A numerical model for the isolation of moving-load induced vibrations by pile rows embedded in layered porous media. (English) Zbl 1176.74085

Lu, JianFei; Xu, Bin; Wang, JianHua

Int. J. Solids Struct. 46, No. 21, 3771-3781 (2009).

Summary: A numerical model is developed to analyse the isolation of moving-load induced vibrations using pile rows embedded in a layered poroelastic half-space. Based on Biot’s theory and the transmission and reflection matrices (TRM) method, the free wave field solution for a moving load applied on the surface of a layered poroelastic half-space and the fundamental solution for an harmonic circular patch load are determined. Using Muki and Sternberg’s method, the second kind of frequency domain Fredholm integral equations for the dynamic interaction between pile rows and the layered poroelastic half-space are derived. The time domain solution is recovered via inverse Fourier transform in order to obtain the amplitude reduction ratio and thus assess the vibration isolation efficiency of pile rows. A special case of the present model shows good agreement with an existing solution. Numerical results of this study show that the speed of moving loads has an important influence on the isolation of vibrations by pile rows: the same pile rows can achieve better isolation efficiencies for higher speed loads than for lower speed loads. Pile rows embedded in a two-layered poroelastic half-space with a softer overlying layer usually generate better vibration isolation effects than those with a stiffer overlying layer. Finally, better isolation vibration may be realized by increasing the pile length and decreasing the net spacing between neighboring piles in a pile row.

MSC:

74H45	Vibrations in dynamical problems in solid mechanics
74L10	Soil and rock mechanics
74F10	Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Keywords:

layered poroelastic half-space; pile rows; vibration isolation; moving loads; the transmission and reflection matrix (TRM) method

References:

[1]	Andersen, L.; Nielsen, S. R. K.: Reduction of ground vibration by means of barriers or soil improvement along a railway track, Soil dynamics and earthquake engineering 25, 701-716 (2005)
[2]	Apirathvorakij, V.; Karasudhi, P.: Quasi-static bending of a cylindrical elastic bar partially embedded in a saturated elastic half-space, International journal of solids and structures 16, 625-644 (1980) · Zbl 0426.73050
[3]	Apsel, R. J.; Luco, J. E.: On the Green’s functions for a layered half-space: part II, Bulletin of the seismological society of America 73, 931-951 (1983)
[4]	De, F. C. P. Barros; Luco, J. E.: Response of a layered viscoelastic half-space to a moving point load, Wave motion 19, 189-210 (1994) · Zbl 0926.74038
[5]	Biot, M. A.: Theory of propagation of elastic waves in a fluid-saturated porous solid: I. Low frequency range, Journal of the acoustical society of America 28, 168-178 (1956)
[6]	Biot, M. A.: Mechanics of deformation and acoustic propagation in porous media, Journal of applied physics 33, 1482-1498 (1962) · Zbl 0104.21401
[7]	Celebi, E.; Schmid, G.: Investigation of ground vibrations induced by moving loads, Engineering structures 27, 1981-1998 (2005)
[8]	Chen, X. F.: Seismogram synthesis for multi-layered media with irregular interfaces by global generalized reflection/transmission matrices method 3: theory of 2D P-SV case, Bulletin of the seismological society of America 86, 389-405 (1996)
[9]	D’appolonia, E.; Romualdi, J. P.: Load transfer in end-bearing steel H-piles, Journal of the geotechnical division ASCE 89, No. SM2, 1-25 (1963)
[10]	Halpern, M. R.; Christiano, P.: Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace, Earthquake engineering and structural dynamics 14, 439-454 (1986)
[11]	Harkrider, D. G.: Surface waves in multilayered elastic medium I: Rayleigh and love waves from buried sources in a multilayered elastic half-space, Bulletin of the seismological society of America 54, 627-629 (1964)
[12]	Haskell, N. A.: Radiation pattern of surface waves from point sources in a multilayered medium, Bulletin of the seismological society of America 54, 377-393 (1964)
[13]	Jin, B.; Zhong, Z.: Lateral dynamic compliance of pile embedded in poroelastic half-space, Soil dynamic and earthquake engineering 21, 519-525 (2001)
[14]	Ju, S. H.; Lin, H. T.: Analysis of train-induced vibrations and vibration reduction schemes above and below critical Rayleigh speeds by finite element method, Soil dynamics and earthquake engineering 24, 993-1002 (2004)
[15]	Karlström, A.; Boström, A.: Efficiency of trenches along railways for trains moving at sub- or supersonic speeds, Soil dynamics and earthquake engineering 27, 625-641 (2007)
[16]	Kattis, S. E.; Polyzos, D.; Beskos, D. E.: Modelling of pile wave barriers by effective trenches and their screening effectiveness, Soil dynamics and earthquake engineering 18, 1-10 (1999)
[17]	Kattis, S. E.; Polyzos, D.; Beskos, D. E.: Vibration isolation by a row of piles using a 3-D frequency domain BEM, International journal for numerical methods in engineering 46, 713-728 (1999) · Zbl 1073.74549
[18]	Leung, K. L.; Beskos, D. E.; Vardoulakis, I. G.: Vibration isolation using open or filled trenches. Part 3: 2-D inhomogeneous soil, Computational mechanics 7, 137-148 (1990) · Zbl 0731.73089
[19]	Leung, K. L.; Vardoulakis, I. G.; Beskos, D. E.; Tassoulas, J. L.: Vibration isolation by trenches in continuously inhomogeneous soil by the BEM, Soil dynamics and earthquake engineering 10, 172-179 (1991)
[20]	Lu, J. F.; Hanyga, A.: Fundamental solution for a layered porous half-space subject to a vertical point force or a point fluid source, Computational mechanics 35, 376-391 (2005) · Zbl 1109.74323
[21]	Lu, J. F.; Jeng, D. S.: A half-space saturated poro-elastic medium subjected to a moving point load, International journal of solids and structures 44, 573-586 (2007) · Zbl 1123.74013
[22]	Lu, J. F.; Jeng, D. S.: Poro-elastic model for pile – porous medium interaction due to seismic waves, International journal for numerical and analytical methods in geomechanics 32, 1-41 (2008) · Zbl 1273.74275
[23]	Luco, J. E.; Apsel, R. J.: On the Green’s functions for a layered half-space: part I, Bulletin of the seismological society of America 73, 909-929 (1983)
[24]	Lysmer, J.; Waas, G.: Shear waves in plane infinite structures, Journal of engineering mechanics division ASCE 98, 85-105 (1972)
[25]	Maeso, O.; Aznarez, J. J.; Garcia, F.: Dynamic impedances of piles and groups of piles in saturated soils, Computers and structures 83, 769-782 (2005)
[26]	May, T. W.; Bolt, B. A.: The effectiveness of trench in reducing seismic motion, Earthquake engineering and structural dynamics 10, 195-210 (1982)
[27]	Muki, R.; Sternberg, E.: On the diffusion of an axial load from an infinite cylindrical pile embedded in an elastic medium, International journal of solids and structures 5, 587-606 (1969) · Zbl 0188.57503
[28]	Muki, R.; Sternberg, E.: Elastostatic load transfer to a half-space from a partially embedded axially loaded rod, International journal of solids and structures 6, 69-90 (1970) · Zbl 0184.50303
[29]	Oppenheim, A. V.; Schafer, R. W.: Discrete-time signal processing, (1999) · Zbl 0676.42001
[30]	Pak, R. Y. S.; Guzina, B. B.: Three-dimensional Green’s functions for a multilayered half-space in displacement potentials, Journal of engineering of mechanics ASCE 128, 449-461 (2002)
[31]	Pak, R. Y. S.; Jennings, P. C.: Elasticdynamic response of pile under transverse excitations, Journal of engineering mechanics division ASCE 113, 1101-1116 (1987)
[32]	Poulos, H. G.; Davis, E. H.: Pile foundation analysis and design, (1980)
[33]	Segol, G. P.; Lee, C. Y.; Abel, J. E.: Amplitude reduction of surface wave by trenches, Journal of engineering mechanics division ASCE 104, 621-641 (1978)
[34]	Senjuntichai, T.; Rajapakse, R. K. N.D.: Exact stiffness method for quasi-statics of a multi-layered poroelastic medium, International journal of solids and structures 32, 1535-1553 (1995) · Zbl 0921.73017
[35]	Sneddon, I. N.: Fourier transforms, (1951) · Zbl 0038.26801
[36]	Woods, R. D.: Screening of surface waves in soil, Journal of soil mechanics and foundation engineering ASCE 94, No. SM4, 951-979 (1968)
[37]	Xu, B.; Lu, J. F.; Wang, J. H.: Dynamic response of a layered and water-saturated poro-elastic half-space subjected to a moving load, Computer and geotechnics 35, 1-10 (2008)