Not by experiment upon a large scale, nor is it probable that they will be; but they have been deduced from experience, reasonable inference, and experiments on a small scale, as has been before mentioned.
The effect of vibration is usually more marked in cuttings than in embankments, although it may nearly approach when they are of little depth or height: because a train in a cutting is contained within the area excavated, whereas in an embankment it is without the area deposited. In a cutting vibration commences upon the formation level and the toe of the slopes, the latter the most vulnerable parts and those most strained. In an embankment it proceeds through the formation to the base and the toes of the slopes which are necessarily the most distant. On the other hand, the material in an embankment is generally in a looser and lighter condition, and therefore more inclined to move and to suffer from vibration. It may also be greater upon one side consequent upon the “lurching” of the engine and carriages.
Obviously, vibration is increased with the speed and weight of a train; probably a short, heavy train travelling at high speed causes a more deleterious effect than a long heavy train travelling at a slow speed: also the higher an embankment or the deeper a cutting the greater the area of the cross section. Assume a train weighs 100 tons, and the weight of the earth is 112 lbs a cubic foot, or 0·05 of a ton; it might be considered that the effects of vibration would be less as the areas increased. Consider the formation to be 18 feet in width and the slopes 1½ to 1, the respective areas of cross section would be as follows:—
| Height. Feet. | Area. | Weight of the Embankment. Tons per Lineal Foot. | Weight of the Train. Tons. | Ratio of the Weight of 1 Foot Lineal of an Embankment to the Weight of the Train. | ||
|---|---|---|---|---|---|---|
| Square Feet. | Lineal Foot. | Ton. | ||||
| 10 | 330 × | 1 × | 0·05 = | 16·5 | 100 | 0·165 to 1 |
| 20 | 960 × | 1 × | 0·05 = | 48·0 | 100 | 0·480 to 1 |
| 30 | 1,890 × | 1 × | 0·05 = | 94·5 | 100 | 0·945 to 1 |
| 40 | 3,120 × | 1 × | 0·05 = | 156·0 | 100 | 1·560 to 1 |
| 50 | 4,650 × | 1 × | 0·05 = | 232·5 | 100 | 2·325 to 1 |
| 60 | 6,480 × | 1 × | 0·05 = | 324·0 | 100 | 3·240 to 1 |
Note.—For the purpose of a comparison of ratios it is not necessary to consider the length of the train.
A simple inspection of the above ratios would lead to a supposition that the effects of vibration would be no less than 3·210
0·165 = 19·6 times greater in a 10 feet than in a 60 feet embankment. Merely comparing the weight of a train with that of an embankment, and assuming that the results of vibration at the same rate of speed are so governed is incorrect, for the effect of vibration at the formation level is not regulated by the height of an embankment or the depth of a cutting. The weight of a train may bear a very small relation to that of the quantity of earth slipped, yet the soil may have gradually become in such a state of delicate equilibrium that at last the least vibration will destroy it, even a little of the top soil falling upon the slope; and it frequently occurs that a slip commences by the detachment of a few small lumps and increases until it becomes of serious dimensions; therefore, the area of a cutting or embankment cannot necessarily be considered as reducing vibration although the source of disturbance may be more distant; but, of course, the heavier the mass the greater the weight and speed required to cause the whole to vibrate.
Lighthouses and such exposed works being constantly subject to vibration, the experience gained through their behaviour may be considered as indicating the direction in which the stability of structures in analogous situations has to be sought. It is generally agreed that it favours weight and bulk, as they are unchangeable, and shows that although the form, execution, and the material may be perfect, a light fabric will gradually be deteriorated by constant tremor and vibratory motion, at length culminating in the loosening and separation of the parts.
Except from actual experiment in each case, it is impossible to determine the greatest weight of and the speed at which a train should be allowed to travel so as to prevent any deleterious effect from vibration, and the circumstances are so various that a practical rule cannot be deduced, except by assuming conditions from experience alone, which would so modify a formula as to make it show any desired result, and cause it to be regarded as too complaisant to be trusted. Perhaps the best test of the effects of vibration that any earthworks can receive is when a temporary railway is laid upon the formation or cess for the carriage of materials, and in a lesser degree a steam excavator, as the weight and vibratory action may show the weak places in a cutting, or so shake portions of an embankment that should the earth be unstable a slip will soon occur.
CHAPTER VIII.
Earthworks in or upon Sidelong Ground.—Some Insecure Conditions.—Precautionary Measures.—Embankments upon Soft Ground.—Embankments Composed of Soft Earth.—The Promotion of Stability and Consolidation.