The author has stated, however, that when the tunnel roof and sides are in place, no further trouble need be feared. On the contrary, in 1885, the Canadian Pacific Railroad built a tunnel through clayey material and lined it with ordinary 12 by 12-in. timber framing, about 2 or 3 ft. apart. After the tunnel was completed, it collapsed. It was re-excavated and lined with 12 by 12-in. timbers side by side, and it collapsed again; then the tunnel was abandoned, and, for some 20 years, the track, carried around on a 23 deg. curve, was used until a new tunnel was built farther in. This trouble could have been caused either by the sliding or swelling of the material, and the speaker is inclined to believe that it was caused by swelling, for it is known, of course, that most material has been deposited by Nature under great pressure, and, by excavating in certain materials, the air and moisture would cause those materials to swell and become an irresistible force.

To carry the load, Mr. Meem prefers to rely on the points of the piles rather than the side friction. In such cases the pile would act as a post, and would probably fail when ordinarily loaded, unless firmly supported at the sides. The speaker has seen piles driven from 80 to 90 ft. in 10 min., which offered almost no resistance, and yet, a few days later, they would sustain 40 tons each. No one would dream of putting 40 tons on a 90-ft. pile resting on rock, if it were not adequately supported.

It is the speaker's opinion that bracing should not be omitted for either piles or coffer-dams.

CHARLES E. GREGORY, ASSOC. M. AM. SOC. C. E.—In describing his last experiment with the hydraulic chambers and plunger, Mr. Meem states that, after letting the pressure stand at 25 lb., etc., the piston came up. This suggests that the piston might have been raised at a much lower pressure, if it had been allowed to stand long enough.

The depth and coarseness of the sand were not varied to ascertain whether any relation exists between them and the pressure required to lift the piston. If the pressure varied with the depth of sand, it would indicate that the reduction was due to the resistance of the water when finely divided by the sand; if it varied with the coarseness of the sand, as it undoubtedly would, especially if the sand grains were increased to spheres 1 in. in diameter, it would show that it was independent of the voids in the sand, but dependent on dividing the water into thin films.

The speaker believes that the greater part of the reduction of pressure on the bottom of the piston might be better explained by the viscosity of the water, than to assume that a considerable part of the plunger is not in contact with it. The water, being divided by fine sand into very thin films, has a tensile strength which is capable of resisting the pressure for at least a limited time.

If the water is capable of exerting its full hydrostatic pressure through the sand, the total pressure would be the full hydrostatic pressure on the bottom of the piston where in contact, and, where separated from it by a grain of sand, the pressure would be decreased only by the weight of the grain. If a large proportion of the top area of a grain is in contact, as assumed by the author, this reduction of pressure would be very small. A correct interpretation can be obtained only after more complete experiments have been made.

For horizontal pressures exerted by saturated sands on vertical walls, it has not been demonstrated that anything should be deducted from full water pressure. No matter how much of the area is in direct contact with the sand rather than the water, the full water pressure would be transmitted through each sand grain from its other side and, if necessary, from and through many other grains which may be in turn in contact with it. The pressure on such a wall will be water pressure over its entire surface, and, in addition, the thrust of the sand after correcting for its loss of weight in the water.

The fact that small cavities may be excavated from the sides of trenches or tunnels back of the sheeting proves only that there is a local temporary arching of the material, or that the cohesion of the particles is sufficient to withstand the stress temporarily, or that there is a combination of cohesion and arching. The possibility of making such excavations does not prove that pressure does not exist at such points. That sand or earth will arch under certain conditions has long been an accepted fact. The sand arches experimented with developed their strength only after considerable yielding and, therefore, give no index of the distribution or intensity of stress before such yielding. Furthermore, sand and earth in Nature are not constrained by forms and reinforcing rods.

Mr. Meem's paper is very valuable in that it presents some unusual phenomena, but many of the conclusions drawn therefrom cannot be accepted without further demonstration.

FRANCIS W. PERRY, ASSOC. M. AM. SOC. C. E.—Pressure-gauge observations on a number of pneumatic caissons recently sunk, through various grades of sand, to rock at depths of from 85 to 105 ft. below ground-water, invariably showed working-chamber air-pressures equal, as closely as could be observed, to the hydrostatic pressures computed, for corresponding depths of cutting-edge, as given in Table 2.

These observations and computations were made by the speaker in connection with the caisson foundations for the Municipal Building, New York City.

TABLE 2.—EQUIVALENT FEET OF DEPTH BELOW WATER PER POUND PRESSURE.

Pressure, Equivalent Equivalent Observed in feet of elevation pressure. pounds. depth. for water at 6.85. M.H.W. Ground-water. 1 2.31 9.06 Practically 2 4.63 11.48 the same as 3 6.94 13.79 computed 4 9.25 16.10 for 5 11.57 18.42 ground-water. 6 13.88 20.73 7 16.19 23.04 8 18.50 25.35 9 20.82 27.67 10 23.13 29.98 11 25.44 32.29 12 27.76 34.61 13 30.07 36.92 14 32.38 39.23 15 34.70 41.55 16 37.01 43.86 17 39.32 46.17 18 41.63 48.48 19 43.95 50.80 20 46.26 53.11 21 48.57 55.42 22 50.89 57.74 23 53.20 60.05 24 55.51 62.36 25 57.82 64.67 26 60.14 66.99 27 62.45 69.30 28 64.76 71.61 29 67.08 73.93 30 69.39 76.24 31 71.70 78.55 32 74.01 80.86 33 76.33 83.18 34 78.64 85.49 35 80.95 87.80 36 83.27 90.12 37 85.58 92.43 38 87.89 94.74 39 90.20 97.05 40 92.52 99.37 41 94.83 101.68 42 97.14 103.99 43 99.46 106.31 44 101.77 108.62 45 104.08 110.93 46 106.39 113.24

34 NOTE.—Equivalent depth in feet = ——— x pressure. 14.7

E.P. GOODRICH, M. AM. SOC. C. E. (by letter).—This paper is to be characterized by superlatives. Parts of it are believed to be exceptionally good, while other parts are considered equally dangerous. The author's experimental work is extremely interesting, and the writer believes the results obtained to be of great value; but the analytical work, both mathematical and logical, is emphatically questioned.

The writer believes that, in the design of permanent structures, consideration of arch action should not be included, at least, not until much more information has been obtained. He also believes that the design of temporary structures with this inclusion is actually dangerous in some instances, and takes the liberty of citing the following statement by the author, with regard to his first experiment:

"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."

The writer emphatically questions the author's ideas as to "the thickness of key" which "should be allowed" over tunnels, believing that conditions within an earth mass, except in very rare instances, are such that true arch action will seldom take place to any definite extent, through any considerable depths. 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 deg., 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. It would seem as if altogether too many unknowable conditions had been assumed. 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.

The author has repeatedly made assumptions which are not borne out by the application of his mathematical formulas to actual extreme conditions. This method of application to limiting conditions is concededly sometimes faulty; but the writer believes that no earth pressure theory, or one concerning arch action, can be considered as satisfactory which does not apply equally well to hydraulic pressure problems when the proper assumptions are made as to the factors for friction, cohesion, etc. For example, when the angle of repose is considered as zero, in the author's first formula for W{1}, the value becomes 1/2 W{1}, whereas it should depend solely on the depth, which does not enter the formula, and not at all on the width of opening, l, which is thus included.

The author has given no experiments to prove his statement that "the arch thrust is greater in dryer sand," and the accuracy of the statement is questioned. Again, no reason is apparent for assuming the direction of the "rakers" in Fig. 3 as that of the angle of repose. The writer cannot see why that particular angle is repeatedly used, when almost any other would give results of a similar kind. The author has made no experiments which show any connection between the angle of repose, as he interprets it, and the lines of arch action which he assumes to exist.

With regard to the illustration of the condition which is thought to exist when the "material is composed of large bowling balls," supposedly all of the same size, the writer believes the conclusion to be erroneous, and that this can be readily seen by inspection of a diagram in which such balls are represented as forming a pile similar to the well-known "pile of shells" of the algebras, in the diagram of which a pile of three shells, resting on the base, has been omitted. It is then seen that unless the pressures at an angle of 60 deg. with the horizontal are sufficient to produce frictional resistance of a very large amount, the balls will roll and instantly break the arch action suggested by the author. Consequently, an almost infinitesimal settlement of the "centering" may cause the complete destruction of an arch of earth.

The author's logic is believed to be entirely faulty in many cases because he repeatedly makes assumptions which are not in accordance with demonstrated fact, and finally sums up the results by the statement: "It is conceded" (line 2, p. 357, for example), when the writer, for one, has not even conceded the accuracy of the assumptions. For instance, the author's well-known theory that 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, New York City, which will soon be published, and in which the usual law of increase of lateral pressure with depth is believed to be demonstrated beyond question. It must be conceded that a considerable arch action (so-called) actually exists in many cases; 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. In consequence, the author's reasoning in regard to the pressures against the faces of retaining walls is believed to be open to grave question as to accuracy of assumption, method, and conclusion.

The author is correct in so far as he assumes that "the character of the stresses due to the thrust of the material will" not "change if bracing should be substituted for the material in the area" designated by him, etc., provided he makes the further assumption that absolutely no motion, however infinitesimal, has taken place meantime; but, unless such motion has actually taken place, no arch action can have developed. An arch thrust can result only with true arch action, that is, with stable abutments, and the mass stressed wholly in compression, with corresponding shortening of the arch line. The arch thrust must be proportional to the elastic deformation (shortening) of the arch line. If any such arch as is shown in Fig. 5 is assumed to carry the whole of the weight of material above it, that assumed arch must relieve all the assumed arches below. Therefore each of the assumed arches can carry nothing more than its own mass. Otherwise the resulting thrust would increase with the depth, which is opposed to the author's theory.

Turning again to the condition that each arch can carry only its own weight: if these arches are assumed of thicknesses proportional to the distance upward from the bottom of the wall, they will be similar figures, and it is easily demonstrated that the thrust will then be uniform in amount throughout the whole height of the wall, except, perhaps, at the very top. This condition is contrary to the author's ideas and also to the facts as demonstrated by the writer's experiment on the 40-ft. retaining wall at St. George. Consequently, the author's statement: "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. Furthermore, "the assumption" made by the author as to "the tendency of the material to slide" so as to cause it "to wedge * * * between the face of the sheeting * * * and some plane between the sheeting and the plane of repose," is considered as absolutely unwarranted, and consequently the whole conclusion is believed to be unjustified. Nor is the author's assumption (line 5, p. 361), that "the thrust * * * is measured by its weight divided by the tangent of the * * * angle of repose" at all obvious.

The author presents some very interesting photographs showing the natural surface slopes of various materials; but it is interesting to note that he describes these slopes as having been produced by the "continual slipping down of particles." The vast difference between angles of repose produced in this manner by the rolling friction of particles and the internal angles of friction, which must be used in all earth-pressure investigations, has been repeatedly called to the attention of engineers by the writer.[H]

The writer's experiments are entirely in accord with those of the author in which the latter claims to demonstrate that "earth and water pressures act independently of each other," and the writer is much delighted that his own experiments have been thus confirmed.

In Experiment No. 3, the query is naturally suggested: "What would have been the result if the nuts and washers had first been tightened and water then added?" Although the writer has not tried the experiment, he is rather inclined to the idea that the arch would have collapsed. With regard to Experiment No. 5, there is to be noted an interesting possibility of its application to the theoretical discussion of masonry dams, in which films of water are assumed to exist beneath the structure or in crevices or cracks of capillary dimensions. The writer has always considered the assumptions made by many designing engineers as unnecessarily conservative. In regard to the author's conclusions from Experiment No. 6, it should be noted that no friction can exist between particles of sand and surrounding water unless there is a tendency of the latter to move; and that water in motion does not exert pressures equal to those produced when in a static condition, the reduction being proportional to the velocity of flow.

The author's conclusion (p. 371), that "pressure will cause the quicksand to set up hydraulic action," does not seem to have been demonstrated by his experiments, but to be only his theory. In this instance, the results of the writer's experiments are contrary to the author's theory and conclusion.

The writer will heartily add his protest to that of the author "against considering semi-aqueous masses, such as soupy sands, soft concrete, etc., as exerting hydrostatic pressure due to their weight in bulk, instead of to the specific gravity of the basic liquid." Again, similarly hearty concurrence is given to the author's statement:

"If the solid material in any liquid is agitated, so that it is virtually in suspension, it cannot add to the pressure, and if allowed to subside it acts as a solid, independently of the water contained with it, although the water may change somewhat the properties of the material, by increasing or changing its cohesion, angle of repose, etc."

On the other hand, it is believed that the author's statement, as to "the tendency of marbles to arch," a few lines above the one last quoted, 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." Again, on the following page, a somewhat similar qualification should be added to the sentence referring to the soft clay arch, that it would "stand if the rods supporting the intrados of the arch were keyed back to washers covering a sufficiently large area," by inserting the words, "unless creeping pressures (such as those encountered by the writer in his experiments) were exceeded."

The writer considers as very doubtful the formula for D{x}, which is the same as that for W{1}, already discussed. The author's statement that "additional back-fill will [under certain circumstances] lighten the load on the structure," is considered subject to modification by some such clause as the following, "the word 'lighten' here being understood to mean the reduction to some extent of what would be the total pressure due to the combined original and added back-fill, provided no arch action occurred."

The writer is in entire agreement with the author as to the probability that water is often "cut off absolutely from its source of pressure," with the attendant results described by the author (p. 378); and again, that too little attention has been given to the bearing power of soil, with the author's accompanying criticism.

The writer cannot see, however, where the author's experiments demonstrate his statement "that pressure is transmitted laterally through ground, most probably along or nearly parallel to the angles of repose," or any of the conclusions drawn by him in the paragraph (p. 381), which contains this questionable statement. Again the writer is at a loss as to how to interpret the statement that the author has found that "better resistance" has been offered by "small open caissons sunk to a depth of a few feet and cleaned out and filled with concrete" than by "spreading the foundation over four or five times the equivalent area." The writer agrees with the author in the majority of his statements as to the "bearing value and friction on piles," but believes that he is indulging in pure theory in some of his succeeding remarks, wherein he ascribes to arch action the results which he believes would be observed if "a long shaft be withdrawn vertically from moulding sand." These phenomena would be due rather to capillary action and the resulting cohesion.

Naturally, the writer doubts the author's conclusions as to the pressure at the top of large square caisson shafts when he states that "the pressure at the top * * * will * * * increase proportionately to the depth." Again, the author is apparently not conversant with experiments made by the Dock Department of New York City, concerning piles driven in the Hudson River silt, which showed that a single heavily loaded pile carried downward with it other unloaded piles, driven considerable distances away, showing that it was not the pile which lacked in resistance, as much as the surrounding earth.

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 deg., 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 deg., 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 deg. 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 deg. 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 deg., 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 deg., 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.

The writer does not know the exact nature of the experiments made at St. George's Ferry by Mr. Goodrich, but he supposes they were measurements of pressures on pistons through holes in the sheeting. He desires to state again that he cannot regard such experiments as conclusive, and believes that they are of comparative value only, as such experiments do not measure in any large degree the pressure of the solid material but only all or a portion of the so-called aqueous matter, that is, the liquid and very fine material which flows with it. Thus it is well known that, during the construction of the recent Hudson and North River Tunnels, pressures were tested in the silt, some of which showed that the silt exerted full hydrostatic pressure. At the same time, W.I. Aims, M. Am. Soc. C. E., stated in a public lecture, and recently also to the writer, that in 1890 he made some tests of the pressure of this silt in normal air for the late W.R. Hutton, M. Am. Soc. C. E. A hole, 12 in. square, was cut through the brickwork and the iron lining, just back of the lock in the north tube (in normal air), and about 1000 ft. from the New Jersey shore. It was found that the silt had become so firm that it did not flow into the opening. Later, a 4-in. collar and piston were built into the opening, and, during a period covering at least 3 months, constant observations showed that no pressure came upon it; in fact, it was stated that the piston was frequently worked back and forth to induce pressure, but no response was obtained during all this period. The conclusion must then be drawn that when construction, with its attendant disturbance, has stopped, the solid material surrounding structures tends to compact itself more or less, and solidify, according as it is more or less porous, forming in many instances what may be virtually a compact arch shutting off a large percentage of the normal, and some percentage even of the aqueous, pressure.

That the pressure of normally dry material cannot be measured through small openings can be verified by any one who will examine such material back of bracing showing evidences of heavy pressure. The investigator will find that, if this material is free from water pressure, paper stuffed lightly into small openings will hold back indefinitely material which in large masses has frequently caused bracing to buckle and sheeting planks to bend and break; and the writer reiterates that such experiments should be made in trenches sheeted with horizontal sheeting bearing against short vertical rangers and braces giving horizontal sections absolutely detached and independent of each other. In no other way can such experiments be of real value (and even then only when made on a large scale) to determine conclusively the pressure of earth on trenches.

As to the questions of the relative thrust of materials under various angles of repose, and of the necessity of dividing by the tangent, etc.; these, to the writer, seem to be merely the solution of problems in simple graphics.

The writer believes that if Mr. Goodrich will make, even on a small scale, some of the experiments noted by the writer, he will be convinced that many of the assumptions which he cannot at present endorse are based on fact, and his co-operation will be welcomed with the greatest interest. Among the experiments which he is asked to make is the one in dry sand, noted as Experiment No. 3, whereby it can be shown very conclusively that additional back-fill will result in increased arching stability, on an arch which would collapse under lighter loading.

The writer is indebted to Mr. Goodrich for pointing out some errors in omission and in typography (now corrected), and for his hearty concurrence in some of the assumptions which the writer believed would meet with greatest disapproval.

In reply to Mr. Pruyn and Mr. Gregory, the writer assumed that the piston area in Experiment No. 6 should be reduced only by the actual contact of material with it. If this material in contact should be composed of theoretical spheres, resulting in a contact with points only, then the theoretical area reduced should be in proportion to this amount only. The writer does not believe, however, that this condition exists in practice, but thinks that the area is reduced very much more than by the actual theoretical contact of the material. He sees no reason, as far as he has gone, to doubt the accuracy of the deductions from this experiment.

Regarding the question of the length of time required to raise the piston, he does not believe that the position of his critics is entirely correct in this matter; that is, it must either be conceded that the piston area is cut off from the source of pressure, or that it is in contact with it through more or less minute channels of water. If it is cut off, then the writer's contention is proved without the need of the experiment, and it is therefore conclusive that a submerged tunnel is not under aqueous pressure or the buoyant action of water. If, on the other hand, the water is in contact through channels bearing directly upon the piston and leading to the clear water chamber, any increase in pressure in the water chamber must necessarily result in a virtually instantaneous increase of the pressure against the piston, and therefore the action on the latter should follow almost immediately. In all cases during the experiments the piston did not respond until the pressure was approximately twice as great as required in clear water, therefore the writer must conclude either that the experiments proved it conclusively or that his assumption is proved without the necessity of the experiments. That is, the pressure is virtually not in evidence until the piston has commenced to move.

Mr. Pruyn has added valuable information in his presentation of data obtained from specific tests of the bearing value of, and friction on, hollow steel piles. These data largely corroborate tests and observations by the writer, and are commended to general attention.

Mr. Carter's information is also of special interest to the writer, as much of it is in the line of confirming his views. Mr. Carter does not yet accept the theory of increased pressure toward the top, but if he will examine or experiment with heavy bracing in deep trenches in clear sand, or material with well-defined angles of repose, he will probably find much to help him toward the acceptance of this view.

The writer regrets that he has not now the means or appliances for further experiments with the piston chamber, but he does not believe that reliable results could be obtained in broken stone with so small a piston, as it is possible that the point of one stone only might be in contact with the piston. This would naturally leave the base exposed almost wholly to a clear water area. He does not believe, however, that in practice the laying of broken stone under inverts will materially change the ultimate pressure unless its cross-section represents a large area.

Mr. Perry will find the following on page 369:

"It should be noted also that although the area subject to pressure is diminished, the pressure on the area remaining corresponds to the full hydrostatic head, as would be shown by the pressure on an air gauge."

This, of course, depends on the porosity of the material and the friction the water meets in passing through it.

As to Mr. Thomson's discussion, the writer notes with regret two points: (a) that specific data are not given in many of the interesting cases of failures of certain structures or bracing; and (b), that he has not in all cases a clear understanding of the paper. For instance, the writer has not advocated the omission of bottom bracing or sheeting. He has seen many instances where it has been, or could have been, safely omitted, but he desires to make it clear that he does not under any circumstances advocate its omission in good work; but only that, in well-designed bracing, its strength may be decreased as it approaches the bottom.

Reference is again made to the diagram, Fig. 12, which shows that, in most cases of coffer-dams in combined aqueous and earth pressure, there may be nearly equal, and in some cases even greater, loading toward the bottom.

The writer also specifically states that in air the difference between aqueous and earth pressure is plainly noted by the fact that bracing is needed so frequently to hold back the earth while the air is keeping out the water.

The lack of specific data is especially noticeable in the account of the rise of the 6-ft. conduit at Toronto. It would be of great interest to know with certainly the weight of the pipe per foot, and whether it was properly bedded and properly back-filled. In all probability the back-filling over certain areas was not properly done, and as the pipe was exposed to an upward pressure of nearly 1600 lb. per ft., with probably only 500 or 600 lb. of weight to counterbalance it, it can readily be seen that it did not conform with the writer's general suggestion, that structures not compactly, or only partially, buried, should have a large factor of safety against the upward pressure. Opposed to Mr. Thomson's experience in this instance is the fact that oftentimes the tunnels under the East River approached very close to the surface, with the material above them so soupy (owing to the escape of compressed air) that their upper surfaces were temporarily in water, yet there was no instance in which they rose, although some of them were under excessive buoyant pressure.

It is also of interest to note, from the papers descriptive of the North River Tunnel, that, with shield doors closed, the shield tended to rise, while by opening the doors to take in muck the shield could be brought down or kept down. The writer concurs with those who believe that the rising of the shield with closed doors was due to the slightly greater density of the material below, and was not in any way due to buoyancy.

Concerning the collapse of the bracing in the tunnel built under a side-hill, the writer believes it was due to the fact that it was under a sliding side-hill, and that, if it had been possible to have back-filled over and above this tunnel to a very large extent, this back-fill would have resulted in checking the sliding of material against the tunnel, and the work would thereafter have been done with safety. This is corroborated by Mr. Thomson's statement that the tunnel was subsequently carried through safely by going farther into the hill.

As to the angle of repose, Mr. Thomson seems to feel that its determination is so often impracticable that it is not to be relied on; and yet all calculations pertaining to earth pressure must be based on this factor. The writer believes that the angle of repose is not difficult to determine, and that observations of, and experiments on, exposed banks in similar material, and general experience in relation thereto, will enable one to determine it in nearly all cases within such reasonably accurate limits that only a small margin of safety need be added.

Engineers are sent to Europe to study sewage disposal, water purification, transit problems, etc., but are rarely sent to an adjoining county or State to look at an exposed bank, which would perhaps solve a vexed problem in bracing and result in great economy in the design of permanent structures.

Mr. Thomson's general views seem to indicate that much of the subject matter noted in the paper relates to unsolvable problems, for it appears that in many cases he believes the Engineer to be dependent on his educated guess, backed perhaps by the experienced guess of the foreman or practical man. The writer, on the contrary, believes that every problem relating to work of this class is capable of being solved, within reasonably accurate limits, and that the time is not far distant when the engineer, with his study of conditions, and samples of material before him, will be able to solve his earth pressure and earth resistance problems as accurately as the bridge engineer, with his knowledge of structural materials, solves bridge problems.

The writer, in the course of his experience, has met with or been interested in the solution of many problems similar to the following:

What difference in timbering should be made for a tunnel in ordinary, normally dry ground at a depth of 20 ft. to the roof, as compared with one at a depth of 90 ft.?

What difference in timbering or in permanent design should be made for a horizontally-sheeted shaft, 5 ft. square, going to a depth of 45 ft. and one 25 by 70 ft., for instance, going to the same depth, assuming each to be braced and sheeted horizontally with independent bracing?

What allowance should be made for the strength of interlock, assuming that a circular bulkhead of sand, 30 ft. in diameter, is to be carried by steel sheet-piling exposed around the outside for a depth of 40 ft.?

What average pressure per square foot of area should be required to drive a section of a 3 by 15-ft. roof shield, as compared with the pressure needed to drive the whole roof shield with an area four times as great?

To what depth could a 12 by 12-in. timber be driven, under gradually added pressure, up to 60 tons, for instance, in normal sand?

What frictional resistance should be assumed on a hollow, steel, smooth-bore pile which had been driven through sharp sand and had penetrated soft, marshy material the bearing resistance of which was practically valueless?

What allowance should be made for the buoyancy of a tunnel 20 ft. in diameter, the top of which was buried to a depth of 20 ft. in sand above which there was 40 ft. of water?

It is believed by the writer that most of the authorities are silent as to the solution of problems similar to the above, and it is because of this lack of available data that he has directed his studies to them. The belief that the results of these studies, together with such observations and experiments as relate thereto, may be of interest, has caused him to set them forth in this paper.

He desires to state his belief that if problems similar to the above were given for definite solution, not based on ordinary safe practice, and without conference, to a number of engineers prominently interested in such matters, the results would vary so widely as to convince some of the critics of this paper that the greater danger lies rather in the non-exploration of such fields than in the setting forth of results of exploration which may appear to be somewhat radical.

Further, if these views result in stimulating enough interest to lead to the hope that eventually the "Pressure, Resistance, and Stability" of ground under varying conditions will be known within reasonably accurate limits and tabulated, the writer will feel that his efforts have not been in vain.

FOOTNOTES:

[Footnote H: "Lateral Earth Pressures and Related Phenomena," Transactions, Am. Soc. C. E., Vol. LIII, p. 272.]

THE END