CHEN Sheng-li, CHEN Long-zhu. The Axisymmetric Mixed Boundary-Value Problem of the Vertical Vibration of a Rigid Foundation on Saturated Layered Soil Subgrade[J]. Applied Mathematics and Mechanics, 2002, 23(2): 201-206.
 Citation: CHEN Sheng-li, CHEN Long-zhu. The Axisymmetric Mixed Boundary-Value Problem of the Vertical Vibration of a Rigid Foundation on Saturated Layered Soil Subgrade[J]. Applied Mathematics and Mechanics, 2002, 23(2): 201-206.

# The Axisymmetric Mixed Boundary-Value Problem of the Vertical Vibration of a Rigid Foundation on Saturated Layered Soil Subgrade

• Rev Recd Date: 2001-09-18
• Publish Date: 2002-02-15
• Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisymmetric vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry elasti clayer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition. The results are reduced to the case for saturated half-space. The set of dual integral equations are reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper and plots of the dynamic compliance coefficient Cv versus the dimensionless frequency a0 are presented.
•  [1] Luco J E,Westmann R A.Dynamic response of circular footings[J].J Eng Mech,ASCE,1971,97(5):1381-1395. [2] Halpern M R,Christiano P.Response of poroelastic halfspace to steady-state harmonic surface tractions[J].Int J Numer Anal Meth Geomech,1986,10(6):609-632. [3] Philippacopoulos A J.Axisymmetric vibration of disk resting on saturated layered half-space[J].J Eng Mech,ASCE,1989,115(10):2301-2322. [4] Bougacha S,Tassoulas J L,Roesset J M.Analysis of foundation on fluid-filled poroelastic stratum[J].J Eng Mech,ASCE,1993,119(8):1632-1648. [5] 陈龙珠,陈胜立.饱和地基上刚性基础的竖向振动分析[J].岩土工程学报,1999,21(4):392-397. [6] 陈龙珠.饱和土中弹性波的传播速度及其应用[D].杭州:浙江大学,1987. [7] Noble B.The solution of Bessel function dual integral equations by a multiplying-factor method[J].Proc Camb Phil Soc,1963,59(351):315-362.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142