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Calibrating and measuring bed load transport with a magnetic detection system Rempel, Jason 2005

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CALIBRATING AND MEASURING BED LOAD TRANSPORT WITH A MAGNETIC DETECTION SYSTEM by JASON REMPEL B . S c , The University of British Co lumb ia , 2002 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in T H E FACULTY OF GRADUATE STUDIES (Geography) T H E UNIVERSITY OF BRITISH COLUMBIA June 2005 © J a s o n Rempe l , 2005 Abstract A ser ies of lab and f lume experiments were des igned to test and calibrate the Bed load Movement Detector (BMD), a magnet ic sys tem for measur ing bed load movement in gravel bed st reams. Exper iments used both artificial and natural s tones, and were specif ical ly des igned to isolate the effects of particle s ize , velocity and magnetic content on the shape of the recorded s ignal . Empir ical relations were derived between the ampli tude, width and integral of the sensor response, with particle s ize , velocity and magnet ic content. B e c a u s e of high variability in response across an individual sensor , the current sys tem cannot be used to reliably predict the particle s ize from an individual s ignal . Resul ts improved at the event sca le , where variability averages out. Over the course of the experiments, a number of w e a k n e s s e s in the sensor des ign were observed; these are d i scussed , and some suggest ions are made of ways to improve the sys tem. i i Table of Contents Abstract ii Table of Contents iii List of Tab les vii List of Figures vii Acknowledgements x Chapter 1: Introduction 1 1.1 Resea rch Context: 1 1.2 Entrainment Thresho lds : 2 1.3 P h a s e s of Transport: 4 1.4 Sed iment Transport Measurement : 5 1.4.1 Samp le rs : 5 1.4.2 Pit Traps: 7 1.4.3 Indirect Measurement : 7 1.5 Cont inuous B e d load Measurement Methods: 8 1.5.1 Vortex Tube Sediment Trap: 9 1.5.2 The Record ing Trap: 11 1.5.3 Acoust ic Methods: 12 1.5.4 The Magnet ic Method: 13 1.6 Resea rch Object ive: 15 Chapter 2: The B M D Sensor : 16 2.1 S e n s o r Phys ics : 17 2.2 Var iab les Control l ing Senso r Response : 20 i i i 2.2.1 Part icle Character ist ics: 20 2.2.2 Part icle Trajectory: 23 Chapter 3: Exper imental Methods: 25 3.1 Rotating Platter Exper iments: 25 3.2 F lume Exper iments: 29 3.3 Data Col lect ion and Signal P rocess ing : 31 Chapter 4: Resul ts and Analys is 35 4.1 Part icle Character ist ics: 35 4.1.1 Signal Ampli tude Resul ts : 35 4.1.2 Empir ical Mode l for S igna l Ampl i tude: 39 4.1.3 Signal Width Resul ts : 41 4.1.4 Empir ical Mode l for S ignal Width: 4 3 4.1.5 Signal Integral Resul ts : 45 4.1.6 Empir ical Model for S ignal Integral: 48 4.2 Part icle Trajectory: 50 4.2.1 Variat ion Ac ross the Senso r F a c e : 50 4.2.2 Variat ion With Distance From the Senso r F a c e : 54 4.3 Incorporating Trajectory into the Empir ical Mode ls : 57 4.4 Part icle Susceptibi l i ty: 60 4.5 Part icle Velocity: 64 4.6 Multiple Stone and S a n d Exper iments: 65 Chapter 5: D iscuss ion 68 5.1 Empir ical Mode ls : 68 iv 5.2 Prob lems with the Current S e n s o r Des ign : 70 5.3 Suggest ions for a New S e n s o r Des ign : 72 Chapter 6: Conc lus ions 75 v List of Tables Table 2.1. Ana lys is of the magnet ic properties of 45 East Creek stones 22 Tab le 3.1. Mixture ratios (by mass) for the artificial s tones 26 Tab le 4.1. Regress ion coefficients for the amplitude model . Separate regressions were run for s tones <12 c m 3 and >12 c m 3 39 Table 4.2 Regress ion coefficients for the integral model . Separate regressions were run for s tones <12 c m 3 and >12 c m 3 48 Table 4.3. Est imated total transport volume and m a s s from flume exper iments 60 vi List of Figures Figure 2.1. A : a schemat ic view of the B M D system installation, B: the B M D system deployed in O 'Ne-e l l C reek 16 Figure 2.2. Schemat ic view of an individual sensor , showing the three main components : the coi l , the doughnut shaped magnet, and the steel cas ing . 17 Figure 2.3. A : the simplif ied c a s e of a magnet ic dipole pass ing over a copper coi l , B: the magnet ic field strength (B) exper ienced in the center of the coi l , C : the voltage response of the coil to the pass ing dipole, which is proportional to the derivative of the magnet ic field strength with time 19 Figure 2.4. Strength of the magnet ic field over the center axis of the sensor at 5 different heights 24 Figure 3.1. Artificial s tones cast in 8 c lass s i zes from 8 - 9 0 mm 26 Figure 3.2. Rotating Platter apparatus, des igned to independently control particle trajectory (both vertical and horizontal) and particle velocity 27 Figure 3.3. R a m p apparatus. Two sensors are inset into the ramp; adjustable s idewal ls confine particles over a given sensor 28 Figure 3.4. F lume set-up. Two rows of 4 sensors each are visible in the foreground. The coloured s tones are the artificial s tones used for these exper iments 30 Figure 3.5. The effect of filter threshold on the recorded signal - too low of a threshold c a u s e s data to be lost. A 55 Hz filter was chosen for the current analys is 32 Figure 3.6. A : R a w data with no filtering. B: Data after filtering with 55 Hz lowpass filter. The horizontal l ines represent the noise range of the sys tem after filtering 32 Figure 3.7. S igna l parameters col lected from each sensor response 34 Figure 4 .1 . Relat ion between particle vo lume and signal ampli tude. The s lope of the relation increases with increasing R P M . There is a consistent break in s lope near 12 c m 3 , above which the s lope dec reases 36 Figure 4.2. Relat ion between particle velocity and signal ampli tude. The s lope of the power relation increases as particle s ize increases 37 vii Figure 4.3. Semi - log relationship between susceptibi l i ty and signal ampli tude 38 Figure 4.4. 3-dimensional plot of the var iables affecting signal ampli tude. For a given susceptibil i ty, the points fall along a plane through the ampli tude-velocity-volume s p a c e 38 Figure 4.5. Est imated particle vo lumes from the empir ical model versus actual particle vo lumes. The logarithmic plot is used in order to show the variability for each particle s ize clearly. The green lines divide the graph into s ize c lasses . Including the scatter about the 1:1 line, data still general ly fall within the correct s ize c lass 40 Figure 4.6. Relat ionship between particle diameter and signal width 42 Figure 4.7. Relat ionship between particle velocity and signal width. There is overlap, but in general for a given velocity, width increases as particle s ize increases 42 Figure 4.8. 3-dimensional plot of the var iables influencing signal width. The data fall nicely on a plane within this s p a c e 43 Figure 4.9. Est imated B-axis diameter from the empir ical model versus actual B-axis diameter. The green lines identify the different s i ze c lass regions. Scat ter in the estimations span 3-4 s ize c l asses 44 Figure 4.10. A : T ime ser ies of a single object pass ing by the sensor at different velocit ies (as seen by the difference in amplitude). B: Integral of the s a m e time ser ies. The ampli tude of the integral is approximately the same , regardless of velocity 46 Figure 4 .11. Relat ionship between susceptibil i ty and signal integral 47 Figure 4.12. Relat ion between particle volume and signal integral. There is good segregat ion between susceptibi l i t ies. Like the relationship between volume and amplitude, there is a break in s lope near 12 c m 3 47 Figure 4.13. Est imates of particle vo lumes from the integral empir ical model versus actual vo lumes. The green l ines on the logarithmic plot divide the y-axis into s ize c l asses . Variabil i ty about the 1:1 line general ly is within the correct s ize c lass 49 viii Figure 4.14. Variat ion in s ignal amplitude across the sensor face 51 Figure 4.15. Normal ized s ignal ampli tude across the senso r face 52 Figure 4.16. Variat ion in s ignal integral ac ross the sensor face 52 Figure 4.17. Normal ized signal integral ac ross the sensor face 53 Figure 4.18. Variat ion in s ignal width across the sensor face 54 Figure 4.19. Variat ion in s ignal amplitude with increasing distance between the center of the stone and the center of the sensor 55 Figure 4.20. Variat ion in s ignal integral with increasing distance between the center of the stone and the center of the sensor 55 Figure 4 .21. Variat ion in s ignal width with increasing distance between the center of the stone and the center of the sensor 56 Figure 4.22. Est imated particle vo lumes from f lume experiments with no adjustment for location across the sensor face 58 Figure 4.23. Est imated particle vo lumes from signal integral model with random location adjustment 59 Figure 4.24. Histogram of particle susceptibi l i t ies measured from 150 s tones from East Creek . The red bars indicate s tones that past by the sensors with no response; the blue bars produced a response 61 Figure 4.25. Normal distribution of the log of particle susceptibil i ty measured from 150 East Creek s tones 62 Figure 4.26. Est imated vo lumes of East Creek stones from the signal integral model . Susceptibi l i t ies >1000 are c loser to the 1:1 line as they are in the range of susceptibi l i t ies used to develop the model 63 Figure 4.27. Compar i son of particle velocit ies measured with the two rows of sensors , and the v ideo recording 65 Figure 4.28. Super imposi t ion of s ignals as the d is tance between part icles dec reases 66 ix Acknowledgements This thesis is a culmination of two great years of research and learning. It was accompl ished with the support of many fr iends, family and co l leagues along the way. First I would like to thank my supervisor Dr. Marwan H a s s a n for giving me the opportunity to work with him and to learn from him. I especia l ly appreciate the fact that your door was always open, and that you dropped whatever you were working on to give me your attention when I c a m e knocking. S e c o n d I would like to thank Dr. Randy Enk in from the G S C ' s Paci f ic G e o s c i e n c e Centre. Not only did you give me a c c e s s to your lab, you spent many hours working through my results with me, helping me to understand them better. I love your enthus iasm. Thanks to Dr. Dan Moore for many helpful comments that improved the final product; to J o n Tunnicliffe for many d iscuss ions , and for teaching me how to use the sys tem; and to Andre Z immermann for helping me learn how to build the models. My time at U B C would not have been complete with out the opportunity to work with many others in the department, especial ly Michael Church , Brett Eaton, F rancesco Brardinoni, Dave Campbe l l , J o s h Caulk ins and Bonnie Smith. To my family, and especial ly to my wife Leah , thanks for your ongoing love and encouragement. Chapter 1: Introduction 1.1 Research Context: The entrainment and deposit ion of sediment from the s t reambed produces the geometry, or morphology, of a stream channel . The most common morphologies in the Paci f ic Northwest are the riffle-pool, and step-pool sys tems (Montgomery and Buffington, 1997). T h e s e morphologies help stabil ize the channel , and produce the different environments needed for aquatic habitats. Sed iment transport and channel morphology are mutually l inked and, therefore, changes in the sediment transport regime will be reflected by changes in channel morphology (e.g. Ashmore and Church , 1998). Sed iment transport regime may change due to natural events, such as an extreme flood event, the re lease of sediment from the break up of a log jam, or sediment input from landsl ide and debris flow activity. It may a lso be affected by anthropogenic activities such as logging, damming, or gravel mining. Therefore, understanding the p rocesses involved in sediment transport has important implications for management of stream sys tems. However, a reliable method for measur ing sediment transport, especia l ly bed load is one of the main problems that limits progress in river mechan ics research. Sediment transport is a function of the sedimentological character of the bed, the turbulent nature of flow, and the supply of sediment to the st ream. T h e s e are all independently complex p rocesses that together produce high variability of sediment transport, both spatial ly and temporal ly (Reid and Frostick, 1987). 1 It is general ly accepted that d ischarge is the only independent factor controll ing the amount of sediment transport. However, at a constant d ischarge, the sediment transport rate is highly variable in both time and s p a c e (e.g. Hayward and Suther land, 1974; Reid and Frostick, 1987; Bunte, 1996). This variability raises a number of quest ions when consider ing bed load transport. What is the threshold for the entrainment of part icles? What sedimentological factors affect the timing and amount of transport? How much sediment is moving? Where is the sediment moving to/from? 1.2 Entrainment Thresholds: A n individual particle will begin moving when the hydraulic forces acting upon it overcome those keeping it in the bed - namely gravity and friction. Hydraul ic forces have general ly been descr ibed in terms of shear stress (x0 = p w g d S ) or stream power (Q = Q S p w ) where p w is the density of water [M/L 3 ] , g is gravity [L/T 2], d is water depth [L], S is s lope [1] and Q is d ischarge [L 3/T]. Theoretical ly, the critical shear stress that will begin entrainment of a particle is proportional to particle s ize (Shields, 1936). The original experiments by Shie lds (1936) were run under the simplif ied c a s e of uniform grain s ize . Many researchers (e.g. Andrews, 1983; Ashworth and Ferguson, 1989) have extended this theory to natural gravel-bed rivers. Their field ev idence supports the idea of "s ize select ive transport", where a given flow has the capaci ty to move everything less than or equal to a given s ize fraction. 2 Parker et a l . (1982) and Parker and K l ingeman (1982) suggested that in gravel bed st reams, where the sediments are widely graded, particle interactions would interfere with movement, making Shie ld 's critical shear stress irrelevant. Instead, they proposed an alternate theory of entrainment where the effect of armouring produces a situation in which all the particles - regardless of s ize -start moving at once, or are "equally mobi le." A coarse-gra ined armour layer shelters the smal ler particles from the hydraulic forces, keeping them in the bed until the hydraulic forces are great enough to cause the larger particles to begin moving. Break up of the armour layer exposes the previously hidden particles, and subsur face material to the flow. Other particle interactions have a lso been observed that further enhance armouring p rocesses , including: imbrication (Powell and Ashworth, 1995), pebble clusters (Brayshaw, 1985; Re id and Frostick, 1987), and stone cel ls (Church et a l . , 1998). T h e s e p rocesses increase the stability of the bed and therefore the critical shear stress required to initiate transport. Church et a l . (1998) were able to show that stone cel ls increase the critical shear stress needed to entrain particles 2-4 t imes, reducing sediment transport up to 1 0 3 t imes. 3 1.3 Phases of Transport: B a s e d on both field research and flume experiments, s ize select ive transport, and equal mobility have been identified as different phases of transport that occur as d ischarge increases. J a c k s o n and Besch ta (1982) deve loped a 2-phase model to descr ibe the transition between types of transport; the model was then extended to a 3-phase model by Ashworth and Ferguson (1989) and Wi lcock and McArdel l (1993). P h a s e 1 is "over-passing sand" , where fine grains pass over a static bed. In this phase , transport rates are extremely low. A s d ischarge increases, individual particles move from exposed areas in the surface layer as "partial transport" (Phase 2). P h a s e 3, a "fully mobi le" phase, occurs at even higher f lows. The largest particles begin to move, al lowing the previously sheltered finer particles, and sub-sur face material to be exposed to the flow. P h a s e 3 transport only occurs under rare f lows. Andrews (1994) determined that at S a g e h e n Creek, 9 5 % of the bed load was transported under partial transport condit ions. Data used by Ashworth and Ferguson (1989) to develop their 3-phase model only approached full mobility. With each phase, the volume and complexity of transport increases; however our ability to measure transport dec reases . It is extremely important to be able to measure the highest transport rates, as they are the channel shaping events. Methods of measurement therefore must be capab le of accommodat ing large rates and vo lumes of transport. A fundamental problem in sediment transport research is that no measurement technique has been commonly accepted as superior, and there are no standard protocols (Hicks and G o m e z , 2003). 4 1.4 Sediment Transport Measurement: Measur ing the amount of sediment transport is difficult, and involves a high level of uncertainty. This is due to a greater than two order of magnitude range of grain s ize (2 mm to >200 mm) that moves as bed load in gravel-bed rivers, high spatial and temporal variability of movement, large vo lumes of sediment, and extremely difficult field logistics. A wide range of methods have been employed to measure the amount of sediment transport, the simplest of which are samplers , pit traps, sediment tracers and morphological surveys. A summary of these methods is provided below. 1.4.1 Samplers: A large number of bed load samplers have been deve loped, the most common of which is the Hel ley-Smith Samp le r (Helley and Smith, 1971). The instrument can be hand-held or cab le mounted. It is p laced on the bed of the st ream, and has a standard 3" x 3" opening with a net to catch moving sediment. All sampl ing dev ices are faced with the s a m e concern : is the sample col lected representative of what is actually moving in the bed at the time of measurement? Any sampler p laced on the bed is an obstruction to the flow, which necessar i ly changes the flow pattern around the sampler . Th is will change the entrainment condit ions and bias sampl ing, both in terms of the texture and the amount of sediment col lected. The exact effect of this is unknown, due to inherent difficulties in calibrating such an instrument (Hubbel l , 1987). 5 Col lect ion of samp les is very labour intensive. Sediment is col lected v ia cross-sect ional t raverses, taking samp les at equal increments across the channel width. The number of samp les col lected, and the length of col lect ion time is dependent on the stream width and the strength of the flow. In order to account for the spatial and temporal variability of transport, multiple t raverses should be made (Ryan and Troendle, 1997). Samp le duration is general ly 30 or 60 seconds (Ryan and Troendle, 1997), however Andrews (1994) took 4-minute samp les to better account for random fluctuations and temporal variability. Even with a long sampl ing duration, the sample still may not be representative; because of the sporadic nature of the movement of large particles, the probability of catching these particles is very low. A lso , due to the smal l opening of the device (3" x 3"), large particles are systematical ly under represented. Samp le rs with larger openings have been used, but they are clumsier, and more difficult to work with, especial ly in strong f lows (Ryan and Troendle, 1997). Due to the irregular shape of the bed surface, the sampler may not sit f lush with the bed, and al low particles to pass under it. A lso , it is difficult to maintain sol id contact with the bed during high f lows. In this case , sediment may be missed , or the bed could be disturbed and sediment may be scooped into the sampler (Ryan and Troendle, 1997). In snowmelt dominated catchments, due to diurnal variation, the peak flows are often around midnight (Bunte, 1996; Tunnicliffe, 2000), making measurement even more difficult, or impossib le. 6 1.4.2 Pit Traps: A n alternative to sampl ing is to install pit traps into the st ream. Pit traps may be in the form of buckets (Powell and Ashworth, 1995; H a s s a n and Church , 2001 ; Church and H a s s a n , 2002), or a trough that spans the entire channel width. They are installed in the bed, f lush with the bed surface s o that they do not disrupt flow. The traps collect all the bed load that moves over them, eliminating the problem of representative sampl ing. However, they only provide an event sca le vo lume of sediment transport; they give no indication of the temporal variability of transport. During large events, the traps may overfil l, in which c a s e data are lost. Installation and maintenance of pit traps may be extremely difficult in the deepest parts of perennial s t reams, where much of the transport may be occurr ing. 1.4.3 Indirect Measurement: Two methods of indirectly determining sediment transport have been deve loped, one using tracer particles, and the other looking at changes in channel morphology. Part icle tracers have been used to track the 3-dimensional movement of individual particles (Hassan and Ergenzinger, 2003). Part ic les are se lected from the stream, and typically tagged with paint, or inserted magnets; radioactive stones, exotic l i thologies and radio transmitters have a lso been used . The initial location of particles is mapped , and after an event, these particles are recovered. The distance of transport, and depth of burial is recorded. A n indirect measure of 7 sediment transport can be est imated, and the depth of the active layer determined. Zones of erosion and deposit ion can be inferred from the mapping. Recover ing the particles is extremely labour intensive, and often the percentage recovered is low, therefore a large sample s ize is necessary . The morphological method is based on the direct relationship between sediment transport and changes in channel morphology. Channe l morphology is monitored through digital elevation models (DEMs) of the stream built from repeated, high density, c ross sect ional surveys, high-resolution (4 points/m 2) reach surveys, or photog ram metric methods (Ashmore and Church , 1998). The net volume change can be determined by subtracting D E M sur faces from before and after an event, providing an estimate of the vo lume of sediment transport. This method is useful for active st reams with high instability. Its use is limited in stable st reams, where the changes are likely within the error of the method. The morphological method provides a minimum estimate of annual sediment transport, as multiple cyc les of erosion and deposit ion may have occurred between surveys. The method does highlight regions of scour and deposit ion, and distance of transport may be inferred (Ashmore and Church , 1998), but like the pit traps and tracers, it provides no resolution of temporal variability. 1.5 Continuous Bed load Measurement Methods: In order to address the lack of resolution and the problems of representative sampl ing, a number of methods have been deve loped to continuously monitor bed load movement. Cont inuous measurement provides a picture of the 8 temporal variation in transport; s o m e instrument des igns can also account for spatial variability ac ross the channel . A number of methods have been developed including the vortex tube sediment trap, the conveyor belt trap, the recording pit trap, acoust ic methods, and the magnet ic method. 1.5.1 Vortex Tube Sediment Trap: Adapt ing an idea used to eject unwanted sand and silt from irrigation cana ls , a vortex trap is installed in the creek to eject transported sediment to a process ing station at the s ide of the st ream. After process ing, sediment is reintroduced to the st ream downstream of the trap. The trap is oriented at a 45° angle to the flow, creating the vortex that forces the sediment out the s ide of the trap. Emptying the trap and weighing the sediment at regular intervals al lows rates of transport to be calcu lated. Vortex sys tems were used by: Mi lhous (1973) at O a k Creek, Oregon , Hayward and Suther land (1974) at Tor lesse St ream, New Zea land , O 'Leary and Besch ta , (1981) at Flynn Creek, Oregon , and Billi and Taccon i (1987) at Virginio Creek, Italy. Hayward and Suther land (1974) weighed samp les every 10 to 20 minutes, while Billi and Taccon i (1987) were able to weigh samp les every minute. Peak flows in nival s t reams may last a number of days , so cont inuous measurement is a very labour intensive procedure that requires 2-3 workers at any one time. At Tor lesse S t ream, workers were able to trap, weigh and return all of the sediment to the st ream for transport rates up to 2000 kg/hr (Hayward and Suther land, 1974). At higher transport rates the workers were overwhelmed 9 and a sampl ing program had to be instituted. At Virginio Creek, a rotating s ieve was used to eliminate water and f ines. The system was able to process up to 42000 kg/hr (Billi and Taccon i , 1987). Installation of a vortex system involves building a concrete f lume in the creek that houses the trap. The sys tem uses conveyor belts to move material to the weighing station, and to return sediment to the st ream. This limits the s t reams that are suitable for a vortex system to ones with easy a c c e s s and reliable power supply. O n c e the vortex sys tem is installed, the data that it produces are extremely valuable. The trap is capable of efficiently trapping sediment from coarse sands to particles greater that 400 mm in diameter (Hayward and Suther land, 1974). Limitations to the system are that there is no ability to resolve spatial variability and that at high flows the trapping eff iciency may decrease , al lowing the sands to over pass the trap (Hayward and Suther land, 1974). Leopold and Emmett (1976, 1977) used a similar sys tem on the East Fork River, Wyoming . Sediment was weighed in the s a m e manner as the vortex trap sys tem, but instead of creating a vortex to force sediment out of the trap, a conveyor belt was installed in the bottom of the trap. The system was capable of handling transport rates up to 9000 kg/hr. A spatial component was incorporated by a gate sys tem, which al lowed sect ions of the trap to be ana lyzed separately (Leopold and Emmett, 1976). 10 1.5.2 The Recording Trap: The Birkbeck bed load sampler is a recording pit trap system that was developed by Re id et a l . (1980) at Turkey Brook, U K . The installation of this sys tem is much simpler than the vortex and conveyor belt sys tems. Pit traps were installed with pressure sensit ive pil lows beneath them. A s the traps fill, the increase in pressure is recorded. With a synchronous record of water depth to account for the weight of water, the increase in pressure can be related to the weight of sediment that is filling the trap. Tempora l variation in sediment transport can then be seen through the rate of weight increase. The weight increase is measured electronically, al lowing this device to measure sediment transport unmanned. Th is provides a distinct advantage over the vortex and conveyor belt sys tems, especial ly s ince flows often occur overnight. After the flow subs ides , workers empty the traps, and can s ieve the col lected material to determine a grain s i ze distribution for the transported material. At Turkey Brook, 2 cross-sect ions with 3 traps each added the ability to resolve spatial variability in transport. A d isadvantage to the recording trap sys tem is that only one grain s ize distribution can be col lected for each event. With the vortex and conveyor belt sys tems, operators are capab le of col lect ing samp les to ana lyze the change in grain s ize distribution over an event. A lso , during large events, the traps often overfill, thereby miss ing important data. Overfi l l ing traps is a significant limitation, and therefore, the sys tem is more appropriate for s t reams with low sediment transport rates. 11 1.5.3 Acoustic Methods: A number of researchers have used acoust ic methods to record sediment transport. Throne et a l . (1989) installed a hydrophone in the bed of a tidal channel . The hydrophone measured sediment generated noise (SGN) from the col l is ions between particles, which they related to sediment transport. The hydrophone was cal ibrated against sediment transport rates measured with underwater v ideo. Similarly, R ickenmann (1994) used nine hydrophones installed in the bed of the Er lenbach stream to record the intensity of bed load transport. By relating the number of impulses recorded to the volume of sediment accumulat ing in a retention bas in, he was able to roughly calibrate the sys tem. Limitations of these systems are that no particle s ize information can be obtained, and there is no way of knowing exactly how many particles are moving. The sys tems do not work well in s t reams with low sediment transport rates, where there are a limited number of col l is ions. More recently, Downing et a l . (2003) have been developing an acoust ic sensor that records an impulse from the col l ision of a moving particle into a piezoelectr ic material. The strength of the recorded impulse is proportional to the momentum of the coll iding particle. With knowledge of the particle velocity, the mass of the stone can be backed out. A n inherent weakness of the sys tem is that the instrument is an obstruction to the flow, and therefore necessar i ly changes the hydraul ics at the measurement site. A lso , s ince particle velocity is 12 required to obtain m a s s information, the sys tem requires an independent means of measur ing, or theoretical est imation of particle velocit ies. 1.5.4 The Magnetic Method: The magnet ic method uses magnet ic induction to detect the movement of individual particles. A detector rod is installed at a stream cross-sect ion; as particles pass over the detector, they induced a voltage spike. The change in voltage is cont inuously logged producing a time ser ies, and allowing one to count the number of particles pass ing over the detector through time. The method was deve loped by Ergenz inger and Cus te r (1982) at Ca labr ia , Italy and S q u a w Creek, Montana, and Re id et al (1984) at Turkey Brook, UK . Originally, particles were tagged with inserted ferrite rods. Improvements to the sensitivity of the method al lowed S q u a w Creek , a stream with naturally magnet ic particles to be chosen . Simi lar to the Birkbeck bed load sampler , there is the potential for unmanned operation with the magnet ic sys tem. S ince particles are detected instead of t rapped, the procedure is much less physical ly demanding; however, initially it w a s t ime consuming to p rocess the number of s ignals recorded. With the strip chart sys tem at S q u a w Creek , Bunte (1996) manual ly counted voltage peaks at a resolution of 200 peaks/hr . Improvements to the system were made s o that the vol tages were t racked digitally (Custer, 1991). Digital recording al lows computer programs to be written to process the s ignals. It a lso al lows for more advanced time ser ies analys is . 13 Tunnicliffe et a l . (2000) have further refined the magnet ic method with the Bed load Movement Detector (BMD) sys tem, which uses high f requency recording, and much smal ler detectors. In S q u a w Creek , 1.55 m long detectors were installed across the creek to give an indication of the spatial variability of movement. Tunnicliffe et al (2000) installed an array of 82 sensors , each 10 c m in diameter, across O'Ne-e l l Creek, British Co lumb ia , providing high spatial resolution. Each sensor was digitally sampled at ~100Hz , increasing the temporal resolution dramatical ly as well . Like the setup at S q u a w Creek , the B M D system is sensit ive enough to detect movement of natural particles. All of these magnet ic sys tems are only able to detect a proportion of the sediment moving due to the mineralogy of the particles. In the case of the artificially tagged sys tems, the sample s ize was 100 s tones (Reid et a l . , 1984). In the case of natural sediments, it was est imated that 4 0 % of the bed material had sufficient magnet ic minerals to be detected in S q u a w Creek ; in O'Ne-e l l Creek, due to the heterogeneity of lithology and sensor spac ing , 3 0 % of the transported material could be detected. This percentage is a s s u m e d to remain constant, because there is no basis for the preferential transport of the more magnet ic particles. Therefore, data col lected by the magnet ic method are still representative. There are many features of the magnetic method that make it attractive: the sensors can detect the movement of natural s tones; unlike pit-traps, there is no capaci ty limit; the system provides high resolution data in both time and space ; and the system has the potential to be run unmanned. However, use of these 14 sys tems has been limited due to an inadequate understanding of how to interpret the col lected data. To date, the sys tems have been used to count the number of s tones pass ing, and to cons ider temporal and spatial trends in the sensor response. No sys tem can yet be used to produce a reliable estimate sediment transport. Sp ieker and Ergenzinger (1987) suggested that the magnitude of the induced voltage could be related to the s ize of the pass ing particle however, no results were produced to support the idea. Similarly, Tunnicliffe (2000) suggest that calibration of the B M D sys tem is required to improve results. 1.6 Research Objective: The magnet ic method has great potential for sediment transport monitoring. However, its appl icat ion has been limited because to date there has been no proper calibration of the method. The objective of this thesis is to test and calibrate the B M D sys tem developed by Tunnicliffe et a l . (2000) to address whether or not the magnitude of the sensor response can be related to particle s ize , and whether the sys tem can be used to reliably measure the amount of sediment transport. To accompl ish this objective, Chapter 2 provides an overview of the B M D sys tem and outl ines the basic phys ics of the sensors . Chapter 3 descr ibes the two methods used to test the sys tem. Chapter 4 provides results from the exper iments, and Chapter 5 d i scusses the results, as well as some problems that were observed with the current sensor des ign. 15 Chapter 2: The BMD Sensor: The BMD system consists of an array of sensors housed in an aluminum beam, buried in the stream channel, flush with the bed surface. The beam can be adjusted vertically to account for scour or fill. Each sensor is digitally sampled via analogue-digital recorders. Figure 2.1 shows a schematic of the BMD system, and the system deployed in the field. Figure 2.1. A: a schematic view of the BMD system installation, B: the BMD system deployed in O'Ne-ell Creek In order to calibrate the system, an understanding of how an individual sensor responds to a passing stone is required. A view of the sensor is shown in Figure 2.2. The sensor is 8 cm in diameter, made of a copper coil set within a strong (-10 mT), vertically magnetized, doughnut-shaped magnet. Both are set inside a steel casing that acts to confine the magnetic field so that the fields of adjacent sensors are isolated from each other. 16 EPOXY RESIN MAGNET:7CM Figure 2.2. Schematic view of an individual sensor, showing the three main components: the coil, the doughnut shaped magnet, and the steel casing 2.1 Sensor Phys ics : The BMD sensor works through the process of electromagnetic induction. As a particle moves over the sensor, the magnetic moments of the ferromagnetic minerals in the particle align to the magnetic field of the doughnut shaped magnet. This alignment produces an induced magnetization in the particle. As this induced magnetic field moves overtop of the sensor coil, a voltage is induced according to Faraday's Law: 17 (1) dt which states that the induced voltage (emf) is equal to the number of coil windings (N), t imes the cross sect ional a rea of the coil (A), t imes the change in magnet ic field strength (B) with time (t). The induced voltage is measured by the analogue-digital recording sys tem; typical recordings are on the order of 1CT3 -10"4V. To descr ibe the typical sensor response, Figure 2.3A shows the simple case of a magnetic dipole moving over a coil at a number of different t imes. The vertical component of the magnet ic field strength (B) exper ienced in the coil is calculated from: where u j s the permeabil i ty of free space and M is the magnet izat ion (uoM/47i in this case is constant); 0 is the angle off of vertical between the center of the dipole, and the center of the coi l ; and r is the distance from the center of the coil to the center of the dipole. The max imum field strength occurs when the dipole is directly over the coil (9 = 0°), and dec reases symmetr ical ly away from the max imum, producing a G a u s s i a n curve (Figure 2.3B). S ince the number of windings (N) and the a rea (A) of the coil are constant, the induced voltage is directly proportional to the change in magnet ic field dB/dt - the time derivative of B = \i0M 3cos 2 8-l 4TI r 3 (2) 18 the G a u s s i a n curve (Figure 2 .3C) . This characterist ic curve, with a peak fol lowed by a valley, is recorded for each stone pass ing over the sensor . The shape of the curve can be descr ibed by its ampli tude, width, and the a rea under the curve. i Figure 2.3. A : the simplif ied c a s e of a magnetic dipole pass ing over a copper coi l , B: the magnet ic field strength (B) exper ienced in the center of the coi l , C : the voltage response of the coil to the pass ing dipole, which is proportional to the derivative of the magnet ic field strength with t ime. 19 2.2 Variables Controlling Sensor Response: Though the shape of the response curve is s imple to descr ibe, the output s ignal of a stone pass ing over the sensor is controlled by a number of var iables. The strength of voltage response, and the exact shape of the resulting curve, will depend on particle characterist ics - velocity, s ize and mineralogy - and the trajectory of the particle moving over the sensor (both a horizontal and vertical component) . S e n s o r calibration requires that each variable can be isolated to character ize its inf luence on the shape and s ize of the response curve. 2.2.1 Particle Characteristics: From Equat ion 1 it is evident that a faster particle will have a greater value of dB/dt, and therefore a larger voltage response. A s a particle moves into the magnetic field of the sensor , it acquires an induced magnet izat ion (M). The strength of the magnetizat ion can be calculated by: B YV M = (3) Ho where B 0 is the strength of the magnetic field from the sensor 's magnet, x is the magnetic susceptibi l i ty of the particle, and V is the volume of the particle. Therefore, the sensor response is directly proportional to particle velocity, vo lume and susceptibil i ty. 20 Magnet ic susceptibi l i ty is a unit less quantity that descr ibes how strongly an object will respond to an external magnet ic f ield. Susceptibi l i ty is related to the mineralogy of the particle, as it is a measure of the amount of magnet ic minerals in the rock. E a c h particle may a lso have a second magnet ic property related to its mineralogy - a remanent magnet izat ion. Remnant magnetizat ion is a natural, inherent magnet ic field due to the abundance and arrangement of magnet ic minerals within the stone. S ince the strength of the magnet ic field is a vector, as a stone with remanent magnetizat ion rolls over the sensor , it may distort the shape of the characterist ic response, increasing the complexity of the s ignal . In order to investigate these two properties, the remanence and susceptibi l i ty of 45 s tones from East Creek were measured . Measurements were made at the Pa leomagnet ism Lab at the Paci f ic G e o s c i e n c e Centre, in Sydney , B C , the results of which are summar ized in Tab le 2.1. The Koenigsberger ratio is a non-dimensional ratio of remanence to susceptibil i ty. It is used in pa leomagnet ism studies as an indicator of a rock's ability to maintain a stable remanence in the presence of the earth's magnet ic field. The ratio is calculated as : K = ^ (4) 21 Tab le 2.1. Ana lys is of the magnet ic properties of 45 E a s t Creek stones Sample # Susceptibility (x10~6) Remnanat Mag (A/m) Koenigsberger Ratio 1 2.96E-01 6.32E-03 0.006 2 5.96E-01 2.36E-03 0.032 3 3.29E+00 1.11 E-02 0.037 4 7.77E-04 3.25E-05 0.003 5 8.36E-02 8.52E-04 0.012 6 4.44E-03 4.03E-05 0.014 7 5.28E-01 2.95E-03 0.023 8 1.38E-02 5.14E-04 0.003 9 1.46E+00 2.51 E-03 0.073 10 3.93E-04 7.04E-06 0.007 11 7.93E-02 4.45E-03 0.002 12 3.94E-01 2.41 E-03 0.021 13 2.65E-01 1.28E-03 0.026 14 1.49E-01 1.01 E-03 0.019 15 1.53E-01 2.49E-03 0.008 16 1.35E-03 3.51 E-05 0.005 17 1.52E-01 9.22E-03 0.002 18 2.53E-01 1.47E-03 0.022 19 2.80E-03 5.61 E-05 0.006 20 3.01 E-01 1.09E-03 0.035 21 2.73E-01 6.49E-03 0.005 22 1.44E-01 3.86E-03 0.005 23 1.64E+00 1.23E-02 0.017 24 1.85E+00 5.05E-03 0.046 25 8.34E-01 8.49E-03 0.012 26 3.88E-02 2.60E-03 0.002 27 4.01 E-02 1.57E-04 0.032 28 1.25E+00 5.00E-03 0.031 29 2.72E-01 1.63E-02 0.002 30 6.10E-03 3.24E-04 0.002 31 3.56E-01 8.80E-03 0.005 32 1.34E-02 1.16E-03 0.001 33 1.26E-02 9.52E-04 0.002 34 8.58E-04 8.33E-05 0.001 35 4.82E-04 134E-05 0.005 36 8.65E-01 6.55E-03 0.017 37 7.78E-02 5.20E-03 0.002 38 5.41 E-01 6.48E-03 0.011 39 6.76E-01 1.26E-02 0.007 40 5.13E-03 4.94E-05 0.013 41 2.67E-01 4.14E-04 0.081 42 2.03E+01 1.52E-02 0.167 43 4.21 E+00 5.24E-03 0.101 44 1.23E+00 3.91 E-03 0.040 45 1.18E+00 7.16E-03 0.021 22 where N R M is the natural remanent magnet izat ion, x i s the susceptibil i ty, B 0 is the local field strength in Tes la , and [i0 is the permeabil i ty of free space Henrys per metre. A ratio >1 indicates a remanence dominated sample , while a value <1 indicates an inductance dominated sample . B e c a u s e of the strength of the field created by the doughnut shaped magnet ( -10 mT), all the Koenigsberger ratios are well below 1, indicating that the response of the sensor is controlled by the induced magnet izat ion, and that the effect of remanence can be ignored. 2.2.2 Particle Trajectory: S e n s o r response is controlled by particle trajectory in two ways . First, the induced voltage will rapidly dec rease with increasing d is tance between the centre of the stone, and the centre of the coi l . F rom Equat ion 2, the strength of a dipole drops off as r"3; for a pass ing stone of finite s ize, a response of similar magnitude is expected. Second ly , from Equat ion 3, the strength of the induced magnet izat ion is directly related to the strength of the magnet ic field produced by the sensor ' s doughnut shaped magnet. The strength of this field w a s mapped using a G a u s s meter, and is shown in Figure 2.4. The strength of the sensor 's magnet ic field varies dramatical ly over the sensor face. Field strength drops off sharply to the sensor edge, indicating that the steel cas ing does a good job of containing the field around the individual sensor . Field strength a lso dec reases with height above the sensor ; therefore a particle pass ing over the edge, or high above the 23 sensor , exper iences a much smal ler field, and will record a proportionally smal ler response. The field strength a lso drops sharply over the doughnut hole. This effect will be d i scussed further in Sect ion 9.2. Height Above Sensor 0 cm 1.27 cm 2.54 cm 3.81 cm 5.08 cm Location relative to center of sensor (cm) Figure 2.4. Strength of the magnet ic field over the center axis of the sensor at 5 different heights 24 Chapter 3: Experimental Methods: The objective of the calibration exper iments was to produce a model that can be used to predict particle s ize from a given signal response. To build this model , two l ines of exper iments were des igned. Rotating platter exper iments were conducted to isolate individual var iables, and build empir ical models relating the shape of the sensor response curve and particle s i ze . F lume exper iments were conducted to test the ability to measure particle velocit ies, and to test the empir ical models using data with more realistic particle movements . Addit ional exper iments were conducted with both the rotating platter and a ramp apparatus to investigate the response of multiple s tones pass ing simultaneously, or in rapid success ion , and sand pulses. 3.1 Rotating Platter Experiments: Rotating platter exper iments were des igned to independently a s s e s s 5 particle var iables: vo lume, susceptibi l i ty, velocity, and trajectory in both the vertical and horizontal. To account for particle volume and susceptibil i ty, artificial s tones were cast using a mixture of portland cement, sand and iron filings. Four different mixtures were used , and are summar ized in Tab le 3.1. For each mixture, 8 s ize c l asses were cast , representing 8, 11, 16, 22, 32, 45, 64 and 90mm s ize c l asses (Figure 3.1). 25 Table 3.1. Mixture ratios (by mass) for the artificial stones Mixture # Sand (%) Cement (%) Iron Filings (%) Average Susceptibility 1 75 20 5 1600 2 70 20 10 3200 3 65 20 15 4800 4 60 20 20 6400 Figure 3.1. Artificial stones cast in 8 class sizes from 8 - 9 0 mm To account for particle trajectory and velocity, a rotating platter was designed (Figure 3.2). Two sensors were located above a rotating styrofoam platter, facing down. Particles were placed on the platter at known radius from the center pole, and passed by the sensor. The styrofoam platter could be adjusted vertically to vary the distance of the particle from the sensor, and the sensors moved along a track to vary the horizontal location of the particle across the 26 sensor face. Platter rotation was powered by a 4-speed turntable. Experiments were conducted at approximately 0.60, 1.15, 1.50 and 2.40 m/s, spanning the range of particle velocities that we might expect in the field (Bridge and Dominic, 1984). Figure 3.2. Rotating Platter apparatus, designed to independently control particle trajectory (both vertical and horizontal) and particle velocity. 27 A ramp apparatus was also used in later experiments. This apparatus was mainly used to record pulses of sand, and groups of particles, which could not be accommodated by the rotating platter apparatus. Two sensors were inset in a piece of wood that acted as a ramp (Figure 3.3). Adjustable sidewalls were used to confine the passage of the particles over one individual sensor. Figure 3.3. Ramp apparatus. Two sensors are inset into the ramp; adjustable sidewalls confine particles over a given sensor. 28 3.2 Flume Experiments: After the rotating platter exper iments, f lume exper iments were conducted to produce more realistic simulat ion of particle movements , and to test the use of the B M D system to measure particle velocit ies. Figure 3.4 shows the f lume set-up, looking upstream from the sensors . The f lume was 45 cm wide, and 6 m long. A fixed bed was produced by gluing stones to a plywood sheet with f ibreglass resin. The flume s lope was set to 1%. Two rows of 4 sensors each spanned the width of the f lume, with 22 c m separat ing the rows. Initially the fixed bed cont inued immediately downst ream of the sensor rows; however, due to the sharp changes in bed roughness from the fixed bed to the smooth aluminum plate of the sensors , and back to the fixed bed, a standing wave deve loped overtop of the second row of sensors . The wave s lowed particle movement , and even stopped the movement of 8 mm particles. To overcome this problem, the bed was kept smooth for a sect ion downstream of the sensors , which had the effect of pushing the standing wave downst ream, al lowing uninhibited movement of the particles over the sensors . Two rows of sensors were used in these experiments to test the ideas of Sp ieker and Ergenz inger (1987) who suggested that the velocity of an individual particle could be ana lyzed through the time lag in the voltage response between the two rows. The exper iments were a lso recorded with an overhead video camera , which was used as a second method of tracking particle velocit ies. Exper iments were run at 5 different d ischarges (11, 17, 22, 27 and 33 L/s) to produce a range of particle velocit ies. 29 The same artificial stones from the rotating platter experiments were also used in the flume experiments. Stones were fed into the flume one by one. Initial experiments used single size classes from a single cement mixture. In later experiments, the complexity was increased by adding multiple size classes from one cement mixture, multiple cement mixtures from one size class, and a complete mix of sizes and cement mixtures. Figure 3.4. Flume set-up. Two rows of 4 sensors each are visible in the foreground. The coloured stones are the artificial stones used for these experiments. 30 3.3 Data Collection and Signal Processing: The resulting data from each experiment is a set of voltage time ser ies. E a c h sensor is connected to an individual channel on an analogue-digital recorder. In the initial field deployment, Tunnicliffe et a l . (2000) recorded at 104 Hz; in the calibration exper iments, the sensors were samp led at 501 Hz . The cho ice of sampl ing f requency is a trade off between adequately capturing the s ignal , and storage s p a c e for the digital data. Data storage technology has improved significantly in the past few years, al lowing for higher f requency recording. LabV iew software was used in order to process and analyze each time ser ies. The raw time ser ies includes information about both the pass ing particles and background noise. LabV iew offers a number of built in filtering features from which a low-pass Butterworth filter was se lected to block out the background noise. The low-pass filter al lows data with f requency content below a speci f ied threshold to pass , while blocking any data with f requency content above the threshold. Figure 3.5 shows the effect of filtering the s a m e signal at a number of different thresholds. The faster particles have higher f requency content, and begin to get filtered out at higher thresholds. If the threshold is set too low, then some of the true signal gets filtered out, and the response diminishes, but if the threshold is too high, too much background noise gets through, increasing the minimum detection threshold above the noise. For analys is of the calibration exper iments, a filter threshold of 55 Hz was chosen , as it represents a good balance of filtering out noise, without losing actual s ignal . Figure 3.6 shows the s a m e time ser ies before and after filtering. 31 0.010 0.008 TO C <§* 0.006 CD o 0.004 0.002 0.000 i i i i I I i i. i " r • i 7 J--l / ! 1 ' 1 -f i i / + ' \-i 1 / | i -i-i I I I i 1 i i i Part ic le Veloci ty 0.6m/s 1.16m/s 1.52m/s 2.42m/s 0 10 20 30 40 50 60 70 80 90 100 Lowpass Thresho ld (Hz) Figure 3.5. The effect of filter threshold on the recorded signal - too low of a threshold c a u s e s data to be lost. A 55 H z filter was chosen for the current analys is . 0 5 10 15 20 25 30 35 40 45 Time (s) 0 5 10 15 20 25 30 35 40 45 Time (s) Figure 3.6. A: R a w data with no filtering. B: Data after filtering with 55 Hz lowpass filter. The horizontal l ines represent the noise range of the sys tem after filtering. 32 After filtering, individual responses were identified. B e c a u s e of the characterist ic shape of the response curve, LabView 's peak detection sequence was suitable for identifying individual s ignals. With the peak detection sequence , a minimum response threshold of 1x10~ 3 V was used , which represents the noise in the recording sys tem (see Figure 3.6). Individual particles were identified from other random noise by detecting pairs of peaks and val leys. A s shown in Figure 3.7, each signal was character ized by its ampli tude, width, and a rea under the curve. S ignal width was calculated as the time difference between the peak and the valley. The integration of the curve was calculated as the average of the area under the peak and the a rea under the val ley from zero cross ing to zero cross ing, using the trapezoidal rule. The minimum signal integral that could be calculated was 2x10" 6 V * s . The a rea under the peak from a given signal is equal to the amplitude of the integral of the s ignal ; therefore, a s impler way to calculate the a rea under the curve would have been to use the built-in integration feature in LabV iew to integrate the time ser ies , and then to use a second peak detection sequence . Th is was attempted however there was low f requency noise that would confound the s ignal . A high pass filter was used to try to block out this noise, but the f requency range of the noise was not consistent between time ser ies, making it difficult to automate the data process ing. 33 Figure 3.7. Signal parameters collected from each sensor response. 34 Chapter 4: Results and Analysis 4.1 Particle Characteristics: Initial exper iments using the rotating platter apparatus were des igned to investigate the relat ionships between sensor response and particle s ize , susceptibi l i ty and velocity. For these experiments, a constant trajectory over the center of the sensor was used . From the data col lected in these experiments, empir ical models can be built to so lve the inverse problem: given a signal response, what is the particle s i ze? The models are deve loped for max imum possib le sensor response (i.e. particles pass ing in contact with, and directly over the center of the sensor face), and a known susceptibi l i ty. Mode ls are deve loped for each signal parameter: ampli tude, width and integral. 4.1.1 Signal Amplitude Results: The signal ampli tude will be controlled by all three var iables (size, susceptibi l i ty and velocity). From Equat ions 1 thru 3, increasing the particle susceptibi l i ty or vo lume will increase the induced magnet izat ion, thereby increasing B and the peak voltage response. Increasing particle velocity will act to increase dB/dt, a lso increasing the ampli tude. The relation between particle vo lume and signal ampli tude is shown in Figure 4 .1 . The log-log plot shows data for s tones from a single susceptibi l i ty (1600), sorted by particle velocity ( R P M ) . The data follow a l inear trend on the log-log plot, indicating a power relationship. There is a consistent break in s lope near 12 35 cm 3 , above which the relation is less steep, suggesting that above this volume the top portion of the stone does not contribute as strongly, due its distance from the sensor. Figure 4.2 shows the relation between particle velocity and signal amplitude. The plot shows data from a single susceptibility (1600), sorted by size class. The slope of the power relation appears to increase as particle size increases. 0.0100 <" 0.0001 0.1 RPM 16 33 45 78 1.0 10.0 100.0 1000.0 Particle Volume (cm 3 ) Figure 4.1. Relation between particle volume and signal amplitude. The slope of the relation increases with increasing R P M . There is a consistent break in slope near 12 cm 3 , above which the slope decreases. 36 0.0100 0.0001 1.0 10.0 Particle Velocity (m/s) Figure 4.2. Relation between particle velocity and signal amplitude. The slope of the power relation increases as particle size increases. The relation between particle susceptibility and signal amplitude is shown in Figure 4.3. The data are from one particle velocity (33 RPM), sorted by particle size, with susceptibility plotted on an arithmetic axis, and signal amplitude plotted on a log axis. Again, the data follow a positive linear trend. Combining all 3 variables, Figure 4.4 is a 3-dimensional log-log-log plot with volume, velocity and amplitude plotted on the x,y and z axes respectively. The data are sorted by susceptibility. For a given susceptibility, the data fall on a plane through the space. The plane shifts up the amplitude axis as susceptibility increases. 37 0.1000 0.0001 L 1000 3000 5000 Susceptibility 7000 Figure 4.3. Semi-log relationship between susceptibility and signal amplitude. Figure 4.4. 3-dimensional plot of the variables affecting signal amplitude. For a given susceptibility, the points fall along a plane through the amplitude-velocity-volume space. 38 4.1.2 Empirical Model for Signal Amplitude: Taking the results from Figure 4.4, the data was run through multiple regression to produce a relationship of the form: log( A) = c + bx [logCV,)] + b2 [log(v)] + b,[S] + e (6) where A is ampli tude in Vol ts, V p is particle volume in c m 3 , v is particle velocity in m/s, S is susceptibi l i ty in SI units per m 3 , c is the regression constant, bi are the regression coeff icients, and e is the error. A s d i scussed in Sect ion 4.1 .1 , there is a break in s lope in the data at approximately 12 c m 3 . Separa te regress ions were run for data above and below this threshold. The results of the regress ions are summar ized in Tab le 4 .1 . The high Ft2 va lues are somewhat mis leading because of the log transformations. Tab le 4.1. Regress ion coeff icients for the amplitude mode l . Separa te regress ions were run for stones <12 c m 3 and >12 c m 3 . Volume < 12cm3 Volume > 12cm3 Coefficient Standard Error Coefficient Standard Error c -3.87 0.029 -3.47 0.037 bi 0.68 0.023 0.32 0.015 b 2 0.71 0.043 0.90 0.032 b 3 1.50x10"4 7x10" 1.44x10"4 5x10"b Ff 0.96 0.96 Equat ion 6 can be rearranged to solve for particle vo lume: vp=io log( A)-h2JlogUJl-y.V | -(7) 39 Equation 7 was used to back-calculate an estimate of particle volume from the same data. Figure 4.5 shows the estimated volume results versus the actual volumes. The results are shown with both arithmetic and logarithmic axes. The logarithmic graph was produced in order to clearly show the results for the smaller volumes. The y-scale of the logarithmic plot is divided into size class regions. The regions were determined by calculating the volume of a sphere for each of the size classes (8, 11, 16, 22, 32, 45, 64, 90 mm). The median error in volume estimation is 29%, with a maximum error of 132%. Including this error, however, it is evident from the logarithmic plot that the estimates still generally fall within the appropriate size classes. £ E _ 3 E UJ 600r 400h 200 1000.0 200 400 Actual Volume (cm 3) 600 1.0 10.0 100.0 1000.0 Actual Volume (cm 3) Figure 4.5. Estimated particle volumes from the empirical model versus actual particle volumes. The logarithmic plot is used in order to show the variability for each particle size clearly. The green lines divide the graph into size classes. Including the scatter about the 1:1 line, data still generally fall within the correct size class. 40 4.1.3 Signal Width Results: Signal width is a measure of the length of time it takes the particle to pass over the sensor . This should be a function of both the particle velocity and the diameter of the pass ing stone. S ince it is only a function of position and time, it should be independent of the particle susceptibil i ty, eliminating one of the var iables. The relation between the diameter of the B-axis and signal width is shown in Figure 4.6. The plot shows data pooled from all 4 susceptibi l i t ies, at a single particle velocity of approximately 1.15 m/s. Though there is s o m e scatter, the data follow a positive trend. Figure 4.7 shows the relation between particle velocity and signal width. The plot shows data pooled from all 4 susceptibi l i t ies, sorted by s ize c lass . There is a negative linear trend - as velocity increases, signal width dec reases . Though there is scatter, there is segregat ion of particle s ize . For a given velocity the signal width increases with particle s ize . A 3-dimensional plot is shown in Figure 4.8, with velocity, B-axis diameter and signal width plotted on the x, y and z axes respectively, all in log space . The data fall nicely on a plane through this space . 41 0.10, 0.01 I '—1 ' ' 1 1 1 Velocity -1.15m/s o « o 0 o o o 10 100 1000 B-Axis Diameter (mm) Figure 4.6. Relat ionship between particle diameter and signal width. 0.1 Or 1.0 Particle Velocity (m/s) 10.0 Figure 4.7. Relat ionship between particle velocity and signal width. There is overlap, but in general for a given velocity, width inc reases as particle s i ze increases. 42 -i.oor Figure 4.8. 3-dimensional plot of the variables influencing signal width. The data fall nicely on a plane within this space. 4.1.4 Empirical Model for Signal Width: Using the data from Figure 4.8, multiple regression analysis was run with signal width (W) in seconds, B-axis diameter (D) in mm, and particle velocity (v) in m/s to produce: log(W) = -1.96 + 0.331og(D) - O.831og(v) (8) 43 This equation can be rearranged to solve for B-axis diameter: D = 10 log(W)+0.83[log(v)]-t-1.96 0.33 0) Equation 9 was used to back-calculate an estimate of the B-axis diameter from the same data. Figure 4.9 shows the estimated versus the known diameters. With this model, the median error is 21%, with a maximum error of 106%. However, this model does not predict as well as the amplitude model; the data do not follow a general linear trend about the 1:1 line, and there is significant overlap between the different size classes so that predictions may be 3-4 size classes in error. Actual B-axis Diameter (mm) Figure 4.9. Estimated B-axis diameter from the empirical model versus actual B-axis diameter. The green lines identify the different size class regions. Scatter in the estimations span 3-4 size classes. 44 4.1.5 Signal Integral Results: The a rea under the curve will depend on both the susceptibi l i ty and volume of the particle, but it is independent of particle velocity. From Equat ion 1, if the s a m e object passes the sensor at two different speeds , the response to the faster pass will have higher amplitude and narrower width. Figure 4.1 OA shows the s a m e object pass ing the sensor over a large range of velocit ies (as seen by the range in ampli tudes); Figure 4.1 OB shows the integration of the s a m e time ser ies. The ampli tude of the integral (which is equivalent to the a rea under the curve of the raw data) is the s a m e for all s ignals, independent of the object 's velocity. This can a lso be proven mathematical ly: r dB , r dB dx , °r dB , °r dB dx r dB , —dt = dt = v—dt = v = —dx (5) _m dt dx dt __ dx *_ dx v dx From Equat ion 1, the number of windings (N) and the a rea (A) of a given coil are constant; therefore the induced voltage is directly proportional to dB/dt. The a rea under the curve then is proportional to the integral of dB/dt with respect to t ime. Equat ion 5 rearranges this integral to show that velocity cance ls out, and that the sensor response is related to position and time independently. 45 > E 0) c « c CO 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 0 B r*~r f 10 15 Time (s) 20 25 Figure 4.10. A: Time series of a single object passing by the sensor at different velocities (as seen by the difference in amplitude). B: Integral of the same time series. The amplitude of the integral is approximately the same, regardless of velocity The relation between susceptibility and signal integral is shown in Figure 4.11. The data include the range of particle velocities, sorted by particle size, with susceptibility plotted on an arithmetic axis, and signal amplitude plotted on a log axis. The data follows a positive linear trend. Figure 4.12 shows the relation between particle volume and signal integral. The plot includes data over the range of particle velocities, sorted by susceptibility. The linear trend again indicates a power relation. The graph is very similar to Figure 4.1; a break in slope is evident above 12cm 3 . 46 0.001000 IP 0.000100 > t— - 0.000010 c g i 0.000001 3000 5000 Susceptibility 7000 Figure 4 .11 . Relat ionship between susceptibil ity and signal integral 0.001000 0.000100 CD to 0.000010^ c g> 0.000001 a TT| ! ! I I ITT^ i Susceptibility 1600 3200 4800 A 6400 1.0 10.0 100.0 1000.0 Particle Volume (cm3) Figure 4.12. Relat ion between particle volume and s ignal integral. There is good segregat ion between susceptibi l i t ies. Like the relationship between vo lume and amplitude, there is a break in s lope near 12 c m 3 47 4.1.6 Empirical Model for Signal Integral: Using the data from Figure 4.12, a multiple regression model was a lso built for signal integral. This regression takes the form: login = c + bl[\ogCV)] + b2[S] + e (10) where I is the signal integral with units V * s . In the s a m e manner as the ampli tude model , separate regressions were run for data above and below a threshold volume of 12 c m 3 . The results of the regressions are summar ized in Table 4.2. Aga in , the high R 2 va lues are somewhat mis leading because of the log transformations. Tab le 4.2 Regress ion coeff icients for the integral model . Separa te regressions were run for stones <12 c m 3 and >12 c m 3 . Volume < 12cm3 Volume > 12cm3 Coefficient Standard Error Coefficient Standard Error c -5.39 0.024 -4.97 0.032 Bi 0.77 0.019 0.39 0.013 B 2 1.52x10~4 5x10"b 1.40x10"4 4x10"b 0.98 0.96 Rearranging equation 10 to so lve for vo lume produces: ("log(/)-fe2[51-c V=lf> (11) 48 which was used to back-calculate an estimate of particle volume from the same data. Figure 4.13 shows the estimated versus the known volumes. The results are shown with both arithmetic and logarithmic axes in order to clearly show the results for the smaller volumes. Like Figure 4.5, the y-scale of the logarithmic plot is divided into size class regions. With this model, the median error in estimation is 13%, with a maximum error of 89%. Similar to the amplitude model, even with the errors, estimates generally fall within the appropriate size class region. 600r 400k 200h 200 400 Actual Volume (cm 3) 600 1000.0 § 100.0 0J £ 5 I ra E 10.0 fc-1.0 fc-0.1 m) | A t 11 n i l 1 — I 0.1 1.0 10.0 100.0 1000.0 Actual Volume (cm 3) Figure 4.13. Estimates of particle volumes from the integral empirical model versus actual volumes. The green lines on the logarithmic plot divide the y-axis into size classes. Variability about the 1:1 line generally is within the correct size class. 49 4.2 Particle Trajectory: The empirical models deve loped above are for the simplif ied case of particles pass ing over the center of the sensor , directly in contact with the sensor face. A second set of rotating platter exper iments addressed particle trajectory by incremental ly varying the location ac ross the sensor face and the distance of the stone above the sensor face. 4.2.1 Variation Across the Sensor Face: Figure 4.14 shows how signal amplitude var ies across the sensor face, for 3 different grain s i zes at the s a m e velocity (78 rpm). The curve is symmetr ic, with the strongest response occurring over the center of the sensor , and dropping off sharply to the edge of the sensor . The data were normal ized by taking the ratio of the ampli tude at a given location to the ampli tude recorded over the center of the sensor . S ince the data are symmetr ic about the center of the sensor , the relation between the absolute value of location and the normal ized response is shown in Figure 4.15. There is a fair amount of spread in the data, but the relationship can be descr ibed by a line. The intercept of the line necessar i ly goes through one s ince the normal ized response is unity at a location of zero; the response drops off to zero at a location of approximately 5 .5cm. The equation of the line is therefore: = ( ~ ) | * |+1 (12) 50 where ANorm is the normal ized amplitude. ANorm represents the percentage of the maximum possib le voltage that was actually recorded. The variation in s ignal integral ac ross the sensor face is shown in Figure 4.16. The plot includes 3 different grain s i zes at the s a m e velocity (78 R P M ) . The curve is very similar to that of the signal amplitude. Us ing the s a m e logic as above, the signal integral data were a lso normal ized, and are plotted against the absolute value of location in Figure 4.17. This data can be descr ibed by the exact s a m e function as the amplitude data, by substituting INorm for ANorm in equation 12. - 5 - 3 - 1 1 3 5 Location Across the Sensor Face (cm) Particle S ize 11mm < 16mm + 22mm Figure 4.14. Variat ion in signal amplitude across the senso r face. 51 Absolute Location Across Sensor Face (cm) Figure 4.15. Normalized signal amplitude across the sensor face 0.00015 0.00010 > e J? _! 75 0.00005 c CO 0.00000 " i 1 1 r + + J I L ° 5 Particle Size o 11mm x 16mm 22mm - 5 - 3 - 1 1 3 5 Location Across Sensor Face (cm) Figure 4.16. Variation in signal integral across the sensor face 52 Absolute Location Across Sensor Face (cm) Figure 4.17. Normalized signal integral across the sensor face The relation between signal width and location across the sensor face is shown in Figure 4.18. Again the data are from 3 different grain sizes at the same velocity. This curve is very different from that of the amplitude and integral. The response is still symmetric about the center of the sensor, but in this case, the signal width is smallest over the center of the sensor. It increases to about 2 cm from the center, before it drops off toward the sensor edge. The results for width across the sensor were somewhat surprising. It was expected that the largest width would occur over the center of the sensor, since that is where the stone passes over the maximum sensor diameter. The results suggest that the magnetic field produced by the doughnut shaped magnet affects these results, as the locations of maximum width coincide with the edge of the doughnut hole. No normalization was attempted with the width results due to their anomalous behaviour. 53 0.05 _ 0.04 0.01 § cost-'s c (7) 0.02K; * » + Particle Size o 11mm * 16mm 22mm - 5 - 3 - 1 1 3 5 Location Across Sensor Face (cm) Figure 4.18. Variation in signal width across the sensor face 4.2.2 Variation With Distance From the Sensor Face: The signal amplitude drops off as the distance between the center of the stone and the center of the sensor coil increases, as shown in Figure 4.19. The plot uses data from a single speed (33 RPM), sorted by particle size. The relation shows a general linear trend that is similar between particle sizes. At small distances the relation bends, which is likely due to the high variability in magnetic field strength close to the sensor due to the doughnut shaped magnet (see Figure 2.4). The relation between signal integral and distance between the center of the stone and the center of the coil is very similar, and is shown in Figure 4.20. 54 -a =3 _ ; CL E < re c g> CO 0.0100 0.0010 0.0001 i — i — i — i i i i ! 1 1 1 — i — I I I ! * X K - x A x v O X + A - 0 x V -a x ^ 0 X i V -1 Particle Size 8mm 11mm 16mm 22mm 32mm 10 100 Distance From Center of Stone to Center of Sensor (cm) Figure 4.19. Variation in signal amplitude with increasing distance between the center of the stone and the center of the sensor 0.001000 M > 0.000100 n 0.000010 c 3 1 CO -1 r 1—I—I I I —I— I I I I I I A V A " X A ? X V r J X A V —J— I I I I i j Particle Size ° 8 mm x 11mm 16mm * 22mm v 32mm 0,000001 1 10 100 Distance From Center of Stone to Center of Sensor (cm) Figure 4.20. Variation in signal integral with increasing distance between the center of the stone and the center of the sensor 55 A plot of signal width and distance between the center of the stone and the center of the sensor coil is shown in Figure 4.21. Like the previous figures, the data are from a single velocity (33 RPM), sorted by particle size. The relation is very different from that of the amplitude and integral; in this case there is a positive relation - signal width increases with height. The slope of the relation is similar for the different particle sizes. The increase in width with height is likely due to the steel yoke that the sensor sits in. The yoke attracts the field lines, confining the field near the sensor face. As distance increases from the sensor face, however, the field lines are less affected by the yoke, allowing the stone to remain in the field for a longer duration. 0,10 S x c CO 0.01 £? -I *9 w _i 1 1 1 k X V I i _i 1 1—i i J i J - j Particle Size ° 8mm x 11mm 16mm A 22mm v 32mm 1 10 100 Distance From Center of Stone to Center of Sensor (cm) Figure 4.21. Variation in signal width with increasing distance between the center of the stone and the center of the sensor 56 4.3 Incorporating Trajectory into the Empirical Models: In the field c a s e , the trajectory of a given particle pass ing over the sensor will not be known; most particles will not pass directly over the center of the sensor . B e c a u s e of how quickly the sensor response drops off both to the edge, and above the sensor , this adds a significant amount of complexity. A simplifying assumpt ion can be made that all particles will pass in contact with the sensor face (i.e. that particles are not saltating when they pass by the sensor) . This was the c a s e in the f lume experiments, and is a reasonable assumpt ion for the gravel s ize fractions that the sensor is able to detect. With this assumpt ion the effect of height above the sensor can be ignored. The effect of location ac ross the sensor face, however, is more complex. F lume exper iments were run in order to simulate more realistic particle trajectories over the sensor . In these experiments, each particle had an equal probability of pass ing over any location across the sensor array. To illustrate the effect that location across the sensor has, the empirical model for the signal integral was used to est imate particle vo lumes from the f lume data. T h e s e results are shown in Figure 4.22. If the model was success fu l , the data should fall a long the 1:1 line; without account ing for location across the sensor , the model significantly underest imates particle vo lumes. 57 1.0 10.0 Actual Volume (cm 3) 100.0 Figure 4.22. Estimated particle volumes from flume experiments with no adjustment for location across the sensor face. One way to try and account for the unknown location is to assign each signal a random location. Since each particle has equal probability of passing over any location, a random number was generated from a uniform distribution between -5 and 5 (the sensor spacing is 10 cm), and assigned to each signal response from the flume data. Using the normalized relations from section 4.2.1, a correction factor of 1+(1- ANorm) or 1+(1- INorm) was applied to each signal response, where AN0rm and lNorm were calculated using the absolute value of the random location. Assuming the random location is correct, the correction factor adjusts the signal response to what it would have been had the particle passed over the center of the sensor. 58 The empirical models for amplitude and integral were used to estimate the particle size for the adjusted data. The results from the integral model are plotted in Figure 4.23. There is still a large amount of variability in the data, but this time the data are spread more evenly about the 1:1 line. The models do not predict an individual particle very accurately, but may still be useful at the event scale. Estimated values from the flume experiments were summed to produce an estimate of the total transported volume and mass. Table 4.3 compares the known total values with results from the models. The model with no location adjustment significantly underestimates. There is a range of estimates from the second model due to the random location component, but by summing over -1800 stones, the estimated total volume from this model are in the correct range. Figure 4.23. Estimated particle volumes from signal integral model with random location adjustment. 59 Table 4.3. Est imated total transport volume and m a s s from flume exper iments Actual Amount Estimated amount with no location adjustment Estimated amount with random location Volume (cm3) 25500 8100 15000-27000 Mass (kg) 67.6 21.5 40-70 4.4 Particle Susceptibility: T o investigate the range of susceptibi l i t ies that could be expected in the field, the susceptibil i ty of 150 s tones from East Creek were measured . Fifty s tones were taken from each of the 22, 32 and 45 mm size c l asses . To measure the susceptibil i ty, samp les needed to fit into a plastic container with a max imum volume of 10 c m 3 , s o only a smal l sample broken off of each stone was measured . The results range from 0.7 - 9500 SI units, with a geometr ic mean of - 2 0 0 . A histogram of the results is shown in Figure 4.24. The histogram is divided into two categor ies, no response and response. Before the susceptibi l i t ies were measured , each of the stones was passed by the sensors on the rotating platter apparatus. Of the 150 s tones, 103 of them recorded a response, while 46 passed by undetected. There is s o m e overlap in susceptibi l i t ies between the two categor ies, but in general the threshold susceptibi l i ty for detection is around 100. There were 8 s tones with a susceptibi l i ty >100 that recorded a response, and 7 s tones with a susceptibi l i ty <100 that failed to record a response. 60 The stone with the lowest measured susceptibility that recorded a response had a susceptibility of 12.3, while the stone with the largest susceptibility that failed to record a response had a susceptibility of 2970, suggesting that for some stones, the small samples used to measure their susceptibility were not representative of the rest of the stone. 50r 40 >-o c • cr 30 20 l . II • • No Response Response 1000 2000 3000 4000 5000 6000 Susceptibility Figure 4.24. Histogram of particle susceptibilities measured from 150 stones from East Creek. The red bars indicate stones that past by the sensors with no response; the blue bars produced a response. Using only stones with susceptibility greater than a threshold of 100, a normal distribution was fitted to the logarithm of the susceptibility data (Figure 4.25). The choice of the threshold was somewhat arbitrary, but because of the skew in the distribution, changing the threshold slightly will not have much effect. The distribution has a mean of 2.817 and a standard deviation of 0.451. 61 1.80 2.20 2.60 3.00 log(Susceptibility) 3.40 3.80 4.20 Mean 1 Std Dev 2 Std Dev Expected Figure 4.25. Normal distribution of the log of particle susceptibility measured from 150 East Creek stones. When converted to arithmetic units, the geometric mean of the distribution is -660. The range within ±1 standard deviation of the mean is 230-1860; 68% of the stones will fall within this range. Another -13.5% of the stones will fall between 80-230 (i.e. between -1 and -2 standard deviations). These values of susceptibility are generally much lower than those of the artificial stones used to build the empirical relations. To test the ability of the relations to extrapolate back to these lower susceptibility values, volumes were estimated from the data for the East Creek rocks on the rotating platter. Figure 4.26 shows estimated versus actual volume results from using the signal integral relation. The data are divided into groups of susceptibility <1000 and >1000. The data points for the >1000 group fall relatively close to the 1:1 line; these data have susceptibilities similar to those used to calibrate the model. On the other hand, the data points 62 from the <1000 group are significantly underestimated. This suggests that the model does not do a good job of extrapolating to smaller susceptibilities. A second empirical model was tested using log(S) in equation 10 instead of S. This model also did a poor job of estimating at low susceptibilities. More data are required with stones of low susceptibility to investigate this relation further. g 100.0 w E •S 10.0 ro E LU 1.0 I 1 M | 1 1 1 1 1 | | | | 1 r 1 1 1 v. Susceptibility / o <1000 * / r >iooo . o . / • : / • ; - / / -o O GB 0 v C O .: ° O : / ? of o : • / o -8 1 o / ° °o° 0 0 a °° oo 0 O < / ° 0 O ~ / o o 0 o -/I 1111 1 : X J J 1 1 1 1 1 I 1 J.I I I i i I I I 11 L 1.0 10.0 100.0 Actual Volume (cm 3 ) Figure 4.26. Estimated volumes of East Creek stones from the signal integral model. Susceptibilities >1000 are closer to the 1:1 line as they are in the range of susceptibilities used to develop the model. 63 4.5 Particle Velocity: In order to use the signal amplitude or signal width models , the particle velocity must be known. This parameter is not general ly known in the field. Other methods of bed load detection use est imates of particle velocity from theoretical calculat ions based on hydraulic parameters. Sp ieker and Ergenzinger (1988) suggested that the magnet ic sys tem could be used to measure particle velocit ies if two rows of senso rs were used . The velocity could be determined from the time lag in s ignal response between the two rows. O n e of the goals of the f lume exper iments was to test this idea. Two rows of sensors were used , s p a c e d 22 c m apart. The signal responses from corresponding sensors were matched up, and where possib le, particle velocit ies were calculated. For some of the s ignals, there was no corresponding match, because the particle was not detected over one of the rows. Part icle velocit ies were obtained for 6 7 % of the - 1 8 0 0 s ignals. A s a check, particle velocit ies were a lso measured with a v ideo camera mounted above the f lume. Using a V C R with individual frame advance , the distance that a particle traveled over 8 f rames was measured and translated into a velocity. V ideo measured velocit ies were matched up with the 2-row measured velocit ies, and are plotted in Figure 4.27. Within the error of the two sys tems, there is good agreement; the data fall evenly around the 1:1 line. 64 Figure 4.27. Compar i son of particle velocit ies measured with the two rows of sensors , and the video recording. 4.6 Multiple Stone and Sand Experiments: In both the rotating platter and flume experiments, individual part icles were passed by the sensors one by one. At high transport rates, however, it is possible that multiple s tones would pass by the sensor s imul taneously, or in rapid success ion . Exper iments were carried out with multiple s tones to investigate how the sensor would respond. Figure 4.28 shows the sensor response to 2 particles pass ing in rapid success ion . The diagram is divided into four; in each sect ion the s a m e two particles pass by, but the spac ing between the particles decreases from left to right. A s the particles get c loser together, the signals from the individual stones become super imposed on one another. The signals are additive, s o that if the shape and location of one s ignal were known, it 65 could be subtracted to leave the other signal behind. Th is is s imple to do in the control led lab sett ing, but with data col lected in the field, this b e c o m e s a complex signal process ing problem. •V oo CO > time Figure 4.28. Super imposi t ion of s ignals as the d is tance between part icles dec reases . A n experiment was a lso des igned to investigate the sensor response to a mass of sand pass ing over. This experiment used the ramp apparatus and a sediment sample of material <8 mm taken from East Creek . A layer of sediment spanning the whole width of the sensor was passed in slurry over the sensor . Approximately 10 k i lograms of sand were passed over the sensor in this manner with no visible response from the sensors . These results suggest that in the field 66 over-pass ing sands will not be recorded, only the coarse fraction will, and that the fine materials will not increase the noise in the data. These results are in contradiction with results presented by Tunnicliffe et al . (2002) who presented observat ions of "streets" of sediment compr ised of sands and gravels pass ing by the sensors . More exper iments are required, looking at the effects of fine materials with a range of lithology to better clarify the ability of the sys tem to detect fine materials. 67 Chapter 5: Discussion 5.1 Empirical Models: The rotating platter experiments successfu l ly showed that for the simplif ied c a s e of a stone with known susceptibil i ty pass ing directly over the center of the sensor , the magnitude of the signal response can be related to particle s ize . Of the three models deve loped, the width model is the poorest. Even in this simplest of c a s e s , est imated particle s ize varied over 3-4 s ize c l asses , which is unfortunate, because the width is independent of susceptibil i ty, eliminating an unknown variable from the analys is . The model results look very similar for the ampli tude and integral models , but the integral model is better, being independent of particle velocity, and having lower error. Independence from velocity is significant, because with the integral model , only one row of sensors would be required to monitor sediment transport, cutting in half the number of sensors required at a given cross-sect ion. A lso , matching up the peaks from the adjacent sensor rows to calculate particle velocit ies is a time consuming task that is difficult to automate. Unfortunately, the simplif ied c a s e will never be met in the field. Due to the way the signal response varies ac ross the sensor face, and the large range of susceptibi l i t ies found in the field, the current sys tem cannot be used to reliably estimate particle s ize from an individual s ignal . The variation across the sensor face is due to a combinat ion of the strength of the magnet ic field from the doughnut-shaped magnet, and the distance of the stone from the center of the coi l . The effect due to distance from the coil is 68 inherent to the physics of the sensor , but the effect due to the strength of the magnet ic field can be manipulated by changing the strength and/or type of magnet used, which will be d i scussed further in Sect ion 5.3. The range in susceptibi l i ty is another factor that is inevitable in the field. It may be possib le to make s o m e assumpt ions to simplify the problem, but unfortunately this cannot be tested further with data from the current sets of exper iments. The susceptibi l i t ies of the artificial s tones were chosen in order to get a strong response, well above the noise range of the sensor , so that c lear relationships could be deve loped. However, because the empir ical models do not extrapolate well to the lower susceptibi l i t ies found in the field, the analys is that can be done with these data is somewhat limited. Further experiments are required at the lower susceptibi l i t ies to better descr ibe the relationship between susceptibi l i ty and s ignal response. The current sys tem may not be reliable for estimating the s ize of each individual particle, however, the system is still useful for studying patterns of spatial and temporal variability of the intensity of movement, and results from the f lume exper iments show that at event time sca les , where the variability can average out, the sys tem can be used to estimate transport vo lumes. T h e s e est imates could be further improved through field calibration against vo lumes col lected in a sediment trap. 69 5.2 Problems with the Current Sensor Design: Over the course of the experiments, s o m e inherent w e a k n e s s e s of the sensor design were observed. A s descr ibed in Sect ion 2.1, and shown in Figure 2 .3C, the expected signal is a s imple c lean curve with a peak fol lowed by a val ley. Whi le the majority of s ignals recorded resembled this ideal shape , s o m e irregular s ignals were a lso recorded. Somet imes , instead of the ideal curve, a double-peaked response was recorded. This effect was especial ly noticeable with smal l s tones at low particle velocit ies. The double peak made measurement of the signal parameters more difficult, caus ing the peak detection sequence to pick up extra peaks . Therefore, addit ional process ing was required to identify the double peaks and c lean up the data. The double peaks especial ly hindered the signal width measurements , which were determined from the time difference between the peak and the valley. If the peak or val ley was poorly def ined, this introduced variability into the width measurement , which is already very sensit ive to changes in particle s ize . In the lab experiments it was known that only one particle passed by the sensor at once. In the field case , however, this will not be known and double peaked signals may be mistaken for multiple s tones pass ing in rapid success ion . For the current experiments, when two peaks were identified very c lose together, the lower of the peaks was d iscarded. The double peak effect is most likely c a u s e d by the magnet ic field created by the doughnut shaped magnet. A s shown in Figure 2.4, near the sensor face, the strength of the magnet ic field is highly variable, and even goes negative in the 70 doughnut hole. The effect dec reases quickly with height above the sensor , so that by 2.5 c m above the sensor the field is def ined by a smooth curve, but the smal lest detectable particles pass directly through this highly variable zone . Two other effects were observed that are a lso likely attributable to the field of the doughnut-shaped magnet. First, in Figure 4.18, which shows how signal width changes across the sensor face, there is a distinct dip in width near the center of the sensor . The region in which this observed directly cor responds with the diameter of the doughnut hole. Second ly , in Figures 4.19 and 4.20, which show the relationship between the distance between the center of the stone and the center of the sensor coil with signal ampli tude and integral respectively, the data c losest to the sensor deviate from the power relation observed at greater d is tances. This deviation is again likely because the s tones near the sensor face are moving through such a highly variable field. Another weakness of the current sensor des ign is that many s tones pass between sensors undetected. B e c a u s e each sensor is isolated from its neighbor by a steel cas ing , the a rea at the edge and in between the sensors has a very weak field. It was thought that large stones pass ing between sensors would induce s imul taneous response in multiple sensors ; however, s tones as large as 45 mm were capab le of pass ing between sensors undetected. O n the other hand, s tones with high susceptibi l i ty often induced an inverted response in the adjacent sensor (i.e. a val ley first, fol lowed by a peak). This type of response was recorded for particles as smal l as 22 mm. T h e s e responses were large enough to be picked up by the peak detector, which was cause for addit ional 71 data process ing. Individual s ignals were identified as peak-val ley pairs; valley-peak pairs were d iscarded. A third weakness of the sensor is that a large range of particle s i zes is descr ibed by a fairly smal l range of response. For example , from Figure 4.10, at a susceptibil i ty of 1600, all 8 s ize c l asses are defined over the range 2 -200x10" 6 V * s . The range becomes even more constr icted at smal ler susceptibi l i t ies. The variability in a given integral measurement is on the order of 2x10" 6 V * s , so that as the range becomes smal ler, the ability to resolve different particle s izes dec reases . The range of response could be increased if the sensor coil responded more strongly to the pass ing particles. The current sensor coil is made of 40 gauge magnet wire with - 3 0 0 0 winds wrapped around a ferrite core; it has an inductance of 108 m H . The inductance could be increased by increasing the number of winds on the coi l , increasing the cross-sect ional a rea of the coi l , or by using a core with higher magnetic permeabil i ty. Another alternative is to increase the strength of the magnet used. 5.3 Suggestions for a New Sensor Design: Recogniz ing the weaknesses of the current des ign, ideas were deve loped to improve the sensor . The first suggest ion is to use a sol id block magnet instead of a doughnut shaped magnet. This would produce a more uniform field for the particles to pass through. 72 Instead of shielding each magnet separately, block magnets could be connected end to end , in e s s e n c e producing one large magnet that could span the channel width. This large magnet could then be set in a steel yoke which would act to strengthen the field near the magnet. With a block magnet, the coi ls would sit on top of the magnet instead of being inset in the magnet like the current des ign. This design would cause the magnet to be further away from the senso r face, thereby decreas ing the field strength. However, it may be a worthwhile tradeoff in order to produce a more uniform field; it may a lso be possib le to increase the strength of the magnet to make up for this loss. In order to keep the magnet as c lose to the sensor face as possib le, the coi ls would have to be des igned as thin as possib le. It would be possib le to reproduce the current coil des ign with a th ickness of 6 mm. Tak ing into account the observat ions from Sect ion 5.2 it would a lso be worthwhile to test ways of increasing the inductance of the coi l . By using one large magnet, and placing the coi ls on top of the magnet, the spac ing of the coi ls could be dec reased , further increasing the spatial resolution of the sys tem. The limit on coil spac ing would be the coil diameter, and the number of channe ls avai lable from the recording sys tem. More importantly, because there would be no shielding between coi ls, a particle would pass through the s a m e uniform field whether it passed over the center of the coi l , or s o m e distance to the s ide of the coi l . In this case , sensor response with location across the coil array would only depend on the distance 73 between the center of the stone and the center of the coi l . A s well , because of the uniform field, particles would be less likely to pass the sensor array undetected. It would be more likely for one stone to induce a response in multiple coi ls. By looking at the strength of response from adjacent coi ls , it may be possib le to determine the location the stone. Addit ionally it may be possib le to estimate the s ize of the stone from the number of coi ls that respond to its pass ing. 74 Chapter 6: Conclusions Resul ts from this research have identified some major problems that do not al low the B M D sys tem to be a reliable means of measur ing sediment transport. A decent estimate of particle s ize can be made for a particle of known susceptibil i ty, pass ing over the center of the sensor ; however, the variability in response across the sensor face, and the wide range of particle susceptibi l i t ies found in natural s tones produce too much scatter to gain meaningful est imates of particle s ize . At best, the current B M D sys tem can provide a semi-quantitative picture of the spatial and temporal variability in bed load transport. The large range in particle susceptibi l i ty is a natural phenomenon that will continue to hamper magnet ic methods. O n the other hand, the variation across the sensor face is due to the current sensor des ign. S o m e ideas have been d i scussed that may improve the sensor des ign; however, at this point they are speculat ive and untested - a potential avenue for future research. 75 R E F E R E N C E S : Andrews, E.D. , 1983. Entrainment of gravel from naturally sorted riverbed material, Geological Society of America Bulletin, 94, 1225-1231. Andrews, E.D. , 1994. Marginal bed load transport in a gravel bed st ream, S a g e h e n Creek , Cal i fornia. Water Resources Research 30(7): 2241-2250. Ashmore , P . E . and Church , M.A., 1998. 'Sediment transport and river morphology: a paradigm for study." In: Grave l Bed Rivers in the Environment. P. K l ingeman, P. Komar , W . Bradley (Eds). John Wi leey & S o n s , Chichester . 115-148. Ashworth, P . J . , and Ferguson, R. I. 1989. S ize-se lect ive entrainment of bed load in gravel bed st reams. Water Resources Research, 25, 627-634. 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S u m e r and A Muller (Eds.) , Proceed ings of Euromech 156, 223-227. G o m e z , B and Church , M. 1989. A n assesmen t of bed load sediment transport formulae for gravel-bed rivers. Water Resources Research 25: 1161-1186. H a m , D.G. , and Church , M. 2000. Bed-mater ia l transport est imated from channel morphodynamics: Chi l l iwack river, British Co lumbia . Earth Surface Processes and Landforms 25, 1123-1142. Haschenburger , J . K . and M. Church . 1998. Bed material transport est imated from the virtual velocity of sediment. Earth Surface Processes and Landforms 23 : 791-808. H a s s a n , M.A., and Ergenzinger, P. 2003. Tracers in fluvial geomorphology, In: Tools in Fluvial Morphology, G . M . Kondolf and H. P iegay (eds.), John Wi ley, pp. 397-423 H a s s a n , M.A. and Church , M. 2001. Sensit ivity of bed load transport in Harris Creek: S e a s o n a l and spatial variation over a cobble-gravel bar. Water Resources Research 37(3) 813-825. H a s s a n , M.A., Sch ick , A . P . and Laronne, J . B . 1984. The recovery of f lood d ispersed coarse sediment particle, a three d imensional magnet ic tracing method. In: Channe l P r o c e s s e s - Water , Sed iment and Catchment Contro ls, A . P . Sch ick (Ed.), C a t e n a supplement 5, 153-162. Hayward, J . A . and Suther land, A . J . 1974. The Tor lesse St ream vortex-tube sediment trap. Journal of Hydrology (New Zealand) 13: 41 -53 Helley, E . J . , and Smi th , W . 1971. The development and calibration of a pressure difference bed load sampler . U.S. Geo log ica l Survey, O p e n File Report, 18 pp. Hicks, D .M. and G o m e z , B. 2003. Sed iment Transport. In: Too ls in Fluvial Geomorpho logy, G . M . Kondolf ad H. P iegay (Eds.) , Wi ley and S o n s , Chichester , UK . 425-461. Hubbel l , D.W., 1987. B e d load sampl ing and analys is . In: Sed iment Transport in Grave l -Bed Rivers. C . R . Thorne, J . C . Bathurst and R.D. Hey (Eds.), John Wiley, Chichester , p. 89-118. 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Water Resources Research, 29, 1297-1312. 79 

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