Exploring ice content on partially saturated frozen soils using dielectric permittivity and bulk electrical conductivity measurements

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1 ES Web of Conferences 9, 7 () DOI:./ esconf/97 E-UNSAT Exporng ce content on partay saturated frozen sos usng deectrc permttvty and buk eectrca conductvty measurements,a Yanxn Mao, Enrque Romero and Antono Gens Dvson of Geotechnca Engneerng and Geoscences, Department of Cv and Envronmenta Engneerng, Unverstat Potècnca de Cataunya, 8, Barceona, Span Abstract. The present paper expores the use of the measurement of buk eectrc conductvty and reatve deectrc permttvty durng freezng and thawng to estmate the ce content of two dfferent partay saturated sos. The sos (Castedefes fne sand and Barceona cayey st) were prepared at dfferent degrees of saturaton and dry denstes at room temperature. Dfferent target temperatures were used, whch were reached at varyng freezng rates and controed wth a therma bath. Modes were used to ft eectrca conductvty and reatve deectrc permttvty resuts under fu unfrozen qud and maxmum ce condtons. The extenson of these modes aows estmatng ce content on partay saturated sos at dfferent porostes. Introducton When deang wth the modeng of thermo-hydromechanca couped processes nduced by freezng of saturated and unsaturated sos, an mportant ssue s the defnton of the freezng retenton mode, whch nks the saturaton degree of the qud phase (unfrozen water) to the temperature of the so. The Causus-Capeyron-Poyntng equaton, whch governs the condton for equbrum between the coexstng qud water and ce phases, together wth a modfed form of the van Genuchten equaton to take nto account the qud-ce surface tenson s usuay adopted to represent ths freezng retenton mode. Thus, determnng expermentay the amount of ce content or unfrozen water n the frozen sos s necessary and hepfu for verfyng the correctness of the retenton mode and aso for defnng the mode parameters. For the drect measurement of ce content n frozen so, severa methods have been used, ncudng gas datometry, deectrc spectroscopy and the heat puse probe method (see for nstance, []). Instead of measurng ce content drecty, some authors combned two methods together to nfer ce content and unfrozen water content n frozen so [, ]. However, t s st dffcut to measure the accurate ce content of frozen so both n drect and ndrect way. The present paper expores ce content on two dfferent partay saturated sos by controng temperature at dfferent qud saturatons durng freezng and thawng process. The sos (a sand and a cayey st) were prepared at dfferent degrees of saturaton and dry denstes at room temperature. The technque used to measure the unfrozen a qud saturaton was based on frequency doman refectometry (FDR) measurements, as we as on eectrca and therma conductvty at dfferent target freezng temperatures. These temperatures were reached at varyng freezng rates and controed by a therma bath. Dfferent modes were used to ft eectrca conductvty and reatve deectrc permttvty resuts of the partay saturated sos under fu unfrozen qud and maxmum ce condtons. These modes were then extended for dfferent degrees of unfrozen qud and ce content, as we as varyng porostes. Ths way, the combnaton of two methods (eectrca conductvty and reatve deectrc permttvty resuts) on a partay saturated so of known porosty w aow nferrng ts ce and unfrozen water contents. Descrpton of the modes A smpe mode was deveoped by Arche (9) reatng the eectrca conductvty of sos to ts porosty and sane qud saturaton. For dfferent qud and ce saturatons, the mode can be wrtten as (see for nstance, []): t a nm Sp and t a n m Sp () where σt denotes the eectrca conductvty of the so, σ represents the eectrca conductvty of sane water, S the degree of saturaton, n the porosty, m an exponent of the matera that can be reated to tortuosty or to pore shape and structure, p a saturaton exponent and a a tortuosty factor. Subscrpts and ndcate the dfferent phases of Correspondng author: enrque.romero-moraes@upc.edu The Authors, pubshed by EDP Scences. Ths s an open access artce dstrbuted under the terms of the Creatve Commons Attrbuton Lcense. (

2 ES Web of Conferences 9, 7 () DOI:./ esconf/97 E-UNSAT the sane water, whch are unfrozen qud water and ce phase respectvey. In unsaturated frozen sos, four phases exst,.e., so sods, ar, unfrozen water and ce. Because of the arge resstance of so sods and ar compared to unfrozen water and ce, they are regarded as nsuators. Thus the eectrca conductvty can be expressed foowng an addtve way as foows (n accordance to a parae confguraton n whch the tota current s the sum of the currents through the ndvdua components): t t t a nm Sp a nm Sp Materas and expermenta methods. Test materas Fne sand of Castedefes (Barceona) and Barceona (BCN) cayey st were studed []. The partce sze of fne sand vared between 7 and µm. The BCN cayey st was modfed to remove partce szes arger than mm. The sod denstes of sand and cayey st are ρss=. Mg/m and ρsc=.7 Mg/m, respectvey. A % NaC souton (mass bass) was used to perform the freezng-thawng test, and to aow better dscrmnatng between ce and unfrozen qud when usng buk eectrca conductvty. () For the sake of smpcty, a smar aw s adopted for (reatve) deectrc permttvty: t a nm Sp a nm Sp. Expermenta methods A commerca Frequency Doman Refectometry (FDR) sensor TE was used for measurng buk eectrca conductvty (EC) and (reatve) deectrc permttvty [] accordng to the scheme depcted n Fgure. Good contact between the sma eectrodes and the sos s requred for EC measurements. The deectrc constant s measured by usng capactance / frequency doman technoogy. In order to mnmse the effects of santy, 7 MHz frequency was used to make the TE sensor accurate. Two addtona thermocoupes were used for measurng so temperature. The FDR sensor and thermocoupes were pushed drecty nto the so sampes, whch were contaned n a cyndrca pastc contaner (heght 9 mm, dameter mm). The contaner was mmersed nto antfreeze qud nsde a thermostatcay controed freezer to conduct the freezngthawng cyce. The temperature ranged from - C to C. The sos wth dfferent degrees of saturaton and porostes were tested durng a freezng-thawng cyce to obtan the vaues of EC and deectrc permttvty at fu qud state S = n freezng and thawng ponts (-. C due to pore water santy effects) and at maxmum ce content S ( C). () Chen et a. [] aso presented a smpfed so resstvty mode to descrbe the reatonshps between eectrca resstvty, degree of saturaton and porosty, whch can be expressed for qud water and ce phases as: t S n c and t S n c () where ρt s the eectrca resstvty of the so, α a structure factor, S the degree of saturaton, n the porosty and c a constant. Subscrpts and ndcate the unfrozen qud or ce phases of the water. Eectrca conductvty σ s defned as the nverse of resstvty. So for a partay saturated so where unfrozen qud and ce coexst, the so eectrca conductvty can be expressed as: t S n S n c S n c S n () Data acquston For (reatve) deectrc permttvty, and for the sake of smpcty, a smar expresson to Eq. () w be aso adopted: S n S n t c S n c S n Thermocoupes Crossnked poypropyene therma nsuaton Thermostat () FDR sensor Frozen so Antfreeze qud The unknown mode parameters n Eqs. () and () under fu unfrozen qud S = and maxmum ce S condtons w be obtaned by fttng the expermenta curves usng a nonnear east square method. At known porosty, the above equatons can be used to estmate ce content n partay saturated frozen sos wth S < and S <, once eectrca conductvty and reatve deectrc permttvty are known. Refrgerator Fgure. Scheme of the expermenta setup.

3 ES Web of Conferences 9, 7 () DOI:./ esconf/97 E-UNSAT deectrc permttvty vaues between freezng and thawng paths, partcuary after the thawng pont. Probaby ths ndcates that the so mcrostructure (more actve due to the wetter state of the cayey st) has changed durng the freezng-thawng cyce. In tota, sand and cayey st sampes have been tested at dfferent vaues of porosty and degree of saturaton, as sted n Tabe. It can be observed that that the porosty of the sand was around n. wth major changes n the degree of saturaton. Ths was not the case of the cayey st, n whch the amount of water added affected the fabrcaton dry densty (the porosty changed from. to.). Expermenta resuts and anayses. Expermenta resuts Fgure shows the tme evouton of buk EC and (reatve) deectrc permttvty of a sand sampe prepared at n =.9 and S =.9%) durng a freezng-thawng cyce. It can be observed that the vaues of buk EC and deectrc permttvty reduce wth decreasng temperature unt they reach a mnmum, whch ndcates that the maxmum ce condton had been acheved. Smar features were observed durng thawng stage (correspondngy, buk EC and deectrc permttvty ncreased durng ths stage). Short pateaus of both buk EC and deectrc permttvty were observed at the freezng and thawng ponts. -,8 Tme [hrs], - Buk EC [ds/m] - Deectrc permttvty [-] Tme [hrs] Cayey st: n=.; S=7.9% Buk EC-Freezng Buk EC-Thawng Permttvty-Freezng Permttvty-Thawng Deectrc permttvty Thermocoupe - 7 Sand: n=.; Sr=.% Buk EC-Freezng Buk EC-Thawng Permttvty-Freezng Permttvty-Thawng,, - 8 -, Permttvty [-] Buk EC [ds/m], Permttvty [-] Buk EC Thermocoupe, Buk eectrca conductvty [ds/m],8 - Fgure. Varaton of buk EC and (reatve) deectrc permttvty wth temperature durng a freezng-thawng cyce: sand; cayey st. Fgure. Tme evouton of buk EC; (reatve) deectrc permttvty durng a freezng-thawng cyce of a sandy sampe (n =.9, S =.9%).. Anayss of buk eectrca conductvty resuts The varaton of buk EC and (reatve) deectrc permttvty wth temperature for the two sos are presented n Fgure. In the reatvey dry sand (n =., S =.%), the same varaton of both buk EC and permttvty was observed durng freezng and thawng. However, n the cayey st prepared at n =. and S = 7.9%, there are some dfferences n the varaton of both buk EC and The buk EC vaues of both partay saturated sand and cayey st sampes at maxmum ce content S (- C) and at fu qud water state S = n freezng and thawng pont (-. C) are presented n Fgure. The qud F and qud T n the graphs denote the vaues measured at fu unfrozen qud state durng freezng and thawng paths.

4 ES Web of Conferences 9, 7 () DOI:./ esconf/97 E-UNSAT Tabe. Inta condtons of so sampes. Castedefes sand BCN cayey st Porosty n/- Degree of saturaton S / % t S n S n.8.8s n..s n n=. EC-qud F Arche's aw-ce Chen et a.-qud n=. Buk eectrca conductvty [ds/m] EC-ce EC-qud T Chen et a.-ce Chen et a.-qud EC-qud F Arche's aw-ce Arche's aw-qud Buk eectrca conductvty [ds/m] Fgure. Buk EC resuts for dfferent nta degrees of qud saturaton for fu unfrozen qud and maxmum ce content: sand; cayey st. (7). Anayss of reatve deectrc permttvty resuts (8) The (reatve) deectrc permttvty vaues of both sand and cayey st sampes at maxmum ce content S ( C) and at fu unfrozen qud state S = n freezng and thawng pont (-. C) are presented n Fgure. The qud F and qud T n the graphs denote the vaues measured at fu unfrozen qud state durng freezng and thawng paths, respectvey. The measured vaues of (reatve) deectrc permttvty of pure % NaC souton at maxmum ce state (- C) and at fu unfrozen qud The equvaent expressons for estmatng ce content from buk EC readngs for the cayey st are: t.7 n.s..8 n. S.7 S n S n t..s n..7 S n 7 Arche s aw and Chen s resstvty mode have been used to ft the expermenta resuts and thereby to obtan the mode parameters. The measured vaues of buk EC of pure % NaC souton at maxmum ce content (- C) and at fu unfrozen qud state (freezng pont) were =.7 ds/m and =. ds/m, respectvey. The remanng mode parameters can be obtaned by fttng the expermenta resuts. The foowng two equatons can then be used for estmatng ce content of partay saturated fne sand from buk EC readngs: t n..98 S..7 S.7 EC-ce EC-qud T Arche's aw-qud Chen et a.-ce 8 Inta degree of water saturaton [%] Dry densty ρd / Mg/m Inta degree of water saturaton [%] Sampe In Fgure b the curves have been potted at constant porosty (n =.), whereas the dfferent ponts dspay mportant varatons n porosty (ths s the reason of the devatons observed at hgh nta degrees of saturaton that were prepared at the denser states). (9) ()

5 ES Web of Conferences 9, 7 () DOI:./ esconf/97 E-UNSAT Inta degree of water saturaton [%] state (-. C) were =. and = 8., respectvey. The vaue at maxmum ce state s very hgh and can be due to the santy effect on the FDR measurement. Nevertheess, t has been accepted for fttng purpose (further tests are currenty been undertaken to better defne the reatve deectrc permttvty vaue at maxmum ce state of ths reference % NaC souton). Permttvty-ce Permttvty-qud T Arche's aw-ce Chen et a.-qud 8 7 In the case of the cayey st, the correspondng expressons are: t.89 n.7 S.8.8 n.s.8 S n S n t.. S n..s n n n Concusons The modfed Arche s aw and Chen s resstvty mode were used to ft the expermenta resuts of both buk eectrca conductvty and reatve deectrc permttvty resuts on two partay saturated sos. The mode parameters were determned under fu unfrozen qud S = and maxmum ce content S condtons. The modes were extended to cover ntermedate states wth S < and S <. The ftted equatons have been proposed for estmatng the ce content from buk eectrca conductvty and deectrc permttvty measurements at dfferent porostes and partay saturated states for fne sand and Barceona cayey st. It s panned to expore n the future some compementary methods for estmatng ce content, nvovng the determnaton of specfc heat capacty, therma conductvty and permeabty of frozen sos. Deectrc permttvty [-] 8 Permttvty-ce Permttvty-qud T Chen et a.-ce Chen et a.-qud Inta degree of water saturaton [%] () Agan, n Fgure b the curves have been potted at constant porosty (n =.), whereas the dfferent ponts dspay mportant varatons n porosty (ths s the reason of the devatons observed at hgh nta degrees of saturaton that were prepared at the denser states). The combnaton of the two measurements (buk eectrca conductvty and reatve deectrc permttvty resuts) together wth the above equatons w aow nferrng the ce and unfrozen water contents of a partay saturated so of known porosty. Permttvty-qud F Chen et a.-ce Arche's aw-qud () Permttvty-qud F Arche's aw-ce Arche's aw-qud Deectrc permttvty [-] Acknowedgements 8 The frst author acknowedges the fnanca support from Chna Schoarshp Counc (CSC). Fgure. Reatve deectrc permttvty resuts for dfferent nta degrees of qud saturaton for fu unfrozen qud and maxmum ce content: sand; cayey st. References. The expressons for estmatng ce content n partay saturated sand sampes from (reatve) deectrc permttvty readngs are: t 8. n. S.9.7 n.s.8 S n S n t.7.8s n..8s n. () () X. Zhou, J. Zhou, W. Knzebach, F. Stauffer, Smutaneous measurement of unfrozen water content and ce content n frozen so usng gamma ray attenuaton and TDR, Water Resour. Res., 9 9 () do:./wr Q. Cheng, Y. Sun, Y. Qn, X. Xue, X. Ca, W. Sheng, Y. Zhao, In stu measurng so ce content wth a combned use of deectrc tube sensor and neutron mosture meter n a common access tube, Agrc. Forest Meteoro. 7, 9 ()

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