Soil-structure interaction with separation of base mat from soil (lifting-off)

In reactor buildings having a separate base mat and a shield-building (outer concrete shell) of large mass, large overturning moments are developed for severe earthquake loading. The standard linear elastic half-space theory is used in the soil-structure interaction model. For a circular base mat, if the overturning moment exceeds the product of the normal force (dead weight minus the effect of the vertical earthquake) and one-third of the radius, then tension will occur in part of the area of contact, assuming distribution of stress as in the static case. For a strip foundation the same arises if the eccentricity of the normal force exceeds a quarter of the total width. As tension is incompatible with the constitutive law of soils, the base mat will become partially separated from the underlying soil.Assuming that only normal stresses in compression and corresponding shear stresses (friction) can occur in the area of contact, a method of analyzing soil-structure interaction including partial lifting-off is derived, which otherwise is based on the elastic behaviour of the soil. A rigorous procedure to determine the nonlinear impedance function of a rigid plate of arbitrary shape, only in partial contact with the elastic half-space, is developed. Complex dynamic influence coefficients for displacements are used which can either be determined with the finite-element method or based on solutions of displacements on the surface of an elastic half-space at a certain distance from a rigid subdisk. Constant and variable stiffness methods of solving the non-linear equations of motion are explained which also determine the area of contact. Slipping of the entire mat or of a part thereof can also be taken into consideration.A simpler approximate method is discussed. For a given force and moment acting on the rigid plate, the area of contact is determined by iteration or based on quadratic programming techniques using the static influence coefficients for displacements. The complex-valued impedance function is estimated by substituting an equivalent circular plate for the actual area of contact. Transforming the equivalent lumped system to the centre of the plate, the non-linear stiffness and damping matrices of the soil are derived. Formulae are given for the partial lifting-off of a disk and a strip. The results of the numerical method are compared to rigorous solutions for full contact. As an example, the dynamic response of the reactor building of a 1000 Mw plant to earthquake motion is calculated using the rigorous and approximate methods. Parametric studies are carried out. The influence of the frequency on the impedance function and on the distribution of stress in the area of contact, which determines the beginning of lift-off, is discussed.