Reconstituting soil beds to a desired density is essential to geotechnical modeling tests. In this study, we apply and assess the method of air uidization to prepare sand beds for geotechnical engineering studies. Through it, an automated bed preparation pro- cess can be realized. The details of device structure and design are presented as a reference for application of the methodology. By quantifying the average and local post- uidization density of the bed, the performance of the uidized bed device is char- acterized. With the addition of vibration and by changing the de uidization rate, the sand can be prepared with volume-based relative densities ranging from 10% to 92%. Local sand density, measured with a cone penetrometer, is nearly uniform across the bed: density variation is less than 13% ( COVDr) for all protocols except for some beds prepared by de uidization only. The variation of local density and penetration resis- tance measured across the bed breadth is comparable to results from beds prepared by the commonly used method of pluviation. This suggests that sand beds reconstituted using air uidization are suitable for geotechnical modeling tests. Keywords: Fluidization; Fluidized bed; Preparation of sand beds; Density variation; Cone penetration; Penetrometer Corresponding author Email addresses: ZhefeiJin2015@u.northwestern.edu (Zhefei Jin), junyue.tang@northwestern.edu (Junyue Tang), umbanhowar@northwestern.edu (Paul B. Umbanhowar), jphambleton@northwestern.edu (James Hambleton), jphambleton@northwestern.edu (James Hambleton) 1. Introduction Relative density, de ned as the ratio of the di erence between the void ratios of a cohesionless soil in its loosest state and existing natural state to the di erence between its void ratio in the loosest and densest states, signi cantly in uences soil behaviour. In the laboratory, preparation of large soil samples to a required density is a fundamental step in investigating geotechnical problems. For example, [1] studied geosynthetic-soil interaction by performing pull-out tests in a 1 :5 m by 0:6 m soil bed; [2] studied the response of footings under planar loading in sand prepared in a cylindrical tank 0 :45 m high and with a 0 :45 m inner diameter. Traditionally, the reconstitution of dry sand samples is achieved by tamping, vibration and di erent types of pluviation. These methods are di erentiated into two groups: for tamping and vibration, the density of the sample is adjusted after deposition; while for pluviation the density is determined during deposition [3]. With tamping, sand is poured in several layers with each layer compressed by a compactor. Using this method, [4] obtained dry sand samples for triaxial tests with relative density ranging from 40% to 90%. [5] achieved an approximately homogeneous sample with relative densities of 40% and 75% with a 2 m 0:6 m sand bed. [6] in- vestigated the in uence of tamped layers and compactor drop height on the void ratio and found that neither increasing the number of layers from three to ve nor increasing the drop height from 20 mm to 50 mm signi cantly altered the void ratio. The main drawbacks of tamping are particle crushing during compaction, low repeatability, and relatively pronounced density variation along the depth [7]. Vibration is generally used to prepare medium to dense sand samples. The sample is rst prepared in a loose state, and then vibrated under a small amount of surcharge provided by a cap. [8] and [9] successfully used this method to prepare dense sand samples for 1 glaboratory and higher gcentrifuge tests, respectively. By monitoring subsidence of the cap, [10] obtained specimens with relative densities ranging from 50% to 90% while controlling the percentage error between actual and desired density to less 2 than 1%. Compared with tamping and vibration, pluviation in air is used more broadly be- cause of its advantages of reduced segregation, lack of particle crushing, and better repeatability [11]. Studies of air pluviation indicate that relative densities achieved by this method generally range from 40% to 100% [12, 11, 13, 3, 14]. For a given type of sand, the main factors a ecting the relative density are the particle drop height, deposition intensity, and the mesh size of the grid through which the sand particles are dropped [15, 16]. A higher drop height leads to a larger fall velocity which in- creases packing density. This densi cation is e ective for drop height below a cer- tain maximum, since the particle velocity plateaus at larger drop heights due to air drag [17]. For a given drop height, increased deposition intensity decreases deposition density [18, 19, 20], since the simultaneous fall of many particles increases inter-particle interference [13]. Increased deposition intensity can be achieved by increasing the mesh size of the grid [18]. Even though air pluviation is widely used to prepare sand samples in the laboratory, it has some limitations. First, air pluviation is usually not fully automated, which costs time and manpower as sand initially inside the bed needs to be emptied and then poured in again. Second, uniform low density ( 30%) samples are hard to achieve, making pluviation more applicable to studies of medium or dense sand packings. Third, the surface of a pluviation reconstituted sample is typically uneven, requiring levelling by post-deposition vacuuming, which is time consuming and can disturb the sample. Air uidization can overcome the limitations of the three techniques for reconstitut- ing a sand bed described above. The process of uidization is similar to liquefaction in which granular material is converted from a static solid-like state to a dynamic uid- like state when a uid (liquid or gas) ows upward through the granular material. Fluidization is widely used in the chemical processing industry for separations, heat transfer operations, and catalytic reactions. Recently, Goldman and co-workers used air- uidization to reconstitute granular material beds [21, 22, 23, 24, 25, 26]. They found that a uidized bed allows control of the relative density and creation of re- 3 peatable homogeneous granular bed states, which were typically composed of 1 mm poppy seeds. Beds prepared in this way exhibit a spatially uniform penetration resis- tance that is highly repeatable. In one process, the bed of particles is reconstituted by uidization and then settled by de uidization. Di erent degrees of compaction can be achieved by changing the de uidization rate [27]. The dense packing state is realized by slow de uidization while the loose packing state is obtained with rapid de uidiza- tion. Generally, varying the de uidization rate is sucient to prepare samples with loose to medium packing states. Samples can be densi ed by other techniques, such as vibration. X-ray absorption measurements con rmed that vertical density variations in samples prepared using this technique are small, with less than 0 :004 variation in the packing fraction, which is calculated by dividing the total grain mass by the bed volume and the particle density [27]. The objectives of this study are to (1) provide details about using air- uidization to reconstitute sand beds; (2) characterize physical properties of sand beds created using this technique; and (3) demonstrate the quali cation of this method for preparing sand beds for geotechnical modeling tests. To do so, we explain the mechanism of uidization and describe the design of a uidized bed device. Through a discussion, we illustrate its potential for use in di erent types of geotechnical modeling tests with various demands on sand bed soil properties and size. In this study, we use three operating modes: de uidization only ( DO), de uidization followed by vibration ( DFV ) and de uidization concurrent with vibration ( DCV ) to prepare sand beds with a broad range of relative density (10 :4% to 91:7%). For each sand bed, we characterize the density globally and locally by volume-based and penetration-based measurements, respectively. The variation of local density and penetration resistance measured across beds are compared to results from beds prepared by pluviation, a widely used method in geotechnical modeling tests. 4 2. Fluidized bed device 2.1. Fundamentals of uidization In a gas- uidized bed, the uidization behaviour di ers depending on the super cial gas velocity and particle properties [28, 29]. When gas ow is introduced through the porous bottom of a bed of particles, it moves upwards through voids between particles. At low gas velocities, the drag force exerted on each particle is low, resulting in a static bed. As the gas velocity is increased, the drag force begins to counteract the gravitational force, causing the bed to expand in volume as the particles move away from each other. With further increase in the gas velocity, a critical value is reached at which the upward drag force equals the downward gravitational force, causing the particles to become suspended. At this critical value, the bed is said to be uidized and exhibits uid behaviour in that it can no longer support internal stresses. With further increases in the gas velocity, the bed begins to bubble. The bulk density of the bed continues to decrease, and the uidization becomes more violent until particles no longer form a bed but are \conveyed" upwards by the gas ow. Stopping the gas ow causes the particle bed to de uidize in three consecutive stages: a rapid initial stage for bubble escape, an intermediate stage of hindered sedimentation with a constant velocity of solids descent, and a nal decelerating stage of solids consolidation [30]. Not all particle beds undergo the full process of uidization and de uidization de- scribed above. The speci c behavior depends on particle properties, primarily size and density. Based on particle size and density, Geldart categorize particles into Groups A-D [28, 29]. Group A designates aeratable particles. These materials (e.g., milk our) normally have a small mean particle size and/or low particle density. Beds of these particles can be uidized at low gas velocities without the formation of bubbles and are subject to the full uidization-de uidization process. Group B particles form bub- bling beds. Most have particles with size between 150 m and 500m and density from about 1:4 to 4 g/cm3. For these particle beds, once the minimum uidization velocity is exceeded, the excess gas appears in the form of bubbles; in the de uidization process, 5 the particle beds reach their nal state as soon as bubbles are expelled [30]. Group C particles are cohesive or very ne powders. They are extremely challenging to uidize and typically exhibit channeling in which gas ow is concentrated in a number of dis- crete \holes" in the bed. Group D particles form spouting beds and are composed of very large or very dense particles, such as co ee beans and wheat. As the gas velocity is increased, a jet forms in the bed, and the material may potentially be blown out of the bed. In this paper, we use silica sand which is a Group B particle. Before discussing the design of the uidized bed device, we review the air ow re- quirements to achieve particle uidization. As stated above, the inception of uidization is triggered when the air velocity reaches a value at which the upward drag forces on the particles equals the downward gravitational force. Considering the entire bed, this force balance condition occurs when the product of the ow induced pressure drop across the bed and the bed cross-sectional area equals the weight of the soil in the bed [31]. The pressure drop across the bed depends on the air velocity, and it has been investigated and described by various models [32, 33, 31, 34]. To illustrate the general approach, we characterize the relationship between the pressure drop across the bed  Pand the super cial airspeed v(calculated as Q=A; whereQis the volumetric air ow rate and Ais the cross-sectional bed area) using Erguns equation: P L=150(1)2v d23+ 1:751 3av2 d; (1) whereLis the particle bed height; is the dynamic viscosity of the uidizing gas; ais the gas density; dis the average grain diameter; and is the bed porosity. The left-hand side of Eq. (1) equals the unit weight of the particle bed ( b). By transforming bto the unit weight of a grain ( g) with the relation b= g(1), the minimum required ow rate (Qmf) for uidization can be calculated from: g=150(1)Qmf d23A+ 1:75aQ2 mf d3A2: (2) 2.2. Design of the uidized bed device In principle, a ow of air at the minimum required ow rate ( Qmf) is required to achieve uidization; however, in practice, a facility is needed to provide the required 6 Blower Soil Gas ductHoneycombDistributorAir out Air in Vibrating actuator Figure 1: Schematic diagram of uidized bed apparatus. air ow. Fig. 1 is a model diagram of our 150 cm (length) 75 cm (width) 50 cm (height) uidized bed located in the Soil-Structure and Soil-Machine Interaction Lab- oratory (SSI-SMI Laboratory) at Northwestern University. A 10 hp centrifugal fan blower with three-phase motor (Chicago Blower Corp.) produces the required ow of high-pressure air, which is transmitted by a duct to the plenum. The 20 cm tall plenum pre-distributes the air, and its walls are 1 :8 cm thick acrylic recessed in the extruded aluminum rails (80 =20 Inc.) which form the frame of the box. At the top of the plenum is a 2:54 cm thick layer of steel honeycomb for structural rigidity and ow distribu- tion. Above the honeycomb, a 1 :27 cm thick layer of porous plastic with 20 m pores (GenPore) forms the distributor. The distributor supports the particles in the bed, and, more importantly, promotes the uniform ow of air through the particle bed. The extra vertical space above the sand surface and below the top of the container box helps to contain the sand. The blower is driven by a variable frequency drive controller (model #CFW110028T2ON1Z, WEG), which supports proportional voltage control of the fan speed. The 0-10 V fan speed control signal comes from a USB 6001 DAQ (National Instruments) controlled by a MATLAB program. To understand the design of the uidized bed device, we explain how the blower works. Air enters the blower at atmospheric pressure, and then is pressurized by the 7 Figure 2: System and blower curves for uidized bed device. The intersection of the blower and system curves determines the operating point. blower. This pressure di erence drives the air through the duct, plenum, distributor, and bed material. As described in the previous section, to uidize the particles, the air ow through the bed must reach the minimum required air ow rate ( Qmf). The air ow rate in the system is determined not only by the operating motor speed of the blower but also the ow resistance of the entire system. At any xed motor speed, the blower operates by delivering air ow against a certain static pressure as speci ed by a \performance curve" such as the one shown in Fig. 2 (the actual performance curve for the blower used in the study). For a system, the static pressure depends on the air ow rate. Therefore, the pressure required by a system over a range of ow rates can be determined, and a \system resistance curve" can be developed and plotted on the blower performance curve to show the blowers actual operating point, i.e., the intersection point. This point moves as the system or the motor speed changes. For example, at a certain motor speed, the operating point is the one with zero ow rate when the system is sealed, and with zero static pressure when the system is totally open. In terms of a given system (such as the one indicated by the red line in Fig. 2), the operating point moves from the red point to the black point as the motor speed is increased from 1740 RPM to 2500 RPM (Revolutions Per Minute). Hence, to uidize a given bed, a speci c motor speed is required corresponding to the minimum required ow rate (Qmf). To obtain this desired operating point, the system resistance curve for the device must be determined. 8 By design, the largest resistance in a uidized bed device comes from the distributor and the particle bed. In most cases, the pressure drop for a given ow rate follows a second-order relationship [35]. The pressure drop of the distributor ( Pd) is generalized as Pd=m A2 dQ2+n AdQ, whereAdis the area of distributor, which is the same as the cross-sectional area of bed ( A);mandnare parameters mainly determined by the hole size, hole number, and the thickness of the porous sheet. For air owing through the bed of particles, the pressure drop can be calculated from Eq. (1) as  Pb =150(1)2L d23AQ+ 1:751 3aL dA2Q2. It should be noted that to equally distribute air ow through the bed, a constraint between the minimum distributor pressure drop and the bed pressure drop is imposed, i.e.  PdcPb, wherecis proposed to range from 0:02 to 1, with 0 :3 as a widely quoted value [36, 37]. By combining the pressure drop from the distributor and the bed, the system resistance is characterized as: Ps= 1:751 3aL dA2+m A2 Q2+150(1)2L d23A+n A Q: (3) Assigning the value of the minimum required ow rate ( Qmf) to the ow rate ( Q) in Eq. (3), the desired operating point ( Q,P) can be located on the system resistance curve, which determines the desired motor speed. To validate the design methodology, tests of the uidized bed in the SSI-SMI lab were performed using silica sand, obtained from Ottawa, Illinois (supplied by U.S. Silica Company) and characterized according to ASTM procedures. Fig. 3 shows the grain- size distribution curve of the sand based on data from the supplier. The particles are round in shape and range in size from 0 :075 mm to 0 :425 mm with a mean diameter of D50= 0:19 mm. Based on the curve, the coecient of uniformity, Cu;and the coecient of curvature, Cc;are 1:61 and 1:03, respectively; hence the sand is classi ed as poorly- graded (SP). The maximum density ( max) of this sand is measured as 1730 kg/m3[38], and its minimum density ( min) is 1450 kg/m3[39]. Fig. 2 shows the actual blower performance curves and the estimated system resis- tance curve. The parameters used to determine the system resistance curve are m= 26808 Pa s2=m2,n= 24488 Pa s/m,d= 0:19 mm, g= 26 kN=m3,L= 0:127 m,= 9 020406080100 0.01 0.1 1Percent finer/Weight Grain size (mm)Figure 3: Cumulative grain-size distribution of the silica sand (Ottawa) used in this study (data provided by U.S. Silica). 0:396,A= 1:125 m2,= 1:81105kg/ms (at 25C),a= 1:225 kg/m3. Among these parameters, mandnare obtained based on the information provided by the porous layer manufacturer; dis determined from the grain size data provided by U.S. Silica; gis approximated as the unit weight of quartz, the main mineral component of Ottawa sand; Lis the average height of the sand bed measured before the veri cation test, which can be used to estimate the bulk density of the bed; and is determined by the sand particle density and the estimated bulk density on the premise that the sand is distributed uniformly. Based on the calculation, the minimum required ow rate and airspeed are 0 :04 m3=s and 0:035 m/s, respectively. The pressure drop across the distributor and particle bed at uidization is predicted to be 2763 Pa, which is close to the actual gauge pressure measured in the plenum of 2922 Pa. According to the above calculation and blower performance curve, the bed of sand should uidize at a motor speed of 1740 RPM, while the actual value to achieve uidization is slightly higher at 1780 RPM. The small di erence may result from air leaks and the unaccounted for ad- ditional resistance from the duct, honeycomb and honeycomb support. Reducing these e ects is vital to the eciency and precise design of the uidized bed device. 10 2.3. Fluidized bed device capabilities The demands on a sand bed for geotechnical model testing vary with the soil prop- erties and bed size. The uidized bed device can be adjusted to accommodate speci c demands, mainly through the selection of the distributor and the operation of the blower. The soil properties a ecting the required air ow for achieving uidization in- clude the unit weight and average diameter of the grains and the soil porosity. Unit weight varies with grain mineral content. Most sand is made of quartz, so the unit weight is generally regarded as constant, i.e., 26 kN =m3[40]. Consequently, only the in uence of grain diameter and porosity are discussed below. With increase of average grain diameter or porosity of the sand bed, the minimum required ow rate increases, which raises the distributor pressure drop ( Pd). However, the bed pressure drop (Pb), which equals the weight of sand per unit area, remains constant. Hence, the desired operating point moves to the position with higher static pressure and ow rate (red square symbol in Fig. 2), which can be reached by increasing the motor speed. Note these desired points in Fig. 2 are plotted to illustrate the in uence of di erent factors on the air ow requirements, and do not correspond to any speci c sand bed. Now we consider the e ects of bed size, which refers to the height and the cross- sectional area of the sand bed. The height of the sand bed has no in uence on the minimum required ow rate and  Pd;while Pbincreases linearly. Accordingly, the blower should provide higher pressure with the same ow rate (triangular symbol in Fig. 2 is the new desired operating point). Note that a distributor with higher resistance (higherm,n) might be required in order to guarantee the design constraint  Pd cPb:Distributor resistance can be increased by increasing its thickness, decreasing the holes size, or decreasing the number of holes. For the uidized bed in the SSI- SMI lab, the maximum motor speed is 3600 RPM, at which the blower can produce a maximum pressure around 11960 Pa and a maximum ow rate of 0 :7 m3/s. At this speed and with the sand described in the previous section, the maximum depth of the uidized sand bed is 0 :72 m. However, in this case,  Pb10812 Pa, and  Pd855 Pa, so the constraint between them, i.e.  PdcPbis not satis ed with c= 0:3. A higher 11 resistance distributor can help this condition. The deepest uidizable sand bed is about 0:61 m for the utilized blower if the  Pdreaches 2760 Pa, which can be accomplished by increasing the current distributor thickness to 4 :1 cm. For sand beds with larger cross-sectional areas, the minimum required ow rate increases, while the minimum required airspeed stays the same. According to Eq. (3), system resistance remains constant at constant airspeed. Therefore, a higher ow rate but the same static pressure is needed. Correspondingly, the desired operating point is shifted purely horizontally (red diamond symbol in Fig. 2). When the uidized bed in the SSI-SMI lab is run at the maximum motor speed, the largest cross-sectional area of the uidizable bed is about 25 m2which limits the maximum sand bed depth to 0 :61 m. 3. Sand bed characterization In this study, sand beds are prepared using three di erent operating modes: de- uidization only ( DO), de udization followed by vibration ( DFV ), and de uidization concurrent with vibration ( DCV ). In mode DO, the sand settles gradually with de- creasing air ow to form the sample. Mode DFV extends the DOmethod by vibrating the the sand bed after de uidization with the same time of de uidization. Mode DCV vibrates the bed during de uidization. The vibration in the latter two modes is induced by a vibrating motor (Fasco #D1130) attached to the middle of one side of the u- idized bed frame, as shown in Fig. 1. In the tests, 227 kg of sand was placed on the bed with an initial height of 0 :130 m. The sand was fully uidized by increasing the motor speed to 1780 RPM, at which point the pressure in the plenum ( P0) is 2922 Pa. The fully uidized stage was maintained for 10 s, after which the de uidization stage was started. The motor speed was linearly decreased from 1780 RPM to 0 over a variable de uidization time ( T) to reduce the pressure and ow rate of air. For each of the three modes listed above, de uidization times ( T) ranging from 50 s (the stopping time of the blower is 40 s) to nearly 10 hrs were applied to reconstitute the sand beds. The volumetric density and local density of the resulting beds were then measured as described below. Note that in addition to vibration, beds also can be densi ed by short 12 sandRobot arm Cone penetrometer20 mm 30˚ (b)Force sensor S S (a)OFigure 4: (a) Locations of sand height measurements and penetration tests. (b) Schematic of cone penetration measurement. periodic air pulses [23]. 3.1. Volumetric density The volume-based density of the bed ( v) is measured as a function of the de uidiza- tion time for the three operating modes. To do so, the volume of each reconstituted sand bed is determined with a laser based distance sensor (Leica Disto E7400X) attached to a six-axis ABB IRB-4400 robot, whose movement is controlled automatically by a connected computer. First, the distance to the distributor (empty bed) Hiis measured at 21 positions on a uniform 17 :5 cm grid, see Fig. 4(a), as the robot moves the distance sensor in a horizontal plane. Then, after the bed is lled and reconstituted, the distance between the end of the robot arm and the surface of the sand hiis measured at the same positions. The top of the distributor (bottom of bed) and the reconstituted sand surfaces are nearly at: Hivaries by less than 0 :2 cm andhiby less than 0 :6 cm for all cases. The volume of sand in the bed is then estimated as V=A(Hihi);whereAis the bed cross-sectional area and the overline indicates the ensemble average. Assuming that the sand bed is uniform in density, the volume-based density of the sand bed is v=M=V , whereMis the mass of sand in the bed, and the corresponding relative density isDr=max(vmin) v(maxmin);wheremaxandminare determined in the section entitled "Design of the uidized bed device." The volume-based relative density of the sand bed versus the pressure ramp rate 13 00.20.40.60.81 0.06 0.6 6 60Relatively density, Dr Pressure ramp rate, RP(Pa/s)DO DFV DCVFigure 5: Relative density of sand prepared by de uidization only ( DO), de uidization followed by vibration ( DFV ), and de uidization with concurrent vibration ( DCV ) for various pressure ramp rates. Rp=P0=Tincreases with decreasing Rpfor all cases as shown in Fig. 5. Drvalues ranging from 0.9 to nearly 0.1 are realized. The relative density is logarithmic in the pressure ramp rate, and can be written as Dr= log(Rp= ). Similar scaling was previously reported by [41]. For the DCV mode, a single pair of and values t the data over the entire range of Rp:However, for DOand DFV operating, there are two distinct regions of response. At higher pressure ramp rates, the increase of Dr with decreasing Rpis noticeably weaker than at lower Rp:In addition, at the same pressure ramp rate, the sample prepared by DCV achieves the largest Dr;while the sample prepared using DOhas the lowest Dr:Comparing the results obtained from DO and DFV, the e ect of vibration is weakened when the pressure ramp rate is less than 2 Pa/s for DFV. 3.2. Local density 3.2.1. Penetration-based density measurement In addition to volume-based density measurements, local density measurements can be used to characterize the bed homogeneity. To do so, a penetration test was developed as a fast and simple method for acquiring information of in situ soil properties. The test 14 04080120160200 0 20 40 60 80Cone index, CI (kPa) Linear regime (shaft penetration) Nonlinear regime (cone penetration) G37.3mm Penetration depth, d (mm) Figure 6: Illustration of a cone index pro le (mode DCV with T= 3000 s), where Gis the slope in the shaft penetration regime (see text). uses the robot arm to drive a penetrometer into the soil at a xed rate while recording the resisting force with a force sensor. Our penetrometer geometry (30circular cone tip and a 3.2 cm2base) is inspired by a United States Army Corps of Engineers Waterways Experiment Station penetrometer design used to determine soil tracability [42]. The resistive forces and moments acting on the penetrometer while it interacts with the sand bed are measured by a six-axis load cell (Sunrise Instruments #3314C) installed at the end of the ABB robot arm, as illustrated schematically in Fig. 4(b). The sensor simultaneously measures forces in three mutually perpendicular directions and torques about three corresponding axes, but only the vertical resistive force is used in this study. At each location tested, the cone penetrometer penetrated the soil to a depth of about 80 mm at a speed of 1 mm/s. The cone index ( CI) characterizes the penetration resistance [42], and is de ned as the force per base area required to penetrate the cone into the soil. A typical cone index pro le for dry sand is illustrated in Fig. 6 and consists of two stages: a non-linear with depth cone penetration regime followed by a linear with depth shaft penetration regime. Previous studies found that factors a ecting CIinclude moisture content, density, and soil type. To illustrate the e ects of di erent de uidization modes and times T; 15 0 20 40 60 8004080120 Cone index, CI (kPa) T = 52 sT = 1500 sT = 5000 sT = 10400 sT = 21600 sT = 43200 sLinear fit (a) Penetration depth, d (mm)0 20 40 60 8004080120160200 T = 50 sT = 350 sT = 1150 sT = 3000 sT = 5050 s 0 20 40 60 8004080120 T = 52 sT = 520 sT = 5000 sT = 10400 s(c) (b)Figure 7: Cone index pro les of reconstituted beds prepared with various de uidization times for (a) DO, (b)DFV, and (c) DCV. Fig. 7 presents plots of CIversus depth obtained at location Oin the bed [see Fig. 4(b)]. TheCIpro les become steeper with increasing Tfor all de uidization modes and di er between modes for the same T:In all cases, CIincreases linearly with depth in the shaft penetration regime. Soil density can be determined as a function of CI[43, 44, 45]. In the shaft penetra- tion regime (cone fully submerged), the linear relation between CIand depth indicates a uniform density [46]. The slope of the cone index curve, G;can be directly related to density [45]: =aln(G=b); (4) whereaandbare constants dependent on soil type. To determine the bed density from G;constantsaandbfrom Eq. (4) must be found. To do so, cone penetration tests were performed on 150 mm deep pluviated samples of known density in a cylindrical container (diameter = 200 mm). Di erent sample densities were achieved by varying the pluviator hole size and the uniform grid spacing of the holes (2 mm holes spaced by 25 mm, 4 mm holes spaced by 20 mm, and 6 mm holes spaced by 20 mm) and by placing the pluviator at various heights (15 :2 cm, 30:5 cm, 71:0 cm, and 91 :5 cm) above the soil surface. The penetrometer was inserted along the central axis of the cylindrical container, and at least three samples were prepared and tested at the same nominal density. By tting the data to Eq. (4) as shown in Fig. 8(a), 16 1450150015501600165017001750 500 5000Pluviated sample density, ρ(kg/m3) Slope of cone index, G (kN/m3)(a) (b) 1450150015501600165017001750 1450 1500 1550 1600 1650 1700 1750Penetration-based density, ρp(kg/m3) Volume-based density, ρv (kg/m3)Figure 8: (a) Volume-based densities vs. dimensionless slopes of cone index curve for samples pre- pared by pluviation. Dashed line is a t to Eq. (4) and is used to determine t parameters aandb (see text). (b) Comparison of volume-based and penetration-based density measurements for various de uidization rates and modes. the constants aandbof the calibration curve were determined to be 110 :6 kg/m3and 7:1104kN/m3, respectively with R2= 0:94:Using the calibration equation [Eq. (4)] and the slope of the cone index curve, local densities can be calculated at any location in the bed. To validate the penetrometer-based approach, the volume-based and penetrometer- based bed densities of various reconstituted sand beds are compared in Fig. 8(b). The penetrometer-based density ( p) is the mean of the densities obtained from the 21 bed positions, and the volume-based density ( v) is determined as described in the section entitled "Volumetric density." The penetrometer-based densities are in good agreement with the volume-based values (coecient of determination R2= 0:78), indicating that the sand density in the bed is reliably determined using the calibration curve. Note that the penetrometer-based densities are slightly larger than the volume-based values forv<1600 kg/m3;and that the reason for this discrepancy is not yet understood. 17 3.2.2. Density variation with depth To characterize possible variation in bed density with depth, we examine the lin- earity of the cone-index pro les in the shaft-penetration regime (see Fig. 6). Typical cone index pro les [obtained at location Oin the bed, see Fig. 4(b)] are presented in Fig. 7 and appear to be quite linear in the shaft-penetration regime. To quantify any possible variation, a linear regression is performed on the data in the shaft penetration regime for the three de uidization modes and various times, and the coecient of de- termination ( R2) is calculated. R2values are determined at all 21 sampling locations, and the minimum values (worst case) are presented in Table 1. The smallest value of R2for all sampling locations, all de uidization modes, and all de uidization times is 0:982;which indicates that variation of density with depth is negligible. 3.2.3. Density variation across the bed Having shown that density variation with depth is minimal, we now examine spatial variation across the bed. To quantify spatial variation, spatially averaged values and standard deviations (SD) of the slope of the cone index curve ( G), density ( p), and relative density ( Dr) are listed in Table 1. The coecients of variation of density (COVp) and relative density ( COVDr) are also provided, where COVX=SDX=X for variable X: COV Drvalues are less than 13% except for beds prepared by DOat intermediate Dr:Beds prepared by DOwith short Texhibit the smallest Drwhere they also show small COVDr;DFV mode prepared beds have 0 :3Dr0:7 with a small variation of density; for sand beds with Dr>0:7, the variation of density is slight when DCV is applied. The data in Table 1 show that density variations across sand beds prepared by uidization are relatively small. However, there is some spatial correlation in density variations as shown in Fig. 9-11 for beds prepared with various de uidization times using DO,DFV , and DCV , respectively. These contours are obtained by spline interpolation (MATLAB function interp2) of the densities at the 21 sampled locations. ForDO(Fig. 9), the highest density of sand appears in two isolated zones located 18 Table 1: Uniformity of sand samples prepared with three de uidization modes and various de uidiza- tion times. Mode De uidization time, T[s]Uniformity in depthUniformity across breadth R2 minSlope of cone index curve, GSD[kN/m3]Density, pSD [kg/m3]COVp [%]Relatively density, DrSDCOVDr [%] DO52 0.987 55128 1499.72 5.70 0.38 0.20 0.02 11.4 1500 0.984 707105 1526.28 16.93 1.11 0.30 0.07 21.6 5000 0.989 957166 1559.23 20.06 1.29 0.43 0.07 17.4 10400 0.991 1346299 1596.03 24.69 1.55 0.56 0.09 15.5 21600 0.992 1498346 1607.67 25.40 1.58 0.60 0.09 14.7 43200 0.993 1832409 1630.10 24.85 1.52 0.68 0.08 12.4 DFV52 0.991 79868 1540.42 9.65 0.63 0.36 0.04 10.2 520 0.982 960121 1560.44 14.06 0.90 0.43 0.05 12.0 5000 0.993 1286157 1592.83 13.35 0.84 0.55 0.05 8.58 10400 0.993 1596162 1616.97 11.30 0.70 0.64 0.04 6.13 DCV50 0.992 928118 1556.67 14.48 0.93 0.42 0.05 12.9 350 0.992 1415227 1602.82 17.86 1.11 0.59 0.06 10.7 1150 0.995 2259479 1653.32 25.14 1.52 0.76 0.08 11.0 3000 0.998 3143581 1690.57 21.26 1.26 0.88 0.07 7.67 5050 0.997 3567684 1704.31 22.96 1.35 0.92 0.07 7.82 19 on opposite sides of the shorter bed midline. From these two peak zones, the density of sand decreases approximately radially. The lowest density is generally found in an area on the left side of the bed (as presented in the gure). Additionally, the density variation in the bed is not symmetric, which might be caused by the momentum of the air exiting the duct. Under this operating mode, the spatial uniformity of the sand bed can be improved by more uniformly distributing the air across the granular bed. For homogenizing the air distribution, the uidized bed described in this paper can be re ned in three ways: (1) increase the height of the plenum and the diameter of the plenum duct inlet to make air distribute more uniformly beneath the distributor; (2) increase the length of the vertical duct segment connecting to the plenum to reduce the asymmetric density distribution caused by the momentum of the air owing from the duct; (3) use a distributor with higher resistance to reduce ow variation by creating a higher pressure drop, which can be realized by either increasing the thickness or reducing the pore size of the distributor. ForDFV (Fig. 10), relatively high density is observed to the left of the bed center, and the density mostly decreases gradually towards the left and right. Overall, the density on the left side of the bed is higher than on the right side. Additionally, the density of sand is higher toward the near side of the bed (smaller ycoordinates). For DCV (Fig. 11), the density distribution of sand is similar to that of DFV . The density is high at the center of the bed and decreases gradually towards the left and right. Note that the density is higher on the far side of the bed (larger ycoordinates) which is the reverse of the case for DFV . This variation likely results from the position of the vibration source at one side of the middle of the uidized bed's frame (see Fig. 1). Compared to the result of DO, it is observed that vibration has a signi cant in uence on the densi cation of a sand bed. By varying the attachment position(s) of the vibrator(s), one can obtain di erent density distributions of the bed. Hence, more vibrators can be added to the bed with a rational arrangement to reconstitute the sand bed more uniformly. 20 Figure 9: Density distribution across sand beds prepared by DOwith de uidization times Tof (a) 52 s (COV p= 0:38% ); (b) 5000 s ( COV p= 1:29% ); (c) 10400 s ( COV p= 1:55% ); and (d) 43200 s (COV p= 1:52% ). Figure 10: Density distribution across sand beds prepared by DFV with de uidization times Tof (a) 52 s ( COV p= 0:63% ); (b) 520 s ( COV p= 0:90% ); (c) 5000 s ( COV p= 0:84% ); and (d) 10400 s ( COV p= 0:70% ). 21 Figure 11: Density distribution across sand beds prepared by DCV with de uidization times Tof (a) 50 s (COV p= 0:93% ); (b) 350 s ( COV p= 1:11% ); (c) 1150 s ( COV p= 1:52% ); and (d) 5050 s (COV p= 1:35%) . 4. Equivalence of beds prepared by uidization and pluviation To show that pluviated beds and beds prepared by uidization are equivalent, Fig. 12 compares the dependence of the penetration-based density pin beds prepared by u- idization to those prepared with pluviation as a function of the slope of the cone index curveG:pandGare averages of measurements performed at the 21 sample locations and are given in Table 1. The horizontal error bars represent the standard derivation of Gat the di erent average densities, and the vertical error bars represent the standard derivation of pat variousG:Error bars illustrate the variations of the correspond- ing quantities. Gray data points are from samples prepared by pluviation, and each data point represents the result from one test. The gure indicates that the density variations and Gfor beds prepared by uidization are within the range of the results from the widely used pluviation method, suggesting that uidized beds are capable of reconstituting sand beds for geotechnical modeling tests. 5. Conclusions This paper explores the application and demonstrates the suitability of air- uidization for reconstituting sand beds for geotechnical modeling tests. Details of the device and 22 1450150015501600165017001750 1450150015501600165017001750 400 4000Penetration-based density, ρp(kg/m3) Slope of cone index, G(kN/m3)DO DFV DCV pluviation data Density of pluviation sample, ρ(kg/m3)Figure 12: Bed density vs. cone index curve slope across sand beds prepared by uidization (colored symbols) and pluviation (gray circles) indicates equivalence of the two bed reconstitution techniques (see text). the design methodology are presented along with the capabilities of the uidized bed device, which provides a reference for future applications of this method. Through the study of volumetric densities and local densities across the beds, sand beds reconsti- tuted using three di erent operating modes ( DO,DFV and DCV ) and with various de uidization times are characterized, and the performance of the uidized bed device is evaluated. The main conclusions are as follows: (i) Sand beds can be prepared with a broad range of volume-based relative density from 10:4% to 91:7% by using the three operating modes and corresponding pres- sure ramp rates illustrated in this study. For DO,DFV and DCV , the relative densities realized are 10 :4% - 54:1%, 27:6% - 53:7%, 34:6% - 91:7%, respectively. These ranges can be further expanded by extending the bounds of the pressure ramp rates used here. (ii) The sand bed is nearly spatially homogeneous based on cone penetration measure- ments. Along the depth, minimum R2values are close to 1 for all beds prepared by the three modes with di erent pressure ramp rates, indicating that their density variations with depth are minimal. Across the breadth of the bed, the coecients of variation of relative density are found to be under about 13% for all beds except 23 for some prepared by DO. In addition, by correlating penetration measurements to local densities, the result also serve as a more direct re ection of the fact that the mechanical properties of sand beds are uniform given that the critical features of the cone index pro les across each bed show little variation. (iii) A uidized bed is quali ed for reconstituting sand beds for geotechnical modeling tests given that the beds prepared by uidization and the widely used method pluviation are comparable. The latter is inferred from the fact that the density variations and slopes of the cone index for beds prepared by uidization are within the range of the results obtained using the pluviation method. (iv) The application of air uidization is not con ned to the material and bed dimen- sions used in this study. Fluidized bed devices are capable of being used in various types of geotechnical modelling tests with di erent soil properties and bed sizes. 6. Acknowledgements We thank Sam Asa and Olisaeloka Anazonwu for their assistance in the experiments related to pluviation. This material is based upon work supported by the National Science Foundation under Grant No. CMMI 1742849.