Effect of Slope Shape on Erosion
Why do most natural slopes have
curvilinear rather than planar profiles? What slope shape is best suited for
minimizing erosion losses … convex, concave, compound (convex-concave), or
planar (uniform)? Why are most man-made slopes constructed with planar surfaces
and uniform gradients? These are not trivial questions—perhaps no other variable
affects the stability of slopes with regard to both surficial erosion and mass
wasting as does topography or slope morphology. Topographic parameters normally
considered in estimating soil erosion losses include inclination and length of
slope. Surprisingly, slope shape is seldom if ever considered.
Conceptual and mathematical
models, as well as the results of laboratory tests and field observations, can
be used to determine the effect of slope shape on both mass stability and
resistance to rainfall erosion. The conceptual and mathematical models described
here are two-dimensional, i.e., they assume slope profiles are invariant in all
vertical planes perpendicular to one of the co-ordinate axes. At first glance
this assumption of two-dimensional symmetry may appear to be unduly restrictive.
However, most engineered or man-made slopes meet this requirement. These slopes
are usually planar in form with an unvarying, down-slope gradient and little, if
any, planform curvature. Benching may be employed on occasion, but planar faces
are generally the rule. These man-made slopes include embankments (dams), cut
slopes along transportation corridors, cut or fill slopes within hillside
developments, and earthen waste stockpiles or landfills.
Conventional grading
practice does not usually promote nor encourage other slope forms, e.g.,
concave, convex, or compound slope profiles. The reasons for this grading
practice and slope form preference are somewhat puzzling. Natural slopes do not
typically exhibit planar slope faces with uniform, unvarying gradients. Instead
natural slopes manifest a variety of complex slope forms and profiles. Slopes
that start out with planar topography also tend to change with time into slopes
with curvilinear shapes in both the down-slope and cross-slope direction. In
other words, slopes tend to evolve over time into equilibrium shapes that
seldom, if ever, are entirely planar.
The simplest way to
determine the effect of slope shape is to invoke a conceptual model or a mental
image of the problem. This provides a way to think rationally about and compare
the relative stability of planar vs. curvilinear slope profiles. More rigorous,
theoretical analyses can also be undertaken based on physical and/or
mathematical models of different slope forms. Finally, the results laboratory
tests and field observations of erosion losses from different slope forms can be
reviewed. The findings in every case are inescapable, viz., concave or compound
slope shapes are superior to planar forms in terms of improving mass stability
and limiting erosion.
A conceptual model for examining the
effect of slope on erosion can be summarized briefly as follows. We start with a
simple, uniform soil slope with a planar face. The slope has a height (H) and
uniform inclination (ß). For
purposes of analysis the slope is divided into a series of horizontal layers.
Each layer, however, has identical soil properties (density and shear strength)
and thickness (DH). The
layering is an artificial construction that allows one to examine the influence
of changing the inclination (ßi) at
the face of each layer on surficial erosion. The critical slope parameters with
regard to soil erosion losses are steepness and length of slope. With other
factors held constant, soil erosion losses increase with both steepness and
length of slope. Increasing length means more opportunity for runoff to
accumulate with resulting larger tractive stresses acting on the slope face. The
tractive stresses increase with increasing slope distance down the face of the
slope.
By gradually decreasing the inclination
of the faces of the layers towards the bottom, the tractive stresses will also
decrease to a more or less constant value thus minimizing soil loss. Thus, a
simple conceptual model demonstrates that adjusting slope angle in a downslope
direction while still reaching the same toe point, i.e., making the slope
concave, will result in a slope shape that is more resistant to erosion. The
same conceptual modeling approach can also be used to demonstrate the
superiority of a curvilinear or concave slope shape with respect to mass
stability.
Visual observations of natural slopes provide yet another way of
gauging the long term stability of different slope profiles or shapes. A good
place to observe these profiles is in arid or desert climates where the absence
or scarcity of significant vegetal cover make it easier to determine slope
forms. Equilibrium slope forms can be observed readily in the mesa and canyon
country of the southwestern United States. A topmost resistant layer of hard
sandstone or igneous rock typically results in erosional remnants—mesas and
buttes with near-vertical rim walls at the top and foot slopes below that
characteristically develop a concave, equilibrium profile over time as
illustrated in Figure 1.
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Concave foot slopes are also
well developed and can be readily observed in the Unaweep Canyon a few miles
south of Grand Junction, Colorado. This canyon cuts through the Umcompahgre
Plateau. At one time the ancestral Gunnison River flowed through the Unaweep
Canyon, but the rate of uplift in the surrounding plateau was too high to allow
the river to maintain its course through the canyon. As a result the river was
forced to change course and flow elsewhere. The present canyon or valley has a
saddle or high point with a relatively small stream draining away in opposite
directions. These conditions have eliminated stream erosion and down-cutting as
a major geomorphic force in the canyon in recent geologic time. Instead more
diffuse erosional slope processes and mass wasting dominate topographic
development. Over geologic time these slope processes have produced a relatively
broad valley with concave foot slopes along canyon margins as illustrated in
Figure 2.
In summary: The results of field
observations and laboratory tests clearly show that concave slope profiles
appear to be more stable and generate less sediment than uniform, planar slopes.
These findings are consistent with conceptual models and they also accord with
results of computer modeling of soil erosion on slopes with irregular shapes and
with time evolved digital terrain models.
Author's Bio: Guest author Donald H. Gray is professor emeritus of civil and environmental engineering at the University of Michigan.
August 4, 2008
Effect of Slope Shape on Erosion
Why do most natural slopes have
curvilinear rather than planar profiles? What slope shape is best suited for
minimizing erosion losses … convex, concave, compound (convex-concave), or
planar (uniform)? Why are most man-made slopes constructed with planar surfaces
and uniform gradients? These are not trivial questions—perhaps no other variable
affects the stability of slopes with regard to both surficial erosion and mass
wasting as does topography or slope morphology. Topographic parameters normally
considered in estimating soil erosion losses include inclination and length of
slope. Surprisingly, slope shape is seldom if ever considered.
Conceptual and mathematical
models, as well as the results of laboratory tests and field observations, can
be used to determine the effect of slope shape on both mass stability and
resistance to rainfall erosion. The conceptual and mathematical models described
here are two-dimensional, i.e., they assume slope profiles are invariant in all
vertical planes perpendicular to one of the co-ordinate axes. At first glance
this assumption of two-dimensional symmetry may appear to be unduly restrictive.
However, most engineered or man-made slopes meet this requirement. These slopes
are usually planar in form with an unvarying, down-slope gradient and little, if
any, planform curvature. Benching may be employed on occasion, but planar faces
are generally the rule. These man-made slopes include embankments (dams), cut
slopes along transportation corridors, cut or fill slopes within hillside
developments, and earthen waste stockpiles or landfills.
Conventional grading
practice does not usually promote nor encourage other slope forms, e.g.,
concave, convex, or compound slope profiles. The reasons for this grading
practice and slope form preference are somewhat puzzling. Natural slopes do not
typically exhibit planar slope faces with uniform, unvarying gradients. Instead
natural slopes manifest a variety of complex slope forms and profiles. Slopes
that start out with planar topography also tend to change with time into slopes
with curvilinear shapes in both the down-slope and cross-slope direction. In
other words, slopes tend to evolve over time into equilibrium shapes that
seldom, if ever, are entirely planar.
The simplest way to
determine the effect of slope shape is to invoke a conceptual model or a mental
image of the problem. This provides a way to think rationally about and compare
the relative stability of planar vs. curvilinear slope profiles. More rigorous,
theoretical analyses can also be undertaken based on physical and/or
mathematical models of different slope forms. Finally, the results laboratory
tests and field observations of erosion losses from different slope forms can be
reviewed. The findings in every case are inescapable, viz., concave or compound
slope shapes are superior to planar forms in terms of improving mass stability
and limiting erosion.
A conceptual model for examining the
effect of slope on erosion can be summarized briefly as follows. We start with a
simple, uniform soil slope with a planar face. The slope has a height (H) and
uniform inclination (ß). For
purposes of analysis the slope is divided into a series of horizontal layers.
Each layer, however, has identical soil properties (density and shear strength)
and thickness (DH). The
layering is an artificial construction that allows one to examine the influence
of changing the inclination (ßi) at
the face of each layer on surficial erosion. The critical slope parameters with
regard to soil erosion losses are steepness and length of slope. With other
factors held constant, soil erosion losses increase with both steepness and
length of slope. Increasing length means more opportunity for runoff to
accumulate with resulting larger tractive stresses acting on the slope face. The
tractive stresses increase with increasing slope distance down the face of the
slope.
By gradually decreasing the inclination
of the faces of the layers towards the bottom, the tractive stresses will also
decrease to a more or less constant value thus minimizing soil loss. Thus, a
simple conceptual model demonstrates that adjusting slope angle in a downslope
direction while still reaching the same toe point, i.e., making the slope
concave, will result in a slope shape that is more resistant to erosion. The
same conceptual modeling approach can also be used to demonstrate the
superiority of a curvilinear or concave slope shape with respect to mass
stability.
Visual observations of natural slopes provide yet another way of
gauging the long term stability of different slope profiles or shapes. A good
place to observe these profiles is in arid or desert climates where the absence
or scarcity of significant vegetal cover make it easier to determine slope
forms. Equilibrium slope forms can be observed readily in the mesa and canyon
country of the southwestern United States. A topmost resistant layer of hard
sandstone or igneous rock typically results in erosional remnants—mesas and
buttes with near-vertical rim walls at the top and foot slopes below that
characteristically develop a concave, equilibrium profile over time as
illustrated in Figure 1.
Concave foot slopes are also
well developed and can be readily observed in the Unaweep Canyon a few miles
south of Grand Junction, Colorado. This canyon cuts through the Umcompahgre
Plateau. At one time the ancestral Gunnison River flowed through the Unaweep
Canyon, but the rate of uplift in the surrounding plateau was too high to allow
the river to maintain its course through the canyon. As a result the river was
forced to change course and flow elsewhere. The present canyon or valley has a
saddle or high point with a relatively small stream draining away in opposite
directions. These conditions have eliminated stream erosion and down-cutting as
a major geomorphic force in the canyon in recent geologic time. Instead more
diffuse erosional slope processes and mass wasting dominate topographic
development. Over geologic time these slope processes have produced a relatively
broad valley with concave foot slopes along canyon margins as illustrated in
Figure 2.
In summary: The results of field
observations and laboratory tests clearly show that concave slope profiles
appear to be more stable and generate less sediment than uniform, planar slopes.
These findings are consistent with conceptual models and they also accord with
results of computer modeling of soil erosion on slopes with irregular shapes and
with time evolved digital terrain models.