Modular analytical solutions for foundation damping in soil-structure interaction applications

Foundation damping incorporates combined effects of energy loss from waves propagating away from a vibrating foundation (radiation damping) and hysteretic action in supporting soil (material damping). Foundation damping appears in analysis and design guidelines for force- and displacement-based analysis of seismic building response (ASCE-7, ASCE-41), typically in graphical form (without predictive equations). We derive closed-form expressions for foundation damping of a flexible-based single degree-of-freedom oscillator from first principles. The expressions are modular in that structure and foundation stiffness terms, along with radiation and hysteretic damping ratios, appear as variables. Assumptions inherent to our derivation have been employed previously, but the present results are differentiated by: (1) the modular nature of the expressions; (2) clearly articulated differences regarding alternate bases for the derivations and their effects on computed damping; and (3) completeness of the derivations. Resulting expressions indicate well-known dependencies of foundation damping on soil-to-structure stiffness ratio, structure aspect ratio, and soil damping. We recommend a preferred expression based on the relative rigor of its derivation.</jats:p

Simplified analytical "m-θ" curves for predicting nonlinear lateral pile response

The relationship between the distributed moment acting on a pile segment due to vertical shear tractions at the pile-soil interface and the corresponding pile rotation (known as an “m-θ” curve) is important when determining the response of offshore monopiles with low slenderness ratios. Two simplified approaches to derive nonlinear “m-θ” curves (for clay under undrained conditions) are considered. Firstly, the vertical shear tractions can be derived in closed-form using known “t-z” curves (power-law and quadratic forms are considered) and integrating with respect to the pile circumference. Secondly, similarity in shape between an “m-θ” and a “t-z” curve is investigated which would enable a linear-transformation between the abscissas of the two normalised curves. This paper derives analytical linear-transformation factors using power-law and quadratic “t-z” curves and compares these with solutions available for a linear-elastic soil material. Finally, the effect of slip at the pile-soil interface on the “m-θ” curve is considered

Physical modelling of the seismic response of gas pipelines in laterally in homogeneous soil

This paper reports on results from a series of 1-g, reduced-scale, shake table tests of a 216mlong portion of an onshore steel gas transmission pipeline embedded in horizontally layered soil. A set of first-order set of dynamic similitude laws was employed to scale system parameters appropriately. Two sands of different mean grain diameter and bulk density were used to assemble a compound symmetrical test soil consisting of three uniform blocks in a dense-loose-dense configuration. The sandpipe interface friction coefficients were measured at 0.23 and 0.27. Modulated harmonic and recorded ground motions were applied as table excitation. To monitor the detailed longitudinal strain profiles in the model pipe, bare Fiber Bragg Grating cables were deployed. In most cases, the pipe response was predominantly axial while bending became significant at stronger excitations. levels. Strain distributions displayed clear peaks at or near the block interfaces, in accord with numerical predictions, with magnitudes increasing at resonant frequencies and with excitation level. By extension to full-scale, peak axial strain amounted to approximately 10-3, a demand half the yield strain, but not negligible given the low in-situ soil stiffness contrast and soil-pipe frictio