Computing displacements in transversely isotropic rocks using influence charts

This paper presents a simple graphical method for computing the displacemen t beneath/at the surface of a transversely isotropic half-space subjected t o surface loads. The surface load can be distributed on an irregularly-shap ed area. The planes of transverse isotropy are assumed to be parallel to th e horizontal surface of the half-space. Based on the point load solutions p resented by the authors, four influence charts are constructed for calculat ing the three displacements at any point in the interior of the half-space. Then, by setting z = 0 of the derived solutions, another four influence ch arts for computing the surface displacements can also be proposed. These ch arts are composed of unit blocks. Each unit block is bounded by two adjacen t radii and arcs, and contributes the same level of influence to the displa cement. Following, a theoretical study was performed and the results showed that the charts for interior displacements are only suitable for transvers ely isotropic rocks with real roots of the characteristic equation; however , the charts for surface displacements are suitable for all transversely is otropic rocks. Finally, to demonstrate the use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal c ircular-shaped load is given. The results from the new graphical method agr ee with those of analytical solutions as well. The new influence charts can be a practical alternative to the existing analytical or numerical solutio ns, and provide results with reasonable accuracy.