... erosion phenomena su ggests that erosion prediction technology and mitigation ..... The loss of soil due to headcut erosion can have enormous environmental consequence, vet the ... programs have provided new insights into these scour processes. .... 9863 '\Si\E Annual International Meetin g, Orlando. FL. July II - 6. 998.
PROCESSES OF HEADCUT GROWTH AND MIGRATION IN RILLS AND GULLIES Kerry M. Robinson'. Sean J. Bennett ' . Ja'.ier Casa li. and Gregory J. Hanson'
ABSTRACT The formation and upstream migration olheadcuts si g nificantly increases soil losses and sediment yield front a g ricultural lands, threatens the structural inte g rity of earthen dams, and can undermine roads and brid g es. Recent research using unique experimental facilities and methodologies has provided new insi g hts on these erosion processes. Under controlled experimental conditions, steady-state soil erosion has been simulated for rills and along crop furrows. During mi gration, headcut due to mi g ratin g shape, size, rate of movement, and sediment yield remained constant. Downstream ot'the headcut, a soil bed was constructed hcre slope as dependent upon the sediment ieId from the headcut and the fio transport capacity. Soil erosion processes were also examined in a large outdoor fticility simulating gully headcuts. Using a compacted cohesive soil. headcut migration rate was observed to decrease as the average density and average unconfined compressive strength increased. While the flow rate and overfall height were not observed to have a major impact on advance rates, a sand layer at the base of an overfall did have a dramatic influence on advance rates. The erosion processes and flow structure within the large g ully headcuts were strikingly similar to those in ruts and crop furrows. The commonality of form and process in these soil erosion phenomena su gg ests that erosion prediction technology and mitigation measures may be developed and widely applied. Key Words: Headcut, Soil loss, Sediment yield, Soil Erosion process, Rill. Gully
1 INTRODUCTION
Headcut erosion within ruts, ephemeral gullies, classic gullies, and streams causes serious environmental problems. Headcut erosion accelerates the loss of topsoil and decreases the productivity of agricultural lands. Eroded sediments often end up in receiving streams, causing water quality problems and negatively impacting biological processes. In addition to landscape degradation, gullies are the dominant form of damage to earth spillways. If a gully can move through an earth spillway and breach the crest of a dam, then the impounded floodwaters will be rapidly released. This floodwater release poses a major threat to people and property downstream. Headcuts or knickpoints that move upstream in rivers cause bank stability problems, threaten the stability of roads and bridges, and undermine existing in-stream structures. Grade control structures and/or stream stabilization measures are often required for channel stabilization. Even though these scour processes may be major contributors to the total amount of observed soil erosion, comparatively little is known about headcut development and migration. While additional tools are needed to predict and mitigate headcut erosion at all scales, the mechanics of this erosion process must first be well understood. The objective of this paper is to describe the dominant mechanisms and erosion characteristics of headcuts in rills, and gullies based on recent experimental research.
2 HEADCUT EROSION IN RILLS AND SMALL GULLIES 2.1 Introduction
Headcuts are step-changes in bed surface elevation at the head of channel networks where intense, localized erosion takes place (Brush and Wolman, 1960; Gardner, 1983). In upland concentrated flows Plant Science and Water Conservation Research Laboratory, USDA-ARS, 1301 N. Western St., Stillwater, OK 74075, USA National Sedimentation Laboratory, USDA-ARS, P.O. Box 1157, Oxford, MS 38655, USA Department of Projects and Rural Engineering, Public University of Navarra. 31006 Pamplona, Navarra, Spain Note: The manucript of this paper was received in March 1999. Discussion open until March 2001. -69International Journal of Sediment Research, Vol. 15, No. 1, 2000, pp. 69-82
(i.e.. within rills and alon g crop furrows), the migration of headcuts is commonly associated with siiznilicant increases in sediment yield (Mosley. 1974: Me y er et al.. 1975; Bryan. 1990; Rdmkens et al., 1996. 1997). For example. Romkens et al. (1996. 1997). in a series of experiments dealing with shallow overland flow over bare soil, observed the failure ot surface soil seals. immediately, followed by headcut formation, bed incision, and nil development. Prior to incision, sediment yield from the soil surface was essentially zero. Moreover, on some soils, up to 60% of total rill erosion has been attributed to migrating headcuts (Elliot and Laflen. 1993). Headcut erosion has been linked to concentration of ocnland flow, nil incision, and gully development (Seginer. 1966: Mosle. 1974: Piest et al.. 1975: Merritt. 1984: Bryan and Poesen. 1989: Brvan, 1990; Slatter y and Brvan. 1992). Experimental investigations have described some basic characteristics of headcut erosion (Brush and Wolman. 1960; Holland and Pickup. 1976; Begin et al. 1980a.h: Gardner. 1983. Br yan. 1990; Stein and Julien. 1993. 1994; Stein et al.. 1993; see review in Bennett et al. 1998b). However, due to logistical difficulties in examining activel y migrating headcuts. little information exists on the dynamics of headcut mi g ration, the variation in scour hole morphology, and the mechanics ofheadcut erosion. Bennett and his co-workers (Bennett et al.. 1997: lSa.h: Bennett. 1998) deeloped a unique experimental methodology to examine in detail actively migrating headcuts in soil. In their studies. Bennett and his co-workers incrementally packed air-dried and crushed sandy loam to sand' clay loam soil into a laboratory flume 2 m long and 0.165 m wide, and constructed a pre-formed headcut at the downstream end. Application of simulated rain produced a surface seal that negated surface soil detachment by overland flow both upstream and downstream of the headcut. and it produced a two-layer stratigraphy (a layer resistant to erosion overlying a layer less resistant to erosion) common to many stepped headcuts in field and flume studies (e.g., Holland and Pickup, 1976). The introduction of overland flows typically obse rved along crop furrows on agricultural plots (e.g. Meyer et al., 1975: Line and Meyer. 1988) caused soil erosion to occur exclusively at the overfall, and a scour hole developed, enlarged, and migrated upstream. Experiments have examined the effect of discharge, bed slope, and initial step height on headcut growth and migration, and key results are presented below. 2.2 Steady-State Soil Erosion, Erosion Mechanics, and Self-Similarity Using constant bed slope (1%) and initial headcut height (25 mm), Bennett et al. (1998a.b) released onto this sealed soil overland flows ranging from about 20 to 80 1/mm (0.00033 to 0.00133 m 3/s). After an initial period of scour hole development, the headcut brinkpoint migrated upstream in a gradual and linear fashion with time (Fig. la). Headcut migration rate was constant within each run, and ranged from 1.2 to 2.0 mm/s among runs. The peak in sediment discharge coincided with initiation of both headcut movement upstream and deposition downstream (Fig. lb), and the deposit represented a self-made bed. After a short period of time. sediment yield remained fairly constant, ranging from 0.007 to 0.014 kg/s. During migration, the geometry of the scour hole also remained invariant. The ratio of length to maximum scour depth (S )-to-maximum scour depth (S ; see Fig. 2) remained unchanged for each run, for all runs was 1.3 (Fig. Ic). By employing a unique experimental methodology, and the mean Bennett and his colleagues were able to generate steady-state soil erosion due to migrating headcuts. Bennett et al. (1998a.b) observed two processes of headcut erosion: surface seal failure and jet impingement scour. During overland flow, the surface seal was intermittently removed from the surface at the headcut brinkpoint. Once removed, the subsurface soil quickly washed away. Seal removal was controlled by crack formation, and these were arcuate in shape, parallel to the headcut. and locally' restricted to the brinkpoint. Subsurface pressure fluctuations, turbulent shear forces, or headcut undercutting and cantilever mass failure could have formed such cracks. At the brinkpoint. ajet or nappe impinged the bed just upstream of the maximum scour depth and split into two wall jets or rollers (Fig. by submerged jets is 2a), causing soil erosion within the scour hole. The dynamics of sediment erosion well described (e.g., Rajaratnam. 1981), and impinging jet scour models have been successfully applied to headcut erosion (Stein and Julien. 1993, 1994; Stein et al., 1993). The erosive power of the impinging jet increased with flow discharge, causing deeper and larger scour holes.
SL /S D
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L
0
International Journal of Sediment Research, Vol. 15, No. 1, 2000, pp. 69-82
'.5 C C C C C
0.0 0.05 0.04 0.03 0.02 0.01
V rJ)
0.00 3
C (..1 -S —J
2
cI
0
0
200 400 600 800 1000
Time (s) Fig. I Time variation of (a) headcut brinkpoint position, (b) sediment yield, and (c) the ratio of the length to Maximum scour depth (S)-to-maximum scour depth (S 0 ) for all experiments described in Bennett et al. (1998a,b). The bars shown in (c) depict the minimum and maximum values observed. Because the wall jets extended over the entire scour hole region, scour hole length scales S L and S0 were used to normalize all time-averaged headcut profiles (Bennett et al., 1998a; Fig 3). Three different morphological fields were observed. In the near field, headcut shape was wholly dependent on the erosive recirculation within the upstream roller, and the bed profiles for the headcut face were virtually the same for all tests (Fig. 3). In the far field, sediment generated during headcut migration was Partitioned, either deposited or transported depending upon the transport capacity of the flow. The soil bed downstream of the headcut aggraded, and bed height tended to increase with flow discharge. Within the transition region, the downstream roller became th ree-dimensional, and complex flow patterns were o bserved. Headcut shape within the near-field flow area displayed self-similarity with increased flow discharge.
Int ernational Journal of Sediment Research, Vol. 15, No. 1, 2000, P
p. 69-82
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I 1% slope
Q=82.41/rnin
I M= 1.2mm/s
L = 1.2
Flow direction
(a)
sition^ Depo
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St
.4 --------
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Q 50.9 1/mm M = 0.8 mm/s S 1 /S ) = 0.6
(b) 'V 0.1 m
Fig. 2 Definition sketch of water and bed surface profile of a steady-state headcut with (a) a non-aerated nappe. and (b) an aerated nappe. These diagrams were derived from actual digitized images from the experiments of Bennett etal. (1998a,b) and Bennett (1998). Generalized flow patterns are shown, the length to maximum scour depth ( S L) and the maximum scour depth (SD) are defined, Q is flow discharge, Mis headcut migration rate, and scale is provided.
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0 2 4 6 8 10
Distance From a Datum/SL Fig. 3 Time averaged bed profiles of the steady-state headcuts for each experiment, normalized by SD and SL, and plotted relative to a datum (from Bennett et al., 1998a). - 72 - International Journal of Sediment Research. Vol. 15, No. 1, 2000, pp. 69-82
Al
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Initial Bed Slope (%) Fig. 4 Variation of headcut and sediment parameters with bed slope (from Bennett, 1998). Shown are (a) average migration rate. (b) rate of change of scour depth with time d(S0)/dt, (c) headcut aspect ratio 5L'50' (d) average bed slope of the sediment deposit S and (e) average sediment yield Q5.
2.3 Effect of Slope on Headcut Dynamics
Using a constant flow discharge of about 52 I/mm (0.00087 m3/s) and an initial headcut height of 25 mm, Bennett (1998) examined the effect of varying bed slope from I to 10% on headcut growth and development. For bed slopes 2% and smaller, the two-dimensional jet or nappe at the headcut brinkpoint remained submerged, and a steady-state condition was achieved: migration rate, sediment yield, and scour hole geometry remained constant during the experiment (similar to the results described above). For bed slopes 3% and greater, although migration rate during the experiment remained constant, the overfall nappe was aerated (Fi g. 2b), and as the headcut migrated upstream depth of scour increased. A change in bed slope impacted headcut dynamics, migration rate, and scour hole geometry. Headcut migration rate tended to decrease with bed slope (Fi g. 4a). Bennett (1998) related this trend to a decrease International Journal of Sediment Research, Vol. 15, No. 1, 2000, pp. 69-82 -73-
in the efficienc y of undercuttin g processes of aerated nappes at the brinkpoint that led to a decrease in crack development as bed slope increased. For bed slopes 3% and greater, scour depth increased during headcut migration. and its rate o1groth also increased with bed slope (Fi g . 4b). For an infinitely long channel, one can assume that the headcut would reach some finite maximum scour depth such that
/S D )/dt would tends toward zero. Despite this observed scour geometry time-dependenc y , mean aspect ratios S I /S D for adjustment in the scour trace would occur (see Bennett et al., l998b) and d (Si
aerated nappes were close to 0.7. and these decreased sli g htl y with bed slope (Fi g . 4c). Conversel y for submerged jets. SL /S / 1.1 . similar to the results described above. Processes of headcut erosion for aerated nappes ere similar to non—aerated or submer g ed nappes. Surface seal future occurred at the headcLit brinkpoint. and this was related to obser v ed crack formation. Plunge-pool scour and the turbulent flow field associated with an impinging nappe caused soil erosion within the headcut scour hole (Fie. 2h). In addition, along the aerated headcut facc. soil material was continuously being removed due to fluidized mass wasting. All three processes contributed to headcut erosion. Despite the large range on initial bed slope and scour hole geometry, the slope of the sediment deposit S downstream of the migrating headcut was always close to 2.2% (Bennett. 1998: Fig. 4d). Factors such as transport capacity, upstream sediment flux (Fig. 4e). and caliber of the sediment will determine slopes of such constructed beds. In these experiments, flow discharge, i.e. flow transport capacity, determined the slope of the constructed bed. Headcut migration governs soil erosion, but flow transport capacity governs sediment yield. 2.4 Effect of Initial Step Height on Headcut Dynamics Using a constant flow discharge of about 70 1/mm (0.0012 m 3/s) and a bed slope of 1%, Casali and Bennett (unpublished data) examined the effect of var y ing the initial step height from 5 to 50 mm on headcut growth and development. In all runs, a steady-state condition was achieved: migration rate, sediment yield. and scour hole geometry remained constant during the experiment (again similar to the results described above). The overfall nappe became aerated when 5D 0.09 m, and the headcut erosion processes discussed above were also observed during these experiments. A change in initial step height impacted headcut dynamics, migration rate, and scour hole geometry. Headcut migration rate, maximum scour depth S0, deposit thickness dr, slope of the self-made bed SF, and sediment yield Q5 increased with initial headcut height (Fig. 5); larger initial steps resulted in progressively deeper but faster moving headcuts. The length to maximum scour SL and SL/SD decreased with initial headcut height. but then remained unchanged once the nappe became aerated (Fig. 5). For a given flow discharge and bed slope, the morpholog y of the steady-state, migrating headcut depended upon the initial step height or bed perturbation. The time and length scales required to attain this steady-state condition decreased exponentially with initial headcut height (Fig. 6). The largest steps required the shortest time and length to reach steady state. Thus for a given runoff event on an agricultural plot, the presence of relatively large headcuts within rills or along crop furrows will produce significantly more sediment erosion and soil loss as compared to smaller headcuts. 2.5 Discussion In agricultural regions and upland areas, the formation and development of headcuts in ruts and along crop furrows can devastate soil resources and farm productivity, and severely degrade the landscape. These experimental studies have shown that within a short period of time headcuts can cause significant amounts of erosion due solely to their upstream migration. Yet headcut size, migration rate, and downstream bed adjustment have been shown to vary systematically, providing an opportunity to derive analytical relations for sediment yields from agricultural areas impacted by headcut erosion. Based on these observations, mitigation techniques might include dispersal of concentrated flows, residue management, use of vegetative covers, enhanced infiltration, and structural treatments.
-74-
International Journal of Sediment Research, Vol. 15, No. 1, 2000, pp. 69-82
(1
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0.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Initial Headcut Height (m) Fig. 5 Variation of headcut and sediment parameters with initial headcut height (from Casali and Bennett, Unpublished data). Shown are (a) average migration rate, (b) maximum scour depth S 0, (c) length to maximum scour depth SL, (d) headcut aspect ratio SL/S, (e) average thickness of the deposit d (f) average bed slope of the sediment deposit S and (g) average sediment yield Q. International Journal of Sediment Research, Vol. 15, No. I, 2000. pp. 69-82
-75 -
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Initial headcut height (m) Fig. 6 Variation of the time (7) and length (D) required in attaining a steady-state condition for different initial headcut heights (HY). 3 LARGE-SCALE HEADCUT EROSION
3.1 Introduction The formation and movement of gullies in earth emergency spillways was the major motivation for examining large-scale headcut erosion mechanics. If a gully can retreat up the spillway and through the crest of a dam, the impounded water can be released. A rapid release of stored floodwater poses an obvious threat to life and property downstream. Spillways experience relatively large unit discharges, and spillway gullies typically are much larger than ephemeral gullies. By design, spillways conduct wide, shallow flows that can be well approximated using a two-dimensional flow assumption. In contrast, rills and ephemeral gullies typically form in areas where flow concentrates. Spillway gullies typically are formed during a single flood flow event much like ephemeral gullies and tills; however, the flood flow duration is much longer in spillways. Spillways conduct relatively clear water, while rills and ephemeral gullies are subject to the influences of sediment transport and deposition. While important differences exist between rills, ephemeral gullies, and spillway gullies, many similarities also exist. Headcut erosion is driven primarily by the forces of flowing water that act to detach, undermine, and scour soil materials in the vicinity of the overfall. Stein-and Julien (1993) describe stepped headcuts and rotating headcuts. Stepped headcuts have a vertical face, while rotating headcuts alter their shape as they migrate. Typically, a rotating headcut changes from a near vertical to a sloping face. Numerous large-scale headcut erosion tests have been conducted, and select results are summarized herein. The hydraulics of flow over an overfall has been investigated by numerous researchers such as Rouse (1936), Moore (1943), and Rand (1955), but little has been done to examine how these hydraulic forces detach and remove soil material at a headcut. -76-
International Journal of Sediment Research, Vol. 15, No. 1. 2000, pp. 69-82
ROW A9E4T
FAY
TAILGATE
knd
DROP TRM4&flCt1
OUTLET BASIN
Fig. 7 Large-scale headcut facility at the USDA-ARS location in SiIlw:er, OK.
3.2 Large-Scale Headcut Test Facility A 29.0-rn long and 1.8-rn 'ide test flume with 2.4-rn tall walls was constructed specificall y to conduct large-scale headcut erosion tests (Fig. 7). The test flow rate was measured with a modified Parshall flume. Flow then passed over a drop structure into a subcritical flow forebay. A transition section and a vane flow straightener were used to provide uniform flow conditions entering the flume. An overflow tailgate allowed the tailwater downstream of an overfall to be regulated. A more complete description of the test facilities is provided in Robinson and Hanson (1995). A sandy clay soil (CL) was used for headcut testin g . The soil exhibited a liquid limit of 26 and a plasticity index of 15. The soil also exhibited a maximum dry density of 1.9 Mg/m 3 at an optimum moisture of 12%. The test flume was filled by placing soil in horizontal loose lift layers of 152-mm thickness. Additional lifts were added until the desired fill depth was achieved. Water was added, if necessary, to achieve the desired soil moisture. A tiller was used to mix the soil la y er, and a selfpropelled vibratory roller was used to compact each soil layer. Typically a vertical overfall was preformed at the downstream end of the compacted fill. Overfall heights of 0.96, 1.25, and 1.55 m were examined at flow rates of 0.75, 1.59, and 2.42 m/s. 3 A constant flow rate was introduced over the horizontal fill material, and the headcut erosion and migration rate were monitored. Dominant erosion processes were also observed. 3.3 Key Results
The discussion that follows is a summary of test results observed over several years of stud y . Headcut advance rate was determined as the slope of headcut position versus time plot. A typical plot of headcut position versus time (Fig. 8) resembles a step function because the headcut moved as a series of discrete mass wasting events, i.e., cantilever mass failure. Typically, hydraulic stresses would undercut the overfall for a period of time until the headcut became unstable and failed. Failure debris would be quickly swept downstream and the undercutting process would begin again. A linear regression performed on the advance data typicall y displayed a correlation coefficient (R) of 0.96 or greater. The uniform movement suggests that the fill was placed consistently. The same soil exhibited widely different headcut advance rates, depending on the soil moisture content and the compaction energy used during fill placement (Hanson et al., 1998). The CL soil exhibited a strong relationship between unconfined compressive strength and dry densit y . Advance rate also dramatically decreased as the dry density increased (Fig. 9), ranging from 0 to 18.6 rn/h. The overiall height and flow rate were not found to be strong functions of headcut advance rate. The placed soil conditions had more influence on the advance rate over the range of overfall heights and discharges examined (Robinson and Hanson. 1996a).
International Journal of Sediment Research, Vol. 15, No. 1, 2000, pp. 69-82
- 77 -
5
E 0 >
.c
0
-o 2
0) =
0 1 2 3 4 5 6
Elapsed Time (h)
Fig. 8 Typical headeut movement versus time.
In earthen spillways the presence of a more erodible material layer in the soil profile has been observed to cause headcuts to move at an accelerated rate. To examine this influence, a 152-mm thick sand layer was placed at the bottom of a 1.2-rn tall overfall. The sand layer extended 4.6 m upstream into the 9.2-rn Ionia fill section. Therefore, the headcut advance rate was examined for a compacted cohesive soil with and without the sand layer. For a highly erodible overburden material, the sand layer had little influence on the advance rate. However, as the erosion resistance of the overburden material increased, the sand layer dramatically accelerated the headcut advance rate (Fig. 10; Robinson and Hanson, 1995). The sand material was removed by the reverse roller acting against the headcut face, and the unsupported material mass failed and was swept downstream. As the moisture content and dr y density increased, the headcut advance rate decreased without the sand layer. t) 18
-
E
16
0)
14 12
10
0) 0 C 8 > 6 4:
4 2 0 1.50 1.55 1.60 1.65 1,70 1.75 1.80 1.85
Average Dry Density (Mg/rn3) Fig. 9 Advance rate versus dry density for a compacted cohesive soil. 78 -
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The tailwater level downstream of an overfall was also examined while holding the discharge, overfall hei ght, and soil , conditions constant. intermediate tailwater levels with a backwater-to-overfall height ratio of approximately 0.8 produced the lar g est headcut advance rates (Fig. I I). A concrete floor limited the erosion depth. so headcut erosion was driven primarily by scour at the base of the overfall. Low tailwaters did not efficiently transfer flow energy to the base of the overtull. and high tailwaters tended to transfer energy downstream. Tailwater level' downstream of the overfall was observed to vary the advance rate hv a factor of 2,6 to 7.5 over the ran g e of soil conditions tested (Robinson and Hanson, 1996b). This study suggests that predictions of headcut advance must incorporate accurate backwater information. 'The tests described above were depth limited because the concrete flume floor was not erodible. While depth limiting conditions are frequently observed in the field, the influence of vertical scour was also of interest. Scour at the base of an overfall acts to deepen and destabilize the headcut. All tests were conducted with a low tailwater level to assure a worst case scour condition. Soil placement and compaction methods influenced the rate of scour, with observations showing increased vertical scour rates as the placed soil density decreased. For the range of overf'all heights examined, the vertical scour rate was not strongly influenced h overfall height (Robinson et at.. 1996). A typical scour profile is shown as Fi g ure 12. - 10-1
4
8 7.
6 5, 4 - Sand Layer Extends 4.6m
cc 3 2
1
00
I
0 Density 1.68 glcc, Moisture 9.2% V Density 1.59 glcc, Moisture 11.6% 0 Density 1.79 g/cc, Moisture 14.4% A Density 1.79 g/cc, Moisture 14.4% 93. Mechanics ot iCi scour di>nstream of a headeuc .1 Hiefraz,l R 3l.723-7
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