filled with clay, and sunk in line round the space to be enclosed; but in the majority of cases, the method is to drive two or more rows of close piling, and to fill up the space between them with clay puddle.

41. Cofferdams are sometimes formed, in shallow water, with a single row of sheet-piling; but this is very precarious work, as, unless the piles are fitted together with great truth, it is impossible to keep the joints close, and to prevent leakage. A single row of sheet-piling may, however, be often used with great advantage as a protection and support in front of an earthen dam, and this is a very economical and satisfactory method of proceeding where there is no depth of water.

42. Cofferdams are subject to heavy external pressure from the water round them, which would crush them in, were they not very firmly strutted. In cofferdams inclosing a small area, as, for instance, the site of the pier of a bridge, the strutting is placed from side to side, in the manner that will give the greatest facility for carrying on the work, the struts being gradually removed as the latter proceeds.

In constructing dams in front of a wharf wall, or similar work, the strutting requires to be effected in a different manner, and the plan usually adopted is to form a series of buttresses, or counterforts, at short intervals, from which the intermediate portions of the dam can be strutted with raking, horizontal struts. The strength given to these counterforts must, of course, depend on the amount of pressure to come on the dam.

43. In rivers subject to heavy freshets it is common, in constructing cofferdams, to keep the top of the dams below the flood level, as it is generally less expensive to pump out the water from the interior of the dam occasionally, than to construct and maintain a dam which should sustain the pressure of the flood waters; and it is always advisable to provide every dam with a sluice, by mean of which the water

can be admitted, if there is any fear of injury from a sudden freshet or from any other cause. In tidal waters the operation of closing a dam is sometimes rather hazardous (unless it can be performed at low water), from the tide falling outside, without the dead water inside being able to escape sufficiently quick through the sluices to maintain an equili brium; and, unless the piles and puddle wall are sufficiently strong to resist this outward pressure, the work will be violently strained, and often permanently injured. When the site to be inclosed is above the level of low water, halftide dams are sometimes resorted to. A half-tide dam is one which is covered and filled at every tide, and emptied by sluices at low water, the available working hours lasting from the time the bottom runs dry until the flood tide reaches the top of the dam.

44. The principal difficulties in the construction of cofferdams may be thus briefly stated :—

1st. To obtain a firm foothold for the piles, which, in either rock or mud, is a matter of great difficulty.

2d. To prevent leakage between the surface of the ground and the bottom of the puddle.

3d. To prevent leakage through the puddle wall.

4th. To keep out the bottom springs.

RETAINING WALLS.

45. The name of retaining wall is applied generally to all walls built to support a mass of earth in an upright or nearly upright position; but the term is, strictly speaking, restricted to walls built to retain an artificial bank, those erected tc sustain the face of the solid ground being called breast walls. (See fig. 8)

RETAINING WALL

Fig. 8.

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46. Retaining Walls.-Many rules have been given by different writers for calculating the thrust which a bank of earth exerts against a retaining wall, and for determining the form of wall which affords the greatest resistance with the least amount of material. The application of these rules to practice is, however, extremely difficult, because we have no means of ascertaining the exact manner in which earth acts against a wall; and they are, therefore, of little value except in determining the general principles on which the stability of these constructions depends.

47. The calculation of the stability of a retaining wall divides itself into two parts:

1st. The thrust of the earth to be supported.

2d. The resistance of the wall.

48. Definitions (see fig. 9.)-The line of rupture is that along which separation takes place in case of a slip of

earth. The slope which the earth would assume, if left totally unsupported, is called the natural slope, and it has been

found that the line of rupture generally divides the angle formed by the natural slope and the back of the wall into nearly equal parts.

The centre of pressure is that point in the back of the wall above and below which there is an equal amount of pressure; and this has been found by experiment and calculation to be at two-thirds of the vertical height of the wall from its top.

The wall is assumed to be a solid mass, incapable of sliding forward, and giving way only by turning over on its front edge as a fulcrum. In the annexed diagrams the foundations of the walls have, in all cases, been omitted, to simplify the subject as much as possible. The term slope in the following investigation is used as synonymous with the expression line of rupture.

49. Amount and Direction of the Thrust.-There are two ways in which this may be calculated-1st, By considering the earth as a solid mass sliding down an inclined plane, all slipping between the earth and the back of the wall being prevented by friction. This gives the minimum thrust of the earth. 2nd, By assuming the particles of earth to have so little cohesion, that there is no friction either on the slope or against the back of the wall. This method of calculation gives the maximum thrust.

The real thrust of any bank will probably be somewhere between the two, depending on a variety of conditions which it is impossible to reduce to calculation; for, although we may by actual experiments with sand, gravel, and earths of different kinds, obtain data whence to calculate the thrust exerted by them in a perfectly dry state, another point must be attended to when we attempt to reduce these results to practice, viz., the action of water, which, by destroying the cohesion of the particles of earth, brings the mass of material behind the wall into a semi-fluid state, rendering its action more or less similar to that of a fluid according to the degree of saturation.