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supported at the bottom only, and the stresses figured somewhat in the same way as in the beam or slab computations. The footing is also considered as an inverted cantilever beam or slab with the pressure acting upward against it, tending to rupture it at the junction and the proportions of steel and concrete must be so arranged as to prevent unsafe strains from being developed.

Reinforced-concrete walls do not depend upon the weight of the masonry alone to resist overturning, but utilize also the weight of the earth backing resting on the base of the wall.

The economy of a reinforced-concrete retaining wall is due

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FIG. 78.-Reinforced Concrete Retaining Wall. Fig. 79.-Reinforced Concrete Retaining Wall with Counterfort. Fig. 80.-Reinforced Concrete Retaining Wall with Counterfort and Centre Platform,

chiefly to the utilization of the downward pressure of the backing in resisting overturning.

In reinforced-concrete retaining walls as in masonry oncs, provisions must be made against sliding, and the wall must have a suitable foundation.

Classes of Reinforced-Concrete Walls.-Reinforced-concrete retaining walls may be divided into three classes: 1. Walls without counterforts; 2. Walls with counterforts; 3. Walls restrained at top and bottom.

Walls without Counterforts. This type is generally economical for walls of low or medium height. More material is used than in

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a wall with counterforts, but the decreased cost of form work and of placing the reinforcing and concrete will, in a wall of average height, more than offset the cost of the extra material.

These walls are simple in form, consisting of a thin reinforced vertical wall rigidly attached to a base formed by a reinforcedconcrete slab. The vertical wall acts as a cantilever, with its maximum bending moment at the upper face of the base. This also is the point of maximum shear, and the vertical wall should be designed accordingly. As the bending moment and shear decrease, as the top of the wall is approached, the thickness of the wail and the amount of reinforcing may also be decreased. The base at the heel also acts as a cantilever, and must resist the weight of the earth resting upon it. The moment and shear are maximum at the rear of the vertical wall and the base should be designed accordingly. The toe of the wall also acts as a cantilever resisting the upward thrust of the earth caused by the tendency of the wall to overturn. It takes its maximum moment and shear at the face of the vertical wall.

Walls with Counterforts.—These walls consist of a broad base, a thin, vertical, curtain wall, and ribs or counterforts spaced 3 to 10 feet on centres, connecting the base with the vertical wall.

This type of wall is very economical of material, and this economy increases in proportion to the height. The cost of form work, however, is great, and except in the case of high walls, the wall without counterforts is generally more economical.

In this type of wall the bending moment produced by the earth pressure is resisted entirely by the counterforts. The vertical wall acts like a floor slab and transmits the horizontal earth pressure to the counterforts. The base at the back of the wall also acts as a floor slab, carrying the weight of the earth above it, and serving as an anchorage to the counterforts. That portion of the base in front of the vertical wall should be designed as a cantilever, fixed into the wall, and resisting the upward pressure of the earth, caused by the tendency of the wall to overturn.

The counterforts should be designed to take care of all stresses due to overturning. Sufficient horizontal and vertical reinforcing rods should be placed in the counterforts to properly tie them to the face wall and base.

In the foregoing types of walls the walls should be so proportioned that the maximum pressure at the toe does not exceed the safe bearing value of the soil.

Walls Restrained at Top and Bottom.-Cellar walls and walls with land ties are of this type. They may consist, in a cellar wall, of a slab reinforced vertically to withstand the pressure of the earth backing, and supported by the adjacent floors, or the slab may be reinforced horizontally carrying the load to vertical beams whieh in turn are supported by the adjacent floors.

A wall with land ties is similar with the exception that a horizontal

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Figs. 81, 82, 83.-Sections of Typical Types of Concrete Foundation Walls.

girder extending from tie to tie is necessary to properly deliver the load to the land tie. The resistance to sliding in a wall of this type depends on frictional resistance and the abutting power of the earth in front of the face at its toe.

Details of Construction. In the construction of retaining walls, of both plain and reinforced concrete, the same general rules apply as to quality of material, details of form work, placing, and inspection, as are given for other structures; the difference between the plain and reinforced concrete being that in the former a much larger aggregate can be used both for the purpose of adding weight and saving cement, and it is excellent practice in the construction of large gravity walls, to employ a rubble concrete, or to embed in successive layers of concrete large blocks of stone.

The special points which must be looked for in the construction of retaining walls of any type are:

1. The preparation of a secure and satisfactory foundation below the frost line (2 to 4 feet, depending upon the climate).

2. The drainage of the foundation and removal of springs, etc., under same. Removal of poor material, stepping of rock surfaces, etc.

3. The construction of a drainage system behind and adjacent to the back of the wall, by means of gravel, channels, or other means and outlets, as weepers or pipes through the wall to carry off the water.

4. The compacting of the material or backing behind the wall (except that immediately adjacent) to reduce the pressure on same as much as possible.

5. The construction of a substantial coping along the top of the wall.

6. Expansion joints should extend through the walls either directly or by means of special connections to prevent temperature cracks. These may be 20 to 30 feet apart in plain concrete walls and 40 to 5c apart in reinforced walls, the reinforcement helping materially to avoid such cracks. Five per cent additional reinforcement will usually be sufficient for this purpose.

Foundations for Retaining Walls.-The management of the foundation of a retaining wall is an important matter, and it is generally admitted that a large majority of the failures of retaining walls are due to defects in the foundations. The nature of the soil should first be determined, and tests made to ascertain its bearing capacity, and the wall then so proportioned that no portion of the soil shall be overloaded. If necessary, the bearing capacity of the soil may be increased by: 1. deeper excavation; 2. drainage; 3. consolidating the soil; or, 4. by means of sand piles. If none, of the above methods give satisfactory results, piles of either timber or reinforced concrete must be used. If the foundation is on rock it is only necessary to cut away the loose and decayed portion of the rock and to dress it to a plane as nearly perpendicular to the direction of the pressure as possible, any fissures being filled with concrete. Other methods of providing adequate foundations are described in Chapter XXI.

Drainage.- Next to faulty foundations, water behind the wall is the most frequent source of failure of retaining walls. The water not only adds to the weight of the backing material, but also softens the material and causes it to flow more readily, thus greatly increasing its lateral thrust. To guard against the possibility of the backing becoming saturated with water, holes, called weep holes, are left through the wall. The holes should be spaced generally from i to 3 sq. yds. of face of wall. When the backing is clean sand the weep holes will allow the water to escape; but if the backing is retentive of water, blind drains should be placed in back of the wall and lead the water to the weep holes.

Land Ties. -Retaining walls may have their stability increased by being anchored to a suitable anchorage embedded in a firm strata of earth a distance behind the wall. The amount of load taken by these rods will depend on their position in the face of the wall. If they are fastened to the wall at the top, they will take one-third of the total earth pressure. If they are fastened in the wall at one-third the height from the top, they will take one-half the total pressure.

Relieving Arches.-In extreme cases the pressure of the earth may be sustained by relieving arches. These consist of one or more rows of arches having their axes at right angles to the face of the bank of earth. Their front ends may not be closed, which then prevents the appearance of a retaining wall, although the length of the archway is such as to prevent the earth from abutting against the wall.

Concrete Abutments.--An abutment has two offices to perform: 1. to support one end of a bridge; 2. to act as a retaining wall.

There are four forms of abutments in more or less general use: 1. A straight abutment-a plain wall with or without wings.

2. Wing abutment-wing walls make an angle with the face of the abutment (usually about 30 degrees).

3. U-abutment-when the ring makes an angle of 90 degrees with the face of the abutment.

4. T-abutment-when the wings are moved to the centre of the abutment and merged into one stem.

The dimensions of an abutment are to be determined as for a retaining wall. These dimensions must be such that the abutment can safely carry the superimposed load.

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