WATER RESOURCES RESEARCH, VOL. 43, W05411, doi:10.1029/2005WR004650, 2007
A numerical method for simulating one-dimensional headcut migration and overtopping breaching in cohesive and zoned embankments Zhengang Wang1,2 and David S. Bowles1 Received 8 October 2005; revised 5 October 2006; accepted 19 January 2007; published 4 May 2007.
[1] An erosion and force/moments equilibrium-based numerical method is proposed to
simulate one-dimensional headcut migration in cohesive embankment overtopping breaches and to simulate the one-dimensional breach process of zoned embankment dams before they fully breach through. At each time step of the simulation the depths and velocities of the breach outflow are calculated by solving the one-dimensional shallow water equations, three-dimensional slope stability is checked, and the eroded soil and instable soil block are removed. The method was tested using data from a U.S. Department of Agriculture Agricultural Research Service cohesive embankment and the Yahekou zoned fuse plug. Test results showed that the proposed method predicts well the one-dimensional headcut shape in the cohesive dam and the breach shape in the zoned embankment dam provided that the inputs are appropriately assigned. Sensitivity studies showed that the breach processes for a weakly cohesive dam under a small overtopping depth and a highly cohesive dam are controlled by erosion only. They also showed that the breach processes for a weakly cohesive dam under a relatively large overtopping depth, a noncohesive dam, and a zoned embankment dam are all controlled by erosion and force/moments equilibrium. Citation: Wang, Z., and D. S. Bowles (2007), A numerical method for simulating one-dimensional headcut migration and overtopping breaching in cohesive and zoned embankments, Water Resour. Res., 43, W05411, doi:10.1029/2005WR004650.
1. Introduction [2] A headcut is a vertical or near-vertical drop or change in elevation of a stream channel, rill, or gully, which occurs where there is a concentrated flow [Hanson et al., 2001b]. Headcuts occur as part of the breach development process in cohesive embankment dams [Ralston, 1987; AlQaser, 1991; AlQaser and Ruff, 1993; Hanson et al., 2001a, 2001b, 2005a, 2005b] and in gully erosion [Bennett, 1999; Collison and Simon, 2001; Alonso et al., 2002]. The migration of headcuts is a mixture of particle erosion and mass failure [Collison and Simon, 2001]. Predicting the rate of headcut migration is a complex problem [Hanson et al., 2001b]. The objective of this paper is to propose a numerical method for simulating the formation and migration of a one-dimensional (1-D) headcut in a cohesive embankment dam overtopping breach, and to apply this method in simulating the zoned embankment dam overtopping breach. [3] On the basis of the observation of two major embankment dam breaches, Ralston [1987] described the progressive erosion process as initiating in the lower reaches of the downstream face of the dam and the overfall advancing progressively headward while the base of the overfall deepens and widens. 1 Institute for Dam Safety Risk Management, Utah Water Research Laboratory and Department of Civil and Environmental Engineering, College of Engineering, Utah State University, Logan, Utah, USA. 2 Now at Michael Baker Jr. Inc., Alexandria, Virginia, USA.
Copyright 2007 by the American Geophysical Union. 0043-1397/07/2005WR004650
[4] AlQaser [1991] predicted the points where steps or headcuts would form on the downstream slope of an overtopped embankment using data from physical experiments. AlQaser [1991] observed that overfalls develop along the downstream face of the embankment during the initial phase of the failure, and that an overfall occurs because of the nonuniform erosion along the downstream face of the embankment induced by the flow associated with nonuniformly distributed tractive shear stresses. Using a momentum analysis for cross sections 1– 1 and 2 – 2 shown in Figure 1, AlQaser [1991] obtained equation (1) to calculate the local tractive shear stress as follows: " D
# 2 dD q2 dD Dx t ¼ gD cos q þ sin q þ cos q ð1Þ D dx gD3 dx 2
where t is the average tractive shear stress, g is the unit is the average flow depth, D is the flow weight of water, D depth at cross section 1 – 1, q is the unit flow rate, g is the acceleration due to gravity, and q is the angle between the downstream face of the embankment and the horizontal. [5] Energy dissipation-based and stress-based approaches have been proposed to calculate headcut migration for gullies in agricultural landscapes, earthen spillway, and cohesive embankment breaches. Energy dissipation-based approaches focus on energy at the overfall as the driving mechanism [De Ploey, 1989; Temple, 1992; Moore et al., 1994; Temple and Moore, 1994]. These approaches have a
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Figure 1. Schematic presentation of gradually varied flow momentum analysis [AlQaser, 1991]. material-dependent factor that requires the user to define the parameters needed to predict the headcut migration rate [Hanson et al., 2001b]. Stress-based approaches calculate the headcut migration rate based on soil strength, erodibility, and hydraulic stress [Hanson et al., 1997, 2001b]. Hanson et al. [1998] and Hanson and Cook [2004] reported that soil erodibility and headcut migration are influenced by compaction, water content, dry unit weight, and soil type. Hanson et al. [1998] reported that increased compactive effort and increased water content up to an optimal value increase resistance to erosion. [6] On the basis of observations from seven large-scale embankment dam overtopping failure tests, Hanson et al. [2005a] proposed a four-stage erosion process for cohesive earthen embankment dams. Stage I begins when the flow initially overtops the dam and ends when the cascading overfalls on the downstream face develop into one large headcut. Stage II is the process of headcut migration from the downstream crest to the upstream crest. Stage III begins from when the embankment crest starts to lower and continues until the downward erosion of the crest has virtually stopped. Stage IV begins after the breach channel has eroded to the base of the upstream toe and continues with breach channel widening. On the basis of the concept of an impinging jet, Temple et al. [2005] and Hanson et al. [2005b] proposed and tested a computational model for simulating headcut migration in stages II and III, which separately predicts headcut migration and downcutting. [7] Collison and Simon [2001] explained gully head retreat in terms of the stresses generated by slope unloading and the loss of suction via flow through a tension crack. In their work, gully retreat is represented by the cycle of stress release, hollow formation, fissure flow, head collapse, and debris removal. [8] Alonso et al. [2002] developed a model to predict scour and migration of headcuts at scales typical of rills on hillslopes, crop furrows on agricultural fields, and ephemeral gullies in upland areas. Bennett [1999] studied the effect of bed slope on the growth and migration of headcuts in rills. Bennett et al. [2000] reported an experimental methodology to examine actively migrating headcuts in a laboratory
channel. Bennett and Casalı´ [2001] studied the effect of initial overflow step height on headcut migration. [9] Powledge et al. [1989] described the overtopping breach process of a zoned embankment dam with an impermeable central core: the downstream soil was eroded; the crest of the core was lowered, which accelerates the erosion process; and the core then cantilevered and sequentially failed in tension. [10] Recently, zoned embankment dam overtopping breaches were investigated and modeled through the European Community funded CADAM and IMPACT projects. By assuming that a large part of the downstream noncohesive soil has been eroded, Mohamed et al. [2002] modeled the failure of the core using the three likely mechanisms of sliding of the core, overturning of the core, and bending of the core. [11] Regarding the function of the core in a zoned dam, Broich [2004] stated that ‘‘if a cohesive core is present, then the erosion is restricted to the downstream face, as long as the core can resist the water pressure.’’ Broich [2004] modeled the stability of the core using shearing and tilting, without using bending. [12] Wang and Bowles [2006a, 2006b] developed and tested an erosion and force/moments equilibrium-based three-dimensional (3-D) dam breach model for noncohesive earthen dam overtopping breaches. Wang and Bowles [2006c] further studied the development of multiple overtopping breaches for a long noncohesive dam under the actions of wind-generated waves and wave overtopping. [13] Noncohesive embankment dams, cohesive embankments dams, and zoned embankment dams with an impermeable central core have distinct differences in their overtopping breach processes, which can be explained by differences in embankment soil properties. In this paper, we revise our numerical method for the noncohesive embankment dam breach model [Wang and Bowles, 2006a, 2006b] to simulate the 1-D headcut migration observed in the cohesive embankment dam overtopping breach process and the zoned embankment dam breach process. In our noncohesive dam breach model [Wang and Bowles, 2006a, 2006b] we used the revised BREACH method [Fread, 1988] to simulate the noncohesive dam breach process
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Figure 2. Sliding soil profile. From Wang and Bowles [2006a], copyright 2006, with permission from Elsevier. before the dam crest is vertically eroded at least 0.61 m across the entire dam crest, such that the flow rate through the breach channel is sufficiently large that we were confident that our approach to modeling the overflow is reasonably accurate. In this paper, we also examine the breach process for noncohesive dams before they are fully breached through. The main revisions to our approach for the formation and migration of headcuts are as follows: solving the 1-D SWEs for 1-D headcut migration, using the erosion method for cohesive soils proposed by Hanson [1989a] of the USDA ARS, and revising the 3-D slope stability analysis for cohesive soils.
2. Theory for the Proposed Numerical Method 2.1. Erodibility of Soils [14] The surface erodibility of four soils in earthen channels under high stresses was studied by Hanson [1989a, 1990a]. Hanson [1989a] used the following equation to calculate the erosion rate, er: er ¼ kd ðt e t c Þ
ð2Þ
[2001] studied gully slope stability in headcut migration in their numerical model. In our 3-D noncohesive earthen dam breach model, we [Wang and Bowles, 2006a, 2006b] used the Hungr [1987] approach to represent 3-D slope stability along the main direction of flow in a breach channel before a dam is fully breached through, as shown in Figures 2 and 3. [16] Hungr [1987] and Hungr et al. [1989] used the following two assumptions in the 3-D Bishop’s simplified method: (1) The vertical intercolumn shear forces are neglected, as shown in Figure 3, and (2) the vertical force equilibrium of each column and the overall moment equilibrium of the column assembly are sufficient conditions to determine all the unknown variables. The following two additional forces act on the upper surface of each column in the dam breach problem and were considered by Wang and Bowles [2006a, 2006b]: Fw, which is the drag force on the plane 5-6-8-7 from the overtopping flow; and Nw, which is the force from the overtopping flow acting normal to the plane 5-6-8-7. In Figure 3, W is the weight of the soil; Ns is the supporting force on the plane 1-2-4-3 from the underlying soil; Fs is the friction force on the plane 1-2-4-3 from
where kd is an erodibility coefficient, t e is the local effective shear stress, and t c is the critical stress. The local effective shear stress, t e, was expressed by Hanson [1990a] as follows: t e ¼ gDS 0
0 2 n n
ð3Þ
where S 0 is the energy slope, n0 is the Manning’s roughness coefficient for the soil grain roughness, and n is the Manning’s roughness coefficient for the overall roughness. Hanson [1989b] stated that a value of n0 = 0.0156 was confirmed for bare earthen channels of cohesive soils. Hanson [1989a] calculated n using the following equation: n¼
pffiffiffiffi D2=3 S 0 u
ð4Þ
where u is the mean velocity. 2.2. Slope Stability Analysis [15] Hungr [1987] and Hungr et al. [1989] extended Bishop’s simplified method of slope stability to three dimensions. Aziz [1994, 2000] used the Hungr [1987] approach to pseudo three-dimensional (3-D) slope stability analysis in his dam breach model. Collison and Simon
Figure 3. Forces acting on a single column. From Wang and Bowles [2006a], copyright 2006, with permission from Elsevier.
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0 h 0 1 U¼ ;A ¼ ; SðUÞ ¼ gh s0 sf hu u2 þ gh 2u
ð8cÞ
where U are the state variables, A is the Jacobean matrix, S is the source term, h is the flow depth, s0 is the bottom slope, and sf is the energy slope, which can be estimated from Manning’s equation. Wang and Bowles [2006a] gave the total variation diminishing (TVD) finite difference scheme (FDM) for equations (8a) and (8c) as follows:
n
n e en en þ S ð U Þ Unþ1 ¼ U l E E
i i iþ1=2 i1=2
Figure 4. Earth pressure coefficient at rest, K0. the underlying soil; Py and (Py + DPy) are the forces from the neighboring cells acting normal to the planes 1-2-6-5 and 3-4-8-7, respectively; Tx and (Tx + DTx) are the shear forces from the neighboring cells acting on the planes 1-2-6-5 and 3-4-8-7, respectively; Px and (Px + DPx) are the forces from the neighboring cells acting normal to plane 1-5-7-3 and 2-6-8-4, respectively; Ty and (Ty + DTy) are the shear forces from the neighboring cells acting on the planes 1-5-7-3 and 2-6-8-4, respectively. 2.3. Coefficient of Earth Pressure at Rest [17] ‘‘The coefficient of earth pressure at rest is the ratio of the lateral to the vertical effective stresses in a soil consolidated under the condition of no lateral deformation, the stresses being principal stresses with no shear stress applied to the planes on which these stresses act’’ [Bishop, 1958], i.e., K0 ¼
s0h s0v
ð5Þ
e is the numerical flux, e where l = Dt/Dx, E S is the numerical source term, and the last two terms are given as follows: e niþ1=2 E
ð6Þ
where f0 is the effective friction angle of the soil. This equation can be simplified to the following: K0 ¼ 1 sin f0
2 X 1 n;l ¼ Rn;l Eniþ1 þ Eni A;iþ1=2 Fiþ1=2 2 l¼1
!
n ðDt Þ2 Ani n
e S Uiþ1 S Uni1 SðUÞ ¼ DtS Uni 4Dx i
ð10Þ
ð11Þ
where % $ 2 n;l n;l n;l n;l 1 Q Fn;l ¼ l a Q þ y a iþ1=2 A;iþ1=2 iþ1=2 A;iþ1=2 iþ1=2 an;l iþ1=2 ;
l ¼ 1; 2
ð12Þ
where the aA terms are the eigenvalues of the Jacobean matrix, A, and the RA terms are the eigenvectors of the Jacobean matrix, A, which are given as follows:
where K0 is the earth pressure coefficient at rest, sh0 is the horizontal effective stress, and sv0 is the vertical effective stress, as shown in Figure 4. K0 can be calculated using a theoretical method by Jaky [1944], as follows: 2 1 þ sin f0 0 3 K0 ¼ ð1 sin f Þ 1 þ sin f0
ð9Þ
i
aA ¼ RA ¼ R1A
a1A a2A
¼
R2A ¼
uC uþC
1 uC
ð13aÞ 1 uþC
ð13bÞ
pffiffiffiffiffi where C = gh is the celerity of the gravity wave, and ail+ 1/2 (l = 1,2) represents the components of Di+1/2U in the coordinate system Rli+1/2 (l = 1,2), which can be calculated as follows: Diþ1=2 U ¼
ð7Þ
X
aliþ1=2 Rliþ1=2
ðl ¼ 1; 2Þ
ð14Þ
l
[18] The total stress at one point in the soil is the sum of the effective stress and the pore pressure, p, at this point.
[20] The two-parameter limiters (TPL) use the following definitions of r and r+ from Wang et al. [2000]:
2.4. Numerical Simulation of the 1-D Dam Break Outflow [19] We expressed the 1-D shallow-water equations (SWEs) as follows [Wang and Bowles, 2006a]: @U @E þ ¼ SðUÞ @t @x
ð8aÞ
r ¼
Di1=2 w Diþ1=2 w
ð15aÞ
rþ ¼
Diþ3=2 w Diþ1=2 w
ð15bÞ
@E , then equation (8a) can be Let the Jacobean matrix, A = @x expressed as:
where w is the independent variable in a scalar hyperbolic conservation law [Wang et al., 2000]:
@U @U þA ¼ SðUÞ @t @x
@w @f ðwÞ þ ¼ 0: @t @x
ð8bÞ
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ð16Þ
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and (8c) using the TVD scheme in equation (9) and the TPL superbee limiter in equation (17). A pseudo gate is considered in the middle of the embankment crest. At time zero of the hydraulic calculations, the initial upstream pool elevation is set at each point upstream from the pseudo gate and the initial dry bed condition is set at each point downstream from the pseudo gate. The downstream condition is calculated based on normal flow using Manning’s equation. It can be seen from the following examples that stable hydraulic results are attained after some time into the simulation and these are used in the erosion and slope stability analyses. The case of 1-D steady flow over a bump was studied by Goutal and Maurelz [1997], Vazquez-Cendon [1999], Zhou et al. [2001], Valiani et al. [2002], Ying et al. [2004], and Wang and Bowles [2006a]. The initial conditions were a water depth of 0.33 m and zero velocity everywhere; the upstream boundary condition is a unit inflow of 0.18 m2/s; and the downstream boundary condition is a water depth of 0.33 m. 3.2. Soil Erosion [25] The erosion rate was calculated using Hanson’s [1989a] method, which is shown in equation (2) and evaluated using equations (3) and (4). In equation (2), the erodibility coefficient, kd, must be known. Hanson [1990b] demonstrated that the field jet test to measure kd, for the soil in an embankment.
Figure 5. Flowchart of the overall methodology. [21] Roe’s superbee limiter in TPL format is given below [Yee, 1987]: Qðr ; rþ Þ ¼ max½0; minð2r ; 1Þ; minðr ; 2Þ
þ max½0; minð2rþ ; 1Þ; minðrþ ; 2Þ 1
ð17Þ
[22] Wang and Bowles [2006a] validated the numerical scheme in equation (9) for the 1-D theoretical dam break with initially dry and initially wet beds, a 1-D steady flow over a bump, a 1-D hydraulic jump in a horizontal rectangular channel, and a 1-D dam break with a bottom slope. Among the investigated limiters, the TPL superbee limiter shown in equation (17) performed the best for the initially dry bed 1-D problem [Wang and Bowles, 2006a].
3. Methodology [23] In this section we revise our force/moments equilibrium-based numerical method used in our noncohesive dam breach model [Wang and Bowles, 2006a, 2006b] to simulate the 1-D headcut migration process for cohesive embankment overtopping breach. At each time step of the simulation, the embankment dam breach outflow is calculated by solving the 1-D SWEs and then erosion is calculated at each spatial point. The 3-D slope stability is checked and the eroded soil and the instable soil block are removed. The flowchart for the overall methodology in our numerical method is shown in Figure 5. The model uses the 3-D cells proposed by Wang and Bowles [2006a, 2006b] for the erosion process and the 3-D slope-stability analysis. The basic and derivative cells used in this model are shown in Figure 6. 3.1. Hydraulic Calculation [24] The water depth and flow velocity at each grid point are calculated by solving the 1-D SWE shown in equations (8a)
3.3. Slope Stability Analysis [26] The slope stability along the flow direction was checked using the same method that was used in our 3-D noncohesive earthen dam breach model [Wang and Bowles, 2006a, 2006b] and as described below. [27] Consider the moment equilibrium around the reference axis as shown in Figure 3, when F0 > 1, as follows: X
X c A0 þ ðNs p A0 Þ tan f Ns LNs F0 X X LFs T LT þ Nw LNw þ Fw LFw þ H LH ¼ 0
W LW
X
ð18Þ
where F0 is the safety factor; c is the cohesive strength of the soil; LW, LNs, LFs, LNw, and LFw are the moment arms of W, Ns, Fs, Nw, and Fw, respectively; H is the resultant of all horizontal components of applied point loads with a moment arm, LH; T is the friction force given by the soil block outside of the potential sliding soil block with a moment arm LT; and F0 is the quotient obtained by dividing the resisting moments by the driving moments. [28] When the soil block loses its moment equilibrium (i.e., F0 < 1), F0 is calculated as follows: P
F0 ¼ P
½c A0 þ ðNs p A0 Þ tan f LFs þ T LT P P P W LW Ns LNs þ Nw LNw þ Fw LFw þ H LH ð19Þ
where A0 is the ‘‘true area of the column base’’ [Hungr, DxDy 1987] on the failure surface, expressed as A0 = cos a0 . The soil block with the maximum soil volume for all blocks with safety factors less than 1 is removed at each time step of the simulation.
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Figure 6. Basic and derivative cells used in this model. From Wang and Bowles [2006a], copyright 2006, with permission from Elsevier. [29] In Figure 2 we consider the anticlockwise driving moments around the reference axis to be positive, and the clockwise resisting moments around the reference axis to be negative. Thus, at each cell shown in Figure 6, the sign of each moment in equation (19) needs to be determined. [30] In the current model, the phreatic surface in the embankment was specified: the soil above the phreatic surface was assumed to be dry and the soil below the phreatic surface was assumed to be saturated; and neither the suction in the soil nor the stress release due to unloading were considered. The initial consolidation stress, Py , shown in Figure 3 is calculated as follows: Z
Py ¼ A1265
K0 s0v dA
ð20Þ
where A1 – 2 – 6 – 5 is the area of the plane 1-2-6-5 (see Figure 3), and sv0 is the vertical effective stress. Tx is calculated by Tx ¼ c A1265 þ Py tan f
ð21Þ
The method of AlQaser [1991] in equation (1) is used to calculate the local tractive shear stress. The drag force of the overtopping flow is calculated as the product of the local tractive shear stress and the area of flow.
4. Application to a Cohesive Soil Dam [31] Hanson et al. [2001a, 2005a] reported seven overtopping tests for homogenous cohesive embankments. The
headcut migration centerline profiles were reported for two of these tests by Hanson et al. [2001a]: embankment 1 with soil 2 and embankment 2 with soil 2. Embankment 1 with soil 2 had a much greater erodibility at the top of the pilot channel and on the downstream face of the embankment than for the inner embankment soil, which appears to display approximately homogeneous erodibility. Embankment 2 with soil 2 displays nonhomogeneous erodibility. We used embankment 1 with soil 2 to test our numerical method in this paper because it appears to best satisfy the homogeneity assumption in the inner embankment soil material. 4.1. Embankment 1 and Model Inputs for Base Case [32] Hanson et al. [2001a, 2005a] reported that embankment 1 with soil 2 was constructed in the spring of 1998 and was tested in 1999. The embankment was 2.29 m high, 7.3 m wide, and had downstream and upstream slopes of 1:3 (V:H). The notch (pilot channel) was 0.46 m deep, 1.83 m wide, and had a length of 4.6 m. The soil was nonplastic SM silt sand with 63% sand, 31% silt, and 6% clay. The unit weight of the soil was 1,730 kg/m3. Soil erodibility was 0.000002 m3/(N s). The critical shear stress of the soil was 0.14 Pa. The measured upstream pool elevation is used as a model input in the test and is shown in Figure 7 after converting the elevation datum. [33] The reservoir was filled in advance of testing to a depth of 1.2 m. On the day of testing the reservoir was
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Figure 7. Used upstream pool elevation for embankment 1 with soil 2 [Hanson et al., 2001a, 2005a]. completely filled and the embankment test section was overtopped [Hanson et al., 2001a]. According to Terzaghi et al. [1996], the permeability, k, of ‘‘very fine sands, organic and inorganic silts, mixtures of sand silt and clay, glacial till, stratified clay deposit, etc.’’ ranges between 105 and 109 m/s. We assumed that the permeability of this nonplastic SM silt sand [Hanson et al., 2001a], was 105 m/s. Simple estimation showed that the water table in the dam does not change much if the embankment breaches in 10 hours. Collison and Simon [2001] also pointed out that many gully heads maintain unsaturated pore conditions throughout rainfall and flow events. Therefore we assumed that the phreatic surface in the embankment does not change during the overtopping breach process as shown in Figure 8, without calculation. The phreatic surface on the upstream side was assumed to be 1.2 m deep, which was the recorded prefilling water surface elevation according to Hanson et al. [2001a]. The downstream face of the dam was dry and therefore the assumed phreatic surface connects with the downstream face at a point a little higher than the toe. [34] For the slope stability analysis, we assumed that the cohesive strength, c, was 2,000 Pa, and that the internal friction angle, f, was 30°. The low value for cohesion is supported by the 6% clay content and the 63% sand content justifies an internal friction angle that is higher than for clay but lower than for pure sand. [35] As shown by the measured results shown in Figure 9, the embankment eroded quickly in the first 19 min and especially in the first minute when the bottom of the embankment at a height of 0.16 m eroded 2.22 m along the flow direction. Between 1 and 19 min, the top of the embankment was vertically eroded 0.11 m at station 10.7 m, but from 19 to 85 min, the top of the embankment remained nearly unchanged. The rapid erosion on the top of the dam and along the downstream face of the embankment during the first 19 min was too rapid to simulate using the same
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erodibility coefficient as predicted the erosion well after this initial period. Therefore we assigned a new initial condition at 19 min by making the following two adjustments in the numerical results: (1) set the top elevation of the embankment to be the same as the measured value upstream from the middle of the embankment crest at 19 min and (2) set the top elevation of the embankment to be the highest measured elevation downstream from the middle of the embankment crest at 19 min. [36] One dam section 1.83 m in width and height, which match the width and height of the pilot channel of embankment 1 with soil 2 [Hanson et al., 2001a, 2005a], was chosen for the numerical test. Even though this soil block is only 1.83 m wide, we put the consolidation stress on both of sides, and thus it simulates the true stress situation in the 3-D slope stability analysis. [37] The time step in our numerical method is 6 min but it was reduced to lower values to match the timing of the erosion measurements in the field test. When solving the 1-D SWE, the slope of the downstream channel was set to 1/200 to obtain normal flow downstream of the breach and Manning’s n was set to 0.02 s/m1/3. 4.2. Results of the Numerical Test [38] The measured centerline profiles [Hanson et al., 2001a] and the calculated centerline profiles using three grid sizes (0.305 m, 0.457 m, and 0.610 m) are shown in Figure 9 for USDA ARS embankment 1 with soil 2 for times ranging from 0 to 407 min. To study the sensitivity of our model, we defined the values of the model parameters for the base case as follows: the unit weight of the soil was 1,730 kg/m3, soil erodibility was 0.000002 m3/(N s), the critical shear stress was 0.14 Pa, the grid size was 0.457 m, and the dam was considered to have the phreatic surface shown in Figure 8. The detailed headcut migration processes calculated by our numerical method for the base case are shown in Figure 10 for times ranging from 0 min to 407 min (6 hours and 47 min). [39] From Figure 9 it can be seen that the centerline profiles calculated using our model match the measured profiles. The differences between the numerical results and the measured results at the beginning of the breach are due to a larger erodibility coefficient kd for the surface soil on the top of the pilot channel and on the downstream face of the embankment than for the soil inside the embankment. After 19 min, the headcut shape, including downstream slopes, are well predicted, although our predicted headcut migration rate is slightly different from the measured value. Hence these results demonstrate that our proposed method has good capability to predict the 1-D headcut formation and migration; and this also demonstrates that the assumed phreatic surface and estimated soil properties are reasonable.
Figure 8. Assumed phreatic surface in embankment 1 with soil 2. 7 of 17
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Figure 9. Measured [Hanson et al., 2001a] and calculated centerline profile for embankment 1 with soil 2 for the base case. [40] From Figure 9, it can be seen that our method is not very sensitive to grid size. However, the grid size should be selected to be small enough to represent reasonably the true shape of the dam, but not so small that it will unnecessarily slow down the calculation speed or perhaps causing a computer memory overflow. 4.3. Sensitivity to Soil Properties [41] We studied the sensitivity of our numerical method to changes in cohesion, internal friction angle, and erod-
ibility of the embankment soil and phreatic surface in the dam for a grid size of 0.457 m. [42] For the case shown in Figure 11a, we increased the cohesion to 5 KN and kept the other soil properties the same as for the base case, which is shown in Figure 9. For the case shown in Figure 11b, we further increased the cohesion to 20 KN, reduced the internal friction angle to 15°, and raised the water table so that the dam is saturated throughout. By comparing Figure 9 and Figure 11a, it can be seen that a higher cohesion resulted in a slower headcut migration rate. However, it can be seen by comparing Figures 11a
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Figure 10. (a –r) Time sequence for the calculated headcut migration process for embankment 1 with soil 2 for the base case. and 11b that the predicted headcut migration rate was about the same for the case in which the cohesion was further increased. For the case shown in Figure 9, the breach process is controlled by erosion and force/moments equilibrium. The cases shown in Figures 11a and 11b are controlled by erosion only, and therefore they are not
sensitive to the values of the soil properties except for the erodibility. [43] For the cases shown in Figures 11c – 11e, we reduced the cohesion to 1.5 KN, reduced the internal friction angle to 15°, and raised the water table so that the dam is saturated throughout, and kept the other soil properties the same as in the base case, which is shown in Figure 9. By comparing
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Figure 11. Calculated centerline profiles for sensitivity studies on soil properties for embankment 1 with soil 2: (a) c = 5 KN/m2, f = 30°, and kd = 0.000002 m3/(N s); (b) c = 20 KN/m2, f = 15°, and kd = 0.000002 m3/(N s), dam is saturated; (c) c = 1.5 KN/m2, f = 30°, and kd = 0.000002 m3/(N s); (d) c = 2 KN/m2, f = 15°, and kd = 0.000002 m3/(N s); (e) c = 2 kN/m2, f = 30°, and kd = 0.000002 m3/(N s), dam is saturated; (f) c = 0 kN/m2, f = 30°, and kd = 0.000002 m3/(N s); (g) c = 2 kN/m2, f = 30°, and kd = 0.000003 m3/(N s); and (h) c = 2 kN/m2, f = 30°, and kd = 0.000001 m3/(N s). 10 of 17
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Figure 12. Sensitivity of calculated centerline profile to upstream water surface levels for embankment 1 with soil 2: (a) c = 2 KN/m2, f = 30°, and kd = 0.000002 m3/(N s), upstream water surface level raised 0.1 m, and (b) c = 5 KN/m2, f = 30°, and kd = 0.000002 m3/(N s), upstream water surface level raised 0.2 m.
the results shown in Figures 9 and 11c – 11e, it can be seen that a lower cohesion resulted in a faster headcut migration rate, a smaller internal friction angle gave a faster headcut migration rate, and a higher water table lead to a slightly faster headcut migration rate. [44] For the case shown in Figure 11f, we reduced the cohesion to zero, and kept the other soil properties the same as the base case, which is shown in Figure 9. Thus Figure 11f represented the breach process in a noncohesive dam. For this case the beginning stage of the breach process still looks like a headcut, but with a smoother downstream slope compared with a cohesive soil dam. The breach shape shown in Figure 11f matches the predetermined breach shape adopted in the BREACH model by Fread [1988]. It also matches the predetermined breach shape adopted by Visser [1998] in his sand dike breach model, which was based on observations from field tests. After the top of the dam is fully eroded through, and the erosion passes the point A, as shown in Figure 11f, the downstream slope tends to be instable, such that a much larger soil block will be removed. After the top of the noncohesive dam was predicted to be fully eroded through, the breach rate was normally predicted to be much faster than before point A is reached; and this can be clearly seen from physical model tests undertaken by HR Wallingford as part of the IMPACT Project [Morris, 2002]. [45] For the cases shown in Figures 11g and 11h, we increased the erodibility to 0.000003 m3/(N s) and reduced the erodibility to 0.000001 m3/(N s), respectively, while keeping the other soil properties the same as the base case, which is shown in Figure 9. By comparing Figures 9, 11g, and 11h, it can be seen that our method is sensitive to the erodibility coefficient with a larger value of this coefficient leading to a higher headcut migration rate. 4.4. Sensitivity to Upstream Water Surface Level [46] We studied the sensitivity of our numerical method to changes in the upstream water surface levels using a grid size of 0.457 m. For the cases shown in Figures 12a and 12b, we increased the upstream water surface level for the entire breach process by 0.1 m and 0.2 m, respectively,
compared with the cases shown in Figures 9 and 11a, respectively. [47] Comparing the results in Figures 9, 11, and 12, it can be seen that the breach process for a weakly cohesive soil embankment dam is sensitive to the upstream water surface level. Even a small increase in upstream water surface level results in a faster breach rate. The breach process for a weak cohesive soil embankment dam is erosion-controlled when the overtopping depth is relatively small, as shown in Figure 11a; whereas, it is controlled by erosion and force/ moments equilibrium when the overtopping depth is relatively large, as shown in Figure 12b. For a weakly cohesive soil embankment dam with the given soil properties (cohesion, internal friction angle, unit weight, erodibility, compaction, and water content during construction) and phreatic surface, the overtopping depth, which is determined by the upstream water surface level, is a critical factor such that the breach process is controlled by erosion only or by erosion and force/moments equilibrium. 4.5. Conclusions from Sensitivity Studies [48] On the basis of the sensitivity studies, we conclude the following for cohesive dams. [49] 1. If the slope is stable, our method is not sensitive to cohesive strength, internal friction angle, and phreatic surface in the dam; and the breach process is erosion controlled. This case occurs in one of the following two situations: (1) a soil with high cohesion and the combination of cohesion, internal friction angle, and phreatic surface in the dam leading to a stable slope or (2) a soil with low cohesion and a small overtopping depth, as was the case for embankment 1 with soil 2. [50] 2. If the slope tends to be instable, our method is sensitive to cohesive strength, internal friction angle, and phreatic surface in the dam; and the breach process is controlled by erosion and force/moments equilibrium. This case occurs in one of the following two situations: (1) a soil with low cohesion and a relatively large overtopping depth and (2) a noncohesive soil. In this case, a lower cohesion or a small internal friction angle results in a faster breach rate;
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Figure 13. Measured upstream and downstream water level for the Yahekou fuse plug [Loukola and Huokuna, 1998]. and a higher phreatic surface in the dam results in a slightly faster breach rate.
5. Application to a Zoned Embankment Dam [51] We applied our numerical method to simulate the breach process in a zoned embankment dam with a noncohesive shell and an impermeable cohesive central core using data from the Yahekou fuse plug [Loukola and Huokuna, 1998; Loukola et al., 1998; Peiter, 2002]. 5.1. Yahekou Fuse Plug and Model Inputs [52] The Yahekou fuse plug was located in Henan Province in China. It was 5.6 m high, 41 m long at the top, 36 m long at the bottom, and had a 4 m wide crest. The upstream and downstream slopes were 1:3 and 1:2.5 (V:H), respectively. The pilot channel in the fuse plug was 1.3 m deep and 1.5 m wide. The core was 1.08 m wide at the top of the pilot channel and 2.5 m wide at the bottom of the fuse plug at elevation 149.5 m. Both the upstream and downstream slopes of the core were 1:0.17 (V:H). The upstream and downstream water surface elevations are plotted in Figure 13 based on information provided by Loukola and Huokuna [1998]. The unit weight, internal friction angle, and cohesion of the core were 16.1 kN/m3, 18°, and 23.5 kPa, respectively. The unit weight, internal friction angle, and cohesion of the sand in the shell were 14.9 kN/m3, 33°, and 0 N/m2, respectively. [53] The breach initiated in the pilot channel, which was located at one end of the dam. After the dam was fully breached through, the breach channel only widened in one direction because the other direction was confined by nonerodible natural material [Loukola et al., 1998]. The overall breach process described by Loukola et al. [1998] is a threedimensional process. We modeled the breach process at the center of the pilot channel using our proposed numerical method and compared our results with the measured centerline profile reported by Loukola et al. [1998]. Following the assumption in the BREACH model [Fread, 1988], we assumed that the soil upstream from the core was saturated and that the core and the soil downstream of the core were dry under the condition of an impermeable core. We used a grid size of dx = 0.61 m and a time step of 1 min. In our model, a cell is a rectangular column, as shown in Figure 6, with the same soil properties throughout each cell. The
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average depth of the core is 1.8 m from the top of the pilot channel to the foundation. Thus, in this model representation, the core was located 16.8 m from the upstream toe, it was 1.8 m wide, and it does not change in width along the vertical direction. [54] A dam section 1.22 m wide and 4.3 m high was chosen for the numerical test. Even though this soil block is only 1.22 m wide, it preserves the consolidation stress on both sides and thus it is an accurate representation in the 3-D slope stability analysis. When solving the 1-D SWE, the slope of the downstream channel was set to 0.022, which is consistent with information given by Loukola and Huokuna [1998] to obtain a normal flow condition and Manning’s n was set to 0.02 s/m1/3. [55] We assumed that the erodibility of the soil in the shell was 0.000048 m3/(N s) and that the erodibility of the material in the core was 0.0000085 m3/(N s). We also assumed that the critical shear stress in the sand in the shell and in the core were 0.1 Pa and 5 Pa, respectively. For the sensitivity studies we defined the base case parameter values as follows: the unit weight, internal friction angle, cohesion, erodibility, and the critical shear stress are 16.1 kN/m3, 18°, 23.5 kPa, 0.0000085 m3/(N s), and 5 Pa, respectively for the core material; and 14.9 kN/m3, 33°, 0 N/m2, 0.000048 m3/(N s), and 0.1 Pa respectively for the shell material. 5.2. Results for the Base Case [56] The calculated and measured centerline profiles are presented in Figure 14 and the breach process is shown in Figure 15. On the basis of the measured breach process in the Yahekou fuse plug, the process for a central zoned embankment dam can be classified as a three-stage process: (1) erode the downstream noncohesive soil and remove the instable part, (2) erode the impermeable core and upstream noncohesive soil, and remove the instable part of the cantilevered core and the upstream soil, and (3) laterally erode the breach channel after the dam is fully breached through. From Figure 14 it can be seen that our numerical method successfully predicts the breach process in this zoned embankment dam during the first two stages. The third stage describes the lateral widening after the dam is fully breached through, which is not studied in this paper. [57] For an overtopping breach of a zoned embankment dam, Powledge et al. [1989, p. 1061] state the following: ‘‘Once overtopping occurs, the seepage existing on the downstream slope accelerates slope erosion.. . .Surface slips and flows quickly occur and propagate rapidly up the slope. Once this phenomenon reaches the crest, the crest is lowered, allowing greater flow rates, which accelerates the erosion process.. . .The impermeable element then cantilevers and sequentially fails in tension as more of the downstream granular fill is washed away.’’ Our model predictions for the Yahekou fuse plug match the descriptions of Powledge et al. [1989] and the observation by Broich [2004] that ‘‘the erosion is restricted to the downstream, as long as the core can resist the water pressure.’’ 5.3. Sensitivity Study on Erodibility [58] We studied the sensitivity of our numerical method to changes in the erodibility of the sand in the shell and
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Figure 14. Measured [Loukola and Huokuna, 1998] and calculated centerline profile at the center of the pilot channel of Yahekou fuse plug dam.
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Figure 14 for the base case, it can be seen that a higher erodibility of the sand in the shell results in a faster breach process, and a smaller erodibility of the sand in the shell results in a slower breach process. [60] While keeping the erodibility of the sand in the shell unchanged at 0.000048 m3/(N s), we reduced the erodibility of material in the core to 0.000005 m3/(N s) and increased it to 0.000001 m3/(N s) in two sensitivity runs. The results for these runs are shown in Figures 16c and 16d, respectively. By comparing these results with those in Figure 14 for the Base case, it can be seen that a higher erodibility of the material in the core results in a faster breach process, and a smaller erodibility of the material in the core results in a slower breach process. If the erodibility of the material in the core is as small as 0.000001 m3/(N s), as shown in Figure 16d, our model predicts that the dam does not fully breach under the given upstream water surface levels. 5.4. Sensitivity Study on Upstream Water Surface Level [61] The results in Figures 16e and 16f are for the same conditions as those in Figures 16c and 16d, respectively, except that the upstream water surface levels were increased by 0.3 m and 1 m over the entire duration of the breach process, respectively. From Figures 16e and 16f, it can be seen that increasing the upstream water surface level results in a faster breach process. However, if the material in the core has a high cohesion, the cantilevered core element can remain in place under a relatively high overtopping depth. As a result, the zoned embankment dam is not as sensitive to upstream water surface level as a dam with a weaker cohesive material in the core.
6. Conclusions
Figure 15. Calculated breach process in the time sequence at the center of the pilot channel of Yahekou Dam. material in the core, and the upstream water surface level, as shown in Figure 16. [59] While keeping the erodibility of the material in the core unchanged at 0.0000085 m3/(N s), we reduced the erodibility of the sand in the shell to 0.000025 m3/(N s) and increased it to 0.0001 m3/(N s) in two sensitivity runs. The results from these runs are shown in Figures 16a and 16b, respectively. By comparing these results with those in
[62] An erosion and force/moments equilibrium-based numerical method is proposed to predict 1-D headcut migration for cohesive embankment overtopping breaches, and the zoned embankment dam overtopping breach process before the dam is fully breached through. This method is a revision of the numerical method used in our noncohesive dam breach model [Wang and Bowles, 2006a, 2006b]. At each time step, the method calculates the flow depth and flow velocity by solving the 1-D SWE using the TVD finite difference scheme proposed by Wang and Bowles [2006a]. It then calculates the erosion at each point using the method of Hanson [1989a], checks the 3-D slope stability using the simplified Bishop method by Hungr [1987], and removes eroded soil and the instable soil block. [63] Our numerical method was tested using a USDA ARS cohesive embankment test (embankment 1 with soil 2 of Hanson et al. [2001a]) and a zoned Yahekou fuse plug dam [Loukola and Huokuna, 1998; Peiter, 2002]. Our numerical method predicts well the 1-D headcut shape in the cohesive dam test provided that the inputs are appropriately assigned. Test results also showed that our numerical method predicts well the breach shape of a zoned embankment dam with a central impermeable core before it is fully breach through. The predicted zoned embankment dam breach shapes before the dam is fully breached through matched the observed shapes [Loukola and Huokuna, 1998] very well. The predicted zoned embankment dam breach process also matched the observations of the breach process
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Figure 16. Calculated centerline profiles for different erodibility and upstream water surface level, Yahekou fuse plug: (a) kd of clay in the core 0.0000085 m3/(N s), kd of sand in the shell 0.000025 m3/ (N s); (b) kd of clay in the core 0.0000085 m3/(N s), kd of sand in the shell 0.0001 m3/(N s); (c) kd of clay in the core 0.000005 m3/(N s), kd of sand in the shell 0.000048 m3/(N s); (d) kd of clay in the core 0.000001 m3/(N s), kd of sand in the shell 0.000048 m3/(N s); (e) kd of clay in the core 0.000005 m3/ (N s), kd of sand in the shell 0.000048 m3/(N s), upstream water surface level raised 0.3 m; and (f) kd of clay in the core 0.000001 m3/(N s), kd of sand in the shell 0.000048 m3/(N s), upstream water surface level raised 1.0 m. by Powledge et al. [1989] and Broich [2004]. The predicted noncohesive dam breach shapes before it is fully breached through matched the predetermined breach shape in BREACH model by Fread [1988] and also matched the predetermined breach shape of Visser [1998] used in his sand dike breach model, which is based on observations in field tests.
[64] The 1-D headcut migration process for a highly cohesive soil dam is an erosion-controlled process, which is relatively insensitive to the changes in all soil properties except erodibility. The 1-D headcut migration process of for weakly cohesive soil dam is only controlled by erosion if the overtopping depth is relatively small, but is controlled by erosion and force/moments equilibrium if the overtopping depth is relatively large. The breach processes for a
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zoned embankment dam with an impermeable central core and a noncohesive dam are also controlled by erosion and force/moments equilibrium.
Notation aA eigenvalues of the Jacobean matrix, A. A Jacobean matrix. A0 true area of the column base on the failure surface, m2. c cohesive strength of the soil, N/m2. C speed of gravity wave, m/s. D flow depth, m. D average flow depth, m. E 1-D flux vector. e numerical flux. E F0 safety factor. Fs friction force in the underlying soil, N. Fw drag force from the overtopping flow, N. g gravity acceleration, m/s2. h flow depth, m. k permeability coefficient, m/s. kd erodibility coefficient, m3/ (N s). K0 earth pressure coefficient at rest. LX moment arm of force X, N m. n Manning’s roughness for the overall roughness, s/m1/3. 0 n Manning’s roughness coefficient for the soil grain roughness, s/m1/3. Ns supporting force in the underlying soil, N. Nw normal force from the overtopping flow, N. p pore pressure, N/m2. q unit flow rate, m2/s. Q limiter function with respect to r. RA eigenvectors of the Jacobean matrix, A. r slope with respect to flux. s0 bottom slope. sf energy slope. S source term. e S numerical source term. S0 energy slope. t time, s. u mean velocity of the flow, m/s. U state variables. w single variable of scalar hyperbolic conservation laws. W weight of the soil, N. x, y orthogonal Cartesian coordinates in physical plane, m. t c critical stress, N/m2. t e local effective shear stress, N/m2. t average tractive shear stress, N/m2. sh0 horizontal effective stress of the soil, N/m2. sv0 vertical effective stress of the soil, N/m2. er erosion rate, m/s. q the angle between the downstream face of the dam and the horizontal line, °. f internal friction angle of the soil, °. f0 effective internal friction angle of the soil, °. y dissipative function. g unit weight of water, N/m3. l ratio of time step to space step, s/m.
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[116] Acknowledgments. We appreciate Alessandro Falappa for making the CGLEnabledView (version 1.4) VC++ code available and granting users the right to use, copy, and modify it. With the necessary revisions, the CGLEnabledView (version 1.4) VC++ code is used to provide the visualization of the headcut migration process that uses the OpenGL. We thank the anonymous reviewers, the anonymous Associate Editor, and the Editor for their insightful comments and suggestions.
References Alonso, C. V., S. J. Bennett, and O. R. Stein (2002), Predicting headcut erosion and migration in upland flows, Water Resour. Res., 38(12), 1303, doi:10.1029/2001WR001173. AlQaser, G. N. (1991), Progressive failure of an overtopped embankment, Ph.D. dissertation, Colo. State Univ., Fort Collins. AlQaser, G., and J. F. Ruff (1993), Progressive failure of an overtopped embankment, paper presented at 1993 National Conference of Hydraulic Engineering, Am. Soc. of Civ. Eng., San Francisco, Calif., 25 – 30 July. Aziz, M. (1994), Dam breaching model, Ph.D. dissertation, Utah State Univ., Logan. Aziz, M. (2000), Dam breaching model, paper presented at 2000 Joint Conference on Water Resources Engineering and Water Resources Planning and Management, Environ. and Water Resour. Inst., Minneapolis, Minn., 30 July to 2 Aug. Bennett, S. J. (1999), Effect of slope on the growth and migration of headcuts in rills, Geomorphology, 30, 273 – 290. Bennett, S. J., and J. Casalı´ (2001), Effect of initial step height on headcut development in upland concentrated flows, Water Resour. Res., 37(5), 1475 – 1484. Bennett, S. J., C. V. Alonso, S. N. Prasad, and M. J. M. Ro¨mkens (2000), An experimental study of head-cut growth and migration in upland concentrated flows, Water Resour. Res., 36(7), 1911 – 1922. Bishop, A. W. (1958), Test requirements for measuring the coefficient of earth pressure at rest, paper presented at Brussels Conference on Earth Pressure Problems, Int. Soc. of Soil Mech. and Found. Eng., Brussels. Broich, K. (2004), Description of the parameter model DEICH-P, paper presented at 4th IMPACT Workshop, Univ. of Zaragoza, Zaragoza, Spain, 3 – 5 Nov. Collison, A., and A. Simon (2001), Modeling gully head-cut recession processes in loess deposits, in Soil Erosion Research for the 21st Century: Proceedings of the International Symposium, pp. 87 – 90, Am. Soc. of Agric. Eng., St. Joseph, Mich. De Ploey, J. (1989), A model for headcut retreat in rills and gullies, Catena Suppl., 14, 81 – 86. Fread, D. L. (1988), BREACH: An erosion model for earthen dam failures, report, Natl. Weather Serv., Silver Spring, Md. (Revised 1991.) Goutal, N., and F. Maurelz (1997), Proceedings of 2nd workshop on dambreak wave simulation, Rep. LNH HE-43/97/016/B, Nat. Hydraul. Lab., Chatou, France. Hanson, G. J. (1989a), Channel erosion study of two compacted soils, Trans. ASAE, 32(2), 485 – 490. Hanson, G. J. (1989b), Surface roughness with erosion of earthen channels, in Sediment Transport Modeling: Proceedings of the International Symposium, pp. 777 – 782, Am. Soc. of Civ. Eng., Reston, Va. Hanson, G. J. (1990a), Surface erodibility of earthen channels at high stresses: Part I—Open channel testing, Trans. ASAE, 33(1), 127 – 131. Hanson, G. J. (1990b), Surface erodibility of earthen channels at high stresses: Part II—Developing an in situ testing device, Trans. ASAE, 33(1), 132 – 137. Hanson, G. J., and K. R. Cook (2004), Apparatus, test procedures, and analytical methods to measure soil erodibility in-situ, Appl. Eng. Agric., 20(4), 455 – 462. Hanson, G. J., K. M. Robinson, and K. R. Cook (1997), Headcut migration analysis of a compacted soil, Trans. ASAE, 40(2), 355 – 361. Hanson, G. J., K. M. Robinson, and K. R. Cook (1998), Effects of compaction on embankment resistance to headcut migration, paper presented at 15th ASDSO Annual Conference, Assoc. of State Dam Safety Off., Las Vegas, Nev., 11 – 16 Oct. Hanson, G. J., K. R. Cook, and W. Hahn (2001a), Evaluating headcut migration rates of earthen embankment breach tests, paper 01-012080 presented at 2001 ASAE Annual Meeting, Am. Soc. of Agric. and Biol. Eng., St. Joseph, Mich. Hanson, G. J., K. M. Robinson, and K. R. Cook (2001b), Prediction of headcut migration using a deterministic approach, Trans. ASAE, 44(3), 525 – 531. Hanson, G. J., K. R. Cook, and S. L. Hunt (2005a), Physical modeling of overtopping erosion and breach formation of cohesive embankments, Trans. ASAE, 48(5), 1783 – 1794.
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Hanson, G. J., D. M. Temple, M. Morris, M. Hassan, and K. Cook (2005b), Simplified breach analysis model for homogeneous embankment: Part II, parameter inputs and variable scale model comparisons, paper presented at 25th USSD Annual Meeting and Conference, U. S. Soc. on Dams, Salt Lake City, Utah, 6 – 10 Jun. Hungr, O. (1987), An extension of Bishop’s simplified method of slope stability analysis to three dimensions, Geotechnique, 37, 113 – 117. Hungr, O., F. M. Salgado, and P. M. Byrne (1989), Evaluation of a threedimensional method of slope stability analysis, Can. Geotech. J., 26, 679 – 686. Jaky, J. (1944), The coefficient of earth pressure at rest, J. Soc. Hung. Archit. Eng., 78(22), 355 – 358. Loukola, E., and M. Huokuna (1998), A numerical erosion model for embankment dams failure and its use for risk assessment, paper presented at EU Concerted Action on Dam Break Modelling (CADAM) Munich Meeting, Univ. der Bunderswehr Mu¨nchen, Neubiberg, Germany, 8 – 9 Oct. Loukola, E., M. Huokuna, and L. X. Wang (1998), Test case 2: Yahekou dam breach test case, paper presented at EU Concerted Action on Dam Break Modelling (CADAM) Munich Meeting, Univ. der Bunderswehr Mu¨nchen, Neubiberg, Germany, 8 – 9 Oct. Mohamed, M. A. A., P. G. Samuels, M. W. Morris, and G. S. Ghataora (2002), Improving the accuracy of prediction of breach formation through embankment dams and flood embankments, paper presented at River Flow 2002—International Conference on Fluvial Hydraulics, Int. Assoc. of Hydraul. Eng. and Res., Louvain-la-Neuve, Belgium, 4 – 6 Sept. Moore, J. S., D. M. Temple, and H. A. D. Kirsten (1994), Headcut advance threshold in earth spillways, Bull. Assoc. Eng. Geol., 31(2), 277 – 280. Morris, M. (2002), Physical model 2: video, paper presented at 2nd IMPACT Project Workshop, SWECO Gro¨ner AS, Mo-i-Rana, Norway, 12 – 13 Sept. Peiter, P. (2002), The Chinese-Finnish cooperative research work on dambreak hydrodynamics, paper presented at 2nd IMPACT Project Workshop, SWECO Gro¨ner AS, Mo-i-Rana, Norway, 12 – 13 Sept. Powledge, G. R., D. C. Ralston, P. Miller, Y. H. Chen, P. E. Clopper, and D. M. Temple (1989), Mechanics of overflow erosion on embankments II: Hydraulic and design considerations, J. Hydraul. Eng., 115(8), 1056 – 1075. Ralston, D. C. (1987), Mechanics of embankment erosion during overflow, paper presented at the ASCE National Conference on Hydraulic Engineering, Am. Soc. of Civ. Eng., Williamsburg, Va., 3 – 7 Aug. Temple, D. M. (1992), Estimating flood damage to vegetated deep soil spillways, Appl. Eng. Agric., 8(2), 237 – 242. Temple, D. M., and J. S. Moore (1994), Headcut advance prediction for earth spillways, paper 94-2540 presented at 1994 ASAE International Winter Meeting, Am. Soc. of Agric. and Biol. Eng., St. Joseph, Mich.
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Temple, D. M., G. J. Hanson, M. L. Neilsen, and K. R. Cook (2005), Simplified breach analysis model for homogeneous and embankments: Part 1, background and model components, paper presented at 25th USSD Annual Meeting and Conference, U. S. Soc. on Dams, Salt Lake City, Utah, 6 – 10 Jun. Terzaghi, K., R. B. Peck, and G. Mesri (1996), Soil Mechanics in Engineering Practice, John Wiley, Hoboken, N. J. Valiani, A., V. Caleff, and A. Zanni (2002), Case study: Malpasset dambreak simulation using a two-dimensional finite volume method, J. Hydraul. Eng., 128(5), 460 – 472. Vazquez-Cendon, M. E. (1999), Improved treatment of source terms in upwind schemes for shallow water equations in channels with irregular geometry, J. Comput. Phys., 148, 497 – 526. Visser, P. J. (1998), Breach growth in sand-dikes, Ph.D. thesis, 173 pp. Delft Univ. of Technol., Delft, Netherlands. Wang, J. S., H. G. Ni, and Y. S. He (2000), Finite-difference TVD scheme for computation of dam-break problems, J. Hydraul. Eng., 126(4), 253 – 262. Wang, Z., and D. S. Bowles (2006a), Three-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodology, Adv. Water Resour., 29(10), 1528 – 1545. Wang, Z., and D. S. Bowles (2006b), Three-dimensional non-cohesive earthen dam breach model. Part 2: Validation and applications, Adv. Water Resour., 29(10), 1490 – 1503. Wang, Z., and D. S. Bowles (2006c), Dam breach simulations with multiple breach locations under wind and wave actions, Adv. Water Resour., 29(8), 1222 – 1237. Yee, H. C. (1987), Construction of explicit and implicit symmetric TVD schemes and their applications, J. Comput. Phys., 68, 151 – 179. Ying, X. Y., A. A. Khan, and S. S. Y. Wang (2004), Upwind conservative scheme for the Saint Venant equations, J. Hydraul. Eng., 130(10), 977 – 987. Zhou, J. G., D. M. Causon, C. G. Mingham, and D. M. Ingram (2001), The surface gradient method for the treatment of source terms in the shallowwater equations, J. Comput. Phys., 168, 1 – 25.
D. S. Bowles, Institute for Dam Safety Risk Management, Utah Water Research Laboratory, Utah State University, Logan, UT 84322, USA. (
[email protected]) Z. Wang, Michael Baker Jr. Inc., 3601 Eisenhower Ave. Suite 600, Alexandria, Virginia 22304, USA. (
[email protected])
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