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, in pounds. | Equivalent feet of depth. | Equivalent elevation for water at—6.85. | Observed pressure. |
| M.H.W. | Ground-water. | ||
| 1 | 2.31 | 9.06 | Practically the same as computed for ground-water. |
| 2 | 4.63 | 11.48 | |
| 3 | 6.94 | 13.79 | |
| 4 | 9.25 | 16.10 | |
| 5 | 11.57 | 18.42 | |
| 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 | |
Note.—Equivalent depth in feet =  × pressure. | |||
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 W1, the value becomes ½ W1, 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.