Approximate formulas for dynamic stiffnesses of rigid foundations

Equivalent-Linear Dynamic Stiffness of Surface Footings on Liquefiable Soil

“…Table 1 provides the comparison of ISoBEM results for normalized static stiffness of rigid square footing on halfspace, for all three oscillation modes, with the empirical formulas from Pais & Kausel [7]. In Table 2, results for the horizontal static stiffness of a two-layer soil profile (v 1 = v 2 = 0.4) are compared against those obtained from Ahmad & Rupani [13].…”

“…On the other hand, the available solutions regarding the dynamic impedance of footings on non-liquefiable soil usually assume linear or equivalent-linear elastic soil behavior and perfect contact between footing and soil [6][7][8][9][10][11][12][13][14]. Moreover, soil-foundation interaction is approached by means of an equivalent spring-dashpot system connected with the footing, as shown in Fig.…”

Quasi-Kinematic Response of Embedded Foundations: Evidence of Foundation Mass Effect From Numerical Analyses and Instrumented Structures

“…To this end, two different approaches were implemented: (i) a standard substructure approach, according to which the FIM motion is computed from a pure kinematic interaction and then the inertial interaction problem is addressed taking into account the mass of both the structure and the foundation; and (ii) a hybrid substructure approach, according to which the FIM motion is derived from a quasi-kinematic interaction and then the inertial interaction problem is solved including the sole mass of the structure. In both approaches, the expressions provided by Pais & Kausel [22] were used to compute the dynamic impedances for the embedded foundation.…”

Finite Element Modeling of Shallow Foundations on Nonlinear Soil Medium

“…Its dynamic stiffness parameter, d 11 , is plotted in Figure 13. It is observed that none of the initial stiffness, yield stress and post-yielding stiffness dominates individually the global trend of the nonlinear radiation curve family.…”

“…strip foundation on elastic half-space [2,3] and on visco-elastic soil layer [4,5], circular foundation on elastic halfspace [6,7] and on visco-elastic half-space [8], rectangular foundation on elastic halfspace or layered medium [9,10], and cylindrical and rectangular embedded foundations [11]. Gazetas [12] and Mylonakis et al [13] compiled an extensive set of graphs and tables for dynamic stiffness of foundations with a variety of geometries and linear soil conditions.…”