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a north-west gale, to which direction the wall was fully exposed, the waves were projected upwards to a height of 40 feet, the water falling in a mass on the backing, which was scooped out. In this case the wall was amply strong enough to resist the direct action of the waves, but not the effect due to the falling water. When the wall was exposed as much as 8 to 9 feet below high-water mark, the shingle was carried away and the foundations laid bare; but where the foundation was in deeper water there was hardly any denudation.

Both at Margate, Ramsgate, and Westgate, where sea-walls have been built resting on, and let into, the hard chalk, the downward action of the waves, after breaking on the walls, cut away the chalk in front of them.

At Westgate, where the base of the wall was placed several feet above low water, and let 2 feet into the chalk, it was found that, after the lapse of a few months, the chalk was cut away by the waves and the foot undermined.

The foundation of the wall at Ramsgate was carried 4 feet. 6 inches into the chalk, and was built with a nosing projecting almost over the toe, with the idea of throwing the water off. In the course of a few years after the construction of the wall, the chalk at the foot had become so disintegrated that the surface of the beach was denuded to within nearly the base of the wall, so that it became necessary to underpin it throughout a great part of its length. As the waves came in contact with this wall the water ran up the face, and, being thrown off by the nosing, dropped down on the toe of the wall in a mass, with sufficient force to break up the chalk.

At Clacton, on the East Coast, a concrete sea-wall about 2000 feet in length was constructed about twenty years ago, for the purpose of forming a promenade in front of the town. Three concrete groynes or buttresses, 4 feet 6 inches high, were carried out at right angles to the wall, with the object of preventing the denudation of the beach in front of it. It was, however, found that, instead of effecting their purpose, the destructive effect of the waves breaking into the bay formed by these projections, and against the wall, had a very damaging effect on the beach, and caused considerable denudation. These concrete groynes were consequently removed. This wall was made with a curved batter, the top overhanging the base. The effect of the waves breaking on this wall has been to cut out the beach from the front, the

surface being 5 feet lower at the east than at the west end, which is under the lee of the pier. The danger of the wall being undermined became so great that a concrete apron had to be put down for its protection.

The top of the timber wall constructed by the Sea Defence Commissioners between Clacton and Walton, when built in 1889, was 6 feet above the beach, the piles being driven into hard clay. Within ten years after its construction the beach was lowered and the clay cut out in front of the wall to a depth of 4 feet, and during a gale in the winter of 1897, a large length of the wall fell down owing to the denudation of the beach in front, and the cutting out of the material at the back of the sheeting by the action of the waves falling on the roadway.

At Sandgate, Seaforth, Poole, Blackpool, and other places, concrete walls have been destroyed due to the scouring away of the beach in front of them, and the displacement of the material at the back by the falling water from the waves projected upwards from the face of the wall.

Strength of Walls.-The ordinary rules for the construction of retaining walls cannot be held to apply to sea-walls, so far as they act as retaining walls. The shocks and vibrations to which they are subjected by the percussion of the waves may set in motion the earth at the back, which under other conditions might have remained stable; and these forces also tend to disintegrate the material with which the stones of the wall, if of masonry, are joined together. The wall is further exposed to disruption by water being forced through crevices into the interior, and by the expansion of the air which may exist in any cavities.

Sir Benjamin Baker, in a paper on the pressure of earthwork contributed to the Institution of Civil Engineers in 1881 (Min. Proc. Inst. C.E., vol. lxv.), states that the uncertainty attending the conditions under which retaining walls are built is so great that no absolute reliance can be placed on any theoretical calculation; but as the result of his experience in constructing nearly 50 miles of retaining walls in soils of all kinds, he found that, under ordinary conditions and with ground of fair character, an average thickness for a retaining wall of one-third the height, measured from the top of the footings, is sufficient; if the wall is indefinitely surcharged, this width may be increased to one-half the height. Beyond this, experience alone could be a guide as to how much,

more or less, the substance of the wall may be due to the conditions with which it will have to contend.

A wall is in a better condition to bear the thrust of the earth behind, when the amount of material used being the same, it slopes back towards the earth from the vertical line. Thus, taking a rectangular vertical wall which requires a section of 33 per cent. of the height, the same section of wall having a batter one-tenth the height would have an equal resisting power if made per cent. of the height; and with a batter one-fifth the height, if made 24 per cent. of the height.

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Experience seems to point out that the mean width of a wall for sea-coast protection should not be made with a less section than one-half the height, measured above the foundation, or from the level of the permanent surface of beach, and this dimension must be increased if the wall is surcharged.

The theory as to the pressure of dry earth at the back of a wall is that the force to be contended with is that due to the weight of the wedge-shaped mass included between the back of the wall and a line intersecting the angle between the vertical face and the natural angle of the material of which the earth consists.

The greatest pressure results when the earth is so saturated with water as to be in a fluid condition, or what is termed mudpressure, and is equal to that produced by a fluid having the same specific gravity as water.

A safe value to assume for the pressure likely to be produced by ordinary earth in a fairly dry condition is one-third that of mud-pressure, which, according to the wedge theory, corresponds to an angle of 30 degrees, or a slope of about 13 to 1. Dry cohesive earth will stand at an angle of 45 degrees, or 1 to 1; some kind of wet clay is not to be depended on at an angle of about 18 degrees, or a slope of 3 to 1.

The simplest formulæ for ascertaining the horizontal pressure against a wall having a vertical back, where P = pressure, W weight of earth, taken at 112 lbs. the cubic foot, H = height of wall exposed above the surface of ground, Q: = the natural angle of repose of the earth at the back of the wall, are

=

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(3) For earth-pressure where a wall is infinitely surcharged,

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The centre of pressure being taken as acting at one-third of the height of the wall measured from the bottom, and direction of centre of pressure as normal to the wall.

For Nos. 2 and 3, the following give the same result, where C is a constant representing the pressure of the earth in cwts. for the different slopes:

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For example, a wall 10 feet high above the beach, weight of earth 1 cwt. per cubic foot, slope 1 to 1. The horizontal pressure acting on 1 foot in length at one-third the height of the wall would be by formula

P = 1 x 102 x 0·14 = 14 cwt.

Or if the wall were infinitely surcharged, the slope of the earth above the top of the wall being continued at the same angle as below

P = 1 x 102 x 0·345 = 34.5 cwt.

If the ground behind were in a semi-fluid condition, or in a state of mud-pressure

1 x 102
P =
2

= 50 cwt.

The strength of the wall to resist this pressure depends on the weight of the material and the position of its centre of gravity. With mud-pressure, the width of the base ought not to be less than three-fourths the height. With fairly good backing, the base may be one-third the height. For example, taking a wall 10 feet high, and having a rectangular section of half the height, a line let fall from the centre of gravity to the base bisects it equally, and gives the leverage as 2·5 feet. Taking the weight of concrete as 140 lbs. to the cubic foot, the weight of

the material in the wall is

10 x 5 x 140

112

= 62.5 cwt. and

62.5 × 2.5 156-22 cwt.

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Taking the earth-pressure as given above, this leaves an ample factor of safety.

Height. The top of the wall should be sufficiently high to prevent the wave itself, independent of the water projected upwards as spray, breaking over the top of the wall. This height depends on the range of the tides, the exposure of the wall, and the height which the waves in heavy on-shore gales approach the wall. Under ordinary conditions, waves beating against walls made for sea-coast protection seldom exceed from 10 to 12 feet in height, one-half of which is above and the other below the normal level of the water. The level of an extraordinary tide may be taken as 4 feet to 5 feet above ordinary spring tides; this would give the top of the wall at high water as from 10 to 11 feet above the level of high water at ordinary spring tides. In sheltered positions and with a good beach in front, this height may be reduced; this accords with the general practice. Thus the top of the wall at Hove is 12 feet above ordinary high water of spring tides, the range of an ordinary spring tide above low water being 20 feet; the new wall at Blackpool is 12 feet above, the range of tide being 25 feet; while at Scarborough the height is 13 feet, the range of tide being 16 feet. The walls at Ramsgate and Margate are from 7 to 8 feet, with a range of 15 feet. With the sloping wall at Dymchurch, the top of the wall is 10 feet above ordinary high water, the range of the tide being 22 feet. At Ostend the top of the wall is 12 feet above ordinary high water, and at Scheveningen 10 feet above the highest known tides, or 16 feet above ordinary tides, the range being respectively 17 and 13 feet.

Material for facing Walls.—It is essential that the material used, whether for facing an upright wall or for pitching a sloping bank, shall be of a hard and durable character.

Concrete in mass is most generally used for upright walls, with a facing of stronger material than the body of the wall. Unless great care is exercised in making this facing, it is liable to become broken and disintegrated by the action of the waves, especially where the beach is covered with shingle.

Concrete has an advantage over masonry walls, due to the absence of joints, and the smoother face which it affords.

At Hove the wall was built with blocks of concrete, the face blocks having flints on the surface bedded 4 inches deep in the concrete. In other walls random granite blocks have been used in place of the flints.

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