﻿ Global equilibrium check

Global equilibrium check

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# Overturning check

The overturning hazard is represented by the possibility for the weir to rotate around its point situated further downstream. In the case of the weir, the actions favouring the overturning are the (static and dynamic) earth thrusts as well as the water-related thrusts. The actions opposing the overturning are for the most part those due to the weight of the materials involved in the work (e.g. the weight peculiar to the weir). In terms of figures, the overturning check is executed carrying out a comparison between the stabilizing moment and the destabilizing moment. Expressed in formulas, the overturning check is the following:

Where Ms is the stabilizing moment, MR is the overturning moment and FSR is the overturning safety factor which as a rule must be no lower than 1.5.

# Sliding check

The sliding hazard is represented by the possibility for the resultant of the forces parallel to the soil-foundation contact plane to be higher than the resistance to sliding by friction. The actions favouring the sliding are – as in the previously described case – the (static and dynamic) earth thrusts as well as the water-related thrusts. The actions opposing the sliding, on the contrary, are those originating from the soil-foundation friction and adhesion. In mathematical terms, the sliding check is the following:

Where Frs is the sliding-resistant force, Fss s the sliding soliciting force and FSS is the sliding safety factor which as a rule must be no lower than 1.3.

# Crushing check

The crushing hazard is represented by the possibility for the strain induced by the weir upon the foundation laying level to be higher than the strain in whose correspondence the breaking of the soil-foundation complex occurs. So, in mathematical terms, the check is executed by comparing the maximum strain acting upon the soil with the limit load of the soil-foundation complex:

Where Qlim is the limit load of the foundation, Qe is the strain transmitted (for a particular load condition) to the foundation ground and FSQlim is the crushing safety factor, which as a rule must be no lower than 2.

In case the la weir under examination belongs to the gabion weir type, the programme further carries out another two checks, called inner stability checks, namely:

Check of the sliding on the interface between gabions

This check is executed I order to prevent – for a given interface between two gabions – the sliding between the group of gabions situated above the interface and the group of gabions situated below the interface from taking place. For each combination, the programme carries out the sliding check of each gabion layer, returning the minimum value of the safety factor. In mathematical terms, the check is executed using a formula similar to that described at the previous point "Sliding check".

Crushing check of the material making up the gabions

This check is executed in order to prevent the material making up the gabions from being submitted to excessive compression strains, i.e. being such as to lead to a crisis by compression breaking. For each load combination, the programme carries out a check of each interface, returning the value of the minimum safety factor. In mathematical terms, the check to be carried out is the following:

Where sam is the admissible strain of the material and sn is the strain underwent by the material making up the weir, while FSch represents the crushing safety factor.