Part 3
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.
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.