil and the critical state at the same mean stress. The critical state void ratio varies with mean effective stress, and is usually referred to as the critical state locus (CSL).
Dense soils have negative ψ and loose contractive soils have positive ψ. Soil constitutive behaviour is related to ψ, and liquefaction behaviour is no different from other aspects of stress-strain response.
In summary, a critical state view and associated generalized constitutive model (NorSand) provides a simple computable model that captures the salient aspects of liquefaction in all its forms. This critical state view is easy to understand, is characterized by a simple state parameter (ψ) with a few material properties (which can be determined on reconstituted samples), and lends itself to all soils.