Dynamic response of cylindrical cavity to anti-plane impact load by using analytical approach

ZHAI Chao-jiao(翟朝娇)^{1, 2}, XIA Tang-dai(夏唐代)^{1, 2}, DU Guo-qing(杜国庆)³, DING Zhi(丁智)^{2, 4}

(1. Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education
(Zhejiang University), Hangzhou 310058, China;
2. Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China;
3. Anhui Electric Power Design Institute, Hefei 230601, China;
4. Department of Civil Engineering, Zhejiang University City College, Hangzhou 310015,China)

Abstract:The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied. Using Laplace transform combining with contour integral of the Laplace inverse transform specifically, the general analytical expressions of the soil displacement and stress are obtained in the time domain, respectively. And the numerical solutions of the problem computed by analytical expressions are presented. In the time domain, the dynamic responses of the infinite elastic soil are analyzed, and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results. One observes good agreement between analytical and numerical inversion results, lending the further support to the method presented. Finally, some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival, and after the shear wave arrival, the stress and the displacement at this point increase abruptly, then reduce and tend to the static value gradually at last. The wave attenuates along the radial, therefore the farther the wave is from the source, the smaller the stress and the displacement are, and the stress and the displacement are just functions of the radial distance from the axis.

Key words:cylindrical cavity; anti-plane; Laplace transform; contour integral; impact load; dynamic responses