Computing Displacements in Transversely Isotropic Rocks Using Influence Charts |
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Authors: | C D Wang J J Liao |
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Institution: | (1) Department of Civil Engineering, National Chiao-Tung University, Hsinchu, Taiwan, Republic of China, TW |
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Abstract: | Summary This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic
half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse
isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented
by the authors, four influence charts are constructed for calculating 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 charts for computing the surface displacements can also be proposed. These
charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level
of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for
interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation;
however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the
use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped
load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence
charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable
accuracy. |
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Keywords: | |
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