Chapter 6

In conclusion, the writer heartily concurs with the statement that "too much has been taken for granted in connection with earth pressures and resistance," and he is sorry to be forced to add that he believes the author to be open to the criticism which he himself suggests, that "both in experimenting and observing, the engineer [and in this case the author] will frequently find what is being looked for or expected and will fail to see the obvious alternative."

FRANCIS L. PRUYN, M. AM. SOC. C. E. (by letter).--Mr. Meem should be congratulated, both in regard to the highly interesting theories which he advances on the subject of sand pressures--the pressures of subaqueous material--and on his interesting experiments in connection therewith.

The experiment in which the plunger on the hydraulic ram is immersed in sand and covered with water does not seem to be conclusive. By this experiment the author attempts to demonstrate that the pressure of the water transmitted through the sand is only about 40% as great as when the sand is not there. The travel of ground-water through the earth is at times very slow, and occasionally only at the rate of from 2 to 3 ft. per hour. In the writer's opinion, Mr. Meem's experiment did not cover sufficient time during which the pressure was maintained at any given point. It is quite probable that it may take 15 or 20 min. for the full pressure to be transmitted through the sand to the bottom of the plunger, and it is hoped, therefore, that he will make further experiments lasting long enough to demonstrate this point.

In regard to the question of skin friction on caissons and piles, it may be of interest to mention an experiment which the writer made during the sinking of the large caissons for the Williamsburg Bridge. These caissons were about 70 ft. long and 50 ft. wide. The river bottom was about 50 ft. below mean high water, and the caissons penetrated sand of good quality to a depth of from 90 to 100 ft. below that level. On two occasions calculations were made to determine the skin friction while the caissons were being settled. With the cutting edge from 20 to 30 ft. below the river bottom, the calculations showed that the skin friction was between 500 and 600 lb. per sq. ft. The writer agrees with Mr. Meem that, in the sinking of caissons, the arch action of sand is, in a great measure, destroyed by the compressed air which escapes under the cutting edge and percolates up through the material close to the sides of the caissons.

With reference to the skin friction on piles, the writer agrees with Mr. Meem that in certain classes of material this is almost a negligible quantity. The writer has jacked down 9-in. pipes in various parts of New York City, and by placing a recording gauge on the hydraulic jack, the skin friction on the pile could be obtained very accurately. In several instances the gauge readings did not vary materially from the surface down to a penetration of 50 ft. In these instances the material inside the pipe was cleaned out to within 1 ft. of the bottom of the pile, so that the gauge reading indicated only the friction on the outside of the pipe plus the bearing value developed by its lower edge. For a 9-in. pipe, the skin friction on the pile plus the bearing area of the bottom of the pipe seems to be about 20 tons, irrespective of the depth. After the pipe had reached sufficient depth, it was concreted, and, after the concrete had set, the jack was again placed on it and gauge readings were taken. It was found that in ordinary sands the concreted steel pile would go down from 3 to 6 in., after which it would bring up to the full capacity of a 60-ton jack, showing, by gauge reading, a reaction of from 70 to 80 tons.

It is the writer's opinion that, in reasonably compact sands situated at a depth below the surface which will not allow of much lateral movement, a reaction of 100 tons per sq. ft. of area can be obtained without any difficulty whatever.

FRANK H. CARTER, ASSOC. M. AM. SOC. C. E. (by letter).--Mr. Meem has contributed much that is of value, particularly on water pressures in sand; just what result would be obtained if coarse crushed stone or similar material were substituted for sand in Experiment No. 6, is not obvious.

It has been the practice lately, among some engineers in Boston, as well as in New York City, to assume that water pressures on the underside of inverts is exerted on one-half the area only. The writer, however, has made it a practice first to lay a few inches of cracked stone on the bottom of wet excavations in order to keep water from concrete which is to be placed in the invert. In addition to the cracked stone under the inverts, shallow trenches dug laterally across the excavation to insure more perfect drainage, have been observed. Both these factors no doubt assist the free course of water in exerting pressure on the finished invert after the underdrains have been closed up on completion of the work. The writer, therefore, awaits with interest the repetition of Experiment No. 6, with water on the bottom of a piston buried in coarse gravel or cracked stone.

As for the arching effect of sand, the writer believes that Mr. Meem has demonstrated an important principle, on a small scale. It must be regretted, however, that the box was not made larger, for, to the writer, it appears unsafe to draw such sweeping conclusions from small experiments. As small models of sailboats fail to develop completely laws for the design and control of large racing yachts, so experiments in small sand boxes may fail to demonstrate the laws governing actual pressures on full-sized structures.

For some time the writer has been using a process of reasoning similar to that of the author for assumptions of earth pressure on the roofs of tunnel arches, except that the vertical forces assumed to hold up the weight of the earth have been ascribed to cohesion and friction, along what might be termed the sides of the "trench excavation."

The writer fails to find proof in this paper of the author's statement that earth pressures on the sides of a structure buried in earth are greater at the top than at the bottom of a trench. That some banks are "top-heavy," is, no doubt, a fact, the writer having often heard similar expressions used by experienced trench foremen, but, in every case called to his attention, local circumstances have caused the top-heaviness, either undermining at the bottom of the trench, too much banked earth on top, or the earth excavated from the trench being too near the edge of the cut.

For some years the writer has been making extended observations on deep trenches, and, thus far, has failed to find evidence, except in aqueous material, of earth pressures which might be expected from the known natural slope of the material after exposure to the elements; and this latter feature may explain why sheeted trenches stand so much better than expected. If air had free access to the material, cohesion would be destroyed, and theoretical pressures would be more easily developed. With closely-sheeted trenches, weathering is practically excluded, and the bracing, which seemingly is far too light, holds up the trench with scarcely a mark of pressure. As an instance, in 1893, the writer was successfully digging sewer trenches from 10 to 14 ft. deep, through gravel, in the central part of Connecticut, without bracing; because of demands of the work in another part of the city, a length of several hundred feet of trench was left open for three days, resulting in the caving-in of the sides. The elements had destroyed the cohesion, and the sides of the trenches no longer stood vertically.

Recently, in the vicinity of Boston, trenches, 32 ft. wide, and from 25 to 35 ft. deep, with heavy buildings on one side, have been braced with 8 by 10-in. stringers, and bracers at 10-ft. centers longitudinally, and from 3 to 5 ft. apart vertically; this timbering apparently was too slight for pressures which, theoretically, might be expected from the natural slope of the material. Just what pressures develop on the sides of the structures in these deep trenches after pulling the top sheeting (the bottom sheeting being left in place) is, of course, a matter of conjecture. There can be no doubt that there is an arching of the material, as suggested by the author. How much this may be assisted by the practical non-disturbance of the virgin material is, of course, indeterminate. That substructures and retaining walls designed according to the Rankine or similar theories have an additional factor of safety from too generous an assumption in regard to earth pressure is practically admitted everywhere. It is almost an engineering axiom that retaining walls generally fail because of insufficient foundation only.

For the foregoing reasons, and particularly from observations on the effect of earth pressures on wooden timbers used as bracing, the writer believes that, ordinarily, the theoretical earth pressures computed by Rankine and Coulomb are not realized by one-half, and sometimes not even by one-third or one-quarter in trenches well under-drained, rapidly excavated, and thoroughly braced.

J.C. MEEM, M. AM. SOC. C. E. (by letter).--The writer has been much interested in this discussion, and believes that it will be of general value to the profession. It is unfortunate, however, that several of the points raised have been due to a careless reading of, or failure to understand, the paper.

Taking up the discussion in detail, the writer will first answer the criticisms of Mr. Goodrich. He says:

"The writer believes that, in the design of permanent structures, consideration of arch action should not be included, at least, not until more information has been obtained. He also believes that the design of temporary structures with this inclusion is actually dangerous in some instances."

If the arching action of earth exists, why should it not be recognized and considered? The design of timbering for a structure to rest, for instance, at a depth of from 200 to 300 ft. in normal dry earth, without considering this action, would be virtually prohibitive.

Mr. Goodrich proceeds to show one of the dangers of considering such action by quoting the writer, as follows:

"About an hour after the superimposed load had been removed, the writer jostled the box with his foot sufficiently to dislodge some of the exposed sand, when the arch at once collapsed and the bottom fell to the ground."

He fails, as do so many other critics of this theory, to distinguish the difference between that portion of the sand which acts as so-called "centering" and that which goes to make up the sustaining arch. The dislodgment of any large portion of this "centering" naturally causes collapse, unless it is caught, in which case the void in the "centering" is filled from the material in the sustaining arch, and this, in turn, is filled from that above, and so on, until the stability of each arch is in turn finally established. This, however, does not mean that, during the process of establishing this equilibrium of the arch stresses, there is no arching action of any of the material above, but only that some of the so-called arches are temporarily sustained by those below. That is, in effect, each area of the material above becomes, in turn, a dependent, an independent, and finally an interdependent arch.

If Mr. Goodrich's experience has led him to examine any large number of tunnel arches or brick sewers, he will have noted in many of them longitudinal cracks at the soffits of the arches and perhaps elsewhere. These result from three causes:

_First._--In tunneling, there is more or less loss of material, while, in back-filling, the material does not at first reach its final compactness. Therefore, in adjusting itself to normal conditions, this material causes impact loads to come upon the green arch, and these tend to crack it.

_Second._--No matter how tightly a brick or other arch is keyed in, there must always be some slight subsidence when the "centers" are struck. This, again, results in a shock, or impact loading, to the detriment of the arch.

_Third._--The most prolific cause, however, is that in tunneling, as well as in back-filling open cuts, the material backing up the haunches is more or less loosened and therefore is not at first compact enough to prevent the spreading of the haunches when the load comes on the arch. This causes cracking, but, as soon as the haunches have been pressed out against the solid material, the cracking usually ceases, unless the pressure has been sufficiently heavy to cause collapse.

An interesting example of this was noted in the Joralemon Street branch of the Rapid Transit Tunnel, in Brooklyn, in which a great many of the cast-iron rings were cracked under the crown of the arch, during construction; but, in spite of this, they sustained, for more than two years, a loading which, according to Mr. Goodrich, was continually increasing. In other words, the cracked arch sustained a greater loading than that which cracked the plates during construction, according to his theory, as noted in the following quotation:

"But it should be equally conceded by the advocates of the existence of such action that changes in humidity, due to moving water, vibration, and appreciable viscosity, etc., will invariably destroy this action in time."

As to the correctness of this theory Mr. Goodrich would probably have great difficulty in convincing naturalists, who are aware that many animals live in enlarged burrows the stability of which is dependent on the arching action of the earth; in fact, many of these burrows have entrances under water. He would also have some difficulty in convincing those experienced miners who, after a cave-in, always wait until the ground has settled and compacted itself before tunneling, usually with apparent safety, over the scene of the cave-in.

The writer quotes as follows from Mr. Goodrich's discussion:

"In any case, no arch action can be brought into play until a certain amount of settlement has taken place so as to bring the particles into closer contact, and in such a way that the internal stresses are practically those only of compression, and the shearing stresses are within the limits possible for the material in question."

Further:

"Consequently, an almost infinitesimal settlement of the 'centering' may cause the complete destruction of an arch of earth."

And further:

"On the other hand, it is believed that the author's statement, as to the 'tendency of marbles to arch,' * * * should be qualified by the addition of the words, 'only when a certain amount of deflection has taken place so as to bring the arch into action.'"

In a large measure the writer agrees with the first and last quotations, but sees no reason to endorse the second, as it is impossible to consider any arch being built which does not settle slightly, at least, when the "centers" are struck.

Regarding his criticism of the lack of arching action in balls or marbles, he seems to reason that the movement of the marbles would destroy the arch action. It is very difficult for the writer to conceive how it would be possible for balls or marbles to move when confined as they would be confined if the earth were composed of them instead of its present ingredients, and under the same conditions otherwise. Mr. Goodrich can demonstrate the correctness of the writer's theories, however, if he will repeat the writer's Experiment No. 3, with marbles, with buckshot, and with dry sand. He is also advised to make the experiment with sand and water, described by the writer, and is assured that, if he will see that the washers are absolutely tight before putting the water into the box, he can do this without bringing about the collapse of the arch; the only essential condition is that the bottom shall be keyed up tightly, so as not to allow the escape of any sand. He is also referred to the two photographs, Plate XXIV, illustrating the writer's first experiment, showing how increases in the loading resulted in compacting the material of the arch and in the consequent lowering of the false bottom. As long as the exposed sand above this false bottom had cohesion enough to prevent the collapse of the "centering," this arch could have been loaded with safety up to the limits of the compressive strength of the sand.

To quote again from Mr. Goodrich:

"Furthermore, the author's reason for bisecting the angle between the vertical and the angle of repose of the material, when he undertakes to determine the thickness of key, is not obvious. This assumption is shown to be absurd when carried to either limit, for when the angle of repose equals zero, as is the case with water, this method would give a definite thickness of key, while there can be absolutely no arch action possible in such a case; and, when the angle of repose is 90°, as may be assumed in the case of rock, this method would give an infinite thickness of key, which is again seen to be absurd."

Mr. Goodrich assumes that water or liquid has an angle of repose equal to zero, which is true, but the writer's assumptions applied only to solid material, and the liquid gives an essentially different condition of pressure, as shown by a careful reading of the paper. In solid rock Mr. Goodrich assumes an angle of repose equal to 90°, for which there is no authority; that is, solid rock has no known angle of repose. In order to carry these assumptions to a definite conclusion, we must assume for that material with an angle of repose of 90° some solid material which has weight but no thrust, such as blocks of ice piled vertically. In this case Mr. Goodrich can readily see that there will be no arching action over the structure, and that the required thickness of key would be infinite. As to the other case, it is somewhat difficult to conceive of a solid with an angle of repose of zero; aqueous material does not fulfill this condition, as it is either a liquid or a combination of water and solid material. The best illustration, perhaps, would be to assume a material composed of iron filings, into which had been driven a powerful magnet, so that the iron filings would be drawn horizontally in one direction. It is easy to conceive, then, that in tunneling through this material there would be no necessity for holding up the roof; the definite thickness of key given, as being at the point of intersection of two 45° angles, would be merely a precautionary measure, and would not be required in practice.

It is thus seen that both these conditions can be fulfilled with practical illustrations; that is, for an angle of repose of 90°, that material which has weight and no thrust, and for an angle of repose of zero, that solid material which has thrust but no weight.

Mr. Goodrich says the author has given no experiments to prove his statement that the arch thrust is greater in dryer sand. If Mr. Goodrich will make the experiment partially described as Experiment No. 3, with absolutely dry sand, and with moist sand, and on a scale large enough to eliminate cohesion, he will probably find enough to convince him that in this assumption the writer is correct. At the same time, the writer has based his theory in this regard on facts which are not entirely conclusive, and his mind is open as to what future experiments on a large scale may develop. It is very probable, however, that an analytical and practical examination of the English experiments noted on pages 379 and 380, will be sufficient to develop this fact conclusively.

The writer is forced to conclude that some of the criticisms by Mr. Goodrich result from a not too careful reading of the paper. For instance, he states:

"'It is conceded' (line 2, p. 357, for example) when the writer, for one, has not even conceded the accuracy of the assumptions."

A more careful reading would have shown Mr. Goodrich that this concession was one of the writer's as to certain pressures against or on tunnels, and, if Mr. Goodrich does not concede this, he is even more radical than the writer.

And again:

"'Nor can anyone * * * doubt that the top timbers are stressed more heavily than those at the bottom' is emphatically doubted and earnestly denied by the writer."

It is unfortunate that Mr. Goodrich failed to make the complete quotation, which reads:

"Nor can anyone, looking at Fig. 5, doubt," etc.

A glance at Fig. 5 will demonstrate that, under conditions there set forth, the writer is probably correct in his assertion as relating to that particular instance. Further:

"For instance, the author's well-known theory that the pressures against retaining walls are a maximum at the top and decrease to zero at the bottom, is in absolute contradiction to the results of experiments conducted on a large scale by the writer on the new reinforced concrete retaining wall near the St. George Ferry, on Staten Island."

The writer's "well-known theory that pressures against retaining walls are a maximum at the top and decrease to zero at the bottom" applies only to pressures exerted by absolutely dry and normally dry material, and it seems to him that this so-called theory is capable of such easy demonstration, by the simple observation of any bracing in a deep trench in material of this class, that it ought to be accepted as at least safer than the old theory which it reverses. As to this "well-known theory" in material subject to water pressure, a careful reading of the paper, or an examination of Fig. 12 and its accompanying text, or an examination of Table 1, will convince Mr. Goodrich that, under the writer's analysis, this pressure does not decrease to zero at the bottom, but that in soft materials it may be approximately constant all the way down, while, in exceptionally soft material, conditions may arise where it may increase toward the bottom. The determination should be made by taking the solid material and drying it sufficiently so that water does not flow or seep from it. When this material is then compacted to the condition in which it would be in its natural state, its angle of repose may be measured, and may be found to be as high as 60 degrees. The very fine matter should then be separated from the coarser material, and the latter weighed, to determine its proportion. Subtracting this from the total, the remainder could be credited to "aqueous matter." It is thus seen that with a material when partially dried in which the natural angle of repose might be 60°, and in which the percentage of water or aqueous matter when submerged might be 60%, there would be an increase of pressure toward the bottom.