Initiation of motion and scour burial of objects underwater

Ocean Engineering 131 (2017) 282–294

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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng

Initiation of motion and scour burial of objects underwater a

a,⁎

Sarah E. Rennie , Alan Brandt , Carl T. Friedrichs a b

MARK

b

Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723, USA Virginia Institute of Marine Science, Gloucester Point, VA 23062, USA

A R T I C L E I N F O

A BS T RAC T

Keywords: Mobility Scour burial UXO

Laboratory experiments were conducted to examine mobility and burial of objects, including onset of motion on a rigid bottom, scour burial into a sand bed, and the interplay between scour and motion onset. Experiments covered a range of object diameter-to-bottom roughness ratios (D/k) of relevance to mobility of unexploded ordnance (UXO). Results indicate that the critical mobility parameter (ΘUcrit) varies as ΘUcrit ≈ 1.6(D/k)−0.72 for cylinders under currents and waves. Modifications of this relation are also presented for accelerating flows. Scour experiments produced formulae for the equilibrium burial depth (Beq) for UXO as a function of the sediment Shields parameter (Θsed) of the form Beq/D = a2 Θsedb2. For current-induced live-bed scour, relatively large cylinders (D > 8 cm) result in a2 ≈1.3 and b2 ≈0.36. Smaller cylinders (D < 3 cm) and a tapered shape bury more easily (a2 ≈15 and b2 ≈1.1). An alternate, physics based relation for Beq incorporating additional length scales is also presented. For objects on mobile sand under accelerating flow, behavior was observed to be a contest between scour burial and the current speed reaching critical mobility. It is shown that by considering pit depth at the moment of mobility to be the effective bottom roughness, a general explanation of the onset of motion can be obtained.

1. Introduction Many former Department of Defense military bases and test sites are contaminated with abandoned underwater munitions that need to be remediated prior to the transfer of the property to the civil sector (SERDP, 2010). These unexploded ordnance (UXO) and discarded munitions have frequently been displaced from their original locations due to local water currents and often are buried under sediment making them difficult to locate during cleanup efforts. (We use the term UXO to refer to all underwater munitions and explosives of concern.) To support site remediation, the Strategic Environmental Research and Development (SERDP) program is supporting the development of an Underwater Munitions Expert System (UnMES), which is a computerbased probabilistic expert system that will synthesize available data and models for munitions burial and mobility. The UnMES will cover the broad range of underwater environments evident at the various sites of interest and is based on the approach previously developed by the Office of Naval Research (ONR) for predicting sea mine burial (Rennie et al., 2007). Underwater UXO exist in a dynamic environment that results in migration, burial and re-exposure as result of waves, currents, and sediment transport. While there have been few studies of migration and burial for objects representative of UXO, there have been models developed for larger sea mines based on field measurements (Bower ⁎

et al., 2007) from which scaling laws were derived using physics-based semi-empirical relationships (Trembanis et al., 2007; Voropayev et al., 2003). The present study is focused on ascertaining the applicability of these models for use in coastal engineering studies (and particularly UnMES), and on extending the models to the smaller size and higher density range characteristic of UXO. Mobility of a bottom sitting object is characterized as the onset fluid velocity at which motion is initiated in relationship to its size and weight. Scour, a common burial mechanism in non-cohesive sandy sediments, is controlled by the fluid velocity in relationship to the surrounding sediment characteristics. The laboratory studies described herein focus on the experimental determination of the conditions that determine the onset of motion, both on a hard surface and on a sand bed in the presence of concurrent scour burial. Studies were also undertaken of scour burial evolution of a bottom-sitting cylinder under a steady current. In the field, local currents are driven by a number of mechanisms including regional pressure gradients, tidal forcing and the orbital velocity of waves. In the laboratory, the resultant fluid forcing is simulated in a flow channel. Waves that produce significant near-bottom orbital velocities in the region offshore of the surf zone generally are longer period and can be reasonably approximated by the slowly-varying flow of the laboratory flume. The overall motivation for the present study is to support development of relatively simple parameterized models for use in the UnMES.

Corresponding author.

http://dx.doi.org/10.1016/j.oceaneng.2016.12.029 Received 30 March 2016; Received in revised form 25 October 2016; Accepted 29 December 2016 Available online 17 January 2017 0029-8018/ © 2017 Elsevier Ltd. All rights reserved.

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stabilizing forces. If initial motion occurs by rotation about a single pivot point, P, then it is appropriate to evaluate the moments of force about P, where the pivot angle, ϕ, is the angle between the horizontal (x) axis and a line tangential to P (see Fig. 1b) (Komar and Li, 1988; James, 1993). If the distance from P to the line of action for each force is about the same, then the threshold condition is given simply by balancing the sum of forces in the Horizontal and vertical directions

Toward this end, the theoretical exposition, new laboratory studies, and data synthesis described here focus on initiation of motion of UXO-like objects on rigid beds of varying roughness, as well as on scour-induced burial of such objects on a sand bed, and on the effect of partial burial on the criteria for initiation of motion. A discussion of the physical processes and modeling of imitation of motion and scour burial is presented in Sections 1.1 and 1.2 respectively. Section 2 presents the experimental material and methods. The results of the experiments are presented in Section 3, including those on motion onset on rigid bottom, (3.1), scour burial in sand (3.2), and motion onset in a sandy bed (3.3). In each situation the results are presented as parameterized models involving the dimensionless parameters that characterize the object properties, the ambient flow forcing and the bottom sediment. Section 4 contains a summary and discussion.

cos ϕ (FD + FI + FW sin β ) = sin ϕ (FW cos β − FL )

where β is the slope of the bed and ϕ is also known as the angle of repose. Under conditions of no flow, FD = FL = FI =0, and incipient motion occurs when ϕ =β. For homogeneous gravel-sized particles, the angle of repose measured in laboratory experiments ranged from 20° to 40° (Li and Komar, 1986), depending on particle shape and pivot geometry. If initial motion occurs by more complex motion than pivoting (e.g. sliding), ϕ can be operationally defined by Eq. (5) (i.e. independent of pivoting), such that tan ϕ is set equal to the ratio of the net force in the horizontal direction relative to the net force in the vertical when incipient motion occurs (García, 2008). With that logic in mind, ϕ is also known as the friction angle (Kirchner et al., 1990) and μ= tan ϕ is known as the friction coefficient (García, 2008). In this context, μ can be used to quantify frictional resistance to initiation of motion whether an object initially moves by pivoting, by sliding, or by some more complex motion. To highlight the role of fluid drag relative to submerged weight, one can re-express FI and FL in terms of FD, and place the ratio of FD to FW to the left hand side of the balance. Doing so for threshold conditions then yields

1.1. Initiation of motion The underwater initial movement of various objects, including gravel, cobbles and spheres, has been parameterized in the past by considering the competing forces of fluid drag (FD), lift (FL), immersed weight (FW), and inertia (FI), the magnitudes of which are reasonably well represented by the following equations and schematically shown in Fig. 1a (Wiberg and Smith, 1987).

FD = ½CD ρw AD U2

(1)

U2

(2)

FL = ½CL ρw AL

FW = (ρobj –ρw ) g VT

(3)

FI = CI ρw VI ∂U /∂t

(4)

(5)

fI ΘUcrit = a γ [μ (cos β )–(sin β )]/[1 + μ ( fL / fI )]

In Eq. (1) to (4), ρw and ρobj are the water and object densities; CD, CL and CI are drag, lift and inertia coefficients; g is the acceleration of gravity; AD and AL are the projected vertical and horizontal crosssectional areas of the object exposed to drag and lift; and VT and VI are the total object volume and the object volume exposed to flow. Following James (1993), U is defined to be the far field velocity at a height near the top of the object which is calculated from measurements of the free-stream flow by assuming a log-layer boundary profile. Measurements of the velocity profiles obtained in the JHU/APL flow channel (see Section 2) are illustrated in Fig. 1a inset, plotted on a semi-log scale to show the logarithmic nature of the upper boundary layer as well as the uniformity of the mean flow above the boundary layer. The threshold of motion condition occurs when the sum of mobilizing forces acting on the object just exceeds the sum of

(6)

where fI =|FD + FI|/FD; γ=(2 VT)/(CD D AD); fL = FL/FD; and

ΘU = U2 /[g D (ρobj / ρw –1)]

(7)

where ΘU is the object's mobility number (Nielsen, 1992), D is the object diameter, and the subscript “crit” in Eq. (6) indicates the critical value for initiation of object motion. The parameter α, where α≤1, is introduced in Eq. (6) to allow for the role of turbulent fluctuations in U causing brief peaks in the mobilizing forces, which reduces ΘUcrit (Komar and Li, 1988). If U in Eq. (7) is replaced by the shear velocity u*= (τb/ρw)½, where τb is the bed stress, Eq. (7) then is defined as the object Shields Parameter, Θobj. Eq. (6) is similar to threshold of motion relationships derived by other authors (e.g., Wiberg and Smith, 1987) for mobility in terms of Θobj, rather than mobility number ΘU, with the objects being sediment particles. For UXO-like objects much larger

Fig. 1. Mobilizing forces on an object resting on the seabed. (a) Object on a rough bed subject to a steady current and the presence of a bottom slope β; (b) Object of diameter D partially blocked by neighboring objects of diameter dbed with effective length scale k, and friction angle ϕ about pivot point P. In this example, k≈0.75 dbed for spheres. Current velocity measurements from flow channel (blue inset in a) are plotted on log scale to illustrate logarithmic nature of the upper portion of the boundary layer. Diagram adapted from Kirchner et al. (1990) and Wiberg and Smith (1987).

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fI = (FD2 + FI2 )1/2 / FD ≈ (1 + 16π 2 (CI / CD )2 (KC )−2)1/2

than the surrounding bed roughness, U can be more relevant than u*(e.g. if the object extends above the wave boundary layer). Additional simplifications to Eq. (6) are common when considering the initiation of motion of objects such as gravel or cobbles. The farfield bed is often considered to be effectively horizontal (β≈0) although it is simple to reintroduce bed slope when relevant. If flow is steady, or for a situation where surface waves are present and the wave orbital excursion distance is much larger than D, then fI ≈1. In that case Eq. (6) reduces to

ΘUcrit = α γ μ /(1 + μ fL ).

where (11)

KC = Uw T / D

is the Keulegan-Carpenter number. Sumer and Fredsøe (2002) indicate that for a cylinder on a bed, CI/CD ≈2 for KC < ~30. (As KC → ∞, the flow becomes effectively steady; FD dominates FI, and fI → 1.) Thus, to compare ΘUcrit for conditions where the ambient flow is oscillatory or otherwise accelerating to those where the flow is steady, the values of ΘUcrit for the former can be divided by fI to account for the role of the inertial force. This will effectively reduce the scatter in the threshold condition, especially for the cylinders observed under waves, and it will be applied to the data comparisons shown in Section 3. The extant data on the onset of motion is limited primarily to laboratory and field studies of natural sediment bedforms where D/k ∽1, or laboratory studies of large objects (Williams, 2001) where D/k > 50. The domain of interest here, however, lies in the mid-range 2≤ D/ k≤50, as UXO generally have diameters that range from 2 to 20 cm. Filling this gap is an objective of this study. The extant data and the present results are discussed in Section 3.

(8)

Studies of mixed sediment sizes as well as mixed sizes of ellipsoids and spheres (Miller and Byrne, 1966; Li and Komar, 1986) suggest that the friction coefficient, μ= tan ϕ, for individual objects sitting atop a non-cohesive sediment bed is a systematically decreasing function of the diameter of the object, D, relative to the roughness of the surrounding bed, k, expressed in terms of the ratio D/k. The physical basis for a decrease in μ as D/k increases is that the larger D is relative to k, the larger the protrusion of the object into the flow, and the easier it is for an object to pivot or slide over the underlying bed roughness. Conversely, the smaller D is relative to k, the more likely the underlying bed roughness will prevent object motion. In sediment dynamics (Soulsby, 1997), the roughness of the sea bed is characterized by the roughness length z0, which is defined by the structure of the velocity profile within the bottom boundary layer, where U(z) ≈(u*/0.41) log(z/ z0)). Alternately, z0 is estimated by the Nikuradse roughness, ks, where ks =30 z0 under fully rough turbulence (Soulsby, 1997). We will characterize the bed roughness important to the initiation of motion using ks. For the case of spheres of various sizes, a complete solution for γ μ/ (1+μ fL) for the right hand side of Eq. (8) as a function of D/k can be obtained from existing literature values. For a sphere placed atop a closely packed bed of similar underlying spheres, geometry (with VT =(4/3)π(D/2)3 and AD =π(D/2)2), gives γ=4/(3CD). For the present focus on UXO-like objects, the range of object Reynolds numbers isRe = DU/ν≈103 to 105 (with D ≈{1, 20} cm, U ≈{10, 50} cm/s, and the kinematic viscosity ν≈10−2 cm2/s). For that range of Re, spheres have CD ≈0.4 (Schlichting and Gersten, 2000), therefore γ=3.33, and fL ≈0.8. Laboratory measurements of the angle of repose for spheres, Li and Komar (1986) found a good fit to ϕ in degrees of ϕ =20.4° (D/dbed)−0.75 where dbed is the bed sphere diameter. Defining k as the bed Nikuradse roughness (García, 2008), such that k=30 z0 in rough turbulence, then the results of Schlichting and Gersten (2000) for a bed of close-packed spheres gives k=0.75 dbed, so that ϕ =(25.3 (D/k)−0.75)°. Putting these all together, we then have for spheres:

ΘUcrit = 3.3 α tan [25.3(D / k )−0.75] { 1 + 0.8 tan [25.3(D / k )−0.75]}−1

(10)

1.2. Scour burial When an object sitting on the bed extends above the surrounding bed roughness, the object will alter the local flow pattern relative to the far field boundary layer. For a cylinder lying on the bed with its axis normal to the flow, vortices can be especially energetic at the cylinder ends (Voropayev et al., 2003). Such perturbations increase the velocities and stresses impinging on the grains of sediment immediately adjacent to the object. This local acceleration lowers the threshold of motion (formulated in terms of the far field velocity) for grains near the object. Nearby grains may then be dispersed away from the object, forming scour pits with depth, B, that grow until the tendency for sediment to be dispersed is balanced by a tendency for sediment to fall back into the pit. The difference in pressure at the bed upstream and downstream of the object also drives seepage flow that can cause piping and tunnel erosion under the object (Voropayev et al., 2003; CatañoLopera and García, 2006). As a result of these processes, the object is likely to become unstable and settle into the scoured depression (Fig. 2), reducing its exposure height (D – B). The equilibrium depth of scour-induced burial, Beq, is anticipated to be a function of the far field velocity, the nature of the surrounding sediment, and the size, shape and density of the object. In an analogy to initiation of object motion, the Shields parameter is also relevant to parameterizing scour-induced burial of objects on sandy beds. However, in this case, the object size, D, and object density, ρobj, are replaced with the sediment grain size, dsed, and sediment

(9)

Given the explicit dependence of Eq. (9) on D/k, μ/(1+μ fL) in Eq. (8) is expected to be a function of D/k for UXO-like objects, and therefore the critical object mobility number will depend on the ratio of the object diameter to the bed roughness. Using a power-law form similar to that used by Miller and Byrne (1966) to describe μ= function(D/k), the relationship is ΘUcrit = a1(D/k)b1. The spherical case in Eq. (9) is best represented by a1 =1.2 and b1 =−0.72. This relationship is used to organize the available data from the sediment transport literature (Friedrichs et al., 2016a) discussed in Section 3 and guide the design of the present laboratory experiments discussed in Section 2. For bottom-sitting objects subjected to short period waves with strongly accelerating currents, the fluid inertial force, FI, can be a significant contributor relative to the drag force, FD. For a near-bed wave orbital described by U = UW sin(2πt/T), where UW is wave orbital velocity amplitude and T is wave period, it follows from the definitions of fI, FD, and FI that the maximum value for fI over the wave cycle in the absence of a mean current is approximately

U

B

D

Fig. 2. Example scour burial pattern from Series 2A laboratory run using cylinder with diameter D =10 cm in sand with median grain size d50 =0.42 mm. Flow speed U was 40 cm/s.

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density (ρsed), yielding the sediment Shields parameter, Θsed: 2 /[g

Θsed = u*

dsed (ρsed / ρw –1)]

constrain the time scale formulation representative of object scour burial.

(12)

where the far field bed stress τb is used in evaluating the shear velocity u*= (τb/ρw)½. Note that the contribution of a lift force is ignored, and homogeneity of the sediment is implied by the use of the single length scale dsed. If an object enhances turbulence enough to initiate local sediment motion, but far-field Θsed is below its critical value for sediment motion, Θsed_crit, then scour around the object is known as clear-water scour. For Θsed > Θsed_crit, scour around an object is known as live-bed scour, where Θsed_crit ≈0.03 to 0.06 for well-sorted sand with u*1/2dsed /ν≥4 (García, 2008). Several authors have empirically found that the dimensionless equilibrium burial depth for cylinders induced by scour (Beq/D) tends to increase as Θsed increases. For live-bed scour, a series of empirical models have applied formulae similar to

Beq / D = a2 Θsed b2 –c2

2. Materials and methods Laboratory data were collected in a closed loop recirculating flow channel 9.1 m long, 0.8 m wide, and 0.6 m deep. Ramps were placed on the tank bottom surrounding a center cavity providing a 15.4 cm deep space for installing a sand-filled section. This created an effective sand bed test section 160 cm long. For the first set of mobility (i.e. onset of motion) experiments, the center cavity was bridged by a rigid horizontal piece of sheet metal creating a flat bottom. For the experiments involving scour, the center cavity was filled with sand. The tank was filled with water to a height of 45–47 cm above the bottom of the tank. A turbulence management system located at the entrance of the channel consisted of a wave damping screens and flow straighteners (an array of small tubes). The mean water speed in the flow channel is set by adjusting the pump motor speed that was calibrated using a SonTek Inc. Acoustic Doppler Velocimeter (ADV) at a 10 Hz sampling rate, positioned in the horizontal centerline of the flow field, with its sampling volume of 0.25 cm3 located 22 cm above the bed and 1 m downstream from the location where the test cylinder was placed. Previous tests in this flow tank had determined that a uniform vertical profile was present in the center half of the water column and a typical log-layer boundary profile extended to the tank bottom (Fig. 1a). The large test cylinders presented a cross-sectional area equal to 12% of the tank test cross section, so the blockage effects could be significant for these runs; this effect is further discussed below. Flow speeds up to 90 cm/s were attained. The experiments were divided into three series:

(13)

For cylinders subject to steady currents, Whitehouse (1998) suggests a2 =11, b2 =0.5, and c2 =1.73, applicable up to Beq/D =1.15. In sharp contrast, for currents alone Sumer et al. (2001) determined that a2 ≈0.7 and b2 = c2 =0. In other words, Sumer et al. (2001) argued that cylinders under steady currents always bury to Beq/D ≈0.7 for all Θsed > Θsed_crit. Later fits to Eq. (13) under waves have found an explicit dependence on Θsed, but suggest a much smaller value for a2 than that found by Whitehouse (1998) (i.e., much smaller Beq for a given Θsed): with a maximum value of Beq/D =1 and c2 =0, Demir and García (2007) found a2 =2 and b2 =0.8. With c2 =0, Cataño-Lopera et al. (2007) found best-fits to Eq. (13) for cylinders under waves to depend on wave period, T. They found that for longer period waves (T > 4 s), a2 ≈1.6 and b2 ≈0.85. The notable inconsistencies in past reported values for a2 and b2, especially for currents in the absence of waves, motivated the collection of additional observations of B/D under currents as part of this study. Several authors (e.g. Whitehouse, 1998) have found that the timevarying burial depth for cylinders before reaching equilibrium follows an exponential relationship for the form

B (t ) = Beq (1– exp (−t / T *) p )

Series 1: Mobility tests on a flat rigid surface with various degrees of bed roughness, Series 2A: Equilibrium scour burial under steady flow on a flat sand bed, Series 2B: Mobility and scour burial due to accelerating flow on a sloped sand bed.

(14)

where T* is the characteristic time-scale of the scour process, and p is a geometry fitting coefficient. For cylinders, Whitehouse (1998) and Demir and Garcia (2007) found p≈0.6, whereas Voropayev et al. (2003) found p≈1. In their consideration of Eq. (14), Cataño-Lopera and Garcia (2006) pointed out that cylinders under constant forcing may still self-bury in discrete, intermittent steps that fit Eq. (14) only after further smoothing of B(t) in time. A form for T* that is similar to that developed previously for scour under pipelines (Sumer and Fredsøe, 1993) has also been applied to self-burying cylinders:

T* = M Θ

sed

N D 2 /(g

(Ssed − 1)dsed 3)0.5

Five surrogate munitions were used during Series 1, all cylinders with diameters from 2.5 and 10.5 cm, approximately covering the size range corresponding to 20 mm caliber ammunition to 5″ naval rounds. The cylinder density ρobj varied over a wide range, from very light (specific gravity ρobj/ρw =1.21) to quite dense (ρobj/ρw =7.9). For Series 2 in sand, an additional surrogate with a tapered shape was used, having a nose portion 1/3 of the total length, similar to the proportion observed in several munitions of interest. The lengths were selected to be representative of typical abandoned underwater munitions. The pertinent values for the surrogate UXO are listed in Table 1.

(15) Table 1 Sizes and density of objects used in laboratory experiments.

where the empirical coefficients M and N are determined by the geometry of the object of interest. Whitehouse (1998) gave values of M =0.095 and N =−2.02 for short cylinders under steady flow. Demir & Garcia (2007) used a similar form for computing T*, but made a scaling argument that N =−1.5 and found the best fit for M to be 0.11 from their wave induced scour burial data. This results in a shorter time constant, i.e. Beq is reached more quickly than when using the Whitehouse coefficients. In addition, Demir & Garcia (2007) suggest a time delay before the burial process is initiated, estimated as, ΔT = L/c, where L is the length of the cylinder, and c is the erosion rate based on the bed-load equations for sediment transport under oscillatory flow (Sleath, 1984). This time interval, given the UXO and sand dimensions, is generally between a few seconds to a few minutes. In contrast, Voropayev et al. (2003) found the very simple expression T*≈ 480 T fit their data well. The present laboratory experiments are used to further 285

UXO Surrogate

Diam. (cm)

Length (cm)

Weight (kg)

Specific gravity

Brass hollow cylinder (BR) Copper sand filled cylinder (CS) Titanium solid cylinder (TT) Aluminum solid cylinder (AL) Stainless steel solid cylinder (SS) Tapered model (TM)

10.50

32.0

3.36

1.21

10.50

32.0

6.71

2.42

10.30

31.9

12.02

4.52

2.54

9.9

0.14

2.72

2.54

10.0

0.40

7.90

7.94

31.8

2.94

2.43

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2.1. Experimental configuration for Series 1: onset of motion on rigid bottom For the Series 1 mobility experiments, a piece of sheet metal was placed across the central test section and braced from below to remain flat. The tank was filled with water to a depth of 32 cm above the test surface. Mobility tests were conducted by placing the surrogate UXO near the center of the test section and slowly increasing the velocity of flow in the channel (at an average acceleration of ∽0.6 cm/s2) until the surrogate was visually observed to roll. The digital record of the ADV was averaged over a 1 s interval and used to determine the onset of motion threshold, Ucrit. Each test was repeated 4–6 times to measure the experimental variability. The first experiments were performed on the bare sheet metal in order to test the measurement systems and procedures and to allow comparison with the previously available laboratory mobility data at large D/k values (Davis et al., 2007). The bed roughness k was then increased by the use of two industrial carpets, providing fixed roughness elements at scales appropriating the characteristics of irregular sandy sediments (mixed gravel and shells, or small ripples). The thickness of the carpet was measured using a standard caliper while deformed under the test cylinder. In some situations no motion was observed even at the highest channel flow speed (~90 cm/s). For example, the 2.5 cm diameter steel cylinder and the titanium cylinder did not move, except on the smooth metal bottom. In order to simulate UXO corrosion due to long time exposure, an additional set of tests was performed where the surrogates were roughened by gluing a layer of sand (grain size ranging from 0.6 to 0.8 mm) around their circumferences. Roughening the surface of the cylinders was interpreted as equivalent to increasing the bottom roughness (smaller D/k) locally, but not in the far field. However, the rougher surface would also increase the drag force on the cylinder at a given speed. This latter effect may cause slightly decreased values of Ucrit than would otherwise be observed.

Fig. 3. Representative scour burial, Series 2 A experiments. (a) Example Video images from 8 min after the start of the burial run. The level of the sand bed prior to the run is shown by the yellow lines. The magenta dots indicate the hand-digitized pixel location of the cylinder top center. (b) Fractional burial time series from a Series 2 A run (BR model). Total burial is estimated as the average of the end positions recorded by Camera 1 (☐) and Camera 2 (o). Flow speed U =40 cm/s.

conducted at nominal speeds of 20, 30, 40, and 60 cm/s, as measured by ADV measurements. At the slow speed (20 cm/s) conditions were observed for up to 1 h and minimal sand grain motion occurred. Data were acquired at speeds of 30 and 40 cm/s for two hours, although equilibrium conditions were usually reached within an hour or less. During the faster runs at 60 cm/s, equilibrium burial occurred more quickly, along with substantially greater sand movement, which led to increased sand loss out of the test bed. To optimize the effort and time to clean up and reset the laboratory tank between runs, burial under faster flow speeds was observed only out to 1 h. Three cameras were used to capture the scour burial behavior: two identical black and white (B & W) cameras (Adimec 1600 m with Fujinon 12.5 mm lenses) placed on either side of the tank and a color video camera (Vixia HF M50) suspended overhead of the tank. All imagery was sampled at 1 Hz during the burial tests. Tracking of the object position was performed by hand-digitizing the pixel location at the cylinder top center, as well as the level of the sand surface as shown in Fig. 3a. The location of the top the UXO surrogate was marked in the images from the two side cameras, noting that the cylinder often sank into the sand at one end before the other; this is typical of scour burial where the object sinks first into the larger pit created at one end of the object. Images were hand digitized at 10 s intervals during the initial phase of rapid burial, and then at 60 s intervals. Equilibrium burial depth was computed as initial vertical position minus the average of the two sides’ vertical locations (Fig. 3b). Images from the overhead color camera were not quantitatively analyzed, but used to provide qualitative information on the burial evolution and scour pit shape. Series 2B determined the threshold of mobility for an object resting on a sloped sand bed where scour burial can develop during the acceleration of the current. The test runs were conducted by increasing the flow rate until the surrogate either rolled away, or buried into the sand to at least half of its diameter. The rate of flow acceleration dU/dt was significantly greater than the acceleration used during Series 2A. The Video imagery was recorded with the B & W cameras positioned on the same side of the tank, one upstream and one at the initial object position, looking slightly downstream. The first runs were recorded at 1 Hz. After a preliminary analysis it was determined that improved time resolution was needed, so that the image data rate was increased to 10 Hz matching the ADV sample rate. To synchronize the Video

2.2. Experimental Configuration for Series 2: scour burial and mobility in sand For the Series 2 experiments, the center cavity of the test section between the ramps was filled with sand. For the scour burial tests, Series 2A, the sand bed was of uniform depth of 15.4 cm. In Series 2B, the experiments for burial and mobility in sand, the upstream depth of sand in the test section was maintained at 15.4 cm while the downstream side was lowered to 7.4 cm resulting in a 2.9° slope across the sand bed; this was to represent a the slope of a typical bedform such as the sand waves observed by Cataño-Lopera et al. (2007). The sand used to fill the cavity was “Play Sand” labeled by the manufacturer Quikrete® as having a grain size range between 0.30– 0.85 mm. The sand grain size distribution was measured using a 15 US sieve set where it was determined that the range was somewhat wider, with 25% of the grains smaller than 0.30 mm, and almost 10% larger than 1 mm. The median grain size was determined to be 0.42 mm and was used as the representative dsed for data analysis. After each run during Series 2A, the sand was restored in the test section and leveled using a flat plank. Periodic loss of sand occurred as it dispersed throughout the tank and could not all be swept back into place. When too much sand was judged to have been lost, additional sand was added to the test section. Sand grain size distribution measurements were sieved both before and after use in the tank and showed a significant difference only in the very finest grain size fraction ( < 0.063 mm), which was apparently washed away during the tests. The equilibrium burial runs in Series 2A were conducted with the surrogate UXO placed on the surface of the sand bed. The channel flow was ramped up slowly to a constant speed which was maintained until equilibrium burial conditions were achieved, as determined from observations of the Video imagery, described below. Runs were 286

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face, the effective bottom roughness was estimated as the effective carpet roughness (1.7 or 2.5 mm) plus the grain size of the sand glued onto the cylinders (0.6 mm). Conditions for the Series 1 tests are summarized in Table 2, where the flow speed at the moment of initiation of motion is shown (mean over repeated trials for each test condition) along with the mean critical object Shields number and D/k ratio. As noted in Table 2, in some cases motion could not be initiated for the most dense UXO (TT and SS, see Table 1) on rougher bottoms due to the maximum flow speed limitation of the tank, about U ~ 90 cm/s at the height of the ADV sampling volume. There was some variability in the measured critical flow speed from repeated runs of the same condition even for the cases where a smooth cylinder was lying on the sheet metal bottom; the standard deviation was about 10% of the mean across the range of bottom roughness; this was likely due to turbulent fluctuations in the flow. The results for the present laboratory experiments are shown in Fig. 5 overlaid on extant data from prior studies from the literature as compiled by Friedrichs et al. (2016a). Prior cases include field and laboratory observations of the initial motion of gravel under currents, lab measurements of spheres under currents, and lab measurements of cylinders under both currents and waves. Included in Fig. 5 are field observations of natural sediments (Komar, 1996; Mao and Surian, 2010), and laboratory studies of non-homogeneous sediment (Kuhnle, 1993; Patel and Ranga Raju, 1999; Wilcock and Kenworthy, 2002), glass spheres (James, 1993), and cylinders (Williams, 2001; Davis et al., 2007). Compilation of the results shown in Fig. 5 required consistent definitions for bed roughness and procedures for estimating Ucrit at z= D. For observations over rough beds, k was taken to be the far-field effective bed roughness as defined by the Nikuradse equivalent roughness height. Following this convention, the effective roughness of gravel beds in the absence of bedforms is approximately k=2.5 d50 (García, 2008) and that for spheres is k=0.75 dbed (Schlichting and Gersten, 2000). For smooth beds, z0 =ν/(9 u*), and k was set to a minimum value of k=30 ν/(9 u*). For steady flow cases where published values were of Θcrit rather than the observed critical flow velocity, Ucrit at a height z= D above the bed was estimated based on a log-profile. If an observed Ucrit under steady flow was provided at a height other than z= D, a boundary layer log-profile was used to adjust Ucrit to its expected value at z= D. For beds intermediate between smooth and fully rough turbulent, z0 for use in the log adjustment was determined as a function of u*k/ν following Yalin (1992) as presented by Garcia (2008). For gravel and spheres, only cases for which D > 0.5 cm and for which D is as large or larger than the bed grain size are included. Data covering the higher end of the D/k range on the right hand side of Fig. 5 were obtained from experiments on fluid-forced motion of surrogate UXO performed in the US Army Corps of Engineers (USACE) wave flume (Williams, 2001) as well as cylinders rolling under a steady current (Davis et al., 2007). Because the bottom of the wave flume used by Williams (2001) was smooth, the effective roughness was computed here as k=30 ν/(9 u*) with the wave friction factor for u* calculated following Pedocchi and Garcia (2009), resulting in D/k ratios for the USACE observations between 50 and 450 (green squares in Fig. 5). Computed ΘUcrit for the wave-driven USACE data points exhibited large variability. It was determined that mobility was forced in the flume by short period waves having a significant contribution from the inertial force, FI. To account for this component, the mobility number was multiplied by the inertial force correction factor fI given by Eq. (10), using CI/CD =2. This correction factor can be applied to all the data in Fig. 5, (not just the wave-driven), because the other data have KC =∞, which results in fI =1. Note that for object sizes of interest, the low KC regime that produces fI notably greater than 1 corresponds to short period waves (T < 3 s), which usually have limited bottom orbital velocities.

Maximum U rolls away

U (cm/s)

inial movement

sediment suspension

paddle dip

Elapsed Time (sec) Fig. 4. Example time series of current flow speed, U, Series 2B, mobility on sand. The grey dashed line indicates the range over the ADV measurements from which the flow acceleration dU/dt was computed.

imagery and the ADV speed measurements, a rigid target was dipped into the tank just upstream of the ADV in the view of Camera 1 that disrupted the ADV signal (“paddle dip” in Fig. 4) and could also be clearly observed in the flow field imagery. Video imagery data on the object position were hand digitized by first marking the initial position of the cylinder, similar to the marking shown in Fig. 3a, but at the center of the cylinder end. This position was then overlaid on subsequent frames, allowing any object motion to be pinpointed. Correlation with the ADV flow measurements allowed determination of the object behavior as a function of time (Fig. 4). Specific conditions noted were: initiation of sediment suspension near the UXO; initiation of downstream movement by the UXO; time when the UXO rolls downstream out of camera frame; or time of burial (settling by the UXO downward into sand bed); these conditions are marked in Fig. 4 in addition to the maximum flow rate during the run. The flow speeds corresponding to each of these states was averaged over a 1 s interval. For some runs, no downstream movement occurred as the cylinder only buried in place or rotated (usually upstream) into its scour pit. During several runs, the UXO started to move downstream, but then stopped, apparently arrested by variations in the sand bed and the concurrent increase in scour. Only the least dense cylinder, BR with a specific gravity of 1.2, was mobilized in the all flow channel tests. Several experiments were performed where the BR and AL cylinders were partially buried into the sand prior to starting the test run, in order to determine at what percentage burial initiation of motion was not possible.

3. Results 3.1. Object onset of motion on a rigid bottom Results for the Series 1 laboratory experiments of cylinder mobility on a flat bottom are representative of naturally occurring hard (i.e. non-mobile) sea beds comprised of rock, shell, or consolidated clay, where no burial can occur. A total of 122 tests were run to examine the behavior of the five UXO surrogates (Table 1) at six different roughness conditions (the bottom was either the smooth metal of the tank floor or one of two fixed roughness carpets, and the UXO surrogate cylinders had either a smooth surface or were coated with sand grains). The physical roughness of the carpets was chosen to produce ratios of the UXO diameter to bottom roughness in the previously un-sampled range between D/k=10 and 100. The heights of the carpet fibers were measured to be 0.39 cm for carpet 1 and 0.59 cm for carpet 2. The carpet was observed to compress substantially under the test cylinders; therefore the effective bottom roughness length scale was measured as the fiber height under compression (approximately 50% of the uncompressed height). For the sand-roughened models on the flat sur287

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Table 2 Laboratory tests in Series 1, mobility onset on a rigid bottom. Average over repeated trials UXO Surrogate

Bottom type

smooth surface on UXO surrogate Brass hollow cylnder (BR) metal Brass hollow cylnder (BR) carpet 1 Brass hollow cylnder (BR) carpet 2 Copper sandfill cylinder (CS) metal Copper sandfill cylinder (CS) carpet 1 Copper sandfill cylinder (CS) carpet 2 Titanium solid cylinder (TT) metal Titanium solid cylinder (TT) carpet 1 Titanium solid cylinder (TT) carpet 2 Aluminum cylinder (AL) metal Aluminum cylinder (AL) carpet 1 Aluminum cylinder (AL) carpet 2 Stainless steel cylinder (SS) metal Stainless steel cylinder (SS) carpet 1 Stainless steel cylinder (SS) carpet 2 Sand-roughened surface on UXO surrogate Brass hollow cylnder (BR) metal Brass hollow cylnder (BR) carpet 1 Brass hollow cylnder (BR) carpet 2 Copper sandfill cylinder (CS) metal Copper sandfill cylinder (CS) carpet 1 Copper sandfill cylinder (CS) carpet 2 Titanium solid cylinder (TT) metal Titanium solid cylinder (TT) carpet 1 Titanium solid cylinder (TT) carpet 2 Aluminum cylinder (AL) metal Aluminum cylinder (AL) carpet 1 Aluminum cylinder (AL) carpet 2 Stainless steel cylinder (SS) metal Stainless steel cylinder (SS) carpet 1 Stainless steel cylinder (SS) carpet 2 a

Standard Deviation

# Trials

D/k

Onset Flow Speed U (cm/s)a

Shields θobj-cr

U (cm/s)

θobj-cr

5 4 4 5 0 5 8 4 1 5 4 4 6 2 1

279 54 35 307 – no data – 35 387 53 – no motion – 73 13 9 104 13 – no motion –

18.00 18.51 19.23 20.02

0.15 0.16 0.17 0.03

1.86 0.29 1.36 1.75

0.032 0.005 0.024 0.005

45.41 26.51 60.17

0.14 0.02 0.10

2.02 2.40 3.65

0.013 0.004 0.012

17.35 31.69 34.45 26.06 54.32

0.07 0.24 0.28 0.04 0.17

3.07 0.024 2.57 0.039 2.34 0.039 4.37 0.013 - motion only on 1 run -

5 5 5 6 6 5 7 6 2 7 5 5 1 1 1

177 55 36 177 55 36 174 54 35 44 14 9 – no motion – – no motion – – no motion –

16.86 17.98 18.01 37.21 40.22 36.32 43.21 59.05 54.83 29.92 27.47 35.35

0.13 0.15 0.15 0.09 0.11 0.09 0.05 0.10 0.08 0.21 0.17 0.29

0.76 1.26 0.89 2.62 3.63 1.91 5.86 7.18 7.70 4.13 0.67 5.46

0.012 0.021 0.015 0.014 0.020 0.009 0.015 0.025 0.023 0.055 0.008 0.079

after log layer adjustment to z=D/2.

The present results from Series 1, shown in Fig. 5 as red circles and magenta triangles, cover the high D/k range and also fill the previous gap in D/k space that is relevant to the initiation of motion of UXO-like objects. The measured U for the larger cylinders was corrected for the flow area blockage, estimated at 12%, however the resulting corrections to the mobility numbers are not conspicuously evident on this log-scale plot. Overall, the observed values of ΘUcrit exhibit a clear decrease with D/k. Overlaid on Fig. 5 (blue dashed line) is the theoretical equation for the mobility of spheres (Eq. (9)) derived in Section 1.1 where the optimal value of the turbulent fluctuation parameter was found to be α=0.86. A power-law fit for all observations most relevant to object mobility (namely the present results plus all literature data for observations where D > 1 cm) was made to determine the coefficients for the relationship ΘUcrit = a1(D/k)b1 proposed in Section 1.1. Using the combined prior and present data, the best fit, with goodness of fit r2 =0.89, was determined to be a1 =1.64 and b1 =−0.71. This equation, ΘUcrit =1.64(D/k)−0.71, shown as the black solid line, has a power-law dependence very close to that of Eq. (9) derived from theory. This relationship provides a method to estimate the threshold of mobility for use in the UnMES. 3.2. Scour burial in sand Fig. 5. Threshold for the initiation of motion of objects on the seabed. Present results shown in magenta triangles (smooth bottom) and red circles (rough bottom). Prior results shown in upper left: (black dots and o) natural sediments (Komar, 1996, Mao and Surian, 2010, Kuhnle, 1993, Patel and Ranga Raju, 1999, Wilcock and Kenworthy, 2002; and (blue +) glass spheres (James, 1993). Prior results for cylinders at large D/k: (☐) under waves (Williams, 2001), and for steady flow Davis et al. (2007). The dashed blue line shows the theoretical power law relationship for the threshold of mobility derived for spheres Eq. (9). The black solid line is the best fit threshold to all previous and present data combined.

The evolution of UXO scour burial into sand under a steady current, Series 2 A, was recorded by the imagery described in Section 2.2. An ADV positioned 10 cm below the water surface measured the current which, after an initial period of slow acceleration was fixed for the duration of the scour experiment. The results are compared to previously published models (Section 1.2) for equilibrium burial depth (Beq) and the rate of burial, assuming an exponential increase with time 288

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Table 3 Series 2A experiments for scour burial into sand under steady flow. UXO Surrogate

Diameter (cm)

Specific Gravity

ADV observed (cm/s)

Equilibrium fractional burial

Run duration (hour)

AL SS CS AL SS TM TT CS TM AL SS TM BR CS CS CS TT TM AL TM TT CS

2.54 2.54 10.5 2.54 2.54 7.94 10.3 10.5 7.94 2.54 2.54 7.94 10.5 10.5 10.5 10.5 10.3 7.94 2.54 7.94 10.3 10.5

2.72 7.90 2.42 2.72 7.90 2.43 4.52 2.42 2.43 2.72 7.90 2.43 1.21 2.42 2.42 2.42 4.52 2.43 2.72 2.43 4.52 2.42

20.0 20.0 20.0 30.8 30.6 29.9 30.3 30.9 35.1 40.5 39.9 41.4 40.1 40.8 40.6 40.7 41.0 48.2 59.5 58.3 58.8 57.0

0.00 0.00 0.00 0.49 0.55 0.12 0.15 0.16 0.32 0.84 1.55 0.72 0.39 0.42 0.42 0.48 0.56 0.51 2.27 1.17 0.63 0.48

0.25 0.25 1 2 2 1.5 1 2 1 2 2 2 2 2 2 2 2 1 1 1 2 1

to represent the fractional burial at any instant in time. The initial level of the sand bed is recorded and shown on each of the images. As the bed level evolves and sand bedforms develop, the value for the degree of burial would differ depending on the baseline reference. Several approaches were examined, and it was determined that using the initial bed level as the baseline provides a consistent reference and is not inherently subjective. From the imagery the vertical position of both ends of the cylinder were recorded and the average used to compute the observed burial depth, representing the scour pit depth (rather than burial by areal coverage). The results for representative tests are plotted versus time as a fraction of the object diameter in Fig. 6(b,c).

(Eq. (14)). The coefficients in the formulae for Beq and for the exponential time constant (T* in Eq. (15)) from Whitehouse (1998) predict deeper, slower burial, while Demir & Garcia (2007) published coefficients that result in shallower burial at equilibrium, but predict that it occurs more quickly. A total of 22 scour burial experiments under steady flow were conducted, listed in Table 3. All the surrogate UXO size and densities shown in Table 1 were tested, with replicates run for the copper cylinder (CS) at a nominal value of 40 cm/s (within 3%) to examine experimental variability. In Fig. 6(a) images taken at the start, middle and end of a two hour test are shown, illustrating the complexity of determining a single value

a) c)

B/D

b)

Elapsed Time (min)

Elapsed Time (min)

Fig. 6. Representative scour burial observations from Series 2 A. a) Example laboratory video frames from beginning, middle, and end of 2-h scour burial test. Yellow line marks initial level of ambient sand bed. b-c) Observed burial (blue solid line) and predicted burial over time from Eq. (14) and (15) using the final observed burial depth as Beq: Whitehouse (1998) – green dashed line, Demir & Garcia (2007)– black dashed line: b) burial of test cylinder TT for U =41 cm/s; c) first 10 min of test in b) expanded to observe the initial increase in burial.

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et al. (2016b), only the observations of Demir & Garcia (2007) are displayed as an example, along with Demir & Garcia's best fit relationship (Eq. (13) with a2=2 and b2=0.8, black chain-dashed line). Under mean currents, the equilibrium burial depth for smaller cylinders (D < 2.6 cm) is significantly larger than for larger cylinders (D > 8.6 cm) (no data has yet been reported for 2.6 cm < D < 8.6 cm). The best-fit trends for cylinders under currents each display a kink in their power law responses to Θsed associated with the transition from clear-water scour to live-bed scour. Relationships for clear-water and live-bed scour displayed in Fig. 7 were found by fitting power laws to Θsed < 0.05 and Θsed > 0.03, respectively. The intersection of the bestfit lines for clear-water and live-bed scour occurred near Θsed_crit ≈0.04 for both the smaller and larger cylinders, with an average value of 0.042. The fits to Eq. (13) for mean currents under live-bed scour for (i) smaller cylinders and (ii) larger cylinders are (i) a2 =15, b2 =1.1 and (ii) a2 =1.3, b2=0.36. For clear-water scour under mean currents, the corresponding fits are (i) a2 =1900, b2 =2.5 and (ii) a2 =280, b2=2.1 (All of these fits are with c2 =0). Under live-bed scour with waves, Beq/D generally exhibits lower values than that seen under mean currents, consistent with the general trends reported by Sumer & Fredsoe (2002). For larger cylinders under mean currents, Beq/D in Fig. 7 is observed to lie in between the predictions of Whitehouse (1998) and of Demir & Garcia (2007), with Whitehouse over-predicting Beq/D and Demir & Garcia under-predicting. Interestingly, the smaller cylinders fall relatively close to the Whitehouse relationship. In implementing the Whitehouse equation, it was assumed that Θsed_crit =0.042. In the present data, a set of five repeated tests at U =40 cm/s using three of the large (D > 10 cm) cylinders (shaded group in Table 3) have Beq/D burial that range from 0.39 to 0.56. There is relatively little variability for the tests with the same density cylinder (CS, Beq/D =0.42 to 0.48), while the equilibrium burial depth is least for the lightest cylinder (BR, Beq/D =0.39) and larger for the most dense (TT, Beq/D =0.56). Object density is a factor that is not accounted for in the sediment Shields parameterization, but density has been shown to be statistically significant for objects of this size subjected to scour under mean currents (Friedrichs et al., 2016b). The limited data obtained with the tapered cylinder (D =7.9 cm, plotted as stars in Fig. 7) suggests a larger equilibrium burial depth for equivalent uniform diameter cylinders. The Video imagery of scour burial revealed a different behavior for the tapered shape than for the cylinders. The cylinders invariably remain close to perpendicular to the flow direction, while the tapered cylinder tends to rotate so that the narrow end points downstream, as illustrated in Fig. 8. Fig. 8(a) is near the start (t =2 min) of the scour forcing, and image 8(b) is 20 min later. During this interval the UXO has rotated about ~45° and a scour pit can be seen forming around the upstream end. Note that it is the different flow field around the cylindrical end and the tapered end (which does not touch the sand, resulting in less bed friction acting to keep the tapered end stationary) that causes that the tapered end to

Fig. 7. Equilibrium scour burial. Green and black chain-dashed lines show Eq. (13) using the coefficients of Whitehouse (1998) and Demir & Garcia (2007), respectively. Red and blue dashed lines are fits of Eq. (13) to the larger and smaller cylinders under steady flow. (A two-part fit is computed in the two regimes for clear-water and live-bed scour).

Comparisons of the present data to the Whitehouse (1998) and Demir & Garcia (2007) predicted time scale (Eq. (15)) for fractional burial are also shown in Fig. 6(b,c). The observed equilibrium burial depth was used for Beq in Eq. (14) (where in this case Beq/D =0.55). The sediment Shields parameter Θsed used in both these models was computed from (Eq. (12)), with the median sand grain size d50 =0.42 mm and u* calculated following Yalin (1992) as presented by Garcia (2008). For the relatively longer period over which the majority of the observed burial occurred (Fig. 6(b), extended time axis), application of the Demir & Garcia time-scale was closer to the observations. In Fig. 6(c), enlargements of the first ten minutes of the burial processes are shown to compare the initial increase in burial where it can be seen that the initial time delay, ΔT, from the Demir & Garcia time formula appears to be over-estimated. A large degree of variability in initial growth patterns was observed across the Series 2A results for burial under steady current. Equilibrium burial that results from the present laboratory experiments are shown in Fig. 7 overlaid on extant data from prior studies from the literature as compiled by Friedrichs et al. (2016b). Prior cases especially relevant to the present experiments include the relatively few available laboratory observations (only 26 data points) of self-burying cylinders subject to live-bed scour by currents without waves (found in Stansby and Starr, 1992, Sumer et al., 2001, and Cataño-Lopera et al., 2007). Shown is the model of Whitehouse (1998) as given by Eq. (13) (a2=11, b2=0.5, c2=1.7, blue chain-dashed line). (Note that the raw data supporting Whitehouse's equations have not been published.) Of the several hundreds of observations available in the literature for scour-induced burial of cylinders under waves compiled by Friedrichs

Fig. 8. Tapered surrogate UXO during Series 2A, U =40 cm/s, obtained with the overhead camera: a) after 2 min, b) after 22 min.

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rotate downstream. It appears that the blunt upstream end increases the local amplification of turbulence, inducing more scour. This is consistent with the finding of Sumer and Fredsøe (2002) that square pilings oriented at 45° toward flow scour more intensely than round pilings or than square pilings oriented at 90°. As noted, there is a substantial amount of scatter in equilibrium burial versus Θsed in Fig. 7 even among the large cylinders. Nonetheless, the simple relationship Beq/D = a2 Θsedb2, with a2 =1.3 and b2 =0.36, captures ¾ of the variability (r2 =0.76) for large UXO under live-bed scour by mean currents. In the case of the smaller cylinders, it was observed in the Video imagery for Series 2A that the upper surface of the bed appeared to become mobilized (e.g. bedload transport) to a depth that was a significant fraction of the cylinder diameter. Therefore, the burial preceded in a manner different that for the larger cylinders. The Beq/D = a2 Θsedb2 relationship for smaller cylinders, with best-fit a2 =15 and b2 =1.1, is much steeper under livebed scour relative to larger cylinders. The equilibrium scour depth for the tapered shapes was similar to the smaller cylinders and was substantially greater than that for the equivalent diameter cylinder. Under clear-water scour, even higher best-fit values of a2 and b2 were found, reflecting the steep curves in Fig. 7. But Θsed is so much smaller for clear-water relative to live-bed scour, that (of course) less total scour is observed under clear-water conditions. For practical use under live-bed conditions within the UnMES, a relevant slope could be assigned to each UXO shape implemented. (Clear-water scour is less relevant to the higher energy conditions of most interest to UnMES.) To account for the distinct behavior of cylinders under a variety of wave conditions, a dependency on KC could also be applied (Cataño-Lopera and Garcia, 2006, Friedrichs et al., 2016b). Pursuit of a universal relationship including both Θsed and KC and thereby simultaneously applying to both current- and wavedominated conditions is a subject of our ongoing research. Alternatively, a different inclusive parameterization could be pursued, such as suggested below, where the effective length of the object is included. In a recent paper, Manes and Brocchini (2015) have derived a physics-based scaling relationship for equilibrium scour at the base of a vertical cylinder (pile) based on paradigms of turbulence phenomenology. The scaling relationship is derived by arguing that the equilibrium burial depth is proportional to the intrinsic length scale, S, of the largest turbulent eddies generated by the scour vortices. By equating turbulent dissipation to the large-scale energy containing eddies causing the scour, an expression for Beq as a function of the cylinder diameter and drag coefficient, Cd, has been derived. To extend the analysis of Manes and Brocchini (2015) to the present case of a bottom sitting cylinder, the intrinsic length scale was associated with the cylinder length, S ≅ L, rather that its diameter as applicable to the vertical cylinder case. The resulting expression, albeit somewhat more complex than that derived by Manes and Brocchini (2015) for the vertical cylinder, is

Beq / D = a3 U 6/5D−3/5 (L / dsed )2/5 (g (ρsed / ρw − 1))−3/5Cd 2/5 = a3 ψ

Fig. 9. Equilibrium scour burial observations scaled by analytically-derived relationship Eq. (16).

tion of scour burial in the UnMES. 3.3. Mobility in sand Series 2B laboratory experiments were performed to explore the onset of motion for a surrogate UXO lying on a bed of sand. Mobility was detected by visual screening of the Video imagery, aided by plotting the hand-digitized initial position on each frame as discussed in Section 2.2. The flow was accelerated at different rates, and acceleration varied from 1 to 8 cm/s2. The flow-field acceleration dU/dt was computed as a linear fit over the observed increasing values of U, as illustrated in Fig. 4. For most of the test runs, the surrogate was initially proud on the surface; for six runs the BR and AL cylinders were partially buried before the start of the run, at initial burial fractions, (B/D)init, between 0.5 and 0.35. Mobility could not be initiated on the lightest cylinder BR when (B/ D)init =0.35; however, given the flow speed limitation of the tank it is uncertain whether this burial depth is enough to preclude further motion completely. Table 4 lists the observations from the 29 tests of initiation of movement on sand, with the ADV current observed at the moment of object movement shown in column 4. The mobility results are categorized (column 6) as: “o” indicating the cylinder rolled away off the test sand bed, or “x” indicating conditions where the object did not move horizontally, but instead buried in place, settling into its scour pit. For these runs, the flow velocity is the maximum recorded. The symbol “m” designates those runs where horizontal movement started, but then was overcome by burial, so that the object did not move over a horizontal distance greater than its diameter. Values of D/k for the surrogates on sand were ∽70 for the larger test cylinders and 22 for the small ones, where the bottom roughness k was based on the sand grain's effective roughness, k=2.5 d50, as was used for evaluating the roughness of beds made of sediment in earlier sections of this paper. The object mobility parameter ΘU, was computed using Eq. (7), using the log-layer adjustment to the flow speed as discussed in Section 3.1. It was then modified by a small scaling factor to account for the slope of the sand bed. A slope β increases the mobilizing force by FW sin β, and decreases the resistive force by FW cos β, as shown in Eq. (5), so that the presence of a slope changes the original object mobility parameter (Eq. (7)) by a factor ΘU,β/ΘU, = cos β - sin β. This adjustment is results in ∽5% change for the slope of the sand bed in the tank, β=2.9°. The factor fI in Eq. (6) is also non-zero because dU/dt > 0. Here we calculate the effect of the inertial force as

(16)

where Ψ is the analytically-derived relationship, and a3 is a multiplicative factor to be empirically determined. This result differs significantly from the Shields parameterization Eqs. (12) and (13) as the U dependence is considerably weaker and that both object length scales, D and L, are fundamentally included. The laboratory burial data collected here plus those of Demir & Garcia (2007) are plotted vs. Eq. (16) in Fig. 9. This parameterization considerably reduces the variability of the data, collapsing much of the JHU/APL small cylinder and tapered cylinder results more in line with the large cylinder data. Fitting these data (excluding the more uncertain data at Beq/D ∽ 1) to Eq. (16) results in the dashed line shown in Fig. 9, with a3 =0.13, and an goodness of fit r2 =0.76. This relationship can potentially be used as an alternative for characteriza-

fI = |FD + FI |/ FD ≈ 1 + (CI / CD ) D (dU / dt )/ U2

(17)

with CI/CD ≈2. For the majority of the runs, the inertial effect was quite small, but for a several cases for the lowest density cylinder fI exceeded 1.2, and fI is thus incorporated into the assessment here as it was in Fig. 5. The threshold for motion fIΘUcrit on sand for these laboratory 291

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Table 4 Laboratory test for Series 2B, mobility on sand under accelerating flow. UXO Surrogate

Diameter (cm)

Specific Gravity

Ucrit or Umaxa (cm/s)

Acceleration dU/dt (cm/s2)

Motion codeb

Initial %Burial

CS BR CS CS TM AL SS BR TT BR AL TM BR AL CS TM BR BR AL BR BR BR BR AL AL AL AL BR AL

10.5 10.5 10.5 10.5 7.94 2.54 2.54 10.5 10.3 10.5 2.54 7.94 10.5 2.54 10.5 7.94 10.5 10.5 2.54 10.5 10.5 10.5 10.5 2.54 2.54 2.54 2.54 10.5 2.54

2.42 1.21 2.42 2.42 2.44 2.69 7.9 1.21 4.52 1.21 2.69 2.44 1.21 2.69 2.42 2.44 1.21 1.21 2.69 1.21 1.21 1.21 1.21 2.69 2.69 2.69 2.69 1.21 2.69

72.5 37.0 72.0 56.0 49.0 54.0 64.3 27.0 70.0 15.0 42.0 38.4 18.2 48.6 46.5 42.9 21.6 20.1 67.3 53.0 72.6 71.5 77.2 65.4 73.1 64.8 51.3 16.0 62.1

4.0 2.0 1.0 8.0 6.7 6.0 5.0 3.4 4.0 4.1 5.3 6.7 3.4 4.5 6.3 5.8 2.1 4.7 4.9 5.1 3.8 5.0 6.4 2.0 3.0 3.4 0.9 1.0 1.0

x o x x m o x o x o m m o o m m o o x o o x o x x x x o x

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 35 25 5 10 0 0 0 0

a b

ADV measurement at moment of motion, or maximum speed reached (if no mobility). Code describing mobility|burial: o= rolls away; m= starts to move, then buries; x= buries.

tests varied well over an order of magnitude for a single D/k value if one assumes k=2.5 d50, indicating that additional factors need to be taken into account to explain the variability. Observing the objects and sand bed under accelerating flow, it was clear that there is a contest between mobilization of sand grains from the bed, which is amplified at the location of the object, causing a scour pit to form, and the initiation of object motion by the increasing drag force of the current. Under these dynamic conditions, it is hypothesized that the relevant bottom roughness scale, k, for the threshold of motion is not the sand grain size, but the depth of the developing scour pit. The time-evolving burial depth, B(t), can be estimated from Eq. (14), with the time scale T* computed with Eq. (15), using the Demir & Garcia (2007) coefficients (found in the previous section to better match the burial evolution observed in the Series 2 A tests). The equilibrium burial depth Beq is evaluated as Eq. (13) using the coefficient values a2 =1.3 and b2 =0.36 for the larger cylinders and a2 =15 and b2 =1.1 for the both the smaller and tapered UXO, as suggested in Section 3.2. B(t) is computed at t= tmove which is estimated as Ucrit/(dU/dt) (see Table 4). The time t is adjusted by the small time interval ΔT suggested by Demir & Garcia, (2007). Then B(tmove) represents the depth of the burial pit, which is used as a time-varying scale of bottom roughness, k, that resists object mobilization. There were six runs where the UXO was positioned partially buried into the sand prior to the start (see shaded lines in Table 4) in order to determine what fraction of burial prevented mobilization. For these runs, the initial burial depth was used as the effective k, until B(t) from Eq. (14) exceeded that initial value, then k= B(t). In Fig. 10, the critical object mobility parameter, fI ΘUcrit, is plotted versus the D/k ratio, where the bottom roughness k is now estimated as B(tmove). Symbol shapes characterize the mobility behavior as in column 6 of Table 4. The red line shows the threshold for the critical object mobility parameter discussed in Section 3.1: ΘUcrit =1.64(D/ k)−0.71. This threshold line generally denotes the separation between

Fig. 10. Initiation of motion for UXO resting on sand bed for the Series 2B laboratory tests listed in Table 4. The threshold line for expected motion based on the empirical fit from Section 3.1 is repeated in red from Fig. 5. Measurements plotted with “x” indicate where burial alone (no mobility) occurred. Open circles denote runs where the object rolled off the sand bed; solid symbols denote runs where a slight amount of horizontal motion preceded burial. Each type of surrogate UXO is shown with a different color.

the highly mobile runs (coded with open circle) and the runs that exhibited no motion, but simply buried (coded with x). One of the no motion data points that appears above the line (black x) was the case where the BR cylinder was deliberately buried into the sand before the run with the largest initial burial of 35%. It is likely that this prior burial behaves differently from the more open scour pit that develops during the accelerating flow. There are 7 runs (solid symbols) where a small amount of initial horizontal movement was observed, but then the object stopped and buried; most of these data points lie close to the threshold line. All the 292

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proposed by Demir & Garcia (2007), albeit with a shorter initial time delay. The role of object shape is significant both for onset of mobility and burial. Under currents, the narrower end of tapered shapes rotates ~45° downstream, because the narrower end has less frictional contact with the bed, so that the blunt end at 45° then sheds vortices intensely, leading to rapid burial. Since tapered shapes are common for UXOs, this is an especially important result. However, additional work is needed to determine if this trend will hold under waves. An alternate physics-based scaling relationship for equilibrium burial accounting for the cylinder aspect ratio provides an improved fit for multiple UXO types and flow conditions (including both cylinders and tapered shapes and both waves and currents) compared to the standard empirical dependence on Θsed. Additional relationships are further investigated in Friedrichs et al., (2016b). When the object was resting on a mobile bed of sand, the mobility behavior under accelerating flow was observed to be a contest between the scour burial caused by the surrounding sand grains being swept away, and the force of the flow reaching the threshold ΘUcrit. It was shown that by using the time-dependent burial equation to estimate the depth of the scour pit at the moment of mobility, and considering that pit depth to be the effective bottom roughness, k, a general explanation of the motion onset can be obtained as a function of D/k so that ΘUcrit can be used to provide a reasonable characterization of the general conditions under which an object will experience burial or migration.

tapered model runs behaved this way, usually because the shape turned obliquely to the flow. The two AL (2.5 cm) cylinders that rolled away have fI ΘUcrit very near the threshold line, predicting that mobility was marginal. It is possible that for the very small cylinders, variations on the sand bed surface provide an enhanced bed slope that is not accounted for in the parameterization, or that bed load transport increases the object mobilization. With the inclusion of a time-dependent estimate of scour burial depth as part of the effective bed roughness, it appears that the relationship of ΘUcrit to D/k generally delineates the threshold of conditions under which an object laying on sand will experience either burial or migration. 4. Summary and discussion A series of laboratory experiments has been conducted to examine mobility and burial of objects resting on the seabed in order to verify and extend currently available engineering models. A set of surrogate unexploded ordnance (UXO) were chosen with a range of diameters, densities and shapes of interest to the military site remediation community. Existing relevant data from the literature was compiled, as well as engineering models proposed to set this empirical knowledge into a universal framework that will allow prediction of object migration and burial behavior for use in a probabilistic expert system. The laboratory experiments were designed to verify and refine these parameterized process models, focusing on the dynamical regime germane to the problem of the state of munitions in natural underwater environments. The first test series investigated the onset of motion on a flat rigid bottom under accelerating flow. The second series studied scour burial in a sand bed in steady flow. The final tests considered the coaction of scour burial and motion onset. The force balance for onset of motion is parameterized by the mobility criteria, fI ΘUcrit where ΘUcrit is the critical object mobility parameter, and fI accounts for the potential effect of inertia in the presence of strong flow acceleration. This threshold mobility parameter is observed to systematically decrease as the diameter, D, of the object increases relative to the size of the roughness elements, k, of a rigid seabed. The present laboratory experiments were specifically constructed to cover the range of D/k representative of UXO lying on the seabed. This range, ~10 < D/k < 100, is intermediate to extant data on ambient sediment motion at the low end and large mine-like objects on the high end; observations from this range were underrepresented in existing data. Theory combined with previous observations suggested a power law relationship with ΘUcrit proportional to (D/k)−0.72. The present laboratory results, covering the D/k the range of interest are best fit by a similar power law, ΘUcrit = a1(D/k)b1, likewise with b1 ≈−0.72, with a1 ≈1.6. It should be noted however, that a range of coefficients is compatible with the relationships previously published in sediment entrainment literature due to the large scatter of the data available. The effect of inertia, as parameterized by fI, is found to be significant only in the presence of strong flow acceleration (e.g., under short period waves) in combination with large D/k or small ρobj. The rate and depth of scour burial in sand are described by functions of the sediment Shields parameter (Θsed) of the form Beq/D = a2 Θsedb2. Tests with surrogate UXO focusing on live-bed scour under currents showed that the equilibrium burial depth for larger cylinders (D > 8 cm) was intermediate to two published power law relationships. Less burial was observed than that predicted by Whitehouse (1998), while greater burial occurred than that predicted by Demir and Garcia (2007), resulting in a revision of power-law coefficients from these previous publications to a2 ≈1.3 and b2 ≈0.36 in the present case. Smaller cylinders (D < 3 cm) and the tapered shape buried more easily, and were best represented using larger coefficients, namely a2 ≈15 and b2 ≈1.1. Still larger best-fit coefficients were found for clear-water scour. The rate of burial under live bed scour exhibited varying patterns but was in reasonable agreement with the timescale

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