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Design of Walls in General.—Methods of Failure. -Kinds of Retaining Walls.—Design

of Gravity Walls.-Reinforced-Concrete Walls.-Details of Construction.Foundations.—Abutments.—Bulkheads.-Appearance of Walls.—Tables for Design of Walls.

UNTIL the advent of concrete, retaining walls for the support of embankments and cuts as well as reservoir walls, bulkheads, etc., were constructed of rubble or ashlar masonry laid with or without mortar as the importance of the problem demanded. Concrete, especially when reinforced, has supplied a material which gives a far greater power of resistance, occupies a minimum of space and may

be built at a much lower cost.

The design of concrete retaining walls follows the same general methods that are employed for ordinary masonry, the design being based upon the action of the wall when the load caused by earth, water, or other material from behind, comes upon it. Certain conditions of failure deduced from observation, experience, and mathematical reasoning are assumed to be possible and the wall so proportioned that it will be safe against any and all such possible failures. Thus it is assumed that:

Assumptions Made in Design.-A wall holding up a bank of earth, or water will be subjected to a pressure: the amount of which will depend upon the depth of the wall below the surface and upon the weight and mobility of the material pressing against it.

The question as to how much pressure is produced by banks of earth resting against walls has given rise to much discussion, and even to-day there is no general agreement among engineers as to what this pressure is. The difficulty arises from the fact that earths vary so much, their weight, consistency, and cohesive power are so constantly changing with change of the contained water, that no general pressure rule can be applied. It is thus that most computations for earth pressure assume a theoretical condition, that of perfectly dry sand, and yet this condition is but seldom found, but as it gives safe values, its assumption is justified.

When a bank of such sand has an unrestricted surface its sides will assume a natural slope of about 1 1/2 feet horizontal to 1 foot vertical. This is referred to as the “Angle of Repose,” or “Angle of Friction."

If a wall is placed at the edge of a bank and the space between the back of the wall and the bank filled in, this earth or "backing” will tend to slide along the line of repose, and thus produce a pressure against the wall. The upper half of this prism is considered as producing the maximum pressure effect on the wall and its weight is employed in computing this pressure.

Effect of Earth Pressure.—Mathematical investigations have determined:

I. That the entire effect of this pressure may be considered as concentrated at a point 1/3 the height from the bottom.

II. That this pressure will tend to either slide or push the wall bodily out of place, or to rotate it about its toe and overturn, or both.

III. That since the wall is rigidly constructed and cannot yield, the effect of the external pressure is to induce strains in the material of the wall.

IV. That the material of the wall can resist safely certain specified strains per unit of area of material such as the square inch or square foot, the amount of such safe strains varying with the kind of strain and the material.

V. That the foundation material must not be subjected to unsafe strains. From these assumed conditions the dimensions of the wall are fixed so that the strain in the material will never exceed what it can safely stand. It is thus seen that the following me hods of failure are possible.

Methods of Failure. -A retaining wall may fail in one or more of the following ways:

1. By revolving about any horizontal line in the face. This is the most frequent mode of failure, and it is due to the overturning moment, due to the earth backing being greater than the righting moment of the wall itself. A failure of this type indicates too light 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. A failure of this type indicates too light a design.

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 earth 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.

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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

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