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ABSTRACT
This article presents a study aiming at assessing the seismic safety and developing the rehabilitation design of a masonry retaining wall, known as Bastione Farnesiano, and placed around the Palatinum hill, in the central archeological area of Rome, in Italy. It is a singular artifact of its kind and hardly identifiable with known stereotypes or constructive models. The phase of survey, together with both the material and degradation analyses, showed the impossibility to define with certainty some features, even geometrical, of the monument, necessary to reach a judgment about its safety. Therefore, it was necessary to formulate the risk assessment problem by taking into due consideration all uncertainties and evaluating them in probabilistic terms. A simple mechanical model, considering different and alternative collapse modes, was developed and, after characterizing the uncertain parameters in probabilistic terms, Monte Carlo simulations were carried out. Based on the obtained results: (a) the value of the current risk index has been determined and (b) a sensitivity analysis has been performed in order to identify the parameters that mostly affect the monument safety. This sensitivity analysis has provided useful information that has allowed to orient the seismic amelioration design strategy by acting on one of the parameters that have greater impact on the risk reduction.
Notation
| = | coefficient of the second-order term | |
| = | acceleration capacity | |
| = | demand acceleration | |
| = | masonry cohesion | |
| d | = | distance of the centroid of the half parabola from the rotation axis |
| = | horizontal virtual displacement of the application point of the i-th weight | |
| = | horizontal virtual displacement of the application point of the j-th weight | |
| = | vertical virtual displacement of the application point of the i-th weight | |
| g | = | gravity acceleration |
| m | = | angular coefficient |
| q | = | ordinate value of the straight line in the origin of the local reference system |
| = | behavior factor | |
| = | wall thickness | |
| = | abscissa of the parabola local reference system | |
| = | abscissa of the backfill soil volume pushing on half parabola | |
| = | abscissa of the half parabola centroid | |
| = | abscissa of the point | |
| = | ordinate of the parabola local reference system | |
| = | ordinate of the soil wedge centroid | |
| = | ordinate of parabola centroid | |
| = | ordinate of the point | |
| z | = | axis of the local reference system |
| A | = | area of the parabolic surface |
| = | area of half parabola | |
| = | degradation coefficient | |
| FC | = | confidence factor |
| = | maximum depth of the wall | |
| = | minimum depth of the wall | |
| = | height of the parabola | |
| = | work of internal forces | |
| = | maximum length of the wall | |
| = | participating mass | |
| = | i-th weight | |
| = | j-th weight | |
| = | weight of vertical prisms of infinitesimal width dx | |
| = | elastic spectral acceleration | |
| = | static moment with respect to the local x axis | |
| = | static moment of the wedge soil volume with respect to xz plane | |
| = | static moment of half parabola with respect to the local y axis | |
| = | static moment with respect to the local yz plane | |
| = | unitary frictional force | |
| = | shorter vibration period of the whole structure | |
| = | volume of the parabolic portion of the wall | |
| = | volume of half parabola | |
| = | soil wedge volume | |
| = | volume of the backfill wedge pushing on half parabola | |
| = | weight of the soil wedge | |
| = | weight of the backfill wedge pushing on half parabola | |
| = | parabolic wall portion weight | |
| = | weight of half parabola | |
| X | = | abscissa of the global Cartesian reference system |
| Y | = | ordinate of the global Cartesian reference system |
| = | inclination angle of the soil wedge | |
| = | vertical loads multiplier | |
| = | masonry unit weight | |
| = | soil unit weight | |
| = | risk index | |
| = | normal stress | |
| = | shear stress | |
| = | frictional tangential stress | |
| ϕ′ | = | masonry friction angle |
| ϕd | = | masonry dilatancy angle |