Design and Data Acquisition for Thermal Conductivity Matric Suction Sensors

Transcription

1 68 TRANSPORTATION RSARCH RCORD 1432 Design and Data Acqisition for Thermal Condctivity Matric Sction Sensors J. K.-M. GAN, D. G. FRDLUND, A. XING, AND W.-X. LI The principles behind sing the thermal condctivity sensor for an indirect measrement of matric sction are described. The factors controlling the thermal condctivity of the sensor are discssed. The reqirements of the sensor for the measrement of matric sction in soils are examined from a theoretical standpoint by sing the capillary model and a heat flow model. The crrent methods for the calibration of the sensors and the evalation of the sensors' otpts are described. Alternative methods for the calibration of the sensors and the evalation of the sensors' otpts are sggested in an attempt to determine a better way to evalate the data. The data acqisition and the related electronics necessary for field monitoring of the matric sction sensors are discssed. The attractiveness of the thermal condctivity matric sction sensors lies primarily in their field application. Data application possibilities provide for the continos and remote monitoring of matric sction. Applications can be made in remote areas ith a battery power spply. Data acqisition systems with atomatic control and large storage memories are possible. The electronics associated with the sensors and the data acqisition system are important aspects in the proper sage of the thermal condctivity matric sction sensors for sction measrements. The role of matric sction in the behavior of nsatrated soil is now well nderstood (1). As a reslt, the need for reliable matric sction measrements is becoming increasingly important. To date there are no simple, accrate, and reliable methods of measring matric sctions above 1 atm. In many of the applications in engineering, matric sctions above 1 atm are common. The filter paper method and the psychrometer method have been sed in the past. Both are indirect methods that measre total sctions rather than matric sction. It is matric sction, however, that is most important in qantifying the mechanical behavior of the soils. The concept of sing the thermal condctivity of a standard ceramic as an indirect measrement of matric sction is attractive. The physics involved is readily comprehended; however, the performance of the sensor has ths far oeen disappointing. Varios difficlties and shortcomings have become apparent as a reslt of increased sage in the field (2,3). The development of the thermal condctivity sensors for the measrement of matric sction has been presented elsewhere (4). Details of the ceramic design are important when sing thermal condctivity matric sction sensors. Strength, drability, and reasonable accracy over a wide range of sctions are the basic reqirements of the sensors. Presently available ceramics with high strengths have niform pore size distribtions. Theoretical design considerations based on the capillary model show that there is need for a continosly varying pore size distribtion to measre matric sctions over a wide range. The challenge is to fabricate a high-strength ceramic with continosly varying pore sizes. The reqirements of the thermal condctivity matric sction sensor are also examined from a heat flow perspective to investigate sch isses as the optimm size of the ceramic tip, the dration of heating, and the rate of heating. J. K.-M. Gan, D. G. Fredlnd, and A. Xing, Department of Civil ngineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N OWO. W.-X. Li, Department of Hydralic ngineering, Tsingha University, Beijing, People's Repblic of China 184. PRINCIPL OF OPRATION The components of the thermal condctivity matric sction sensors are shown in Figre 1. The key component of the sensor is the ceramic. The ceramic has niqe water retention characteristics that are a fnction of its pore size distribtion. When the ceramic is placed in contact with soil, water will move between the soil and the ceramic ntil the matric sction in the ceramic eqalizes with the matric sction in the soil. The matric sction in the soil will determine the water content of the ceramic at eqilibrim, in accordance with the niqe water retention characteristics of the ceramic. The variables controlling the changes in the thermal condctivity of the sensor are its air and water contents. Air is a poor condctor of heat. Under atmospheric conditions and a temperatre of 2 C, air has a thermal condctivity of.26 W/m K. Water, on the other hand, has a thermal condctivity of.6 W/m K, abot 23 times greater than the thermal condctivity of air (5). Ths, the changes in the thermal condctivity of the sensor are a fnction of the changes in the water content of the ceramic. Throgh a calibration process, the matric sction of the ceramic can be correlated with the thermal condctivity of the ceramic. The thermal condctivity of the ceramic is reflected in the temperatre rise of the ceramic when a precise heat plse is applied. The crrent practice when sing thermal condctivity matric sction sensors consists of the following process. An initial reference temperatre is taken. This is followed immediately by applying a precise heat plse for 6 sec. The heat plse is generated by applying a constant voltage of 1 V to the heating element inside the sensor. At the end of the 6-sec heating period the power spply is removed and a second temperatre reading is taken. The temperatre rise at the end of the heating period is the net reslt of the heat spplied and the heat that is dissipated dring the 6-sec heating period. The heat spplied is a constant qantity. It is controlled by the electrical power that is spplied and by the dration over which the electrical power is spplied. The heat

2 Gan et al. 69 DSIGN CONSIDRATIONS OF TH CRAMiC Temperatre,- sensor poxy 1-Plastic jacket 11-t:i'.i:i!it-Heater resistor FIGUR 1 Components of a thermal condctivity matric sction sensor. dissipated is dependent on the thermal condctivity of the ceramic. The thermal condctivity of the ceramic is a fnction of its water content. The water content of the ceramic is controlled by the matric sction of the soil in which the sensor is bried. Conseqently, a relationship between the temperatre rise in the sensor and the matric sction of the soil can be established. It is desirable that the ceramic of the thermal condctivity matric sction sensor be of high porosity to obtain large changes in the water content of the ceramic with varying matric sctions. The accracy of the measrements increases with an increase in the porosity of the ceramic. Previos commercially available sensors had a porosity of abot 7 percent. The calibrations obtained for some of these sensors are shown in Figre 2. The calibrations shown in Figre 2 show that the relationships between the rise in temperatre de to the 6-sec heat plse and the matric sction of the soil are nonlinear. The maximm change in temperatre over a matric sction range of 3 kpa was abot 2 C to 2.5 C for some recent, commercially available sensors with 32-fl heating elements operating with a 6-sec heat plse spplied by a 1-V power sorce. Older model sensors have 1-fl heating elements. Tests have been condcted to investigate the maximm change in temperatre obtainable by sing different electrical power inpts. These tests were performed on sensors sbjected to two extreme conditions: at satration (i.e., matric sction eqal to zero) and in the completely dry condition (i.e., corresponding to maximm sction in 3 25 Resistance of sensor heating element = I n Heat plse dration = 6 seconds Voltage= IO V DC 2 co... c 15 ::I (/) ;:: (ti Temperatre change (OC) 9 FIGUR 2 Calibration crves of some thermal condctivity matric sction sensors plotted as a fnction of matric sction verss change in temperatre.

3 7 excess of 5 kpa). The reslts are presented in Figre 3. The reslts show that for an electrical power inpt of 1 V, the maximm difference in temperatre between the two extreme conditions is abot C. This maximm difference in temperatre is increased to 3.75 C if the electrical power inpt is increased to 12 v. It is desirable that the ceramic have a continosly varying pore size distribtion to cover a wide range of matric sctions. The maximm pore size that can be sstained withot draining the ceramic at a specified matric sction is defined as follows. Ts Ua - Uw = 2 - COS O'. r where = pore air pressre, w = pore water pressre, Ts= srface tension of water (i.e., X 1-3 Nim), r =radis of pore (m), and ex= contact angle between the water and the pore material (sally assmed to be eqal to zero). The theoretical relationship between pore radis and the matric sction obtained from qation 1, over the range of.1 to 1 kpa is shown in Figre 4. The corresponding pore radii vary from 1 mm down to 1 X 1-s mm (i.e., both variables extend over a range of five orders of magnitde). The range of matric sctions of most common interest to geotechnical engineers is from to 1 kpa. The corresponding variation of pore size distribtion wold range from 1 mm down to 1 X 1-4 mm, a span of over for orders of magnitde. (1) TRANSPORTATION RSARCH RCORD 1432 The conditions of a high-porosity and a continosly varying pore size distribtion are reqired to ensre accracy and range. These aspects make it difficlt to obtain a high-strength ceramic. A high-strength ceramic is typically of low porosity with niform pore sizes. To avoid compromising on the strength of the ceramic, it is necessary to design a sensor for a specific matric sction range. For example, a sensor designed for a matric sction range of 1 to 4 kpa wold have pore radii varying from X 1-3 to X 1-4 mm according to qation 1. It is desirable to have a linear relationship between matric sction and thermal condctivity to ensre accracy in the measrement of sction. A linear relationship between matric sction and thermal condctivity is possible if the sensor has a continosly varying pore size distribtion in which the volmes corresponding to every pore size are eqal. Materials meeting this reqirement will have a linear water retention characteristic relationship similar to Relationships A, B, and C shown in' Figre 5. A typical water retention characteristic relationship for the ceramic from an AGWA-II sensor (6) is also shown in Figre 5 for comparison. The calibrations obtained so far have also shown that the matric sction verss temperatre change relationship for the AGWA-II sensors is nonlinear (Figre 2). THORY OF HAT FLOW The thermal condctivity matric sction sensor shold be as small as possible to expedite the moistre eqilibration process between the sensor and the soil. However, the ceramic portion of the sensor mst be sfficiently large to flly contain the applied heat plse. Otherwise, the sensor reading will be inflenced by the thermal I e..s 2 ) g 15.::it:.. en 1 Satrated, 1 O volts s ) c: co.r:; ::I 1 CD c.. CD I Heating time in seconds FIGUR 3 Seebeck voltage measred with time for a sensor in a satrated state and in a dry state heated at a 1- and a 12-V spply.

4 Gan et al. 71 1o5 14 ' " :: ::: I I I II II (i CL 1o3 c: I o2 g.g "' a; 11 1oO ' I I I " I I Ill II Ill Ill ' "' Pore radis (mm) I' Matric sction, (kpa) FIGUR 6 Calibration crves of a sensor when flly embedded in kaolin and when srronded by air. 3 FIGUR 4 Relationship between pore radis and matric sction. properties of both the soil and the sensor. If this is the case, the calibration obtained for the sensor will not be niqe bt will vary with the medim in which the sensor is bried. Calibration tests have been condcted sing a commercially available -sensor that has a diameter of 23 mm. The sensor was first calibrated with the sensor bried in a kaolin paste. The same sensor was then calibrated with the sensor srronded by air while only the end of the sensor was in contact with the high air entry disk via a thin layer of kaolin. The reslts from these calibrations are presented in Figre 6. The reslts indicate that the size of the sensor does not appear to be adeqate. The calibrations obtained with the sensor srronded by air consistently recorded a higher temperatre (i CL c "' c: a; ::? C") b T""" fl) :- a. " «i 5 O" w rise than those obtained when the same sensor was bried in a kaolin paste. An infinite sphere (Figre 7) with a radis r ( < r < oo) can be sed as a model to determine the optimal size of the sensor for a fixed heating rate and a fixed heating period. The heater has a radis r eqal to a. The heater is assmed to be made of copper. The poros ceramic is assmed to be satrated with water. The thermal condctivity of the poros ceramic is at a maximm when the poros ceramic is satrated. This is the most critical case in the consideration of the optimal radis reqired to completely contain the applied heat plse. The variable v( t, r) denotes the temperatre n the sphere at time t and radis r. An initial temperatre of zero is assmed for the theoretical stdy. That is, v(o, r) is eqal to for < r < oo. When heat is generated at the center of the sphere for a period of time tp, there will be a temperatre rise in the area near the center of the sphere [i.e., v(tp, r) for small vales of r] and the temperatre, v(tp, r), eventally becomes as r increases. Since radial heat flow is being considered, there exists a radis R beyond which the temperatre rise is less than a given error tolerance. The radis R beyond which the temperatre rise is less than the Volmetric water content,(%) FIGUR S Ideal water content characteristic relationship of ceramics [actal water content characteristic relationship from an AGWA sensor (6) is shown for comparison]. FIGUR 7 Spherical model sed for the heat flow analysis.

5 72 TRANSPORTATION RSARCH RCORD 1432 given error tolerance can be called the optimal radis. Any point with r R is then considered not to be affected by the heat plse. The radial heat condction eqation in an infinite medim, when expressed in spherical coordinates, is (7) where At is the length of the time step and Ar is the length of the radis step. From the bondary condition, qation 3, it follows that where v = v(t, r) is the temperatre in degrees celsis and k is the thermal diffsivity (cm 2 /sec) of the satrated poros medim. Since the thermal condctivity of copper is mch higher than that of the ceramic medim, it is assmed that the inner sphere (i.e., < r < a) acts like a perfect condctor. It is also assmed that there is no contact resistance between the heater and the ceramic (i.e., at r = a). Some of the heat generated within the inner sphere is dissipated. The ndissipated heat will reslt in a temperatre rise in the inner sphere. Let Q denote the heating rate (cal/sec) generated in the inner sphere. The bondary condition at r eqal to a is given as follows: 4 3 av? av Q = - -rra pc rra-K- 3 at or where K =thermal condctivity of the poros medim (cal/sec-cmoq, p = density of copper (g/cm'), and c = specific heat of copper ( cal/g- C). The first term on the right side of qation 3 acconts for the contribtion to the heat balance owing to the heater, which is also the inner sphere in the model. The second term of qation 3 acconts for the heat that is dissipated in the poros medim. Solving qation 2 sing an explicit finite difference method gives V;+lj = V;,j + : [vi,j+i - 2vi,j + V;,j-1 + a/fl:+ j (vi,j - V;.1-1)] i =, 1, 2,... j = 1, 2,... (4) (2) (3) 4 3 dratq 3 'ITa pcar 4Tia 2 KAt V1+1,o = --A- + --X.-- V;,o + A V;+1,1 where i =, 1, 2,... If the thermal condctivity K is not a fnction of temperatre, the soltion obtained is not affected by the initial bondary condition. If the thermal condctivity K is a fnction of the temperatre, the soltion will vary with the choice of the initial bondary condition. As a reslt, a thermal condctivity sction sensor wold not have a niqe calibration relationship. Rather, there wold be a calibration crve for each initial temperatre. Fortnately, the thermal condctivities of ceramic and water are fairly constant within a wide range of temperatres. Using an initial bondary condition of v = gives Vo,o = Vo,1 = Vo,2 = Vo.3 = = (6) Nmerical reslts based on qations 4 and 6 are shown in Figres 8 and 9 for heating period tp eqal to 6 sec. Figre 8 shows the temperatre distribtion (i.e., in the infinite sphere) at the end of the heating period for different heating rates. The heating rate crrently sed in thermal condctivity matric sction sensor measrement is approximately.24 cal/sec for a fixed heating dration of 6 sec. According to Figre 8, a minimm sensor radis of 15 mm wold be reqired to flly contain the heat within the sensor. Figre 9 shows the effect of the srronding soil on the temperatre distribtion within the ceramic, where K,. is the ther- (5) , , , a la= 3 mml --a =.2 calls --o-- Q = O.Q1 calls ' i - a=.24 calls..c Radis (mm) 15 2 FIGUR 8 Temperatre distribtion at the end of heating for varios heating rates.

6 - Gan et al a =.24 calls -- Ks =.192 cal/s-cm- c o-- Ks=.192 cal/s-cm- C s - Ks= K =.192 cal/s-cm- C O'l c::: ca 1.5..c. a Srronding soil :: a..5 I Radis (mm) FIGUR 9 Inflence of the thermal condctivity of the srronding soil on the temperatre distribtion within the ceramic. mal condctivity of the srronding soil. Figre 9 was obtained for a sensor of 1-mm radis sbjected to a heating rate of.24 cal/sec for 6 sec. CALIBRATION AND ACTUAL RADING Calibration of the thermal condctivity matric sction sensors can be condcted by sing a modified pressre plate apparats. The modified pressre plate apparats has special ports to accommodate the sensor leads. The sensors are bried in the soil inside the modified pressre plate apparats. The matric sction of the sensors is controlled by maintaining a constant matric sction in the soil by the axis translation techniqe. Details of the procedre have been described elsewhere (8). The crrent measring procedre when sing thermal condctivity matric sction sensors has been to take two temperatre readings: one prior to applying heat and one at exactly 1 min after the application of a precise heat plse. The difference between these two temperatre readings is the temperatre rise de to the heat plse. The temperatre rise de to the heat plse is then calibrated against the matric sction. There are other possibilities for handling the data otpt from the thermal condctivity matric sction sensor. One possibility is to se a continos recording of the characteristic Seebeck voltage otpts of the sensor over the entire heating and cooling cycle. The area enclosed by the characteristic Seebeck voltage otpt crve over an entire heating and cooling cycle (Figre 1) can be correlated against the matric sction of the soil. Another possibility may be to se the rate of change of voltage (or temperatre) along some sections of both the heating and the cooling crves. The rate of change of voltage (or temperatre) along the heating crve may prove to be more reliable. For instance, the rate of heat generated and dissipated early in the heating cycle will not be affected by the soil srronding the sensor. Later in the heating cycle, as the inflence zone from the applied heat expands, the effect of the srronding soil will become increasingly important, particlarly if the sensor is not sfficiently large for the specified heating rate and the specified heating period. Frther stdies into the rate of heat generation and the rate e : _ 6 O.s 4 2 I - 1 minte heating I I / Time (seconds) s. 2 O c I ca..c... :: \.. \ \ "@ a FIGUR 1 Seebeck voltage otpt measrd over an entire heating and cooling cycle. 3 I-

7 74 of heat dissipation are needed to find the most satisfactory method for the indirect measrement of matric sction., The Seebeck voltage otpts measred with time for a ceramic in a satrated state and in an air-dry state were presented earlier (Figre 3). It is possible to generate a series of crves between these two crves for any range of matric sction vales (Figre 11). That is, rather than sing only the maximm change in temperatre to correlate with matric sction, another possibility wold be to nmerically best-fit the Seebeck voltage response crves. It may be possible to obtain greater accracy in the measrement of sction by this approach. FILD MONITORING The thermal condctivity sensors constitte an attractive option for the field monitoring of matric sction becase of their sitability to data acqisition systems. The data acqisition possibilities provide for almost continos and remote monitoring. These are of vale when attempting to obtain information related to environmental changes. The pore water pressre conditions in the nsatrated zone are qite variable becase of the inflence of the microclimate and the variability of the soil properties. Mltiple TRANSPORTATION RSARCH RCORD 1432 sensors are sally reqired at each instrmentation site to properly characterize the matric sction profile changes. A typical monitoring site is sally remote and sally has no power spply. The layot of one sch typical monitoring scheme sed in a railway embankment is shown in Figre 12. Typically, mltiple sensors involving leads of varios lengths are sed. The electrical connections to link the sensors to the data acqisition system become complex. Having sensors with leads of varios lengths is ndesirable from a fabrication and calibration standpoint. Mltiple sensors will reqire a mltiplexing system to control and monitor the sensor readings. Depending on the distance of the site from the control office, visits to the site to retrieve data may occr infreqently. The power sorce to the system mst be able to last for long drations. Other means of providing power sch as the se of solar power panels are options. The system shold also be able to store large amonts of data between site visits. A modem may be reqired for commnicating with the data logger. The data acqisition system mst be able to take an initial temperatre reading and then spply a constant heat plse to the sensor for a specific dration (e.g., for 6 sec) and then take another temperatre reading. The system nist be able to carry ot this exection atomatically and seqentially for all of the sensors e 15. C'. en Heating time (seconds) FIGUR 11 Idealized Seebeck voltage characteristic crves of a sensor at varios matric sction vales.

8 FIGUR 12 Layot of thermal condctivity matric sction sensors installation in a railway embankment. The data acqisition system presently sed in the field monitoring of matric sction with thermal condctivity matric sction sensors is fairly complex. A simpler data acqisition system dedicated specifically to the thermal condctivity matric sction sensors wold be desirable. CONCLUSION There is need for an indirect method of measring matric sction. One sch possibility is the se of thermal condctivity matric sction sensors. Fabrication of a drable ceramic for an accrate matric sction sensor is difficlt. Theoretical considerations show that it is necessary to fabricate sensors for specific ranges of matric sction. The theory of heat flow in a poros medim shows that the calibration of a thermal condctivity sensor is niqe since the thermal condctivity of the ceramic, water, and air are not a fnction of the temperatre within the normal working range of temperatres., The present method of measring inatric sction by sing the maximm temperatre change does not necessarily reslt in the most accrate measrements possible. As a reslt consideration shold be given to other possible procedres for analyzing the otpts from the thermal condctivity matric sction sensors. The data acqisition system presently sed with the thermal condctivity matric sction sensors is complex. A simpler dedicated data acqisition system is needed. RFRNCS 1. Fredlnd, D. G., and H. Rahardjo. Soil Mechanics for Unsatrated Soils. John Wiley and Sons, Inc., New York, Loi, J., D. G. Fredlnd, J. K. Gan, and R. A. Widger. Monitoring of Soil Sction in an Indoor Test Track Facility. In Transportation Research Record 1362, TRB, National Research Concil, Washington, D.C., 1992, pp Fredlnd, D. G., P. J. Sattler, and J. K. Gan. Insit Sction Measrement sing Thermal Sensors. Proc., 7th International Conference on xpansive Soils, Dallas, Tex., 1992, pp Fredlnd, D. G. Backgrond, Theory, and Research Related to the Use of Thermal Condctivity Sensors for Matric Sction Measrement. Advances in Measrement of Soil Physical Properties: Bringing Theory into Practice, SSSA Special Pblication No. 3, Soil Science Society of America, Madison, Wis., 1992, pp van Wijk, W. R., ed. Physics of Plant nvironment, 2nd ed. North Holland, Amsterdam, The Netherlands, Mandziak, T. Development of a Matric Sction Sensor. M.S. thesis. University of Saskatchewan, Saskatoon, Saskatchewan, Canada, Carslaw, H. S., and J.C. Jaeger. Condction of Heat in Solids, 2nd ed. Oxford University Press, New York, Fredlnd, D. G., and D. K. H. Wong. Calibration of Thermal Condctivity Sensors for Measring Soil Sction. Geotechnical Testing J ornal, Vol. 12, No. 3, 1989, pp