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 27 per cent. of the height; and with a batter one-fifth the height, if made 24 per cent. of the height.

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 12 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 formula 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

=

(3) For earth-pressure where a wall is infinitely surcharged, WH2 x cos2 Q

P =

2

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:

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 × 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 × 102 × 0·345 = 34.5 cwt.

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

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 10 × 5 × 140 the material in the wall is= 62.5 cwt. and

112

62·5 × 2·5 = 156-22 cwt. 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.

In Belgium and Holland columnar basalt has been very largely used during recent years, both for upright walls and for the facing of sloping banks. The hexagonal shape of the basalt blocks lends itself to the keying of the stones in a much better manner than the random shape of flints or granite.

At Hastings it has been in use for some time past, for the facing of the granite blocks used for groynes, and for the aprons to a sea-wall, and has been found to answer more satisfactorily than granite or Kentish Rag, the stones previously employed. For the new sea-wall in course of construction at Southend-on-sea, as also that at Clacton, basalt blocks from 4 to 7 inches in depth have been adopted in substitution of Kentish Rag stone, the material formerly used. For the protective works in the Maas and the Rhine this stone is exclusively used, as it has also been for the sea-walls at Scheveningen, Norway, and other places. Granite has also been superseded by basalt for the sea-wall, and for pitching the great sea-banks at Petten and West Kapelle, as hereafter described.

Timber Walls. For mere protective purposes, and where economy of outlay is a consideration, sea-walls may in some cases with advantage be constructed of timber.

Ten feet may be taken as the greatest height to which such walls should be built when dependence is placed on the strength of the piles used. Beyond this the strength of the timber is not calculated to resist the pressure, and ties have to be resorted to. When such a wall is at the foot of a cliff of unstable material, difficulty may be encountered in fixing the tie-piles in a reliable position. In any case, these should be well beyond the line of the angle of repose of the earth.

Pitchpine is frequently used for construction, but this timber is very uncertain in its strength and lasting qualities. Although due care may have been exercised in the selection of the wood, it will frequently be found, on examination, that in the exposed part, such as the walings and the tops of the piles, decay will have set in soon after the construction, and at the end of ten years this will have extended to such an extent as to materially impair the strength of the timber. Sound Memel fir, creosoted with 10 lbs. of oil, will be found a more reliable material, and its life may be placed at three times that of timber that has not been creosoted. Pitchpine will not absorb more than from 4 to 6 lbs. of oil.

A wall consists of main piles, walings extending horizontally between the main piles, and sheet piles or boarding. In some