a wall for the work imposed upon it or too heavy a load on the soil at the base of the wall.

A wall which shows signs of failure by this method may be strengthened by buttressing.

2. By Sliding on any Horizontal Plane.-This is the least frequent method of failure, and in a monolithic wall free from all horizontal joints as is the case in a wall of concrete, is practically impossible except by the sliding of the entire wall on its foundation bed. This is a rare occurrence, and when it occurs is probably the result of the wall having been founded on an unstable material, perhaps an inclined bed of moist and uncertain soil. When the foundation rests upon piles, a simple expedient is to drive piles in front of and against the edge of the foundation. When the foundation rests on rock, the resistance to sliding may be increased by leaving the surface of the bed rough, or in case the rock quarries out with smooth surfaces, the bed of the foundation may be channelled longitudinally, and the channels afterward filled with masonry. In case of the wall resting on earth, increasing the depth of the foundation below the ground level at the face of the wall, thereby increasing the area against which the face of the wall abuts, greatly increases its stability against sliding.

3. By the Bulging of the Body of the Masonry.-This form of failure can occur only in walls restrained at both top and bottom, as in cellar walls, some abutments, walls with land ties, etc. failure of this type indicates too light a design.

A

Some of the causes of failure of retaining walls which cannot readily be taken care of in computation are: settlement of foundation, bulging due to poor drainage, formation of ice, etc. These must be looked after in the plans and construction and will be referred to later.

Types of Retaining Walls.-Concrete retaining walls are constructed in three general types, depending upon local conditions and often upon the mood of the designer. These are:

I. Gravity walls, with or without reinforcement which depend for their stability entirely upon the weight of concrete.

II. Reinforced-concrete cantilever walls of uniform thickness and wide reinforced base footing.

III. Reinforced-concrete walls having buttresses at regular intervals on the rear face of the walls.

Gravity Retaining Walls.-The gravity wall is adapted for low banks or fills as in any large work the amount of concrete necessary to give the required weight makes it very costly. In such cases the reinforced-concrete wall is always employed.

In the gravity wall the side subjected to pressure is stepped, and the exposed side slopes away from the bank to give increased stability. It is an important principle of mechanics that the resultant of all forces acting on a wall should never pass outside of the middle third of the cross-section, and it is in order to follow this principle that the outside of the wall is stepped or sloped. By following this principle, no tensional or pulling stresses develop in the plain concrete which, by assumption, it cannot safely carry.

This principle holds true in all homogeneous masonry structures. Design of Gravity Walls.-The design of the gravity wall is usually a rather simple matter, as it is only necessary to assume a width of base of about 4 of the height. Make it 2 feet or up, wide on the top, according to practical requirements, and then compute its weight and the pressure due to the earth backing (or water in case of a dam), and compare the effect of this pressure to produce sliding and rotation, with the power of resistance as deduced from the weight. If the latter is greater, the wall is theoretically safe.

The steps followed in the theoretical design of a gravity retaining wall are well outlined in Lewis and Kempners' Manual of Examinations, as follows:

1. The height of the wall is determined by local conditions. 2. Assume total thickness of wall.

1/5 the height at top.

2/5 the height at bottom.

3. Plot the wall to scale.

4. Compute the weight of the maximum carth prism. Also compute the thrust of same, which equals about .64 of this weight. (Earth weighs 100 lbs. per cu. ft.)

5. Compute weight of wall-concrete weighing about 140 lbs. per cu. ft. Also compute position of centre of gravity.

6. Draw to scale, the line of thrust making an angle equal to the angle of friction with the normal to the back of the wall (see Fig. 77), and passing through the centre of pressure, which is 1/3 of the height from the bottom.

7. To same scale draw line representing weight of wall through its centre of gravity.

8. Combine these as shown. The resulting pressure line should fall within the middle third of the base to insure absence of tension in the joints.

9. Compute the overturning moment due to thrust. Also compute resisting moment of the wall. The resisting moment should exceed the overturning moment by a safe margin.

FIG. 77.-Diagram Showing Forces Acting on Gravity Retaining Wall.

10. Compute the horizontal thrust, also frictional resistance to sliding (weight X coefficient friction). The latter should be equal to or exceed 3 times the former.

11. Test security of foundation by computing unit load at the toe (total load per running foot divided by 1/2 width of base).

All conditions of stability must be satisfied and all unit loads should be within safe limits; if not, change dimensions and recompute.

REINFORCED-CONCRETE WALLS

Reinforced-concrete walls are designed along different lines. The external loading is the same as in the gravity wall, but the wall itself and the buttresses are considered as cantilever slabs or beams

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

IIF

78

79

80

FIG. 79.-Reinforced Concrete

FIG. 78.-Reinforced Concrete Retaining Wall. 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 ones, 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

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.