Another instance of the effect of time is found in many retaining walls, in which a very slow motion has occurred, though the walls appeared to be entirely stable when first built.
A frictional or tangential force along the back of the wall may tend to prevent motion, but it is difficult to conceive of this tangential force being perpetually present on the back of a stationary wall after the back-filling has become settled and consolidated. In the interior of the mass of earth at rest the author admits that the reaction between particles is not along inclined lines, but rather that the lines of pressure are vertical and horizontal. The vertical lines of force are, of course, caused by gravity, and the horizontal lines by the tendency of particles to wedge in between those below and to spread them.
If this conception of the forces within a mass of earth is reasonable, it would seem as if it might also be extended to the pressure against an immovable vertical wall. One must then consider whether it is possible for a horizontal pressure to cause the wall to move, without changing the conditions and introducing the inclined stresses. It would seem within the bounds of possibility that a very minute motion might be produced, and that this would be followed by a readjustment of stresses in the earth by which the forces would gradually resume the horizontal direction.
The nature of the soil undoubtedly has much to do with this question. In some kinds of clay there appears to be a sort of viscosity, such as is frequently seen in pitch and other materials, or a tendency toward a slow flowing. No amount of pressure would cause a sudden motion, but time will effect a motion under a slight pressure or even the force of gravity alone. It appears that this condition is produced by the very minute particles, each moving individually into a position in which the surrounding forces balance. If one cuts a vertical face in such material one cannot force the exposed particles out of their position by crowding them from behind, but each in its turn will feel the pressure unbalanced and will slowly move out. This may not be true to the same extent with granular materials of large diameter, but a familiar instance is seen in fine wet sand. If a small excavation is dug in a wet beach sand, the banks will stand vertically at first, but, by watching closely, one may see the particles, beginning at the foot of the bank where there is most water, gradually moving out, overcoming the force of cohesion, and ever tending to seek a condition with a level surface. It seems quite likely that a similar tendency would exist in almost all soils, to greater or less degree, though perhaps it might be safely neglected in a mass of hard, irregularly-shaped fragments of stone which could interlock.
The point which the writer wishes to make is that a word of caution should accompany this argument for the frictional and cohesive forces; that they cannot always be relied on; and that sometimes the Rankine theory may be better than the wedge theory in designing, even though it does not seem to fit the experimental results.
Another warning may not be amiss, in considering the safe thickness to allow for retaining walls, and that is the effect of frost, where the surface of the ground is level and likely to retain moisture. The swelling force of freezing, under these circumstances, may be more than sufficient to overcome the beneficial effects of both cohesion and friction. Presumably this must be provided for in the “factor of safety,” and is in itself a justification for a very appreciable factor.
It may be well to emphasize the fact that a large part of the author’s assumed factor of safety seems to be absorbed in keeping the resultant within the middle third of the base. The proportions between width of wall and height, determined on [pages 433] and 434, are such as to keep this resultant just within the base. If, with these same proportions of wall, the factor were assumed so that the resultant were within the middle third, it would be found to be nearer 1¼ than 3. The author’s statement on [page 435], that he “does not advocate the middle-third limit method in design,” is not wholly clear, but the implication is that the resultant should be well within this limit. In this case, it seems as if the factor of safety would be wholly absorbed in thus locating the resultant, and would leave nothing for other elements of uncertainty.
J. C. MEEM, M. Am. Soc. C. E. (by letter).—In the writer’s judgment the author has gone a step forward in developing the relation of cohesion and friction to walls and tunnels, but he has not given sufficient value to the larger consideration of what may be called “cohesive friction” induced by the lateral pressure of earth against retaining walls and other faces. This will be noted later in the discussion.
The author states that “from all that precedes, it is seen that the results of experiments on small models in the past have proved to be very misleading, and that experiments on large models are desirable, and can alone give confidence.”[Footnote 21] ] To a certain extent this is fully in accordance with the writer’s views, as noted in his papers on earth pressures,[Footnote 22] ] and he feels justified in once more calling attention to the fact that, in his judgment, the only experiments which can definitely establish the value of earth pressures against walls and sheeted faces should be made on a large scale and against independently laid and independently braced horizontal sheeting. If these experiments are made in a homogeneous material, such as dry sand of a known angle of repose, it is believed that it will be conclusively and definitely shown that the pressures at a point above the middle plane will be greater than below it, and, further, that it will be proved that the pressure near the bottom, for example, of a 20-ft. trench, will not be perceptibly greater than that against a brace at the same distance from the bottom of a 40- or a 60-ft. trench.
The writer agrees with the author that the theory of a sliding wedge is the best practical one for retaining walls, and if the face of the wedge be keyed tight, as stated by the author, or through the compacting of the material into a more solid mass, it will be seen that, with no break, the resultant pressures against the wall or face are virtually those, not only of a sliding, but of a solid wedge tending to slide on the plane of repose, the mass being compactly held together by cohesion induced by lateral pressure. Although the general solidity of this mass is dependent on the stability of the wall or bracing, the pressures caused by the tendency of this solid wedge to slide are not affected materially by slight changes in form due to gradual settlement, which, in turn, may be caused by the normal yielding of the wall or shrinkage of the bracing, or by any small losses of material, as long as any of those or their sum is not sufficient to cause partial or final collapse. Assuming then that this theory of the solid wedge tending to slide is the true one, it is difficult to reconcile it with the results of experiments on revolving boards or revolving walls, except in so far as they relate to the more accurate determination of the coefficients of friction and cohesion.