Elastic Solutions to 2D Plane Strain Problems: Nonlinear Contact and Settlement Analysis for Shallow Foundations

Taylor, Adam G.; Chung, Jae H.

doi:10.3390/geotechnics2030032

Elastic Solutions to 2D Plane Strain Problems: Nonlinear Contact and Settlement Analysis for Shallow Foundations

Journal Article · Mon Aug 15 00:00:00 EDT 2022 · Geotechnics

DOI:https://doi.org/10.3390/geotechnics2030032· OSTI ID:1902005

Taylor, Adam G. ^[1]; Chung, Jae H. ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

The classical Neumann boundary value problem of an isotropic, homogeneous elastic half-plane under plane strain conditions is readdressed as the limiting case of the fully three-dimensional problem. Analytical solutions of the stress and strain tensors are obtained by taking the limit from known three-dimensional solutions. It is shown that the displacement fields for the plane strain problem are not well defined. A small number of simple expressions are developed, which provide a general solution for linearly-varying traction over arbitrary regions on the boundary. A simple, efficient, and rapidly convergent algorithm is developed which uses these solutions as analytic elements and provides a solution approach to the general boundary value problem. The method is verified against known solutions for Hertzian contact between parallel cylinders. Two numerical examples are presented for the analysis of shallow foundation systems. In the first, the boundary conditions are informed by analytical elastoplastic calculations and a strain influence analysis is performed and compared with the Schmertmann method. Subsequently, empirical laboratory contact traction distributions measured by Bauer et al., in both the normal and tangential directions are employed as boundary conditions for an analysis of the underlying stress field.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1902005

Report Number(s):: LLNL-JRNL-832460; 1049764

Journal Information:: Geotechnics, Journal Name: Geotechnics Journal Issue: 3 Vol. 2; ISSN 2673-7094

Publisher:: MDPICopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
elasticity
plane strain
shallow foundations
soil-structure interaction

Elastic Solutions to 2D Plane Strain Problems: Nonlinear Contact and Settlement Analysis for Shallow Foundations

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