Dynamic interaction of slip displacement accumulation in a two-block Newmark model

Engineering structures may include discontinuities or predefined interfaces separating different construction materials, or failure planes generated for example within soil in the case of geotechnical applications. Due to seismic motion permanent slip displacements may accumulate along the aforementioned interfaces.

The well-known Newmark’s sliding block has been widely applied to mimic the seismic response of structures with distinct interfaces. In the current study a new model is presented, which is based on the principles of Newmark’s approach. This model comprises of three stacked rigid blocks, being separated by prescribed interfaces of finite shear strength, thus, they are capable of developing relative displacements under seismic loading.

For this purpose, a semi-analytical procedure was formulated and the accuracy of the calculated slip displacements was verified by finite element analyses of the corresponding model. In addition, parametric analyses were performed in order to address the impact of the main factors influencing the interaction of the slip displacement accumulation along the two interfaces.

It is shown, that taking into account the effect of the interaction leads to reduction of the permanent relative displacements along both interfaces. The interaction mechanism is dominated by the inclination of the sliding planes, the mass ratio of the two blocks, the ratio of the yield acceleration of the two interfaces and the angle of friction of the lower interface.

Moreover, the sensitivity of the interaction mechanism to the excitation characteristics and to the mass of the two blocks was also investigated