cut slope design recommendations for sub-horizontal hard sedimentary rock units in ohio, usa
TRANSCRIPT
ORIGINAL PAPER
Cut Slope Design Recommendations for Sub-HorizontalHard Sedimentary Rock Units in Ohio, USA
Yonathan Admassu • Abdul Shakoor
Received: 21 November 2012 / Accepted: 28 March 2013 / Published online: 4 April 2013
� Springer Science+Business Media Dordrecht 2013
Abstract Although most cut slopes in Ohio consist
of inter-layered, sub-horizontal units of hard and soft
sedimentary rocks (sandstone, limestone, dolostone,
shale, claystone, mudstone), slopes consisting of
relatively thick hard rock units are not uncommon.
Design of stable cut slopes in hard rock units needs to
consider rock mass strength and orientation of
discontinuities with respect to slope face. Results of
kinematic stability analyses show that hard-rock cut
slopes are less likely to have conventional plane and
wedge failures, caused by unfavorable orientation of
discontinuities. The main cause of failure is identified
to be the undercutting-induced toppling, which is not
amenable to traditional kinematic or rock mass
strength-based analyses. Therefore, to recommend a
suitable slope angle, numerical models, using UDEC
software, were employed to study how various slope
angles affect the process of undercutting-induced
toppling failures. The UDEC models showed a slope
angle of 45� (1H:1 V) to be the most stable angle.
However, a 63� (0.5H:1 V) slope angle can signifi-
cantly reduce the potential for such failures and is
therefore more appropriate than the widely used angle
of 76� (0.25H:1 V).
Keywords Cut slope design � Kinematic analysis �UDEC � Toppling
1 Introduction
In this paper, cut slopes refer to slopes excavated into
bedrock during road construction. Cut slopes can fail
due to:
• Unfavorable orientation of discontinuities (joints,
bedding planes, foliation, faults and shear zones)
with respect to slope face, causing plane, wedge,
and toppling failures.
• Low rock mass strength which can result in
rotational slides. Low rock mass strength can be
attributed to low intact rock strength and undesir-
able discontinuity characteristics such as close
spacing, wide aperture, low roughness, clayey
infilling material, and presence of groundwater
(Bieniawski 1976).
The potential for slope failures associated with
unfavorable orientation of discontinuities, i.e. plane,
wedge, and toppling failures, is usually evaluated by
performing kinematic analyses. Criteria leading to
such failures are provided by Hoek and Bray (1981)
and Goodman (1989) (Figs. 1, 2). In order to perform
kinematic analysis, poles of discontinuity planes are
Y. Admassu (&)
Kent State University Ashtabula, Ashtabula,
OH 44004, USA
e-mail: [email protected]
A. Shakoor
Department of Geology,
Kent State University, Kent, OH 44242, USA
123
Geotech Geol Eng (2013) 31:1207–1219
DOI 10.1007/s10706-013-9644-4
plotted on a stereonet. Discontinuity cluster sets can be
identified by using density contours or visual
inspection of poles of discontinuities on a stereonet
(Fig. 3). Mean orientation values as determined from
pole clusters are then used as representative values for
kinematic analysis (Fig. 3). Great circles for each
representative pole concentration, a great circle rep-
resenting the slope face and a friction circle repre-
senting the friction angle are plotted on the same
stereonet for kinematic analysis (Fig. 1) (Hoek and
Bray 1981; Watts et al. 2003).
The representativeness of mean or highest density
values for cluster sets depends on how well tightly
poles are clustered. Representative values for poorly
clustered poles may result in unreliable kinematic
analysis results. Due to the unreliability of results from
using stereonets an alternative method, probabilistic
kinematic analysis, is becoming popular. The proba-
bilistic kinematic analysis considers the uncertainty in
dip direction, dip amount, and friction angle values
Plane Failure
Wedge Failure
Toppling Failure
Great circle representing slope face
Great circle representing a discontinuity set
Friction angle shown as friction circle
Shaded critical zone for plane and wedge failures
Great circle representing slope face
Great circle representing a discontinuity set
Friction angle shown as friction circle
Great circle representing slope face
Great circle representing a discontinuity set
Friction angle shown as friction circle
Shaded critical zone for plane and wedge
Shaded critical zone for toppling failures
Fig. 1 Slope failures
associated with unfavorable
orientation of
discontinuities. Based on
stereonets, plane failure
occurs if the dip vector
(middle point of the great
circle representing a
discontinuity) falls within
the shaded area bounded by
the slope face and the
friction circle, wedge failure
occurs if the intersection of
two great circles
representing discontinuities
falls within the shaded area
bounded by the slope face
and the friction circle, and
toppling failure occurs if the
great circle representing a
discontinuity is sub-parallel
(within 30�) to the great
circle representing the slope
face and its dip vector
(middle point of the great
circle) falls in the triangular
shaded zone (Modified after
Hoek and Bray 1981)
90 -
j
N
Fig. 2 Kinematics of toppling failure (Goodman 1989). a is
slope angle, r is dip of discontinuity, Uj is the friction angle
along discontinuity surfaces and N is the normal to discontinuity
planes. The condition for toppling is (90 - r) ? Uj \a
1208 Geotech Geol Eng (2013) 31:1207–1219
123
used in the kinematic analysis. Instead of using
representative discontinuity values, a range of random
values, that satisfy a chosen probability density
function (PDF), are generated for each discontinuity
and evaluated for failure potential (Park and West,
2001). The Monte Carlo simulation techniques can be
used to generate random values based on the chosen
PDF (Park and West 2001). If kinematic analysis
indicates the potential for failure, a gentler slope angle
maybe used to reduce failure potential.
Highway slopes in eastern and southeastern parts of
Ohio are cut into sub-horizontal Paleozoic age (Fig. 4)
hard rock units (sandstones, limestones, dolostones),
soft rock units (shlales, mudstones, claystones), and
inter-layered hard/soft rock units. The definition of
hard and soft rock units is purely dependent upon
durability (resistance to weathering), where hard rocks
are highly resistant to weathering and soft rocks can
easily weather. Although most cut slopes in Ohio are
composed of inter-layered hard/soft rock units, cut
slopes consisting entirely of hard rock units up to 100
ft (33 m) thick do exist in a number of places. Field
investigations revealed slope failures mainly along
sub vertical joints (Figs. 5, 6). Failures due to low rock
mass strength were not identified, and therefore, only
kinematic analysis was performed to investigate the
potential for discontinuity-orientation controlled fail-
ures. This paper focuses on stability analysis of cut
slopes in hard sedimentary rock units, specifically
sandstones and limestones, for the purpose of selecting
appropriate design slope angles.
2 Research Methods
2.1 Site Selection
Twelve sites consisting of thick units of sandstone and
limestone were selected for the study (Fig. 4; Table 1).
Site designation followed the ODOT (Ohio Depart-
ment of Transportation) standard, hyphenated notation
which uses a three letter county code, the numerical
route code of the road, and the mile marker measured
from the county line (also referred to as the section).
For example, WAS-77-15 refers to a site in Washing-
ton County along Interstate 77 at mile marker 15.
Discontinuity data for the 12 sites were collected
using the detailed line survey method (Piteau and
Martin 1977), the window mapping method (Wyllie
and Mah 2004), and random measurements. Based on
visual observations, a representative portion of the
rock layer was chosen and, in most cases, discontinu-
ities were measured along an approximately 100 ft
(30 m) long line crossing 40–100 discontinuities.
Random measurements were made to capture prom-
inent discontinuities missed in the detailed line survey.
A pocket transit compass was used to measure
discontinuity orientations (strike and dip).
2.2 Laboratory Testing
The tilt test, proposed by Stimpson (1981), was used to
determine the basic friction angle used for kinematic
analyses. The test consisted of placing two cores of the
Discontinuity cluster sets
Highest density within a cluster set
Fig. 3 a Stereonet showing
4 cluster sets of poles,
b Contoured poles for the
poles in (a). Contours
spaced at every 1 % pole
density
Geotech Geol Eng (2013) 31:1207–1219 1209
123
Fig. 4 Geologic map of Ohio and location of study sites
1210 Geotech Geol Eng (2013) 31:1207–1219
123
rock on a horizontal base in contact with each other. A
third core from the same rock unit was placed on top of
the two, forming a triangular stack. The two base cores
were restricted from sliding whereas the top core was
free to slide. The base on which the cores were placed
was slowly tilted until the top core began to slide. The
angle of tilt (a) was recorded and the basic friction
angle (/) calculated using the following equation:
Tan/ ¼ 1:115� tanða� 2�ÞÞ ð1Þ
�a ¼ 1.
2Xðaþ 2
� Þ=nþXða� 2
� Þ=n� �
ð2Þ
where n is number of trials, a is the weighted average
of tilt angles (a).
The tilt test was performed on both sandstone and
limestone cores. The test was repeated several times
on each set of cores and the average tilt angle (a) was
used to estimate the friction angle.
2.3 Data Analysis
Kinematic analyses, based on Markland’s criteria
(Hoek and Bray 1981) and Goodman (1989) proce-
dures were conducted for all 12 sites to evaluate the
potential for discontinuity-controlled failures (plane,
wedge, and toppling failures). RockPack, software
(available from RockWare) for slope stability analy-
sis, was used for the stereonet-based kinematic
analyses of all discontinuity dependent failures.
RockPack software does not have a pole contouring
module therefore, the DIPS software, another stere-
onet software (available from RocScience) was used
to contour poles and evaluate mean dip direction and
dip of discontinuity cluster sets. DIPS was also used to
generate 95 and 68 % confidence interval values for
the calculated mean values. After obtaining mean
orientation values from DIPS, RockPack was used for
kinematic analysis using the great circles representing
the mean dip direction and dip values of each cluster
set.
A major challenge with using stereonets for kine-
matic analysis is that for each cluster set, a single mean
dip direction/dip value, represented by a great circle, is
used. Mean values may or may not be good represen-
tation of a data cluster depending on how tight the
cluster is. Therefore, a more practical approach that
considers variability is to use two great circles that
represent the upper and lower bounds of mean
orientation values. The upper and lower bounds are
based on the 95 % confidence interval of mean values
as calculated by DIPS. To obtain the dip of great
circles representing the upper bound, the 95 %
confidence interval is added to the mean dip, whereas
for the lower limit, the interval is subtracted. However,
Vertical planes defining a wedge
Near vertical line of intersection
Fig. 5 Example of a wedge toppling failure within a slope
consisting mostly of sandstone. Notice the near vertical line of
intersection
Vertical planes defining a wedge
Near vertical line of intersection
Fig. 6 Example of wedge toppling slope failure within a slope
consisting mostly of limestone. Notice the near vertical line of
intersection
Geotech Geol Eng (2013) 31:1207–1219 1211
123
the dip direction for both the upper and lower bounds
is the same as that of the mean dip direction. In
addition, great circle representing mean dip direction/
dip is used. Therefore, three great circles for each
discontinuity set are used to perform kinematic
analysis, which would be more reliable than just using
a single great circle for each cluster set (Fig. 7). It is
also useful to vary dip directions in addition to dip
amounts. However, the major controlling factor to
failure at the study sites was the steepness of dip
amounts, and therefore only dip amounts variation was
considered.
3 Data Summary
Discontinuity orientation data for the hard sedimen-
tary rock units of the study sites were plotted on
Table 1 Sites selected for
stability analysis of hard
rock units
Site Rock unit Hard rock unit
thickness
Slope angle
(degrees)
Slope azimuth
(degrees)
ADA-32-12 Limestone 59 ft (18 m) 75 315
ATH-33-14 Sandstone 98 ft (30 m) 79 50
BEL-470-6 Limestone 23 ft (7 m) 65 350
CLA-4-8 Limestone 26 ft (8 m) 69 330
COL-7-5 Sandstone 16 ft (5 m) 75 175
GUE-77-8 Sandstone 40 ft (12 m) 59 280
JEF-CR77-0.38 Sandstone 19 ft (6 m) 76 15
LAW-52-11 Sandstone 32 ft (10 m) 58 215
LIC-16-28 Sandstone 58 ft (18 m) 69 170
MUS-70-11 Sandstone 12 ft (4 m) 75 180
RIC-30-12 Sandstone 36 ft (11 m) 79 0
WAS-7-18 Sandstone 19 ft (6 m) 80 130
Great circle for slope face
Great circle for J1Great circle for J2
Cluster set for discontinuity set 2 (J2)
Cluster set for discontinuity set 1 (J1)
Bounding great circles for J1
Bounding great circles for J2
Fig. 7 An example of
kinematic analysis by
RockPack software. The red
great circle represents the
mean dip direction and dip
for a discontinuity set. The
green represents the lower
bound of mean value
whereas the blue represents
the upper bound. Bedding
planes are excluded
1212 Geotech Geol Eng (2013) 31:1207–1219
123
Ta
ble
2D
escr
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stat
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csfo
rd
isco
nti
nu
ity
ori
enta
tio
n
Sit
eN
o.
of
dis
con
tin
uit
ies
Set
*K
Dip
(deg
rees
)
Dip
dir
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on
(deg
rees
mea
sure
d
east
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no
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)
Co
nfi
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terv
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(deg
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uit
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Inte
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tin
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sets
Inte
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n
azim
uth
(deg
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mea
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)
Inte
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tio
n
plu
ng
e
(deg
rees
)6
8.2
6%
95
.44
%
AD
A-3
2-1
25
71
65
89
31
31
.93
.13
32
/11
68
7
28
08
73
13
.35
.39
AT
H-3
3-1
41
31
53
71
24
6.0
9.9
43
/11
87
2
22
16
87
23
4.2
6.9
23
/27
88
3
35
18
38
85
.59
.05
BE
L-4
70
-61
27
16
67
91
1.5
2.4
55
2/1
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80
22
88
92
87
2.6
4.2
43
2/1
31
88
5
CO
L-7
-59
31
27
73
16
92
.34
3.8
45
2
CL
A-4
-85
51
14
68
62
79
1.5
2.5
22
25
28
61
2.7
4.5
20
2/1
34
18
6
GU
E-7
7-8
87
12
08
32
71
3.8
6.3
28
2/1
33
57
6
21
35
75
33
52
.74
.48
3/1
34
56
7
34
66
96
4.3
7.1
9
LA
W-5
2-1
15
11
11
27
82
26
2.5
4.1
11
3/2
34
25
6
28
98
92
52
.24
.26
.95
3/1
29
55
4
33
75
73
21
.75
.99
.76
2/1
16
53
7
LIC
-16
-28
28
14
15
81
69
.24
.98
.08
3/1
10
03
2
25
93
71
33
.84
.77
.76
2/1
23
82
9
36
68
61
51
.02
.43
.92
2/3
61
12
MU
S-7
0-1
16
61
61
81
15
1.1
2.9
4.7
15
2/1
20
17
7
23
07
72
20
.73
.86
.21
8
RIC
-30
-12
91
12
48
82
92
.72
.54
.05
42
/12
06
84
25
1.2
85
20
5.2
2.5
4.1
24
JEF
-CR
77
-0.3
83
91
26
.38
99
7.4
2.7
4.4
41
2/1
90
90
24
0.6
89
20
1.3
2.8
4.6
24
WA
S-7
-18
87
11
10
83
11
5.8
2.9
4.8
83
/11
09
82
21
01
86
19
2.0
3.9
6.4
52
/11
33
81
39
8.5
84
67
.05
.08
.33
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Geotech Geol Eng (2013) 31:1207–1219 1213
123
stereonets and contoured to determine principal joint
sets (clusters of poles of discontinuities on the
stereonets), using the DIPS software. The software
program also calculated the confidence interval for
mean dip direction and dip values of all discontinuity
sets (Table 2). Figure 8 shows the means of all
discontinuity sets for all sites, along with their
corresponding confidence circles, plotted on a single
stereonet. It can be seen from Fig. 8 that there are no
preferred dip directions and the dip values are
predominantly steep with an average dip value of
79�. The DIPS software also calculated the plunge of
intersection lines between discontinuity sets for each
site (Table 2). A histogram for plunge of lines of
intersection between discontinuity sets (Fig. 9) shows
that 70 % of the lines of intersection plunge at angles
greater than 70�.
The average friction angle calculated using Eqs. (1)
and (2) was 36� for sandstones and 44� for limestones.
Although surfaces of sandstone samples appeared
rougher, their friction angle values turned out to be
lower than those of limestones. The major disconti-
nuity surfaces are planar, not having irregular surfaces
and therefore basic friction angles were used.
Fig. 8 Stereoplot of mean orientation of poles for all discon-
tinuity sets with their corresponding circles of confidence as
determined by DIPS
Fig. 9 Frequency distribution of the mean plunge of the lines of
intersection of discontinuity sets as determined by DIPS
Table 3 Results of kinematic analyses for slopes composed of sandstone and limestone rock units, using RockPack software
Site Plane failure potential Wedge failure potential Toppling failure potential
Upper bound
mean values
Mean
values
Lower bound
mean values
Upper bound
mean values
Mean
values
Lower bound
mean values
Upper bound
mean values
Mean
values
Lower bound
mean values
ADA-32-12- No No No No No No No No No
ATH-33-14 No No No Yes No No No No No
BEL-470-6 No No No No No No No No No
CLA-4-8 No No No No No No No No No
COL-7-5 Yes Yes No No Yes No No No No
GUE-77-8 No No No No No No No No No
JEF-CR77-0.38 No No No Yes No No No No No
LAW-52-11 No No No No No No No No No
LIC-16-28 Yes Yes Yes No No Yes No No No
MUS-70-11 No No No Yes No No No No No
RIC-30-12 No No No No No No Yes No No
WAS-7-18 No No No Yes No No No No No
1214 Geotech Geol Eng (2013) 31:1207–1219
123
4 Results
The results of kinematic analysis, using RockPack
software applications, are summarized in Table 3.
Based on mean dip direction and dip values, 10 sites
show no potential for plane failure, 11 sites show no
wedge failure potential and no site shows toppling at
the present slope angles. Based on the great circles
representing the upper and lower bounds, no other
sites show plane failure potentials but 5 more sites
show potential for wedge failure and one site shows
the potential for toppling failure (Table 3).
The results of kinematic analysis based on mean dip
direction, show very little likelihood for plane, wedge
or toppling failures. Although considering the upper
and lower bounds of mean values show more sites
having the potential for wedge failure, but still 87 % of
the analyzed discontinuity intersections do not show
any potential for wedge failure (Table 3).
The result of the kinematic analysis is in agreement
with field observations that revealed very few discon-
tinuities, or their intersections, emerging unsupported
on the slope face and causing the potential for plane or
wedge failures. This is because of the dominance of
the steep dip angles and intersection plunges at the
study sites (Figs. 5, 6).
5 Cut Slope Design
Although the potential for discontinuity orientation
controlled failures does not appear to be significant at
the 12 study sites, ample evidence exists for the
occurrence of a special type of toppling failures. The
rock blocks involved in these failures are bounded by
steeply dipping, intersecting discontinuities. Such
discontinuities cannot lead to failures unless the lines
of intersection day-light on the slope face. Careful
examination of the failures in Figs. 5 and 6 reveals the
Fig. 10 An example of undercutting-induced rockfall bounded
between two steep discontinuity planes. Note the undercutting
being promoted by the presence thin layers of friable sandstone
Fig. 11 An example of undercutting-induced wedge toppling
failures with undercutting being promoted by the presence thin
shale layers
Geotech Geol Eng (2013) 31:1207–1219 1215
123
presence of friable layers within the hard rock units.
The rapid weathering of these friable layers results in
undercutting of the overlying stronger layers, eventu-
ally causing rockfalls that appear to have begun as
toppling of wedge-shaped rock blocks. Such failures,
therefore, require not only the presence of steeply
dipping and intersecting discontinuities \3–4 ft
(1–1.3 m) apart, but also the presence of layers of
friable layers of sandstone (Fig. 10) or thin layers of
shale (Fig. 11). These failures are similar to the
undercutting-induced wedge-falls described by Sha-
koor and Weber (1988). The presence of thin layers of
friable sandstone can also be seen promoting rockfalls
in the adjacent state of Pennsylvania (Fig. 12). Ster-
onets were used to identify the sites that have steeply
plunging ([80�) intersection lines. The results show
that 7 of the 12 sites have discontinuities intersecting at
[80� (Table 2). These sites have the potential for
undercutting-induced rockfalls, if friable layers are
present.
Steronets can be used to identify the sites with
intersecting steeply dipping discontinuities, but cannot
be used to define a slope angle that would eliminate the
type of failure described above. A stable slope angle
needs to be a unique uniform angle across the entire
slope since the friable layers promoting undercutting,
which ultimately leads to failure, are too thin for
independent consideration during design.
In order to obtain a unique, stable angle, 2D
computer models generated by UDEC (universal
distinct element code) software were used. UDEC is
a distinct element program which treats discontinuity
bounded blocks as distinct elements having contacts or
interfaces (UDEC 2011). Distinct element programs
allow finite displacements, rotations, and complete
detachments of rigid or deformable blocks. Blocks can
be rigid in cases of low stress situations such as slopes
(UDEC 2011). Simple 2D (10 m 9 10 m) models,
with horizontal bedding (spaced at 1 m) and through-
going vertical jointing (spaced at 1 m), were generated
considering rigid blocks with zero cohesion and a
friction angle of 36�. The first set of models use an ideal
slope cut into equi-dimensional rock blocks bounded
by equally spaced horizontal bedding planes and
vertical joints (Fig. 13). Four slope angles are chosen
to illustrate the models: 90�, 76� (0.25H:1 V slope),
63� (0.5H:1 V slope), and 45� (1H:1 V slope). The
purpose of the analysis was to investigate the effect of
undercutting by removing the two bottom left corner
blocks to mimic a 2 m undercutting (Fig. 13). After
removing the rock blocks and upon running UDEC,
unstable rock blocks can be observed displaced from
their original positions (Fig. 13). To analyze the result
of the simulated undercutting, the total volume of
displaced blocks is measured (Table 4). The least
amount of displaced rockfalls in terms of volume is
observed for a 1H:1 V slope. Additional models, where
joints are not through going (spaced at 2 m) were also
investigated with similar inputs (Fig. 13). Again the
1H:1 V slope resulted in the least volume of rockfalls
generated by a 2 m undercutting at the base of the slope
Table 4 Results of simulation of undercutting using UDEC
software
Slope angle Thoroughgoing
continuous joints
Non-thoroughgoing
discontinuous joints
Volume of displaced
rockfalls*
Volume of displaced
rockfalls*
Vertical (90�) 18 m3 1 m3
0.25H:1 V (76�) 6.1 m3 0.87 m3
0.5H:1 V (63�) 2.26 m3 0.25 m3
1H:1 V (45�) 0.5 m3 0 m3
* Volume is calculated by multiplying cross-sectional area by
1 m
Fig. 12 Undercutting-induced rockfall with undercutting being
promoted by the presence thin layers of friable sandstone.
(Photo taken just north of Pittsburgh, PA along I-279 N)
1216 Geotech Geol Eng (2013) 31:1207–1219
123
(Table 4). Comparing the two sets of models, the non-
through going discontinuities appear to result in less
amount of rockfalls.
Although a 1H:1 V slope angle would be the
optimum angle to prevent toppling or associated
rockfalls, it would result in excessive excavation. A
slope angle of 63� (0.5H:1 V slope) can adequately
minimize these undercutting-induced failures based
on the results of the above models. It should also be
noted that slope angles steeper that 1H:1 V are highly
preferred for cutting slopes by pre-split blasting
technique. In addition to slope angle considerations,
the trajectory of released rockfalls is also taken into
account during slope design for the purpose of
designing the catchment ditch (ditch at the base of
the slope to contain rockfalls). According to the charts
by Pierson et al. (2001), the 0.5H:1 V slope results in
shorter roll out distances of rockfalls than that of
1.H:1 V and 0.25H:1 V (Fig. 14). Although the
0.5H:1 V slope may not be as good as the 1H:1 V in
regards to minimizing undercutting-induced failures,
it would require a narrower catchment area in addition
to requiring less excavation.
The above recommended slope angle of 0.5H:1 V
can be used for thick, sub-horizontal non-tectonized
hard rock units similar to the rocks in Ohio, Pennsyl-
vania, West Virginia, and Kentucky where 0.25H:1 V
is widely used for such rocks. Such non-tectonized
sedimentary sequences as those found in continental
interiors or bordering orogenic belts, consistently
exhibit vertical orthogonal joints (Van Der Pluijm
and Marshak 2004). Cut slopes in rocks involving such
joint patterns are prone to undercutting-induced rock-
falls as described in this study.
Fig. 13 Examples of UDEC models for 0.25H:1 V slope. a For through going discontinuities and b non-through going discontinuities.
The red blocks shown on the left column are removed before running UDEC. The right column diagrams show how destabilized blocks
behave after running UDEC
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Fig. 14 Rockfall rollout distance for different slope heights, slope angle and catchment ditch slope (after Pierson et al. 2001)
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6 Conclusions
The following conclusions can be drawn from this
study:
1. Cut slopes consisting of sub-horizontal hard
sedimentary rock strata in Ohio usually do not
exhibit conventional plane, wedge, or toppling
failures. Instead, undercutting-induced rockfalls/
toppling failures, promoted by closely spaced,
steeply dipping, intersecting joints and presence
of friable sandstone or soft rock layers are the
most common slope failures. Based on UDEC
models and catchment ditch criteria, a design
slope angle of 63� (0.5H:1 V slope) is considered
adequate to reduce undercutting-induced rock-
falls/toppling failures.
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