Effect of a symmetric V‐shaped canyon on the seismic response of an adjacent building under oblique incident SH waves

Abstract

To elucidate whether an irregular topography affects the seismic response of nearby structures, an analytical solution to the dynamic interaction between a symmetric V-shaped canyon and an adjacent building under the incidence of SH waves is proposed by using the wave function expansion method. The dynamic canyon-soil-structure interaction is decomposed into two problems of scattering and radiation. The building is idealized as a shear wall supported by a semicircular rigid foundation. The analytical solution can be degenerated theoretically to the canonical model of a shear wall embedded in a half-space for either a zero depth-to-width ratio of the canyon or an infinite canyon-building distance. Through a numerical comparison with two past exact solutions to the sole shear wall model as well as the sole V-shaped canyon model, the correctness of the method in this paper is verified. A systematic parametrical analysis in both frequency and time domains is performed. It is found that the seismic response of the building may be amplified when it is on the wave-facing side of the canyon. The degree of amplification is closely related to the size and depth-to-width ratio of canyon, the wave velocity of half-space, and the incident angle and frequency content of seismic waves. The potential adverse effects of the V-shaped canyon on the ground motion input of adjacent buildings should be considered in the seismic design.

Effect of a V‐shaped canyon on the seismic response of a bridge under oblique incident SH waves

“…According to Zhang et al 18 . and with aid of Equation (), the free wave u f in various coordinate systems ( r j , θ j ) for j = 1, 2, 3 can be expressed in a unified form as $$$$\begin{equation}{u^f}\left( {{r_j},{\theta _j}} \right) = \sum_{n = 0}^\infty {{U_{n,j}}} {J_n}\left( {k{r_j}} \right)\cos \left( {n{\theta _j}} \right)\end{equation}$$$$where J n (•) is the Bessel function of the first kind with order n and $$$$\begin{equation}{U_{n,j}} = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {2{{\left( { - 1} \right)}^n}{\varepsilon _n}\cos \left( {n\alpha } \right)\exp \left( {ik{D_{12}}\cos \alpha } \right)}&{j = 1}\\[4pt] {2{{\left( { - 1} \right)}^n}{\varepsilon _n}\cos \left( {n\alpha } \right)}&{j = 2}\\[4pt] {2{{\left( { - 1} \right)}^n}{\varepsilon _n}\cos \left( {n\alpha } \right)\exp \left( { - ik{D_{23}}\cos \alpha } \right)}&{j = 3} \end{array} } \right.\end{equation}$$$$with ε n being the Newman factor ( ε n = 1, n = 0; ε n = 2, n > 0).…”

“…Based on the above problem decomposition strategy similar to Zhang et al., 18 once the Problems I, II and III are solved, the total scattering wavefields us 1, us 2 and us 3 in the outer region and the total wavefield u in in the inner region can be obtained by the following relations: $$$$\begin{equation}u_m^s = u_{m,I}^s + u_{m,II}^s{\Delta _1} + u_{m,III}^s{\Delta _3},m = 1,2,3\end{equation}$$$$ $$$$\begin{equation}{u^{in}} = u_I^{in} + u_{II}^{in}{\Delta _1} + u_{III}^{in}{\Delta _3}\end{equation}$$$$…”

“…However, among the many influencing factors, the canyon topography has usually been ignored. In fact, the presence of a canyon can modify the amplitude and phase of ground motions, 14–16 which will have a strong influence on the seismic response of structures in a canyon site 17,18 …”

“…However, there is no such rigorous solution for a bridge crossing a more common V‐shaped canyon. Following the success of previous study on the dynamic interaction between a V‐shaped canyon and a nearby building, 18 this study focuses on the effect of a V‐shaped canyon on a bridge. With the aid of an analytical solution for the dynamic canyon‐bridge interaction problem, the influence of key parameters including the size and shape of the canyon, and the incident angle and frequency of the seismic wave on the dynamic response of the bridge is studied systematically.…”

“…In fact, the presence of a canyon can modify the amplitude and phase of ground motions, [14][15][16] which will have a strong influence on the seismic response of structures in a canyon site. 17,18 Only a few scholars have studied the effect of canyon topography on seismic response of bridges in recent years. Zhou et al 19 used the finite element method to obtain the seismic response of the multi-supported continuous rigid frame bridge under incident SV waves, and the results showed that the canyon topography enhanced the response of the bridge.…”