Simplified Analytical Solution of <i>R-F</i> Relation for Prefabricated Rectangular Underground Structures

The discussion about the seismic behavior of prefabricated rectangular underground structures is mainly focused on the specific structure form, and there is a lack of a more extensive and regular discussion from the theoretical point of view. In this study, a simplified analytical solution of racking ratio–flexibility ratio (R-F) relationship for prefabricated rectangular underground structures is proposed. This solution assumes that the seismic action on deep underground structures can be reduced to far-field shear action. A numerical model verifies the feasibility of this solution. The suggested evaluation index of the rock model of the prefabricated rectangular underground structure is presented. The results show the simplified calculation theory is accurate, especially for structures with an F greater than 1; the error is less than 10%. The rotation of the column midpoint can be used as the estimation result of the rock mode of the prefabricated structure. When two structures have the same F, the R of the prefabricated structure is more diminutive.