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.
dynamic analysis
Analisi di stabilità dinamica di un movimento franoso utilizzando un modello semplificato applicando accelerogrammi generati e registrati
In the paper the analyses, the results and the comparison performed on a landslide located in Costafiore in the municipality of Muccia (MC) are presented. The aim of the analyses has been to verify the pseudo-static and dynamic stability of the landslide, using two simplified models. In particular, for the pseudo-static analyses a code deriving by the method of Sarma /22, 23, 24, 25/ has been applied; for the dynamic analyses a code deriving by the method of Newmark /11/ has been used. To perform the dynamic analysis, it is necessary to have assessorgrams, in this project both recorded and synthetic accelerograms have been applied; so a comparison on the obtained results, in term of expected displacements, has been performed; therefore the influence of the two applied sets has been evaluated. The synthetic accelerograms have been calculated considering the results of the seismic hazard analyses performed by the Gruppo di Lavoro 2004 /9/, in particular the acceleration elastic response spectra, at 5% of the critical damping, considering a return period of 475 years, furthermore as reference spectra, the spectra proposed by the New Italian Code for the Buildings have been considered, characterized by different return periods (72, 475, 975 years). The accelerograms, compatible with the spectra, have been performed using the procedure of Sabetta and Pugliese /20/. The recorded accelerograms have been selected by the project of the Reluis /11/ where, for each seismic zone and for each type of soil, a series of 7 recorded accelerograms are proposed, the average of their response spectra is compatible with the spectrum proposed by Ordinanza del Presidente del Consiglio dei Ministri (OPCM n. 3431/05) /17/. Two sets of accelerograms useful for the seismic zone 2 and for the soil type A, considering a return period of 475 years, have been extracted. The results, in term of expected displacements, are similar, confirming the procedure and their importance for urban planning both to perform planning choices and to perform project useful to the security of the landslide.
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.
Influenza delle Tamponature sulla statica dei telai in c.a. in zona sismica
This paper describes a model able to evaluate the effect of masonry panels on reinforced concrete frames subjected to a seismic action. The panel is modelled as an equivalent diagonal element with a bilinear constitutive relation. The efficacy of the model is verified with an hysteretic model which considers some fundamental characteristics of masonry subjected to a seismic action (transitory phase between elastic and elasto-plastic behaviour, stiffness and strength decay, reduction of the hysteresis cycles due to the opening and closing of the cracks). This study shows that the presence of masonry panels causes a different distribution of the seismic action that usually concentrates in the lower floors (with accumulation of the damage in these levels) and the whole structure keeps in the elastic field.
This paper is available in Italian only.