Geosynthetics April/May 2021 - 23

the damping ratio, ξ s, of the compacted embankment fill.
The penetration depth on the upstream face is then computed, according
to the method presented by Carotti et
al. (2000), based on the theory of totally
anelastic impact, through the lumped
mass model made up by a 1-DOF (one
degree of freedom) oscillator, characterized by a viscous damper and a spring
(Figure 7), which undergoes a deformative cycle with angular frequency, ω. The
lumped mass, m, of the 1-DOF oscillator
is the mass of the soil contained in the
cone as previously identified.
According to these assumptions, the
parameters of the equivalent 1-DOF
oscillator depend on the geotechnical
properties of the embankment fill, the
type and properties of the reinforcement,
and its distribution in the embankment
(namely, the number and vertical spacing
of reinforcement layers); the embankment geometry; and the type of upstream
facing (Figure 8).
Considering the viscous work during a deformative cycle, it is possible to
calculate the maximum displacement of
the 1-DOF oscillator, which is equal to
the penetration length, Lp.
The 1-DOF oscillator model allows a
calculation of the part, Ep, of the impact
energy, Eo, which is dissipated to stop the
boulder through deformation, while the
residual energy, Es, is assumed to spread
downstream of the penetration depth,
generating the tensioned zone that produces the extrusion on the valley side face
of the embankment.
The following rational assumptions
are made for the tensioned zone between
the penetration length and the downstream face:
*	 The fill resists the extrusion movement through its frictional stresses
developed on the top and bottom horizontal surfaces of the extrusion cone.

*	 The geosynthetic reinforcements confine the fill and increase the loadspreading angle, α.
*	 The increase of the load-spreading
angle, α, depends on the type of
reinforcement (geogrid, woven geotextile, geostrip, woven wire mesh,
etc.); on the number of reinforcements
within the height of the extruded
cone; and on the presence or not of
the longitudinal reinforcements.
*	 In the tensioned zone, the transversal
reinforcement resists extrusion by
pullout resistance between the downstream facing and the penetration
depth. Pullout resistance can be activated only if reinforcement is properly
wrapped around the downstream face
with adequate wrapping length or
connected to facing elements, which
can transfer the pullout force to the
whole fill thickness between two consecutive reinforcement layers.
*	 Since pullout resistance cannot
increase indefinitely and the extrusion length strongly depends on the
reinforcement deformation, the pullout
force shall be produced with limited
tensile elongation; hence, the pullout
resistance is assumed to be limited to
the tensile strength at 2% elongation,
T2%, of the transversal reinforcements.

FIGURE 8 43-foot (13-m) high RPE
construction in Norway: Gabion face and
high-strength geogrids. Courtesy of Strata
Geosystems (India) Pvt Ltd.

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