Effect of material damping on the impedance functions of an embedded circular foundation under vertical and horizontal e
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TECHNICAL PAPER
Effect of material damping on the impedance functions of an embedded circular foundation under vertical and horizontal excitation Suvendu Kumar Sasmal1 · Pradip Kumar Pradhan1 Received: 4 February 2020 / Accepted: 12 September 2020 © Springer Nature Switzerland AG 2020
Abstract Machine foundations are generally affected by the vibratory shocks from different machines. The behavior of these foundations is influenced by the properties of underlying soil and the excitation frequency of the applied dynamic load. The influence of material damping on the dynamic impedance functions of a circular disk embedded in homogeneous elastic half space is analyzed using one-dimensional wave propagation in cones (cone model) and the results are presented in the form of dimensionless plots to observe the more realistic response of machine foundations. Three different types of material damping models viz., Hysteretic, Voigt and Kelvin model are introduced in the above elastic solutions using correspondence principle. The spring and damping coefficients of the embedded foundation are then computed in a wide range of frequency of excitation under vertical and horizontal mode of vibration varying the influencing parameters namely dimensionless frequency (a0), Poisson’s ratio (ν), embedment ratio (e/r0) and damping ratio (ξ). The outcomes from the present analysis suggest that the spring coefficient is nonlinearly affected by the dimensionless frequency and embedment ratio, for both the modes of vibration. The effect of material damping on spring coefficient is only significant for a0> 2, irrespective of the damping model used. Keywords Material damping · Impedance functions · Kelvin model · Correspondence principle · Embedment ratio List of symbols a0 Dimensionless frequency c Appropriate wave velocity cs Shear wave velocity e Embedment of foundation KStatic Static stiffness coefficient of disk on homogeneous half space r0 Radius of foundation z0 Apex height of the truncated cone ω Excitation frequency ν Poisson’s ratio ξ Damping ratio S (ω) Dynamic impedance as a function of excitation frequency * Suvendu Kumar Sasmal [email protected] Pradip Kumar Pradhan [email protected] 1
Department of Civil Engineering, Veer Surendra Sai University of Technology, Burla, India
S (a0) Dynamic impedance as a function of nondimensional frequency S (a0)damped Dynamic impedance, considering material damping k* (a0) Spring coefficient, considering material damping c* (a0) Damping coefficient, considering material damping
Introduction The analysis of the response of machine foundations is a cumbersome task as the soil behavior during dynamic loading is significantly different from that in the case of static loading. The analysis and design of these foundations have attracted researchers in the field of geotechnical engineering and foundation engineering. As this is an important problem domain in the area of soil dynamics, a number of techniques are available to study the response of these foundations
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