Wm. Cain

“ It seems that in order to accord our views to the theory of greater pressure at the bottom, we must assume that any given area of the face of a wall is borne on by a prism of material reaching to the top of the bank, and that its pressure is measured by the weight of its cross-section by some multiple of its length. ”

“ For a surcharge of sufficient inclination, and especially when it slopes at the angle of repose, the Rankine thrust involves more friction at the back of the wall than the method illustrated in Fig. 15, where only one-third of the friction is used for ordinary cases; but, even granting, for the sake of argument, that at some time this friction is null and that subsequently rains and vibration cause an increased thrust, then the top of the wall moves over slightly, the earth will again get its frictional grip on the wall, so that this friction is always exerted when required for stability. ”

“ 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 [452] induced by lateral pressure. ”

“ If this tunnel has been driven by the use of a shield or poling boards, the ground will tend to settle over it, and part of the weight of will be sustained by cohesion and friction (resulting from the lateral thrust) exerted along the sides, vertically upward. The earth will probably arch itself, or form a series of domes superposed one upon the other, but the external forces acting on such domes will be the same as those acting on a corresponding horizontal lamina, and the theory, given in full in the Appendix, begins with the considerations pertaining to the equilibrium of such a lamina. ”

“ The writer does not advocate the middle-third limit method in design, as it gives variable factors of safety for different types of walls. Besides, if the actual resultant on the base passes one-third of its width from the outer toe, there is no pressure at the inner toe, and the unit pressure at the outer toe is double the average. If vibration or other cause increases the thrust, the joint at the inner toe opens, and the pressure is concentrated too much near the outer toe. In the reinforced concrete wall, the earth thrust on a vertical plane through the inner toe is required. ”

“ However, with sand, or earth with much fine material, the pores are more or less clogged up and there is perhaps intimate contact of a part of the earth with the roof of the tunnel, so that the water cannot get under it to produce a lifting effect, and if such intimate contact is found along any horizontal or vertical section, of the earth on either side of the section, it is plain that the buoyant effort of the water on a cubic foot of material will be much diminished. ”

“ An embankment from 100 to 150 ft. high, supported by a low wall, may approximate the conditions assumed, but, before it is finished, the earth has consolidated to such an extent that the actual thrust is doubtless much less than the computed one. The truth is that, in nearly all back-filling of ordinary earth, the cohesive and chemical affinities commence their work very soon after the filling is deposited, and consolidation is gradually effected; so that, as has been stated, the actual thrust is often much less than is estimated in the design of the wall, where cohesive forces are neglected. ”

“ 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. ”

“ 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. ”

“ It is very evident, though, that for most cases in practice, the formulas give a very appreciable excess over the true thrust, and that the true plane of rupture never coincides with the natural slope. ”

“ Meem’s paper, “The Bracing of Trenches and Tunnels, With Practical Formulas for Earth Pressures.”
As to the exact distribution of the stresses, theory cannot speak definitely, for the conditions are different from those in the case of the retaining wall, the passive resistance of which opposes the active earth thrust. For the braced trench, the earth, at first, simply resists the active pressure exerted by the braces, when first put in and keyed-up tight, particularly on that upper portion where the active earth thrust is nothing or very small. ”

“ The theory that cohesion in the earth and frictional resistance on the back of the retaining wall account for the experimental results seems indisputable, but such experiments must needs be carried through in a reasonable time, and, in that respect, at least, must needs differ from actual constructions which are intended to be permanent. ”

“ From the present state of our knowledge with respect to the theory and physical constants pertaining to consolidated earth, it would seem that experience must largely be the guide in dealing with it. The facts are supreme—the rational theory may come later. ”

“ 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. ”

“ The full reaction of the plane can be found by combining the forces, given in magnitude and direction by and , but it is not needed.
It is to be noted that is the least thrust for which equilibrium is possible. The other trial thrusts should now be lengthened to equal , since this is the true thrust or reaction of the wall, . All the new points, , , , , , will now lie to the right of the old points; hence the new , , , , , will all make less angles than with the normals to the planes, , etc.; hence stability everywhere in the earth mass is assured. ”

“ 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. ”

“ If each arch has the vertical thickness, , it will have the same volume and weight, , as the horizontal lamina. The reactions marked on Fig. 20 can be assumed to be those of the corresponding arch, and the resultant of the horizontal and vertical reactions represents the thrust of the arch at the sides; its direction will be that of the tangent line of the arch. When is small, the horizontal reaction is much greater than the vertical one, and the arches are all very flat. ”

“ It must be noted especially, however, that if the original earth thrust, when combined as usual with the weight of wall, gives a resultant which passes outside of the middle third of the base of the wall as computed above, then the thickness must be increased, so that the resultant will at least pass through the outer middle-third limit. ”

“ For, if the earth below was removed, the thrust on would have to be sufficient to prevent the whole mass, , from descending, which is far greater than , which balances only the thrust of the wedge of rupture, the inclined base of which passes through . ”

“ The observation of any tunneling operations in soft normally dry ground, or the examination of existing structures, will convince any one that, after a depth of approximately twice the greatest diameter of opening has been reached, it is impossible to tell, by any difference in the pressure, the depth of the tunnel. ”

“ While such experiments on a small scale give definite results with very dry sand or wheat, they will not be conclusive unless made on a very large scale in cases where dampness adds materially to the normal cohesion of small masses. ”

“ It has been the main object of this paper to show that, although cohesive forces must be included in interpreting properly the results on small models and many retaining walls, yet, for walls more than 6 or 10 ft. in height, backed with dry fresh material, not consolidated, the cohesive forces can be practically neglected in design. Hence, experimenters are strongly advised to leave small models severely alone and confine their experiments to walls from 6 to 10 ft. ”

“ As the writer proceeds in this investigation, he hopes to make clear the conception of arch action alluded to, and will derive the limiting values of and in the simple manner outlined briefly in the Appendix. Before considering these matters, however, it may be well to call attention to the fact that a vertical prism of earth can be held up by the cohesion of its sides alone when is large enough. Take the vertical prism of depth and cross-section area , Fig. 20, its weight being . In a long tunnel, two sides only can be counted on to furnish cohesive forces. ”

“ Thus, for the wall 12 ft. high, the plane of rupture and the value of , for , correspond to the old values for , for , to the old values for . For fresh earth filling, slightly packed, it is possible that the values, , , may be reached, with a material reduction in from the values given by Equations (1) and (2) . As the height of the wall increases, say to 25 or 50 ft., the influence of cohesion, in diminishing the thrust, becomes very small, and it is better to ignore it altogether. ”

“ Where the sheeting and bracing are of sufficient size, are tightly keyed up, and extend to the bottom of the trench, or where the bank is supported by a retaining wall, the earth near the bottom cannot break out, and the equation is not valid.
However, if, from any cause, such as insufficient sheeting, the break has taken place over even a part of , the mass, , above will tend to tip over at the top, giving the greatest pressure on the top braces. ”

“ This is generally an extreme lower value; for any earth endowed with much cohesion must be capable of exerting tension. If the tension exerted is sufficient to drag down (which can stand unsupported) , that is, if the wedge, , acts as a whole, then the free unsupported height will be double that given by Equation (8) . This is evidently an extreme upper limit, perhaps rarely attained; for vertical cracks have often been observed to precede a fall of earth into a vertical trench. For , , and ft., Equation (8) gives , whereas the usual equation gives lb. per sq. ft. ”

“ This well illustrates what constructors tell us of the importance of getting in well-keyed-up bracing in time to prevent any crack from developing, which, as we have seen, largely increases the thrust. Even when cracks do not appear, a heavy rain, shortly after a trench is opened, is a frequent cause of falls ”

“ The experimental wall of Col. Michon was 40 ft. high, with very deep counterforts, only 5 ft. from center to center. The very heavy and wet filling between the counterforts, being treated as a part of the wall, a construction (made on the printed drawing) shows that the resultant of earth thrust and weight of wall passes through the outer toe. Doubtless the cohesion factor in this wall was large. In the paper mentioned, the details as to Gen. Burgoyne’s experimental walls are given. There were four of these walls, each 20 ft. long, 20 ft. high, and with a mean thickness of 3 ft. ”

“ 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 relative decrease in the lines representing cohesive forces will be still more marked for a wall ft. high, the weights of prisms being 400 times as great, but the cohesive forces only 20 times as great as before. It is evident from this reasoning that, for , the cohesive forces are practically negligible for walls, say, 10 ft. high, especially if the earth surface is level. In fact, a little examination of the original drawings showed, for walls about 6 ft. high, that the earth thrust, neglecting cohesion, was only from 1 to 5% in excess over that for . ”