The soil-pile interaction will be captured by means of a macroelement comprising three compo¬nents that represent the primary resistance mechanisms of the continuum to the foundation ele¬ments upon transient loading: (i) the pressure in the direction of loading, (ii) the pressure and gap formation in the opposite direction, and (iii) the potential drag exerted by the pile due to flow of soil for the case of large deformations. These mechanisms and corresponding mechanical components of the macroelement are shown in the figure below, while the individual components are briefly described in the ensuing.

1. The Front Face element: The front face element captures the response of soil in front of the pile. It comprises of the following components:
   • Gap element: The gap element simulates the development of active and passive condi¬tions in soil on front of the pile during cyclic loading. It is characterized by a tensile strength σt. On reversal of loading direction, when the developed tensile stress exceeds the tensile strength, gap formation between pile and soil interface takes place and there is minimal contribution from front face to the total soil resistance.
   • Spring element: The spring element is a non-linear spring with a characteristic loading curve. The loading curve will be able to capture the soil response to varying degree of complexity depending on type of constitutive model used for soil, which is further governed, by the amount of experimental data available. The soil parameters controlling the shape of curve are shear modulus, Poisson ratio and strain dependent modulus degradation. The spring also captures hysteretic damping of soil in cyclic loading by using Masing Rule and the backbone curve.
   • Dashpot element: The dashpot element captures the energy dissipation due to geometrical attenuation of waves emanating from the pile surface and transporting energy away from the foundation. It is characterized by a damping coefficient C that is controlled by both soil properties (shear modulus and density) as well as shape of cross section of pile.
   • Coulomb Friction element: The friction element is characterized by the ultimate resistance σy that is offered by the soil, i.e., the stress at which the plastic zone around the pile is sufficiently big so that soil can mobilize no additional resistance for incremental displa¬cement.
2. Rear Face element: The rear face element captures the response of soil in rear side of the pile and has the same components as front face element. The only difference is that gap element is connected in opposite orientation and hence the whole element works in opposite phase as front face element, i.e., when the front element is in active condition, the rear element is in passive and vice-versa.
3. Drag element: The drag element captures the drag exerted by flow of soil around the pile during large displacements. It consists of the following components:
   • Spring element: The spring element captures the behavior of soil-pile interface as a non-linear spring and is characterized by a loading curve whose complexity depends on the amount of experimental data available regarding the interface behavior.
   • Coulomb-friction element: It captures the maximum frictional drag resistance between soil and pile when soil begins to flow around the pile.

The figure below shows the target response (lateral displacement) of a short pile subjected to transverse loading, to be captured by the simplified macroelement described above. Note that on the rear side of pile, the formation of a gap is depicted by the estimated zero displacement. Once the formulation of the individual components will be completed, the effectiveness of the simplified approach will be compared against the target 3D FE simulations.

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