Nested Lumped-Parameter Model for Foundation with Strongly Frequency-dependent Impedance

An adaptive finite‐unit method for simulating frequency‐dependent responses of shallow foundations in layered soil under vertical dynamic loads

“…Since 1990, researchers have continued to apply a top‐down strategy in the development of simple models in which the layout of elements is formulated using several different procedures 13–20 . The top‐down strategic approach applies a polynomial‐fraction approximation to represent a target function of a soil‐foundation system and then establishes a simple model through specific connections of small discrete‐element models which are derived from expanding polynomial fractions.…”

“…The top‐down strategic approach applies a polynomial‐fraction approximation to represent a target function of a soil‐foundation system and then establishes a simple model through specific connections of small discrete‐element models which are derived from expanding polynomial fractions. The target functions of the existing studies include the impedance function 13–16 and the compliance function 17–20 . The types of layout of connections in existing models include parallel type, 13–16,19 serial type, 17 and nested type 18,20 .…”

“…The target functions of the existing studies include the impedance function 13–16 and the compliance function 17–20 . The types of layout of connections in existing models include parallel type, 13–16,19 serial type, 17 and nested type 18,20 . In addition, previous studies have commonly conducted a partial‐fraction expansion, implemented by complex analysis 13–17,19 and nested division 18,20 .…”

“…The types of layout of connections in existing models include parallel type, 13–16,19 serial type, 17 and nested type 18,20 . In addition, previous studies have commonly conducted a partial‐fraction expansion, implemented by complex analysis 13–17,19 and nested division 18,20 . In the aforementioned studies, the number of model elements increased with the number of polynomial terms given in the polynomial‐fraction approximation, which improved modeling accuracy.…”

Simple formulas for estimating a lumped parameter model to reproduce impedances of end-bearing pile foundations

“…However, dynamic impedances must be known, determined through not familiar numerical tools, and the most suitable LPM has to be selected among those available in the literature, and calibrated to best reproduce impedances of the specific foundation (e.g. [15][16][17][18][19]).…”