Issue 49

M. L. Puppio et alii, Frattura ed Integrità Strutturale, 49 (2019) 725-738; DOI: 10.3221/IGF-ESIS.49.65 732 that, due both to a lack of a proper drainage system behind the wall and to the heavy rainfall occurred on an already saturated soil, the hydraulic head gradually increased behind the wall, reaching a level able to cause the masonry failure. The water load was applied as small load steps, increasing the hydraulic head by 1 cm from one step to the next one. Non-linear static analysis are carried out and results are showed in Fig. 5 considering the relative displacement of two control point placed at the bottom and at the top of the wall. Figure 5: Control points for the capacity curves. [31] Results of the analysis in the as-built state In this paragraph the results of the analysis are represented as capacity curves, showing the hydraulic head - corresponding to the wall failure - against displacements (Fig. 6) with variable tensile strength. The diagrams show the curves for values of tensile strength from 1.25 kN/m 2 to 12.50 kN/m 2 and for two fracture energies: G f = 0.00075 kN/m (Fig. 6a) and G f = 0.03 kN/m (Fig. 6 b). A monotonic trend is clearly visible, starting from a linear behavior up to values of hydraulic head of about 2 m. Beyond this value, the trend is non-linear and the hydraulic head leading to collapse is asymptotically approaches 3.5 m. This means that, even adopting higher (unrealistic) values of tensile strength for masonry, the critical water level cannot conceivably overcome such a value. (a) (b) Figure 6: Capacity curves of the parametric analysis: variation of the tensile strength (in the legend, values in kN/m 2 ): G f = 0.00075 kN/m (a) and G f = 0.03 kN/m (b) Investigating the failure pattern, a great difference in the propagation of the cracking is noticeable depending on the assumed values of strength:  Case 1. For low values of tensile strength (say f t < f t.lim ), the wall starts to crack in its inner part due to the attainment of the tensile strength in the material. Once the inner core is reached, the cracks rapidly spread through it, given its low resistance. At this moment, only the external wall is able to provide support to the retaining wall, until the breakage propagates in its lower part, causing the collapse. This suggests that the collapse occurs due to the masonry material failure (tensile failure), caused by the stresses that develop in the structure under the imposed loads. The crack propagation pattern remains the same and spread to the external wall at the same height, included in a range of 1.5 to