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diff --git a/16938-8.txt b/16938-8.txt new file mode 100644 index 0000000..e8cdf84 --- /dev/null +++ b/16938-8.txt @@ -0,0 +1,3166 @@ +The Project Gutenberg EBook of Pressure, Resistance, and Stability of Earth +by J. C. Meem + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Pressure, Resistance, and Stability of Earth + American Society of Civil Engineers: Transactions, Paper No. 1174, + Volume LXX, December 1910 + +Author: J. C. Meem + +Release Date: October 25, 2005 [EBook #16938] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK PRESSURE AND RESISTANCE *** + + + + +Produced by Juliet Sutherland, Taavi Kalju and the Online +Distributed Proofreading Team at https://www.pgdp.net + + + + + + + + + +AMERICAN SOCIETY OF CIVIL ENGINEERS INSTITUTED 1852 + +TRANSACTIONS + +Paper No. 1174 + +PRESSURE, RESISTANCE, AND STABILITY OF EARTH.[A] + +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 | +______________|________|________|________|____________|____________| + + +APPROXIMATE PRESSURES ON TUNNELS, PER SQUARE FOOT. + +_________________________________________________________________________ + | | | | || | | | +Pressure | I_{1}| I_{3}| I_{3}| I_{3} || I_{2}| I_{4}| I_{4}| I_{4} +per square|Earth.|Earth.|Water.|Combined.||Earth.|Earth.|Water.|Combined. +foot, at | | | | || | | | +__________|______|______|______|_________||______|______|______|_________ + | | | | || | | | + A | 3,240| 3,690| 1,500| 5,190 || 2,325| 2,880| 2,250| 5,130 + B | 2,745| 3,105| 1,500| 4,605 || 1,845| 2,385| 2,250| 4,635 + C | 2,160| 2,475| 1,500| 3,975 || 1,350| 1,800| 2,250| 4,050 + D | 450| 540| 1,500| 2,040 || 450| 450| 2,250| 2,700 + E | 360| 360| 1,625| 1,985 || 450| 450| 2,438| 2,888 + F | 270| 270| 1,750| 2,025 || 450| 360| 2,626| 2,986 + G | 225| 225| 1,875| 2,100 || 360| 270| 2,814| 3,084 +__________|______|______|______|_________||______|______|______|_________ +_________________________________________________________________________ + | | | | || | | | +Pressure |II_{1}|II_{3}|II_{3}|II_{3} ||II_{2}|II_{4}|II_{4}|II_{4} +per square|Earth.|Earth.|Water.|Combined.||Earth.|Earth.|Water.|Combined. +foot at | | | | || | | | +__________|______|______|______|_________||______|______|______|_________ + | | | | || | | | + A | 1,485| 1,755| 1,500| 3,255 || 1,035| 1,305| 2,250| 3,555 + B | 1,305| 1,485| 1,500| 2,985 || 945| 1,170| 2,250| 3,420 + C | 1,125| 1,215| 1,500| 2,715 || 810| 990| 2,250| 3,240 + D | 405| 405| 1,500| 1,905 || 540| 450| 2,250| 2,700 + E | 405| 405| 1,625| 2,030 || 540| 450| 2,438| 2,888 + F | 360| 360| 1,750| 2,110 || 540| 450| 2,626| 3,076 + G | 315| 315| 1,875| 2,190 || 360| 360| 2,814| 3,174 + H | 180| 225| 2,000| 2,225 || 180| 180| 3,000| 3,180 + I | 90| 110| 2,175| 2,285 || 135| 135| 3,188| 3,323 +__________|______|______|______|_________||______|______|______|_________ + + +APPROXIMATE PRESSURES ON SHEETED TRENCH FACES OR WALLS + +___________________________________________________________________________ + | | | | || | | | +Pressure |III_{1}|III_{3}|III_{3}|III_{3}||III_{2}|III_{4}|III_{4}|III_{4} +per square|Earth. |Earth. |Water. | Total ||Earth. |Earth. |Water. | Total +foot at | | | | earth || | | | earth + | | | | and || | | | and + | | | | water.|| | | | water. +__________|_______|_______|_______|_______||_______|_______|_______|_______ + | | | | || | | | + A | 575 | 510 | 100 | 610 || 1,350 | 810 | 140 | 950 + B | 400 | 350 | 190 | 540 || 900 | 540 | 260 | 800 + C | 200 | 175 | 280 | 455 || 450 | 270 | 380 | 650 +__________|_______|_______|_______|_______||_______|_______|_______|_______ +___________________________________________________________________ + | | | | || | | | +Pressure |IV_{1}|IV_{3}|IV_{3}|IV_{3}||IV_{2}|IV_{4}|IV_{4}|IV_{4} +per square|Earth.|Earth.|Water.|Total ||Earth.|Earth.|Water.|Total +foot at | | | |earth || | | |earth + | | | | and || | | | and + | | | |water.|| | | |water. +__________|______|______|______|______||______|______|______|______ + | | | | || | | | + A | 1,370| 1,210| 100 | 1,310|| 3,175| 1,910| 150| 2,060 + B | 1,170| 1,030| 200 | 1,230|| 2,700| 1,610| 290| 1,900 + C | 970| 855| 290 | 1,145|| 2,250| 1,355| 430| 1,785 + D | 775| 680| 370 | 1,050|| 1,800| 1,100| 570| 1,670 + E | 590| 515| 460 | 975|| 1,350| 820| 710| 1,530 + F | 400| 350| 560 | 910|| 900| 540| 860| 1,400 + G | 190| 170| 650 | 820|| 450| 275| 1,000| 1,275 +__________|______|______|______|______||______|______|______|______ + + +FOOTNOTES: + +[Footnote A: Presented at the meeting of May 18th, 1910.] + +[Footnote B: _Transactions_, Am. Soc. C. E., Vol. LX, p. 1.] + +[Footnote C: _Engineering News_, July 1st, 1909.] + +[Footnote D: From "Gravel for Good Roads."] + +[Footnote E: _Transactions_, Am. Soc. C. E., Vol. LXVIII, pp. 58-60.] + +[Footnote F: "Discoveries and Inventions of the Nineteenth Century," by +Robert Routledge, Assistant Examiner in Chemistry and in Natural +Philosophy to the University of London.] + +[Footnote G: _Engineering News_, January 15th, 1909.] + + + + +DISCUSSION + + +T. KENNARD THOMSON, M. AM. SOC. C. E.--Although the author +deserves great credit for the careful and thorough manner in which he +has handled this subject, his paper should be labeled "Dangerous for +Beginners," especially as he is an engineer of great practical +experience; if he were not, comparatively little attention would be paid +to his statements. The paper is dangerous because many will read only +portions of it, or will not read it thoroughly. For instance, at the +beginning, the author cites several experiments in which considerable +force is required to start the lifting of a weight or plunger in sand +and water and much less after the start. This reminds the speaker of the +time when, as a schoolboy, he tried to pick up stones from the bottom of +the river and was told that the "suction" was caused by atmospheric +pressure. + +The inference is that tunnels, etc., in sand, etc., are not in any +danger of rising, even though they are lighter than water. Toward the +end of the paper, however, the author states that tunnels should be +weighted, but he rather spoils this by stating that they should be +weighted only enough to overcome the actual water pressure, that is, +between the voids of the sand. It seems to the speaker that the only +really safe way is to make the tunnel at least as heavy as the water +displaced in order to prevent it from coming up, and to take other +measures to prevent it from going down. The City of Toronto, Canada, +formerly pumped its water supply through a 6-ft. iron pipe, buried in +the sand under Toronto Bay and then under Toronto Island, with an intake +in the deep water of the lake. During a storm a mass of seaweed, etc., +was washed against the intake, completely blocking it, and although the +man at the pumping station knew that something was wrong, he continued +to pump until the water was drawn out of the pipe, with the result that +about half a mile of the conduit started to rise and then broke at +several places, thus allowing it to fill with water. Eventually, the +city went down to bed-rock under the Bay for its water tunnel. + +Another reason for calling this paper dangerous for beginners is that it +is improbable that experienced engineers or contractors will omit the +bracing at the bottom, although, since the paper was printed, a glaring +instance has occurred where comparatively little bracing was put in the +bottom of a 40-ft. cut, the result being a bad cave-in from the bottom, +although all the top braces remained in place. Most engineers will agree +that nearly every crib which has failed slipped out from the bottom, and +did not turn over. + +The objection to the angle of repose is that it is not possible to +ascertain it for any material deposited by Nature. It could probably be +ascertained for a sand bank deposited by Man, but not for an excavation +to be made in the ground, for it is known that nearly all earth, etc., +has been deposited under great pressure, and is likely to be cemented +together by clay, loam, roots, trees, boulders, etc., and differs in +character every few feet. + +A deep vertical cut can often be made, even in New York quicksand, from +which the water has been drawn, and, if not subjected to jars, water, +etc., this material will stand for considerable time and then come down +like an avalanche, killing any one in its way. In such cases very little +bracing would prevent the slide from starting, provided rain, etc., did +not loosen the material. + +The author, of course, treats dry and wet materials differently, but +there are very few places where dry material is not likely to become wet +before the excavation is completed. + +In caisson work, if the caisson can be kept absolutely plumb, it can be +sunk without having to overcome much friction, while, on the other hand, +if it is not kept plumb, the material is more or less disturbed and +begins to bind, causing considerable friction. The author claims that +the pressure does not increase with the depth, but all caisson men will +probably remember that the friction to be overcome per square foot of +surface increases with the depth. + +In calculating retaining walls, many engineers add the weight of the +soil to the water, and calculate for from 90 to 100 lb. per cu. ft. The +speaker is satisfied that in the so-called New York quicksand it is +sufficient to use the weight of the water only. If the sand increased +the side pressure above the water pressure, engineers would expect to +use more compressed air to hold it back, while, as a matter of fact, the +air pressure used seldom varies much from that called for by the +hydrostatic head. + +Although allowance for water pressure is sufficient for designing +retaining walls in New York quicksand, it is far from sufficient in +certain silty materials. For instance, in Maryland, a coffer-dam, +excavated to a depth of 30 ft. in silt and water, had the bottom shoved +in 2 ft., in spite of the fact that the waling pieces were 5 ft. apart +vertically at the top and 3 ft. at the bottom, and were braced with 12 +by 12-in. timbers, every 7 ft. horizontally. The walings split, and the +cross-braces cut into the waling pieces from 1 to 2 in.; in other words, +the pressure seemed to be almost irresistible. This is quite a contrast +to certain excavations in Brooklyn, which, without any bracing whatever, +were safely carried down 15 ft. + +Any engineer who tries to guess at the angle of repose, and, from the +resulting calculations, economizes on his bottom struts, will find that +sooner or later an accident on one job will cause enough loss of life +and money to pay for conservative timbers for the rest of his life. So +much for side pressures. As to the pressure in the roof of a tunnel, +probably every engineer will agree that almost any material except +unfrozen water will tend to arch more or less, but how much it is +impossible to say. It is doubtful whether any experienced engineer would +ever try to carry all the weight over the roof, except in the case of +back-fill, and even then he would have to make his own assumption (which +sounds more polite than "guess"). + +The author has stated, however, that when the tunnel roof and sides are +in place, no further trouble need be feared. On the contrary, in 1885, +the Canadian Pacific Railroad built a tunnel through clayey material and +lined it with ordinary 12 by 12-in. timber framing, about 2 or 3 ft. +apart. After the tunnel was completed, it collapsed. It was re-excavated +and lined with 12 by 12-in. timbers side by side, and it collapsed +again; then the tunnel was abandoned, and, for some 20 years, the track, +carried around on a 23° curve, was used until a new tunnel was built +farther in. This trouble could have been caused either by the sliding or +swelling of the material, and the speaker is inclined to believe that it +was caused by swelling, for it is known, of course, that most material +has been deposited by Nature under great pressure, and, by excavating in +certain materials, the air and moisture would cause those materials to +swell and become an irresistible force. + +To carry the load, Mr. Meem prefers to rely on the points of the piles +rather than the side friction. In such cases the pile would act as a +post, and would probably fail when ordinarily loaded, unless firmly +supported at the sides. The speaker has seen piles driven from 80 to 90 +ft. in 10 min., which offered almost no resistance, and yet, a few days +later, they would sustain 40 tons each. No one would dream of putting 40 +tons on a 90-ft. pile resting on rock, if it were not adequately +supported. + +It is the speaker's opinion that bracing should not be omitted for +either piles or coffer-dams. + + +CHARLES E. GREGORY, ASSOC. M. AM. SOC. C. E.--In describing his +last experiment with the hydraulic chambers and plunger, Mr. Meem states +that, after letting the pressure stand at 25 lb., etc., the piston came +up. This suggests that the piston might have been raised at a much lower +pressure, if it had been allowed to stand long enough. + +The depth and coarseness of the sand were not varied to ascertain +whether any relation exists between them and the pressure required to +lift the piston. If the pressure varied with the depth of sand, it would +indicate that the reduction was due to the resistance of the water when +finely divided by the sand; if it varied with the coarseness of the +sand, as it undoubtedly would, especially if the sand grains were +increased to spheres 1 in. in diameter, it would show that it was +independent of the voids in the sand, but dependent on dividing the +water into thin films. + +The speaker believes that the greater part of the reduction of pressure +on the bottom of the piston might be better explained by the viscosity +of the water, than to assume that a considerable part of the plunger is +not in contact with it. The water, being divided by fine sand into very +thin films, has a tensile strength which is capable of resisting the +pressure for at least a limited time. + +If the water is capable of exerting its full hydrostatic pressure +through the sand, the total pressure would be the full hydrostatic +pressure on the bottom of the piston where in contact, and, where +separated from it by a grain of sand, the pressure would be decreased +only by the weight of the grain. If a large proportion of the top area +of a grain is in contact, as assumed by the author, this reduction of +pressure would be very small. A correct interpretation can be obtained +only after more complete experiments have been made. + +For horizontal pressures exerted by saturated sands on vertical walls, +it has not been demonstrated that anything should be deducted from full +water pressure. No matter how much of the area is in direct contact with +the sand rather than the water, the full water pressure would be +transmitted through each sand grain from its other side and, if +necessary, from and through many other grains which may be in turn in +contact with it. The pressure on such a wall will be water pressure over +its entire surface, and, in addition, the thrust of the sand after +correcting for its loss of weight in the water. + +The fact that small cavities may be excavated from the sides of trenches +or tunnels back of the sheeting proves only that there is a local +temporary arching of the material, or that the cohesion of the particles +is sufficient to withstand the stress temporarily, or that there is a +combination of cohesion and arching. The possibility of making such +excavations does not prove that pressure does not exist at such points. +That sand or earth will arch under certain conditions has long been an +accepted fact. The sand arches experimented with developed their +strength only after considerable yielding and, therefore, give no index +of the distribution or intensity of stress before such yielding. +Furthermore, sand and earth in Nature are not constrained by forms and +reinforcing rods. + +Mr. Meem's paper is very valuable in that it presents some unusual +phenomena, but many of the conclusions drawn therefrom cannot be +accepted without further demonstration. + + +FRANCIS W. PERRY, ASSOC. M. AM. SOC. C. E.--Pressure-gauge +observations on a number of pneumatic caissons recently sunk, through +various grades of sand, to rock at depths of from 85 to 105 ft. below +ground-water, invariably showed working-chamber air-pressures equal, as +closely as could be observed, to the hydrostatic pressures computed, for +corresponding depths of cutting-edge, as given in Table 2. + +These observations and computations were made by the speaker in +connection with the caisson foundations for the Municipal Building, New +York City. + + +TABLE 2.--EQUIVALENT FEET OF DEPTH BELOW WATER PER POUND +PRESSURE. + +Pressure, |Equivalent |Equivalent |Observed | +in |feet of |elevation |pressure. | +pounds. |depth. |for water | | + | |at--6.85. | | + |___________|_____________| | + | | | | + |M.H.W. |Ground-water.| | +__________|___________|_____________|______________| + | | | | + 1 | 2.31 | 9.06 |Practically | + 2 | 4.63 | 11.48 |the same as | + 3 | 6.94 | 13.79 |computed | + 4 | 9.25 | 16.10 |for | + 5 | 11.57 | 18.42 |ground-water. | + 6 | 13.88 | 20.73 | | + 7 | 16.19 | 23.04 | | + 8 | 18.50 | 25.35 | | + 9 | 20.82 | 27.67 | | + 10 | 23.13 | 29.98 | | + 11 | 25.44 | 32.29 | | + 12 | 27.76 | 34.61 | | + 13 | 30.07 | 36.92 | | + 14 | 32.38 | 39.23 | | + 15 | 34.70 | 41.55 | | + 16 | 37.01 | 43.86 | | + 17 | 39.32 | 46.17 | | + 18 | 41.63 | 48.48 | | + 19 | 43.95 | 50.80 | | + 20 | 46.26 | 53.11 | | + 21 | 48.57 | 55.42 | | + 22 | 50.89 | 57.74 | | + 23 | 53.20 | 60.05 | | + 24 | 55.51 | 62.36 | | + 25 | 57.82 | 64.67 | | + 26 | 60.14 | 66.99 | | + 27 | 62.45 | 69.30 | | + 28 | 64.76 | 71.61 | | + 29 | 67.08 | 73.93 | | + 30 | 69.39 | 76.24 | | + 31 | 71.70 | 78.55 | | + 32 | 74.01 | 80.86 | | + 33 | 76.33 | 83.18 | | + 34 | 78.64 | 85.49 | | + 35 | 80.95 | 87.80 | | + 36 | 83.27 | 90.12 | | + 37 | 85.58 | 92.43 | | + 38 | 87.89 | 94.74 | | + 39 | 90.20 | 97.05 | | + 40 | 92.52 | 99.37 | | + 41 | 94.83 |101.68 | | + 42 | 97.14 |103.99 | | + 43 | 99.46 |106.31 | | + 44 |101.77 |108.62 | | + 45 |104.08 |110.93 | | + 46 |106.39 |113.24 | | +__________|___________|_____________|______________| + + 34 +NOTE.--Equivalent depth in feet = ------ × pressure. + 14.7 + + +E.P. GOODRICH, M. AM. SOC. C. E. (by letter).--This paper is to +be characterized by superlatives. Parts of it are believed to be +exceptionally good, while other parts are considered equally dangerous. +The author's experimental work is extremely interesting, and the writer +believes the results obtained to be of great value; but the analytical +work, both mathematical and logical, is emphatically questioned. + +The writer believes that, in the design of permanent structures, +consideration of arch action should not be included, at least, not until +much more information has been obtained. He also believes that the +design of temporary structures with this inclusion is actually dangerous +in some instances, and takes the liberty of citing the following +statement by the author, with regard to his first experiment: + + "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." + +The writer emphatically questions the author's ideas as to "the +thickness of key" which "should be allowed" over tunnels, believing that +conditions within an earth mass, except in very rare instances, are +such that true arch action will seldom take place to any definite +extent, through any considerable depths. Furthermore, the author's +reason for bisecting the angle between the vertical and the angle of +repose of the material, when he undertakes to determine the thickness of +key, is not obvious. This assumption is shown to be absurd when carried +to either limit, for when the angle of repose equals zero, as is the +case with water, this, method would give a definite thickness of key, +while there can be absolutely no arch action possible in such a case; +and, when the angle of repose is 90°, as may be assumed in the case of +rock, this method would give an infinite thickness of key, which is +again seen to be absurd. It would seem as if altogether too many +unknowable conditions had been assumed. In any case, no arch action can +be brought into play until a certain amount of settlement has taken +place so as to bring the particles into closer contact, and in such a +way that the internal stresses are practically those only of +compression, and the shearing stresses are within the limits possible +for the material in question. + +The author has repeatedly made assumptions which are not borne out by +the application of his mathematical formulas to actual extreme +conditions. This method of application to limiting conditions is +concededly sometimes faulty; but the writer believes that no earth +pressure theory, or one concerning arch action, can be considered as +satisfactory which does not apply equally well to hydraulic pressure +problems when the proper assumptions are made as to the factors for +friction, cohesion, etc. For example, when the angle of repose is +considered as zero, in the author's first formula for _W_{1}_, the value +becomes ½ _W_{1}_, whereas it should depend solely on the depth, which +does not enter the formula, and not at all on the width of opening, _l_, +which is thus included. + +The author has given no experiments to prove his statement that "the +arch thrust is greater in dryer sand," and the accuracy of the statement +is questioned. Again, no reason is apparent for assuming the direction +of the "rakers" in Fig. 3 as that of the angle of repose. The writer +cannot see why that particular angle is repeatedly used, when almost any +other would give results of a similar kind. The author has made no +experiments which show any connection between the angle of repose, as he +interprets it, and the lines of arch action which he assumes to exist. + +With regard to the illustration of the condition which is thought to +exist when the "material is composed of large bowling balls," supposedly +all of the same size, the writer believes the conclusion to be +erroneous, and that this can be readily seen by inspection of a diagram +in which such balls are represented as forming a pile similar to the +well-known "pile of shells" of the algebras, in the diagram of which a +pile of three shells, resting on the base, has been omitted. It is then +seen that unless the pressures at an angle of 60° with the horizontal +are sufficient to produce frictional resistance of a very large amount, +the balls will roll and instantly break the arch action suggested by the +author. Consequently, an almost infinitesimal settlement of the +"centering" may cause the complete destruction of an arch of earth. + +The author's logic is believed to be entirely faulty in many cases +because he repeatedly makes assumptions which are not in accordance with +demonstrated fact, and finally sums up the results by the statement: "It +is conceded" (line 2, p. 357, for example), when the writer, for one, +has not even conceded the accuracy of the assumptions. For instance, the +author's well-known theory that pressures against retaining walls are a +maximum at the top and decrease to zero at the bottom, is in absolute +contradiction to the results of experiments conducted on a large scale +by the writer on the new reinforced concrete retaining wall near the St. +George Ferry, on Staten Island, New York City, which will soon be +published, and in which the usual law of increase of lateral pressure +with depth is believed to be demonstrated beyond question. It must be +conceded that a considerable arch action (so-called) actually exists in +many cases; but it should be equally conceded by the advocates of the +existence of such action that changes in humidity, due to moving water, +vibration, and appreciable viscosity, etc., will invariably destroy this +action in time. In consequence, the author's reasoning in regard to the +pressures against the faces of retaining walls is believed to be open to +grave question as to accuracy of assumption, method, and conclusion. + +The author is correct in so far as he assumes that "the character of the +stresses due to the thrust of the material will" not "change if bracing +should be substituted for the material in the area" designated by him, +etc., provided he makes the further assumption that absolutely no +motion, however infinitesimal, has taken place meantime; but, unless +such motion has actually taken place, no arch action can have developed. +An arch thrust can result only with true arch action, that is, with +stable abutments, and the mass stressed wholly in compression, with +corresponding shortening of the arch line. The arch thrust must be +proportional to the elastic deformation (shortening) of the arch line. +If any such arch as is shown in Fig. 5 is assumed to carry the whole of +the weight of material above it, that assumed arch must relieve all the +assumed arches below. Therefore each of the assumed arches can carry +nothing more than its own mass. Otherwise the resulting thrust would +increase with the depth, which is opposed to the author's theory. + +Turning again to the condition that each arch can carry only its own +weight: if these arches are assumed of thicknesses proportional to the +distance upward from the bottom of the wall, they will be similar +figures, and it is easily demonstrated that the thrust will then be +uniform in amount throughout the whole height of the wall, except, +perhaps, at the very top. This condition is contrary to the author's +ideas and also to the facts as demonstrated by the writer's experiment +on the 40-ft. retaining wall at St. George. Consequently, the author's +statement: "nor can anyone * * * doubt that the top timbers are stressed +more heavily than those at the bottom," is emphatically doubted and +earnestly denied by the writer. Furthermore, "the assumption" made by +the author as to "the tendency of the material to slide" so as to cause +it "to wedge * * * between the face of the sheeting * * * and some plane +between the sheeting and the plane of repose," is considered as +absolutely unwarranted, and consequently the whole conclusion is +believed to be unjustified. Nor is the author's assumption (line 5, p. +361), that "the thrust * * * is measured by its weight divided by the +tangent of the * * * angle of repose" at all obvious. + +The author presents some very interesting photographs showing the +natural surface slopes of various materials; but it is interesting to +note that he describes these slopes as having been produced by the +"continual slipping down of particles." The vast difference between +angles of repose produced in this manner by the rolling friction of +particles and the internal angles of friction, which must be used in all +earth-pressure investigations, has been repeatedly called to the +attention of engineers by the writer.[H] + +The writer's experiments are entirely in accord with those of the author +in which the latter claims to demonstrate that "earth and water +pressures act independently of each other," and the writer is much +delighted that his own experiments have been thus confirmed. + +In Experiment No. 3, the query is naturally suggested: "What would have +been the result if the nuts and washers had first been tightened and +water then added?" Although the writer has not tried the experiment, he +is rather inclined to the idea that the arch would have collapsed. With +regard to Experiment No. 5, there is to be noted an interesting +possibility of its application to the theoretical discussion of masonry +dams, in which films of water are assumed to exist beneath the structure +or in crevices or cracks of capillary dimensions. The writer has always +considered the assumptions made by many designing engineers as +unnecessarily conservative. In regard to the author's conclusions from +Experiment No. 6, it should be noted that no friction can exist between +particles of sand and surrounding water unless there is a tendency of +the latter to move; and that water in motion does not exert pressures +equal to those produced when in a static condition, the reduction being +proportional to the velocity of flow. + +The author's conclusion (p. 371), that "pressure will cause the +quicksand to set up hydraulic action," does not seem to have been +demonstrated by his experiments, but to be only his theory. In this +instance, the results of the writer's experiments are contrary to the +author's theory and conclusion. + +The writer will heartily add his protest to that of the author "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." Again, +similarly hearty concurrence is given to the author's statement: + + "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." + +On the other hand, it is believed that the author's statement, as to +"the tendency of marbles to arch," a few lines above the one last +quoted, should be qualified by the addition of the words, "only when a +certain amount of deflection has taken place so as to bring the arch +into action." Again, on the following page, a somewhat similar +qualification should be added to the sentence referring to the soft clay +arch, that it would "stand if the rods supporting the intrados of the +arch were keyed back to washers covering a sufficiently large area," by +inserting the words, "unless creeping pressures (such as those +encountered by the writer in his experiments) were exceeded." + +The writer considers as very doubtful the formula for _D_{x}_, which is +the same as that for _W_{1}_, already discussed. The author's statement +that "additional back-fill will [under certain circumstances] lighten +the load on the structure," is considered subject to modification by +some such clause as the following, "the word 'lighten' here being +understood to mean the reduction to some extent of what would be the +total pressure due to the combined original and added back-fill, +provided no arch action occurred." + +The writer is in entire agreement with the author as to the probability +that water is often "cut off absolutely from its source of pressure," +with the attendant results described by the author (p. 378); and again, +that too little attention has been given to the bearing power of soil, +with the author's accompanying criticism. + +The writer cannot see, however, where the author's experiments +demonstrate his statement "that pressure is transmitted laterally +through ground, most probably along or nearly parallel to the angles of +repose," or any of the conclusions drawn by him in the paragraph (p. +381), which contains this questionable statement. Again the writer is at +a loss as to how to interpret the statement that the author has found +that "better resistance" has been offered by "small open caissons sunk +to a depth of a few feet and cleaned out and filled with concrete" than +by "spreading the foundation over four or five times the equivalent +area." The writer agrees with the author in the majority of his +statements as to the "bearing value and friction on piles," but believes +that he is indulging in pure theory in some of his succeeding remarks, +wherein he ascribes to arch action the results which he believes would +be observed if "a long shaft be withdrawn vertically from moulding +sand." These phenomena would be due rather to capillary action and the +resulting cohesion. + +Naturally, the writer doubts the author's conclusions as to the pressure +at the top of large square caisson shafts when he states that "the +pressure at the top * * * will * * * increase proportionately to the +depth." Again, the author is apparently not conversant with experiments +made by the Dock Department of New York City, concerning piles driven in +the Hudson River silt, which showed that a single heavily loaded pile +carried downward with it other unloaded piles, driven considerable +distances away, showing that it was not the pile which lacked in +resistance, as much as the surrounding earth. + +In conclusion, the writer heartily concurs with the statement that "too +much has been taken for granted in connection with earth pressures and +resistance," and he is sorry to be forced to add that he believes the +author to be open to the criticism which he himself suggests, that "both +in experimenting and observing, the engineer [and in this case the +author] will frequently find what is being looked for or expected and +will fail to see the obvious alternative." + + +FRANCIS L. PRUYN, M. AM. SOC. C. E. (by letter).--Mr. Meem +should be congratulated, both in regard to the highly interesting +theories which he advances on the subject of sand pressures--the +pressures of subaqueous material--and on his interesting experiments in +connection therewith. + +The experiment in which the plunger on the hydraulic ram is immersed in +sand and covered with water does not seem to be conclusive. By this +experiment the author attempts to demonstrate that the pressure of the +water transmitted through the sand is only about 40% as great as when +the sand is not there. The travel of ground-water through the earth is +at times very slow, and occasionally only at the rate of from 2 to 3 ft. +per hour. In the writer's opinion, Mr. Meem's experiment did not cover +sufficient time during which the pressure was maintained at any given +point. It is quite probable that it may take 15 or 20 min. for the full +pressure to be transmitted through the sand to the bottom of the +plunger, and it is hoped, therefore, that he will make further +experiments lasting long enough to demonstrate this point. + +In regard to the question of skin friction on caissons and piles, it may +be of interest to mention an experiment which the writer made during the +sinking of the large caissons for the Williamsburg Bridge. These +caissons were about 70 ft. long and 50 ft. wide. The river bottom was +about 50 ft. below mean high water, and the caissons penetrated sand of +good quality to a depth of from 90 to 100 ft. below that level. On two +occasions calculations were made to determine the skin friction while +the caissons were being settled. With the cutting edge from 20 to 30 ft. +below the river bottom, the calculations showed that the skin friction +was between 500 and 600 lb. per sq. ft. The writer agrees with Mr. Meem +that, in the sinking of caissons, the arch action of sand is, in a great +measure, destroyed by the compressed air which escapes under the cutting +edge and percolates up through the material close to the sides of the +caissons. + +With reference to the skin friction on piles, the writer agrees with Mr. +Meem that in certain classes of material this is almost a negligible +quantity. The writer has jacked down 9-in. pipes in various parts of New +York City, and by placing a recording gauge on the hydraulic jack, the +skin friction on the pile could be obtained very accurately. In several +instances the gauge readings did not vary materially from the surface +down to a penetration of 50 ft. In these instances the material inside +the pipe was cleaned out to within 1 ft. of the bottom of the pile, so +that the gauge reading indicated only the friction on the outside of the +pipe plus the bearing value developed by its lower edge. For a 9-in. +pipe, the skin friction on the pile plus the bearing area of the bottom +of the pipe seems to be about 20 tons, irrespective of the depth. After +the pipe had reached sufficient depth, it was concreted, and, after the +concrete had set, the jack was again placed on it and gauge readings +were taken. It was found that in ordinary sands the concreted steel pile +would go down from 3 to 6 in., after which it would bring up to the full +capacity of a 60-ton jack, showing, by gauge reading, a reaction of from +70 to 80 tons. + +It is the writer's opinion that, in reasonably compact sands situated at +a depth below the surface which will not allow of much lateral movement, +a reaction of 100 tons per sq. ft. of area can be obtained without any +difficulty whatever. + + +FRANK H. CARTER, ASSOC. M. AM. SOC. C. E. (by letter).--Mr. +Meem has contributed much that is of value, particularly on water +pressures in sand; just what result would be obtained if coarse crushed +stone or similar material were substituted for sand in Experiment No. 6, +is not obvious. + +It has been the practice lately, among some engineers in Boston, as well +as in New York City, to assume that water pressures on the underside of +inverts is exerted on one-half the area only. The writer, however, has +made it a practice first to lay a few inches of cracked stone on the +bottom of wet excavations in order to keep water from concrete which is +to be placed in the invert. In addition to the cracked stone under the +inverts, shallow trenches dug laterally across the excavation to insure +more perfect drainage, have been observed. Both these factors no doubt +assist the free course of water in exerting pressure on the finished +invert after the underdrains have been closed up on completion of the +work. The writer, therefore, awaits with interest the repetition of +Experiment No. 6, with water on the bottom of a piston buried in coarse +gravel or cracked stone. + +As for the arching effect of sand, the writer believes that Mr. Meem has +demonstrated an important principle, on a small scale. It must be +regretted, however, that the box was not made larger, for, to the +writer, it appears unsafe to draw such sweeping conclusions from small +experiments. As small models of sailboats fail to develop completely +laws for the design and control of large racing yachts, so experiments +in small sand boxes may fail to demonstrate the laws governing actual +pressures on full-sized structures. + +For some time the writer has been using a process of reasoning similar +to that of the author for assumptions of earth pressure on the roofs of +tunnel arches, except that the vertical forces assumed to hold up the +weight of the earth have been ascribed to cohesion and friction, along +what might be termed the sides of the "trench excavation." + +The writer fails to find proof in this paper of the author's statement +that earth pressures on the sides of a structure buried in earth are +greater at the top than at the bottom of a trench. That some banks are +"top-heavy," is, no doubt, a fact, the writer having often heard similar +expressions used by experienced trench foremen, but, in every case +called to his attention, local circumstances have caused the +top-heaviness, either undermining at the bottom of the trench, too much +banked earth on top, or the earth excavated from the trench being too +near the edge of the cut. + +For some years the writer has been making extended observations on deep +trenches, and, thus far, has failed to find evidence, except in aqueous +material, of earth pressures which might be expected from the known +natural slope of the material after exposure to the elements; and this +latter feature may explain why sheeted trenches stand so much better +than expected. If air had free access to the material, cohesion would be +destroyed, and theoretical pressures would be more easily developed. +With closely-sheeted trenches, weathering is practically excluded, and +the bracing, which seemingly is far too light, holds up the trench with +scarcely a mark of pressure. As an instance, in 1893, the writer was +successfully digging sewer trenches from 10 to 14 ft. deep, through +gravel, in the central part of Connecticut, without bracing; because of +demands of the work in another part of the city, a length of several +hundred feet of trench was left open for three days, resulting in the +caving-in of the sides. The elements had destroyed the cohesion, and the +sides of the trenches no longer stood vertically. + +Recently, in the vicinity of Boston, trenches, 32 ft. wide, and from 25 +to 35 ft. deep, with heavy buildings on one side, have been braced with +8 by 10-in. stringers, and bracers at 10-ft. centers longitudinally, and +from 3 to 5 ft. apart vertically; this timbering apparently was too +slight for pressures which, theoretically, might be expected from the +natural slope of the material. Just what pressures develop on the sides +of the structures in these deep trenches after pulling the top sheeting +(the bottom sheeting being left in place) is, of course, a matter of +conjecture. There can be no doubt that there is an arching of the +material, as suggested by the author. How much this may be assisted by +the practical non-disturbance of the virgin material is, of course, +indeterminate. That substructures and retaining walls designed according +to the Rankine or similar theories have an additional factor of safety +from too generous an assumption in regard to earth pressure is +practically admitted everywhere. It is almost an engineering axiom that +retaining walls generally fail because of insufficient foundation only. + +For the foregoing reasons, and particularly from observations on the +effect of earth pressures on wooden timbers used as bracing, the writer +believes that, ordinarily, the theoretical earth pressures computed by +Rankine and Coulomb are not realized by one-half, and sometimes not even +by one-third or one-quarter in trenches well under-drained, rapidly +excavated, and thoroughly braced. + + +J.C. MEEM, M. AM. SOC. C. E. (by letter).--The writer has been +much interested in this discussion, and believes that it will be of +general value to the profession. It is unfortunate, however, that +several of the points raised have been due to a careless reading of, or +failure to understand, the paper. + +Taking up the discussion in detail, the writer will first answer the +criticisms of Mr. Goodrich. He says: + + "The writer believes that, in the design of permanent structures, + consideration of arch action should not be included, at least, not + until more information has been obtained. He also believes that the + design of temporary structures with this inclusion is actually + dangerous in some instances." + +If the arching action of earth exists, why should it not be recognized +and considered? The design of timbering for a structure to rest, for +instance, at a depth of from 200 to 300 ft. in normal dry earth, without +considering this action, would be virtually prohibitive. + +Mr. Goodrich proceeds to show one of the dangers of considering such +action by quoting the writer, as follows: + + "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." + +He fails, as do so many other critics of this theory, to distinguish the +difference between that portion of the sand which acts as so-called +"centering" and that which goes to make up the sustaining arch. The +dislodgment of any large portion of this "centering" naturally causes +collapse, unless it is caught, in which case the void in the "centering" +is filled from the material in the sustaining arch, and this, in turn, +is filled from that above, and so on, until the stability of each arch +is in turn finally established. This, however, does not mean that, +during the process of establishing this equilibrium of the arch +stresses, there is no arching action of any of the material above, but +only that some of the so-called arches are temporarily sustained by +those below. That is, in effect, each area of the material above +becomes, in turn, a dependent, an independent, and finally an +interdependent arch. + +If Mr. Goodrich's experience has led him to examine any large number of +tunnel arches or brick sewers, he will have noted in many of them +longitudinal cracks at the soffits of the arches and perhaps elsewhere. +These result from three causes: + +_First._--In tunneling, there is more or less loss of material, while, +in back-filling, the material does not at first reach its final +compactness. Therefore, in adjusting itself to normal conditions, this +material causes impact loads to come upon the green arch, and these tend +to crack it. + +_Second._--No matter how tightly a brick or other arch is keyed in, +there must always be some slight subsidence when the "centers" are +struck. This, again, results in a shock, or impact loading, to the +detriment of the arch. + +_Third._--The most prolific cause, however, is that in tunneling, as +well as in back-filling open cuts, the material backing up the haunches +is more or less loosened and therefore is not at first compact enough to +prevent the spreading of the haunches when the load comes on the arch. +This causes cracking, but, as soon as the haunches have been pressed out +against the solid material, the cracking usually ceases, unless the +pressure has been sufficiently heavy to cause collapse. + +An interesting example of this was noted in the Joralemon Street branch +of the Rapid Transit Tunnel, in Brooklyn, in which a great many of the +cast-iron rings were cracked under the crown of the arch, during +construction; but, in spite of this, they sustained, for more than two +years, a loading which, according to Mr. Goodrich, was continually +increasing. In other words, the cracked arch sustained a greater loading +than that which cracked the plates during construction, according to his +theory, as noted in the following quotation: + + "But it should be equally conceded by the advocates of the + existence of such action that changes in humidity, due to moving + water, vibration, and appreciable viscosity, etc., will invariably + destroy this action in time." + +As to the correctness of this theory Mr. Goodrich would probably have +great difficulty in convincing naturalists, who are aware that many +animals live in enlarged burrows the stability of which is dependent on +the arching action of the earth; in fact, many of these burrows have +entrances under water. He would also have some difficulty in convincing +those experienced miners who, after a cave-in, always wait until the +ground has settled and compacted itself before tunneling, usually with +apparent safety, over the scene of the cave-in. + +The writer quotes as follows from Mr. Goodrich's discussion: + + "In any case, no arch action can be brought into play until a + certain amount of settlement has taken place so as to bring the + particles into closer contact, and in such a way that the internal + stresses are practically those only of compression, and the + shearing stresses are within the limits possible for the material + in question." + +Further: + + "Consequently, an almost infinitesimal settlement of the + 'centering' may cause the complete destruction of an arch of + earth." + +And further: + + "On the other hand, it is believed that the author's statement, as + to the 'tendency of marbles to arch,' * * * should be qualified by + the addition of the words, 'only when a certain amount of + deflection has taken place so as to bring the arch into action.'" + +In a large measure the writer agrees with the first and last quotations, +but sees no reason to endorse the second, as it is impossible to +consider any arch being built which does not settle slightly, at least, +when the "centers" are struck. + +Regarding his criticism of the lack of arching action in balls or +marbles, he seems to reason that the movement of the marbles would +destroy the arch action. It is very difficult for the writer to conceive +how it would be possible for balls or marbles to move when confined as +they would be confined if the earth were composed of them instead of its +present ingredients, and under the same conditions otherwise. Mr. +Goodrich can demonstrate the correctness of the writer's theories, +however, if he will repeat the writer's Experiment No. 3, with marbles, +with buckshot, and with dry sand. He is also advised to make the +experiment with sand and water, described by the writer, and is assured +that, if he will see that the washers are absolutely tight before +putting the water into the box, he can do this without bringing about +the collapse of the arch; the only essential condition is that the +bottom shall be keyed up tightly, so as not to allow the escape of any +sand. He is also referred to the two photographs, Plate XXIV, +illustrating the writer's first experiment, showing how increases in the +loading resulted in compacting the material of the arch and in the +consequent lowering of the false bottom. As long as the exposed sand +above this false bottom had cohesion enough to prevent the collapse of +the "centering," this arch could have been loaded with safety up to the +limits of the compressive strength of the sand. + +To quote again from Mr. Goodrich: + + "Furthermore, the author's reason for bisecting the angle between + the vertical and the angle of repose of the material, when he + undertakes to determine the thickness of key, is not obvious. This + assumption is shown to be absurd when carried to either limit, for + when the angle of repose equals zero, as is the case with water, + this method would give a definite thickness of key, while there can + be absolutely no arch action possible in such a case; and, when the + angle of repose is 90°, as may be assumed in the case of rock, this + method would give an infinite thickness of key, which is again seen + to be absurd." + +Mr. Goodrich assumes that water or liquid has an angle of repose equal +to zero, which is true, but the writer's assumptions applied only to +solid material, and the liquid gives an essentially different condition +of pressure, as shown by a careful reading of the paper. In solid rock +Mr. Goodrich assumes an angle of repose equal to 90°, for which there is +no authority; that is, solid rock has no known angle of repose. In order +to carry these assumptions to a definite conclusion, we must assume for +that material with an angle of repose of 90° some solid material which +has weight but no thrust, such as blocks of ice piled vertically. In +this case Mr. Goodrich can readily see that there will be no arching +action over the structure, and that the required thickness of key would +be infinite. As to the other case, it is somewhat difficult to conceive +of a solid with an angle of repose of zero; aqueous material does not +fulfill this condition, as it is either a liquid or a combination of +water and solid material. The best illustration, perhaps, would be to +assume a material composed of iron filings, into which had been driven a +powerful magnet, so that the iron filings would be drawn horizontally in +one direction. It is easy to conceive, then, that in tunneling through +this material there would be no necessity for holding up the roof; the +definite thickness of key given, as being at the point of intersection +of two 45° angles, would be merely a precautionary measure, and would +not be required in practice. + +It is thus seen that both these conditions can be fulfilled with +practical illustrations; that is, for an angle of repose of 90°, that +material which has weight and no thrust, and for an angle of repose of +zero, that solid material which has thrust but no weight. + +Mr. Goodrich says the author has given no experiments to prove his +statement that the arch thrust is greater in dryer sand. If Mr. Goodrich +will make the experiment partially described as Experiment No. 3, with +absolutely dry sand, and with moist sand, and on a scale large enough +to eliminate cohesion, he will probably find enough to convince him that +in this assumption the writer is correct. At the same time, the writer +has based his theory in this regard on facts which are not entirely +conclusive, and his mind is open as to what future experiments on a +large scale may develop. It is very probable, however, that an +analytical and practical examination of the English experiments noted on +pages 379 and 380, will be sufficient to develop this fact conclusively. + +The writer is forced to conclude that some of the criticisms by Mr. +Goodrich result from a not too careful reading of the paper. For +instance, he states: + + "'It is conceded' (line 2, p. 357, for example) when the writer, + for one, has not even conceded the accuracy of the assumptions." + +A more careful reading would have shown Mr. Goodrich that this +concession was one of the writer's as to certain pressures against or on +tunnels, and, if Mr. Goodrich does not concede this, he is even more +radical than the writer. + +And again: + + "'Nor can anyone * * * doubt that the top timbers are stressed more + heavily than those at the bottom' is emphatically doubted and + earnestly denied by the writer." + +It is unfortunate that Mr. Goodrich failed to make the complete +quotation, which reads: + + "Nor can anyone, looking at Fig. 5, doubt," etc. + +A glance at Fig. 5 will demonstrate that, under conditions there set +forth, the writer is probably correct in his assertion as relating to +that particular instance. Further: + + "For instance, the author's well-known theory that the pressures + against retaining walls are a maximum at the top and decrease to + zero at the bottom, is in absolute contradiction to the results of + experiments conducted on a large scale by the writer on the new + reinforced concrete retaining wall near the St. George Ferry, on + Staten Island." + +The writer's "well-known theory that pressures against retaining walls +are a maximum at the top and decrease to zero at the bottom" applies +only to pressures exerted by absolutely dry and normally dry material, +and it seems to him that this so-called theory is capable of such easy +demonstration, by the simple observation of any bracing in a deep trench +in material of this class, that it ought to be accepted as at least +safer than the old theory which it reverses. As to this "well-known +theory" in material subject to water pressure, a careful reading of the +paper, or an examination of Fig. 12 and its accompanying text, or an +examination of Table 1, will convince Mr. Goodrich that, under the +writer's analysis, this pressure does not decrease to zero at the +bottom, but that in soft materials it may be approximately constant all +the way down, while, in exceptionally soft material, conditions may +arise where it may increase toward the bottom. The determination should +be made by taking the solid material and drying it sufficiently so that +water does not flow or seep from it. When this material is then +compacted to the condition in which it would be in its natural state, +its angle of repose may be measured, and may be found to be as high as +60 degrees. The very fine matter should then be separated from the +coarser material, and the latter weighed, to determine its proportion. +Subtracting this from the total, the remainder could be credited to +"aqueous matter." It is thus seen that with a material when partially +dried in which the natural angle of repose might be 60°, and in which +the percentage of water or aqueous matter when submerged might be 60%, +there would be an increase of pressure toward the bottom. + +The writer does not know the exact nature of the experiments made at St. +George's Ferry by Mr. Goodrich, but he supposes they were measurements +of pressures on pistons through holes in the sheeting. He desires to +state again that he cannot regard such experiments as conclusive, and +believes that they are of comparative value only, as such experiments do +not measure in any large degree the pressure of the solid material but +only all or a portion of the so-called aqueous matter, that is, the +liquid and very fine material which flows with it. Thus it is well known +that, during the construction of the recent Hudson and North River +Tunnels, pressures were tested in the silt, some of which showed that +the silt exerted full hydrostatic pressure. At the same time, W.I. Aims, +M. Am. Soc. C. E., stated in a public lecture, and recently also to the +writer, that in 1890 he made some tests of the pressure of this silt in +normal air for the late W.R. Hutton, M. Am. Soc. C. E. A hole, 12 in. +square, was cut through the brickwork and the iron lining, just back of +the lock in the north tube (in normal air), and about 1000 ft. from the +New Jersey shore. It was found that the silt had become so firm that it +did not flow into the opening. Later, a 4-in. collar and piston were +built into the opening, and, during a period covering at least 3 months, +constant observations showed that no pressure came upon it; in fact, it +was stated that the piston was frequently worked back and forth to +induce pressure, but no response was obtained during all this period. +The conclusion must then be drawn that when construction, with its +attendant disturbance, has stopped, the solid material surrounding +structures tends to compact itself more or less, and solidify, according +as it is more or less porous, forming in many instances what may be +virtually a compact arch shutting off a large percentage of the normal, +and some percentage even of the aqueous, pressure. + +That the pressure of normally dry material cannot be measured through +small openings can be verified by any one who will examine such material +back of bracing showing evidences of heavy pressure. The investigator +will find that, if this material is free from water pressure, paper +stuffed lightly into small openings will hold back indefinitely material +which in large masses has frequently caused bracing to buckle and +sheeting planks to bend and break; and the writer reiterates that such +experiments should be made in trenches sheeted with horizontal sheeting +bearing against short vertical rangers and braces giving horizontal +sections absolutely detached and independent of each other. In no other +way can such experiments be of real value (and even then only when made +on a large scale) to determine conclusively the pressure of earth on +trenches. + +As to the questions of the relative thrust of materials under various +angles of repose, and of the necessity of dividing by the tangent, etc.; +these, to the writer, seem to be merely the solution of problems in +simple graphics. + +The writer believes that if Mr. Goodrich will make, even on a small +scale, some of the experiments noted by the writer, he will be convinced +that many of the assumptions which he cannot at present endorse are +based on fact, and his co-operation will be welcomed with the greatest +interest. Among the experiments which he is asked to make is the one in +dry sand, noted as Experiment No. 3, whereby it can be shown very +conclusively that additional back-fill will result in increased arching +stability, on an arch which would collapse under lighter loading. + +The writer is indebted to Mr. Goodrich for pointing out some errors in +omission and in typography (now corrected), and for his hearty +concurrence in some of the assumptions which the writer believed would +meet with greatest disapproval. + +In reply to Mr. Pruyn and Mr. Gregory, the writer assumed that the +piston area in Experiment No. 6 should be reduced only by the actual +contact of material with it. If this material in contact should be +composed of theoretical spheres, resulting in a contact with points +only, then the theoretical area reduced should be in proportion to this +amount only. The writer does not believe, however, that this condition +exists in practice, but thinks that the area is reduced very much more +than by the actual theoretical contact of the material. He sees no +reason, as far as he has gone, to doubt the accuracy of the deductions +from this experiment. + +Regarding the question of the length of time required to raise the +piston, he does not believe that the position of his critics is entirely +correct in this matter; that is, it must either be conceded that the +piston area is cut off from the source of pressure, or that it is in +contact with it through more or less minute channels of water. If it is +cut off, then the writer's contention is proved without the need of the +experiment, and it is therefore conclusive that a submerged tunnel is +not under aqueous pressure or the buoyant action of water. If, on the +other hand, the water is in contact through channels bearing directly +upon the piston and leading to the clear water chamber, any increase in +pressure in the water chamber must necessarily result in a virtually +instantaneous increase of the pressure against the piston, and therefore +the action on the latter should follow almost immediately. In all cases +during the experiments the piston did not respond until the pressure was +approximately twice as great as required in clear water, therefore the +writer must conclude either that the experiments proved it conclusively +or that his assumption is proved without the necessity of the +experiments. That is, the pressure is virtually not in evidence until +the piston has commenced to move. + +Mr. Pruyn has added valuable information in his presentation of data +obtained from specific tests of the bearing value of, and friction on, +hollow steel piles. These data largely corroborate tests and +observations by the writer, and are commended to general attention. + +Mr. Carter's information is also of special interest to the writer, as +much of it is in the line of confirming his views. Mr. Carter does not +yet accept the theory of increased pressure toward the top, but if he +will examine or experiment with heavy bracing in deep trenches in clear +sand, or material with well-defined angles of repose, he will probably +find much to help him toward the acceptance of this view. + +The writer regrets that he has not now the means or appliances for +further experiments with the piston chamber, but he does not believe +that reliable results could be obtained in broken stone with so small a +piston, as it is possible that the point of one stone only might be in +contact with the piston. This would naturally leave the base exposed +almost wholly to a clear water area. He does not believe, however, that +in practice the laying of broken stone under inverts will materially +change the ultimate pressure unless its cross-section represents a large +area. + +Mr. Perry will find the following on page 369: + + "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." + +This, of course, depends on the porosity of the material and the +friction the water meets in passing through it. + +As to Mr. Thomson's discussion, the writer notes with regret two points: +(_a_) that specific data are not given in many of the interesting cases +of failures of certain structures or bracing; and (_b_), that he has +not in all cases a clear understanding of the paper. For instance, the +writer has not advocated the omission of bottom bracing or sheeting. He +has seen many instances where it has been, or could have been, safely +omitted, but he desires to make it clear that he does not under any +circumstances advocate its omission in good work; but only that, in +well-designed bracing, its strength may be decreased as it approaches +the bottom. + +Reference is again made to the diagram, Fig. 12, which shows that, in +most cases of coffer-dams in combined aqueous and earth pressure, there +may be nearly equal, and in some cases even greater, loading toward the +bottom. + +The writer also specifically states that in air the difference between +aqueous and earth pressure is plainly noted by the fact that bracing is +needed so frequently to hold back the earth while the air is keeping out +the water. + +The lack of specific data is especially noticeable in the account of the +rise of the 6-ft. conduit at Toronto. It would be of great interest to +know with certainly the weight of the pipe per foot, and whether it was +properly bedded and properly back-filled. In all probability the +back-filling over certain areas was not properly done, and as the pipe +was exposed to an upward pressure of nearly 1600 lb. per ft., with +probably only 500 or 600 lb. of weight to counterbalance it, it can +readily be seen that it did not conform with the writer's general +suggestion, that structures not compactly, or only partially, buried, +should have a large factor of safety against the upward pressure. +Opposed to Mr. Thomson's experience in this instance is the fact that +oftentimes the tunnels under the East River approached very close to the +surface, with the material above them so soupy (owing to the escape of +compressed air) that their upper surfaces were temporarily in water, yet +there was no instance in which they rose, although some of them were +under excessive buoyant pressure. + +It is also of interest to note, from the papers descriptive of the North +River Tunnel, that, with shield doors closed, the shield tended to rise, +while by opening the doors to take in muck the shield could be brought +down or kept down. The writer concurs with those who believe that the +rising of the shield with closed doors was due to the slightly greater +density of the material below, and was not in any way due to buoyancy. + +Concerning the collapse of the bracing in the tunnel built under a +side-hill, the writer believes it was due to the fact that it was under +a sliding side-hill, and that, if it had been possible to have +back-filled over and above this tunnel to a very large extent, this +back-fill would have resulted in checking the sliding of material +against the tunnel, and the work would thereafter have been done with +safety. This is corroborated by Mr. Thomson's statement that the tunnel +was subsequently carried through safely by going farther into the hill. + +As to the angle of repose, Mr. Thomson seems to feel that its +determination is so often impracticable that it is not to be relied on; +and yet all calculations pertaining to earth pressure must be based on +this factor. The writer believes that the angle of repose is not +difficult to determine, and that observations of, and experiments on, +exposed banks in similar material, and general experience in relation +thereto, will enable one to determine it in nearly all cases within such +reasonably accurate limits that only a small margin of safety need be +added. + +Engineers are sent to Europe to study sewage disposal, water +purification, transit problems, etc., but are rarely sent to an +adjoining county or State to look at an exposed bank, which would +perhaps solve a vexed problem in bracing and result in great economy in +the design of permanent structures. + +Mr. Thomson's general views seem to indicate that much of the subject +matter noted in the paper relates to unsolvable problems, for it appears +that in many cases he believes the Engineer to be dependent on his +educated guess, backed perhaps by the experienced guess of the foreman +or practical man. The writer, on the contrary, believes that every +problem relating to work of this class is capable of being solved, +within reasonably accurate limits, and that the time is not far distant +when the engineer, with his study of conditions, and samples of material +before him, will be able to solve his earth pressure and earth +resistance problems as accurately as the bridge engineer, with his +knowledge of structural materials, solves bridge problems. + +The writer, in the course of his experience, has met with or been +interested in the solution of many problems similar to the following: + +What difference in timbering should be made for a tunnel in ordinary, +normally dry ground at a depth of 20 ft. to the roof, as compared with +one at a depth of 90 ft.? + +What difference in timbering or in permanent design should be made for a +horizontally-sheeted shaft, 5 ft. square, going to a depth of 45 ft. and +one 25 by 70 ft., for instance, going to the same depth, assuming each +to be braced and sheeted horizontally with independent bracing? + +What allowance should be made for the strength of interlock, assuming +that a circular bulkhead of sand, 30 ft. in diameter, is to be carried +by steel sheet-piling exposed around the outside for a depth of 40 ft.? + +What average pressure per square foot of area should be required to +drive a section of a 3 by 15-ft. roof shield, as compared with the +pressure needed to drive the whole roof shield with an area four times +as great? + +To what depth could a 12 by 12-in. timber be driven, under gradually +added pressure, up to 60 tons, for instance, in normal sand? + +What frictional resistance should be assumed on a hollow, steel, +smooth-bore pile which had been driven through sharp sand and had +penetrated soft, marshy material the bearing resistance of which was +practically valueless? + +What allowance should be made for the buoyancy of a tunnel 20 ft. in +diameter, the top of which was buried to a depth of 20 ft. in sand above +which there was 40 ft. of water? + +It is believed by the writer that most of the authorities are silent as +to the solution of problems similar to the above, and it is because of +this lack of available data that he has directed his studies to them. +The belief that the results of these studies, together with such +observations and experiments as relate thereto, may be of interest, has +caused him to set them forth in this paper. + +He desires to state his belief that if problems similar to the above +were given for definite solution, not based on ordinary safe practice, +and without conference, to a number of engineers prominently interested +in such matters, the results would vary so widely as to convince some of +the critics of this paper that the greater danger lies rather in the +non-exploration of such fields than in the setting forth of results of +exploration which may appear to be somewhat radical. + +Further, if these views result in stimulating enough interest to lead to +the hope that eventually the "Pressure, Resistance, and Stability" of +ground under varying conditions will be known within reasonably accurate +limits and tabulated, the writer will feel that his efforts have not +been in vain. + + +FOOTNOTES: + +[Footnote H: "Lateral Earth Pressures and Related Phenomena," +_Transactions_, Am. Soc. C. E., Vol. LIII, p. 272.] + + + + + +End of the Project Gutenberg EBook of Pressure, Resistance, and Stability of +Earth, by J. C. Meem + +*** END OF THIS PROJECT GUTENBERG EBOOK PRESSURE AND RESISTANCE *** + +***** This file should be named 16938-8.txt or 16938-8.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/1/6/9/3/16938/ + +Produced by Juliet Sutherland, Taavi Kalju and the Online +Distributed Proofreading Team at https://www.pgdp.net + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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