Point Loads on a Flat Uniform Transversely Isotropic Linear Elastic Half-Space: Closed-Form Solutions

The calculation of ground movements under small-strain serviceability limit-state conditions is a common task in practical geotechnical engineering. Point load solutions are the basis of analytical solutions for this task. For situations in which soils can be characterized as linear and elastic, a commonly used simplifying assumption is that soils are fully isotropic. However, it is now well established that most field soils are anisotropic, with transverse isotropy (also called cross anisotropy) being a common form, and with full isotropy being a special case. The general material has one axis of rotation and reflection symmetry that is typically vertical in field deposits, whereas every possible axis is an axis of symmetry for full isotropy. Except for the special case, transverse isotropy can produce different behaviors in laboratory tests depending on how samples are aligned in a testing device. This technical note provides analytical solutions for this more realistic type of material model. The solutions are for material displacements, strains, and stresses due to vertical and lateral point loads on a uniform soil deposit modeled as a flat, transversely isotropic linear-elastic half-space. They were developed after it was noticed that an otherwise excellent set of existing solutions by previous authors contained errors. This technical note introduces the proposed notation and provides the corrected solutions and the information needed to use them in an analytical framework, including a flow diagram. Supplemental Materials provide detailed validation in the form of calculation sheets, including full checks that the proposals satisfy all required compatibility, material behavior, equilibrium, and boundary conditions.