Dynamic response of a multilayered half-plane under moving loads with analytical layer-element method
AI Zhi-yong1,2, LIU Wen-jie1,2, REN Guang-peng1,2, LIU Chun-lin1,2
1.Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China 2.Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China
Abstract：The analytical layer-element method owns higher computation efficiency and numerical stability. Hence, this method is utilized to analyze the dynamic response of an isotropic multilayered half-plane subjected to a moving load. It is assumed that the studied system moves synchronously with the moving load, therefore, the moving load is considered to be motionless relative to the moving system. Combining the governing equations of motion in the moving system and the Fourier transform, the analytical layer-elements for a single layer with a finite thickness and a half-plane are derived in the Fourier transform domain. The global matrix of the problem can be obtained by assembling the analytical layer-element of each layer. The solutions in the integral transform domain are obtained by combining with the boundary conditions. The corresponding solution in the frequency domain is further recovered by applying the inverse Fourier transform. Several examples are given to confirm the accuracy of the proposed method and to illustrate the influences of velocity, depth of the load, layering and reinforced thickness and effects on the dynamic response in layered soils. The following conclusions can be obtained. The vertical displacement and vertical stress increase with the increase of load velocity, and their increments increase rapidly when the load velocity gets close to the shear velocity of soils. Besides, the vertical displacement is affected by the layering of soils and the superstratum is the key factor. The reinforcement of the superstratum has a remarkable result in decreasing the settlement of foundation, but the decrease gets weak when the reinforcement effect increases.
艾智勇, 刘文杰, 任广鹏, 刘春林. 基于解析层元法的成层半平面地基移动荷载动力响应研究[J]. 岩土工程学报, 2018, 40(2): 237-243.
AI Zhi-yong, LIU Wen-jie, REN Guang-peng, LIU Chun-lin. Dynamic response of a multilayered half-plane under moving loads with analytical layer-element method. Chinese J. Geot. Eng., 2018, 40(2): 237-243.
[1] SNEDDON I N.The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid[J]. Rendiconti del Circolo Matematico di Palermo, 1952, 1(1): 57-62. [2] 曹彩芹, 黄义, 高超. 移动荷载下单相弹性地基三维稳态响应[J]. 计算力学学报, 2012, 29(6): 972-977. (CAO Cai-qin, HUANG Yi, GAO Chao, Three-dimensional steady-state responses of single-phase elastic foundation by moving loads[J]. Chinese Journal of Computational Mechanics, 2012, 29(6): 972-977. (in Chinese)) [3] 蒋建群, 周华飞, 张土乔. 弹性半空间体在移动集中荷载作用下的稳态响应[J]. 岩土工程学报, 2004, 26(4): 440-444. (JIANG Jian-qun, ZHOU Hua-fei, ZHANG Tu-qiao.Steady-state response of an elastic half-space under a moving point load[J]. Chinese Journal of Geotechnical Engineering, 2004, 26(4): 440-444. (in Chinese)) [4] HUNG H H, YANG Y B.Elastic waves in visco-elastic half-space generated by various vehicle loads[J]. Soil Dynamics and Earthquake Engineering, 2001,21(1): 1-17. [5] 边学成, 陈云敏. 列车移动荷载作用下分层地基响应特性[J]. 岩石力学与工程学报, 2007, 26(1): 182-189. (BIAN Xue-cheng, CHEN Yun-min. Characteristics of layered ground responses under train moving loads[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 2 6(1): 182-189. (in Chinese)) [6] AI Z Y, ZHANG Y F.Plane strain dynamic response of a transversely isotropic multilayered half-plane[J]. Soil Dynamics and Earthquake Engineering, 2015, 75: 211-219. [7] SNEDDON I N.The use of integral transforms[M]. New York: McGraw-Hill, 1972. [8] MUKHOPADHYAY A.Stresses produced by a normal load moving over a transversely isotropic layer of ice lying on a rigid foundation[J]. Pure and Applied Geophysics, 1965, 60(1): 29-41. [9] APSEL R J, LUCO J E.On the Green's functions for a layered half space, Part II[J]. The Bulletin of the Seismological Society of America, 1983, 73(4): 931-951. [10] COLE J D, HUTH J H.Stress produced in a half-plane by moving surface load[J]. Journal of Applied Mechanics, ASME, 1958, 25: 669-704. [11] VERRUIJT A.An introduction to soil dynamics[M]. Netherlands: Springer, 2010.
