2. Should they be left undrained and uncovered and be excavated to a flat slope. Provided a cutting can be readily drained and covered and there is no probability of any sudden or permanent increase of moisture, perhaps the first method is the more economical; but much depends upon the quantity of water held by the earth in its normal state, whether it is of the same character throughout, and the depth of a cutting. Should the beds be upheaved or intermixed, then a flat slope is necessary and no covering except a wall may make it stable at a steep slope, and, for instance, should clay be always in a semi-saturated condition, 3 to 1 is the least slope at which it will permanently stand, and it will usually require a more moderate inclination. A medium course to adopt is that of varying the inclination of the slopes, the steepest, of course, being at the top and the flattest towards the toe; this is in accordance with the laws of pressure and a mathematical investigation of the theoretically correct slope, which nearly corresponds with the actual slope a high embankment will assume when allowed to weather and settle: for by varying the inclination of the slope the latter becomes practically a curved line and approximates to that of the curve of equilibrium. In almost all slips the surface from which the fallen mass has become detached is curved, the upper part being concave and the lower slightly convex, the outline being caused from the upper portion falling, the lower receiving it and being pressed outwards; however, it may happen that the lower part of a slope has remained intact, and only the upper slipped and become deposited upon it.
The varying slope system has recently been adopted by Mr. Francis Fox, M. Inst. C.E., upon the Scarborough and Whitby Railway, where an embankment about 90 feet in height in treacherous clay had slopes of 1½ to 1 for the upper 30 feet in height, 2 to 1 for the middle 30 feet, and 3 to 1 for the bottom 30 feet. Formation width 28 feet. A calculation of the insistent weight per square foot, without a train, at stated heights gives the following results; taking the weight of the earth at 0·055 of a ton a cubic foot, or 1½ ton a cubic yard, and assuming the worst case, that of the earth for the width of the formation, viz., 28 feet, to act simply as a column 1 foot square and the load as not being distributed over the area of the entire base at any point.
At the base of the upper 30 feet, 1½ to 1 slopes, it would be about 1·65 ton per square foot.
At the base of the middle 30 feet, 2 to 1 slopes, it would be about 3·30 tons per square foot.
At the base of the lower 30 feet, 3 to 1 slopes, it would be about 4·95 tons per square foot.
If the weight of 1 foot lineal of the embankment is taken and considered as equally distributed over the whole area of the base at the 30 feet divisions, the strain per square foot would be as follows:
At the base of the upper 30 feet, 1½ to 1 slopes, about 1 ton per square foot.
At the base of the middle 30 feet, 2 to 1 slopes, about 1¾ ton per square foot.
At the base of the lower 30 feet, 3 to 1 slopes, about 2¼ tons per square foot.
Note.—The actual strain is probably approximate to a mean between the two values, and is nearer the latter than the former.