Part 5
Any engineer who tries to guess at the angle of repose, and, from the resulting calculations, economizes on his bottom struts, will find that sooner or later an accident on one job will cause enough loss of life and money to pay for conservative timbers for the rest of his life. So much for side pressures. As to the pressure in the roof of a tunnel, probably every engineer will agree that almost any material except unfrozen water will tend to arch more or less, but how much it is impossible to say. It is doubtful whether any experienced engineer would ever try to carry all the weight over the roof, except in the case of back-fill, and even then he would have to make his own assumption (which sounds more polite than "guess").
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° 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 = ------ × 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°, 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 ½ _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° 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.