Steady state response of a saturated half-space with an unsaturated super-stratum
HU An-feng1,2LI Yi-jun1,2 JIA Yu-shuai3
1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China;
2. MOE Key Lab of Soft and Geo-environmental Engineering, Zhejiang University, Hangzhou 310058, China;
3. Guangzhou Construction Quality & Safety Detecting Center, Guangzhou 510600,China
Abstract：Based on dynamic governing equations of saturated poro-elastic medium and unsaturated poro-elastic medium, steady state response of a layered subgrade subjected to vertical surface concentrated harmonic loads was investigated. By introducing displacement functions and making use of Cauchy-Reimann conditions, displacements, stresses and pore water pressures of saturated soil and unsaturated soil were solved, respectively. Combined with different boundary conditions and continuity conditions, the integral form solutions to steady-state responses of layered soil subjected to vertical surface concentrated harmonic loads were obtained through Fourier inverse transformation. When the layered subgrade was reduced to a homogeneous saturated ground or a saturated half-space with an elastic super-stratum, the results obtained here agreed well with those in literature. Using several numerical examples, effects of saturation and thickness of unsaturated super-stratum, and exhaust-drainage condition of ground surface on these dynamic responses were investigated.
胡安峰1,2李怡君1,2贾玉帅3. 上覆非饱和层的饱和地基稳态响应分析[J]. 振动与冲击, 2018, 37(11): 34-41.
HU An-feng1,2LI Yi-jun1,2 JIA Yu-shuai3. Steady state response of a saturated half-space with an unsaturated super-stratum. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(11): 34-41.
[1]LAMB H. On the Propagation of Tremors over the Surface of an Elastic Solid[J]. Philosophical Transactions of the RoyalSociety of London, 1904, 203(359-371):1-42.
[2]BIOTMA. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range[J]. Journal of the Acoustical Society of America, 2005, 28(2):179-191..
[3]BIOTMA. Mechanicsofdeformationandacousticpropagationinporousmedia[J]. Journal of applied physics,1962, 33(4): 1482-1498.
[4]PAUL S. On the disturbance produced in a semi-infinite poroelastic medium by a surface load[J]. Pure & Applied Geophysics, 1976, 114(4):615-627.
[5]PHILIPPACOPOULOS A J. Lamb's problem for fluid-saturated, porous media[J]. Bulletin of the Seismological Society of America, 1988, 78(2):908-923.
[6]王立忠, 陈云敏, 吴世明,等. 饱和弹性半空间在低频谐和集中力下的积分形式解[J]. 水利学报, 1996(02):84-88。
WANG Li-zhong, CHEN Yun-min, WU Shi-ming, et al. A
solution to saturated elastic half-space under harmonic force of low frequency [J]. Journal of Hydraulic Engineering, 1996(02):84-88.
[7]陈龙珠，陈胜立，梁发云. 饱和地基竖向振动的衰减特性[J]. 上海交通大学学报，2002，36(3)：376-381.
CHEN Long-zhu, CHEN Sheng-li, LIANG Yun-fa. Vibration attenuation of saturated strata by vertical surface loads[J], Journal of Shanghai Jiaotong University,2002，36(3)：376-381.
[8]杨峻, 吴世明. 弹性层和饱和半空间体系稳定动力响应[J]. 土木工程学报, 1997(03):39-48.
YANG Jun, WU Shi-ming. Steady state response of elastic soil layer and saturated layered half-space[J].China Civil Engineering Journal, 1997(03):39-48.
[9]孙宏磊, 蔡袁强, 陈成振. 列车荷载作用下路轨系统及饱和弹性半空间上覆盖土层的动力响应[J]. 岩土工程学报, 2009, 31(06):922-928.
SUN Hong-lei, CAI Yuan-qiang, CHEN Cheng zhen.Dynamic response of railways on layered half-space subjected tomoving train load[J].Chinese Journal of Geotechnical Engineering,2009, 31(06):922-928.
[10] GRUNDMANN H, LIEB M, TROMMER E. The response of a layered half-space to traffic loads moving along its surface[J]. Archive of Applied Mechanics, 1999, 69(1):55-67.
[11]刘洪波，刘洁，闻敏杰.深埋圆形隧洞非饱和土-衬砌结构系统的动力特性[J].振动与冲击,2016,35 (13):36-41.
LIU Hong-bo,LIU Jie,WEN Min-jie.Dynamic characteristics of unsaturated soil and lining system with a deeply embedded circular tunnel[J].Journal of Vibration and Shock,2016,35 (13):36-41.
[12]BRUTSAETW. Thepropagationofelasticwavesinunconsolidatedunsaturatedgranularmediums[J]. Journal of geophysical research,1964, 69(2): 243-257.
[13] 徐长节, 史焱永. 非饱和土中波的传播特性[J]. 岩土力学, 2004, 25(3):354-358.
XU Chang-jie, Shi Yan-yong. Characteristics of wave propagation in unsaturated soils. [J]. Rock and Soil Mechanics, 2004, 25(3):354-358.
[14] Vardoulakis I, Beskos D E. Dynamic behavior of nearly saturated porous media[J].Mechanics of Materials, 1986, 5: 87-108 .
[15] 徐明江. 非饱和土地基与基础的动力响应研究[D]. 广州：华南理工大学. 2009.
XU Ming-jiang, Investigation on dynamic response of unsaturated soils and foundation[D].Guangzhou:South China University of Technology,2009.
[16]刘志军, 夏唐代, 黄睿等. Biot理论与修正的Biot理论比较及讨论[J]. 振动与冲击, 2015(4):148-152.
LIU Zhi-jun, XIA Tang-dai, Huang Rui, et al.Comparison and discussion for Biot theory and modified Biot one[J].Journal of Vibration and Shock, 2015(4):148-152.
[17]Bishop A W, et al. Fractors controlling the strength of partly saturated cohesive soils. In: Research Conf on Shear Strength of Cohesive Soils. London, 1960.503~502.
[18] Cai Y, Sun H, Xu C. Steady state responses of poroelastic half-space soil medium to a moving rectangular load[J]. International Journal of Solids and Structures, 2007,44(22): 7183-7196.
