Fundamentals of surface deformation and application to construction monitoring

The rigorous approach to plane deformation developed by the author is extended to the case of curved surfaces and is applied to the monitoring of surface-like constructions by repeated surveys. From coordinates of discrete points at two survey epochs, interpolation of the displacements produces displacement functions expressed in terms of surface curvilinear coordinates, which can be used for the computation of coordinate-invariant deformation parameters which are meaningful from the strength-of-materials point of view. In addition, it is shown how to incorporate information from additional in situ measurements by strainmeters, extensiometers, tiltmeters, etc. in the interpolation process. The computed invariant parameters at any surface point are the dilatation, the maximum shear strain, and the maximum bending expressed in terms of the maximum change of radius curvature among all surface directions. In addition to the theoretical tools, a complete algorithm is presented for direct practical implementation.