1
Introduction 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....