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Frontmatter

Soil Mechanics

Frontmatter

1. Introduction to Soil Mechanics

The most important papers of Professor G. de Josselin de Jong on soil mechanics can be subdivided into three main topics: consolidation of soils, the stability of a vertical cut off, and the kinematics of granular soils in the plastic zone. This last topic contains his main contribution to threoretical soil mechanics, and has been rather controversial for some time, before being recognized as a important fundamental frame work for the analysis of soil behaviour. He also made significant contributions to the development of measuring techniques in the laboratory and in the field.Some of these can be found in his theoretical papers, some were published separately.

2. Lower bound collapse theorem and lack of normality of strain rate to yield surface for soils

In soil mechanics practice there is a need for a lower bound collapse theorem, which permits an analysis with a result on the safe side. The usual analysis of slip surfaces may give unsafe results for a purelyl cohesive soil, since it is based upon a kinematically admissable collapse system and therefore constitutes an upper bound. It is therefore necessary to investigate a great number of slip surfaces and the smallest load is an approximation to the actual load which will produce collapse, but it is never known how much the computed load exceeds the actual one.
G. De Josselin de Jong

3. Proceedings of the Geotechnical Conference OSLO 1968

On shear strength properties of natural soils and rocks
In their paper (3/14) Roscoe, Bassett and Cole review concepts pertaining to the coincidence of principal directions of stress and strain. Besides the points mentioned, it must be noted that a case of non-coincidence is to be expected if rupture planes or rupture zones develop erratically throughout the soil mass. Such planes or zones originate if the material yields in these discrete regions before the rest of the soil mass deforms excessively.

4. The double sliding, free rotating model for granular assemblies

The sliding block model for the mechanism of deformation, in a body composed of grains, is based on the concept that movements of grains with respect to each other occur along planes that coincide preferably with the stress characteristic planes. In the case of plane strain these planes interest the two-dimensional plane of consideration along two characteristics lines called S1 and S2.
The object of this Note is not to consider the probable veracity of such a model, but to establish the flow rule and the constitutive equations which follow from the special character of the model. The properties are taken to be those that were proposed by de Josselin de Jong (1958,1959). In that model sliding can occur simultaneously in the S1 and S2 directions at different shear strain rates, but limited in sense, and in addition the sliding elements are free to rotate.
G. De Josselin de Jong

5. Photoelastic verification of a mechanical model for the flow of a granular material

This Paper describes experiments performed on an assembly of discs constituting a two-dimensional analogue of a granular material. The use of photo-elasticity techniques allows the determination of average stress and strain-rate tensors in the interior of the assembly. In this way, a comparison can be made with the behaviour predicted theortically on the basis of a mechanical model. Test results indicate that the main features of the mechanical model, namely, the sub-division of the assembly into sliding elements, a possible non-coaxiality of stress and strain-rate tensors, and a free rotation of the elements are all indeed observed in practice.
A. Drescher, G. De Josselin de Jong

6. Elasto-plastic version of the double sliding model in undrained simple shear tests

In this Paper it is shown how to use the double sliding, free rotating model for materials with internal friction to predict the stress history in undrained simple shear tests. In its original rigid plastic form this model could not be used, because there was no unique failure mode. By adding some elasticity to the prefailure stage (thus producing an elasto-plastic version of the model) this unique selection becomes possible. The extended model leads to explicit expressions for the stress history in a simple shear test. It is also shown how the failure mode taken by the model depends on the stress state at the start of the test. An active initial stress state leads to a ’toppling bookrow’ mode of failure, while a passive initial stress state produces horizontal sliding planes. With the exception of elasticity, the other properties of the double sliding model, including dilatancy, are taken in their original form. The essential features of the stress history obtained from the analysis resemble those actually observed in tests.
L’ article montre comment utiliser le modè àglissement double et rotation libre pour preédire l’histoire des contraintes dans des essais de cisaillement simple non-drainés. Dans sa forme plastique rigide originale ce modèle ne pouvait pass’employer, car il n’ y avait pas de mode unique de rupture. En ajoutant de l’é lasticité à l’état précédant la rupture, produisant ainsi une version é lastoplastique du modèle, cette sélection unique devient possible. Le modè le élargi conduit a des expressions explicites pour l’histoire des contraintes dans un essai de cisaillement simple. On démontre comment le mode de rupture choisi par le modèle depend de l’état de contrainte initial actif conduit à un mode de rupture analogue à celui d’une rangée de livres qui s’écroulent, tandis qu’un état de contrainte initial passif produit des plans deglissement horizontaux. À l’exception de l’élasticité les autres propriétés du modèle à glissement double, y compris la dilatance, sont prises dans leur forme originale. Les caractéristiques essentielles de l’historie des contraintes obtenues à partir de l’analyse ressemblent à celles observées au cours des essais.
Keywords: constitutive relations; elasticity; plasticity ; shear tests; strain rates; stress rates.
G. De Josselin de Jong

7. Improvement of the lowerbound solution for the vertical cut off in a cohesive, frictionless soil

Without Abstract
G. De Josselin de Jong

8. Application of the calculus of variations to the vertical cut off in cohesive frictionless soil

The collapse height of a vertical cut off is computed by use of the variational calculus assuming the existence of a real slip line at collapse. A class of lilnes containing the real slip line is defined by total and local equilibrium conditions of the limit stress state. The extremal of the class is found to be an involute. Verification of the solution shows that the extremal gives either an unsafe estimate of the collapse height or corresponds to no extreme at all. These disappointing results are a consequence of the inadequate formulation of slope stability problems, when slip lines are computed by the calculus of variations.
La hauteur, correspondant à la rupture d’un talus vertical, est déterminée à l’aide du calcul de variations en présupposant l’existence d’une ligne de glissement unique en cas de rupture. La classe de lignes, contenart cette ligne de glissement, est definie parl’équilibre total et local sous condition d’état de contraintes limites. L ’extrémale de la class possède la forme d’une involute. En vérifiant la solution, il est démontré que l’extrémale produit une hauteur de talus plus élevée que la hauteur de rupture, où une hauteur qui ne correspond pas du tout à un extremum. Ces résultats décevants sont engendrés par la formulation inepte des problémes de stabilité, quand des lignes de glissement sont déterminées à l’aide du calcul de variations.
G. De Josselin de Jong

9. A variational fallacy

It is unfortunate that valuable information concerning fallacies in soil mechanics can get lost in the course of time. This has happened with the use of variational calculus in slope stability problems.
The variational method, for determining the critical slip surface as the surface that minimizes the load at rupture, was presented in soil mechanics by Kopácsy (1957, 1961). He published in the 1957 London conference a three-dimensional version of it. The shape of the surface is suitably established in the 1957 paper by vector analysis and described by equation (16) of that paper which, with ϖ defined by equation (20), can be expressed in words as follows.
G. De Josselin de Jong

10. Consolidation around pore pressure meters

Response of pore pressure meter on variations in loading conditions of surrounding soil is retarded by the necessity that pore water has to enter the instrument. This property is introduced as an instruments coefficient influencing the boundary conditions. With regard to the surface of the instrument, two types are considered: a rigid type and a cavernous type. At t=0 for unit step loading, consolidation has not yet started and the response of the instrument depends on shear modulus of soil only. Calculation of response as a function of time involves three-dimensional consolidation theory and is established with the aid of spherical solutions for simple harmonic and unit step loading conditions.
G. De Josselin de Jong

11. Application of stress functions to consolidation problems

The number of stress functions necessary and sufficient for the solution of consolidation problems in axial symmetry is three: one for compression, one for rotation and a function satisfying ∇2F = 0. The boundary conditions referring to the grain skeleton, as well as to the pore water, are then accounted for.
The use is shown for the case of a rigid sphere embedded in an infinite soil mass and loaded uniformly over a circular area of its surface, considering both an impervious and a pervious boundary.
G. De Josselin de Jong

12. Consolidation models consisting of an assembly of viscous elements or a cavity channel network

A cavity channel network consisting of many cavities with different compressibility interconnected by channels with different conductivity can serve as a model for a consolidating soil in both the primary and the secondary periods of consolidation.
The abundance of the constituting elements is introduced as a continuous frequency function using the spring dashpot assembly as a model because it produces similar effects. It is shown how this frequency function can be determined from test results.
Un réseau de cavités et de canaux comprenant de nombreuses cavités à compressibilités différentes reliées entre elles par des canaux à conductivités différentes peut servir de modéle pour un sol de consolidation aux deux périodes, primaire et secondaire de consolidation.
L’abondance des éléments prenant part à la constitution est introduite comme fonction de fréquence continue en utilisant l’ ensemble à amortisseur comme modèle parce qu’il produit les mêmes résultats. On montre comment cette fonction de fréquence peut être établie à partir des résultats d’essais.
G. De Josselin de Jong

13. Verification of the use of peak area for the quantitative differential thermal analysis

The amount of reacting material in a sample investigated by differential thermal analysis can be determined from the peak area according to the Boersma equation, which accounts for heat flow through sample and thermocouple wires. This relation has been checked by experiment and it has been found that the use of different thermocouples for the calibrations may lead to variations of about 30%. The values obtained for heat transfer through a sample and thermocouple have been checked by comparison of computations and observation of base-line offset at the beginning of a run and exponential decay of the amount of heat dissipating out of a sample. It is shown that according to the equation it is not the total amount of reacting material that determines the peak area but merely the density of the material near the thermocouple. The sensitivity of the method for quantitative analysis is discussed in relation to the possible variations in the factors involved, namely, density and heat conductivity of the sample and heat transfer through the thermocouple.
G. De Josselin de Jong

14. A capacitative cell apparatus

The article describes a test device which permits the determination of the horizontal strain of cylindrical samples under loading conditions without touching the sample by means of an electrical capacitive method. Tests on samples to study at rest pressure, compression and shear separately are outlined.
The conception of shear resistance, according to the sample behavior as determined by this test device, is discussed.
G. De Josselin de Jong

15. Étude photo-Élastique d’un empilement de disques

Des essais exécutés sur un empilement de disques, constituant un modèle de milieu pulvérulent, sont décrits. Les disques ont été fabriqués avec un matériau photo - élastique, ce qui permet d’étudier les constraintes à l’intérieur des disques. Il est montré comment l’ analyse des essais conduit à la détermination des forces de contact entre les disques, aussi bien en grandeur qu’en direction. Les conditions d’équilibre des disques individuels sont vérifiées à l’aide d’une épure des forces.
G. De Josselin de Jong

Flow and Transport in Porous Media

Frontmatter

16. Introduction to Flow and Transport in Porous Media

When studying a certain probelm, Gerard de Josselin de Jong’ way of approach was to create a clear visual concept of mechanism of the underlying physical process. Each time this was the most important step in his research. He could make no progress without it. In the early days of his carrer only quite primitive two dimensional visualization techniques, basically Hele - Shaw models, were available to see what actually goes on inside a porous medium. Nowadays, advanced three dimensional computer aided techniques have been developed to study flow processes in porous media.
G. De Josselin de Jong

17. Singularity distributions for the analysis of multiple-fluid flow through porous media

In Part 1 the simultaneous flow of fluids of different properties is treated by substituting these fluids by one hypothetical fluid and applying singularities at those points where the properties of the actual fluids change. Their magnitude is chosen so that the specific discharges in the hypothetical fluid are everywhere identical to the specific discharges in the actual fluids. The flow in the hypothetical fluid can be determined by potential theory from the transformed boundary conditions and the influence of the singularities.
For the determination of the discharge a stream function is used which contains singularities in the form of vortices. For the determination of the fluid pressures a multiple-fluid potential is defined which contains singularities in the form of source and sink distributions. The stream and the potential functions each combine with auxiliary, many-valued functions to form complex potentials. These permit solutions in the form of one integral in complex variables, valid for any point in the entire field, irrespective of the fluid present. The solution for the transition zone between fluids as well as the abrupt interface is elaborated.
In Part 2 the two-dimensional example of an infinite, confined aquifer with an initial vertical interface between two fluids of different specific weight is elaborated, giving as a result the movement of the fluids in the entire field at the first moment and a first approximation for the rotation of the interface around the center as a function of time.
These results are verified by a parallel plate model and an electric resistance model. In the latter model the vortices are replaced by sources for the tracing of streamlines and by source sink combinations forming doublets for the potential lines.
G. De Josselin de Jong

18. Moiré patterns of the membrane analogy for ground-water movement applied to multiple fluid flow

In the membrane analogy for flow through porous media, contour lines of a deflected membrane represent either streamlines or equipotential lines. The membrane was used by Prandil [1903] to solve torsion problems. Hansen [1952] gave a description of the application of the analogy to solve the flow patterns resulting from systems of sources and sinks. Multiple fluid flow through porous media may be treated by considering a suitable distribution of sources and sinks [de Josselin de Jong, 1960] and therefore the membrane analogy is also applicable to this problem.
G. De Josselin de Jong

19. A many-valued hodograph in an interface problem

The hodograph method for determining patterns of flow of groundwater in a coastal aquifer with a drain requires the treatment of double-sheeted hodograph planes. This many-valuedness does not prohibit the use of Schwarz-Christoffel analysis if the hodograph domain is simply connected. In the two-fluid case of fresh water flowing over stationary salt water the hodograph is simply connected, and the hodograph method is shown to give a solution. This solution was verified by a test that showed a stable interface in the predicted position.
G. De Josselin de Jong

20. Generating functions in the theory of flow through porous media

In this study the flow of fluids through porous media is considered for the case in which fluid and porous medium are inhomogeneous. The properties that may differ from place to place in the field are the density and viscosity of the fluid and the intrinsic permeability of the medium. These inhomogeneities are responsible for rotations in the flow pattern. Since the Darcian flow of fluids through porous media is usually irrotational, it was considered instructive in this presentation to elaborate especially the character of these rotations.
G. De Josselin de Jong

21. Vortex theory for multiple fluid in three dimensions

The specific discharge in a pore fluid with specific weight, γ , that is variable in space, is a rotational flow possessing vorticity in those regions, where γ varies in horizontal direction. The vortices have horizontal axes parallel to lines of constant γ. They create a circulating flow in the aquifer around them. On a sharp interface the contourlines of equal height form vortex lines, that enclose reentrant vortex ribbons of constant strength. Formulas are given for the specific discharge in an arbitrary point of the aquifer, created by the vortices in a triangular part of an interface. These relations are suitable for determining the displacement of an interface in time. Finally the specific discharge in a point of the interface, as created by the vortices in a small circular region of the interface around that point, is demonstrated to consist of a shear flow only, similar to the shear flow occuring in the two dimensional case.
G. De Josselin de Jong

22. The simultaneous flow of fresh and salt water in aquifers of large horizontal extension determined by shear flow and vortex theory

An interface motion equation is derived, taking into account the compete Edelman shear flow conditions and the Dietz-Dupuit approximations. A solution is verified with a result from exact vortex theory.
G. De Josselin de Jong

23. L’entrainement de particules par le courant intersticiel

The pore system of a packed bed is schematized of canals in order to permit probability-computations for a strange particle carried by the pore water movement to arrive at a certain place in certain time.
The computations lead to explicit values for the coefficient of longitudinal and transversal diffusivity.
A test device is described which permits determination of longitudinal difffusivity. Relation between test result and theory is discussed.
G. De Josselin de Jong

24. Longitudinal and transverse diffusion in granular deposits

The flow of liquids through porous media is defined by Darcy’s law when bulk movement is considered. In several cases, however, it is of interest to know how elements of volume or discrete particles carried by the liquid will travell. For instance, in the study of ground-water movement, radio active salts are injected into the soil. The salt will travel through different pores and after a given interval of time will arrive at different places, their distance from the starting point being dependent upon how tortuous was the path they followed.
G. De Josselin de Jong

25. Discussion of ”Longitudinal and transverse diffusion in granular deposits“

J. A. Cole (Department of Geodesy and Geo-physics, University of Cambridge, Cambridge, England)-The writer finds the paper most valuable, because he [Cole, 1957] has made experiments with columns of granular material, basically similar to those described by the author, in order to determine the relative importance of: Effect (a) radial molecular diffusion in each pore combined with a velocity gradient across the pore, and Effect (b) the geometry of the pore system in producing a longitudinal dispersion of an injected substance.
G. De Josselin de Jong

26. Transverse dispersion from an originally sharp fresh–salt interface caused by shear flow

In this paper the influence of transversal dispersion and molecular diffusion on the distribution of salt in a plane flow through a homogeneous porous medium is studied. Since the dispersion depends on the velocity and the velocity on the distribution of salt (through the specific weight) this is a nonlinear phenomenon. In particular for the flow situation considered, this leads to a differential equation which has the character of nonlinear diffusion.
The initial situation (at t = 0) is chosen such that the fresh- and salt water are separated by an interface, and each fluid has a constant specific weight γ1 and γ2, respectively. For this initial situation, the solution of the nonlinear diffusion equation has the form of a similarity solution, depending only on ζ/\(\sqrt t \), where ζ denotes the local coordinate normal to the original interface plane and t denotes time.
Properties of this similarity solution are discussed. In particular it is shown how to obtain this solution numerically. The interpretation of these mathematical results in terms of their hydrological significance is given for a number of worked out examples. These examples describe the distribution of salt, as a function of ζ and t, for various flow conditions at the boundaries ζ = ± ∞. Also examples are given where the molecular diffusion can be disregarded with respect to the transversal dispersion.
G. De Josselin de Jong

27. The tensor character of the dispersion coefficient in anisotropic porous media

In their attempt to describe dispersion phenomena in mathematical form several authors arrived at the conclusion, that a porous medium possesses a coefficient of dispersion, which has the character of a tensor. This tensor is formulated in such a manner, that it represents the geometrical aspects of the porous medium responsible for the scatter of tracer particles, when carried by a fluid flowing through it. It is therefore a poperty of the porous medium alone, and can be considered to materialize the tortuosity of the particle trails caused by the random arrangement and the interconnectivity of the channels constituining the pore space.
G. De Josselin de Jong

28. Dispersion in fissured rock

It is the pupose of this study to show that the dispersion of particles, transported by a fluid flowing through a system of fissures in rock, can be treated as a special case of the general theory for dispersion, developed by use of the probability theory (DE JOSSELIN DE JONG, 1969).
A case study of the dispersion of a large amount of locally injected particles will first be presented computation wise. It will be computed how the particles are partitioned at each intersection of the fissures, how the subgroups of particles are transported through the fissures and where the subgroups will be located at successive time intervals. The result consists of a distribution of particles at a certain time, T, after injection, with discrete amounts of particles at discrete points.
G. De Josselin de Jong, Shah-Chih Way

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