Finite Element Analysis of Active Isolation of Deep Foundation in Clayey Soil by Rectangula Tenches Mehab Jesmani Assistant Pofesso, Depatment. of Civil Engineeing, Imam Khomeini Intenational Univesity, Qazvin, Ian mehabjesmani@yahoo.com Mohammad Reza Shafie M.S. Candidate, Depatment of Civil Engineeing, Imam Khomeini Intenational Univesity, Qazvin, Ian mohammadeza_shafie@yahoo.com Reza SadeghiVileh Consultant Enginee, Seven Diamonds Industial Company, Qazvin, Ian esa_34136@yahoo.com ABSTRACT Wave baies ae intended to mitigate the tansmission of vibations in the soil actively o passively including open and in-filled tenches, sheet piles, etc. In most pevious studies, the effects of govening paametes on sceening induced by shallow foundations wee examined in which the Rayleigh waves ae of impotance, In this study, howeve, the gound vibation isolation of deep foundations, pedominantly geneating body waves, in clayey soils esting on an homogeneous half-space has been investigated. The effects of geometical popeties of an open tench ae studied in details. Thee dimensional finite element analyses (FEM) with ANSYS softwae ae utilized to conduct an extensive paametic study on active isolation. The suface to suface contact element fo the nonlineaity state of the soil-pile inteface as well as nonlinea Ducke-Page soil behavio unde Full Tansient analysis have been utilized to obtain moe accuate esults. KEYWORDS: Active Isolation, Vibation Reduction, Rayleigh Wave, Pile Foundations, Clay, Rectangula Tenches, Body Waves, ANSYS pogam
Vol. 13, Bund. E 2 INTRODUCTION The vibation that occus in most machines, stuctues and dynamic systems is undesiable, not only because of the esulting unpleasant motions, the noise and the dynamic stesses which may lead to fatigue and failue of the stuctue o machine, but also because of the enegy losses and the eduction in pefomance that accompany the vibations. Geneally, installing the wave baie nea the vibation souce to mitigate advese effects of vibations is known as active isolation; wheeas, passive isolation is emote fom the souce suounding o in the immediate vicinity of the stuctue to be potected. Regading the liteatue on gound-bone vibations, Bakan (1962) pefomed field tests to evaluate motions in the sceened zone behind tenches and sheet piles concluding that eductions of displacement amplitude could be achievable when tench dimensions ae lage enough elative to the wavelength of the suface motions. Woods (1968-1969) conducted a seies of field tests to study the sceening pefomance of diffeent govening paametes of tenches in active and passive isolation systems. Woods defined Amplitude-Reduction Ratio (A ) and concluded that a minimum tench depth of.6 times the Rayleigh wave length is epoted to achieve a 75% eduction in gound displacement amplitude. Woods et al. (1974) simulated vibation in half-space employing the pinciple of hologaphy to investigate the sceening efficiency of hollow cylindical piles as baies in passive system. Using finite element method (FEM) in the fequency domain and unde the assumption of a plane stain condition, Lysme and Waas (1972), Haupt (1977) and Segol et al (1978) assessed the vibation sceening isolation. Meanwhile, May and Bolt (1982), Emad and Manolis (1985), Haupt (1977), conducted in the fequency as well as in the time domain to examine isolation efficiency of wave baies. Aboudi (1973) conducted a eseach to evaluate the gound suface esponse of wave baies unde a time-dependent suface load in elastic half-space; moeove, Fuykui M, Matsumoto Y (198) studied Rayleigh wave eaching an open tench though finite diffeence method (FDM). Beskos et al (1985-1991) employed bounday element method (BEM) to study open and in-filled tenches as well as pile wave baies. Ahmad and Al-Hussaini (1991, 1996, and 2) concentated on simplified design methodologies fo vibation sceening of machine foundations by tenches using a thee-dimensional bounday element algoithm. Kattis et al (1999a, 1999b) developed an advanced-fequency domain BEM code to examine the isolation sceening efficiency of open, in-filled tenches and pile baies. They summaized that tenches ae moe efficient than pile baies, except fo the vibation with lage wavelength, whee deep tenches ae impactical. Hollow piles ae obseved to be moe efficient than concete piles. Futhemoe, cicula coss-section piles have a simila behavio to those of squae coss-section. Shivastava (22) examined the effectiveness of open and filled tenches fo sceening Rayleigh waves due to impulse loads in a 3D FE model consideing the effects of the geometic paametes of tench baie to educe gound displacements. Soil, in his eseach, was idealized as linea, isotopic continuum. Adam (25) inspected the effectiveness of open and in-filled tenches in educing the six-stoey building vibations due to passing tains using a two-dimensional FEM analysis. An 8% eduction in the building vibations and intenal foces wee epoted. El Nagga (25) exploed the efficiency of soft and stiff baies in sceening pulse-induced waves fo shallow foundations esting on an elastic half-space. The efficiency of diffeent types of wave baies in vibation isolation fo shock-poducing equipment was assessed and esults wee pesented in A. Celebi, E et al (26) pesented two mathematical
Vol. 13, Bund. E 3 models and numeical techniques fo solving poblems associated with the wave popagation in a tack and an undelying soil owing to passing tains in the fequency domain. They utilized BEM to investigate the thee-dimensional dynamic esponse of the fee field neaby ailway lines induced by the moving loads acting on the suface of a homogeneous soil deposit. In addition, Celebi et al (26b) conducted compehensive numeical investigation to indicate the influence of wave baies on the complex dynamic stiffness coefficients of the suface suppoted foundations unde dynamic loads. Tsai et al (27) conducted a numeical eseach using thee-dimensional BEM in fequency domain to scutinize the sceening effectiveness of cicula piles in a ow fo a massless squae foundation subject to hamonic vetical loading. They epoted that sceening effectiveness of steel pipe piles is geneally bette than that of solid piles, and that a concete hollow pile baie can be ineffective due to its stiffness. Fom the above eview, eseaches mainly focused on vibation eduction of open and infilled tenches by shallow foundations in which the Rayleigh waves play significant ole in tansmission of gound vibations. In this study, howeve, the gound vibation isolation of deep foundations, mainly geneating body waves, has been investigated in clayey soils. PROPAGATION AND ATTENUATION CHARACTERISTICS DEEP FOUNDATION Emanated waves fom deep pile foundations in the gound ae elastic waves in the fom of shea wave, compession waves, and suface waves (Figue 1) (Attewll and Fame, 1973). Vetically polaized shea waves ae geneated by soil shaft contact which popagate adially fom the shaft on a cylindical suface; meanwhile, shea and compession waves popagate in all diections fom the toe on a spheical wave font especially at the pile toe, and Rayleigh waves popagate adially on a cylindical wave font along the suface. In an elastic half space, both body waves and Rayleigh waves decease in amplitude with inceasing distance fom the pile foundation due to the geometical damping. Theoetically, gound vibations in the fa field attenuate invesely popotional to the squae of the aea of the wave font o accoding to n with the distance and n the geometical attenuation coefficient. The latte is equal to.5 fo suface waves popagating on a cylindical wave font and equal to 1 fo body waves popagating on a spheical wave font in the inteio of the half space; fo body waves popagating along the suface, the coefficient n is equal to 2 (Wolf 1994). PROBLEM DEFINITION AND ASSUMPTIONS A igid cicula footing of adius 9m (B f ), with 17 piles of diamete 8cm and length L esting on a soil laye of a limited thickness undelain by a had statum at a depth of H and length L is subjected to a hamonic (f=3hz) compessive suface load P o sin(ωt) (Figue 2). An annula open tench of depth D and width W is located at a cente-to-cente distance of R fom the foundation (Table1). The soil is assumed isotopic and homogenous with Ducke-Page soil behavio fo plastic defomations and soil yielding. The had statum is pesumed to be vey igid elative to the soil laye.
Vol. 13, Bund. E 4 Figue 1: Wave popagation induced by deep foundation Table1: Geometical popeties of the tench and the piles Pile Length (m) Tench Location (R) Tench Depth (D) Tench Width Footing Radius 1 As an example Paamete L1 L2 L3 L4 R1 R2 R3 R4 D1 D2 D3 W Bf Value 5m 1m 15m 2m 1.5 B f 2 B f 2.5 B f 3 B f L/4 L/2 L 75 cm 9m 1
Vol. 13, Bund. E 5 Figue 2: Poblem definition: active isolation by open tench in deep foundation. GEOMETRICAL MODEL Taking advantage of the axisymmety in plan, only 1/4 of the actual model is built esulting in significant eduction in computation time. Model dimensions ae selected optimally lage enough to pevent the suface wave eflection which decays much moe slowly with distance than the body waves. The depth of model to pevent any wave eflection fom the base of model is computed though tial and eo as thee times of pile length which shall not be less than 3m. FINITE ELEMENT MODELING STRATEGIES Ducke-Page yield citeion [3] fo plastic defomations and yielding is applied to simulate the soil behavio defined by the following paametes: C: The cohesion value; C=6 kn/m 2 Φ: The angle of intenal fiction; Φ=5º. The angle of dilatancy was assumed to be equal to the angle of intenal fiction (associated flow ule). Thee was no stain hadening; theefoe, no pogessive yielding was consideed. To simulate behavio of soil and the foundation such as sliding o any pobable sepaation at the soil-stuctue inteface, thee dimensional suface-to-suface contact elements (Contac174, Tage17) have been employed. The soil suface and pile ae taken as contact suface and taget suface, espectively because of the igidity of the foundation compaing the undelying soil. Nomal contact stiffness facto was assumed to be equal to 1 and maximum contact fiction coefficient was taken.6. Solid45 (figue 3) is used to model the soil and the foundation block. The element is defined by eight nodes having thee degees of feedom at each node: tanslations in the nodal x, y, and z diections. The element has plasticity, ceep, swelling, stess stiffening, lage deflection, and lage stain capabilities (ANSYS Manual).
Vol. 13, Bund. E 6 Figue 3: Eight-noded element (Solid45). Meshing and Bounday Condition The pecision is achieved by smalle element size in the vicinity of the foundation and tench inceasing in size gadually, fo distant elements fom the tench oute edge. Bounday conditions ae assigned by estaining the displacement in the x and y diections: the y displacements in x diection togethe with x displacement along y axis ae estained. The oute edge of model is also estained in x and y diections. The had statum undelying the soil laye is assumed to be a igid bounday theefoe the feedom degees in the thee diected has been estained. The geomety of FEM, meshing method and bounday conditions ae shown in Figue 4. (4a) 3D Model (4b) Plan (4c) Elevation Figue 4: The geomety of finite element model
Vol. 13, Bund. E 7 Damping Model The damping matix (C) in ANSYS softwae is calculated by multiplying the following constants to the mass matix (M) and stiffness matix (K). C M K [1] In which The Rayleigh damping is mateial-dependent damping ( β s ) calculated by: i S [2] 2 2 Whee ω i is the natual cicula fequency of mode i. In many pactical poblems that a lage mass intoduced into the model, alpha damping is ignoed, α =, esulting in undesiable esults. By selecting β s =.5, α and β could be evaluated as following: i 5.5 5*1 f,, [3] Model Veification The geneal equation modeling popagation of gound vibation fom point a (a location at distance a fom the souce) to point b (a location at distance b fom the souce) can be stated in the fom of Equation (4) u b u a a b e ( ) a b [4] Whee γ depends upon the type of popagation mechanism and α is a mateial damping coefficient (Amick and Gendeau, 2). Table 2: Summay of theoetical geometic attenuation coefficients, based on wave type. Souce Wave Type Measuement Point γ Point on Suface Rayleigh Suface.5 Point on Suface body Suface 2 Point at Depth body Suface 1 Point at Depth body Depth 1 As no analytical and expeimental esults have been pesented in the liteatue, theefoe, the accuacy of the obtained esults fom the cuent study is validated simply by the assessment of the body wave popagation of deep foundation by equation 4. Pile foundation can be classified as a point on souce geneating body wave and the tavel distance can be estimated as a hoizontal distance fom the souce. Figue 5 exhibits a easonable ageement between the cuent FEM model and the equation (4).
Nomalized Displacement Vol. 13, Bund. E 8.2.15.1 Theoetical Fomulation This Study.5 5 1 15 Distance (m) Figue 5: Compaative study of obtained esults. The vaiation of displacements is not identical; this may be accounted to the appoximation used in deiving the equation. Results fom the finite element analyses Woods (1968-1969) poposed an aveaged amplitude, A, fo assessment tench effectiveness; the amplitude, A, is the atio between amplitude with tench and amplitude without tench. A Amplitudewith thetench baie Amplitudewithout the tench baie [5] To evaluate the sceening effectiveness of tench, the aveaged amplitude, A, is calculated along all adial lines ight behind the tench and in the length of one Rayleigh wave length. The Rayleigh wave length is calculated by dynamic modulus of elasticity. whee A nl 1 l Ad [6] t n t is the adial distance between the tench and the oute edge of the baie; t n epesents the numbe of points along the adial distances. Fo the sake of genealization, the geometic paametes and the esults ae pesented in a dimensionless fom. The cuves of A plotted against the depth of tench and tench location nomalized by length of pile and Rayleigh wavelength espectively. d D, Lp R [7]
Aveage Amplitude Aveage Amplitude Vol. 13, Bund. E 9 Effect of Tench Depth The effect of tench depth is demonstated in figues 5 though 8. Geneally, inceasing the depth of tench cause a decease in A. Simila behavio is obseved in vibation eduction of shallow foundations epoted in many published eseaches. Deep foundations pimaily geneate body waves; in othe wods, Rayleigh waves tansmit a small pat of vibation enegy by compaison. Results eveal that except shallow pile foundations, (L<5m), a minimum tench depth of.5 times the pile length is the optimal depth fo achieving an ideal eduction in gound displacement amplitude. In case of d<.5 and in shot piles (L=5m), the A is effectively depends on the tench location; wheeas A is mostly independent of tench location in case of inceasing pile length, (L>1m), which may leads to an exceptionally small vibation eduction, theefoe, deep tenches ae uneconomically pactical and ae not ecommended..7.6.5.4.3.2.1 L = 5m.25.5.75 1 1.25 Nomalized Depth Of Tench = 1.63 = 14.17 = 17.72 = 21.26.2.1 Figue 5: Effect of tench depth (L=5) L = 1m = 1.63 = 14.17 = 17.72 = 21.26. -.1.25.5.75 1 1.25 Nomalized Depth Of Tench Figue 6: Effect of tench depth (L=1)
Aveage Amplitude Aveage Amplitude Vol. 13, Bund. E 1.7.6.5.4.3.2.1 -.1 L = 15m = 1.63 = 14.17.25.5.75 1 1.25 Nomalized Depth Of Tench Figue 7: Effect of tench depth (L=15).8.6.4.2 L = 2m = 1.63 = 14.17 -.2.25.5.75 1 1.25 Nomalized Depth Of Tench Figue 8: Effect of tench depth (L=2) Effect of Tench Location Geneally, inceasing the tench location lead an incease in A. In shot pile foundation, as can be seen in Figue 9, fo tenches located at 1.5Bf body waves ae not capable of passing though tench baie due to the shot distance between the souce and the tench. This may lead to a bette tench pefomance. Fo tenches location at 2.5Bf body waves each the suface and vey deep tench is necessay to povide sceened zone. Hence the A inceases and pooe pefomance is obtained by compaison. Fo futhe distances ( 2.5Bf ) due to mateial and geometical damping A appea to decease. Thus 2Bf is highly ecommended fo shot piles (L<5m) to obtain ideal vibation eduction.
Aveage Amplitude Aveage Amplitude Aveage Amplitude Vol. 13, Bund. E 11.7.6.5.4.3.2.1 d=.25 L = 5m d=.5 d= 1 8 13 18 23 Nomalized Tench Location Figue 9:Tench location vs A with 5m pile..2.15.1 d=.25 d=.5 d= 1 L = 1m.5 8 13 18 23 Nomalized Tench Location Figue 1:Tench location vs A with 1m pile.7.6.5.4.3.2.1 L = 15m d=.25 d=.5 d= 1 8 13 18 23 Nomalized Tench Location Figue 11: Tench location vs A with 15m pile.
Aveage Amplitude Aveage Amplitude Vol. 13, Bund. E 12.8.7.6.5.4.3.2.1 L = 2m d=.25 d=.5 d= 1 8 13 18 23 Nomalized Tench Location Figue 12:Tench location vs A with 2m pile. Effect of Pile Length Geneally, inceasing the pile length leads a decease in A due to shea wave popagation induced by pile foundation. When the pile toe is nea the gound suface (L = 5, 1 m), the maximum vibation amplitude occus in the field located about 2.5Bf. Howeve, slighte value of A is extacted fom the esults fo close tench locations. In cases of othe pile lengths (L = 15, 2 m), It is also obseved that the pesent model pedicts lowe gound vibations, especially when the pile length is lage, thee is an inceasing tend fo A diagam plotted against tench..3.25.2.15.1.5 -.5 = 1.63 d=.25 d=.5 d= 1 5 1 15 2 25 Pile Length Figue 13: Pile length vs A at 1.5Bf
Aveage Amplitude Aveage Amplitude Aveage Amplitude Vol. 13, Bund. E 13.25.2.15 = 14.17 d=.25 d=.5 d= 1.1.5 -.5 5 1 15 2 25 Pile Length Figue 14: Pile length vs A at 2Bf.8.6.4 = 17.72 d=.25 d=.5 d= 1.2 -.2 5 1 15 2 25 Pile Length Figue 15: Pile length vs A at 2.5Bf.12.1.8.6.4.2 = 21.26 d=.25 d=.5 d= 1 -.2 5 1 15 2 25 Pile Length Figue 16: Pile length vs A at 3Bf
Vol. 13, Bund. E 14 CONCLUSIONS In this eseach, a thee-dimensional finite element analysis of a vibation isolation of deep foundation in active system has been conducted employing tansient analyses with the compute pogam ANSYS. Depending on the obtained esults, the following conclusions may be dawn: A minimum tench depth of.5 times the pile length is the optimal depth fo achieving an ideal eduction in gound displacement amplitude and installing deepe tench ae uneconomically pactical. The optimum tench location fo deep pile foundation is foundation is 2Bf. 1.5Bf and fo shot pile Majo pat of vibation enegy tansmits by Rayleigh waves in shot pile foundation theefoe tench location and depth should be caefully detemined to achieve ideal vibation eduction. Amplitude s fo vey deep piles ae exponentially small. Efficiency of tench in vey deep pile foundation majoly is independent of tench depth and location. Cae must be taken to select a easonable tench location. REFERENCES 1. Aboudi J. (1973) Elastic waves in half-space with thin baie. J Eng Mech (ASCE) 1973;99(1):69 83. 2. Adam.M, Estoff.O. (25) Reduction of tain-induced building vibations by using open and filled tenches. Computes and Stuctues, 83, 11 24. 3. Ahmad, S. and Al-Hussaini, T. M. (1991) Simplified design fo vibation sceening by open and in-filled tenches. J. Geot. Eng., ASCE, 117(1), 67-88. 4. Ahmad, S., Al-Hussaini, T. M. and Fishman, K. L. (1996a) Investigation on active isolation of machine foundations by open tenches. J. Geot. Eng., ASCE, 122(6), 454-461. 5. Al-Hussaini, T. M. and Ahmad, S. (1996b) Active isolation of machine foundations by infilled tench baies. J. Geot. Eng., ASCE, 122(4), 288-294. 6. Al-Hussaini T.M, and Ahmad, S. (2) Numeical and expeimental studies on vibation sceening by open and in-filled tench baies. In: Chouw N, Schmid G, editos. Intenational Wokshop on Wave Popagation, Moving Load and Vibation Reduction, (WAVE2). Rottedam: Balkema, 241 25. 7. Amick H and Gendeau M (2) ASCE Constuction Conges 6 Olando, Floida, Febuay 22, 2.
Vol. 13, Bund. E 15 8. ANSYS Use s manual, ANSYS Inc., Canonsbug, Pa. 9. Attewell PB, Fame IW, (1973) Attenuation of gound vibations fom pile diving. Gound Engineeing 6(4):26 9. 1. Bakan, D. D. (1962) Dynamics of Bases and Foundations McGaw-Hill, New Yok. 11. Beskos, D., Dasgupta, G., and Vadoulakis, I.G. (1985) Vibation isolation of machine foundations. In Vibation poblems in geotechnical engineeing. Edited by Gazetas,G. and Selig, E.T. ASCE, NY. 138 151. 12. Beskos, D.E., Dasgupta, G., and Vadoulakis, I.G. (1986a) Vibation isolation using open o filled tenches, Pat 1: 2-D homogeneous soil. Computational Mechanics, 1(1), 43 63. 13. Beskos, D., Leung, K, Vadoulakis, I.G. (1986) Vibation isolation of stuctues fom suface waves in layeed soil. In Recent applications in computational mechanics. ASCE, NY. 125 14. 14. Beskos, D.E., Leung, K.L., and Vadoulakis, I.G. (199) Vibation isolation using open o filled tenches, Pat 3: 2-D non-homogeneous soil. Computational Mechanics, 7(1), 137 148. 15. Beskos, D.E., Leung, K.L., and Vadoulakis, I.G. (1991) Vibation isolation by tenches in continuously nonhomogeneous soil by the BEM. Soil Dynamics and Eathquake Engg., 1(3), 172 179. 16. Celebi, E. (26) Thee-dimensional modelling of tain-tack and sub-soil analysis fo suface vibations due to moving loads. Applied Mathematics and Computation, 1-22. 17. Celebi E., Fıat S., Cankayac I. (26) The effectiveness of wave baies on the dynamic stiffness coefficients of foundations using bounday element method Applied Mathematics and Computation doi: 1.116/ j.amc. 26.1.8 18. Ducke, D.C, and W. Page (1952) Soil mechanics and plastic analysis o limit design. Quat Applied Mathematics,1,157-165 19. El Nagga, M.H., Chehab,A.G. (25) Vibation baies fo shock-poducing equipment. Can. Geotech. J. 42, 297 36. 2. Emad, K. and Manolis, G. D. (1985) Shallow tenches and popagation of suface waves. J. Eng. Mech., ASCE, 111(2), 279-282. 21. Fuykui M, Matsumoto Y. (198) Finite diffeence analysis of Rayleigh wave scatteing at a tench. Bull Seismol Soc Ame (198;7(6):251 69. 22. Haupt (1977) Suface waves in nonhomogeneous halfspace, Poc. DMSR77 Kalsuhe 1, 355-367.
Vol. 13, Bund. E 16 23. Haupt WA. (1977) Isolation of vibations by concete coe walls. In: Poceedings of the ninth intenational confeence on soil mechanics and foundation engineeing, vol. 2. Tokyo, Japan, 1 p. 251 6. 24. Kattis, S.E., Polyzos, D., and Beskos, D.E. (1999a) Modelling of pile baies by effective tenches and thei sceening effectiveness. Soil Dynamics and Eathquake Engg, 18(1), 1 1. 25. Kattis, S.E., Polyzos, D., and Beskos, D.E. (1999b) Vibation isolation by a ow of piles using a 3-D fequency domain BEM. Intenational J. fo Numeical Methods in Engg, 46: 713 728. 26. J. Lysme and Waas (1972) Shea waves in plane infinite stuctues, J. eng. mech. diu. ASCE 98, 85-15. 27. May, T.W., and Bolt, B.A. (1982) The effectiveness of tenches in educing seismic motion. Eathquake Engg. and Stuctual Dynamics, 1(2), 195 21. 28. G. Segol, P. C. Y. Lee and J. F. Abel (1978) Amplitude eduction of suface waves by tenches, J. eng. mech, div. ASCE 14, 621441. 29. Shivastava, R.K., Kameswaa Rao, N.S.V. (22) Response of soil media due to impulse loads and isolation using tenches. Soil Dynamics and Eathquake Engg, 22, 695 72. 3. Tsai PH et al. (27) Thee-dimensional analysis of the sceening effectiveness of hollow pile baies fo foundation-induced vetical vibation Comput Geotech(27), doi:1.116/ j.compgeo. 27.5.1 31. Woods, R. D. (1967) Sceening of suface waves by tencbes. PhD dissetation. Univ. of Michigan, Ann Abo. Mich. 32. Woods, R. D. (1968) Sceening of suface waves in soils. J. Soil Mech. and Found. Engg. ASCE, 94(4), 951-979. 33. Woods, R. D., Banett NE, Sagesse R. (1974) Hologaphy, a new tool fo soil dynamics J Geotechn Eng (ASCE) 1974;1(11):1231 47. 34. Wolf, JP. (1994) Foundation Vibation Analysis Using Simple Physical Models, Englewood Cliffs, NJ: Pentice-Hall. 28 ejge