BY J.C. MEEM, M. AM. SOC. C. E.

WITH DISCUSSION BY MESSRS. T. KENNARD THOMSON, CHARLES E. GREGORY,

FRANCIS W. PERRY, E.P. GOODRICH, FRANCIS L. PRUYN, FRANK H. CARTER, AND

J.C. MEEM.

In the final discussion of the writer's paper, "The Bracing of Trenches

and Tunnels, With Practical Formulas for Earth Pressures,"[B] certain

minor experiments were noted in connection with the arching properties

of sand. In the present paper it is proposed to take up again the

question of earth pressures, but in more detail, and to note some

further experiments and deductions therefrom, and also to consider the

resistance and stability of earth as applied to piling and foundations,

and the pressure on and buoyancy of subaqueous structures in soft

ground.

In order to make this paper complete in itself, it will be necessary, in

some instances, to include in substance some of the matter of the former

paper, and indulgence is asked from those readers who may note this

fact.

[Illustration: FIG. 1. SECTIONS OF BOX-FRAME FOR SAND-ARCH

EXPERIMENT]

_Experiment No. 1._--As the sand-box experiments described in the former

paper were on a small scale, exception might be taken to them, and

therefore the writer has made this experiment on a scale sufficiently

large to be much more conclusive. As shown in Fig. 1, wooden abutments,

3 ft. wide, 3 ft. apart, and about 1 ft. high, were built and filled

solidly with sand. Wooden walls, 3 ft. apart and 4 ft. high, were then

built crossing the abutments, and solidly cleated and braced frames were

placed across their ends about 2 ft. back of each abutment. A false

bottom, made to slide freely up and down between the abutments, and

projecting slightly beyond the walls on each side, was then blocked up

snugly to the bottom edges of the sides, thus obtaining a box 3 by 4 by

7 ft., the last dimension not being important. Bolts, 44 in. long, with

long threads, were run up through the false bottom and through 6 by 15

by 2-in. pine washers to nuts on the top. The box was filled with

ordinary coarse sand from the trench, the sand being compacted as

thoroughly as possible. The ends were tightened down on the washers,

which in turn bore on the compacted sand. The blocking was then knocked

out from under the false bottom, and the following was noted:

As soon as the blocking was removed the bottom settled nearly 2 in., as

noted in Fig. 1, Plate XXIV, due to the initial compacting of the sand

under the arching stresses. A measurement was taken from the bottom of

the washers to the top of the false bottom, and it was noted as 41 in.

(Fig. 1). After some three or four hours, as the arch had not been

broken, it was decided to test it under greater loading, and four men

were placed on it, four others standing on the haunches, as shown in

Fig. 2, Plate XXIV. Under this additional loading of about 600 lb. the

bottom settled 2 in. more, or nearly 4 in. in all, due to the further

compression of the sand arch. About an hour after the superimposed load

had been removed, the writer jostled the box with his foot sufficiently

to dislodge some of the exposed sand, when the arch at once collapsed

and the bottom fell to the ground.

Referring to Fig. 2, if, instead of being ordinary sand, the block

comprised within the area, _A U J V X_, had been frozen sand, there can

be no reason to suppose that it would not have sustained itself, forming

a perfect arch, with all material removed below the line, _V E J_, in

fact, the freezing process of tunneling in soft ground is based on this

well-known principle.

[Illustration: FIG. 2.]

[Illustration: FIG. 3.]

If, then, instead of removing the mass, _J E V_, it is allowed to remain

and is supported from the mass above, one must concede to this mass in

its normal state the same arching properties it would have had if

frozen, excepting, of course, that a greater thickness of key should be

allowed, to offset a greater tendency to compression in moist and dry as

against frozen sand, where both are measured in a confined area.

If, in Fig. 2, _E V J_ = [phi] = the angle of repose, and it be assumed

that _A J_, the line bisecting the angle between that of repose and the

perpendicular, measures at its intersection with the middle vertical

(_A_, Fig. 2) the height which is necessary to give a sufficient

thickness of key, it may be concluded that this sand arch will be

self-sustaining. That is, it is assumed that the arching effect is taken

up virtually within the limits of the area, _A N_{1} V E J N A_, thus

relieving the structure below of the stresses due to the weight or

thrust of any of the material above; and that the portion of the

material below _V E J_ is probably dead weight on any structure

underneath, and when sustained from below forms a natural "centering"

for the natural arch above. It is also probably true that the material

in the areas, _X N_{1} A_ and _A N U_, does not add to the arching

strength, more especially in those materials where cohesion may not be

counted on as a factor. This is borne out by the fact that, in the

experiment noted, a well-defined crack developed on the surface of the

sand at about the point _U_{1}_, and extended apparently a considerable

depth, assumed to be at _N_, where the haunch line is intersected by the

slope line from _A_.

[Illustration: PLATE XXIV, FIG. 1.--INITIAL SETTLEMENT IN 3-FT. SAND

ARCH, DUE TO COMPRESSION OF MATERIAL ON REMOVING SUPPORTS FROM

BOTTOM.]

[Illustration: PLATE XXIV, FIG. 2.--FINAL SETTLEMENT OF SAND ARCH,

DUE TO COMPRESSION IN EXCESS LOADING.]

In this experiment the sand was good and sharp, containing some gravel,

and was taken directly from the adjoining excavation. When thrown

loosely in a heap, it assumed an angle of repose of about 45 degrees. It

should be noted that this material when tested was not compacted as

much, nor did it possess the same cohesion, as sand in its normal

undisturbed condition in a bank, and for this reason it is believed that

the depth of key given here is absolutely safe for all except

extraordinary conditions, such as non-homogeneous material and others

which may require special consideration.

Referring again to the area, _A N_{1} V J N A_, Fig. 2, it is probable

that, while self-sustaining, some at least of the lower portion must

derive its initial support from the "centering" below, and the writer

has made the arbitrary assumption that the lower half of it is carried

by the structure while the upper half is entirely independent of it,

and, in making this assumption, he believes he is adding a factor of

safety thereto. The area, then, which is assumed to be carried by an

underground structure the depth of which is sufficient to allow the

lines, _V A_ and _J A_, to intersect below the surface, is the lower

half of _A N_{1} V E J N A_, or its equivalent, _A V E J A_, plus the

area, _V E J_, or _A V J A_, the angle, _A V J_, being

1 [phi]

[alpha] = --- ( 90° - [phi] ) + [phi] = 45° + -------.

2 2

It is not probable that these lines of thrust or pressure transmission,

_A N_, _D K_, etc., will be straight, but, for purposes of calculation,

they will be assumed to be so; also, that they will act along and

parallel to the lines of repose of their natural slope, and that the

thrust of the earth will therefore be measured by the relation between

the radius and the tangent of this angle multiplied by the weight of

material affected. The dead weight on a plane, _V J_, due to the

material above, is, therefore, where

_l_ = span or extreme width of opening = _V J_,

_W_ = weight per cubic foot of material, and

_W_{1}_ = weight per linear foot.

2 × (_l_ / 2) tan. [alpha] × _W_

_W_{1}_ = ---------------------------------- =

2

1 / 1 \

--- _l_ tan. { --- (90° - [phi]) + [phi] } _W_ =

2 \ 2 /

_l_ [phi]

----- tan. ( 45° + ------- ) _W_.

2 2

The application of the above to flat-arched or circular tunnels is very

simple, except that the question of side thrust should be considered

also as a factor. The thrust against the side of a tunnel in dry sand

having a flat angle of repose will necessarily be greater than in very

moist sand or clay, which stands at a much steeper angle, and, for the

same reason, the arch thrust is greater in dryer sand and therefore the

load on a tunnel structure should not be as great, the material being

compact and excluding cohesion as a factor. This can be illustrated by

referring to Fig. 3 in which it is seen that the flatter the position of

the "rakers" keying at _W_{1}_, _W_{2}_, and _W_, the greater will be

the side thrust at _A_, _C_, and _F_. It can also be illustrated by

assuming that the arching material is composed of cubes of polished

marble set one vertically above the other in close columns. There would

then be absolutely no side thrust, but, likewise, no arching properties

would be developed, and an indefinite height would probably be reached

above the tunnel roof before friction enough would be developed to cause

it to relieve the structure of any part of its load. Conversely, if it

be assumed that the superadjacent material is composed of large bowling

balls, interlocking with some degree of regularity, it can be seen that

those above will form themselves into an arch over the "centering" made

up of those supported directly by the roof of the structure, thus

relieving the structure of any load except that due to this "centering."

If, now, the line, _A B_, in Fig. 4, be drawn so as to form with _A C_

the angle, [beta], to be noted later, and it be assumed that it measures

the area of pressure against _A C_, and if the line, _C F_, be drawn,

forming with _C G_, the angle, [alpha], noted above, then _G F_ can be

reduced in some measure by reason of the increase of _G C_ to _C B_,

because the side thrust above the line, _B C_, has slightly diminished

the loading above. The writer makes the arbitrary assumption that this

decrease in _G F_ should equal 20% of _B C_ = _F D_{1}_. If, then, the

line, _B D_{1}_ be drawn, it is conceded that all the material within

the area, _A B D_{1} G C A_, causes direct pressure against or upon the

structure, _G C A_, the vertical lines being the ordinates of pressure

due to weight, and the horizontal lines (qualified by certain ratios)

being the abscissas of pressure due to thrust. An extreme measurement of

this area of pressure is doubtless approximately more nearly a curve

than the straight lines given, and the curve, _A R T I D_{II}_, is

therefore drawn in to give graphically and approximately the safe area

of which any vertical ordinate, multiplied by the weight, gives the

pressure on the roof at that point, and any horizontal line, or

abscissa, divided by the tangent of the angle of repose and multiplied

by the weight per foot, gives the pressure on the side at that point.

[Illustration: FIG. 4.]

The practical conclusion of this whole assumption is that the material

in the area, _F E C B B_{1}_, forms with the equivalent opposite area an

arch reacting against the face, _C B B_{1}_ and that, as heretofore

noted, the lower half (or its equivalent, _B D_{1} G B_) of the weight

of this is assumed to be carried by the structure, the upper half being

self-sustaining, as shown by the line, _B_{III} D_{IV}_ (or, for

absolute safety, the curved line), and therefore, if rods could be run

from sheeting inside the tunnel area to a point outside the line, _F

B_{1}_, as indicated by the lines, 5, 6, 7, 8, 11, 12, 13, etc., that

the internal bracing of this tunnel could be omitted, or that the tunnel

itself would be relieved of all loading, whereas these rods would be

carrying some large portion at least of the weight within the area

circumscribed by the curve, _D_{II} I T G_, and further, that a tunnel

structure of the approximate dimensions shown would carry its maximum

load with the surface of the ground between _D_{IV}_ and _F_, beyond

which point the pressure would remain the same for all depths.

In calculating pressures on circular arches, the arched area should

first be graphically resolved into a rectangular equivalent, as in the

right half of Fig. 4, proceeding subsequently as noted.

The following instances are given as partial evidence that in ordinary

ground, not submerged, the pressures do not exceed in any instance those

found by the above methods, and it is very probable that similar

instances or experiences have been met by every engineer engaged in

soft-ground tunneling:

In building the Bay Ridge tunnel sewer, in 62d and 64th Streets,

Brooklyn, the arch timber bracing shown in Fig. 1, Plate XXVI, was used

for more than 4,000 ft., or for two-thirds of the whole 5,800 ft. called

for in the contract. The external width of opening, measured at the

wall-plate, averaged about 19 ft. for the 14½-ft. circular sewer and 19½

ft. for the 15-ft. sewer. The arch timber segments in the cross-section

were 10 by 12-in. North Carolina pine of good grade, with 2 in. off the

butt for a bearing to take up the thrust. They were set 5 ft. apart on

centers, and rested on 6 by 12-in. wall-plates of the same material as

noted above. The ultimate strength of this material, across the grain,

when dry and in good condition, as given by the United States Forestry

Department tests is about 1,000 lb. in compression. Some tests[C] made

in 1907 by Mr. E.F. Sherman for the Charles River Dam in Boston, Mass.,

show that in yellow pine, which had been water-soaked for two years,

checks began to open at from 388 to 581 lb. per sq. in., and that yields

of ¼ in. were noted at from 600 to 1,000 lb. As the tunnel wall-plates

described in this paper were subject to occasional saturation, and

always to a moist atmosphere, they could never have been considered as

equal to dry material. Had the full loading shown by the foregoing

come on these wall-plates, they would have been subjected to a stress of

about 25 tons each, or nearly one-half of their ultimate strength. In

only one or two instances, covering stretches of 100 ft. in one case and

200 ft. in another, where there were large areas of quicksand sufficient

to cause semi-aqueous pressure, or pockets of the same material causing

eccentric loading, did these wall-plates show any signs of heavy

pressure, and in many instances they were in such good condition that

they could be taken out and used a second and a third time. Two

especially interesting instances came under the writer's observation: In

one case, due to a collapse of the internal bracing, the load of an

entire section, 25 ft. long and 19 ft. wide, was carried for several

hours on ribs spaced 5 ft. apart. The minimum cross-section of these

ribs was 73 sq. in., and they were under a stress, as noted above, of

50,000 lb., or nearly up to the actual limit of strength of the

wall-plate where the rib bore on it. When these wall-plates were

examined, after replacing the internal bracing, they did not appear to

have been under any unusual stress.

[Illustration: PLATE XXV, FIG. 1.--NORMAL SLOPES AND STRATA

OF NEWLY EXCAVATED BANKS.]

[Illustration: PLATE XXV, FIG. 2.--NORMAL SLOPES AND STRATA

OF NEWLY EXCAVATED BANKS.]

In another instance, for a distance of more than 700 ft., the sub-grade

of the sewer was 4 ft. below the level of the water in sharp sand. In

excavating for "bottoms" the water had to be pumped at the rate of more

than 300 gal. per min., and it was necessary to close-sheet a trench

between the wall-plates in which to place a section of "bottom." In

spite of the utmost care, some ground was necessarily lost, and this was

shown by the slight subsidence of the wall-plates and a loosening up of

the wedges in the supports bearing on the arch timbers. During this

operation of "bottoming," two men on each side were constantly employed

in tightening up wedges and shims above the arch timbers. It is

impossible to explain the fact that these timbers slackened (without

proportionate roof settlement) by any other theory than that the arching

was so nearly perfect that it relieved the bracing of a large part of

the load, the ordinary loose material being held in place by the arching

or wedging together of the 2-in. by 3-ft. sheeting boards in the roof,

arranged in the form of a segmental arch. The material above this roof

was coarse, sharp sand, through which it had been difficult to tunnel

without losing ground, and it had admitted water freely after each rain

until the drainage of a neighboring pond had been completed, the men

never being willing to resume work until the influx of water had

stopped.

The foregoing applies only to material ordinarily found under ground not

subaqueous, or which cannot be classed as aqueous or semi-aqueous

material. These conditions will be noted later.

[Illustration: FIG. 5.]

[Illustration: FIG. 6.]

The writer will take up next the question of pressures against the faces

of sheeted trenches or retaining walls, in material of the same

character as noted above. Referring to Fig. 2, it is not reasonable to

suppose that having passed the line, _R F J_, the character of the

stresses due to the thrust of the material will change, if bracing

should be substituted for the material in the area, _W V J R_, or if, as

in Fig. 3, canvas is rolled down along the lines, _E G_ and _A O_, and

if, as this section is excavated between the canvas faces, temporary

struts are erected, there is no reason to believe that with properly

adjusted weights at _W_ or _W_{2}_, an exact equilibrium of forces and

conditions cannot be obtained. Or, again, if, as in Fig. 5, the face,

_P Q_, is sheeted and rodded back to the surface, keying the rods taut,

there is undoubtedly a stable condition and one which could not fail in

theory or practice, nor can anyone, looking at Fig. 5, doubt that the

top timbers are stressed more heavily than those at the bottom. The

assumption is that the tendency of the material to slide toward the toe

causes it to wedge itself between the face of the sheeting on the one

hand and some plane between the sheeting and the plane of repose on the

other, and that the resistance to this tendency will cause an arching

thrust to be developed along or parallel to the lines, _A N_, _B M_,

etc., Fig. 2, which are assumed to be the lines of repose, or curves

approximating thereto. As the thrust is greatest in that material

directly at the face, _A O_, Fig. 6, and is nothing at the plane of

repose, _C O_, it may be assumed arbitrarily that the line, _B O_,

bisecting this angle divides this area into two, in one of which the

weight resolves itself wholly into thrust, the other being an area of no

thrust, or wholly of weight bearing on the plane of repose. Calling this

line, _B O_, the haunch line, the thrust in the area, _A O B_, is

measured by its weight divided by the tangent of the angle,

_P Q R_ = [phi], which is the angle of repose; that is, the thrust at

any given point, _R_ = _R Q_ ÷ tan. [phi].

The writer suggests that, in those materials which have steeper angles

of repose than 45°, the area of pressure may be calculated as above, the

thrust being computed, however, as for an angle of 45 degrees.

In calculating the bending moment against a wall or bracing, there is

the weight of the mass multiplied by the distance of its center of

gravity vertically above the toe, or, approximately:

2

Area, _A O B_ × weight per unit × --- height,

3

where _h_ = height,

_W_ = weight per cubic foot of material = 90 lb.,

90° - [phi]

and [beta] = -------------

2

_P_ = pressure per linear foot (vertically),

_h_ 2

then _P_ = _h_ × ----- (tan. [beta]) × _W_ × --- _h_ =

2 3

1

--- _h^{3}_ _W_ tan. [beta].

3

When the angle of repose, [phi], is less than 45°, this result must be

reduced by dividing by tan. [phi]; that is,

1

_h_ = --- _h^{3}_ tan. [beta] ÷ tan. [phi].

3

Figs. 1 and 2, Plate XXV, show recently excavated banks of gravel and

sand, which, standing at a general angle of 45°, were in process of

"working," that is, there was continual slipping down of particles of

the sand, and it may be well to note that in time, under exposure to

weather conditions, these banks would finally assume a slope of about 33

degrees. They are typical, however, as showing the normal slope of

freshly excavated sandy material, and a slope which may be used in

ordinary calculations. The steps seen in Plate XXV show the different

characteristics of ground in close proximity. In Fig. 2, Plate XXVI,[D]

may be seen a typical bank of gravel and sand; it shows the well-defined

slope of sand adjacent to and in connection with the cohesive properties

of gravel.

The next points to be considered are the more difficult problems

concerning subaqueous or saturated earths. The writer has made some

experiments which appear to be conclusive, showing that, except in pure

quicksand or wholly aqueous material, as described later, the earth and

water pressures act independently of each other.

For a better understanding of the scope and purpose of this paper, the

writer divides supersaturated or subaqueous materials into three

classes:

_Class A._--Firm materials, such as coarse and fine gravels, gravel and

sands mixed, coarse sands, and fine sands in which there is not a large

proportion of fine material, such as loam, clay, or pure quicksand.

_Class B._--Semi-aqueous materials, such as fine sands in which there is

a large proportion of clay, etc., pure clays, silts, peats, etc.

_Class C._--Aqueous materials, such as pure quicksands, in which the

solid matter is so finely divided that it is amorphous and virtually

held in suspension, oils, quicksilver, etc.

Here it may be stated that the term, "quicksand," is so illusive that a

true definition of it is badly needed. Many engineers call quicksand any

sand which flows under the influence of water in motion. The writer

believes the term should be applied only to material so "soupy" that its

properties are practically the same as water under static conditions, it

being understood that any material may be unstable under the influence

of water at sufficiently high velocities, and that it is with a static

condition, or one approximately so, that this paper deals.

A clear understanding of the firm materials noted in Class A will lead

to a better solution of problems dealing with those under Class B, as it

is to this Class A that the experiments largely relate.

The experiments noted below were made with varying material, though the

principal type used was a fine sand, under the conditions in which it is

ordinarily found in excavations, with less than 40% voids and less than

10% of very fine material.

[Illustration: FIG. 7.]

_Experiment No. 2._--The first of these experiments, which in this

series will be called No. 2, was simple, and was made in order to show

that this material does not flow readily under ordinary conditions, when

not coupled with the discharge of water under high velocity. A bucket 12

in. in diameter, containing another bucket 9 in. in diameter, was used.

A 6 by 6-in. hole was cut in the bottom of the inner bucket. About 3 in.

of sand was first placed in the bottom of the larger bucket and it was

partly filled with water. The inside bucket was then given a false

bottom and partly filled with wet sand, resting on the sand in the

larger bucket. Both were filled with water, and the weight, _W_, Fig. 7,

on the arm was shifted until it balanced the weight of the inside bucket

in the water, the distance of the weight, _W_, from the pivot being

noted. The false bottom was then removed and the inside bucket, resting

on the sand in the larger one, was partly filled with sand and both were

filled with water, the conditions at the point of weighing being exactly

the same, except that the false bottom was removed, leaving the sand in

contact through the 6 by 6-in. opening. It is readily seen that, if the

sand had possessed the aqueous properties sometimes attributed to sand

under water, that in the inside bucket would have flowed out through the

square hole in the bottom, allowing it to be lifted by any weight in

excess of the actual weight of the bucket, less its buoyancy, as would

be the case if it contained only water instead of sand and water. It was

found, however, that the weight, resting at a distance of more than

nine-tenths of the original distance from the pivot, would not raise the

inside bucket. On lifting this inside bucket bodily, however, the water

at once forced the sand out through the bottom, leaving a hole almost

exactly the shape and size of the bottom orifice, as shown in Fig. 1,

Plate XXVII. It should be stated that, in each case, the sand was put in

in small handfuls and thoroughly mixed with water, but not packed, and

allowed to stand for some time before the experiments were tried, to

insure the compactness of ordinary conditions. It is seen from Fig. 1,

Plate XXVII, that the sand was stable enough to allow the bucket to be

put on its side for the moment of being photographed, although it had

been pulled out of the water a little less than 3 min.

[Illustration: PLATE XXVI, FIG. 1.--TYPES OF ARCH TIMBERS USED IN

BAY RIDGE TUNNEL SEWER.]

[Illustration: PLATE XXVI, FIG. 2.--NORMAL SLOPE OF LOOSE SAND,

GRAVEL, AND CEMENTED GRAVEL, IN CLOSE PROXIMITY.]

_Experiment No. 3._--In order to show that the arching properties of

sand are not destroyed under subaqueous conditions, a small sand-box,

having a capacity of about 1 cu. ft., and similar to that described in

Experiment No. 1, was made. The bottom was cut out, with the exception

of a ¾-in. projection on two sides, and a false bottom was placed below

and outside of the original bottom, with bolts running through it,

keying to washers on top of the sand, with which the box was partly

filled. One side of the box contained a glass front, in order that

conditions of saturation could be observed. The box of sand was then

filled with water and, after saturation had been completed and the nuts

and washers had been tightened down, the box was lifted off the floor.

There was found to be no tendency whatever for the bottom to fall away,

showing conclusively that the arching properties had not been destroyed

by the saturation of the sand.

The next three experiments were intended to show the relative pressure

over any given area in contact with the water in the one case or sand

and water in the other.

[Illustration: FIG. 8.]

_Experiment No. 4._--The apparatus for this experiment consisted of a

3-in. pipe about 4-in. long and connected with a ¾-in. goose-neck pipe

17 in. high above the top of the bowl shown in Fig. 8 and in Fig. 2,

Plate XXVII. A loose rubber valve was intended to be seated on the upper

face of the machined edge of the bowl and weighted down sufficiently to

balance it against a head of water corresponding to the 17-in. head in

the goose-neck. The bowl was then to be filled with sand and the

difference, if any, noted between the weight required to hold the

flap-valve down under the same head of water flowing through the sand.

The results of this experiment were not conclusive, owing to the

difficulty of making contact over the whole area of the sand and the rim

of the bowl at the same time. At times, for instance, less than 1 lb.

would hold back the water indefinitely, while, again, 2 or 3 lb. would

be required as opposed to the 4½ lb. approximate pressure required to

hold down the clear water. Again, at times the water would not flow

through the neck at all, even after several hours, and after increasing

the head by attaching a longer rubber tube thereto. In view of these

conditions, this experiment would not be noted here, except that it

unexpectedly developed one interesting fact. In order to insure against

a stoppage of water, as above referred to, gravel was first put into the

bottom of the bowl and the flap-valve was then rubbed down and held

tightly while the pipe was filled. On being released, the pressure of

water invariably forced out the whole body of sand, as shown in Fig. 2,

Plate XXVII. Care was taken to see that the sand was saturated in each

case, and the experiment was repeated numberless times, and invariably

with the same result. The sand contained about 40% of voids. The

deduction from this experiment is that the pressure of water is against

rather than through sand and that any excess of voids occurring adjacent

to a face against which there is pressure of water will be filled with

sand, excepting in so far, of course, as the normal existing voids allow

the pressure of the water to be transmitted through them.

[Illustration: PLATE XXVII, FIG. 1.--EXPERIMENT SHOWING PROPERTIES

OF SAND.]

[Illustration: PLATE XXVII, FIG. 2.--SAND PUSHED UP FROM BOWL BY

WATER PRESSURE THROUGH GOOSE-NECK.]

If, then, the covering of sand over a structure is sufficiently heavy to

allow arching action to be set up, the structure against which the

pressure is applied must be relieved of much of the pressure of water

against the area of sand not constituted as voids acting outside of the

arching area. This is confirmed by the two following experiments:

_Experiment No. 5._--The same apparatus was used here as in Experiment

No. 2, Fig. 7, except that the inside bucket had a solid bottom. The

inside and outside buckets were filled with water and the point was

noted at which the weight would balance the inside bucket at a point

some 3 in. off the bottom of the outside bucket. This point was

measured, and the bottom of the larger bucket was covered over with sand

so that in setting solidly in the sand the inside bucket would occupy

the same relative position as it did in the water. The same weight was

then applied and would not begin to lift the inner bucket. For instance,

in the first part of the experiment the weight stood at 12 in. from the

pivot, while in the next step the weight, standing at the end of the

bar, had no effect, and considerable external pressure had to be exerted

before the bucket could be lifted. Immediately after it was relieved,

however, the weight at 12 in. would hold it clear of the sand. No

attempt was made to work the bucket into the sand; the sand was leveled

up and the bucket was seated on it, turned once or twice to insure

contact, and then allowed to stand for some time before making the

experiment. No attempt was made to establish the relationship between

sands of varying voids, the general fact only being established, by a

sufficient number of experiments, that the weight required to lift the

bucket was more than double in sand having 40% of voids than that

required to lift the bucket in water only.

[Illustration: FIG. 9.]

_Experiment No. 6._--The apparatus for this experiment consisted

essentially of a hydraulic chamber about 8 in. in diameter and 1 ft.

high, the top being removable and containing a collar with suitable

packing, through which a 2½-in. piston moved freely up and down, the

whole being similar to the cylinder and piston of a large hydraulic

jack, as shown in Fig. 1, Plate XXVIII. Just below the collar and above

the chamber there was a ½-in. inlet leading to a copper pipe and thence

to a high-pressure pump. Attached to this there was a gauge to show the

pressure obtained in the chamber, all as shown in Fig. 9. The purpose of

the apparatus was to test the difference in pressure on any object

submerged in clear water and on the same object buried in the sand under

water. It is readily seen that, if pressure be applied to the water in

this chamber, the amount of pressure (as measured by the gauge)

necessary to lift the piston will be that due to the weight of the

piston, less its displacement, plus the friction of the piston in the

collar.

[Illustration: PLATE XXVIII, FIG. 1.--APPARATUS FOR MEASURING LOSS

OF PRESSURE IN SUBAQUEOUS MATERIALS.]

[Illustration: PLATE XXVIII, FIG. 2.--RAISING ROOF OF BATTERY TUBES,

IN BROOKLYN, BY "BLEEDING" SAND THROUGH DISPLACED PLATES.]

Now, if for any reason the bottom area of the piston against which the

water pressure acts be reduced, it will necessarily require a

proportionate amount of increase in the pressure to lift this piston.

If, therefore, it is found that 10 lb., for illustration, be required to

lift the piston when plunged in clear water, and 20 lb. be required to

lift it when buried in sand, it can be assumed at once that the area of

the piston has been reduced 50% by being buried in the sand, eliminating

the question of the friction of the sand itself around the piston. In

order to determine what this friction might be, the writer arranged a

table standing on legs above the bottom of the chamber, allowing the

piston to move freely through a hole in its center. Through this table

pipes were entered (as shown in part of Fig. 9). The whole was then

placed in the chamber with the piston in place, and the area above was

filled with sand and water. It is thus seen that, the end of the piston

being free and in clear water, the difference, if any, between the

pressure required to lift the piston when in clear water alone and in

the case thus noted, where it was surrounded by sand, would measure the

friction of the sand on the piston. After several trials of this,

however, it was clearly seen that the friction was too slight to be

noted accurately by a gauge registering single pounds, that is, with a

piston in contact with 6 in. of sand vertically, a friction of 25 lb.

per sq. ft. would only require an increase of 1.8 lb. on the gauge. It

is therefore assumed that the friction on so small a piston in sand need

not be considered as a material factor in the experiments made.

The piston was plunged into clear water, and it was found that the

pressure required to lift it was about 4 lb. The cap was then taken off,

a depth of about 2 in. of sand was placed in the bottom of the chamber,

and then the piston was set in place and surrounded by sand to a depth

of some 6 in., water being added so that the sand was completely

saturated. This was allowed to stand until it had regained the stability

of ordinary sand in place, whereupon the cap with the collar bearing was

set in place over the piston, the machine was coupled up, and the pump

was started. A series of four experiments, extending over a period of

two or three days, gave the following results:

_Test 1._--The piston began to move at a pressure of 25 lb. The pressure

gradually dropped to 7½ lb., at which point, apparently, it came out of

the sand, and continued at 7½ lb. during the remainder of the test.

_Test 2._--The piston was plunged back into the sand, without removing

the cap, and allowed to stand for about 2 hours. No attempt was made to

pack the sand or to see its condition around the piston, it being

presumed, however, that it had reasonable time to get a fair amount of

set. At slightly above 20 lb. the piston began to move, and as soon as a

pocket of water accumulated behind the piston the pressure immediately

dropped to 9 lb. and continued at this point until it came out of the

sand.

_Test 3._--The piston was plunged into the sand and hammered down

without waiting for the sand to come to a definite set. In this case the

initial pressure shown by the gauge was 17½ lb., which immediately

dropped to 8 lb. as soon as the piston had moved sufficiently far to

allow water to accumulate below it.

_Test 4._--The cap was again removed, the piston set up in place, the

sand compacted around it in approximately the same condition it would

have had if the sand had been in place underground; the cap was then set

in place and, after an hour, the pump was started. The pressure

registered was 25 lb. and extended over a period of several seconds

before there was any movement in the piston. The piston responded

finally without any increase of pressure, and, after lifting an inch or

two, the pressure gradually dropped to 10 lb., where it remained until

the piston came out of the sand.

The sum and average of these tests shows a relation of 22 lb. for the

piston in sand to about 8½ lb. as soon as the volume of water had

accumulated below it, which would correspond very closely to a sand

containing 40% of voids, which was the characteristic of the sand used

in this experiment.

The conclusions from this experiment appear to be absolutely final in

illustrating the pressure due to water on a tunnel buried in sand,

either on the arch above or on the sides or bottom, as well as the

buoyant effect upon the tunnel bottom under the same conditions.

While the apparatus would have to be designed and built on a much larger

scale in order to measure accurately the pressures due to sands and

earths of varying characteristics, it appears to be conclusive in

showing the principle, and near enough to the theoretical value to be

taken for practical purposes in designing structures against water

pressures when buried in sand or earth.

It should be carefully noted that the friction of the water through

sand, which is always a large factor in subaqueous construction, is

virtually eliminated here, as the water pressure has to be transmitted

only some 6 or 8 in. to actuate the base of the piston, whereas in a

tunnel only half submerged this distance might be as many feet, and

would be a considerable factor.

It should be noted also that although the area subject to pressure is

diminished, the pressure on the area remaining corresponds to the full

hydrostatic head, as would be shown by the pressure on an air gauge

required to hold back the water, except, of course, as it may be

diminished more or less by friction.

The writer understands that experiments of a similar nature and with

similar apparatus have been tried on clays and peats with results

considerably higher; that is, in one case, there was a pressure of 40

lb. before the piston started to move.

The following is given, in part, as an analysis and explanation of the

above experiments and notes:

It is well known that if lead be placed in a hydraulic press and

subjected to a sufficient pressure it will exhibit properties somewhat

similar to soft clay or quicksand under pressure. It will flow out of an

orifice or more than one orifice at the same pressure. This is due to

the fact that practically voids do not exist and that the pressure is so

great, compared with the molecular cohesion, that the latter is

virtually nullified. It is also theoretically true that solid stone

under infinitely high pressure may be liquefied. If in the cylinder of a

hydraulic press there be put a certain quantity of cobblestones, leaving

a clearance between the top of the stone and the piston, and if this

space, together with the voids, be filled with water and subjected to a

great pressure, the sides or the walls of the cylinder are acted on by

two pressures, one almost negligible, where they are in contact with the

stone, restraining the tendency of the stone to roll or slide outward,

and the other due to the pressure of the water over the area against

which there is no contact of stone. That this area of contact should be

deducted from the pressure area can be clearly shown by assuming another

cylinder with cross-sticks jammed into it, as shown in Fig. 10. A glance

at this figure will show that there is no aqueous pressure on the walls

of the cylinder with which the ends of the sticks come in contact and

the loss of the pressure against the walls due to this is equal to the

least sectional area of the stick or tube either at the point of contact

or intermediate thereto.

Following this reasoning, in Fig. 11 it is found that an equivalent area

may be deducted covering the least area of continuous contact of the

cobblestones, as shown along the dotted lines in the right half of the

figure. Returning, if, when the pressure is applied, an orifice be made

in the cylinder, the water will at once flow out under pressure,

allowing the piston to come in contact with the cobblestones. If the

flow of the water were controlled, so as to stop it at the point where

the stone and water are both under direct pressure, it would be found

that the pressures were totally independent of each other. The aqueous

pressure, for instance, would be equal at every point, while the

pressure on the stone would be through and along the lines of contact.

If this contact was reasonably well made and covered 40% of the area,

one would expect the stone, independently of the water, to stand 40% of

the pressure which a full area of solid stone would stand. If this

pressure should be enormously increased after excluding the water, it

would finally result in crushing the stone into a solid mass; and if the

pressure should be increased indefinitely, some theoretical point would

be reached, as above noted, where the stone would eventually be

liquefied and would assume liquid properties.

[Illustration: FIG. 10.]

[Illustration: FIG. 11.]

The same general reasoning applies to pure sand, sand being in effect

cobblestones in miniature. In pressing the piston down on dry sand it

will be displaced into every existing abnormal void, but will be

displaced into these voids rather than pressed into them, in the true

definition of the word, and while it would flow out of an orifice in the

sides or bottom, allowing the piston to be forced down as in a

sand-jack, it would not flow out of an orifice in the top of the piston,

except under pressures so abnormally high as to make the mass

theoretically aqueous. If the positions of cylinder and piston be

reversed, the piston pointing vertically upward and the sand "bled" into

an orifice in or through it, the void caused by the outflow of this sand

would be filled by sand displaced by the piston pressing upward rather

than by sand from above.

It was the knowledge of this principle which enabled the contractors to

jack up successfully the roof of a long section of the cast-iron lined

tubes under Joralemon Street in Brooklyn, in connection with the

reconstruction of the Battery tubes at that point, the method of

operation, as partly shown in Fig. 2, Plate XXVIII, being to cut through

a section of the roof, 4 by 10 ft. in area, through which holes were

drilled and through which again the sand was "bled," heavy pressure

being applied from below through the medium of hydraulic jacks. By a

careful manipulation of both these operations, sections of the roof of

the above dimensions were eventually raised the required height of 30

in. and permanently braced there in a single shift.

If water in excess be put into a cylinder containing sand, and pressure

be applied thereto, the water, if allowed to flow out of an orifice,

will carry with it a certain quantity of sand, according to the

velocity, and the observation of this might easily give rise to the

erroneous impression that the sand, as well as the water, was flowing

out under pressure, and, as heretofore stated, has caused many engineers

and contractors to apply the term "quicksand" to any sand flowing

through an orifice with water.

Sand in its natural bed always contains some fine material, and where

this is largely less than the percentage of voids, it has no material

effect on the pressure exerted by the sand with or without water, as

above noted. If, however, this fine material be largely in excess of the

voids, it allows greater initial compression to take place when dry, and

allows to be set up a certain amount of hydraulic action when saturated.

If the base of the material be sand and the fill be so-called quicksand

in excess of the voids, pressure will cause the quicksand to set up

hydraulic action, and the action of the piston will appear to be similar

to that of a piston acting on purely aqueous material.

Just here the writer desires to protest against considering semi-aqueous

masses, such as soupy sands, soft concrete, etc., as exerting

hydrostatic pressure due to their weight in bulk, instead of to the

specific gravity of the basic liquid. For instance, resorting again to

the illustration of cubes and spheres, it may be assumed that a cubical

receptacle has been partly filled with small cubes of polished marble,

piled vertically in columns. When this receptacle is filled with liquid

around the piles of cubes there will be no pressure on the sides except

that due to the hydrostatic pressure of the water at 62½ lb. The bottom,

however, will resist a combined pressure due to the water and the weight

of the cubes. Again, assume that the receptacle is filled with small

spheres, such as marbles, and that water is then poured in. The pressure

due to the weight of the solids on the bottom is relieved by the loss in

weight of the marbles due to the water, and also to the tendency of the

marbles to arch over the bottom, and while the pressure on the sides is

increased by this amount of thrust, the aqueous pressure is still that

of a liquid at 62½ lb., and it is inconceivable that some engineers, in

calculating the thrust of aqueous masses, speak of it as a liquid

weighing, say, 120 or 150 lb. per cu. ft.; as well might they expect to

anchor spherical copper floats in front of a bulkhead and expect the

hydrostatic pressure against this bulkhead to be diminished because the

actual volume and weight of the water directly in front of the bulkhead

has been diminished. Those who have had experience in tying narrow deep

forms for concrete with small wires or bolts and quickly filling them

with liquid concrete, must realize that no such pressures are ever

developed as would correspond to liquids of 150 lb. per cu. ft. If the

solid material in any liquid is agitated, so that it is virtually in

suspension, it cannot add to the pressure, and if allowed to subside it

acts as a solid, independently of the water contained with it, although

the water may change somewhat the properties of the material, by

increasing or changing its cohesion, angle of repose, etc. That is, in

substance, those particles which rest solidly on the bottom and are in

contact to the top of the solid material, do not derive any buoyancy

from the water, while those particles not in contact with the bottom

directly or through other particles, lose just so much weight through

buoyancy. If, then, the vertical depth of the earthy particles or sand

above the bottom is so small that the arching effect against the sides

is negligible, the full weight of the particles in contact, directly or

vicariously, with the bottom acts as pressure on the bottom, while the

full pressure of the water acts through the voids or on them, or is

transmitted through material in contact with the bottom.

Referring now to materials such as clays, peats, and other soft or

plastic materials, it is idle to assume that these do not possess

pressure-resisting and arching properties. For instance, a soft clay

arch of larger dimensions, under the condition described early in this

paper, would undoubtedly stand if the rods supporting the intrados of

the arch were keyed back to washers covering a sufficiently large area.

The fact that compressed air can be used at all in tunnel work is

evidence that semi-aqueous materials have arching properties, and the

fact that "blows" usually occur in light cover is further evidence of

it.

When air pressure is used to hold back the water in faces of large area,

bracing has to be resorted to. This again shows that while full

hydrostatic pressure is required to hold back the water, the pressure of

the earth is in a measure independent of it.

In a peaty or boggy material there is a condition somewhat different,

but sufficiently allied to the soft clayey or soupy sands to place it

under the same head in ordinary practice. It is undoubtedly true that

piles can be driven to an indefinite depth in this material, and it is

also true that the action of the pile is to displace rather than

compress, as shown by the fact of driving portions of the tunnels under

the North River for long distances without opening the doors of the

shield or removing any of the material. The case of filling in bogs or

marshes, causing them to sink at the point of filling and rise

elsewhere, is readily explained by the fact that the water is confined

in the interstices of the material, admitting of displacement but no

compression.

The application of the above to pressures over tunnels in materials of

Class A is that the sand or solid matter is virtually assumed to be a

series of columns with their bases in such intimate contact with the

tunnel roof that water cannot exert pressure on the tunnel or buoyancy

on the sand at the point of contact, and that if these columns are

sufficiently deep to have their upper portions wholly or partly carried

by the arching or wedging action, the pressure of any water on their

surfaces is not transferred to the tunnel, and the only aqueous pressure

is that which acts on the tunnel between the assumed columns or through

the voids.

Let _l_ = exterior width of tunnel,

_d_ = depth of cover, as:

_D_{W}_ = depth, water to roof,

_D_{E}_ = " earth to roof,

_D_{X}_ = " of cover of earth necessary to arching stability,

that is:

_l_ / 90° - [phi] \

_D_{X}_ = ----- ( tan. { ------------- } + [phi] ) =

2 \ 2 /

_l_ [phi]

----- tan. (45° + ------- ),

2 2

where [phi] = angle of repose,

and _D_{W}_ > _D_{E}_ > _D_{X}_.

Then the pressure on any square foot of roof, as _V_{P}_ as at the base of

any vertical ordinate, as 9 in Fig. 2, = _V_{O}_,

_W_{E}_ = weight per cubic foot of earth (90 lb.),

_W_{W}_ = " " " " " water (62½ lb.), we have

_V_{P}_ = _V_{O}_ × _W_{E}_ + _D_{W}_ × _W_{W}_ × 0.40 =

1

_V_{O}_ × 90 + _D_{W}_ × 62--- × 0.4 = _V_{O}_ 90 + _D_{W}_ × 25.

2

And for horizontal pressure:

_P_{h}_ = the horizontal pressure at any abscissa (10), Fig. 2, = _A_{10}_

at depth of water _D_{W1}_ is

_A_{10}_ × 90 1

_P_{h}_ = --------------- + _D_{W1}_ × 62--- × 0.4 =

tan. [phi] 2

_A_{10}_ × 90

--------------- + _D_{W1}_ × 25.

tan. [phi]

The only question of serious doubt is at just what depth the sand is

incapable of arching itself, but, for purposes of safety, the writer has

put this at the point, _F_, as noted above, = _D_{X}_, although he

believes that experiments on a large scale would show it to be nearer

0.67·_D_{X}_, above which the placing of additional back-fill will

lighten the load on the structure.

We have, then, for _D_{E}_ < _D_{X}_, the weight of the total prism of

the earth plus the water in the voids, plus the added pressure of the

water above the earth prism, that is:

The pressure per square foot at the base of any vertical ordinate =

_V_{P}_

1

_V_{P}_ = _D_{E}_ × 90 + _D_{E}_ × 62--- × 0.40 +

2

1

( _D_{W}_ - _D_{E}_ ) × 62---.

2

To those who may contend that water acting through so shallow a prism of

earth would exert full pressure over the full area of the tunnel, it may

be stated that the water cannot maintain pressure over the whole area

without likewise giving buoyancy to the sand previously assumed to be in

columns, in which case there is the total weight of the water plus the

weight of the prism of earth, less its buoyancy in water, that is

1 1

_V_{P}_ = _D_{W}_ × 62--- + _D_{E}_ × ( 90 - 62--- ),

2 2

which, by comparison with the former method, would appear to be less

safe in its reasoning.

[Illustration: COMBINED EARTH AND WATER PRESSURES. FIG. 12.]

Next is the question of pressure against a wall or braced trench for

materials under Class A. The pressure of sand is first calculated

independently, as shown in Fig. 6. Reducing this to a basis of 100 lb.

for each division of the scale measured horizontally, as shown, gives

the line, _B O_, Fig. 12, measuring the outside limit of pressure due to

the earth, the horizontal distance at any point between this line and

the vertical face equalling the pressure against that face divided by

the tangent of the angle of repose, which in this case is assumed to be

45°, equalling unity. If the water pressure line, _C F_, is drawn, it

shows the relative pressure of the water. In order to reduce this to the

scale of 100 lb. horizontal measurement, the line, _C E_, is drawn,

representing the water pressure to scale, that is, so that each

horizontal measurement of the scale gives the pressure on the face at

that point; and, allowing 50% for voids, halving this area gives the

line, _C D_, between which and the vertical face any horizontal line

measures the water pressure. Extending these pressure areas where they

overlap gives the line, _B D_, which represents the total pressure

against the face, measured horizontally.

Next, as to the question of buoyancy in Class A materials. If a

submerged structure rests firmly on a bottom of more or less firm sand,

its buoyancy, as indicated by the experiments, will only be a percentage

of its buoyancy in pure water, corresponding to the voids in the sand.

In practice, however, an attempt to show this condition will fail, owing

to the fact that in such a structure the water will almost immediately

work under the edge and bottom, and cause the structure to rise, and the

test can only be made by measuring the difference in uplift in a

heavier-than-water structure, as shown in Experiment No. 5. For, if a

structure lighter than the displaced water be buried in sand

sufficiently deep to insure it against the influx of large volumes of

water below, it will not rise. That this is not due entirely to the

friction of the solid material on the sides has been demonstrated by the

observation of subaqueous structures, which always tend to subside

rather than to lift during or following disturbance of the surrounding

earth.

The following is quoted from the paper by Charles M. Jacobs, M. Am. Soc.

C. E., on the North River Division of the Pennsylvania Railroad

Tunnels:[E]

"There was considerable subsidence in the tunnels during

construction and lining, amounting to an average of 0.34 ft.

between the bulkhead lines. This settlement has been constantly

decreasing since construction, and appears to have been due almost

entirely to the disturbances of the surrounding materials during

construction. The silt weighs about 100 lb. per cu. ft. * * * and

contains about 38% of water. It was found that whenever this

material was disturbed outside the tunnels a displacement of the

tunnels followed."

This in substance confirms observations made in the Battery tubes that

subsidence of the structure followed disturbance of the outside

material, although theoretically the tubes were buoyant in the aqueous

material.

The writer would urge, however, that, in all cases of submerged

structures only partially buried in solid material, excess weighting be

used to cover the contingencies of vibration, oscillation, etc., to

which such structures may be subjected and which may ultimately allow

leads of water to work their way underneath.

On the other hand, he urges that, in cases of floor areas of deeply

submerged structures, such as tunnels or cellars, the pressure to be

resisted should be assumed to be only slightly in excess of that

corresponding to the pressure due to the water through the voids.

The question of pressure, etc., in Class B, or semi-aqueous materials

will be considered next. Of these materials, as already shown, there are

two types: (_a_) sand in which the so-called quicksand is largely in

excess of any normal voids, and (_b_) plastic and viscous materials. The

writer believes that these materials should be treated as mixtures of

solid and watery particles, in the first of which the quicksand, or

aqueous portion, being virtually in suspension, may be treated as water,

and it must be concluded that the action here will be similar to that of

sand and pure water, giving a larger value to the properties of water

than actually exists. If, for instance, it should be found that such a

mixture contained 40% of pure water, the writer would estimate its

pressure on or against a structure as (_a_) that of a moist sand

standing at a steep angle of repose, and (_b_) that of clear water, an

allowance of 60% of the total volume being assumed, and the sum of these

two results giving the total pressure. Until more definite data can be

obtained by experiments on a larger scale, this assumed value of 60% of

the total volume for the aqueous portion may be taken for all conditions

of semi-aqueous materials, except, of course, where the solid and

aqueous particles may be clearly defined, the pressures being computed

as described in the preceding pages.

As to the question of pure quicksand (if such there be) and other

aqueous materials of Class C, such as water, oil, mercury, etc., it has

already been shown that they are to be considered as liquids of their

normal specific gravity; that is, in calculating the air pressure

necessary to displace them, one should consider their specific gravity

only, as a factor, and not the total weight per volume including any

impurities which they might contain undissolved.

In order to have a clearer conception of aqueous and semi-aqueous

materials and their action, they must be viewed under conditions not

ordinarily apparent. For instance, ideas of so-called quicksand are

largely drawn from seeing structures sinking into it, or from observing

it flowing through voids in the sheeting or casing. The action of sand

and water under pressure is viewed during or after a slump, when the

damage is being done, or has been done, whereas the correct view-point

is under static conditions, before the slump takes place.

The following is quoted from the report of Mr. C.M. Jacobs, Chief

Engineer of the East River Gas Tunnel, built in 1892-93:

"We found that the material which had heretofore been firm or stiff

had, under erosion, obtained a soup-like consistency, and that a

huge cavity some 3 ft. wide and 26 ft. deep had been washed up

toward the river bed."

This would probably be a fair description of much of the material of

this class met with in such work, if compressed air had not been used.

The writer believes that in soft material surrounding submerged

structures the water actually contained in the voids is not

infrequently, after a prolonged period of rest, cut off absolutely from

its sources of pressure and that contact with these sources of pressure

will not again be resumed until a leak takes place through the

structure; and, even when there is a small flow or trickling of water

through such material, it confines itself to certain paths or channels,

and is largely excluded from the general mass.

The broad principle of the bearing power of soil has been made the

subject of too many experiments and too much controversy to be

considered in a paper which is intended to be a description of

experiments and observed data and notes therefrom. The writer is of the

opinion, however, that entirely too little attention has been given to

this bearing power of the soil; that while progress has been made in our

knowledge of all classes of materials for structures, very little has

been done which leads to any real knowledge of the material on which the

foundation rests. For instance, it is inconceivable that 1 or 2 tons may

sometimes be allowed on a square foot of soft clay, while the load on

firm gravel is limited to from 4 to 6 tons. The writer's practical

observations have convinced him that it is frequently much safer to put

four times 6 tons on a square foot of gravel than it is to put

one-fourth of 2 tons on a square foot of soft clay.

In connection with the bearing power of soil, the writer also believes

that too little study has been given to the questions of the lateral

pressure of earth, and he desires to quote here from some experiments

described in a book[F] published in England in 1876, to which his

attention has recently been called. This book appears to have been

intended for young people, but it is of interest to note the following

quotations from a chapter entitled "Sand." This chapter begins by

stating that:

"During the course of a lecture on the Suez Canal by Mr. John H.

Pepper, which was delivered nightly by him at the Polytechnic

Institute in London, he illustrated his lecture by some experiments

designed to exhibit certain properties of sand, which had reference

to the construction of the Suez Canal, and it is stated that though

the properties in question were by no means to be classed among

recent discoveries, the experiments were novel in form and served

to interest the public audience."

Further quotation follows:

"When the Suez Canal was projected, many prophesied evil to the

undertaking, from the sand in the desert being drifted by the wind

into the canal, and others were apprehensive that where the canal

was cut through the sand the bottom would be pushed up by the

pressure on the banks * * *.

"The principle of lateral pressure may now be strikingly

illustrated by taking an American wooden pail and, having

previously cut a large circular hole in the bottom, this is now

covered with fine tissue paper, which should be carefully pasted on

to prevent the particles of sand from flowing through the small

openings between the paper and the wood * * * and being placed

upright and rapidly filled with sand, it may be carried about by

the handle without the slightest fear of the weight of the sand

breaking through the thin medium. * * *

"Probably one of the most convincing experiments is that which may

be performed with a cylindrical tube 18 in. long and 2 in. in

diameter, open at both ends. A piece of tissue paper is carefully

pasted on one end, so that when dry no cracks or interstices are

left. The tube is filled with dry sand to a height of say 12 in. In

the upper part is inserted a solid plug of wood 12 in. long and of

the same or very nearly the same diameter as the inside of the

tube, so that it will move freely up and down like the piston of an

air pump. The tube, sand, and piston being arranged as described,

may now be held by an assistant and the demonstrator, taking a

sledge hammer, may proceed to strike steadily on the end of the

piston and, although the paper will bulge out a little, the force

of the blow will not break it.

"If the assistant holding the tube allows it to jerk or rebound

after each blow of the hammer, the paper may break, because air and

sand are driven down by the succeeding blow, and therefore it must

be held steadily so that the piston bears fairly on the sand each

time.

"A still more conclusive and striking experiment may be shown with

a framework of metal constructed to represent a pail, the sides of

which are closed up by pasting sheets of tissue paper inside and

over the lower part. As before demonstrated, when a quantity of

sand is poured into the pail the tissue paper casing at the bottom

does not break, but if a sufficient quantity is used the sides

formed of tissue paper bulge out and usually give way in

consequence of the lateral pressure exerted by the particles of

sand."

The writer has made the second experiment noted, with special apparatus,

and finds that with tissue paper over the bottom of a 2-in. pipe, 15 in.

long, about 12 in. of sand will stand the blow of a heavy sledge hammer,

transmitted through a wooden piston, at least once and sometimes two or

three times, while heavy blows given with a lighter hammer have no

effect at all. That this is not due in any large measure to inertia can

be shown by the fact that more than 200 lb. can safely be put on top of

the wooden piston. It cannot be accounted for entirely by the friction,

as the removal of the paper allows the sand to drop in a mass. The

explanation is that the pressure is transmitted laterally to the sides,

and as the friction is directly proportional to the pressure, the load

or effect of the blow is carried by the proportional increase in the

friction, and any diaphragm which will carry the direct bottom load will

not have its stresses largely increased by any greater loading on top.

The writer believes that experiments will show that in a sand-jack the

tendency will be for the sides to burst rather than the bottom, and that

the outflow from an orifice at or near the bottom is not either greatly

retarded or accelerated by ordinary pressure on top. The occurrence of

abnormal voids, however, causes the sand to be displaced into them.

The important consideration of this paper is that all the experiments

and observations noted point conclusively to the fact that pressure is

transmitted laterally through ground, most probably along or nearly

parallel to the angles of repose, or in cases of rock or stiff material,

along a line which, until more conclusive experiments are made, may be

taken as a mean between the horizontal and vertical, or approximately 45

degrees. There is no reason to believe that this is not the case

throughout the entire mass of the earth, that each cubic foot, or yard,

or mile is supported or in turn supports its neighboring equivalent

along such lines. The theory is not a new one, and its field is too

large to encompass within the limits of a single paper, but, for

practical purposes, and within the limited areas to which we must

necessarily be confined, the writer believes it can be established

beyond controversy as true. Certain it is that no one has yet found, in

ground free from water pressure or abnormal conditions, any evidence of

greater pressure at the bottom of a deep shaft or tunnel than that near

the surface. Pressures due to the widening of mines beyond the limits of

safety must not be taken as a controversion of this statement, as all

arches have limits of safety, more especially if the useless material

below the theoretical intrados is only partly supported, or is allowed

to be suspended from the natural arch.

The writer believes, also, that the question of confined foundations, in

contradistinction to that of the spreading of foundations, may be worthy

of full discussion, as it applies to safe and economical construction,

and he offers, without special comment, the following observations:

He has found that, in soft ground, results are often obtained with small

open caissons sunk to a depth of a few feet and cleaned out and filled

with concrete, which offer much better resistance than spreading the

foundation over four or five times the equivalent area.

He has found that small steel piles and coffer-dams, from 1-ft.

cylinders to coffer-dams 4 or 5 ft. square, sunk to a depth of only 1 or

2 ft. below adjacent excavations in ordinary sand, have safely resisted

loads four or five times as great as those usually allowed.

He believes that short cylinders, cleaned out and filled with concrete,

or coffer-dams of short steel piling with the surface cleaned out to a

reasonable depth and filled with concrete horizontally reinforced, will,

in many instances, give as good results as, and, in most cases, very

much better than, placing the foundation on an equivalent number of

small long piles or a proportionately greater spread of foundation area,

the idea being that the transmission of pressure to the sides of the

coffer-dam will not only confine the side thrust, but will also transfer

the loading in mass to a greater depth where the resistance to lateral

pressure in the ground will be more stable; that is, the greater depth

of foundation is gained without the increased excessive loading, or

necessity for deep excavation.

As to the question of the bearing value and friction on piles, the

writer believes that while the literature on engineering is full of

experimental data relating to friction on caissons, there is little to

show the real value of friction on piles. The assumption generally made

of an assumed bearing value, and the deduction therefrom of a value for

the skin friction is fallacious. Distinction, also, is not made, but

should be clearly drawn between skin friction, pure and simple, on

smooth surfaces, and the friction due to pressure. Too often the bearing

value on irregular surfaces as well as the bearing due to taper in

piles, and lastly the resistance offered by binding, enter into the

determination of so-called skin friction formulas. The essential

condition of sinking a caisson is keeping it plumb; and binding, which

is another way of writing increased bearing value, will oftentimes be

fatal to success.

The writer believes that a series of observations on caissons sunk plumb

under homogeneous conditions of ground and superficial smoothness will

show a proportional increase of skin friction per square foot average

for each increase in the size of caissons, as well as for increase of

depth in the sinking up to certain points, where it may finally become

constant, as will be shown later. The determination of the actual

friction or coefficient of friction between the surfaces of the pile and

the material it encounters, is not difficult to determine. In sand it is

approximately 40% of the pressure for reasonably smooth iron or steel,

and 45% of the pressure for ordinary wood surfaces. If, for instance, a

long shaft be withdrawn vertically from moulding sand, the hole may

remain indefinitely as long as water does not get into it or it does not

dry out. This is due to the tendency of the sand to arch itself

horizontally over small areas. The same operation cannot be performed on

dry sand, as the arching properties, while protecting the pile from

excessive pressure due to excessive length, will not prevent the loose

sand immediately surrounding the pile from exerting a constant pressure

against the pile, and it is of this pressure that 45% may be taken as

the real value of skin friction on piles in dry sand.

In soft clays or peats which are displaced by driving, the tendency of

this material to flow back into the original space causes pressure, of

which the friction will be a measured percentage. In this case, however,

the friction itself between the material and the clays or peat is

usually very much less than 40%, and it is for this reason that piles of

almost indefinite length may be driven in materials of this character

without offering sufficient resistance to be depended on, as long as no

good bearing ground is found at the point.

If this material is under water, and is so soft as to be considered

semi-aqueous, the pressure per square foot will increase in diminishing

proportion to the depth, and the pressure per area will soon approach

and become a constant, due to the resistance offered by the lateral

arching of the solid material; whereas, in large circular caissons, or

caisson shafts, where the horizontal arching effect is virtually

destroyed, or at least rendered non-effective until a great depth is

reached, the pressure must necessarily vary under these conditions

proportionately to the depth and size of the caisson in semi-aqueous

material. On the other hand, in large caisson shafts, especially those

which are square, the pressure at the top due to the solid material will

also increase proportionately to the depth, as already explained in

connection with the pressures of earth against sheeting and retaining

walls.

The writer believes that the pressure on these surfaces may be

determined with reasonable accuracy by the formulas already given in

this paper, and with these pressures, multiplied by the coefficient of

friction determined by the simplest experiment on the ground, results

may be obtained which will closely approximate the actual friction on

caissons at given depths. The friction on caissons, which is usually

given at from 200 to 600 lb. per sq. ft., is frequently assumed to be

the same on piles 12 in. or less in diameter, whereas the pressures on

these surfaces, as shown, are in no way comparable.

The following notes and observations are given in connection with the

skin friction and the bearing value of piles:

The writer has in his possession a copy of an official print which was

recently furnished to bidders in connection with the foundation for a

large public building in New York City. The experiments were made on

good sand at a depth of approximately 43 ft. below water and 47 ft.

below an adjacent excavation. In this instance a 16-in. pipe was sunk to

the depth stated, cleaned out, and a 14-in. piston connected to a 10-in.

pipe was inserted and the ground at the bottom of the 16-in. pipe

subjected to a loading approximating 28 tons per sq. ft. After an

initial settlement of nearly 3 in., there was no further settlement over

an extended period, although the load of 28 tons per sq. ft. was

continued.

In connection with some recent underpinning work, 14-in. hollow

cylindrical piles 6 ft. long were sunk to a depth of 6 ft. with an

ordinary hand-hammer, being excavated as driven. These piles were then

filled with concrete and subjected to a loading in some cases

approximating 60 tons. After a settlement ranging from 9 to 13 in., no

further settlement took place, although the loading was maintained for a

considerable period.

In connection with some other pile work, the writer has seen a 10-in.

pipe, 3/8 in. thick, 4 ft. below the bottom of an open cylinder, at a

depth of about 20 ft., sustain in gravel and sand a load approximating

50 tons when cleaned out to within 2 ft. of the bottom.

He has seen other cylindrical piles with a bearing ring of not more than

¾ in. resting on gravel at a depth of from 20 to 30 ft., cleaned out

practically to the bottom, sustain a measured load of 60 tons without

settlement.

As to skin friction in sand, a case came under his observation wherein a

14-in. hollow cylindrical pile which had stood for 28 days at a depth of

about 30 ft. in the sand, was cleaned out to its bottom and subjected to

hydraulic pressure, measured by a gauge, and sunk 2 ft. into the sand

without any pressure being registered on the gauge. It should be

explained, however, that the gauge could be subjected to a pressure of

250 lb., equal to a total pressure of 7,000 lb. on the piston of the

jack without registering, which corresponded, assuming it all as skin

friction, to a maximum of not more than 78 lb. per sq. ft., but it

should be noted that this included bearing value as well, and that the

pressure was very far from 7,000 lb., in all probability, at the

beginning of the test.

In the case of the California stove-pipe wells driven by the Board of

Water Supply on Long Island, the writer is informed that one of these

tubes, 12 in. in diameter, was sunk to a depth of 850 ft. In doing this

work the pile was excavated below the footing with a sand pump and was

then sunk by hydraulic pressure. Assuming the maximum capacity of the

jacks at 100 tons, which is not probable, the skin friction could not

have amounted to more than 75 lb. per sq. ft. It cannot be assumed in

this case that the excavation of the material below the pile relieved

the skin itself of some of its friction, as the operation consumed more

than 6 weeks, and, even if excess material was removed, it is certain

that a large percentage of it would have had time to adjust itself

before the operation was completed.

[Illustration: PLATE XXIX, FIG. 1.--A 14-GAUGE, 14-IN., HOLLOW

(NON-TELESCOPIC), CALIFORNIA STOVE-PIPE PILE WHICH MET IMPENETRABLE

MATERIAL.]

[Illustration: PLATE XXIX, FIG. 2.--CHENOWETH PILE, PENETRATING HARD

MATERIAL.]

In connection with this, the writer may call attention to the fact that

piles driven in silt along the North River, and in soft material at

other places, are sometimes 90 ft. in length, and even then do not offer

sufficient resistance to be depended on for loading. This is due to the

fact that the end of the pile does not bear in good material.

The relation between bearing value and skin friction on a pile, where

the end bearing is in good material, is well shown by a case where a

wooden pile[G] struck solid material, was distorted under the continual

blows of the hammer, and was afterward exposed. It is also shown in the

case of a 14-in. California stove-pipe pile, No. 14 gauge, the point of

which met firm material. The result, as shown by Fig. 1, Plate XXIX,

speaks for itself. Fig. 2, Plate XXIX, shows a Chenoweth pile which was

an experimental one driven by its designer. This pile, after getting

into hard material, was subjected to the blow of a 4,000-lb. hammer

falling the full length of the pile-driver, and the only result was to

shatter the head of the pile, and not cause further penetration. Mr.

Chenoweth has stated to the writer that he has found material so compact

that it could not be penetrated with a solid pile--either with or

without jetting--which is in line with the writer's experience.

The writer believes that the foregoing notes will show conclusively that

the factor to be sought in pile work is bearing value rather than depth

or skin friction, and, however valuable skin friction may be in the

larger caissons, it cannot be depended on in the case of small piles,

except in values ranging from 25 to 100 lb. per sq. ft.

In conclusion, he desires to thank the following gentlemen, who have

contributed to the success of the experiments noted herein: Mr. James W.

Nelson, of Richard Dudgeon, New York; Mr. George Noble, of John Simmons

and Company, New York; and Mr. Pendleton, of Hindley and Pendleton,

Brooklyn, N.Y.; all of whom have furnished apparatus for the experiments

and have taken an interest in the results. And lastly, he desires

especially to thank Mr. F.L. Cranford, of the Cranford Company, for men

and material with which to make the experiments and without whose

co-operation it would have been impracticable for the writer to have

made them.

Throughout this paper the writer has endeavored, as far as possible, to

deduce from his observations and from the observations of others, as far

as he has been able to obtain them, practical data and formulas which

may be of use in establishing the relationship between the pressure,

resistance, and stability of earths; and, while he does not wish to

dictate the character of the discussion, he does ask that those who have

made observations of a similar character or who have available data,

will, as far as possible, contribute the same to this discussion. It is

only by such observations and experiments, and deductions therefrom,

that engineers may obtain a better knowledge of the handling of such

materials.

The writer believes that too much has been taken for granted in

connection with earth pressures and resistance; and that, far too often,

observations of the results of natural laws have been set down as

phenomena. He believes that, both in experimenting and observing, the

engineer will frequently find what is being looked for or expected and

will fail to see the obvious alternative. He may add that his own

experiments and observations may be criticized for the same reason, and

he asks, therefore, that all possible light be thrown on this subject. A

comparative study of much of our expert testimony or of the plans of

almost any of the structures designed in connection with their bearing

upon earth, or resistance to earth pressure, will show that under the

present methods of interpretation of the underlying principles governing

the calculations and designs relating to such structures, the results

vary far too widely. Too much is left to the judgment of the engineer,

and too frequently no fixed standards can be found for some of the most

essential conditions.

Until the engineer can say with certainty that his calculations are

reasonably based on facts, he is forced to admit that his design must be

lacking, either in the elements of safety, on the one hand, or of

economy, on the other, and, until he can give to his client a full

measure of both these factors in fair proportion, he cannot justly claim

that his profession has reached its full development.

Table 1 gives approximate calculations of pressures on two types of

tunnels and on two heights of sheeted faces or walls, due to four

varying classes of materials.

TABLE 1.--PRESSURES ON TYPICAL STRUCTURES UNDER VARYING ASSUMED

CONDITIONS.

[Illustration: Key to Table of Pressures, etc.]

_h_ = exterior height, _l_ = exterior width,

{ [delta] = depth of cover, that is,

{ _D_{E}_ = earth, and _D_{W}_ = water depth,

[phi] = angle of repose, and, for tunnels _D_{W}_ > _D_{E}_ a depth

_l_ [phi]

= ----- ( 45° + ------- )

2 2

_W_{E}_ = weight of 1 cu. ft. of earth = 90 lb.; _W_{W}_ = weight of 1

cu. ft. of water = 62½ lb.

Conditions: 1 = normal sand, 2 = dry sand, 3 = supersaturated firm sand

with 40% of voids, 4 = supersaturated semi-aqueous material, 60%

aqueous, that is, 60% water and aqueous material.

_______________________________________________________

| | | | |

Combined | | | | |

assumed | _h_ | _l_ | [phi] | _D_{E}_ |

conditions. | | | | |

______________|________|________|________|____________|

| | | | |

I_{1} | 20 | 30 | 45° | 40 |

I_{2} | 20 | 30 | 30° | 40 |

II_{1} | 15 | 15 | 45° | 40 |

II_{2} | 15 | 15 | 30° | 40 |

III_{1} | 15 | | 45° | 15 |

III_{2} | 15 | | 30° | 15 |

IV_{1} | 30 | | 45° | 30 |

IV_{2} | 30 | | 30° | 30 |

______________|________|________|________|____________|

____________________________________________________________________

| | | | | |

Combined | | | | | |

assumed | _h_ | _l_ | [phi] | _D_{E}_ | _D_{W}_ |

conditions. | | | | | |

______________|________|________|________|____________|____________|

| | | | | |

I_{3} | 20 | 30 | 50° | 40 | 60 |

I_{4} | 20 | 30 | 40° | 40 | 60 |

II_{3} | 15 | 15 | 50° | 40 | 60 |

II_{4} | 15 | 15 | 40° | 40 | 60 |

III_{3} | 15 | | 50° | 15 | 15 |

III_{4} | 15 | | 40° | 15 | 15 |

IV_{3} | 30 | | 50° | 30 | 30 |

IV_{4} | 30 | | 40° | 30 | 30 |

______________|________|________|________|____________|____________|