Computational Geomechanics E-Book

Andrew H. C. Chan

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 756

Veröffentlichungsjahr: 2022

Beschreibung

COMPUTATIONAL GEOMECHANICS

The new edition of the first book to cover the computational dynamic aspects of geomechanics, now including more practical applications and up-to-date coverage of current research in the field

Advances in computational geomechanics have dramatically improved understanding of the behavior of soils and the ability of engineers to design increasingly sophisticated constructions in the ground. When Professor Olek Zienkiewicz began the application of numerical approaches to solid dynamics at Swansea University, it became evident that realistic prediction of the behavior of soil masses could only be achieved if the total stress approaches were abandoned. Computational Geomechanics introduces the theory and application of Zienkiewicz’s computational approaches that remain the basis for work in the area of saturated and unsaturated soil to this day.

Written by past students and colleagues of Professor Zienkiewicz, this extended Second Edition provides formulations for a broader range of problems, including failure load under static loading, saturated and unsaturated consolidation, hydraulic fracturing, and liquefaction of soil under earthquake loading. The internationally-recognized team of authors incorporates current computer technologies and new developments in the field, particularly in the area of partial saturation, as they guide readers on how to properly apply the formulation in their work. This one-of-a-kind volume:

• Explains the Biot-Zienkiewicz formulation for saturated and unsaturated soil
• Covers multiple applications to static and dynamic problems for saturated and unsaturated soil in areas such as earthquake engineering and fracturing of soils and rocks
• Features a completely new chapter on fast catastrophic landslides using depth integrated equations and smoothed particle hydrodynamics with applications
• Presents the theory of porous media in the saturated and unsaturated states to establish the foundation of the problem of soil mechanics
• Provides a quantitative description of soil behavior including simple plasticity models, generalized plasticity, and critical state soil mechanics
• Includes numerous questions, problems, hands-on experiments, applications to other situations, and example code for GeHoMadrid

Computational Geomechanics: Theory and Applications, Second Edition is an ideal textbook for specialist and general geotechnical postgraduate courses, and a must-have reference for researchers in geomechanics and geotechnical engineering, for software developers and users of geotechnical finite element software, and for geotechnical analysts and engineers making use of the numerical results obtained from the Biot-Zienkiewicz formulation.

Leseprobe

Computational Geomechanics

Theory and Applications

Second Edition

Andrew H. C. Chan

University of Tasmania

Manuel Pastor

ETS de Ingenieros de Caminos

Universidad Politécnica de Madrid, Spain

formerly at Centro de Estudios y Experimentación de Obras Públicas,

Madrid, Spain

Bernhard A. Schrefler

University of Padua

Tadahiko Shiomi

Mind Inc., 3D Laboratory, Japan

O. C. Zienkiewicz

CINME, UNESCO former Professor of Numerical Methods in Engineering at

Technical University of Catalonia (UPC), Spain

This edition first published 2022© 2022 John Wiley & Sons Ltd

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The right of Andrew H. C. Chan, Manuel Pastor, Bernhard A. Schrefler, Tadahiko Shiomi and O.C. Zienkiewicz to beidentified as the authors of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication Data

Names: Chan, Andrew H. C., author. | Pastor, Manuel, author. | Schrefler, B. A., author. | Shiomi, Tadahiko, author. | Zienkiewicz, O. C., author.Title: Computational geomechanics : theory and applications / Andrew H. C Chan, University of Tasmania, Manuel Pastor, Bernard Schrefler, University of Padua, Tadahiko Shiomi, Olgierd C. Zienkiewicz, CINME, UNESCO Professor of Numerical Methods in Engineering at Technical University of Catalonia (UPC), Spain.Description: Second edition. | Hoboken, NJ : John Wiley & Sons, Inc., 2022. | Revised edition of: Computational geomechanics with special reference to earthquake engineering / O.C. Zienkiewicz ... [et al.]. 1999.Identifiers: LCCN 2021049320 (print) | LCCN 2021049321 (ebook) | ISBN 9781118350478 (cloth) | ISBN 9781118535318 (adobe pdf) | ISBN 9781118535301 (epub)Subjects: LCSH: Geotechnical engineering--Mathematics. | Earthquake engineering--Mathematics.Classification: LCC TA705 .C46 2022 (print) | LCC TA705 (ebook) | DDC 624.1/51--dc23/eng/20211208LC record available at https://lccn.loc.gov/2021049320LC ebook record available at https://lccn.loc.gov/2021049321

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Preface

Our first text on this subject Computational Geomechanics with Special Reference to Earthquake Engineering was published 23 years ago and has been out of print for much of the past decade. It was the first book of its kind having as the main topic Computational Dynamic Aspects of Geomechanics which obviously comprise statics also. In the intervening period, there was a rapid expansion in the research and practical applications of these types of problems, which has prompted us to write this new and thoroughly updated version.

It contains not only the results of research carried out at our four institutions but also reports on the work done elsewhere. The chapters from the previous edition have been extensively updated and new chapters have been added to give a much broader coverage of recent research interests. The Preface to the first edition was written by the Late Professor Oleg Cecil Zienkiewicz. Its validity is still fully conserved today. So, we reprinted large parts of it.

Although the concept of effective stress in soils is accepted by all soil mechanicians, practical predictions and engineering calculations are traditionally based on total stress approaches. When the senior author began, in the early seventies, the application of numerical approaches to the field of soil mechanics in general and to soil dynamics in particular, it became clear to him that a realistic prediction of the behavior of soil masses could only be achieved if the total stress approaches were abandoned. The essential model should consider the coupled interaction of the soil skeleton and of the pore fluid. Indeed, the phenomena of weakening and of “liquefaction” in soil, when subjected to repeated loading such as that which occurs in earthquakes, can only be explained by considering this “two‐phase” action and the quantitative analysis and prediction of real behaviour can only be achieved by sophisticated computation. The simple limit methods often applied in statics are no longer useful. It, therefore, seems necessary at the present time to present, in a single volume, the basis of such computational approaches because a wider audience of practitioners and engineering students will require the knowledge which hitherto has only been available through scientific publications scattered throughout many journals and conferences. The present book is an attempt to provide a rapid answer to this need. Since 1975, a large number of research workers, both students and colleagues, have participated both at Swansea and elsewhere in laying the foundations of numerical predictions which were based largely on concepts introduced in the early forties by Biot. However, the total stress calculation continues to be used by some engineers for earthquake response analysis, often introduced with linear approximations. Such simplifications are generally not useful and can lead to erroneous predictions. In recent years, centrifuge experiments have permitted the study of some soil problems involving both statics and dynamics. These provide a useful set of benchmark predictions. Here a validation of the two‐phase approach was available and a close agreement between computation and experiment was found. A very important landmark was a workshop held at the University of California, Davis, in 1993, which reported results of the VELACS project (Verification of Liquefaction Analysis by Centrifuge Studies) sponsored by the National Science Foundation of the USA.

At this workshop, a full vindication of the effective stress, two‐phase approaches was clearly available and it is evident that these will be the bases of future engineering computations and prediction of behavior for important soil problems. The book shows some examples of this validation and also indicates examples of the practical application of the procedures described. During numerical studies, it became clear that the geomaterial – soil would often be present in a state of incomplete saturation when part of the void was filled with air. Such partial saturation is responsible for the presence of negative pressures which allow some “apparent” cohesion to be developed in noncohesive soils. This phenomenon may be present at the outset of loading or may indeed develop during the dynamic process. We have therefore incorporated its presence in the treatment presented in this book and thus achieved wider applicability for the methods described.

Despite a large number of authors, we have endeavored to present a unified approach and have used the same notation, style, and spirit throughout. The first three chapters present the theory of porous media in the saturated and unsaturated states and thus establish general backbone to the problem of soil mechanics.

Even though the fundamental nature of the basic theory remains unchanged as shown in Chapters 2 and 3, many of the other chapters have been substantially updated. The following part of the book has been extensively restructured, reworked, and updated, and new chapters have been added such as to cover essentially all the important aspects of computational soil mechanics.

Chapter 4, essential before numerical approximation, deals with the very important matter of the quantitative description of soil behavior which is necessary for realistic computations. This chapter has been substantially rewritten such as to introduce new developments. It is necessarily long and devotes a large part to generalized plasticity and critical‐state soil mechanics and also includes a simple plasticity model. The generalized plasticity model is then extended to partially saturated soil mechanics. Presentation of alternative advanced models such as bounding surface models and hypoplasticity concludes the chapter.

Chapter 5 addresses some special aspects of analysis and formulation such as far‐field solutions in quasi‐static problems, input for earthquake analysis and radiation damping, adaptive finite element requirements, the capture of localized phenomena, regularization aspects and stabilization for nearly incompressible soil behavior both in dynamics and consolidation permitting to use equal order interpolation for displacements and pressures.

Chapter 6 presents applications to static problems, seepage, soil consolidation, hydraulic fracturing, and also examples of dynamic fracturing in saturated porous media. Validation of the predictions by dynamic experiments in a centrifuge is dealt with in Chapter 7.

Chapter 8 is entirely devoted to application in unsaturated soils, including the dynamic analysis with a full two‐phase fluid flow solution, analysis of land subsidence related to exploitation of gas reservoirs, and initiation of landslides.

Chapter 9 addresses practical prediction, application, and back analysis of earthquake engineering examples. Finally, Chapter 10 pushes the limits of the analysis beyond failure showing the modeling of fluidized geomaterials with application to fast catastrophic landslides.

We are indebted to many of our coworkers and colleagues and, in particular, we thank the following people who over the years have contributed to the work (in alphabetical order of their surnames):

T. Blanc,

G. Bugno,

T.D. Cao,

P. Cuéllar,

S. Cuomo (MP),

P. Dutto,

E. González,

B. Haddad,

M.I. Herreros,

Maosong Huang,

E. Kakogiannou,

M. Lazari,

Chuan Lin,

Hongen Li,

Li Tongchun,

Liu Xiaoqing,

D. Manzanal,

M. Martín Stickle

A. Menin,

J.A. Fernández Merodo,

E. Milanese,

P. Mira,

M. Molinos,

S. Moussavi,

R. Ngaradoumbe Nanhornguè,

P. Navas,

T. Ni,

Jianhua Ou,

M. Passarotto,

M.J. Pastor,

C. Peruzzo,

F. Pisanò,

M. Quecedo,

V. Salomoni,

L. Sanavia,

M. Sánchez‐Morles,

R. Santagiuliana,

R. Scotta,

S. Secchi,

Y. Shigeno,

L. Simoni,

C. Song,

A. Yagüe,

Jianhong Ye,

M. Yoshizawa,

H.W. Zhang.

Finally, we would like to dedicate this edition to the memory of the Late Oleg Cecil Zienkiewicz. Without his inspiration and enthusiasm, we would not have undertaken the research work reported here. We would also like to thank our beloved Late Helen Zienkiewicz, wife of Professor Zienkiewicz, who kindly allowed us to celebrate Oleg’s decades of pioneering and research field defining achievements in computational geomechanics.

Andrew H. C. ChanManuel PastorBernhard A. SchreflerTadahiko ShiomiHobart, Madrid, Padua, Tokyo, January 2022

1Introduction and the Concept of Effective Stress

1.1 Preliminary Remarks

The engineer designing such soil structures as embankments, dams, or building foundations should be able to predict the safety of these against collapse or excessive deformation under various loading conditions which are deemed possible. On occasion, he may have to apply his predictive knowledge to events in natural soil or rock outcrops, subject perhaps to new, man‐made conditions. Typical of this is the disastrous collapse of the mountain (Mount Toc) bounding the Vajont reservoir which occurred on 9 October 1963 in Italy (Müller 1965). Figure 1.1 shows both a sketch indicating the extent of the failure and a diagram indicating the cross section of the encountered ground movement.

In the above collapse, the evident cause and the “straw that broke the camel’s back” was the filling and the subsequent drawdown of the reservoir. The phenomenon proceeded essentially in a static (or quasi‐static) manner until the last moment when the moving mass of soil acquired the speed of “an express train” at which point, it tumbled into the reservoir, displacing the water dynamically and causing an unprecedented death toll of some 4000 people from the neighboring town of Longarone.

Such static failures which occur, fortunately at a much smaller scale, in many embankments and cuttings are subjects of typical concern to practicing engineers. However, dynamic effects such as those frequently caused by earthquakes are more spectacular and much more difficult to predict.

We illustrate the dynamic problem by the near‐collapse of the Lower San Fernando dam near Los Angeles during the 1971 earthquake (Figure 1.2) (Seed, 1979; Seed et al. 1975). This failure, fortunately, did not involve any loss of life as the level to which the dam “slumped” still contained the reservoir. Had this been but a few feet lower, the overtopping of the dam would indeed have caused a major catastrophe with the flood hitting a densely populated area of Los Angeles.

It is evident that the two examples quoted so far involved the interaction of pore water pressure and the soil skeleton. Perhaps the particular feature of this interaction, however, escapes immediate attention. This is due to the “weakening” of the soil–fluid composite during the periodic motion such as that which is involved in an earthquake. However, it is this rather than the overall acceleration forces which caused the collapse of the Lower San Fernando dam. What appears to have happened here is that during the motion, the interstitial pore pressure increased, thus reducing the interparticle forces in the solid phase of the soil and its strength.1

Figure 1.1 The Vajont reservoir, failure of Mant Toc in 1963 (9 October): (a) hypothetical slip plane; (b) downhill end of the slide (Müller, 1965). Plate 1 shows a photo of the slides (front page).

This phenomenon is well documented and, in some instances, the strength can drop to near‐zero values with the soil then behaving almost like a fluid. This behavior is known as soil liquefaction and Plate 2 shows a photograph of some buildings in Niigata, Japan taken after the 1964 earthquake. It is clear here that the buildings behaved as if they were floating during the active part of the motion.

Figure 1.2 Failure and reconstruction of original conditions of Lower San Fernando dam after 1971 earthquake, according to Seed (1979): (a) cross section through embankment after the earthquake; (b) reconstructed cross section.

Source: Based on Seed (1979).

In this book, we shall discuss the nature and detailed behavior of the various static, quasi‐static and dynamic phenomena which occur in soils and will indicate how a computer‐based, finite element, analysis can be effective in predicting all these aspects quantitatively.

1.2 The Nature of Soils and Other Porous Media: Why a Full Deformation Analysis Is the Only Viable Approach for Prediction

For single‐phase media such as those encountered in structural mechanics, it is possible to predict the ultimate (failure) load of a structure by relatively simple calculations, at least for static problems. Similarly, for soil mechanics problems, such simple, limit‐load calculations are frequently used under static conditions, but even here, full justification of such procedures is not generally valid. However, for problems of soil dynamics, the use of such simplified procedures is almost never admissible.

The reason for this lies in the fact that the behavior of soil or such a rock‐like material as concrete, in which the pores of the solid phase are filled with one fluid, cannot be described by behavior of a single‐phase material. Indeed, to some, it may be an open question whether such porous materials as shown in Figure 1.3 can be treated at all by the methods of continuum mechanics. Here we illustrate two apparently very different materials. The first has a granular structure of loose, generally uncemented, particles in contact with each other. The second is a solid matrix with pores that are interconnected by narrow passages.

From this figure, the answer to the query concerning the possibility of continuum treatment is self‐evident. Provided that the dimension of interest and the so‐called “infinitesimals” dx, dy, etc., are large enough when compared to the size of the grains and the pores, it is evident that the approximation of a continuum behavior holds. However, it is equally clear that the intergranular forces will be much affected by the pressures of the fluid–p in single phase (or p1, p2, etc., if two or more fluids are present). The strength of the solid, porous material on which both deformations and failure depend can thus only be determined once such pressures are known.

Figure 1.3 Various idealized structures of fluid-saturated porous solids: (a) a granular material; (b) a perforated solid with interconnecting voids.

Using the concept of effective stress, which we shall discuss in detail in the next section, it is possible to reduce the soil mechanics problem to that of the behavior of a single phase once all the pore pressures are known. Then we can again use the simple, single‐phase analysis approaches. Indeed, on occasion, the limit load procedures are again possible. One such case is that occurring under long‐term load conditions in the material of appreciable permeability when a steady‐state drainage pattern has been established and the pore pressures are independent of the material deformation and can be determined by uncoupled calculations.

Such drained behavior, however, seldom occurs even in problems that we may be tempted to consider as static due to the slow movement of the pore fluid and, theoretically, the infinite time required to reach this asymptotic behavior. In very finely grained materials such as silts or clays, this situation may never be established even as an approximation.

Thus, in a general situation, the complete solution of the problem of solid material deformation coupled to a transient fluid flow needs to be solved generally. Here no shortcuts are possible and full coupled analyses of equations which we shall introduce in Chapter 2 become necessary.

We have not mentioned so far the notion of the so‐called undrained behavior, which is frequently assumed for rapidly loaded soil. Indeed, if all fluid motion is prevented, by zero permeability being implied or by extreme speed of the loading phenomena, the pressures developed in the fluid will be linked in a unique manner to deformation of the solid material and a single‐phase behavior can again be specified. While the artifice of simple undrained behavior is occasionally useful in static studies, it is not applicable to dynamic phenomena such as those which occur in earthquakes as the pressures developed will, in general, be linked again to the straining (or loading) history and this must always be taken into account. Although in early attempts to deal with earthquake analyses and to predict the damage and response, such undrained analyses were invariably used, adding generally a linearization of the total behavior and a heuristic assumption linking the pressure development with cycles of loading and the behavior predictions were poor. Indeed, comparisons with centrifuge experiments confirmed the inability of such methods to predict either the pressure development or deformations (VELACS – Arulanandan and Scott 1993). For this reason, we believe that the only realistic type of analysis is of the type indicated in this book. This was demonstrated in the same VELACS tests to which we shall frequently refer in Chapter 7.

At this point, perhaps it is useful to interject an observation about the possible experimental approaches. The question which could be addressed is whether a scale model study can be made relatively inexpensively in place of elaborate computation. A typical civil engineer may well consider here the analogy with hydraulic models used to solve such problems as spillway flow patterns where the cost of a small‐scale model is frequently small compared to equivalent calculations.

Unfortunately, many factors conspire to deny in geomechanics a readily accessible model study. Scale models placed on shaking tables cannot adequately model the main force acting on the soil structure, i.e. that of gravity, though, of course, the dynamic forces are reproducible and scalable.

To remedy this defect, centrifuge models have been introduced and, here, though, at considerable cost, gravity effects can be well modeled. With suitable fluids substituting water, it is indeed also possible to reproduce the seepage timescale and the centrifuge undoubtedly provides a powerful tool for modeling earthquake and consolidation problems in fully saturated materials. Unfortunately, even here a barrier is reached which appears to be insurmountable. As we shall see later under conditions when two fluids, such as air and water, for instance, fill the pores, capillary effects occur and these are extremely important. So far, no significant success has been achieved in modeling these and, hence, studies of structures with free (phreatic) water surface are excluded. This, of course, eliminates the possible practical applications of the centrifuge for dams and embankments in what otherwise is a useful experimental procedure.

1.3 Concepts of Effective Stress in Saturated or Partially Saturated Media

1.3.1 A Single Fluid Present in the Pores – Historical Note

The essential concepts defining the stresses which control the strength and constitutive behavior of a porous material with internal pore pressure of fluid appear to have been defined, at least qualitatively two centuries ago. The work of Lyell (1871), Boussinesq (1876), and Reynolds (1886) was here of considerable note for problems of soils. Later, similar concepts were used to define the behavior of concrete in dams (Levy 1895 and Fillunger 1913a, 1913b, 1915) and indeed for other soil or rock structures. In all of these approaches, the concept of division of the total stress between the part carried by the solid skeleton and the fluid pressure is introduced and the assumption made that the strength and deformation of the skeleton is its intrinsic property and not dependent on the fluid pressure.

If we thus define the total stressσ by its components σij using indicial notation, these are determined by summing the appropriate forces in the i‐direction on the projection, or cuts, dxj (or dx, dy, and dz in conventional notation). The surfaces of cuts are shown for two kinds of porous material structure in Figure 1.3 and include the total area of the porous skeleton.

In the context of the finite element computation, we shall frequently use a vectorial notation for stresses, writing

(1.1a)

or

(1.1b)

This notation reduces the components to six rather than nine and has some computational merit.

Now if the stress in the solid skeleton is defined as the effective stress σ′ again over the whole cross sectional area, then the hydrostatic stress due to the pore pressure, p acting, only on the pore area should be

(1.2)

where n is the porosity and δij is the Kronecker delta. The negative sign is introduced as it is a general convention to take tensile components of stress as positive.

The above, plausible, argument leads to the following relation between total and effective stress with total stress

(1.3)

or if the vectorial notation is used, we have

(1.4)

where m is a vector written as

(1.5)

The above arguments do not stand the test of experiment as it would appear that, with values of porosity n with a magnitude of 0.1–0.2, it would be possible to damage a specimen of a porous material (such as concrete, for instance) by subjecting it to external and internal pressures simultaneously. Further, it would appear from Equation (1.3) that the strength of the material would be always influenced by the pressure p.

Fillunger introduced the concepts implicit in (1.3) in 1913 but despite conducting experiments in 1915 on the tensile strength of concrete subject to water pressure in the pores, which gave the correct answers, he was not willing to depart from the simple statements made above.

It was the work of Terzaghi and Rendulic (1934) and by Terzaghi (1936) which finally modified the definition of effective stress to

(1.6)

where nw is now called the effective area coefficient and is such that

(1.7)

Much further experimentation on such porous solids as the concrete had to be performed before the above statement was generally accepted. Here the work of Leliavsky (1947), McHenry (1948), and Serafim (1954, 1964) made important contributions by experiments and arguments showing that it is more rational to take sections for determining the pore water effect through arbitrary surfaces with minimum contact points.

Bishop (1959) and Skempton (1960) analyzed the historical perspective and, more recently, de Boer (1996) and de Boer et al. (1996) addressed the same problem showing how an acrimonious debate between Fillunger and Terzaghi terminated in the tragic suicide of the former in 1937.

Zienkiewicz (1947, 1963) found that interpretation of the various experiments was not always convincing. However, the work of Biot (1941, 1955, 1956a, 1956b, 1962) and Biot and Willis (1957) clarified many concepts in the interpretation of effective stress and indeed of the coupled fluid and solid interaction. In the following section, we shall present a somewhat different argument leading to Equations (1.6) and (1.7).

If the quantity σ′ of (1.3) and (1.4) is interpreted as the volume‐averaged solid stress (1 − n) ts used in the mixture theory (partial stress), see Gray et al. (2009), then we recover the stress split introduced in Biot (1955). There the fluid pressure, as opposed to the effective stress concept, is weighted by the porosity. Biot (1955) declares that “the remaining components of the stress tensor are the forces applied to that portion of the cube faces occupied by the solid.” In this book, we use the much more common concept of effective stress.

1.3.2 An Alternative Approach to Effective Stress

Let us now consider the effect of the simultaneous application of a total external hydrostatic stress and a pore pressure change, both equal to Δp, to any porous material. The above requirement can be written in tensorial notation as requiring that the total stress increment is defined as

(1.8a)

or, using the vector notation

(1.8b)

In the above, the negative sign is introduced since “pressures” are generally defined as being positive in compression, while it is convenient to define stress components as positive in tension.

It is evident that for the loading mentioned, only a very uniform and small volumetric strain will occur in the skeleton and the material will not suffer any damage provided that the grains of the solid are all made of identical material. This is simply because all parts of the porous medium solid component will be subjected to identical compressive stress.

However, if the microstructure of the porous medium is composed of different materials, it appears possible that nonuniform, localized stresses, can occur and that local grain damage may be suffered. Experiments performed on many soils and rocks and rock‐like materials show, however, that such effects are insignificant. Thus, in general, the grains and, hence, the total material will be in a state of pure volumetric strain

(1.9)

where Ks is the average material bulk modulus of the solid components of the skeleton. Alternatively, adopting a vectorial notation for strain in a manner involved in (1.1)

(1.10a)

where ε is the vector defining the strains in the manner corresponding to that of stress increment definition. Again, assuming that the material is isotropic, we shall have

(1.10b)

Those not familiar with soil mechanics may find the following hypothetical experiment illustrative. A block of porous, sponge‐like rubber is immersed in a fluid to which an increase in pressure of Δp is applied as shown in Figure 1.4. If the pores are connected to the fluid, the volumetric strain will be negligible as the solid components of the sponge rubber are virtually incompressible.

If, on the other hand, the block is first encased in a membrane and the interior is allowed to drain freely, then again a purely volumetric strain will be realized but now of a much larger magnitude.

The facts mentioned above were established by the very early experiments of Fillunger (1915