Field characterization of the relationship between electrical potential gradients and soil water flux

0 Acadkmie des sciences / Elsevier, Internal geophysics / Gkophysique

Paris

inferne

Field characterization electrical potential

of the relationship between gradients and soil water flux

Mise en hidence in situ d’une corr6lation entre gradient de potentiel6lectrique et flux hydrique dans le sol Jean-Louis THONY’, Pierre MORAT~’3, Georges VACHAUD~* and Jean-Louis LE MOUEL~ ’ Laboratoire d&de des tramfetis en hydrologic et environnement, LUTE, BP 53, 38041 Grenoble CJro%CNRS-LMR5564; ’ Institut depbysique du globe de Paris, CNRSLJRA729, 4, place Jussieu, 752252Paris cedex 05, ’ Institut depbysique du globe de Paris, Obsen;atoire mag&bque national, 4S340 Chambon-La-For&, France

ABSTRACT Electrical potential differences between electrodes installed vertically at four depths (0.3, 0.5, 0.7 and 0.8 m> were monitored continuously during a 2-month period in a measurement site under natural fallow. Simultaneously, changes in soil water content and in hydraulic head were measured on a daily basis at different depths of the soil profile at the same site. They were analysed to obtain daily values of the soil water flux at the depth z= 0.4 m. This was in particular carried out over a lo-day period following a rainfall event. At that depth the water flux was first oriented downwards (infiltration), then shifted progressively upwards (evaporation). It is clearly shown that there exists a very significant linear correlation between the electric potential gradient at that level and the value of the flux. Owing probably to electrode potential problems, there is a residual value when the flux is null. If the relationship is legitimately forced through the origin, it becomes clear that electrode measurements could be used to infer water circulation in the soil in terms of direction and amount of flow. Keywords:

Necfricd

potential,

Soil wafer flux, Unsafured soil

RBSUMB Les variations temporelles des d@krences de potentiel Blectrique entre des glectrodes implantkes verticalement d quatre profondeurs CO,3, 0,5, 0,7, et 0,s m. sous un couuert de jack&e ont 6ttZ mesukes en continu durant une p&ode de 2 mois. En mZme temps, et sur le mt?me site, ont ktk igalement enregistrkes les variations de la teneur en eau volumique et de la charge hydraulique d d&%rentes profondeurs, d une j%quence journali&e, par des m&odes non destructives. Ces dernih-es mesures ont dtk analyskespour obtenir 1Evolution duflux hydrique vertical ci laprofondeur z = 0,4 m, enparticulierpendant unepkiode de 10 journees cons&uti~les faisant suite d: un 6pisode pluvieux. Durant cette pkiode, le jlux hydrique d ce niveau est d’abord orient6 uers le bas (injiltration) ; il s’annule au bout d’une semainepour ensuite s’orienter uers le haut (6uaporationI. L ha&e des rhultats montre qu’une relation linkaire tr& significatiue lie la deference depotentiel ilectrique entre 03 et 0,5 m au jlux hydrique d 0,4 m. Du fait de l’existence d’un potentiel d@lectrode, l’ordonnt?e d l’origine de la droite reprksentatiue de cette relation estpositiue. Si lbn force cette droite d passer par l’origine, il deuient possible de quantifier l’koulement de l’eau et de dkterminer son sens d partir de la seule connaissance du gradient depotentiel klectrique. Mots

cl&

: Potentiel

blectrique,

Flux hydrique,

Sol non

suture

Kate p&e&e par Jean-PaulPokier Note remix le 21 avril 1997, accept& aprb revision le 2 juin 1997 Correspondence

and reprints. E-mail. [email protected]

C. R. Acad Sci. Paris, Sciences 1997. 325.317-321

de la terre

et des planetes

/ Earth & PlanetarySciences

J.-L. Thony

VERSION

et al.

ABF&G~E

11 existe de nombreuses evidences dune relation entre Ccoulement d’eau et generation dun signal electrique dans de nombreux contextes geologiques (zones geothermales, volcaniques, sismiques, etc. (Zlotnicki et Le Mouel, 1990 ; Morat et Le Mouel, 1990 ; Mitzutani et al., 1976 ; Morgan et al., 1989 ; Corwin et Hoover, 1979) ou en milieu naturel, comme dans le cas de l’ecoulement de ske P travers un tronc d’arbre (Morat et al., 1994). En raison de l’absence de mesures simultanees des flux hydriques et du champ electrique, il s’agit toutefois plus souvent d’hypotheses que de relations Ctablies, sauf dans le cas d’essais de laboratoire portant sur des Cchantillons satures soumis a de fortes contraintes (Pozzi et Jouniaux, 1994 ; Jouniaux et Pozzi, 1995). Le but de cette etude, effect&e dans le cadre d’un programme de recherches du CNRS-INSU, a Cti: d’arriver a une quantification de cette relation dans le cas de transferts hydriques en conditions naturelles dans la zone non saturee du sol. On s’est, pour cela, appuye sur l’existence dun site de mesure intensement instrumenti: et originellement dedie a l’etude des transferts d’eau et d’azote sous culture irriguee.

MatCriel Les essais ont ete effectues sur le site atelier de la Cote Saint-Andre, P 50 km au nord-ouest de Grenoble (Kengni et al., 19941, au milieu dune zone d’agriculture intensive entre les Alpes et la vallee du Rhone. C’est une structure de terrasse glaciaire, avec une faible epaisseur de sol (mains de 1 m), au-dessus d’alluvions tres grossieres contenant une nappe a surface libre de tres fort debit, dont le niveau fluctue entre 10 et 15 m au-dessous de la surface du sol. Ce site est instrumenti: depuis plusieurs annees pour caracteriser les transferts d’eau et d’azote dans la zone de sol non saturee. Une station de mesure specifique a eti: equipee pour les besoins de l’experimentation d&rite dans cette note, afin de caracteriser sous jachere l’evolution temporelle simultanee des flux d’eau et des potentiels Clectriques avec les capteurs suivants : - pour les mesures hydriques, humidimetre neutronique (Vachaud et al., 1977) et tensiometres permettant d’obtenir respectivement, sur une base journaliere, de facon non destructive, les variations de teneur volumique en eau (m3/m3> O(z) (tous les 0,l m jusqu’a 1 m), et de charge hydraulique (m) Hz) (a cinq profondeurs : 0,15, 0,3, 0,5, 0,7 et 0,8 m) ; - pour les mesures electriques, des electrodes non polarisables, permettant de mesurer a trois profondeurs (0,3, 0,5 et 0,7 m> la difference de potentiel par rapport a une electrode de reference install&e a 0,8 m. Les diiferences de potentiel correspondantes sont obtenues toutes les 2 minutes, stockees sur une carte RAM, puis moyennees sur la journee. On dispose aussi de l’acquisition de donnees climatologiques obtenues au pas de temps de 30 minutes. La periode de mesure a dure 2 mois ; on ne prendra en compte, pour illustrer cet article, que les resultats obtenus sur une duree de 10 jours suivant un episode pluvieux de 28,2 mm.

318

C. R. Acad.

Caractkrisation

du flux hydrique

La periode evenementielle choisie correspond a un cas d’ecole bien connu en physique du sol : la * methode du plan de flux nul b)(Vachaud et al., 19781, reposant sur l’analyse de la loi de Darcy, generalisee aux transferts en milieu non sature leq. 11, dans laquelle q, m/j est la densite de flux volumique a travers le niveau z; KB), m/j est la relation reliant conductiviti: hydraulique et teneur en eau, et grad H est le gradient de charge hydraulique a z, dont le signe donne la direction de l’ecoulement. Quel que soit 8, il apparait, d’apres eq. 1, que le flux est nul, si grad H= 0 a la profondeur zO. En cas de redistribution de la quantite d’eau infiltree dans le sol apres une pluie, l’amplitude et l’orientation du flux P travers zvarient, de facon continue, pour passer progressivement d’un transfert orient6 positivement vers le bas vers un transfert en evaporation, le moment ou le flux est nul correspondant a celui oh le maximum du profil de charge Hz) atteint ce niveau. L’evolution des profils de charge hydraulique en fonction du temps est repartee figure Ia ; on trouvera Cgalement (figure lb) la courbe z& t), donnant la profondeur de penetration du plan de flux nul en fonction du temps. Le flux a toute profondeur z peut etre facilement calcule par les variations de teneur en eau entre z,(t) et zdurant un intervalle de temps At(Vachaud et al., 1978). La figure 2 presente l’evolution des flux hydriques journaliers a z= 0,4 m (de 2.10-’ a - 6.10~ 4 m/j).

Potentiel Clectrique et flux hydrique

L’evolution continue des differences de potentiel electrique (entre respectivement 0,8 et 0.3 m et 0,8 et 0,5 m) durant la m&me periode est repartee figure 3. Les deux courbes se croisent le 11/06.Si l’on suppose homogene la couche de sol entre 0,3 et 0,5 m, on peut s’attendre, d’apres les lois phenomenologiques d’electrocinetique (Rocard, 1962 ; Nourberecht, 1963) a une relation lineaire entre le flux hydrique q et le champ electrique E, mV/m. caracterise par le gradient de potentiel electrique que l’on approximera par l’eq. 2, oh la valeur surlignee au numerateur correspond a la moyenne journaliere de la difference de potentiel electrique entre 0,3 et 0,5 m. La figure 4 montre qu’il existe une relation clairement lineaire entre qet E, cette derniere valeur variant de + 35 mV/m a - 1 mV/m durant la periode de 10 jours consideree. Cette relation ne passe toutefois pas par l’origine, probablement du fait de l’existence de differences de potentiel entre electrode et sol ou m@me entre electrodes, comme cela a ete constate par la suite en placant les electrodes dans la meme solution de reference. 11 est legitime de decaler la droite representative de cette relation pour la forcer a passer par l’origine ; cela revient a faire co’incider le temps d’ intersection des deux courbes de la figure 3 avec le moment auquel le plan de flux nul arrive a la profondeur z= 0,4 m.

Sci. Paris, Sciences

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et des plan&es

/ Earth & Planefary Sciences 1997. 325,317.321

Electric

Conclusion Cette etude etablit une causalite entre flux hydrique et champ electrique, en condition naturelle, dans un sol non sature. Le coefficient de proportionnalite est certainement dependant de

Introduction It has been

for

a long

time

that

fluid

circulation

in

porous material is associated with electric exist a lot of examples of electrical signals water flow in various geological contexts

fields. There generated by [in geothermal

areas, on volcanoes, in tectonically active neighborhood of dams, in limestone quarries al., 1976; Corwin and Hoover, 1979; Morgan

areas, in the (Mitzutani et et al., 1989;

Morat and 1990)1, and Most of the

Le Mouel, 1990; Zlotnicki and Le Mouel, also by sap flow in trees (Morat et al., 1994). time the relationship between fluid flux and

zone flow,

of the soil. One was implemented

changes volumetric day; five 0.3,

0.5,

0.7

and

0.8

m, to measure

This

differences was

programme, recherche

one

has not yet

of the aims

funded scientifique,

been

performed. research

port from the soil to the groundwater under by running in parallel several experiments geophysical potentials,

irrigated devoted

crops, to the

methods, one to the hydrology

of them of the

were

v,.,-Vo.7 All relevant tained on the The 1996. from span

conducted

0.3,

0.5,

0.7

and

Pb/PbCI, made every

and recorded m as a reference:

meteorological site.

experiment

0.8

lasted

m.

electrode. Differen2 min with a highon a RAM V,,-V,,,;

observations from

17

installed

The

memory, V,,8-V0,j;

were

May

1996

also to

ob-

24 July

analysis

of data

concerns

gradients

at the

soil depth

water z=

flux

0.4

and

electric

m.

Soil water flux The

selected

event

corresponds

to a well-known

on the experimental

site of la

unsaturated

water

sites have been installed of water and N-Nitrate

C. R. Acad. Sci. Paris, Sciences 1997. 325,317-321

de la terre

since in the

et des planetes

1991 unsat/ Earth

et al., gravity time of

the flow of water through the reference level (0.4 m) from a quite important downward flux (infiltration at the end of the rain span) to weak upward losses by evaporation at the

layer of coarse pebbles with a water table aquifer depth varying over the year between IO to 15 m below soil surface.

at a the

applica-

tion in soil physics: the “zero flux method” (Vachaud 1978). Owing to the combination of capillarity, and evaporation, there is a continuous change with

the

measuring the fluxes

the

We will consider here the most interesting period, 3 June to 12 June, corresponding to a IO-day dry following a 23.8 mm rainfall occurring on 2 June.

potential

C&e St. Andre, 50 km NW of Grenoble. This site is described in detail by Kengni L. et al. (1994). Briefly, it is located in the middle of an agricultural watershed; the geological structure is that of a glacial terrace; the soil is quite shallow (approximately 1 m thick); it rests above a

Several to monitor

basis

sensitive

at z=

end of the period. In agreementwith generalized Darcy law, applied

Materials Experiments

a daily

by CNRS-INSU (Centre national de la lnstitut national des sciences de

I’Univers, Paris). The idea was to benefit from the existence of a very intensively monitored experimental site, initially devoted to the study of water and nitrogen trans-

application of surface concerning electrical vadose zone.

on

vertically

The

of an interdisciplinary

to soil It com-

of water)

impedance voltmeter with the value at 0.8

potential

devoted fallow.

hydraulic head profiles [H(z), with H (meters the hydraulic head]; - in terms of electric field: a set of four probes

tory experiments in which submitted to high pressure

1995). As for field experiments, measurements of the streaming electric potential in soils have already been performed to monitor water transport, but to the best of our knowledge, independent quantification of water flux and

of these, solely on natural

in soil moisture profiles [EI( z), with 8 (m3/m3) the water content] every 0.1 m to 1 m depth every mercury tensiometers installed vertically at 0.15,

device is an unpolarizable tial measurements were

tive relationships between the circulation of water (in fact the gradient of hydraulic head) and the electric potential difference (Pozzi and Jouniaux, 1994; Jouniaux and Pozzi,

flux

prises the following instrumentation: - in terms of soil water: one access tube for neutron moisture meter (Vachaud et al., 1977) to determine

electric field is rather assumed than actually established owing to the lack of simultaneous measurements of the two fields. Few works have been devoted to soils. Laborasaturated samples of soils were have provided some quantita-

and soil water

conditions locales. D’autres essais. notamment avec des electrodes ameliorees sont encore necessaires. 11spourraient aboutir a des conclusions prometteuses sur la possibilite de quantifier les flux hydriques en milieu non sature et leur direction a partir de simples mesures electriques.

urated water

known

potential

the formulation to flow of water

soil:

H

q=-k(B).grad

depth

flux

density z0 where

zero. In equation (m/day), a value content

q (m/day) the

Sciences

per

hydraulic

unit head

soil

(1) area

gradient,

(I), k(B) is the hydraulic varying very strongly with 8 (m3/m3).

files are given in figure representing the time depth (figure 1 b). & Planetary

of the through

Measured

grad

at the

H, is

conductivity the volumetric

hydraulic

1 a, together with course evolution

is zero

head

pro-

the curve zO( t) of the zero-flux

319

J.-L. Thonv

et al

H 04 -60

40

40

40

-2,0

-I,0

.,.

60

.a)

- OS8

fsci.-Figure

~- 69

_pi__-1. a. Evolution

a. ivolution

darts

with le temps

time

- VJ

of measured

des profils

de charge

hydraulic

head

hydraulique

profiles; mesur&.

b. Time b.

The water flux through a reference level z can be determined by the change in soil water content between z,,(t) and z during a time interval At (Vachaud et al., 1978). The time distribution of daily values of soil water flux at z = 0.4 m is given in figure 2. By definition, the flux is positive when oriented downwards. During the considered period the soil water flux at that level varies from 2.1 Om3to -6.1 Om4m/day, with a zero value on 8 June.

-1 B -f&5 eE *)0 0

course

ivolution

evolution dans

Electrical

of the

le temps

zero

flux

depth.

de la profondeur

potential

du plan

de flux

nul.

differences

Changes of electrical potential (relative to 0.8 m) measured during the same period at 0.3 and 0.5 m are given in figure 3. First, there is a very rapid signal change on 2 June, corresponding most probably to the passage of the wetting front resulting from rainfall. Then the shape of signal evolution differs markedly from one depth to the other: a quick increase, followed by a plateau and a slow decrease at 0.3 m; a continuous gentle increase at 0.5 m. Both curves cross on 11 June.

Volts

t 2 ii:

095

1 195 2

235 216 3/6 416 516 616 716 6I6 916 1046 1116 12i6 Figure

2. Time

distribution

z = 0.4 m (positive ,(,. ;((: Distribution profondeur ment orient6

320

values

of daily refer

values

to downward

of soil

water

oriented

temporelle des valeurs journalikres de flux z = 0,4 m l/es valeurs positives s’appliquent vers le has).

flux

hydrique 2 la 2 un koule-

C. R. Acad.

Time

at

flow).

Sci. Paris,

Figure 3. Changes red at 0.3 and 0.5 ,( ,(,((f Variations rapport Sciences

of electrical m.

de potent/e/ 2 me rPf&ence de

la terre

potential

electrique 2 0,s ml. et des

plan&es

(relative

mesurees

/ Earth

to 0.6

2 O,3

et

m) measu-

0,s m

& PlanetarySciences 1997, 325.3

(par

17-32

1

Electric

Electrical

potential

and water fJux

potential

or id soil water

14.489~ + 6,35as

40

By assuming that the soil layer (0.3-0.5 m) is homogeneous, let us now analyse jointly the two sets of information. Electrokinetic laws (Rocard, 1962; Nourberecht, 1963) show that a linear relationship is expected between the vertical flux of water q and the electric field ,F(mV/m), i.e. the electric potential gradient at z= 0.4 m in the soil. This quantity can be approximately expressed as:

flux

R2

=0,99?7

35 30 -

2s

2;

15

E 520 E

10 5 0

where AV, 2 represents the mean daily value of the difference ii electrical potential between the electrodes at 0.3 and 0.5 m, and 0.2 is the distance (in meters) between these electrodes. During the period of reference, the electric field varies from + 35 to - 1 mV/m. A clear linear relationship exists between the water fl;x and the electric field as illustrated by figure 4, which displays the pairs of points (q, E,,,) corresponding to the lo-day period of measurement. The straight line representing this relationship does not pass through the origin; but it is well known that potential differences, generally unknown but hopefully constant during the experiment, exist between electrodes and the soil in their immediate neighborhood (the so-called “electrode potential”). This shift from the origin can also in part be explained by electric potential differences of a few millivolts existing between electrodes, as this was observed at the end of the experiment with the electrodes immersed in the same reference solution. The straight line can then be legitimately shifted and forced to the origin, which comes down to make the two curves of figure 3 cross at the time the flux q at z = 0.4 m is zero. Acknowledgements:

This work

was supported

by the

“Programme

REFERENCES Corwin R.F. and Hoover D.B. 1979. The self potential method in geothermal exploration, Geophysics, 44,226.245 Jouniaux L. and Poni J.P. 1995. Streaming potentials and permeability of saturated sandstones under triaxial stress, Consequences for electrotelluric anomalies prior to earthquakes, J. Geophys. Res., 100, 10197-10209 Kengni L.. Vachaud G.. Thony J.L.. Laty R. and Garino 8. 1994. Measurement of water and nitrate leaching under irrigated ma’ize, J. of Hydrology, 162,23-46 Mitzutani H.. lshido T.. Vokokura T. and Ohnishi S. 1976. Electrokinetic phenomena associated with earthquakes, Geophys. Res. Left., 3.365-368 Morgan F.F.. Williams ED and Madden T.R 1989. Streaming potential properties of westerly granites with applications, J. Geophys. Res.. 94, 12449-12461 Morat P. and Le MO&I J.L. 1990. Signaux 6lectriques engendr& par des variations de contrainte dans des roches poreuses non saturGes. C. R. Acud. Sci. Paris. Series II, 315.955-963

C. R. Acad. Sci. Paris, Sciences 1997. 325,317-321

de la terre

et des planetes

45 -1

-0,s

0

0,5

1

I,5

2

23

Water flux (%I5 m/day) Figure 4. Relationship between daily values of vertical flux of water 9 and the electric field Eat 0.4 m in the soil. ” :’ :’ ~’ Relation entre /es valeurs journaliPres de flux hydrique vertical q et le champ klectrique E 2 la profondeur 0,4 m.

Conclusion The causality between soil water flux and electrical potential gradients seems to be well established. The proportionality coefficient depends certainly on local conditions, such as the nature and the physico-chemical characteristics of the soil. Some similar experiments, in different soils and with more electrodes are needed to confirm and enlarge these first conclusions. The spurious electrode potential could probably be estimated or reduced. In any case the results show how promising electrode measurements could be to infer water circulation in the soil in terms of both direction and amount of water flow. de Recherches

en Hydrologic”.

INSU. CNRS.

Paris.

Morat P., Le MO& J.L. and Granier A. 1994. Electrical potential on a tree A measurement of sap flow? C. R. Acad. ScLParis, La Vie des Sciences, 317.98-101 Nourberecht 8. 1963. Irreversible thermodynamic effects in inhomogeneous media and their applications in certain geoelectric problems, PhD Thesis, MIT, Cambridge, USA, Pozzi J.P. and Jouniaux L. 1994. Effets blectriques des circulations de fludes dans les roches sedimentaires et pr&ision des s&smes. C. R. Acao’. Sci. Paris, Series II, 318, 73-77 Rocard V 1962. Le signal du sourcier. Paris, Dunod ed.. 200 p. Vachaud G., Royer J.M. and Cooper D. 1977. Comparison of methods of calibration of a neutron probe by gravimetry or neutron capture model, J. Hydrol., 34,343.356 Vachaud G , Dancette C., Sonko M. and Thony J.L. 1978. MBthodes de caracterisation hydrodynamique in situ d’un sol non satur8. Application ti deux types de sol du %nbgal en vue de la determination des termes du bilan hydrique, Ann. Agron., 29, l-36 Zlotnicki J. and Le Moue1 J.L 1990. Possible electrokinetic origin of large magnetic variations at la Fournaise volcano, Nature. 343. 633-635

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