RETAINING WALLS.
275. A wall made to sustain a mass of earth or water, to resist overthrow, requires a certain thickness. A body of earth assumes what is termed the natural slope, the inclination of which depends upon the adhesion of the soil, but may be taken as one and one half horizontal, to one vertical, (1½ to 1), as an average.
The problem is, knowing the height of the wall and the form of the mass of earth to be supported, to find the thickness of the wall.
Let A B 6 F, represent the thickness of the wall. Its centre of gravity is at O, and is horizontally projected at m. The centre of gravity of the thrusting triangle of earth, B 4 6, is C, (found by the cutting of lines joining any two angles to the centre of the opposite sides,) is horizontally projected at Ca, and the horizontal component of the thrust is exerted at 2, tending to overthrow the wall with a leverage, 6 2.
Fig. 133.
The overthrowing power is, then, the area of the triangle B46 × the weight of the unit of area × the leverage 6 2. And the resisting power, the area AB × B6 × the weight of a unit of area by one half breadth, or m 6; or, calling w the weight of the wall, and w′ that of the triangle, B 4 6, and L and L′ the leverage respectively of the wall to resist and of the earth to overthrow; we must have at least
wL = w′L′,
and to insure stability,
wL > w′L′
or,
L = w′L′
w,
and as L = half base finally, the thickness, or
2L = 2w′L′
w
276. Example.—Let the height of wall be twenty feet, slope one and one half to one; if a cubic foot of earth weighs one hundred lbs., and of masonry, one hundred and sixty lbs., we have the overthrowing force,
20 × 15 × 1 × 100 × 2 × 20
3,
and the resisting force, (assuming the thickness as eight feet, in order to get the area),
20 × 8 × 1 × 160 × 8
2.
Or performing the operations,
| For overthrowing, | 100,000 lbs. |
| For resisting, | 102,400 lbs. |
If the wall in place of retaining only the mass B 4 6, retains the bank B E Fa, the pressure will evidently be increased. The centre of gravity of the trapezoid B E Fa 6, is at C′, which is horizontally projected at C′a, and the horizontal component of the thrust acts at 3 with the leverage 63.
Any superincumbent load, as a train of cars at E Fa, will again increase the pressure, not only by reason of weight, but from shocks and vibration.
For resisting lateral pressure, the beds of masonry are best when rough dressed. For vertical loads, hammer dressed beds are the best.
The leverage of resistance is very much increased by battering the wall in front, as at A D. The centre of gravity is then horizontally projected at m′, but the distance D m′ is much greater than F m.
Fig. 134.
The amount of masonry remaining the same, by decreasing the top, and increasing the base, the strength is very much increased.
When retaining walls are exposed to shocks or pressures special directions, they may be very much aided by buttresses opposing directly such forces, as in fig. 134.
The increase of strength thus made by a small bulk of masonry is very great.
All abutments, wing-walls, and side walls of culverts, come under the head of retaining walls.
When the face of the wall does not by its position admit of buttresses, as in fig. 134, it may be dovetailed into the earth; the latter being firmly rammed around the masonry, as in fig. 135.
Fig. 135.
277. The weight of the different earths and stones are shown in the following table.
| Name of material. | Weight per cubic foot. |
|---|---|
| Brick, common | 97 to 125 |
| Brick, stock | 115 to 135 |
| Brickwork, (average,) | 90 to 95 |
| Chalk, | 144 to 166 |
| Granite, | 164 to 187 |
| Marble, | 111 to 117 |
| Mortar, (hair,) dry | 80 to 86 |
| Puzzolano, | 160 to 178 |
| Slate, | 157 to 180 |
| Stone, (average,) | 140 to 150 |
| Clay, (common,) | 110 to 125 |
| Clay and gravel, | 150 to 170 |
| Earth, common, | 95 to 126 |
| Gravel, | 100 to 110 |
| Quick-lime, | 50 to 55 |
| Quartz sand, | 170 to 175 |
| Common sand, | 88 to 93 |
| Shingle, | 88 to 92 |
| Earth, loose | 90 to 95 |
| Stone work, (hewn,) in wall, | 160 to 175 |
| Stone work, (unhewn,) in wall, | 125 to 140 |
CHAPTER XII.
FOUNDATIONS.
278. Foundations may be divided into four classes.
Those on firm, dry land.
Those on unfirm dry land.
Those on solid bottom, under water.
Those on unfirm bottom, under water.
Foundations upon firm dry land require only to be placed at a sufficient depth to be out of the way of frost; varying from one foot in the Southern, to two and three feet in the Middle, and four and five feet in the Northern States. The first course should consist of small, flat stones placed dry, but well packed by hand, upon the bottom; upon the top of this layer, the mortared or cement masonry should be commenced. The object of the first course of small stones is to apply the weight of the superincumbent masonry as equally as possible to the ground. All boulders and rounded stones should be carefully kept out of the foundation.
Unfirm soils are prepared by driving piles, upon which a platform holding the masonry is placed; or by placing the lower courses directly upon the heads of the piles. Sand piles are made either by driving and withdrawing a wooden pile and filling the hole thus made with sand; or by digging trenches and filling such with sand. The applied weight is thus spread over the entire surface of the sides and bottom, instead of being placed upon the bottom only. When the weight of a heavy structure is thrown upon a few small points of support, they may be made the piers and abutments of a series of inverted arches, by which the whole surface beneath the structure is made to assist in bearing the load. Foundations upon yielding or sandy and wet soils may be secured by piling around the whole structure; by which the earth is kept from spreading. Foundations upon dry land do not generally give much trouble to the engineer; but operations carried on under water require all the science and patience that he is master of.
279. Three methods of founding under water may be noticed,
By driving piles.
By coffer-dam.
By caisson.
In very shallow water, where no danger arises from contracting the water-way, we may throw in loose stones until the surface is reached; and commence thereon the lower courses of the masonry. This is termed “Enrockment.”