US 3748800 A
The present invention relates to earthquake-insulation foundation construction consisting of floating a spring-centered building-base upon a water-filled excavation which has been lined with a spring-tensioned cable network covered with an expansible, pleated, water-tight sheet. Alternative means consist of resting a flat-bottomed building-base upon an excavation filled with a dry granular particulate such as sand.
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Description (OCR text may contain errors)
United States Patent 1 Glicksherg [451 July 31, 1973 EARTHQUAKE-INSULATION FOUNDATIONS  Inventor: iiayinlind Charles cliclr sberg m l Santa Monica Boulevard, Monica, Calif. 90401  Filed: Apr. 22, 1971  Appl, No.: 136,514
 US. Cl 52/167, 52/168, 52/169  Int. Cl E04h 9/02, E02d 27/34  Field of Search 52/1, 606, 167, 206,
[5 6] V 9 References Cited UNITED STATES PATENTS 1,088,239 2/1914 Paine 52/167 X 3,232,015 2/1966 Latham 52/167 2,035,009 Rager 52/167 3 ,204,5 85 9/1965 Carlisle 3,546,720 12/1967 Hoch et al.
R26,121 12/1966 Wiegand 1,847,820 3/1932 Montalk 52/167 Primary Examiner-Frank L. Abbott Assistant Examiner-Carl D. Friedman  ABSTRACT The present invention relates to earthquake-insulation foundation construction consisting of floating a springcentered building-base upon a water-filled excavation which has been lined with a spring-tensioned cable network covered with an expansible, pleated, watertight sheet. Alternative means consist of resting a flatbottomed building-base upon an excavation filled with a dry granular particulate such as sand.
7 Claims, 11 Drawing Figures PATENIED JUL3 1 I973 3.748,8OO
SHEET 1 OF 6 O OOOOOOOO Y A MW! J PATENIEDJUL31 ma 74 1300 sum 3 OF 6 Ill/III], $3 54 1 EARTHQUAKE-INSULATION FOUNDATIONS SUMMARY OF THE INVENTION Earthquake-insulation foundations limit the magnitudes of accelerations, velocities, and displacements transmitted to the framework of various types of buildings and structures by theearth during earthquakes. Present construction techniques of the vast majority of buildings and structures reveal that no earthquakeinsulation of foundations is provided, as dramatically demonstrated by earthquake-induced damage, destruction, and resultant loss of human life in recent earthquakes throughout the world. Even the most modern building techniques, utilizing reinforced concrete, deep-pile foundations, and/or steel frame construction, which are termed earthquake-resistance or earthquake-proof, have been shown to be, more realistically speaking, earthquake-prone, as proven, for example, by the destruction at the modern and recentlycompleted Olive View Hospital in the San Fernando, Cal. earthquake on Feb. 9, 1971. The destruction of hundreds of homes and buildings during this earthquake, with attendant loss of life, injury, and damage running in excess of $250 million, where earthquake magnitude was only 6.6 on the Richter scale at the epicenter, bears testimony to the potential destruction possible to major urban centers during even larger even so-called earthquake-resistant or earthquakeproof construction, mainly of buildings of all types, is that the foundations of these buildings are rigidly fixed to the ground, so that when'the earth moves, the foundation moves directly with it. All of the jolts, jostles, rocking and rolling of the earth are directly transmitted to the building foundation, and hence to the building itself. No matter how strongly the buildings are constructed, or how flexible their high-rise frameworks, these earthquake forces are directly transmitted to them, and, if large enough, can bring about partial or even total structural failure. If the building is situated in an area where faulting, crazing, lateral slippage and- /or vertical buckling of the earth occurs during the quake, the internal structural members of the building can be moved in relationship to each other, causing immediate, catastrophic collapse and total desctruction.
Liquifaction of certain soils during a quake can cause the soil to give way, with the building sinking or toppling as a result.
It is the object of this invention to produce new,
unique, and generally applicable basic methods of in sulating" building foundations from ground movement of all types, hence drastically reducing earthquakeinduced forces on the structures themselves to safe,-
In order to fulfill the above objective, this paper presents two basic methods of earthquake-insulation foundation construction, termed hydraulic and nonhydraulic, that provide limitations on the magnitudes of the accelerations, velocities, and displacements transmitted to the framework of various types of buildings and structures by the earth.
The hydraulic means basically consists of a floating, watertight building-base within a water-filled pool which has been excavated in the earth, and which watertight pool sides and bottom are appropriately and flexibly reinforced. The base of the building is centrally positioned within the pool by means of centering springs which provide a return force between the sides of the pool excavation and the sides of the base.
The non-hydraulic means of earthquake-insulation basically consists of resting a flat-bottomed buildingbaseon the surface of a pit of sand or other suitable low-coefficient-of-friction dry granular material, such as a mixture of sand and gravel.
Of the two means, hydraulic and non-hydraulic, the hydraulic is intended for' use with the larger buildings, including high-rise and skyscraper-type structures, and provides the maximum in earthquake-insulation protectiveness, reducing the amount .of earthquakeinduced accelerations of the structure to the lowest values possible, both laterally and vertically, while alleviating the dangers due to any faulting and slippage of adjacent sections of the earth. The non-hydraulic means is more intended for use with homes, stores, and two or three-story apartments and other structures, being less expensive, and although transmitting a larger degree of earthquake-induced shock than its hydraulic counterpart, especially any vertical components, still providing a safe limitation on transmitted accelerations and protection against damage due to faulting and slippage of the earth, as determined by the low coefficient-offriction of the non-hydraulic medium and the flat, sliding bottom surface of the building-base. Both means provide adequate protection against possible liquifaction of certain types of soils during a quake, alleviating the dangers of sinking or toppling.
IN THE DRAWINGS FIG. 1 is a front view schematic drawing illustrating the basic, general features' of the hydraulic earthquakeinsulation foundation.
FIG. 2 is a top view schematic of the same foundation. I
FIG. 3 is a perspective view schematic drawing illustrating the basic, general features of the flexible springtension cable network reinforcing the pool sides, edges, and bottom, with-sheets of loose-dirt-retaining material held underneath.
FIG. 4 is a perspective view of the'foldcd, watertight exterior lining of the pool sides, edges, and bottom.
FIG. 5 is a side view of a possible method of providing the spring-centering action for the building-base.
FIG. 6 is a front view schematic drawing of a nonhydraulic earthquake-insulation foundation.
FIG. 7 is a table of unidirectional velocities and displacements of the earth crust for some simple acceleration pulses from 0.25 to 1.0 g in magnitude.
FIG. 8 is a table of bidirectional velocities and displacements of the earth crust for some sinusoidal accelerations from 0.25 to 1.0 g in rms magnitude.
TECHNICAL DESCRIPTION Referring to FIG. 1, which is a generalized embodiment of the hydraulic earthquake-insulation foundation, it can be seen that the main building structure 1 is rigidly constructed upon a base 2, both of which can be of any desired and practicable shape. It is possible that a multiplicity of various structures could be constructed upon a single, large base, such as an entire city block. Typically, the broader the base, the less the depth requirement for the base and the hydraulic liquid-filled pool 3, typically water, which the base floats in, and the more the inherent buoyant stability or restoring moment for the entire floating structure. Buoyant stability is maintained provided the center of grav ity of the displaced water moves outboard of the center of gravity 4 of the entire structure during any rotational disturbance. The building 1 and base 2 are maintained at a long-term center position within the pool by means of multiple centering springs 5 which typically provide tension from the sides of the pool excavation to the sides of the base by means of connecting cables 6. These centering springs are possibly arranged in at least two rows, upper and lower, to provide increased effectiveness against rotational disturbing torques about the horizontal and/or wider spacing between springs. The sides and bottom 7 of the base are watertight and may typically be constructed of reinforced concrete, metal,
plastic reinforced with fiberglass, and/or any other suitable watertight materials. The interior of the base can be constructed in a manner similar to the building itself and/or basements, perhaps including some watertight compartments. Within the base is a pumping-filtrationheating system 8 for the pool water, similar to those utilized for swimming pools, which circulates and purifies the water and maintains its temperature at least above freezing. All water, gas, sewer, electricity, telephone, and any other and all wire or pipe connections to the building structure are made through flexible tubes 9 which have suitable slack, and which may be located either above, below, or floated upon the water level. All pool coverings l0, typically consisting of sidewalks, driveways, stairways, planters and the like, which enclose the pool surface and join the building-base structure with the surrounding ground 11 and pavement 12, are connected to the building-base structure by means of pivot supports 13 which allow rotation of said coverings about the horizontal, and are freely-resting upon and capable of sliding, slipping, or rolling upon the surrounding pavement 12, so as to permit both rotational and translational movement of the building-base struc ture relative to the ground. These be further divided into shorter, independentlymoveable segments to provide them greater protection against longitudinal stresses due to possible raising and lowering of adjacent sections of the earth during a quake.
pool coverings may FIG. 2 illustrates the same hydraulic earthquakeinsulation foundation as seen from the top view. The number of centering springs about the periphery of the base is determined by the total spring force requirement and the force coefficient of the individual springs.
FIG. 3 illustrates the basic, general features of the flexible spring-tension cable network, which may be considered a typical but not necessarily only means of reinforcing the pool sides, edges, and bottom. The flexibility of the reinforcing is a desired characteristic to allow for the possibility of lateral slipping and/or vertical buckling of adjacent sections of the earth during an earthquake, which movements of parts of the earth crust relative to each other cause such damaging and even catastrophic failures in present-day rigid structures which are firmly attached to hard, solid ground. The cable network consists of cables 30 which are freely-woven into squares whose optimum size may be partly determined by particular soil characteristics, and which are not attached to each other except at the ends 31. Two-way stretch is provided by springs 32 which may be conveniently placed within each cable line, and the entire cable network is firmly attached to the ground at various corner points by anchors, piles, or any other support means 33. Held underneath the cable network may be large, interlapping sheets of loose-dirtretaining material 34, such as wire mesh or a plastic fabric.
FIG. 4 illustrates a typical embodiment of the watertight pool lining 40 which may be made of a suitable type of plastic material. The lining is folded, typically into square folds 41, so that possible bulging of the pool sides and bottom during an earthquake will permit the lining to expand with the bulge in all directions, rather than crack and leak as with a rigid, brittle lining.
FIG. 5 illustrates a possible method of providing the spring-centering action for the building-base, consisting of a metallic coil tension spring which is firmly attached to the side of the building base, typically by means of a recessed casing 51. The recess is large enough to contain the entire spring during its slight extension to maintain a small tension force at the neutral centering position of the base. The outer end of the spring is a loop 52 and is attached to a similar loop 53 of a cable 54 which in turn is attached to the earthern pool side through loops 55 and 56, recessed plate 57, which is tightly sealed against the plastic pool lining, and further supported against pull forces by anchor, pile, or other support means 58.
As can be seen from FIGS. 1 and 2, the floating, spring-centered building-base structure presents an interesting problem in dynamic response to various types of accelerations of the earth crust or parts of it relative to each other. A rigorous mathematical treatment of this motion would result in non-linear differential equations describing both translational and rotational movement of the structure, taking into consideration such complex effects as the shift of the center of buoyancy with rotation about the horizontal, the dependence of the pressure and friction drag of the water against the base not only upon the square of the water velocity but also upon Reynolds number, the variation of density and viscosity of water with temperature, the slant of the water surface during acceleration, rotation about both horizontal and vertical axes, the hydraulic jump effect for open-channel flow, in addition to the simpler linear forces contributed by the centering springs. Such a rigorous mathematical analysis could be suitably solved, preferrably by means of computer simulation, or else a small-scale physical model could be employed, but these means are beyond the scope and intent of this paper.
Fortunately, the problem can be simplified into its first-order-of-magnitude effects quite readily, by means of a gross estimate of the forces involved. A qualitative and quantitative judgement of resultant motion can then be made which can suffice for comparison purposes vis a vis orthodox, earthquake-prone foundations.
It should be noted that the basic concept behind the hydraulic earthquake-insulation foundation is that a body at rest tends to remain at rest, according to Newtons first law, and will only begin to move when acted upon by exterior forces. If these forces are purposely reduced in magnitude to be quite small, then it follows that the resultant movement of the body will be quite small also.
It is desirable for analysis, therefore, to assume a simple acceleration waveform of the earth crust which surrounds the entire structure, of a magnitude comparable to earthquake strength and in a direction which is perpendicular to a pool-lining surface, and to estimate the resultant magnitudes of the major forces acting upon the floating building-base structure, namely, the water drag forces, the spring forces, and the incremental buoyant forces, if any. The magnitudes of these major forces can then be used to estimate the resulting translational and rotational motion.
FIG. 7 is a table of peak velocity, average velocity, and displacement of the earth crust for acceleration pulses of 0.25, 0.50, 0.75, and 1.0 g for a positive and a negative pulse of 0.5 second each, and 0.25 second each. Such a pulse combination yields a unidirectional movement and resultant displacement of the earth crust from zero, which, while probably not a typical type of motion for earthquakes, can be used for the purpose of a simple analysis of building-base motion. It is interesting to note here that after the San Fernando earthquake of Feb. 9, 1971, it was found that there was a relative and permanent displacement between the San Gabriel Mountains and the San Fernando Valley floor of approximately 3 feet laterally and 3 feet vertically, although this displacement probably occured over the entire duration of the most intense shaking, anywhere from 15 to 60 seconds.
FIG. 8 is a table of peak velocity, rms velocity, and peak-to-peak displacement amplitude (or i displacement from zero) for earth-crust sinusoidal accelerations of 0.25, 0.5, 0.75, and L0 g rms, for frequencies of 0.5 and 1.0 cycle per second. It is interesting to note here that the published values for lateral acceleration (probably peak acceleration) for the San Fernando earthquake ranged from 0.5 to 0.75 g for the Van Norman dam and reservoir area, where a cement-coated earth-fill dam was destroyed, to 0.13 g for downtown Los Angeles, where several unreinforcedrbrick-type structures were either damaged or destroyed.
In orderto estimate the major forces involved, a typical building structure example will be assumed, of certain average density and dimensions. Round numbers will be used where practical.
Assuming the general shape of the structure to be that of FIGS. 1 and 2, it is known that the side dimensions of the building 1 are to be 120 ft. X 120 ft. The
building is to be 35 stories high, at 10 ft. per story average, which is 350 ft. The building is situated in the center of a square base 2, which is 300 ft. on each side. The
' densities of the building and the base are taken to be equal at 20 lbs. per cubic foot, and the density of water 62 lbs./cu. ft. Assume that it is desired to have the water level 3 feet below the top of the base.
It is known that the weight of the displaced water must be equal the weight of the entire floating structure. Therefore, if d is the depth of the water from its surface to the bottom of the base, then 300 X 300 X d X 62= X 120 X 350 X 20+300 X 300 X (d+ 3) X 20, and d= 28 ft. Also, d+ 3 31 ft., so that for this structure, the base is approximately 3 stories deep. A base of lesser plan-view area would result in an almost proportionally greater depth.
The weight of the entire structure is 300 X 300 X 28 X 62 1.56 X 10 lbs. 78,000 tons.
As a starting point for analysis, assume that the dimensions of the pool extend 6 feet beyond the base on sides and bottom. As will be seen later, the width of the water surrounding the sides and bottom of the base is primarily determined by a judgement of the type and intensity of the most severe earthquake to be protected against, and may also involve economic and'real estate considerations. It is expected that a reasonable range of water width may vary from 3 to 10 feet, depending upon these judgements. The dimensions of the pool of this example, therefore, are 312 X 312 ft. by 37 ft. deep.
The first major forces to consider that act upon the building-base structure when the earth crust accelerates laterally are the forces exerted by the moving water upon the partially submerged base. The water is caused to move by the advancing wall of the pool side, and for all practical purposes, can be considered to be an incompressible liquid. These water drag forces are divided into two types: pressure drag, which is caused by the downstream components of the forces transmitted from the water which are normal to the submerged surfaces of the base; and friction drag, which is caused by the downstream components of the forces transmitted from the water which are tangential to the submerged surfaces of the base.
The pressure drag is given as D,,= /& C A p V, where A is the area of the projection of the submerged portion of the base on a plane normal to the direction of V. V is normal to the advancing pool side, and is of a magnitude relative to the base identical to that of the pool side. For the example chosen, A is the area of one submerged side of the base, or 300 X 28 8,400 sq. ft. p is water density, which at 68 F is 62/32 appr. 2 slugs per cu. ft.
For this example, assume that earthquake acceleration pulses of plus 0.75 g and minus 0.75 g occur, each lasting 0.5 second. FlG. 7 shows that the average velocity of the earth crust during this time interval of movement is 6 ft./sec. This is to be taken as the average freestream water velocity, V.
The coefficient. of drag, C is an experimentally found quantity for submerged bodies of various shapes, and is a function of Reynolds Number, N, V d p/n, although C changes very little with N, for brusque ob jects. From avabilable fluid flow literature, the closest object shape for which C is listed is a flat plate, which approximates the front and rear surfaces of the base, which are the only two surfaces of the base which are normal to the flow and upon which pressure drag forces can be induced. N is computed at 68 F as 6 X 28 X 2/0.000021 1.55 X 10 From the literature. at this value of N,, C, is listed as 2.
Thus, D A X 2 X 8,400 X 2 X 36 600,000 lhs. 300 tons. Since the weight of the structure is 78,000 tons, it can be seen that the pressure drag for the average water velocity during the 0.75 g and 0.5 second earthquake acceleration pulses amounts to 300/78,000 0.0038 appr. 1/250 g.
Next to be estimated is the magnitude of the water friction drag which exists along the two submerged sides and bottom of the base which are tangential to the water flow. These areas are taken to be smooth flat plates, for which the total frictional drag is diven as D, =%C,A p V A is the area of the submerged sides and bottom of the base 2 X 300 X 28 300 X 300 106,800 sq. ft. C, is listed from experimentally derived data in the fluid flow literature and is dependent on whether the boundary layer flow is laminar or turbulent, for which N, is the criterion. N, V L p/p., where L is the length of the flat plate, or 300 ft. In this case, V is not the freestream water velocity in front of the base, but is the water velocity alongside the submerged sides and bottom, which is somewhat higher. This velocity can be computed as V=A v/A where A area of the submerged portion of the front of the base 300 X 28 8,400 sq. ft., A sides and bottom crosssectional areas of water flow 312 X 34 8,400 2,200 sq. ft., and v is the average freestream velocity 6 ft./sec. Therefore, V= 8.400 X 6/2200 23 ft./sec. Thus, Nr= 23 X 300 X 2/0.000021= 6.55X For this value of Reynolds Number it can be seen from the literature that the boundary layer flow is turbulent, and C, is given as 0.455/(log N,) for smooth flat plates, which, from a chart, is 0.0017. Thus, D,= 560.0017 X 106,800 X 2 X 530 96,000 lbs. appr. 50 tons. It can be seen that the friction drag for the average water velocity during the 0.75 g and 0.5 second earthquake acceleration pulses amounts to 50/78,000 0.00064 appr. l/l500 g.
Although the main lateral forces acting upon the base to consider during an earthquake are the water drag and spring forces, it becomes desirable to first investigate the magnitude of the possible range of wind forces upon the structure, before the spring forces. This is so because wind forces will occur much more often than earthquake forces, and the maximum computed wind forces will dictate the minimum spring forces necessary to maintain the structure somewhere near the center of the pool and prevent it from striking the sides during windy periods.
Asuume that the wind is blowing normal to one of the sides of the building, and that friction drag is negligible compared to pressure drag. The air is at 60 F, 14.7 lb./in. and two pressure drag cases for wind velocity are to be computed: 50 mph and 100 mph.
Pressure drag is given as D, =%C,, A p V where A area of a sidein the building 350 X 120 42,000 sq. ft. V=free stream wind velocity, and V 100 mph 100 X 5280/3600= 147 ft./sec.; V 50 mph=74 ft./sec. Cd is a function of Reynolds Number, NT Vdp/u, where d=width of building=120 ft., so that Nr 147 X 120 X 0.00237/3.75 X 10 1.1 X 10" for V=l00 mph, and for V=50 mph, N,-= 74 X 120 X 0.00237/3.75 X 10" 0.5 X 10". From a graph for a flat plate at these Reynold's Numbers,
8 Cd is found to be 2. Therefore, at 100 mph, D,,= /2 X 2 X 42,000 X 0.00237 X (147) =2,l40.000 lbs. =appr. 1.000 tons, which is equivalent to 1.000/ 78,000 appr. l/8( g. A1 50 mph. 1),, /2 X 2 X 42.000 X 0.00237 X (74) 540,000 lbs. I 270 tons, which is equivalent to 270/78.000 appr. l/300 g.
Now having a good estimate of the wind forces, certain criteria for proper selection of the centering-spring force coefficient can be ascertained. Simple economics dictates that the smaller the coefficient, the smaller and lighter the springs, and hence the lower thecost. The spring force coefficient should therefore be kept as low as possible consistent with adequate and proper operation during all design-point circumstances.
In the case of no wind, the spring force requirement would be the bare minimum necessary to maintain long-term centering of the building. During an earthquake, the spring force should also be a bare minimum, ideally no more than approximately the equivalent magnitude of water drag force, and in general should not exceed that of water drag force if possible, as this would transmit unncessary force to the building during the quake. In the case of a strong wind, the spring force must be large enough to counteract the translational motion of the structure that the wind causes and to limit this motion to within reasonable limits. Thus, it is the action of the highest design-point wind that imposes the most rigid constraint on the strength of the spring force coefficient requirement, and this requirement should not severly contradict the desire for the spring force to be generally equal to or less than the water drag force 'during an earthquake.
The resultant of the wind forces against the entire side of the building acts through the center of pressure halfway up or 175 feet above the top of the base. The center of gravity of the entire building base structure can be computed as being 109.5 feet above the top of the base, as shown under following computations for moment of inertia. Thus, the resultant wind force acts through a lever arm which is 65.5 feet above the center of gravity, and the wind force creates a rotational moment which is counteracted by the restoring moment of the buoyant force acting through a center of buoyancy which has moved a certain distance outboard of the center of gravity of the building-base structure for a certain small inclination angle of the structure. The entire translational force due to the wind must be counteracted by the springs, and a good approximation of the total spring force requirement is to equate it to the wind force. Thus, the total spring force must equal the 1,000 tons wind force for some acceptable displacement of the structure. Setting this acceptable displacement for a 100 mph wind at 5 feet, leaving a 1 foot margin from the pool side, yields a total spring force coefficient requirement of 1,000 tons/5 ft. 200 tons/ft. A 50 mph wind acting upon the structure would thus cause a displacement of 270 tons/200 1.35 ft. Trade-offs will exist among types, costs, force coefficients, length-to-diameter ratio, wire size, operational characteristics, and spacing of individual springs or nests of springs, one inside the other, versus the total number of springs to be used. Assuming that, for this example, individual springs on a side are to be used, the force coefficient for the individual springs would be approximately 200/100 2 tons/ft./spring. Actually, the additional force contributed by the springs on the other two sides of the base which are parallel to the motion would subtract from this requirement somewhat.
Comparing the magnitude of the spring force with the water drag force, it can be seen that for a 0.75 g, unidirectional quake with 0.5 second pulses: at A second, v 6 ft./sec., s (the displacement) 1.5 ft., and the water drag is 300 tons pressure drag plus 50 tons friction drag 350 tons. The spring force is 1.5 X 200 300 tons, which is less than the water drag. At A second, v =12 ft./sec., and s 3 ft. Water drag 4 X 350 1,400 tons, and spring force 3 X 200 600 tons. At 0.75 seconds, v 6 ft./sec., and s 4.5 ft. Water drag 350 tons, and sprihg force 4.5 X 200 900 tons. Thus it can be seen that the spring force is of the same order of magnitude as water drag, and for the positive acceleration pulse of the quake, is less than water drag. Therefore, unwanted, excessive spring force during a quake is not incurred by meeting the design-point wind condition requirement.
A summation of the forces acting upon the buildingbase structure reveals that for the 0.75 g, unidirectional earthquake with 0.5 second pulses, and for the designpoint 100 mph maximum wind criterion, the maximum water drag MOO/78,000 appr. 1/50 g; the maximum wind force 1,000/78,000 appr. 1/80 g; and the maximum spring force 1,200/78',000 appr. 1/60 g. All of these maximum forces are in the range of H100 to 1/50 g, and thus it can be seen that, providing the translational distance of earth motion during the quake does not exceed the limits of the width of the water space, the transmitted forces to the building itself are on the order of H100 to 1/50 g peak values. Compared to the directly-transmitted force to an orthodox foundation of 0.75 g during the same quake, the preceding calculations reveal that a hydraulic earthquakeinsulation foundation provides dramatic protection from earthshock. Considering that the massive weights of some present-day buildings are substantially contributed to by earthquake proof reinforcing, buildings utilizing hydraulic earthquake-insulation foundations may possibly be much lighter and-less expensive than those currently being constructed.
lt is interesting to consider the magnitude of the lateral motion of the building-base structure during an earthquake. Because the resultant of the water drag and spring forces are acting upon the base, the lateral movement can be divided into two types of motion: a translational movement of the center of gravity and thus the structure as a whole, and a translational movement of the base due to rotation of the structure approximately about the center of gravity, which is the metacenter for small rotations.
Assuming a 0.75 g unidirectional quake with 0.5 second pulses, the average velocity is 6 ft./sec. and the.
total displacement of the earth crust is 6 feet. The water drag at the average velocity is 350 tons, and the average spring force is 3 X 200 600 tons. The approximate total average forces tending to accelerate the structure are therefore 350 600 950 tons appr. l/80 g. The translational movement of the center of gravity and thus the structure as a whole is es X l/80 X 32 X (l) 0.2 ft. 2.4 inches during the 1 second quake.
The total average force acting upon the base also produces some rotation of the structure approximately about the center of gravity. Neglecting the restoring moment due to a shifting center of buoyancy with rotation, and the restoring moment due to the slant of the water level during earthquake acceleration, a worst case rotational displacement of the base can be computed. The rotational displacement of the base in the lateral direction is given by 0L, for small 6, where 0 is the angle of rotation about the c.g., and L is the height from mid-water depth of the base to the c.g. 9 FL/I where F is the total average force acting upon the base during the quake, and I is the moment of inertia of the structure about a horizontal axis through its c.g.
Referring to FIG. 11, a simple approximation to I,. can be computed as follows: I mg, m r m n, slug-ft. Since m m m, and r r r; l, m r, 2mr
Also, r K h, where h Km,/(m 2m) and r (a l l M). For the building-base structure: K= 175' 15.5 190.5
m X 120 X 350 X 20/32 appr. 3.3 X 10 slugs. 2m 300 X 300 X 31 X 20/32=appr. 1.75 X 10 slugs. h 190.5 X 3.3 X 10/(3.3 X 10 1.75 X 10) r 190.5 125 65.5 r= (5,600+ 15,600)" appr. Thus, I, 3.3 X 10 X (65.5) 1.75 X 10 X (145) 5.1 X 10 slug-ft. Therefore, 0 FL/I 950 X 2,000 X (125 l.5)/5.1 X 10 0.0047 rad/sec. And, 0, m, Va X 0.0047 X (1) 0.0023 rad. Thus, the worst case rotational displacement of the base in the lateral direction during the quake is OL 0.0023 X 126.5 0.28 3.4 inches. This results in a total worst case lateral displacement of the base of the structure of 2.4 3.4 5.8 inches during that time that the earth has moved 6 feet. The neglected center of buoyancy shift and water surface slant restoring moments will diminish this somewhat.
Because the assumed quake is a unidirectional one, and the center of gravity of the structure will be moved 2.4 inches at the end of the 1 second quake, the structure will be displaced 5 feet 9.6 inches from its center position within the pool. lt wil'l'have an initial average centering velocity of its e.g., relative to a pool side of 0.2 ft./sec. It can be seen that at this point, the buildingbase structure will experience a maximum acceleration towards center caused by the maximum excursion of the springs, and the least amount of opposing water drag due to its relatively slow velocity through the wa ter. At some point, the decreasing spring force will be surpassed by the increasing water drag, and the structure will begin to decelerate, finally reaching center position, perhaps after mild oscillations. A fast case" simplified estimate can be made of the centering time by neglecting water drag entirely. The average spring force is 3 X 200 600 tons, and if this amount of force is assumed to act for the entire distance to center, s v fizat, where s 5.8, v 0.2 lt./sec., and a 600 X 32/78,000. Therefore: t v lu :t (m? 4 X 1781:. .s'W /u ().2 i (0.04 2 X 600 X 32 X5.l'4/78,000)' /600 X 32/78,()()() 6.3 seconds. The average centering velocity during this time would be 5.8'/6.3 sec. 0.92 appr. l ft./sec. The average water drag would be 350 tons/36 9.8 tons, which is small compared to the average spring force of 600 tons. Thus, a centering time of 6.3 seconds is a fairly close minimum estimate.
Also of interest is the possible vertical motion of the structure due to any vertical components of an earthquake. Assume a quake with a rather large unidirectional upward vertical acceleration of 0.5 g with 0.5 second pulses. From FIG. 7, the average velocity is 4 ft./sec. and the total displacement is 4 ft. The incremental forces pushing upward on the base are the water drag forces, the increase in buoyant force, and the vertical components of the incremental spring forces. Neglecting friction drag, the average pressure drag =%C,, A p V, where A area of the bottom of the base 300 X 300 90,000 ft. Therefore, the average pressure drag X 2 X 90,000 X 2 X (4) appr. 290 X lbs. 1,450 tons. This should be divided by 2, however, since the pressure drag is acting only upon one surface, the bottom of the base, or k of a flat plate. Thus, the average pressure drag 725 tons. The average increase in buoyant force is taken as the average weight of incremental water displaced by the 4 ft. vertical rise of the water surface which equals (4' y) X 300 X 300 X 62/2 lbs., where y the upward rise of the building base structure. Neglecting the relatively smaller incremental spring forces, the average incremental upward force on the base is 725 X 2000 (4 y) X 300 X 300 X 62/2 lbs. Since y rat solving for y at 1 second yields y "a appr. 1 ft. This leaves another 3 ft. for the structure to rise after the I second quake, the water level havingjust reached the top of the base for this example, which requires approximately another 3 seconds. It can be seen that any vertical accelerations of an earthquake are thus substantially reduced.
The foregoing analysis reveals that sharp, strong, and potentially devastating earthquakes cause only mild, gentle motions of a building with a hydraulic earthquake-insulation foundation, much the same as a ship at anchor in a shallow harbor might be slightly disturbed by one, and pose no serious threat to the structural integrity of the building itself, or the lives and well-being of the occupants. Although the type of quake thus far analyzed has been that where the earth crust surrounding the structure is moving as a whole, it can be seen that lateral and/or vertical buckling of the earth surrounding the foundation will have no detrimental effect on the building-base structure due to the fluidity of the hydraulic medium, provided, of course, that the limits of the width of the water space are not exceeded by the relative movements of parts of the surrounding earth. Further, the watertight integrity of the pool sides and bottom can be maintained even with lateral and/or vertical buckling of the earth due to their flexible expandability. It is interesting to note here that relative, permanent displacements of adjacent parts of the earth crust after the San Fernando earthquake of Feb. 9, l97l reached a maximum, in some instances, of 5 feet, and it is believed that this type of buckling was responsible for more damage than the actual accelcrations of the shaking itself.
Although a unidirectional quake was utilized in the analysis in order to consider a strong jolt in a simple manner, earthquakes more typically consist of a shaking motion back and forth from the zero point. FIG. 8 is a table which lists the earth velocities and displacements for sinusoidal motions of various rms values of acceleration, for frequencies of 0.5 and 1 cycle per second. For example, a l g quake at 0.5 cycle/second can cause a i 4.6 feet displacement from zero, and a 0.5 g quake at the same frequency can cause a $2.3 feet displacement from zero. The judgement of proper water width to use for a certain building in a certain location will depend upon consideration of these factors, and the most severe type of quake desired to protect against.
FIG. 9 illustrates the lateral acceleration waveform, along an arbitrary axis, of a hypothetical earthquake as it is directly transmitted to an ordinary building foundation. In contrast, Curve 1 of FIG. 10 illustrates the typicalexpected type of lateral acceleration waveform of the same hypothetical earthquake as indirectly transmitted to the base of a hydraulic earthquake-insulation foundation. Typically, the motion of the building-base structure will consist of mild oscillations about the neutral position.
Referring to FIG. 6, which is a front view schematic drawing of a general embodiment of a non-hydraulic earthquake-insulation foundation, it can be seen that the main building structure 60 is rigidly constructed upon a flat-bottomed base 61, both of which can be of any desired and practicable shape. The sides and bottom of the base may be typically constructed of reinforced concrete, metal, or any other suitable materials. The base rests upon a pit of low-coefficient-of-friction granular or particulate material 62, typically such as sand or a mixture of sand and gravel, and the sides and bottom of the pit 63 can be constructed in a similar manner to the pool sides and bottom of the hydraulic earthquake-insulation foundation, if waterproofing is desired, or else left in their earthern state, if waterproofing is not desired or required. These choices will depend upon location, local weather history, soil characteristics, and any difference in the wet and dry coefficient-of-friction of the non-hydraulic medium selected. All water, gas, sewer, and any other and all pipe connections to the building structure are made through flexible tubes 64 which have suitable slack, and which may be located either above, below, or on the top surface of the non-hydraulic supporting medium. All pit coverings 65, typically consisting of sidewalks, driveways, stairways, planters and the like, which enclose the pit surface and join the building-base structure with the surrounding ground 66 and pavement 67, are connected to the building-base structure by means of pivot supports 68 which allow rotation of said coverings about the horizontal, and are freely resting upon and capable of sliding, slipping, or rolling upon the surrounding pavement 67, so as to permit both rotational and translational movement of the building-base structure relative to the ground.
Because the building structure rests upon a solidparticle, non-hydraulic sliding medium, rather than liquid, the dynamic response of the structure to simple acceleration pulses of the surrounding earth are more simply analyzed. No buoyant forces exist, and assuming that the incremental compressive strain of the nonhydraulic medium is essentially the same as the surrounding ground during an earthquake, any vertical aceelerations of the quake are thus directly transmitted to the structure. The protection afforded from earthshock accelerations of the earth crust as a whole therefore consists of a limitation on the more-usuallyencountered lateral accelerations, as provided by the sideways slippage of the flat-bottomed base over the non-hydraulic medium.
The frictional force acting laterally against the bottom of the base due to acceleration of the sand pit and surrounding earth crust during a quake can only build up to be a maximum equal to the product of the weight of the structure and the coefficient-of-friction between the non-hydrauilc mediumand the bottom of the base.
Thus, the transmitted lateral accelerations to the structure are limited solely by the coefficient-of-friction, which may typically lie between 0.1 and 0.2, and therefore the lateral accelerations of the structure are limited to between 0.1 and 0.2 g. Present-day construction techniques can provide adequate structural strength to successfully withstand this moderate amount of lateral acceleration without major damage, as borne out by the vast majority of homes and apartments in the greater Los Angeles area during the Feb. 9, 1971 earthquake, which area sustained lateral accelerations in that general range-of magnitude.
Curve 2 of FIG. shows the typical acceleration waveform as indirectly transmitted to a building-base structure of a non-hydraulic earthquake-insulation foundation with eoefficient-of-friction of 0.2, by the hypothetical earthquake of FIG. 9. Curve 2 shows that the acceleration waveforms are clipped at 0.2 g, thus producing limited motion of the structure.
The magnitude of the lateral displacement of the structure within the sand pit can be ascertained by considering a unidirectional quake consisting of a positive and a negative pulse of 0.75 g, each of 0.5 second duration. The relative acceleration between structure and earth is 0.75 0.2 0.55 g, and the relative displacement is 2 X /5 X 0.55 X 32 X (0.5) 4.4 feet. The actual movement of the structure from zero is 6 4.4 1.6 feet, compared with the movement of the earth crust of 6 feet. As with hydraulic earthquake-insulation foundations, the selection of proper pit-space between structure and pit-side will depend upon the type and intensity of the most severe quake desired to protect against.
For an earthquake where lateral and/or vertical buckling of the earth crust occurs, it can be seen from FIG. 6 that the shifting characteristic of the nonhydraulic medium and the sliding characteristic of the bottom of the base provide excellent protection against structural damage. Any permanent displacement of the structure within the pit after a quake can be corrected if desired by bringing in heavy-duty pulling or moving equipment; a much more'attractive alternative than suffering the injuries, deaths, structural damage, destruetion, and economic setbacks permitted by presentday earthquake-prone foundations.
In conclusion, earthquake-insulation foundations in general can provide definate and dramatic protection against earthquakes that far exceeds anything now being used or considered.
Various modifications of course may be made from the illustrative embodiment hercinbefore described and any part may be omitted and replaced by a substitute which performs the same function or the same function plus one or more additional functions, and changes or reversals of position may be made without departing from the broad spirit of the invention as succinctly set forth in the appended claims.
1. A hydraulic earthquake-insulation foundation which limits the magnitude of horizontal and vertical accelerations transmitted to the framework of various types of buildings and structures by the earth during earthquakes, and which also provides protection of said buildings and structures against horizontal and vertical buckling of the earth during earthquakes, comprising a watertight building-base upon which said building or buildings or structures are constructed, said buildingbase floating within a liquid-filled pool, typically water, which said pool has been excavated in the earth, said building-base being of appropriate shape and dimen sions so as to provide buoyant stability, the center of gravity of displaced liquid moving outboard of the center of gravity of the entire floating structure for any rotation of said structure about the horizontal; centering means consisting of multiple centering springs typically contained within recesses in the sides of the base, which said centering springs provide tension from the sides of said building-base to the sides of the pool excavation through cables connected to anchors implanted in the sides of the pool excavation, said springs maintaining said building-base at a long-term center position within the pool; pool-lining means consisting of watertight, flexible, and expandably-reinforced pool sides and bottom to provide protection against possible horizontal and vertical buckling of the earth during earthquakes, by means of a flexibe, spring-tension cable network which consists of cables which are freely woven into squares and which are not attached to each other except at the outer end-points of the network, which network has two-way stretch provided by springs in each cable line, and which cable network is firmly attached to the ground at various corner points by anchors, piles, or other support means, said cable network holding large, interlapping sheets of loose-dirtretaining material underneath, and which said cable network is covered by a watertight pool lining, typically plastic, which is folded, typically into square pleats, so as to permit expansion in all directions without leaking.
2. The foundation of claim 1 in which is included a pumping-filtration-heating system for the pool liquid, which said system is similar to those utilized for swimming pools and which circulates and purifies the liquid and maintains its temperature at least above freezing.
3. The foundation of claim 1 in which various water, gas, sewer, electricity, telephone, and any other pipe or wire connections to the building structure are made through flexible tubes with suitable slack, and which flexible tubes may be located above, below, or floated upon the pool-liquid surface.
4. The foundation of claim 1 in which pool coverings enclose the pool. surface and join the building-base structure with the surrounding ground and pavement, said covering typically consisting of sidewalks, driveways, planters, and the like, which said coverings are connected to the building-base structure by means of pivot supports which allow rotation of said coverings about the horizontal, and which said coverings are freely-resting and capable of sliding, slipping, or rolling upon the surrounding pavement, so as to permit both rotational and translational movement of the buildingbase structure relative to the ground.
5. A non-hydraulic earthquake-insulation foundation which limits the magnitude of horizontal accelerations transmitted to the framework of various buildings and structures by the earth during earthquakes, and which also provides protection of said buildings and structures against horizontal and vertical buckling of the earth during earthquakes, comprising a flat-bottomed building-base upon which said building or buildings or structures are constructed, said building-base resting uopn the surface of a pit of sand or other suitable low-.coefficient-of-friction dry granular or particulate material, which said pit has typically been excavated in the earth; pit-lining means consisting of watertight, flexible, and/or expandably reinforced pit sides and bottom, by means of a flexible, spring-tension cable network which consists of cables which are freely woven into squares and which are not attached to each other except at the outer end points of the network, which network has two-way stretch provided by springs in each cable line, and which cable network is firmly attached to the ground at various corner points by anchors, piles, or other support means; said cable network holding large, interlapping sheets of loose-dirtretaining material underneath; and which said cable network is covered by a watertight pit lining which is folded, typically into square pleats, so as to permit expansion in all directions without leaking.
6. The foundation of claim 5 in which various water,
Stairways, planters, and the like, which said coverings are connected to the building-base structure by means of pivot supports which allow rotation of said coverings about the horizontal, and which said coverings are freely resting and capable of sliding, slipping, or rolling upon the surrounding pavement, so as to permit both rotational and translational movement of the buildingbase structure relative to the ground.