Manuel Pastor - Computational Geomechanics

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.

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 1.3can 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” d x , d y , 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 p 1, p 2, 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 2become 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.

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.