INSIGHT ON 2D-MODELING VERSUS 3D-MODELING OF SURFACE FOUNDATIONS VIA STRENGTH-OF-MATERIALS SOLUTIONS FOR SOIL DYNAMICS

To simplify the analysis, three-dimensional soil-structure interaction problems are often modelled by considering a two-dimensional slice wi thout changing the material properties of the soil. This procedure, al though convenient, is of questionable validity because two-dimensional modelling inherently overestimates the radiation damping for translat ional and rocking motions. To make matters worse, two-dimensional mode lling always entails an underestimation of the dynamic-spring coeffici ent for the translational motions. The damping ratio of the two-dimens ional case, which is proportional to the ratio of the damping coeffici ent to the spring coefficient, will thus be even larger. Thus, relianc e upon a two-dimensional analysis based on an equivalent slice of a st rip foundation may result in a dangerously nonconservative design. Val uable insights into the essence of radiation damping and the differenc e between two-dimensional and three-dimensional models may be obtained via approximate strength-of-materials solutions based on cone-wedge m odels and travel-time considerations. By examining the decay of the wa ves along the axes of the cone-wedge models, the essence of radiation damping can be grasped. The heuristic concept of more spreading of wav es in three dimensions than in two is misleading. Indeed, just the opp osite is true: The less the amplitude spreads and diminishes with dist ance, the greater is the radiation damping. Because the damping ratio is grossly overestimated, two-dimensional modelling of a three-dimensi onal case cannot be recommended for actual engineering applications. I t is more feasible to take the opposite approach and idealize slender soil-structure interaction problems with a radially symmetric model. A s an alternative, when defining the equivalent slice of the two-dimens ional strip foundation, the impedance of the soil can be changed to ac hieve a much better agreement of the high-frequency limits of the damp ing coefficients. In the low-frequency range this modified two-dimensi onal model also overestimates radiation damping, although to a lesser extent. As a by-product, the dimensions of the equivalent slice of a t wo-dimensional strip foundation are discussed; and equations for the a spect ratios determining the opening angles of the corresponding wedge s are derived. Also addressed is the quite separate but related topic of the transition from square to slender rectangular foundations.