The plans, from the earliest stages, contemplated founding the
retaining wall on the surface of the rock, where of suitable quality,
and afterward excavating the rock in front of the toe of the wall
to sub-grade. This plan was definitely adopted soon after the borings
were completed, on account of the great danger of blasting out large
quantities of rock in timbered trenches close to buildings founded on
soft material, and also to avoid the additional cost and delay that
would have been caused by carrying the walls to sub-grade. The retaining
walls in Seventh Avenue, south of the viaduct, and in Ninth Avenue,
north of the viaduct, were not governed by the same conditions as in the
streets. The dip and quality of the rock at both points required that
the walls be carried to sub-grade, and they are, in fact, face walls;
the Ninth Avenue wall, in particular, having little thrust to sustain,
is very light.
The results aimed at in the design and location of the retaining walls
in 31st and 33d Streets were:
_First._--A perfectly stable wall under all conditions that might
reasonably be expected;
_Second._--As much room as possible at the elevation of the top of
rail;
_Third._--The least necessary interference with adjoining property
during construction; and,
_Fourth._--The most economical wall that would fulfill the other
conditions.
As stated in the paper by Alfred Noble, Past-President, Am. Soc. C. E.,
the third stipulation required the relinquishing of a portion of the
space under these streets granted by the City, but it was finally
decided not to approach the south house line of 31st Street with the
back of the walls nearer than 9 ft., while on 33d 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 previously
mentioned as the minimum. This gave a maximum batter of 3 in. per ft. The
variation is so gradual that it is unnoticeable, and is not sufficient
to introduce any complications in construction.
The wall was designed with a stepped back, primarily to allow the
water-proofing and brick protection to be held in position more readily.
The first step was put at 13 ft. below the surface of the ground. This
gave a vertical back above that point for a 3-in. battered face, and a
slightly battered back for sections having a less batter in front. Below
that point a step was added for each 5 ft. of depth to the elevation
of the top of rail, or to the foundation of the wall if above that
elevation. As the horizontal distance of the heel of the wall, at its
greatest width, from its face at the top of rail would determine the
effective room to be occupied by the wall, it was determined to make the
back vertical below the top of rail and gain the necessary increase in
width below that point by making a heavy batter on the face.
The type of wall having been thus determined, calculations were made
of the width of base required for each ¼-in. batter from 2 to 3 in.,
inclusive, first for a depth of 13 ft. below the top of the curb and
then for each 5 ft. below that elevation, to a depth corresponding to
the distance between the top of the curb and the top of the rail at the
point of greatest variation. These widths of wall were determined for
the two pressures previously decided on, and curves were then plotted
showing the thickness of wall required for each batter calculated and
for each pressure. They are shown on Plate LIV. The curves in broken
lines represent the widths required for saturated material, and the
curves in dotted lines for hydraulic pressure. Mean curves were then
drawn between each broken and its corresponding dotted curve. These are
shown in solid lines, and represent the widths of wall which were used
in the construction. Typical sections of the wall and pipes back of it
are shown on Fig. 3.
The extreme positions of the back of the wall on the two streets having
been determined, as previously stated, the width of base required at
those points fixed the toe of the wall at the top of rail as 254.5 ft.
south of the center line of the Terminal in 31st Street, and 258.5 ft.
north of the center line in 33d Street.
[Illustration:
Fig. 3.
TYPICAL SECTIONS OF RETAINING WALL IN THIRTY-FIRST STREET]