Experimental Investigation of Subaqueous Clay-Rich Debris Flows, Turbidity Generation and Sediment Deposition A. Zakeri, G. Si, J.D.G. Marr, and K. Høeg Abstract The characteristics of submarine debris flows and the generated turbidity as well as their relationship with the deposit thickness are discussed herein. There is a gap in our understanding of the processes in which a submarine debris flow and the overriding turbidity form seabed deposits and how the deposits relate to the parent landslide. The experimental program reported here studied subaqueous gravity flows of different clay-rich slurries in a flume. The flume results provide insight into the thickness of the slurry flows with the overriding turbidity clouds and the deposited sediments and lays groundwork for future studies. The thickness of the slurry head tends to decrease with increasing slurry clay content whereas the thickness of the turbidity overriding the slurry head tends to decrease with increasing clay content. Further, the thickness of the deposited layer measured a few seconds after termination of the slurry flow increases with clay content. Geometrically, the flume experiments represented flowing debris of a landslide from 50 m to 120 m water depths with a 600 m travelling distance and downstream velocities between 5 and 13.5 m/s. Keywords Rheology • model scaling • subaqueous clay-rich debris flow • overriding turbidity thickness • deposited sediment thickness A. Zakeri () Geotechnical Engineering Group, C-CORE, St. John’s, Newfoundland, Canada International Centre for Geohazards (ICG), Sognsveien 72, 0855, Oslo, Norway e-mail: arash.zakeri@c-core.ca G. Si Department of Geosciences, University of Oslo, P.O. Box 1047 Blindern, NO-0316 Oslo, Norway J.D.G. Marr National Center for Earth-Surface Dynamics, St. Anthony Falls Laboratory, Minneapolis, MN, USA K. Høeg Department of Geosciences, University of Oslo, P.O. Box 1047 Blindern, NO-0316 Oslo, Norway; International Centre for Geohazards (ICG), Sognsveien 72, 0855, Oslo, Norway D.C. Mosher et al. (eds.), Submarine Mass Movements and Their Consequences, Advances in Natural and Technological Hazards Research, Vol 28, © Springer Science + Business Media B.V. 2010 105 106 1 A. Zakeri et al. Introduction The dynamics of submarine debris flows and the resultant turbidity currents are not fully understood. These processes are important as their occurrence can have severe consequences for infrastructure (e.g. pipelines). Subaqueous debris flows undergo various flow transformations, involving dilution and stripping of surface materials into the ambient water in the form of an overriding, suspended sediment cloud (turbidity), penetration of ambient water into the flow interior, and detachment or disintegration of hydroplaning flow fronts (Sohn 2000b). Unlike subaerial debris flows, the head of a submarine debris flow devoid of permeable girth of gravel and coarser particles, tends to hydroplane over a wedge of ambient water sandwiched between the substrate and the overriding debris. The phenomenon has been observed and studied in a number of recently conducted laboratory experiments (e.g. Harbitz et al. 2003; Ilstad et al. 2004a, b; Mohrig et al. 1998; Zakeri et al. 2008) and numerically simulated (e.g. Gauer et al. 2006; Marr et al. 2002; Zakeri et al. 2009). The development of acoustic techniques for mapping the seafloor and imaging the subsurface has led to a significant increase in understanding geomorphology and geology. In particular, it has led to the identification of numerous deposits of submarine landslides and debris flows on continental slopes. Interpretation of submarine debris flow deposits resulting from slope failures is hampered by the paucity of information concerning their dynamics. This lack of information hinders the development and evaluation of numerical models necessary to understand deposition from submarine debris flow (Mohrig et al. 1999). Estimating debris flow thickness from a deposit thickness is difficult given that debris flows typically have several surges. A deposit forms as result of the main debris flow event as well as the progressive aggregation of individual surges. In many cases, deposition from surges has laterally variable thickness, which complicates back-analysis of a debris flow. As a result, some authors have resorted to the assumption that deposit thickness reflects flow thickness in their studies (e.g. Sohn 2000a). There is a gap in understanding the process in which a submarine debris flow and the overriding turbidity form the seabed deposits and how the deposits relate to the parent landslide. The results of the experimental program reported herein partly fill this gap. They lay the groundwork for future studies on clay-rich submarine debris flow dynamics, generated turbidity and sediment deposition. The experimental program was part of a research study aimed at investigating drag forces on submarine pipelines exerted by clay-rich debris flows. The slurries were a mixture of kaolin clay, sand and water. Prior to the flume experiments, an extensive rheological study using laboratory rheometers was carried out to determine the slurry properties and suitable mix design. The situations tested in the experiments have also been numerically analyzed using Computational Fluid Dynamics (CFD) methods (Zakeri et al. 2009). Sonar data in particular proved important to assess deposition from the debris flows during and shortly after termination of the flow process. Experimental Investigation of Subaqueous Clay-Rich Debris Flows 2 107 Experimental Program 2.1 Rheology Experiments Table 1 presents slurry compositions and material properties for the different experiments. Sand grain size plays an important factor in flow dynamics as slurries made with coarse sand particles are prone to gradual particle settlement during the flow causing change in rheology. As such, the slurries were prepared using two different gradations of sand, Sand A (coarse) and Sand B (fine), to investigate the effects of sand particle coarseness and to select a suitable sand for the experiments. Two different rheometers were used: the Brookfield DV-III Ultra vane-in-cup and the Physica Modular Compact Rheometer (MCR) 300 Ball Measuring System (BMS). The vane-in-cup rheometer has a number of advantages over others: minimal disruption to the sample during vane spindle immersion; low possibility of wall slip effect; and more flexibility with the use of coarse grain size than the coaxialcylinder geometry (Barnes and Carnali 1990). The BMS rheometer was initially developed in 1999 with the purpose of determining rheological behavior of construction materials (e.g. plaster and mortar) with maximum particle size of 10 mm, and later adapted to conventional rotation rheometers (Schatzmann et al. 2003). This exercise was carried out to determine which rheometer more appropriately determines the rheological properties of the slurries when compared with the results of the CFD back-analysis of the flume experiments. Table 1 Slurry composition and material properties Sand gradation Mesh Size (mm) Percentage material by mass Slurry 10% Clay 15% Clay 20% Clay 25% Clay 30% Clay 35% Clay Clay 10 15 20 25 30 35 Water 35 35 35 35 35 35 Sand 55 50 45 40 35 30 Density (kg/m3) 1,681.0 1,685.7 1,687.7 1,689.6 1,691.6 1,694.0 2.0 1.0 0.425 0.300 0.212 0.150 0.106 0.075 0.053 % Passing Sand A Sand B 100 96.5 76.8 – 12.0 – 0.6 – – – – 100 99.5 95.5 77.5 33.5 8.5 0.5 Specific Gravity, Gs: Sand A = 2.7 and Sand B = 2.65 Uniformity coefficient (Cu) = 1.7 for both sands defined as the ratio of the maximum particle size of the smallest 60% (d60) over that of the smallest 10% (d10) of the granular sample. Cu = 1 for a single-sized soil, Cu < 3 a fairly uniform grading and Cu > 5 a well-graded (Whitlow 2001) About 5% of the mass of sand was replaced by black diamond coal slag for visual purposes. The black diamond slag had the same specific gravity and grain size distribution as the sand 108 A. Zakeri et al. The slurry preparation and vane-in-cup rheology experiments were carried out in accordance with the ASTM (D2196-05) procedures. Given the relatively recent development of the BMS as a rheometer, there are no standards available to which non-Newtonian fluids such as the slurries presented here could be tested. As such, the ASTM (D2196-05) guidelines were followed as closely as possible in the BMS tests. The slurries exhibited significant rheopectic behavior, as the fluid shear strength increased with time. Therefore, time-dependency tests were also performed on each slurry sample by studying the hysteresis loop. The Brookfield vane rheometer also has the capability of directly measuring the static yield stress (undrained shear strength) of a sample. For this purpose, a separate batch of slurry samples was prepared and the tests were carried out in accordance with the ASTM (D 4648-94) procedures. 2.2 Flume Experiments The flume experimental program was designed at the International Centre for Geohazards (ICG) at the Norwegian Geotechnical Institute (NGI) and conducted in the St. Anthony Falls Laboratory (SAFL), Minneapolis, USA, in the spring of 2007. A total of 50 experiments were carried out in a 0.20 m wide and 9.5 m long flume suspended inside a 0.6 m wide tank (Fig. 1). The bed was rough with adjustable slope (3° and 6°). For each experiment, 190 L of slurry was prepared in the mixing tank located some 6 m above the flume and conveyed into the head tank. The instrumentation to image the flow consisted of: • Two Canon GL2 cameras for measuring the slurry head velocities near the gate and 5.9 m downstream − 720 W × 480 H pixels frame size at 30 frames per second • One submersible sonar to measure slurry flow and overriding turbidity heights. Transducer: A301S-SU, Olympus NDT and pulser/receiver: DPR300, JSR Ultrasonics Sonar (min. 0.62m from Bed) 3.0 m Ball Valve Plug 150mm I.D. P.V.C. Pipe 0.45 m x 0.45 m x 0.85 m H Flume Walls - Clear Plexiglass - 6 mm Thick Head Tank 0.3 m Rod, Supporting Sonar at Tip (20 mm O.D.) GL2 Camera (30 fps) 1.0 m 5.9 m Gate (0.2 m W x 0.075 m H) 0.20 m Wide Flume Sloped at 3 and 6 Degrees GL2 Camera (30 fps) Chute (0.2 m x 0.2 m x 0.3 m H) 10.0 m Fig. 1 Experimental setup for flume experiments 2.3 m Sonar Data Acquisition System Slurry Mixing Tank (190 Lit.) Experimental Investigation of Subaqueous Clay-Rich Debris Flows 109 The high frequency sonar system is a stationary 500 kHz transceiver oriented normal to the sloping bed, approximately 0.62 m above the bed surface (just below the mean water surface). The data collection protocol involved two sampling periods: the first period at 50 Hz for 60 s and the second period at 6 Hz for the next 30 min. For each ping, the system sampled backscatter at a rate of 8 MHz for 10,000 samples (1.25 ms). Zakeri et al. (2008) give the details of the experimental procedures. 3 Model Scaling to Prototype Situations Geometrically, the length scale in the flume experiments corresponds to 0.01. It should be noted that the flume experiments only model a mass gravity flow of a landslide that has turned into debris subsequent to failure (i.e. not the full scale slope failure from triggering and initial disintegration). Thus, prototype water depths at the gate and the sonar are 50 and 120 m, respectively, with a travel distance of about 600 m. The water flow is turbulent both in the flume and prototype hence, the Re similitude for the water is met on fixed boundaries. Slurry head velocities in the experiments ranged between about 0.5 and 1.35 m/s that correspond to Froude numbers ( Fr = U Δrgl r ) in the range of 0.45 to 1.25. The Froude number formulation, l is some characteristic length of the prototype, g is gravitational acceleration, U is fluid velocity, and r and Dr are fluid density and differential density with respect to the ambient fluid, respectively. Given that the ratio of the model to prototype velocities is equal to the square root of the geometric length scale, the flume velocities correspond to a range of about 5 to 13.5 m/s in the prototype. The slurries are non-Newtonian fluids, therefore the Reynolds numbers depend on the apparent viscosity which is a function of the shear rate. The shear rate at the base is quite high – in the order of 103 s−1 or higher – dropping to 10 s−1 at about 2 mm from the base (Zakeri et al. 2009). Given the high shear rates at the base, the Re similitude is also met for the slurry. The ratio of the model to prototype viscosities is equal to the geometric length scale to the power 1.5. As such, the viscosity of the slurries corresponds to debris flow viscosities that are about three orders of magnitude higher (i.e. slurry stresses of between about 7 and 250 Pa versus 7 to 250 kPa in a prototype situation). This is at least an order of magnitude higher than what is expected in the prototype. Therefore, the similitude of the slurries is distorted. However, this distortion mainly affects the study of the flow dynamics within the slurry itself and not the system as a whole. The shear rates at the slurry-water interface are high and therefore, the Re similitude at this free-surface holds. A criterion in the flume experiments was that the slurry properties should remain constant (i.e. no sand particle settling). A given grain size can be regarded as part of a fluid if the time scale of settling exceeds the duration of the debris flow, particularly when the grains have diameter of about 0.05 mm or less (Iverson 1997). Hence, only the Bagnold number (NBag), was considered. The Bagnold number is defined as: ( ) 110 A. Zakeri et al. N Bag = rsd 2g 1 2 l m app (1) where, rs is grain density, d is grain diameter, g is shear strain rate, and mapp is slurry/ debris flow apparent viscosity. l is the linear concentration defined by Bagnold (1954) and is obtained from the following expression: λ= Vs1 3 13 Vmax − Vs1 3 (2) where, Vs is the grain volume fraction and Vmax is the maximum volume fraction equal to 0.74 for spheres of equal diameter (Bagnold 1954) and 0.64 for wellgraded natural sands (Bagnold 1966). Assuming the maximum volume fraction for Sand B to be 0.70, the linear concentration of Bagnold would be equal to 8.42. For Sand B 10% clay slurry, the NBag at or very close to the base is about 8 and 17 for the d60 and d90 grain sizes, respectively. These values are far below the 40 limit, and therefore viscous effects are dominant must be considered for the flume experiments. For Sand A slurries, these NBag values are close to or greater than 40. 4 4.1 Experimental Results, Analysis and Discussion Results of Rheology Tests Figure 2 presents the rheology test results. Slurries made with Sand B experience a larger range of shear stresses than those made with Sand A. Particle size affects the rheological behavior of suspension fluids through the specific surface defined as the grain surface area per gram of mass (m2/g) – the smaller the particle, the higher the specific surface. The behavior of fine-grained slurries is mainly controlled by the clayey matrix. Decrease in sand size largely increases total surface area of particles per unit volume, which in turn, increases the amount of bound water, and decreases the amount of free water in the slurry system (Major and Pierson 1992). Sand A particles are about 2.6 times larger in diameter than Sand B which gives significantly higher specific surface for Sand B. This influences rheological characteristics of the 10% clay slurry made with Sand A having shear stresses roughly twice than that of the 15% clay (Fig. 2). Sand A particles in the 10% clay slurry settle at high shear rates in the rheology tests, and at high rates of shear the fluid’s apparent viscosity decreased. Sand A 35% clay slurry exhibited a flow curve with decreasing shear stress (see the dip in curve in Fig. 2 left) for shear rates less than about 5 s−1. As such, Sand B was used for the slurries in the flume experiments. Results of the rheological experiments were repeatable within ± 5%. The four mathematical models had a confidence of fit of greater than 95% through the data (Table 2). All slurries exhibited strong rheopectic characteristics (i.e. the shear strength increased with time). Therefore, Experimental Investigation of Subaqueous Clay-Rich Debris Flows 300 Sand A Slurries 10% Clay 15% Clay 20% Clay 25% Clay 30% Clay 35% Clay Herschel-Bulkley Power-Law 200 100 0 Shear Stress (Pa) 300 Shear Stress (Pa) 111 Sand B Slurries 10% Clay 15% Clay 20% Clay 25% Clay 30% Clay 35% Clay Herschel-Bulkley Power-Law 200 100 0 0 10 20 30 40 50 60 0 Shear Rate (1/s) 10 20 30 40 50 60 Shear Rate (1/s) Fig. 2 Rheological experiments results and Herschel-Bulkley and Power-Law mathematical model fits: (left) Sand A (coarse) slurries and (right) Sand B (fine) slurries Table 2 Slurry rheological models for slurries made with Sand B (fine). Shear stresses are in Pascals Slurry Herschel-Bulkley Power-Law Casson Bingham . . . . t = 10.3g 0.125 t = 10.6 + 0.20g 10% Clay t = 7.5 + 3g 0.35 t = 9.0 + 0.04 g . . . . t = 23.6 + 0.06 g 15% Clay t = 20.5 + 5.5g 0.35 t = 25g 0.125 t = 26.7 + 0.37g . . . . t = 50.4 + 0.10 g t = 50g 0.12 t = 55.9 + 0.66g 20% Clay t = 43 + 10g 0.35 . . . . t = 88.3 + 0.16 g 25% Clay t = 85 + 12g 0.4 t = 91.5g 0.11 t = 97.6 + 1.11g . . . . t = 115.2 + 0.27 g 30% Clay t = 110 + 15g 0.45 t = 118g 0.125 t = 127.7 + 1.80g . . . . 35% Clay t = 161 + 25g 0.4 t = 165g 0.13 t = 12. + 5.5 g t = 168.0 + 0.31 g slurry preparation and release in the flume experiments were designed to strictly comply with that of the standard rheology tests. The flow curves measured from the BMS rheology tests were generally 10% to 30% less than those obtained from the vane-in-cup rheometer. The results of the CFD simulations of the flume experiments suggest that the vane-in-cup rheometer provides a better estimate of the rheological characteristics of the slurries (Zakeri et al. 2009). The undrained shear strength (static yield stress) test results obtained by using the vane rheometer in accordance with the ASTM (D 4648–94) procedures. In magnitude, the yield stress values were close to the shear stresses measured at very low shear rates (<< 1 s − 1) in the vane-in-cup rheology tests. 4.2 Results of the Sonar Observations Sonar data provide information on the internal structure of the gravity flow. The outgoing initial ping moves toward the bed, and as it density and/or velocity contrasts, it is partially reflected back to the transducer and recorded as backscatter. It 112 A. Zakeri et al. Fig. 3 Greyscale rendering of the backscatter data (left) 38 s of recording: 15% clay slurry, head velocity: 0.74 m/s and (right) 25 s of recording: 20% clay slurry, head velocity: 1.33 m/s. Vertical grid spacing: 20 mm, horizontal grid spacing: 1 s allows for accurate measurements of the flow geometries including thickness of the initial slurry head, overriding turbidity but also the deposited layer after the termination of the flow. Examples of the greyscale rendering of the backscatter data from the runs are shown on Fig. 3. Figure 4 presents the summary results from the rendered images. Table 3 summarizes the results for all 50 runs based on sonar data and camera recordings. A major portion of the turbidity is generated from the slurry head. As the head flows downstream, thin sheets of materials are peeled off and diffuse into the ambient water forming the turbidity. The water entrainment into the slurry flow is restricted to a thin zone located at the surface of the slurry. The ambient water does not penetrate deep enough into the slurry to affect its rheology. The generated turbidity can be divided into two categories: the one overriding the slurry head and the trailing turbidity over the deposited sediments. In general, the thickness of the slurry head decreases with increasing clay content, whereas the thickness of the overriding turbidity decreases with the increasing clay content. However, the trailing turbidity thickness appears to be approximately the same for all slurries reaching the water surface shortly after termination of the flow. The thickness of the deposited layer measured a few seconds after termination of the slurry flow increases with the Experimental Investigation of Subaqueous Clay-Rich Debris Flows 600 Flow Turbidity 200 600 End of Slurry Flow (App. 1.7 Sec.) Flow 400 Turbidity 200 0 0 Slurry 1 Head Vel. = 1.25 m/s 2 3 4 0 5 Slurry 1 0 Head Vel. = 1.25 m/s Time (s) 600 200 Turbidity 3 4 5 Time (s) 600 End of Slurry Flow (App. 3.6 Sec.) 400 200 Turbidity 0 Slurry 1 0 Head Vel. = 1.0 m/s 2 3 4 0 5 0 Time (s) Slurry 1 Head Vel. = 0.74 m/s 2 3 4 5 Time (s) 10% Clay 15% Clay 600 400 200 Turbidity 600 Flow 400 End of Slurry Flow (App. 2.3 Sec.) 200 Turbidity 0 Slurry 1 0 Head Vel. = 1.35 m/s 2 3 4 0 Slurry 1 0 Head Vel. = 1.16 m/s 5 Time (s) 2 3 4 5 Time (s) 600 400 End of Slurry Flow (App. 2.6 Sec.) 200 400 Flow End of Slurry Flow Turbidity (App. 3.1 Sec.) 200 0 Slurry 1 0 Head Vel. = 0.88 m/s 2 3 4 0 5 0 Time (s) Slurry 1 Head Vel. = 0.87 m/s 2 3 4 5 Time (s) 20% Clay 25% Clay 600 End of Slurry Flow Turbidity (App. 2.7 Sec.) 200 600 Flow End of Slurry Flow (App. 1.8 Sec.) 400 200 Turbidity 0 Slurry 1 Head Vel. = 1.07 m/s 2 3 4 0 5 Slurry 1 0 Head Vel. = 0.80 m/s Time (s) 2 3 4 5 Time (s) 600 End of Slurry Flow (App. 3.6 Sec.) 200 End of Slurry Flow (App. 2.7 Sec.) 400 200 Turbidity 0 0 Slurry 1 Head Vel. = 0.80 m/s 2 3 Time (s) 30% Clay 4 5 Height (mm) Turbidity 600 Height (mm) 400 Flow Height (mm) 400 Height (mm) Flow 0 Height (mm) Turbidity 600 Height (mm) Flow Height (mm) End of Slurry Flow (App. 1.7 Sec.) Height (mm) Flow Height (mm) 400 2 Flow Height (mm) End of Slurry Flow (App. 3.3 Sec.) Flow Height (mm) 400 Height (mm) End of Slurry Flow (App. 1.6 Sec.) 113 0 0 Slurry 1 Head Vel. = 0.56 m/s 2 3 4 5 Time (s) 35% Clay Fig. 4 Analysis results of the grayscale rendered images produced from the experiments with the maximum and minimum slurry head velocities clay content, after which gravity-controlled compaction or consolidation will start. The distinct shape of the slurry head (single or double-hump) is a result of the velocity field developed in the water due to the momentum transfer between the water and slurry (Zakeri 2007; Zakeri et al. 2009). The flow in the water is in the form of large circulating eddy vertices slightly lagging behind the slurry head, which in turn affects the its shape. The extent of which the shape of the slurry head is affected by this momentum transfer depends on the strength of the slurry (e.g. a more pronounced double hump shape in slurries of 25% clay and less). 114 A. Zakeri et al. Table 3 Analysis results based on the rendered grayscale sonar data and camera recordings Slurry Flowing slurry head (% Clay) characteristics Deposit thickness Turbidity thickness Thickness of deposited as percentage of overriding slurry layer (mm)b slurry flow head (mm)a Velocity (m/s) Height (mm)a Min. Max. Min. Max Min. Max Min. Max Min. (%) Max (%) 10% 1.0 1.25 225 365 95 215 5 10 2.2 15% 0.74 1.25 210 270 140 165 27 35 12.9 20% 0.88 1.35 300 310 60 70 32 35 10.7 25% 0.87 1.16 210 225 70 155 52 62 24.8 30% 0.80 1.07 150 185 90 95 52 64 34.7 35% 0.56 0.80 120 145 90 75 53 65 44.2 a The measured values were rounded off to the nearest fifth millimeter dividend b The readings were rounded off to nearest millimeter 5 2.7 13.0 11.3 27.6 35.1 44.8 Conclusions The effects of particle size and time-dependency characteristics have to be considered when studying sediment deposition from debris flows. The vanein-cup rheometer better captures the rheological behavior of the kaolin-sand-water slurries than the BMS rheometer. The slurry head velocities in the flume experiments ranged between about 0.5 and 1.35 m/s, which correspond to prototype velocities ranging from 5 to 13.5 m/s for a clay-rich submarine debris flow. Flume experiments modelled transition between subcritical and supercritical flow regimes. Using sonar data, it is possible measure flow geometries accurately, including the thickness of initial slurry head, overriding turbidity, and the layer deposited after termination of the flow. The results showed that the thickness of the slurry head tends to decrease with increase in clay content whereas the thickness of the overriding turbidity decreases with clay content. However, the trailing turbidity thickness is approximately the same for all slurries reaching the water surface shortly after termination of the flow. The thickness of the deposited layer measured a few seconds after termination of the slurry flow increased with the clay content. With further investigation, it may be possible to relate the measured deposit thicknesses to those of similar prototype conditions (e.g. with the help of the conventional consolidation theory, etc.). The work presented here outlines the procedures for similar type experiments and lays the groundwork for future studies. Acknowledgements The work (ICG Contribution No. 229) presented here was supported by the Research Council of Norway through the International Centre for Geohazards (ICG) and the LeifEiriksson stipend awarded to the first author. Their support is gratefully acknowledged. We also extend our thanks to Statoil for funding the experimental program and to the St. Anthony Falls Laboratory (SAFL) staff for their contributions to the experiments. The authors are thankful to Dr. Maarten Vanneste and Prof. Christopher Baxter for their review efforts and constructive comments. Experimental Investigation of Subaqueous Clay-Rich Debris Flows 115 References ASTM (D2196–05) Standard Test Methods for Rheological Properties of Non-Newtonian Materials by Rotational (Brookfield type) Viscometer. In: Materials ASfT (ed) D2196–05: ASTM Internat ASTM (D 4648–94) Standard Test Method for Laboratory Miniature Vane Shear Test for Saturated Fine-grained Clayey Soils. 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