Dynamic Interaction of Slip Displacement Accumulation in a Two-Block Newmark Model

Abstract eng:
Engineering structures commonly include distinct interfaces or discontinuities, which attain low shear strength. The presence of these interfaces has been acknowledged to substantially modify the dynamic response of engineering structures. The main mechanism that dominates their response is the accumulation of permanent displacements (slip) along the interface. A well known approach to estimate the accumulated slippage is the Newmark’s sliding block model [1], in which displacements are derived via the double integration of the relative acceleration, which is obtained after the formulation of the differential equations governing the equilibrium along the sliding plane. However, in many cases in engineering practice more than one potentially sliding planes may be developed. These may be discontinuities or predefined interfaces, or failure planes within a continuum (like soil). Some representative examples are: (a) earth dams or soil embankments where the first sliding plane is along their base [2] and the other develops due to soil yielding, (b) waste landfills, where the inclusion of geosynthetics provides more than one sliding planes, (c) geosynthetically reinforced slopes or gabion walls, (d) columns and pillars comprising of stacked rigid blocks (e) foundation of machinery equipment, and (f) base isolation systems. In the current study a new model was developed, which is based on the principles of Newmark’s sliding block approach. This model comprises of three rigid blocks separated by predefined interfaces of finite shear strength. A semi-analytical procedure was followed and the validity of the method 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 parameters involved. The interaction of the slip displacement accumulation along the two interfaces appears to be a rather complicated mechanism. It is shown, that taking into account the effect of the interaction leads to a reduction of the displacements along both interfaces. However, 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. It is also proven that the excitation characteristics do not affect substantially the interaction mechanism, expressed as the ratio of the slip displacements of the two blocks, but only the absolute magnitude of the slippage. References [1] N.M. Newmark, Effect of earthquakes on dams and embankments. Geotechnique, 15 (2), 139160, 1965. [2] A.K.Chopra and L. Zhang, Earthquake-induced base sliding on concrete gravity dams. Journal of Structural Engineering, 117 (12), 3698-3719, 1991.

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