Pressure, Resistance, and Stability of Earth / American Society of Civil Engineers: Transactions, Paper No. 1174, Volume LXX, December 1910

by J. C. Meem

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: