Two finite element approaches for the dynamic analysis of seepage flows are discussed here. This represents the first step of a study on the effects of earthquakes on retaining or embedded structures in saturated granular soils. The equations governing the flow of a liquid within a porous skeleton under an acceleration field varying with time are recalled first. Then they are combined in two differential equations that, reduced to their weak form, lead to a finite formulation of the problem in terms of discharge velocity. Due to the relatively large number of nodal variables, and to the iterative structure of the time integration algorithm, this approach requires a non negligible computational cost. Then a second approach is presented, based on some simplifying assumptions, where the pore pressure represents the nodal variable and that adopts a direct time integration scheme. The finite element programs implementing the two formulations are finally applied to the solution of a bench mark problem presented in the literature. The numerical results permit drawing some conclusions on the accuracy of the two approaches that will guide in the choice of the most convenient of them in extending the study towards the analysis of coupled two-phase problems.
Finite elements
Analisi sismica di edifici esistenti in muratura con metodo dinamico: applicazione a Villa Faule (SI)
In this paper a general method is given to evaluate the collapse seismic load of existing masonry buildings. The method is based on numerical analyses in which both linear and nonlinear models are used to evaluate the seismic response of the masonry assemblage. The structure is first idealized by a F.E. model to investigate the stress patterns produced by the static loads, then a simplified nonlinear dynamic model is used to predict the collapse seismic load. In addition, the F.E. model is useful to identify some mechanical parameters of the masonry and to establish the accuracy of the simplified approach. To this aim the first two modal shapes of the building are used. To exemplify the general methodology here discussed an application is presented for Villa Faule, to be found in the Tuscany countryside in the neighborhood of Colle di Val d’Elsa (Siena). The Villa Faule was built at the end of XVIII century and is representative of many similar country houses located in the same geographic zone. Considering the dilapidated state of the walls, of the timber floor slabs and of other architectural elements, in recent times a design was approved to strengthen and to rehabilitate the building. The subject of this study is the strengthened building because the large-scale numerical models are more reliable for such types of structures. The results showed that both the procedures were useful to investigate the structural problem. The F.E. model furnished a good prediction of the masonry stresses under vertical loads and predicted the modal shapes of the structure; at the same time it revealed that the simplified model was accurate. The nonlinear simplified method gave a prediction of the seismic ground acceleration intensity to be applied to achieve the building collapse. To this purpose the structure was subjected to the N-S acceleration record of El-Centro (Imperial Valley’s earthquake, 1940). The results showed that the value of the collapse peak ground acceleration was equal or more than 2.75 m/s2.
This paper is available in Italian only.