Keywords: soil-structure interaction, buried structures, added mass, cylindrical structures, dynamic loading, concrete cylinders.

To design an underground structure against the earthquake or blast loading, the dynamic properties of such structures are often first established. These properties which include; natural frequencies, mode shapes of vibration and damping are affected by the presence of soil and the level of dynamic interaction between the structure and the surrounding soil. A rigorous solution of the interaction may be carried out by finite element (FE) analysis. Other, approximate, methods have also been used in the past to model the interaction and determine the natural frequencies of the structure-soil system. The 'added mass' solution is one such approximate approach supported and used by a number of codes of practice [1]. In this method, a specific amount of soil mass is added to the mass of the structure to account for the interaction effects and the structure is then solved without the soil but with an augmented mass.

In this paper, a finite element parametric dynamic analysis of the structure-soil system is carried out. The structures considered are three cylindrical concrete structures with identical material properties but of different size. The main problem variable parameters include; the radius of the cylindrical structure (R), the ratio of the horizontal extent of the soil considered in the analysis to the radius of the structure (L/R), the ratio of the vertical extent of the underlying soil considered in the FE model to the radius of the structure (H/R) and the ratio of depth of burial to the radius of the structure (D/R). The effect of the horizontal extent of the soil considered for the FE mesh was first investigated for the three structures. Extent ratios (L/R) between 3 and 25 were investigated. It is found that the fundamental frequency of the buried structure is close to the exact solution at L/R=10 and higher. This value was used for the horizontal extent of the soil in the subsequent analyses. The influence of the vertical extent of the underlying soil on the accuracy of the results was also investigated. Ratios (H/R) of 1 to 6 were studied. The extent ratios, H/R=3 to 4 were found to produce optimum results.

The main variable parameter in this study is the depth of the buried cylindrical structure and the effects of the overburden on the dynamic properties of the buried cylindrical structure. Comparisons between the fundamental frequency of the structures when in air and when buried to different depths indicates the added-mass effect of the surrounding soil on reducing these frequencies. In the traditional added-mass solution, only the effects of the mass of the body of soil on the dynamic properties of the structure are considered. The soil, however, also contributes to the stiffness of the buried structure. As a result, it is expected that the added-mass approach to produce approximate results.

It is shown in this paper that the conventional added-mass approach greatly overestimates the natural frequencies of the soil-structure system and the level of overestimation is more profound for the shallow-buried structures. For the deep-buried structures, the added-mass of soil dominates the response and the effect of the added-stiffness is reduced. Also it is found that the discrepancies in the results of the added-mass solution and the FE solution increases as the structure becomes more flexible.

1

ASCE, Manuals and Reports on Engineering Practice - No. 42, "Design of Structures to Resist Nuclear Weapons Effect", ASCE, 1985.

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