Transactions of the American Society of Civil Engineers, vol. LXVIII, Sept. 1910 | Page 4

Street the extreme position of the back was fixed at the north line, as there were no buildings, except those belonging to the Railroad Company, on the house line at the low points in the rock.
The assumptions made in designing the wall were as follows:
First.--Weight of concrete, 140 lb. per cu. ft.
Second.--Weight of material from the surface of the ground to a depth of 12 ft. (which was shown by tests made in bore-holes to be the elevation of the ground-water surface), 100 lb. per cu. ft.; and angle of repose, 30 degrees. The distance of 12 ft. below the surface was the depth of the inverts of the sewers, which undoubtedly drained the ground above them, thus accounting for the standing of the ground-water in planes practically parallel with the surface.
Third.--Weight of buildings back of wall neglected, as that of the present type will about equal the cellars filled with material at 100 lb. per cu. ft., and if large buildings are erected in the future they will undoubtedly be carried to rock.
Fourth.--Reaction from superstructure, live and dead load, 20,000 lb. per lin. ft. of wall.
Fifth.--Weight of materials below the 12-ft. line, 124 lb. per cu. ft., ascertained as follows: The material was considered as weighing 165 lb. per cu. ft. in the solid, and having 40% of voids filled with water at 62.5 lb. per cu. ft., the resulting weight being (165 �� 60/100) + (62.5 �� 40/100) = 124 lb. per cu. ft.
Various angles of repose were used for this material in the investigation, and it was finally decided that 30�� was the greatest angle that could be expected, whereas the worst condition that could be anticipated was that the sand and water would act separately and give a pressure as follows:
Hydraulic pressure from liquid weighing 62.5 lb. per cu. ft. plus pressure from sand with angle of repose at 30�� and weight as follows:
Weight of 1 cu. ft. in air = 165 �� 60/100 = 99 lb.
Weight of water displaced by 1 cu. ft. = 60/100 �� 62.5 lb. = 37.5 lb.
Weight in water, therefore = 61.5 lb. per cu. ft.
These combined weights, of course, are equal to the weight of the combined material in the previous assumption.
Sixth.--The usual requirement that the resultant of both horizontal and vertical forces should, at all points, fall within the middle third of the wall, or, in other words, that there should be no tension in the concrete.
[Illustration: Plate LIV. Diagram Showing Widths of Base of Retaining Wall Required for Different Batters and Pressures, Pennsylvania Station]
With these assumptions, investigation was made of walls with various batters and differently designed backs. This investigation developed the fact that the reaction from the superstructure was so great that, for economy, both in first cost and space occupied, the batter must be sufficient to cause that reaction to fall within or very close to the middle third. Nothing could have been gained by having that reaction fall back of the front of the middle third, as the wall was required to be stable against the full pressure before the superstructure was erected, and in case it should ever be removed; or, to state the matter more clearly, the reaction from the superstructure was so great in comparison to the weight of the wall, that, if it fell in front of the resultant of all the other forces, the width of base required would be greatly increased to make the wall stable after the superstructure was erected; whereas, if the reaction from the superstructure fell back of the resultant of all the other forces, the width of base could not be correspondingly decreased without danger of the wall being overturned before the superstructure was erected. The least batter that would answer those conditions was found to be 2 in. per ft.
For convenience in designing, and economy in constructing, the steelwork, the faces of the bridge seat and of the backwall were laid parallel to the center line of the Terminal, and in elevation on line parallel to the top of the curb and as near to it as the economical depth of steel would permit, without bringing the finished construction above the plane fixed in the ordinance. As there is a variation of 13 ft. in the elevation of the top of the curb of 31st Street above the top of rail and a variation of 18 ft. in 33d Street, a uniform batter, with the top parallel to the center line, would produce a toe varying in distance from it and from the other constructions. It was decided, therefore, for the sake of appearance, to make the face of the wall (or wall produced) at the top of rail parallel to the center line, and to vary the batter accordingly, using the 2-in. batter