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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (3) : 632-645
Anisotropy of multi-layered structure with sliding and bonded interlayer conditions
Lingyun YOU1,2, Kezhen YAN1(), Jianhong MAN1, Nengyuan LIU1
1. College of Civil Engineering, Hunan University, Changsha 410082, China
2. Department of Civil and Environmental Engineering, Michigan Technological University, Houghton, MI 49931, USA
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A better understanding of the mechanical behavior of the multi-layered structure under external loading is the most important item for the structural design and the risk assessment. The objective of this study are to propose and develop an analytical solution for the mechanical behaviors of multi-layered structure generated by axisymmetric loading, and to investigate the impact of anisotropic layers and interlayer conditions on the multi-layered structure. To reach these objectives, first, according to the governing equations, the analytical solution for a single layer was formulated by adopting the spatial Hankel transform. Then the global matrix technique is applied to achieve the analytical solution of multi-layered structure in Hankel domain. The sliding and bonded interlayer conditions were considered in this process. Finally, the numerical inversion of integral transform was used to solve the components of displacement and stress in real domain. Gauss-Legendre quadrature is a key scheme in the numerical inversion process. Moreover, following by the verification of the proposed analytical solution, one typical three-layered flexible pavement was applied as the computing carrier of numerical analysis for the multi-layered structure. The results have shown that the anisotropic layers and the interlayer conditions significantly affect the mechanical behaviors of the proposed structure.

Keywords multi-layered structure      Hankel transformation      anisotropic      transversely isotropic      interlayer condition      Gauss-Legendre quadrature     
Corresponding Author(s): Kezhen YAN   
Just Accepted Date: 11 April 2020   Online First Date: 25 May 2020    Issue Date: 13 July 2020
 Cite this article:   
Lingyun YOU,Kezhen YAN,Jianhong MAN, et al. Anisotropy of multi-layered structure with sliding and bonded interlayer conditions[J]. Front. Struct. Civ. Eng., 2020, 14(3): 632-645.
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Lingyun YOU
Kezhen YAN
Jianhong MAN
Nengyuan LIU
Fig.1  Sketch of the studied interlayer between layer-i and layer-(i + 1).
Fig.2  Vertical displacements comparison with the example in Ref. [59].
Fig.3  Radial stresses comparison with results from BISAR 3.0.
layers thickness (m) average vertical modulus (MPa) vertical Poisson’s ratio average horizontal modulus (MPa) horizontal Poisson’s ratio density (kg/m3)
layer-1 0.0889 1723.69 0.35 2354.71
layer-2 0.2032 282.79 0.43 108.10 0.15 2194.53
layer-3 1.2700 55.16 0.40 1681.94
Tab.1  Model parameters used in comparisons [37]
response top layer-3 top layer-2 top layer-1
σz (MPa) εz (1E–6) εz (1E–6) δz (mm)
average measured 0.068 2000 580 0.4318
GT-PAVE (40 ksi) 0.074 2112 408 0.4318
present solution 0.070 2095 496 0.4064
Tab.2  Response variable comparison with measured results from Ref [37].
layers thickness (m) vertical modulus (MPa) Passion’s ratio density (kg/m3) interlayer condition
layer-1 0.18 2300 0.25 2100 sliding/bonded
layer-2 0.30 900 0.25 2000
layer-3 infinite 100 0.25 1800 bonded with layer-2
Tab.3  Properties of the elastic layers for multi-layered structure
case number interlayer n1 n2
K1 bonded 1 (isotropy) 1 (isotropy)
K2 bonded 0.5 0.5
K3 sliding 1 (isotropy) 1 (isotropy)
K4 sliding 0.5 0.5
Tab.4  The combination cases of interlayer condition and modulus ratio
Fig.4  Vertical displacement of top-surface versus radial distance.
Fig.5  Radial stress versus structure depth.
Fig.6  Horizontal shear stress versus structure depth.
Fig.7  Impact of transversely isotropic properties on maximum displacements: (a) transversely isotropic of layer-1 and (b) transversely isotropic of layer-2.
Fig.8  Impact of transversely isotropic properties on maximum radial stresses: (a) transversely isotropic of layer-1 and (b) transversely isotropic of layer-2.
Fig.9  Impact of transversely isotropic properties on maximum horizontal shear stresses: (a) transversely isotropic of layer-1 and (b) transversely isotropic of layer-2.
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