DESIGN OF REINFOROED-OONORETE RETAINING WALLS.
There are two types of reinforced-concrete retaining walls, viz.: (1) a vertical stem which resists the thrust of the earth by virtue of its strength as a cantilever beam; and (2) a comparatively thin face or curtain wall which is supported at intervals by counterforts. The first is ordinarily called a cantilever retaining wall, and the second a counterforted retaining wall. The first type is most suitable for com paratively low walls, and the second for high ones.
A wall of each of these types will be designed—the cantilever wall by use of a formula for the earth pressure (* 1022-23) and the counterforted wall by giving it a stability equal to that of a solid wall (1022 and § 1024).
Retaining Wall. Assume that a wall is to be designed to restrain an earth bank 10 ft. high, and assume also that the foundation is to be 3 ft. below the natural surface. Assume that the width on top, exclusive of the projection of the coping, is to be 12 inches, and also that the face of the wall is to have a batter of an inch to 1 foot; then the thickness at the bottom of the stem will be 18 inches. The appearance of the wall requires a coping, but that does not materially affect the stability which alone is under consideration here. The thickness of the footing can not be determined in advance of the solution of the remainder of the problem; but for the present it will be assumed to be 12 inches. Then the height of the stem above the top of the footing will be 12 ft. The length of the footing can not be determined in advance, but it will be tentatively assumed at 6.0 feet. The most economical position of the back of the wall along the line A B, Fig. 114, can not be determined except by trial. As the stem is moved nearer the front of the footing, the resisting moment of the weight of the stem is decreased, and the maximum pressure on the soil under the footing is increased; but sometimes it is necessary to place the face of the wall as near the prop erty line as possible, in which case it is not possible to have the foot ing project in front. In the case in hand, it will be assumed that the footing projects 2.5 ft., i.e., BL = 2.5 ft. The effect of the earth above AF is neglected, which increases the stability of the wall.
We will assume that the section is perfectly rigid, and determine its stability as a unit; and later inquire into its structural integrity.
Stability against Overturning. To find the thrust of the earth against the wall, Cou lomb's formula (equation 4, page 493) will be used. It will be assumed (1) that the surface of the back-filling is level; (2) that the natural slope is 11 to 1, i.e., = 34°; (3) that w = 100 lb. per cu. ft.; (4) that h = 12 ft.; and (5) that the weight of concrete = 150 lb. per cu. ft. Then The weight of the concrete in the stem Flih = 11 X 12 X 150 =2,250 lb. This force acts 10.40 inches = 0.87 ft. from F, or 2.87 feet from A. The weight of the earth vertically above LB = 21 X 12 X 100 = 3,000 lb., and it acts 1.25 ft. to the right of L, or 4.75 ft. from A. The weight of the concrete in the footing = 6 X 1 X 150 = 900 lb., and it acts 3.00 ft. from A. Taking moments about C and dividing by the sum of the weights, it is found that the resultant vertical force acts 3.81 ft. from C.
The tangent of the angle which the resultant makes with the vertical is 2,040 _ 6,150 = 0.33; and the horizontal distance from K to the point in which the resultant pierces the line CD = (4.00 + 1.00) X 0.33 = 1.66 ft.; or the distance from C = 3.81 — 1.66 = 2.15 ft., which is greater than 1 of 6.00, i.e., than 2.00; and hence the resultant cuts the base of the footing within the middle third. There fore, the approximate factor of safety against overturning (equation 13, page 468) is more than 3.
Pressure on the Soil. To determine the pressure on the soil, use equation 22, page 473, • by using the plus sign; and the minimum, that at D, by using the minus sign. The pressure at C = 1,897 lb. per sq. ft., and that at D = 153 lb. per sq. ft. Whether or not this maximum pressure is safe depends upon the character of the soil; but as almost any soil will bear a ton per sq. ft. (see Table 59, page 342), it will be as sumed that it is safe. One advantage of a reinforced-concrete re taining wall is that the wall itself is light, and hence the pressure upon the soil is less than that of a solid wall.