Rapid consolidation and compaction method for soil improvement of various layers of soils and intermediate geomaterials in a soil deposit
11124937 · 2021-09-21
Inventors
Cpc classification
E02D3/106
FIXED CONSTRUCTIONS
E02D3/08
FIXED CONSTRUCTIONS
International classification
Abstract
The rapid consolidation and compaction method comprises (i) first driving a hollow pipe, (ii) driving a pipe with a removable end plate after filling and compacting the sandy material in it, through the hollow pipe, to required depth, creating high excess pore-water pressures in the range of 50 to 300 KPa in clayey soils, (iv) pulling out the pipe section leaving behind the removable end plate and thereby installing porous displacement piles which allows dissipation of the excess pore-water pressures horizontally to the porous displacement pile, in which the excess water flows out vertically to the ground surface, and (v) the length of the drainage path is reduced to half the spacing between adjoining porous displacement piles, allowing rapid consolidation resulting in increase in density. Installing the porous displacement piles in the layer of loose to medium dense sand layer results in the instantaneous increase in its density.
Claims
1. A rapid consolidation and compaction method for densifying various layers of soils and intermediate geomaterials in a soil deposit, the rapid consolidation and compaction method comprising: (i) installing porous displacement piles comprising prestressed reinforced porous concrete piles in at least one layer of very soft, soft, medium stiff, stiff, very stiff clayey and silty soil for the rapid consolidation and densification of the clayey and silty soil and/or of very loose, loose, medium dense, dense sandy soil for instantaneous densification of the sandy soil; (ii) first driving a non-displacement pile comprising of a pipe section into ground; (iii) driving the prestressed reinforced porous concrete pile into the ground through inside the non-displacement pile; (iv) the prestressed reinforced porous concrete pile to be used as the porous displacement pile if (1) drivable by a pile drivable hammer into the soil without exceeding allowable driving stresses, and (2) allow free drainage and flow of water and also prevent migration of the fine particles of the in-situ soil in accordance with a filter design criterion; (v) the prestressed reinforced porous concrete pile when driven inside the ground occupies space previously occupied by the clayey and silty soil and develops excess pore-water pressures in saturated clayey and silty soil and the excess pore-water pressures in partially saturated clayey and silty soil, by pressurizing the pore-water and pore-air present in the pores of the saturated clayey and silty soil; (vi) the excess pore-water pressures and pore-air pressures developed in the clayey and silty soil are rapidly dissipated by flow of the pressurized pore-water and pore-air through the prestressed reinforced porous concrete pile to the ground surface or to a sandy layer located within the ground, thereby densifying the clayey and silty soils; (vii) installing a plurality of the prestressed reinforced porous concrete piles spaced apart in a grid pattern in an entire area requiring densification; (viii) installing the prestressed reinforced porous concrete pile vertically or at a batter; (ix) wherein spacing and diameter of the prestressed reinforced porous concrete pile in the grid pattern to depend on subsurface soil conditions at a site, and specifications up to which subsurface soil layers to be densified at that site.
Description
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
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DETAILED DESCRIPTION OF INVENTION
(22) The main motivation for the invention of the rapid consolidation and compaction method (RCCM) is to develop a method for soil improvement which can densify a layer of the soil or the intermediate geomaterial (IGM) in a soil deposit. Cohesionless soils are defined as having N.sub.60 less than 50 blows/0.3 m, whereas cohesionless Category 3 IGMs are defined as having N.sub.60 greater than 50 blows/0.3 m (AASHTO, 2012). Cohesive soils are defined as having undrained shear strength less than 0.25 MN/m.sup.2, whereas cohesive IGMs Category 1 are defined as having undrained shear strength greater than 0.25 MN/m.sup.2 (AASHTO, 2012). The invention in this application comprises of a rapid consolidation and compaction method (RCCM) to produce rapid consolidation of the layer of clayey soil resulting in increase of its density and consistency. The RCCM comprises (i) first driving a hollow pipe section to some depth to minimize heave at the ground surface or above the layer of soil requiring improvement, (ii) driving a displacement pile consisting pipe section with a removable or detachable end plate after filling and compacting the sandy material in the pipe section closed with the removable end plate, to the required depth in the layer of clayey soil through inside the hollow pipe section previously driven, (iii) because the pipe section with detachable end plate performs as a displacement pile displacing the in-situ clayey soil and creates high excess pore-water pressures, which are expected to be generally in a range of 100 kPa to 800 kPa, but could be as high as 2500 KPa (Note: values of excess pore-water pressures shall depend on the consistency and depth of the clay below the ground surface. Pore-water pressures in the range between 260 psi (1793 kPa) and 400 psi (2758 kPa) were recorded in Cooper Marl in South Carolina, USA. Peuchen et al. (2010) recorded pore-water pressures in the range between 50 kPa (7.25 psi) and 800 kPa (261 psi) during piezocone penetration in heavily overconsolidated cohesive soil.), (iv) before pulling out the pipe section out of the ground, a heavy weight is placed top of the compacted material inside the pipe section, (v) while removing or pulling out the pipe section out of the ground, the heavy weight continues to push down the column of compacted sandy material to occupy space left by the thickness of the pipe section (123) and prevents any necking to form in the column of the compacted material, (vi) the detachable or removable end plate opens the 100 percent of the inside area and thus forms a column of compacted sandy material equal to inside area of the inside area and weight further imposes the downward force which further laterally displaces compacted sandy soil to occupy space equal to the outside area of the pipe section, (vii) thus, the column of compacted sandy material behaves as a porous displacement pile embedded in the clayey soil and allows the excess pore-water pressures to first develop and then rapidly dissipate them causing excess pore-water to flow first horizontally to the porous displacement pile and then vertically flow through it to the ground surface or to a sandy layer above or below the porous displacement pile, and (v) when the porous displacement piles adjoining to the first one in a grid pattern are installed, the length of the drainage path is further reduced to half the spacing between adjoining porous displacement piles, allowing rapid consolidation of the layer of clayey soil resulting in its increase of density and consistency sufficiently enough to support loads of the required structure, such as pavement, civil structure, airport or oil storage tank, etc. Installing the porous displacement piles in the layer of loose to dense sand layer in a grid pattern results in the instantaneous increase in its density. Therefore, the rapid consolidation and compaction method (i.e., RCCM) presented in this application as an invention, improves and increases the density of all types of soils and intermediate geomaterials (whether, loose condition or dense, soft or very stiff, to support loads of the structures of a project. The sandy material is compacted to relative density equal or greater than 70% or even up to 100% inside the pipe section, depending on the requirement of supporting loads of the structure and also the subsurface soil conditions. When footing of a structure is constructed on the soil which has been densified by the RCCM, its weight further creates excess pore-water, which also gets rapidly consolidated and footing may continue to settle uniformly by very small magnitude as the substructure and superstructure is being constructed, but after completion of the superstructure, there shall be hardly any settlement and if any, shall occur uniformly.
(23) For the above process, a hollow pipe section (120) is driven into soil to the selected depth (121) to minimize the heave at the ground surface. A hollow pipe sections have very small annular area compared to its outside or inside area, and therefore, for geotechnical purposes, the hollow pipe piles are called non-displacement piles. Similarly, piles consisting of HP-section and channel sections etc. are called non-displacement piles. After the non-displacement pile (120) has been driven into the ground, as shown in
(24) The hollow pipe or tube section could be round, square or rectangular or any shape available or made in the industry. Sometimes, two angle sections or two channel sections welded together could also be used as a hollow pipe section. When such sections are attached with a detachable or removable end plate and used as a displacement pile to be driven in to ground, then for geotechnical purposes, it is called a displacement pile as it displaces the soil by occupying its place. When these sections without any end plate at its bottom (i.e. a hollow section) is driven in to ground then for geotechnical purposes, it is called a non-displacement pile. The sandy material can be compacted inside the pipe section at the location where it is to be driven or at the ground other than the location where it is be driven or otherwise in the pipe section after being driven in to ground if the ground below it is sufficiently dense to limit settlement to keep the end plate intact at the bottom of the displacement pile.
(25) The non-displacement pile is driven into the ground first, in order to minimize heave at the ground surface or at the top the layer which is to be densified. Ideally, during driving the displacement pile, there should not be any heave of the ground surface to achieve maximum lateral displacement of the soil by the porous displacement pile, in order to achieve maximum densification. That is why to minimize heave, first a non-displacement pile is driven to selected depth and then the displacement pile is driven through the non-displacement pile. If this step of driving displacement pile through a non-displacement pile is omitted and displacement pile is driven directly, due to economics or for any other reason such as not very practical at a particular site, etc., or when non-displacement pile has not been driven to adequate depth to minimize or prevent heave, then although full densification of in-situ soil would not occur because of some heave at the ground surface. In such cases, the amount of densification will be less as the volume of the in-situ soil displaced by the displacement pile will be sum of the reduction of voids in the in-situ soil plus the volume soil which heaved at the ground surface or at the top of the layer to be densified. The overburden soil above the depth of the bottom of the non-displacement pile (120) acts to prevent or minimize the heave at the ground surface to a reasonable limit, when the weight of the overburden soil above the bottom of the non-displacement pile (120) is sufficient enough to prevent heave at the ground surface. According to the presently available research, the overburden depth between 7 to 10 times or more may be sufficient to limit heave at the ground surface, depending upon the soil conditions. However, not enough or substantial research is available at the present, to predict the reasonable depth (121) in different types of soils at various densities or consistencies to prevent or minimize the heave at the ground surface when a displacement pile is being driven into the ground. Sufficient research shall be developed to predict the reasonable depth (121) in different types of soils at various densities or consistencies, when the projects involving ground improvement using the RCCM are being implemented.
(26) The sandy soil (125) is filled in layers in the pipe section (123) and each layer compacted by a specified number of drops of a hammer or a weight (118) to achieve a specified dry density or relative density. The connecting pipe or rod (127) connects the weight or hammer to a boom of crane or to a pile driving hammer system (not shown in the
(27) The density of the compacted sandy material inside the pipe section is generally based on equal or greater than 70% relative density, because this is the requirement which is generally followed for compacting embankments. When densification of stiff to very stiff clays to hard clayey soils or medium dense or dense sand to very dense sand is required, then relative density of compacted sandy material in the pipe section to more than 70% or even up to 100% may be more appropriate. In earth quake zones and over faults, or under atomic power plants, even very stiff clays or dense sands may require further densification, in such cases, the relative density of more than 70% to even up to 100% for the column of compacted sandy soil to perform as porous displacement pile could be specified. However, when very soft clays or soft clays to be densified to medium stiff clays or loose to very loose sand is to be densified to medium dense sand, then relative density requirement could be relaxed to about 60%, if structural support requirement of the site could be met. However, preferred method shall always remain to densify the compacted sandy material in the pipe to equal or greater than 70% relative density.
(28) There are various types of hammer/weight available to drop on the sandy soil placed inside the pipe section (123) for densifying the sandy soil; any of these hammers/weights and the required attachments to the connecting rod etc. can be used when considered appropriate according to specifications or brochures of the manufacturers of the equipment. There are many types of surface vibrators available in the industry which can be used around the pipe to densify sand inside the pipe section (123), when the weight or hammer has already been placed on top of the sandy material to compact it, or placing the vibrator on top of a plate or vibrating weight to densify sandy soil inside the pipe; any of the available systems if appropriate with required attachments can be used following the manufacture's brochure or specification. There are many types of pile driving hammers including vibratory hammers available in the industry to drive a non-displacement or displacement pile; any of these driving hammers with required attachments can be used when considered appropriate. There are many types of pile pipe pullers including vibratory pullers or pullers with hydraulically operated jaws to grab the pile available in the industry to pull the non-displacement or displacement pile out of the ground; any of these pullers with required attachments can be used when considered appropriate. The attachments between the pipe section or rod (127) and the crane by U-Bolts or hooks etc., or attachment between the puller and the pipe section (123) or the surface vibrator to the pipe section (123) or plate vibrators etc. shall be in accordance with the manufacture's specification and brochure. When the pipe section is being driven, all attachments of pile driving hammer shall be in accordance with pile driving specifications. Many organizations do not allow vibratory hammers to drive non-displacement or displacement piles in clayey silty soils, because it is considered that vibration remolds and disturbs the matrix and lock-in-stresses of clayey silty soils.
(29) Few typical examples of detachable or removable end plates are shown in
(30) The above details are applicable when the field operations to compact the sandy material are being performed at the location where the pipe section (123) is to be driven. When the sandy material is being compacted in the pipe section (123) at some other location and then to be transported to the selected location where it is to be driven in to the ground, the additional attachments to end plate (124) are required. In such cases, the detachable plate arrangement of
(31) For pulling the pipe section (123) successfully out of the ground, weight of the weight or hammer (126) kept on top of the compacted sandy material, is designed based on the side frictional resistance developed between the compacted sandy material inside pipe section (123) and/or side frictional resistance between outside of the pipe section (123) and in-situ soil around it and also any suction force exerted by the in-situ soil on the end plate during pulling of the pipe section. Similarly, weight of the weight or hammer and number and height of drops is designed to achieve the specified density. Although, structural members described for non-displacement and displacement pile consist of circular section as shown in the text and figures, any non-common section of hollow rectangular, or elliptical section or any other non-common section will work with the RCCM and can be used on demand by a client. During driving the non-displacement or displacement pile, sometimes, it becomes important to limit noise and vibrations, in such cases, heavy hammers with very small height drops or hydraulically pushing the piles into the ground may become important so as to minimize or limit the damage or risk to adjoining structures. To monitor settlement of the adjoining structures, the settlement readings both at the structure and at the ground surface and at some depth in the ground may also be made. Also, it may be advisable to perform wave equation analyses for driving the pipe section (123) with a selected hammer (Pile Dynamics, Inc., 2005). To determine amount of improvement and increase in density of the improved in-situ soils, the subsurface exploration using the in-situ testing methods and laboratory tests on the extracted samples from the in-situ soil may also be performed before and after installation of the porous displacement piles.
(32) The porous displacement pile consisting of the column of compacted sandy material besides densifying and improving soil around it, has another important function to perform, which is to prevent the passage or migration of clay or silty particles into the compacted sandy material while allowing free flow of water through the column of the compacted sandy material in order to dissipate the excess pore-water pressure. The gradation of the compacted sandy material to perform a function of a filter to limit migration of the fine material and allow free flow of water shall be designed based on the design criteria for filters or chimney filters used in earth dams or earth and rockfill dams, using the Terzaghi's criteria with or without some modification made by several organization such as US Bureau of Reclamation, etc. (Prakash and Gupta, 1972). The sandy material may consist of mixture of sand and little quantity of small gravel mixture, but should satisfy requirements of allowing free flow of water and to prevent migration of fine particle of in-situ soil into the column of compacted sandy material. The sandy material should not contain more than specified quantity of fine particles in order to maintain its property of free flow of water. Generally, well graded clean sands have been used in sand drains; the same type of material, when meeting the filter Criteria, could be used for the porous displacement piles.
(33) Briefly Terzaghi's Criteria is briefly described as below:
(34) (1) Piping or Migration of particles criteria: D.sub.85(Base) represents the particle size that must be retained. D.sub.15(Filter) is representative of average pore size. Filter to trap particle size larger than about 0.1 D.sub.15(Filter)
(35) D.sub.15 (filter)<4 to 5 D.sub.85 (Base)
(36) Permeability or Free Flow Criteria:
(37) D.sub.15 (filter)>4 to 5 D.sub.15 (Base)
(38) Gradation Control
(39) D.sub.50(filter)<25 D.sub.50 (Base)
(40) Sandy material in porous displacement pile performs as the filter. In-situ clayey silty soil which surrounds the compacted sandy material of the porous displacement pile, performs as the base in the above criteria. D.sub.15 is the diameter for which 15% of the material by weight is finer and D.sub.85 is the particle diameter for which 85% of the material by weight is finer.
(41) During piezocone cone penetration sounding in highly stratified and heavily overconsolidated soft to stiff soil with cone penetration resistance (q.sub.c) between 0.1 and 1 MPa, the penetration pore-water pressures ranging from 50 to 1.8 MPa (7.25 to 261 psi), values increasing with depth below ground surface were recorded from ground surface to depth of about 22-meter depth (Peuchen, 2010). During penetration of displacement piles in cohesive soils, penetration pore-water pressures of this magnitude shall be expected. Penetration pore-water pressures of 1.8 MPa equals 183.6 meter of water head from a 183 m (600 feet) high earth/concrete dam reservoir. Therefore, the compacted sandy soil of the porous displacement piles could experience such high pore-water pressures and therefore should meet the chimney filter criteria as used for earth and rockfill dams.
(42) The porous displacement piles comprising of the column of compacted sandy soil have been described above. There is another equally attractive method to install porous displacement piles to perform the same type of function, but it is more costly than the method already explained. Porous reinforced prestressed concrete piles (or even without prestress), or porous pipe section with the end plate, or pipe section with small holes and the end plate, filled by the compacted sandy material shall also be installed through inside the non-displacement piles and shall be used as the porous displacement piles, if (1) drivable by a pile driving hammer into the soil without exceeding allowable driving stresses, (2) allow free drainage and flow of water and prevent migration of fine soil particles of clays and silts or fine sand, (3) the holes in the tube or pipe section need to be quite small so as to retain sandy material during compaction in the pipe section. These porous displacement piles will not require pulling out of the pipe section out of the ground and the installation will also become easier and faster. In many cases where soil layers consist of very sticky clays or when batter piles are involved or when any more vibration or noise cannot be tolerated, pulling out a pipe section could be difficult or may not be allowed by authorities.
(43) In many areas such as in earthquake zones, the local building code may not allow construction unless the relative density is above a certain value. Table 1 gives liquefaction-potential relationships between magnitude of earthquake and relative density for a water table 1.5 m below ground surface:
(44) TABLE-US-00001 TABLE 1 Approximate relationship between earthquake magnitude, relative density (D.sub.r) and liquefaction potential for water table 1.5 m below ground surface (From Seed and Idriss, 1971) High Potential for liquefaction Low Earthquake Liquefaction depends on soil type Liquefaction Acceleration Probability and earthquake acceleration Probability 0.10 g D.sub.r < 33% 33% < D.sub.r < 54% D.sub.r > 54% 0.15 g D.sub.r < 48% 48% < D.sub.r < 73% D.sub.r > 73% 0.20 g D.sub.r < 60% 60% < D.sub.r < 85% D.sub.r > 85% 0.25 g D.sub.r < 70% 70% < D.sub.r < 92% D.sub.r > 92%
(45) In such cases, RCCM shall be used to densify soil layers as needed for the areas in 0.10 g zones to Dr more than 70%, in areas of 0.15 g to Dr more than 75%, in area of 0.20 g to Dr more than 85% and in areas of 0.25 g to Dr more than 95%, in order to bring such areas in low liquefaction probability. For areas where earthquake acceleration is 0.15 g, the sandy soil in the pipe section (123) shall be compacted to relative density greater than 75%. For areas where earthquake acceleration is 0.20 g, the sandy soil in the pipe section (123) shall be compacted to relative density greater than 85%. For areas where earthquake acceleration is 0.25 g, the sandy soil in the pipe section (123) shall be compacted to relative density greater than 95%.
(46) Typical Examples of Industrial Applications of the RCCM
(47) Ground Improvement Under a Spread Footing
(48) When a project requires ground improvement of the layer of soil, the RCCM can provide an economical and very useful solution. For example, a spread footing of a bridge foundation is to founded on soil which consists of a week layer of soil (140) and needs soil improvement in order to support the loads from the bridge superstructure.
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(50) Ground Improvement Under Embankments
(51) The RCCM can be used under mechanically stabilized walls (such as reinforcement earth wall) to reduce and limit their settlements and also to develop required stability. The slopes which are found not to have enough factor of safety based on slope stability analyses when densified by use of the RCCM, shall be able to develop required factor safety for slope failures. The road and highway embankments founded on very soft layers of soils sink and settle sometimes by several inches or feet or meters; and slopes of 2H:1V generally provided on opposite sides of the embankment are found to be unstable, therefore requiring very flat slopes. In such cases the RCCM shall densify the weak or soft soils under the embankments and reduce settlements to the reasonable limits and also improve the slope stability of the embankment slopes without requiring flatter slopes. One typical example is shown in
(52) The rapid consolidation and compaction method (RCCM) can also be used in coastal regions where embankment is to be further extended into the ocean to build new land for airports and housing projects etc., and where the subsurface soils consist of loose sands and soft to very soft clays. Similarly, new islands can be built even where subsurface soils consist of loose and soft and very soft soils underlies as these subsurface soils can be densified by the rapid consolidation and compaction method. To reduce down drag on the piles driven in clayey and silty soils, the sand drains or PVC (wick) drains are installed and an embankment is built over them to consolidate the clayey silty layer for certain time period for generally up to 90% consolidation and then sometimes the embankment is removed and the piles are driven. In place of sand drains or wick drains, the RCCM to install porous displacement piles can be used, which shall rapidly consolidate the layer without requiring to build an embankment and waiting for up to 90% consolidation. The RCCM can be used very economically for any layer of soils or intermediate geomaterial where soil improvement to densify it is required and also, where ever, presently existing methods such as jet grouted columns, columns of cement or lime mixed with clayey material or Geopiers or vibro-replacement or vibro-floatation using a Vibro-probe, stone-columns as bottom feed or top feed, etc., are being used.
(53) Ground Improvement Under Tilting or Leaning Structures Such as the Leaning Tower of Pisa
(54) There are many structures throughout the world which have tilted either during construction or after completion of the construction. The ground improvement using the rapid consolidation and compaction method for installation of porous displacement piles can improve the foundation soils which will also result in reducing the angle of tilt significantly and bring the leaning structure close to about vertical. There are many other structures in the Town of Pisa, Italy, which are tilting like Leaning Tower of Pisa, but not to this extent. First the porous displacement piles should be installed at other tilting structures of Town of Pisa to demonstrate the effectiveness of soil improvement in succeeding to reduce the tilt with underlying subsurface conditions, before considering to install porous displacement piles at the Leaning Tower of Pisa to reduce the tilt. To reduce the angle of tilt of the Leaning Tower of Pisa, (i) the lead weights have been placed on the north side on prestressed concrete ring around the foundation of the leaning tower of Pisa, (ii) steel cables to anchor the tower on north side to limit movement towards south, (iii) Drill holes installed to remove soil from the drilled holes on the north side, and (iv) some excavation in east-west direction (Jamiolkowsky, et al., 1993). However, no construction on the southside has been permitted and even subsurface exploration consisting cone penetration soundings has been permitted 10 to 20 meters from the south edge of the tower in order not to disturb the tower, although construction as stated above has been permitted on the north side. Prior to installation of porous displacement piles, the additional steel cables to anchor the tower could be considered to further anchor the tower by steel cables in north-east and north-west directions. If permission is granted by the concerned authorities, the scheme of installation of porous displacement piles as shown in
Densification Under a Structure Undergoing Settlement
(55) When a structure such as a building or an oil or water tank is continuously undergoing settlement on all of its sides, then batter porous displacement piles on all sides penetrating under the structure could be installed to prevent or reduce further settlements significantly. The batter displacement piles shall be required to be installed in particular sequence, so that any instant, these are evenly located symmetrically around a structure. Porous displacement piles might consist of the column of compacted sandy soil and installed as described above. To reduce vibrations, noise and disturbance, the porous displacement piles comprising porous pipe section or pipe section with small holes and with end plate and filled with compacted sandy soil could also be considered to be installed. All displacement piles shall be driven through inside the non-displacement piles. The selection shall be made for a particular site based on soil conditions and environment around the structure.
(56) Teachings of this Application
(57) The various aspects of what is described in the above sections, can be used alone or in other combinations for other type of applications. The teaching of this application is not limited to the industrial applications described here-in-before, but it may have other applications. Therefore, teaching of the present application has numerous advantages and uses. It should therefore be noted that this is not an exhaustive list and there may have other advantages and uses which are not described herein. Although the teaching of the present application has been described in detail for purpose of illustration, it is understood that such detail is solely for that purpose, and variations can be made therein by those skilled in the art without departing from the scope of the teaching of this application. Features described in the preceding description/specification may be used in combination, other than the combinations explicitly described. Whilst endeavoring in the forgoing specification/description to draw attention to those features of the invention believed to be of particular importance, it should be understood that Applicant and Inventor claims protection in respect of any patentable feature or combinations of features hereinbefore referred to and/or shown in the drawings/figures whether or not particular emphasis has been placed thereon. The term “comprising” as used in the claims does not exclude other elements or steps. The term “a” or “an” as used in the claims does not exclude plurality. A unit or other means may fulfill the functions of several units or means recited in the claims. As various possible embodiments might be made of the above invention, and as various changes might be made in the embodiments above set forth, it is to be understood that all matter herein described or shown in the accompanying drawings is to be interpreted as illustrative and not in a limiting sense.
REFERENCES
(58) Bowles, E. B. Foundation Analysis and Design, Fourth Edition, 1981, McGraw-Hill Book Company, New York, N.Y., USA. Jamiolkowski, M., Lancellotta, R., and Pepe, C. (1993) “Leaning Tower of Pisa-Updated Information”, Proceedings, Third International Conference on Case Histories in Geotechnical Engineering, Jun. 1-4, 1993, SOA, St. Louis, Mo., USA. Kennedy, G. D., and Woods, K. B. (1954). “Vertical Sand Drains,” Highway Research Board, Bulletin 90, Washington, D.C., USA. Mars, B. N., “Compaction of Soil,” U.S. Pat. No. 4,126,007, issued on Nov. 21, 1978, United States Patent and Trade Mark Office, Alexandria, Va., USA. Peuchen, J., Berghes, J. F. V., and Coulais, C. (2010), “Estimation of u.sub.1/u.sub.2 conversion factor for piezocone,” Second International Symposium on Cone Penetration Testing, California, USA. Pile Dynamics, Inc. (2005) “GRLWEAP, Wave Equation Analysis of Pile Driving”, Cleveland, Ohio, USA. Prakash, D. and Gupta, R. C. (1972), “Laboratory Studies on Filter Materials Placed at Ramganga Main Dam,” Indian Geotechnical Journal, Vol. 2, No. 3, July 1972, pp. 203-219, New Delhi, India. Schaefer, V. R., Berg, R. R., Collin, J. G., Christofer, B. R., DiMaggio. J. A., J, A, Filz, G. M., Bruce, D. A., and Ayala, D. (2016). “Ground Modification Methods-Reference Manual”, Volume 1, Geotechnical Engineering Circular No. 13, FHWA-NHI-16-027, US Department of Transportation, Washington, D. C. USA. Seed, H. B., and Idriss, I. M. (1971) “Simplified Procedure for Evaluating Soil Liquefaction Potential”, JSMFD, ASCE, Vol. 97, SM 9, September, pp. 1249-1273.