Geosynthetics April/May 2021 - 19

to evaluate the effects of block impacts
on RPEs. FEM and DEM often represent
the reinforced soil embankment with the
inclusion of geosynthetics as a soil mass
with an increased rigidity. But the geosynthetic choice and performance are
still not addressed.
In addition, FEM and DEM approaches
are less accessible to design engineers
in general, as they require specific skills
and backgrounds. Even if, at first glance,
models developed based on commercially
available software seem easy to use, satisfactorily modeling the impact response of
RPEs requires highly specific expertise.
These concerns are not only related to the
constitutive laws and mechanical characteristics of the model itself, but also require
a comprehensive knowledge of the different numerical methods and their limits.
For this reason, numerical tools are out
of reach for most of the companies concerned with the design of RPEs. Also, the
computation time is very long for some of
the existing numerical models (Lambert
and Kister 2017).
Analytical methods are more commonly used, as they are much more accessible and rapid to use. These methods were
developed over the years based on block
penetration or impact force to provide
design engineers with easy-to-use tools.
Nevertheless, their applicability can be limited due to the uncertainty associated with
their assumptions and calculations, which
are not necessarily related to geotechnics
or rock mechanics. These methods can
then lead the engineer to use formulas
derived from research performed in specific contexts that differ from the impact of
a block on a RPE. For example, the method
proposed by Kar (1978) is based on the
penetration depth of bombs and missiles
on soil shelter/protection structures.
As mentioned in the research of
Lambert and Kister (2017), Kar's model
was developed for cohesive nonfrictional
soils impacted by ogive-nose projectiles

at a minimum velocity of 671 mph (300
m/s). Mayne and Jones's model (1983)
was developed for heavy soil tamping, with a hammer having a flat tip.
Labiouse's model (Labiouse et al. 1996)
was developed for granular strata, a 3.3foot (1-m) maximum thickness, lying on
a rigid support and exposed to impact by
a spherical object producing less than 100
kJ in energy.
That said, RPEs are generally 9.8-26.2
feet (3-8 m) in thickness and made by
frictional, noncohesive material (Figure
4); they are subject to block impact with
different shapes (cubic or spherical),
which generate energy from 1,000 kJ to
tens of megajoules.

FIGURE 4 Trans-Canada Hwy #1; 23-foot
(7-m) high reinforced rockfall embankment
with gabion face, Fraser Canyon, B.C., Canada.
Courtesy of Maccaferri Canada Ltd.

Rimoldi-Brusa RPEs method
The authors of this article, being in the
geotechnics and geosynthetics industry
for many years (almost 50 years combined), have developed a new analytic
approach methodology. Both authors welcome comments from any geosynthetic
suppliers and industry experts in order to
explore and expand the proposed method.
The present article introduces the basics
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Geosynthetics April/May 2021

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