PSI - Issue 62

Salvatore Misiano et al. / Procedia Structural Integrity 62 (2024) 576–584 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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the gradient in the negative direction, i.e., finding among the 8 neighboring of a particular point in the DEM, which is the next point to follow down to the minimum (Fig. 2b).

a

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Fig. 2. (a) Gradient descent; (b) Point by point approach.

In order to use both these methods, the entire landslide body must be schematized as a single point in space, corresponding to the center mass. In addition to this, a second note should be pointed out: the local minimum corresponds to the lowest deposit point that can be reached in space but, if the stabilizing forces are sufficiently high, the deposit point could be somewhere in the middle of the path, before the predetermined end. Moreover, by means of gradient descent, the gradient can be assessed only over the DEM points, which means that in every step, a snapping procedure must be performed to link the end of the step to an existing DEM point. Once the path is defined, the mass follows the uniformly accelerated motion in each step, i.e., inside of each step the mass is ruled by a single fixed acceleration, whose value can change in every step. The latter acceleration, to apply in the steps, comes from the balance of forces applied to the moving mass. In particular, during the first step, the forces to apply are the same as evaluated in the SLIP model. After the first step, the stabilizing force is simply the basal friction, while the destabilizing force is the component of the mass along the moving plane.

Fig. 3. Rectification process and forces.

=1

The formulation is the following:

1 = 1 − 1 1 = 1 ∙(1− 1 ) 1 = ∙ δ ∙ (1 − 1 ) 1 = { ∙ ∙ δ ∙ ∙ [ Г+m∙n w ]} ∙ δ 1 = ∙ ∙ δ ∙ ∙[ Г+m∙n w ]

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