PSI - Issue 62

578 Salvatore Misiano et al. / Procedia Structural Integrity 62 (2024) 576–584 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 3 analysis ); state (specific gravity ; porosity ; degree of saturation ); mechanical resistance (friction angle φ ′ ; effective cohesion ′ ); partial saturation ( and λ , which are modeling parameters); internal model coefficients, related to the simplified approach ( α ); drainage coefficient of slope ( ); unit weight of water ( ); and precipitation height ( ℎ ). The formulation is the following: F S = cot δ∙ tan φ'∙ [ Г+m∙ ( n w Ǧ 1 )] Г+m∙n w + Г+ C m '∙Ω ∙n w (1) Г = G s ∙(1 Ǧ n)+n∙S r (2) n w = n∙(1 Ǧ S r ) (3) Ω = sin(2δ2)∙H∙γ w (4) C ' = [ c ' +A∙S r ∙ ( 1 Ǧ S r ) λ ∙ ( 1 Ǧ m ) α ] ∙L (5) m = n∙H∙( ξ 1 Ǧ S r ) ∙∑ h i ∙e Ǧ k t ∙(t i Ǧ t 0 ) ω i=1 (6) Whenever the is lower or equal to 1, it means that the schematized slope is unstable. Nevertheless, because of the simplifications adopted in the model, a more common threshold which defines the instability is around 1.5. As a result of the straight formulation and of the hydraulic simplification, SLIP is particularly suitable for large scale applications or when recurrent and fast predictions are needed; in fact, it was used in several case studies (Montrasio et al. 2009, 2011, 2012, 2014, 2015, 2016) and validated over the years. The reader is referred to Montrasio 2000 and 2008 for a more in-detail description of SLIP, Gatto and Montrasio 2023 for a deepening on X SLIP platform, and Montrasio et al. 2023 for the G-SLIP model.

Fig. 1. SLIP scheme.

2.2. Landslide Path and Equations of Motion The main principle of the following simplified method consists in the fact that the path followed by the landslide body is primarily dictated by the morphology of the slope. Specifically, it is assumed that the mass follows the route with the maximum negative gradient, down to the point of deposit. Based on this, it is possible to use two different approaches in following the steepest path: the first one is based on the definition of elementary steps for the discretization of movements and on the use of them through the gradient descent, to reach a local minimum (Fig. 2a); the second one consists in searching, point by point based on the DEM, the neighboring point which maximize