English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper aims at investigating the existence of localized stationary wavesin the shallow subsurface whose constitutive behaviour is governed by thehyperbolic model, implying non-polynomial nonlinearity and strain-dependentshear modulus. To this end, we derive a novel equation of motion for anonlinear gradient elasticity model, where the higher-order gradient termscapture the effect of small-scale soil heterogeneity/micro-structure. We alsopresent a novel finite-difference scheme to solve the nonlinear equation ofmotion in space and time. Simulations of the propagation of arbitrary initialpulses clearly reveal the influence of the nonlinearity: strain-dependent speedin general and, as a result, sharpening of the pulses. Stationary solutions ofthe equation of motion are obtained by introducing the moving reference frametogether with the stationarity assumption. Periodic (with and without adescending trend), as well as localized stationary waves, are found byanalyzing the obtained ordinary differential equation in the phase portrait,and integrating it along the different trajectories. The localized stationarywave is in fact a kink wave and is obtained by integration along a homoclinicorbit. In general, the closer the trajectory lies to a homoclinic orbit, thesharper the edges of the corresponding periodic stationary wave and the largerits period. Finally, we find that the kink wave is in fact not a true solitonas the original shapes of two colliding kink waves are not recovered afterinteraction. However, it may have high amplitude and reach the surfacedepending on the damping mechanisms (which have not been considered).Therefore, seismic site response analyses should not a priori exclude thepresence of such localized stationary waves.

Localized stationary seismic waves predicted using a nonlinear gradient elasticity model