Non-linear rocking stiffness of embedded foundations in sand

Abstract

The rocking response of embedded foundations in sand is studied, combining centrifuge modelling and numerical analysis. In total, 51 centrifuge model tests are conducted at ETH Zurich, varying the embedment ratio D/B and the factor of safety against vertical loading (bearing capacity), Fs. The experimental results are used to validate three-dimensional finite-element models, which are subsequently employed for a parametric study. The initial two phases of non-linear response are studied, namely quasi-elastic and non-linear response, while the third phase (plastic response) will be examined in a forthcoming publication. Regarding small-strain rocking stiffness, Kr (first phase), an extended formula is proposed, accounting for soil inhomogeneity along the embedded sidewalls. Kr is shown to decrease with Fs, due to initial soil yielding from vertical loading. The formula is further extended to account for the role of Fs, offering improved estimation of small-strain rocking stiffness. With respect to the non-linear response (second phase), it is shown that the degradation curves of rocking stiffness with rotation can become approximately dimensionless, if the rotation θ is normalised to a characteristic rotation, θs. The increase of D/B leads to a reduction of the normalised rotation θ/θs at which the non-linear response is initiated, due to the increasing participation of sidewall friction.

Isolated shallow rocking foundation on different soils with varying embedment depth

“…On the other hand, foundation uplift causes a larger dissipation of energy and prevents the elements of the superstructure from yielding when there is a seismic force applied to the structure. Based on the experimental and numerical studies, several researchers [16][17][18][19][20][21][22][23][24] have suggested that rocking foundation has self-centring ability, elongates the structure period during excitation, and reduces the demands on the superstructure. Subsequently, simplified methods to predict the nonlinear rocking stiffnesses were provided [25][26][27][28][29] .…”

Investigation on the Behavior of Bridge Piers Considering Rocking Isolation Constructed on Non-plastic Silts and Sands Using 1g Shaking Table Tests

“…Giouvanidis and Dong [8] compared the results of the conventional design approaches of bridge columns with design approaches that consider rocking isolation effects. Different researchers used shaking table tests to investigate the behavior of rocking foundations on sands [9][10][11] while, for better simulation of stress distribution of models, some other researchers employed centrifuge tests to investigate the behavior of rocking foundations [12][13][14][15][16][17]. Kim et al [18] and Liu et al [19] used centrifuge tests to investigate the behavior of low rises buildings with rock foundations.…”

Empirical Models to Formulate the Nonlinear Response of Rocking Shallow Foundations

“…Deng (2012) and Deng et al (2014) introduced a trilinear moment-rotation model for the nonlinear foundations consisted of an elastic and a plastic element in series so that the elastic element stiffness was the initial stiffness and the equivalentlinear stiffness of the plastic element was equal to the secant stiffness regarding maximum rotation and moment capacity of foundation. Taeseri et al (2019) emphasized the shortcomings of the existing impedance formulations, e.g., Gazetas (1991) in considering soil inhomogeneity and addressed its effects on the small strain rocking stiffness of embedded foundations. In line with the simplified methods, Sieber et al (2020) investigated a nonlinear and a bilinear rocking stiffness model for simulation of bridge piers with square foundations on stiff clay and observed such simplified models were appropriate for the maximum rotation prediction while not for the rotation time history and M-θ loops.…”