Surface displacements due to batter piles driven in cross‐anisotropic media

Hou

2010

JOMMS

Self Cite

This work derives the fundamental solutions for displacements and stresses due to horizontal and vertical line loads acting in a continuously inhomogeneous plane strain cross-anisotropic full space with Young's and shear moduli varying exponentially with depth. The governing equations can be obtained by combining the generalized Hooke's law, the strain-displacement relationships, and the equilibrium equations. Then, utilizing Fourier transforms, the governing equations are transformed into ordinary differential equations. Additionally, by using the variation of parameters, the solutions of the displacements in the Fourier domain are found. However, the stress solutions in the same domain can also be found by employing the stress-strain-displacement relationships. Eventually, performing inverse Fourier transforms by means of the numerical integration program QDAGI, the displacements and stresses induced by horizontal and vertical plane strain line loads can be calculated. The solutions indicate that the displacements and stresses are profoundly influenced by the nondimensional inhomogeneity parameter, the type and degree of material anisotropy, the types of loading, and the nondimensional horizontal distance. The proposed solutions are identical to those of Wang and Liao after suitable integration, as derived in an appendix, when the full space is a homogeneous cross-anisotropic material. A series of parametric studies are conducted to demonstrate the present solutions, and to elucidate the effects of aforementioned factors on the vertical normal stress. The results reveal that estimates of displacement and stress should take the inhomogeneity into account when studying cross-anisotropic materials under applied line loads.

Section: An Illustrative Examplementioning

confidence: 80%

Fundamental solutions for an inhomogeneous cross-anisotropic material due to horizontal and vertical plane strain line loads

Hou

2010

JOMMS

Self Cite

Section: An Illustrative Examplementioning

confidence: 83%

Untitled

2010

JOMMS

Delamination in layered composites and debonding in adhesive joints are modeled and analyzed using interfacial mechanics, consisting of interface elements for the kinematical assumption and tractionseparation equations for the constitutive model. Material equations are presented for the inelastic behavior of pure and ductile-modified epoxy resins, used for the matrix phase of the composite and in a chemically modified form for the adhesive in bonded structures. Two different modeling approaches are proposed. The first is a brittle fracture model with a stressbased failure criterion and rate-dependent strength parameters together with a mixed-mode energy criterion for the interaction of the three different modes of failure. The second makes use of an elastic-plastic approach with a traction-separation equation for ductile materials and rate-dependent yield stresses. Standard tests for the delamination of layered composites under various modes of failure are simulated by making use of the interface element for bonding/debonding. The model for the inelastic behavior of a thin layer of the structural adhesive is validated up to fracture for various modes of failure due to pure and combined loading in the normal and shear directions. Therefore, the relevant part of the experimental setup for the testing is meshed with finite elements and the results of the simulation are compared to the corresponding test data.

“…The present vertical stress solutions as well as the surface displacement solutions [14] could offer practical engineers a complete and useful reference when piles are driven in an isotropic/crossanisotropic earth mass. Furthermore, a parametric analysis demonstrates that the vertical stresses with the consideration of pile batter are considerably different from those calculated from plumb piles.…”

Section: Discussionmentioning

confidence: 99%

Vertical stress distributions around batter piles driven in cross‐anisotropic media

Num Anal Meth Geomechanics

Lee

Chen

2008

Self Cite

SUMMARYThis work presents analytical solutions to compute the vertical stresses for a cross-anisotropic half-space due to various loading types by batter piles. The loading types are an embedded point load for an end-bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The crossanisotropic planes are parallel to the horizontal ground surface. The proposed solutions can be obtained by utilizing Wang and Liao's solutions for a horizontal and vertical point load acting in the interior of a cross-anisotropic medium. The derived cross-anisotropic solutions using a limiting approach are in perfect agreement with the isotropic solutions of Ramiah and Chickanagappa with the consideration of pile inclination. Additionally, the present solutions are identical to the cross-anisotropic solutions by Wang for the batter angle equals to 0. The influential factors in yielded solutions include the type and degree of geomaterial anisotropy, pile inclination, and distinct loading types. An example is illustrated to clarify the effect of aforementioned factors on the vertical stresses. The parametric results reveal that the stresses considering the geomaterial anisotropy and pile batter differ from those of previous isotropic and cross-anisotropic solutions. Hence, it is imperative to take the pile inclination into account when piles are required to transmit both the axial and lateral loads in the cross-anisotropic media.