SUMMARYThis work presents analytical solutions for displacements caused by three-dimensional point loads in a transversely isotropic full space, in which transversely isotropic planes are inclined with respect to the horizontal loading surface. In the derivation, the triple Fourier transforms are employed to yield integral expressions of Green's displacement; then, the triple inverse Fourier transforms and residue calculus are performed to integrate the contours. The solutions herein indicate that the displacements are governed by (1) the rotation of the transversely isotropic planes (), (2) the type and degree of material anisotropy (E/E , / , G/G ), (3) the geometric position (r, , ) and (4) the types of loading (P x , P y , P z ). The solutions are identical to those of Liao and Wang (Int. J. Numer. Anal. Methods Geomechanics 1998; 22(6):425-447) if the full space is homogeneous and linearly elastic and the transversely isotropic planes are parallel to the horizontal surface. Additionally, a series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of the aforementioned factors on the displacements. The results demonstrate that the displacements in the infinite isotropic/transversely isotropic rocks, subjected to three-dimensional point loads could be easily determined using the proposed solutions. Also, these solutions could realistically imitate the actual stratum of loading situations in numerous areas of engineering.

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Based on the finite element analysis software Midas, it takes response spectrum analysis, and posts the failure mechanism and characteristics of Girder Bridge under intense earthquake. Through the seismic response spectrum displacement maps of Girder Bridge, it finds out that the abutment and foundation deformation is in evidence, especially the top of abutment foundation. Through the study of seismic internal force variation on girder and pier, it indicates that the longitudinal earthquake controls axial force, vertical shearing force and in-plane bending moment, transversal earthquake dominates transversal shearing force and out-planes bending moment. And it shows that the pier and mid-span section are seismic response sensitivity parts. The three parts, axial force, longitudinal shearing force and in-plane bending moment, becomes the controlling index of pier intensity. According to the seismic response spectrum displacement for pier and abutment, the transversal anti-seismic stiffness of pier is smaller than longitudinal one, longitudinal seismic force shows no effect on transversal displacement, and the transversal seismic force can augments longitudinal displacement. At the same condition, longitudinal seismic force changes the longitudinal distributing form of abutment and concaves it deeply, and the transversal seismic force can not change its shape, but augment its value.

Based on the example, red-Flag Bridge in Chongzhou City, using the finite element to analyze the response spectrum of seismic performance for the concrete arch bridge under two conditions. Through the numerical analysis of vibrational damage on the whole bridge, reveals the nether structure and elements of bridge is affected by the seismic waves under the seismic effect and the great stiffness in upper structure, and posts that the anti-inertia in longitudinal direction is more powerful than the transverse and vertical ones. The deformation of arch ring is mostly affected by the displacement on transverse line, DY direction, and less in the longitudinal, vertical and rotational direction. According to the analysis of spectrum value displacement on abutment, finds out that the transverse direction of abutment is mostly affected by the displacement on DZ direction, for the abutment displacement, less in the middle, big in both sides. And for the vertical one, it is mostly affected by DY displacement, in the DY displacement of abutment, big in top, less in base.