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GeoFlorida 2010: Advances in Analysis, Modeling & Design
(GSP 199) © 2010 ASCE
Rock catchment area design charts
L. Pantelidis1
1
Department of Civil Infrastructure Engineering, Technological Educational Institute
of Thessaloniki, 57400 Thessaloniki, Greece, PH (+30) 6937 440 234;
[email protected]
ABSTRACT
Studies on the effectiveness of deep ditches against rockfalls have shown
that, the original Ritchie (1963) guidelines are not as conservative as previously
thought. Moreover, following these guidelines, a unique ditch “depth – width” pair of
values is obtained for a given rock cutting not allowing for the chosen of the most
economical solution. The above findings gave rise to the research presented herein,
where, a number of design charts based on a computer simulation program
(RocFallTM) are proposed for deep rockfall ditches. Rockfall concrete walls and
fences became also subject of research as there are no relevant design charts
currently available. The assumptions made for the derivation of the proposed charts
are: a) the number of falling rocks is one hundred, b) the rocks are detached from the
slope crest, c) the initial speed of falling rocks is zero, d) the material of slope is a
clean hard bedrock and e) the base of the catchment area is covered by a layer of
gravel to absorb the energy of falling rocks. For the case of deep rockfall ditches it
was additionally assumed that, the ditch foreslope adjacent to the roadway is
vegetated. Furthermore, as a cut slope can be of any rock type and thus, charts of this
category provide indicative dimensions, the RocFallTM default material settings (e.g.
coefficient of restitution) were adopted. Finally, it is noted that, for the simple
geometries studied using RocFallTM (slopes without outcrops and benches) the rock
impact distance was always zero and therefore, the calculated catchment area width
should be corrected adding the maximum impact distance of rocks obtained by
Pierson et al. (2001) empirical study.
1.
INTRODUCTION
Ritchie studied the problem of rockfalls along highways and in 1963
proposed an empirical design table of rock ditch dimensions (minimum depth and
width) required to restrict rocks from rolling up onto the pavement. This table was
later adapted into a design chart (FHWA, 1989), which is still used by numerous
transportation agencies to dimension catchment areas. A major limitation of the
design criteria of Ritchie, however, is that, for a given slope having height H and
gradient n:1 a unique rock ditch pair of values is obtained, expressed in “depth –
width”. The ditch foreslope gradient next to the roadway is also standard (1V:1.25).
It is obvious that, such a rigid methodology does not allow for the most cost-effective
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solution. Moreover, a pilot study conducted by Pierson et al. (1994) showed that the
original Ritchie guidelines are not as conservative as previously thought. Pierson et
al. (2001) carried out a comprehensive study of rock fall behavior and the
dimensions of even catchment areas with gradients 1V:4H, 1V:6H and zero (flat). In
the study in question slopes with height from 12.2m up to 24.4m and gradient
ranging from vertical to 1V:1H were examined. The main disadvantage of this
rockfall catchment area design guide, however, is that, it calls for the construction of
very wide catchment areas. Therefore, this design guide is a very useful tool in
highway engineering only in case where the additional catchment area width does
not create construction difficulties and considerable increase in construction cost.
The above findings gave rise to the research presented herein, where, design
charts based on computer simulation program (RocFallTM) have been obtained for
deep rockfall ditches with a 1V:1H and 1V:1.5H foreslope adjacent to the roadway
(tanβ) as well as for rockfall concrete walls or fences (Figure 1).
Figure 1. i) Ritchie type ditch and ii) Flat catchment area in combination with concrete wall or
fence. “w” is the ditch width obtained using RocFallΤΜ and “wo” is the maximum impact
distance of the 99% of rockfalls derived through Pierson et al. (2001) empirical study.
2.
EXISTING ROCKFALL SIMULATION MODELS
Since the 1980s, a number of models that simulate the behavior of rockfalls
as they roll and bounce down slope faces have been proposed. Some of the more
recent rockfall simulation approaches, either mathematical models or computer
programs, are those of Agliardi and Crosta (2003), Azzoni and De Freitas (1995),
Azzoni et al. (1995), Bozzolo, D. and Pamini (1986), Bozzolo et al. (1988),
Descoeudres and Zimmerman (1987), Guzzetti et al. (2002), Hungr and Evans
(1989), Jones et al. (2000), Kobayashi et al. (1990), Pfeiffer and Bowen (1989),
Pfeiffer et al. (1990), Piteau (1980), Rocscience (2002), Spang (1987), Spang and
Rautenstrauch (1988) and Wu (1984).
Perhaps the most well known computer programs are the RocFallTM
(Rocscience, 2002) and the Colorado Rockfall Simulation ProgramTM (Jones et al.,
2000). These are statistical analysis programs that have been designed to assist with
assessment of slopes at risk for rockfalls and in determining remedial measures.
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3.
PROPOSED ROCK CATCHMENT AREA DESIGN CHARTS
Deep ditches (Ritchie type)
Catch ditches at the toe of slopes are often a cost-effective means of stopping
rock falls, provided that there is adequate space at the toe of the slope (Wyllie and
Mah, 2004). A set of design charts based on computer simulation program
(RocFallTM) is proposed for deep rockfall ditches with a 1V:1H and 1V:1.5H (tanβ)
foreslope adjacent to the roadway and for ditch depth equal to 1.0, 1.5 and 2.0m
(Figure 2 and 3). The required ditch dimensions, as defined by the depth (d) and
width (w), are related to the height (H) and the gradient of cut slope (tanα). The
criterion for the determination of the minimum ditch width was that no rocks are
allowed to roll up onto the pavement (100% retention in ditch). Interpolation
between charts can be used.
According to Rocsience (2003), the roll-out distance of rocks depends mainly
on the retarding capacity of the surface materials expressed mathematically by the
coefficient of restitution and the slope geometry. Other factors such as the size and
shape of the rock boulders, the coefficients of friction of the rock surfaces and
whether or not the rock breaks into smaller pieces on impact are all of lesser
significance (Hoek, 2009). As regards to the above input material parameters, it is
mentioned that, the default values found in the Project Settings and Material Editor
menu dialogs in RocFallTM were used.
In addition, the basic assumptions made in derivation of the proposed charts
are: a) the number of falling rocks is one hundred, b) the rocks are detached from the
slope crest (highest point), c) both the vertical and horizontal components of initial
speed of falling rocks are zero, d) the material of slope is a clean hard bedrock, e) the
base of the catchment area is covered by a layer of gravel to absorb the energy of
falling rocks (as commonly done in practice) and f) the material of ditch foreslope
adjacent to the roadway is a soil with vegetation.
As it resulted from the computer simulations, for small slope gradients (generally
less than 1.75V:1H) and small ditch widths the curves of Figures 2 and 3 concave
upwards due to the fact that, rock blocks strike on the foreslope surface at small
angle (nearly parallel) that cause them to cover a long distance bouncing and rolling.
3.1
Rockfall concrete walls or fences
Rockfall concrete walls or fences are commonly used as alternative means of
stopping rock falls, provided that there is also adequate space at the toe of the slope.
Applying the same methodology as for deep ditches, a set of design charts is
proposed for rockfall concrete walls and fences having height equal to 1.0, 1.5 and
2.0m. The required width (w) of catchment area and height of wall or fence (d) are
related to the height (H) and the gradient of slope (tanα). The criterion of “100%
retention” applied to deep ditches for the determination of the minimum catchment
area width was also used for the case of concrete walls and fences. Furthermore, the
implementation of the present analysis was also based on the default values of
material parameters found in RocFallTM menu dialogs. Finally, the assumptions “a”
to “e” mentioned in the previous paragraph stand for the case which is examined
herein as well. Interpolation between charts can be used.
3.2
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Figure 2. Proposed rock catchment area design charts: Ritchie type ditches with
a 1V:1H foreslope.
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GeoFlorida 2010: Advances in Analysis, Modeling & Design
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Figure 3. Proposed rock catchment area design charts: Ritchie type ditches
with a 1V:1.5H foreslope.
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Figure 4. Proposed rock catchment area design charts: Rockfall concrete walls
and fences.
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As it resulted from the computer simulations, for small slope gradients and
catchment area widths the curves of Figure 4 concave upwards due to the fact that,
the rockfall trajectories are interrupted by the wall or fence before gaining their
maximum height during the first bounce. Therefore, a wall or fence as short as 2.0m
(or less) is adequate to stop the falling blocks even in case of high cuttings.
Impact distance of falling rocks (wo)
It is noted that, the maximum impact distance of rocks taken from Pierson et
al. (2001) design guide of even catchment areas (Figure 5) should be summed to the
calculated catchment area width. Impact distance is defined as the measured distance
from the base of the rock cut slope to the point where a falling rock first strikes the
ground. This is done due to the fact that, for the simple geometries studied using
RocFallTM (slopes without benches and outcrops) the impact distance was always
equal to zero.
3.3
Figure 5. Maximum impact distance of the 99% of rockfalls (after Pierson et
al., 2001). The curves have been slightly refined.
4.
RELIABILITY OF THE PROPOSED CHARTS
The validity of the proposed charts depends mainly on the reliability of
RocFallTM codes used to simulate rockfall trajectories and, as previously mentioned,
on the chosen values of coefficient of restitution. A recent research carried out by
Alejano et al. (2007) concluded that the computer simulations performed using
RocFallTM approximate sufficiently well the trend in the curves obtained empirically
by Pierson et al. (2001), provided that the input material parameters are well
calibrated. It is important to be noted that, the design charts developed by Pierson et
al. (2001) and Ritchie (1963) refer to specific rock types. The first, indeed, are
considered conservative as the rock type at the test site is a hard durable basalt that
rebounds well after impact and rolls well (Pierson et al., 2001). Consequently, as a
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cut slope can be of any rock type, charts of this category provide indicative ditch
dimensions. On this basis, regarding the proposed charts (Figures 2, 3 and 4) the
RocFallTM default material settings were used as the best available data.
The reliability of the proposed charts is also shown through the following
example. Pierson et al. (1994), as part of a pilot study rolled 275 rocks from a 24.4
meter high 4V:1H slope into a “Ritchie” catchment area to determine its
effectiveness. The tested ditch was 7.3 meters wide, 2.0 meters deep with a flat
bottom and 1V:1H foreslope. Although the Ritchie shaped ditch used for testing was
wider, deeper and contained a steeper foreslope than a standard Ritchie ditch, 8% of
the rocks were still able to escape the catchment area (92% were retained). Pierson et
al. (2001) also demonstrated that, had the catchment area been designed to a standard
Ritchie width of 6.1 meters, the ditch would have been capable of retaining around
85% of falling blocks. Evans (1989) drew a similar conclusion based on real tests
with mine benches. On the other hand, according to the proposed methodology the
required width and depth of a flat bottom ditch with a 1V:1H foreslope for the
retention of the 99% of falling blocks are 11.2 and 2.0 meters respectively. The width
of 11.2 meters derives from the third chart of Figure 2 (w=4.5m) and Figure 5
(wo=6.7m, maximum impact distance of the 99% of rocks). Using the same
comparison chart with Pierson (1994, 2001), it is inferred that the calculated ditch is
capable of retaining the 98.5% of rockfalls. The last shows the agreement with the
99% used (Figure 5).
5.
CONCLUSIONS
A number of catchment area designs charts have been proposed by simulating
rockfalls in computer. The effectiveness of deep ditches as well as concrete walls and
fences were studied. The fact that for a given rock cut slope, different catchment
areas with the same rockfall retention effectiveness expressed in “depth – width” can
be obtained, allows for the investigation of the optimum technical–economic
solution. The methodology proposed herein is an innovative procedure, where
computer simulation is combined with published field data. More specifically, the
maximum impact distance of rocks taken from Pierson et al. (2001) empirical study
of even catchment areas is summed to the calculated catchment area width. The last
is done due to the fact that, contrary to what stands in practice, for the simple
geometries studied using RocFallTM (slopes without benches and outcrops) the
impact distance was always zero. Finally, it is noted that, comparison of the results
obtained by the proposed methodology with respective actual field data provided by
Pierson et al. (2001) showed full agreement.
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