This article describes the simulation of an excavation supported by a cantilevered sheet pile wall. The model considers plane strain conditions in two-dimensions, using quadrilateral elements with a pressure dependent constitutive model to simulate cohesionless soil, and beam-column elements to simulate a unit width of sheet pile wall. Beam-solid contact elements are used to model a frictional interface between the linear beam elements and the quadrilateral soil elements.
The sheet pile wall considered in this example is 0.5 m wide and has a height of 10.5 m. Beam contact elements are used to create a frictional interface between the beam and solid elements that accounts for the full kinematics of the beam elements and allows the constant width of the wall to be represented in the model. To represent the 0.5 m width of the wall, the beam contact elements (described further below) maintain a constant distance between the wall centerline and the surrounding soil elements of 0.25 m, resulting in the gap between the blue beam elements and the green solid elements.
The excavation is simulated by incrementally removing layers of solid elements from one side of the sheet pile wall. After each removal, the model is analyzed for a sufficient number of steps such that equilibrium is reached prior to the removal of the next layer of elements. The removal process continues until an excavation depth of 5 m is achieved. The deformed configuration of the mesh after the completion of the excavation analysis. The removal of material from one side of the sheet pile wall allows the wall to be pushed laterally by the remaining soil on the other side.
Sheet Pile Wall
The sheet pile wall is modeled using the displacement-based beam-column elements with elastic sections used to define the constitutive behavior. The beam elements are placed along the neutral axis of the sheet pile wall, and to ensure the best behavior for the beam contact elements, the beam elements are defined such that their nodes are centered vertically between the nodes of the adjacent soil elements. The beam elements extend beyond the boundaries of the soil domain to allow the elements at the ends of the wall to be in contact with the soil.
The beam-solid contact approach used in this example allows for the use of beam-column elements to model the sheet pile wall, enabling the results to be interpreted in the context of traditional beam theory, i.e. it is simple to extract shear and moment diagrams from the recorded data.
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