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Current design methodologies for underground structures subjected to earthquake action are based on closedform solutions of the so-called racking coefficient, which relates the soil free-field distortion deformation to the structure distortion deformation. Existent closed-form expressions for this racking coefficient are derived for circular tunnel geometries embedded in an elastic and homogeneous medium, while expressions for rectangular geometries are based on analogies of the circular case. In this paper, a new and intuitive methodology derived from first principles to obtain a closed-form expression for the racking coefficient for rectangular-like tunnel geometries buried at a sufficient depth is presented, and it is shown that it provides a good fit to finite element analyses results. Similarly, a procedure to obtain closed-form expressions for the rocking rotation of the structure, and the racking deformation profile at different distances from the soil-tunnel interface is presented.

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