Newmark

Calculation of the relative and maximum displacements of a block sliding on an inclined plane with the Newmark Method.

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The pseudo-static method for slope stability analysis provides a safety factor on stability, but it does not provide any information about the deformation associated with a potential sliding surface. With the analysis method introduced by Newmark (1965) it is possible to predict for a potentially unstable mass what the total permanent displacement of the slope will be under the action of a time-varying acceleration. He schematized the potentially unstable mass subjected to inertia forces as a rigid block sliding on an inclined plane subjected to an acceleration that induces inertia forces in it in the direction of the plane.

The safety factor, which is the ratio between the available resistance and the destabilizing force, variable over time, is obtained from:

F_s(t)=R_d(t)/D_d(t)=((cosβ-k_h(t)sinβ)tanφ)/(sinβ-k_h(t)cosβ)

Where:
β = inclination angle of the plane;
φ = friction angle between the block and the plane;
kh = horizontal seismic coefficient

Reference documentation: NEWMARK