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In recent years, many different methods for calculating the structural forces caused by earthquakes to be created in circular and rectangular tunnels have been devised. However, it is still unclear how sub-rectangular tunnels would behave when subjected to seismic loadings. A new pseudo-static loading scheme for sub-rectangular tunnels using the Hyperstatic Reaction Method (HRM) is the main topic of the current paper. In order to depict the interaction between the soil and the tunnel lining, new equations that allow for the computation of applied active loading as well as a variable spring stiffness coefficient are developed. Through a numerical study that takes into account a variety of seismic magnitudes, soil parameters, lining thickness, tunnel dimension, tunnel geometries, and tunnel depth, the proposed loading scheme is calibrated and validated. The comparisons demonstrate the effectiveness of the developed HRM method for the preliminary seismic design of sub-rectangular tunnels.

A new pseudo-static loading scheme for the hyperstatic reaction method - case of sub-rectangular tunnels under seismic conditions