Seismic Response of Liquid Storage Tanks Incorporating Soil Structure Interaction

A frequency domain method is presented to compute the impulsive seismic response of circular surface mounted steel and concrete liquid storage tanks incorporating soil-structure interaction (SSI) for layered sites. The method introduces the concept of a near field region in close proximity to the mat foundation and a far field at distance. The near field is modeled as a region of nonlinear soil response with strain compatible shear stiffness and viscous material damping. The shear strain in a representative soil element is used as the basis for strain compatibility in the near field. In the far field, radiation damping using low strain soil response is used. Frequency dependent complex dynamic impedance functions are used in a model that incorporates horizontal displacement and rotation of the foundation. The focus of the paper is on the computation of the horizontal shear force and moment on the tank foundation to enable foundation design. Significant SSI effects are shown to occur for tanks sited on soft soil, especially tanks of a tall slender nature. SSI effects take the form of period elongation and energy loss by radiation damping and foundation soil damping. The effects of SSI for tanks are shown to reverse the trend of force and moment reduction under earthquake loading as is usually assumed by designers. The reasons for this important effect in tank design are given in the paper and relate to the very short period of most tanks, hence, period lengthening may result in load increase. A comparison is made with SSI effects evaluated using the code SEI/ASCE 7-02. Period elongation is found to be similar for relatively stiff soils when assessed by the code compared with the results of the dynamic analysis. For soft soils, the agreement is not as good. Code values of system damping are found to agree reasonably well with an assessment based on the dynamic analyses for the range of periods covered by the code. Energy loss by material damping and radiation damping is discussed. It is shown that energy loss may be computed using the complex dynamic impedance function associated with the viscous dashpot in the analytical model. The proportion of energy loss in the translation mode compared to that dissipated in the rotational mode is addressed as a function of the slenderness of the tank. Energy loss increases substantially with the volume of liquid being stored.