Effect of physical properties of frozen ground on electrical resistivity logging

cold regions science and technology Cold RegionsScienceand Technology22 (1994) 361-384

ELSEVIER

Effect of physical properties of frozen ground on electrical resistivity logging R i c h a r d Fortier, M i c h e l Allard, M.-K. Seguin Centre d'btudes nordiques, Universitb Laval, Sainte-Foy, Qubbec G IK 7P4, Canada

(Received 1 March 1993;acceptedafter revision3 November1993)

Abstract

During a two-month period from late April to early July 1990, variations of apparent electrical resistivity and temperature with time in the upper 4 m of a silty permafrost were recorded at Umiujaq, Nunavik (Canada). Electrical contact with the ground was ensured through regularly spaced metal electrodes along multiconductor cables vertically buried inside drill holes. Thermistors located at the same depths yielded a temperature profile in the ground. In conjunction with these measurements, a weekly core sampling program allowed a visual description of soil cryostructures. In addition, unfrozen water and ice contents of frozen ground were directly measured in the field using adiabatic calorimetry to define the relationship between the physical properties of frozen ground and electrical resistivity values. It was observed that the active layer thaw and permafrost warming induce variation in the physical properties which can be detected by resistivity measurements. The numerical analysis of the results provided correlations between the parameters of the silty permafrost and the measured resistivity and temperature values. Thus, the variations of apparent resistivity with time at various depths can be used to predict parameters such as unfrozen water and ice contents of the frozen ground. Apparent resistivity logging can therefore be used to monitor changing permafrost conditions caused by climatic variations or man-made disturbances.

1. Introduction

Appropriate knowledge of permafrost occurrence and its physical, chemical and mechanical properties is essential for foundation design and construction. Mapping cryogenic landforms through interpretation of aerial photographs (l.~vesque et al., 1988), field surveying with drilling programs (Ruffel et al., 1990), investigation by geophysical methods (Kay et al., 1983 ) and geotechnical testing (Anderson and Morgenstern, 1973; Leroueil et al., 1990) represent some of the techniques available to gain knowledge about the permafrost environment. In addition to the usual measurement of

ground temperature profiles, the principal geophysical methods used for permafrost study are electrical resistivity sounding (Segnin et al. 1989; Kay et al., 1983), seismic refraction (Seguin et al., 1988), electromagnetic method (Kay et al., 1983 ) and ground penetrating radar (Pilon et al., 1990). These methods provide information about the spatial distribution, thickness and the physical properties of permafrost. For the electrical methods, interpretations are usually based on the sharp increase of electrical resistivity between unfrozen and frozen ground. Supported by proper understanding of regional geomorphology and stratigraphy, apparent resistivity can provide indirect information on material type,

0165-232X/94/$07.00 © 1994 ElsevierScienceB.V. All rights reserved SSDI O165-232X ( 93 )EOO34-G

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R. Fortier et al. / Cold Regtons Science and Technology 22 (1994) 361-384

unfrozen water and ice contents, and ground temperature. Geophysical logging techniques (Delaney et al., 1988; Fortier et al., 1991 ) are not widely employed in permafrost work, although they yield better information than surface methods. Temperature (Delaney et al., 1988), self-potential (Fortier et al., 1993; Parameswaran and Mackay, 1983), induced polarization (Fortier et al., 1991 ) and electrical resistivity (Arcone and Delaney, 1988) are usually measured in logging using multiconductor cables and multiple metal electrodes and thermistors distributed regularly inside a borehole. All of these measurements are sensitive to ground temperature, unfrozen water and ice contents, material types, interstitial water salinity, and porosity (Garg, 1973 ). Continuous recording of these measurements in permafrost over many months or years can give a good idea of the changes that occur in the physical properties in frozen ground with changing temperature and time. Although electrical methods have been used widely in permafrost research, very few studies have attempted to establish quantitative or semiquantitative relationships between specific electrical properties, such as apparent electrical resistivity and permafrost parameters such as temperature, ice content, unfrozen water content, grain size and cryostructure. This paper describes the instrumentation, the electrode arrays used and the field methodology used for measurement of apparent electrical resistivity. Correlations between permafrost conditions measured with the calorimetric method and electrical properties are provided for frozen soil within a silty permafrost mound at Umiujaq, Nunavik (Canada).

2. Study area

The Inuit community of Umiujaq (56 ° 33'N, 76 ° 32'W ) is on the east side of Hudson Bay (Fig. 1 ). The village is built on raised sandy and gravelly shoreline sediments of the post-glacial Tyrrell Sea. Some areas at the periphery of the village also have silty clay soils of marine origin.

These Quaternary sediments vary in thickness from almost nothing to over 50 m and they overlie basaltic rocks dating from the Proterozoic. Carbon dating of the post-glacial marine limit shows that deglaciation of the area occurred 7600-7300 years ago (Hillaire-Marcel, 1976; Allard and Seguin, 1987b). After the retreat of Wisconsin ice, the land below the present elevation of 270 m was submerged by the Tyrrell sea. Afterwards, it gradually emerged due to isostatic rebound. Marine silty clay were left by the sea in topographic basins. After emergence, the silty terrains were subjected to erosion, settlement by vegetation and invasion by permafrost (Allard and Seguin, 1987b). The study area is located in the discontinuous, but widespread, permafrost zone (AUard and Seguin, 1987a). The tree line in the region is aligned from South to North, some fifteen kilometers away from the coastline (Payette, 1983 ) as the proximity of Hudson Bay produces a colder climate along the coast. The climate is subarctic and characterized by cold winters (about - 2 4 °C for January) and cool summers (about 9 ° C for August) with mean annual air temperature about - 5 . 6 ° C . The freezing index is about 3,000°C days while the thawing index is 1,000 ° C-days. In winter, strong winds, predominantly from west and northwest, sweep snow across open areas and favor permafrost preservation by removing large quantities of heat. A few permafrost mounds, or cryogenic mounds, are located on the outskirts of the village (Fig. 2 ) at an elevation of about 35 m above sea level. According to the regional sea level curve (Hillaire-Marcel, 1976), emergence of the site can be estimated at about 2400 BP. This date represents a maximum age for permafrost aggradation in the mounds which originate from ground heave due to the formation of abundant segregation ice. With their oval or approximately round shape, their neighbouring thermokarst pounds, and the active layer failures on their flanks, the mounds are of the same type as those described by Allard et al. (1987) and others. The permafrost mounds at Umiujaq are 3 m higher than the surrounding terrain and 50 m in diameter. Their tops are covered by a tundra vegeta-

R. Fortier et al. / Cold Regions Science and Technology 22 (I 994) 361-384

363

#m

% Sites no. 1,2 and 3

%

0

1000

2000 rn

Fig. 1. Location of the village of Umiujaq.

tion consisting principallyof lichen, moss and birch shrubs. Frost boils with an average diameter of 0.5 m are alsopresent and widely scattered on theirsummits. O n the sidesof the permafrost mounds and in hollows between them, I-2 m high shrub thicketsmaintain a thick snow cover in winter. Consequently, there is no permafrost in the hollows between the mounds. Permafrost is 20-25 m thick beneath the mounds, while the active layerthickness is I.I m. Although the permafrost mounds wcrc the object of many geomorphologic descriptions (AIlard ctal., 1987) and despite the fact that thc general processes of their formation is understood (Lagarec, 1982), very few detailed gcocryologic studies have been done on their internal cryostructure or their thermal and hydrological regimes. Fortier et al. ( 1991, 1992b) described in detail the internal cryostructure and the ground ice distribution in permafrost mounds of Kangiqsualujjuaq and Umiujaq. They used

sample coring, temperature profiles, induced polarization and apparent electrical resistivity logs to gain information about the properties of permafrost inside the mounds. They found that permafrost mounds have complex cryostructures and they estimated the freezing point depression at permafrost base due to dissolved minerals in interstitial water and overburden pressure.

3. Methods

Among the available methods to study permafrost, two were chosen. The first one is electrical resistivity logging and the second one is adiabatic calorimetry on core samples. The latter provides a direct measurement of unfrozen water content in the field.

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R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

Fig. 2. Aerial view showing permafrost mounds close to the village of Umiujaq (see the width of road for scale).

3.1. Apparent electrical resistivity Electrical resistivity of a conductive material is a measure of the difficulty with which an electrical current flows through it (McNeill, 1980). For a heterogeneous a n d / o r anisotropic conductive material, the term "apparent electrical resistivity" is used. The range of electrical resistivity displayed by moist unconsolidated materials at room temperature usually lies between 1 and 103 f~-m. At temperatures below freezing, the resistivity of the same material can vary from a few hundreds f~-m to as much as 106 f~-m. Most minerals in the soil have very high resistivity. In general, the conductivity of soils is electrolytic and takes place due to the presence of conductive fluids in the pores between insulating grains. The soil conductivity is determined by porosity, fluid saturation, nature of the electrolyte, temperature, phase composition of interstitial water, amount and composition of clay in soil (McNeill, 1980). The electrical resistivity of soil is proportional to the electrical resistivity of water and inversely proportional to porosity and de-

gree of saturation. Electrical resistivity of interstitial water changes largely with the amount of dissolved minerals such as chlorides and sulfates. Soil freezing also induces an increase in electrical resistivity. As water freezes, the ice content increases and the electrical resistivity rises, because the resistivity of ice is extremely high. For a saturated clean sand, ice fills all of the interstitial space, and the resistivity of frozen sand is very high. The addition of clay particles to the clean sand can drastically change its electrical behavior during freezing. When ground temperature drops just below 0 ° C, only a small amount of interstitial water freezes and continuous water films remain available for current flow. Adsorbed ions on clay particle surfaces create an electric field that locally orients the nearby water molecules and impede their freezing (Ananyan, 1973 ). This process produces an adsorbed water film on clay particle surfaces. But, the thickness of the unfrozen water film around clay particles decreases with cooling temperature. Hence an increase in the effective length of current paths and a reduction of cross-sectional area for cur-

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

rent flow as temperatures dip below 0°C produces a slow increase of electrical resistivity (Hoekstra and McNeiU, 1973 ). Electrical resistivity of frozen ground does not directly depend on the presence of interstitial ice. Ice, like soil grains, is a good insulator. Current flow takes place only in unfrozen water films around a grain surface. However, ground ice structures such as stratified, reticulated and massive cryostructures also affect electrical resistivity (Bogolyubov, 1973), such that, frozen ground with a massive cryostructure, characterized by a predominance of interstitial ice which contains continuous unfrozen water films, has an electrical resistivity lower than a soil with a stratified structure.

Field instrumentation and electrode arrays used The resistivity meter used was a Terrameter ABEM digital SAS 300 made by Atlas Copco Geophysics. It contains a transmitter, receiver and microprocessor in a single case. On the receiver, discrimination circuitry and programming separate DC voltages, self-potentials and noise from the incoming signal. Ratio of potential difference AV to current flow I is calculated automatically by the microprocessor and displayed in digital form. The overall range extends from 0.5 m ~ to 1,999 k.Q. For each investigated site, a 4 m long electric cable with 41 stainless steel electrodes distributed regularly every 0.1 m was used. The first and last electrodes were 0.05 and 4.05 m deep. The electrodes consisted of stainless steel circular bands fixed around the electric cable. Each electrode was linked to a contact box at ground surface by an individual electric conductor. In parallel with the electrodes, 21 thermistors distributed regularly every 0.2 m on another cable provided a temperature control. Three different electrode arrays were used to measure the apparent electrical resistivity of frozen ground: Wenner, double-dipole, and lateral dipole arrays (Fig. 3). They were composed of four downward-moving electrodes along one or two electric cables. For these arrays, apparent electrical resistivity values depend on the geometric arrangement of electrodes used. Calcu-

365

lated resistivity values for each array are given in Fig. 3 as a function of ratio of potential difference to current flow and geometric constant proportional to the spacing between electrodes and dipoles (Telford et al., 1984). The Wenner array consists of an alignment of four equidistant electrodes (Fig. 3A) on the same electric cable. The spacing a between each electrode (a = 0.1 m in this study) and total length L (L = 3a) of the array are constant. Current flows between the outer electrodes while the potential difference is measured between the inner electrodes of the array. After the first measurement is made close to the surface, the alignment is moved down in increments of one electrode spacing for the next measurement until the last electrode is reached. The depth of investigation at each measurement is located in the center of the alignment. This method provided a discrete logging of apparent electrical resistivity. The double-dipole array also consists of four electrodes (Fig. 3B). The top pair of electrodes forms the current dipole, while the bottom pair forms the potential dipole. The spacing a between each pair of electrodes is constant. Spacing n. a between current and potential dipoles is variable as well as the total length L ( L = [ n + 2 ] a ) of the array. In this study, spacing increment n varied from 1 to 5. Initially, the current dipole remains fixed and the potential dipole is moved downwards for n from 1 to 5. Then the current dipole is moved down in increments of one electrode spacing and the sequence is repeated. The radial depth of investigation r from the center of the electric cable (Fig. 3A and B) is given by (Barker, 1989 ): Wenner array:

r=0.17 L=0.51a

(1)

Double-dipole array: r=0.25 L=O.25(n+2)a

(2)

Values of apparent electrical resistivity obtained with these arrays depend on the true electrical resistivities of all materials inside a spherical volume of radius r. For the Wenner array, the radial depth of investigation is constant, while for the double-dipole array, it varies with the spac-

366

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

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A

B

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C

Fig. 3. Apparent electrical resistivity logging with three electrode arrays (Wenner, double-dipole and lateral dipole arrays ).

ing between the two dipoles. In the latter case, a pseudo-section of apparent electrical resistivity values (Fig. 3B) is obtained, while for the former, it is a discrete profile (Fig. 3A ). The lateral dipole array requires two electric cables separated by distance b (Fig. 3C). Two electrodes in one hole form the current dipole and another pair in an adjacent hole at the same depth forms the potential dipole. Similar to the Wenner array, a discrete profile of apparent electrical resistivity values is obtained when the dipoles are moved downwards. During the study period in 1990, apparent resistivity variations in the active layer and the permafrost were measured at three different sites (Fig. 4) on the silty permafrost mounds. Four holes were drilled in August 1989 with a portable drill and a CRREL coring auger kit for frozen ground (Brocket and Lawson, 1985). Thermoelectric cables were then placed in the holes and these letters were filled back with a silty mud from drill cuttings. Mud was packed down firmly to ensure good physical, thermal and electrical contact between the metal electrodes and ground.

The time interval between cable installation and study was sufficient to refreeze the slurry and reach a thermal equilibrium. For each site, one thermoelectric cable was buried into the ground. Ground temperature and apparent resistivity logging with the Wenner and double-dipole arrays were measured weekly for each site. For Site 1 only, an electric cable was installed in a hole 0.5 m away from the thermoelectric cable (Fig. 4) to measure the apparent electrical resistivity in lateral dipole array weekly. At Site 1, the measurements of ground temperature and apparent resistivity using the Wenner array were made daily during the study period.

3.2. Adiabatic calorimetry The calorimetric method was used in the field to determine unfrozen water and ice contents in frozen samples (Martynov, 1956). A sample of frozen ground at initial temperature below 0°C is immersed in a calorimeter filled with distilled water above 0 ° C. As a result of heat exchange between the water and the frozen sample, the let-

367

R. Fortier et aL / Cold Regions Science and Technology 22 (1994) 361-384

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Fig. 4. Locations of geophysical cables, access tubes and drill holes on permafrost mounds of Umiujaq.

ter thaws and an equilibrium temperature is established in the calorimeter. The mass of ice in a frozen sample is given by (Fortier et al., 1992a): m i -~ [ Vwpc w JrA ) ( Tcalo - Tequi ) --(mdCd+mwCw)(Tequi--Tsample)]/

(3)

(Cw- Ca) (T~mp~e- 273.15K) + L and the mass of unfrozen water in frozen sample is given by: muw = ms

-

md

-- mi

(4)

where cd, ci, and Cware heat capacities of the dry soil (0.795 J / g . K for a silt), ice (2.039 J / g . K at 0 ° C ) and water (4.1921 J/g- K), respectively, p is density of water (1 g/cm3), .4 is calorimetric constant of calorimeter ( J / K ) because a calorimeter is an imperfect closed adiabatic system, L is latent heat of fusion of ice (333.51 J/g at 0 oC), Tc,~o,T,amp~e,and T~quiare temperatures of

distilled water in the calorimeter, frozen sample, and equilibrium (K), respectively, Vwvolume of distilled water in the calorimeter (cma), and m,, row, rod, mi, and muw are masses of sample, water, dry soil, ice and unfrozen water in sample (g), respectively. The calorimeters used consisted of Thermos bottles. The temperatures of distilled water and frozen sample-distilled water mixing were measured with a thermistor. The temperature of a frozen sample used in the calculation is obtained by the ground temperature profile measured on a thermoelectric cable no more than 2-3 m away. The accuracy of the calorimetric method depends principally on the accuracy of the temperature measurement (Fortier et al., 1992a). Although the calorimetric method is supported by some theoretical hypotheses, Fortier et al. (1992a) calculated a power law between the unfrozen water content of silty frozen soil at Umiujaq and its temperature below the freezing point. This relation is similar to that found by

368

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

Anderson et al. (1973 ) for the Fairbanks silt, a comparable material.

Drilling During the 1990 thaw period, twelve additional holes were drilled in the permafrost mounds (Fig. 4) to characterize the ground ice cryostructures to a depth of 4 m and to allow measurement of the unfrozen water content and ice content of the frozen samples. The coring auger supplied continuous and undisturbed core samples along the entire section. When a sample was removed from the coring auger, a photograph was taken. Second, a detailed description (depth of coring, length of core sample, sketch of cryostructure, visual estimation of ice content, color of sample, texture, etc. ) was made. Third, a representative part of the core was extracted for the calorimetric test. The test was immediately performed in the field to avoid thermal disturbance on the samples. On-site analysis capability is the principal usefulness of the calorimetric method. During the 1990 core sampling, calorimetric tests were also conducted on frozen samples of the active layer, because it was only partially thawed during the study period.

4. Results of calorimetry and apparent electrical resistivity Only three drilling locations out of twelve were selected for correlation with field measurements because they were located close to the thermoelectric cables. Given the marked heterogeneity of the soil, the calorimetric observations could not be correlated with temperature logs when holes were too far away. The three cores used for correlation are from drill holes 5 (26/05/90), 11 (22/06/90), and 12 (28/06/90) (Fig. 4). The results of the calorimetric tests (mass proportions of unfrozen water, ice and dry soil), sketch of cryostructures for each related drill hole, temperature profiles and apparent Wenner resistivity logs are given as a function of depth in Fig. 5. The mass proportion of unfrozen water during the study varied with depth and time between 5

and 10% in the active layer below the thawing front, and stayed approximately constant at 5% in permafrost (Fig. 5 ). The mass proportion of ice in the active layer increased gradually with depth from 5 to 25% toward the active layerpermafrost interface. At a depth of about I. 1 m, the active layer-permafrost interface was well defined by a sharp increase of the mass proportion of ice from 25 to 40% and even until 90% (Fig. 5C). In permafrost, the ice content was generally between 30 and 55%. The active layer is characterized by a polyhedral cryotexture (Fig. 6). Repeated freeze-thaw cycles and formation of segregated ice resulted in a process which broke silty sediments more or less horizontally into layers 2 mm thick. During the formation of segregated ice, sediments are dessicated by cryosuction to supply water for the growth of ice lenses. This process is partly irreversible because the sediments are consolidated during the formation of ice lenses. When active layer temperature drops, vertical thermal cracks 1 to 2 mm wide appear. In warm periods, these cracks fill with sublimated ice crystals after vapor diffusion into the ground. When the ice melts, horizontal (segregated ice) and vertical (thermal cracks ) planar openings separate sediments into polyhedrons and form a network of open, smooth-walled fissures (Fig. 6). This network increases the permeability of the active layer and prevents interstitial overpressure during thaw (Leroueil et al., 1990). The active layer-permafrost interface, at a depth of about 1.1 m, is well delineated by the appearance of horizontal lenses of segregated ice which thicken at depth (Fig. 7 ). Between 1.1 and 2.2 m, ice lenses and beds of frozen soil form a horizontally stratified or reticulated cryostructure (Fig. 8). Between 2.2 and 3.3 m, frozen ground volumes are enclosed in an ice matrix and permafrost has an erratic cryostructure (Fig. 9 ). At depths greater than 3.3 m, the cryostructure changes from erratic into a massive one in which interstitial ice predominates (Fig. 10 ). Apparent electrical resistivity in the active layer is two orders of magnitude lower than in permafrost (Fig. 5). Resistivity in the active layer increases gradually with depth from 10z to

R. Fortier et al. I Cold Regions Science and Technology 22 (1994) 361-384

Mass proportion (%) 0

Mass proportion (%)

Electrical resistivity (Ohm-m)

20 40 60 80 100

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Fig. 5. Results from core sample observation, calorimetric tests and electrical resistivity logging (drill hole 5, 26/05/90; drill hole I l, 22/06/90; drill hole 12, 28/06/90).

370

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

Fig. 6. Polyhedral cryotexture in active layer (drill hole 2, 19/05/90, 0.85 m).

103 t - m , while in permafrost, values are close to 105 fl-m. A sharp increase in resistivity from 103 to 105 fl-m well defines the active layer-permafrost interface. At depths greater than 3.5 m, resistivity is fairly constant.

4.1. Numerical analysis Numerical analysis permits correlations between physical properties of the active layer and permafrost such as the unfrozen water and ice contents on the one hand and apparent resistivity on the other. With the help of statistical correlations, a relationship can be established between them. The numerical analysis particularly focusses on ( 1 ) the association of variables in pairs, and (2) correlations between variables. The matrix of calorimetric and geophysical variables is composed of object-lines and descriptor-columns. The object-lines correspond to 54 levels of measurement (or depths) studied in the three drill holes. Each object is characterized by 10 quantitative descriptor-columns (or variables). De-

scriptors are divided into two groups. The first group includes the calorimetric variables, which are Z, depth of calorimetric measurement (m) M i = m i X 100/ms (5), mass proportion of ice

(%)

Muw=muw×lOO/ms (6), mass proportion of unfrozen water (%) Wuw=muw × lO0/md (7), unfrozen water content (%) M w = m ~ x l 0 0 / m ~ (8), mass proportion of water (%) Md =rod × 100/ms (9), mass proportion of dry soil (%) The second group includes the geophysical variables interpolated to the depths of calorimetric measurement Z, which are Tg ground temperature (°C), Pw apparent electrical resistivity with the Wenher array (fl-m),

R. Fortier et al. / Cold Regions Science and Technology 22 (I 994) 361-384

Fig. 7. Interface between active layer and permafrost at 1.1 m. Stratified cryostructure in permafrost (drill hole 9, 17/06/90, 1.02-1.30 m).

Pdd apparent electrical resistivity with the double-dipole array (f2-m), and /hd apparent electrical resistivity with the lateral dipole array (f~-m).

4.2. Associations of variables in pairs For the association of variables in pairs, a lower triangular scatterplot matrix (Fig. 11 ) was constructed. Variables appear on the matrix diagonal and each graph shows the association of one pair of variables. For example, the association between ground temperature Tg and unfrozen water content Wuwis given by a little square graph at the intersection of the column under Ts with the line of Wuw. The curve drawn in each graph is a non-linear regression similar to a power law. Pearson's correlation coefficient r (Legendre and Legendre, 1984) is also given for each pair of

371

Fig. 8. Reticulated cryostructure in permafrost (drill hole 9, 17/06/90, 2.00-2.18 m).

variables (Fig. 11 ). This coefficient is a measure of the linear dependence between descriptors. A non-significance (coefficient equal to zero ) may not be interpreted as an absence of relation since a non-linear relation between two variables can yield a very low coefficient (Legendre and Legendre, 1984). From this analysis, the relations of interest are: ( 1 ) mass proportions of ice and unfrozen water between themselves (r = - 0.608 ) and with ground temperature below freezing point (r = 0.539 and - 0.421 respectively), (2) apparent electrical resistivity (Wenner array) with ground temperature below freezing point (r = 0.514) and with the two other apparent electrical resistivities (double-dipole array, r=0.673; lateral dipole array, r=0.509), and (3) mass proportions of ice and unfrozen water with apparent electrical resistivities (in spite

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R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

Fig. 9. Ice-rich permafrost, frozen ground volume in ice matrix (drill hole 8, 08/06/90, 2.42-2.75 m).

Fig. 10. Massive cryostructure in permafrost (drill hole 8, 08/06/90, 3.26-3.57 m).

of low Pearson's correlation coefficients since the relations are non-linear).

parent resistivity (Wenner) over time for one particular depth following the progressive warming of ground and its possible thawing. The active layer at depths of 0.3 and 0.8 m thawed completely during the study period and the resistivity values decreased accordingly. Results from other studies are presented for comparison. The apparent resistivity of porous materials increase by a factor of at least 10 when its temperature decreases progressively from + 5 to - 5 °C (Fig. 12 ). The sharp increase in resistivity between unfrozen and frozen ground is well illustrated on this figure. Indeed, the dependence of apparent resistivity on temperature is closely related to the unfrozen water content. When a porous material freezes, a gradual increase of electrical resistivity results from a progressive reduction of unfrozen water content due to falling temperature. Near the freezing point, however, the electrical behavior of frozen ground

4.3. Correlations From the numerical analysis, relations of apparent electrical resistivity with mass proportions of unfrozen water and ice, and temperature are well highlighted and will be subsequently studied in detail. The correlation between these variables can provide a cause-and-effect relation.

Apparent electrical resistivity as a function of temperature The dependence of resistivity of frozen ground on temperature has been well known for many years (Bogolyubov, 1973; Hoekstra and McNeill, 1973) and is shown in Fig. 12. For this study, each thick line gives the variation of ap-

373

R. Fortier et al. I Cold Regions Science and Technology 22 (1994) 361-384 A

oo

~0.

E

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Fig. 11. Scatterplot matrix of physicaland electrical properties of frozen ground. varies with material type. Frozen clayey material retains a substantial unfrozen water content close to 0°C (Anderson et al., 1973 ) and electrical re-

sistivity consequently increases smoothly (from 15 to 25 ~ - m between + 1 and - 1 °C). In sandy materials, all interstitial water freezes at 0°C and

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

374

1000000

Cryostructure observed on core sample: - 0.3 and 0.8 m: polyhedral cryotexture - 1.2, 1.3, 1.5, and 2.0 m: stratified cryostructure - 2.3, 2.5, 2.7 and 3.0 m: reticulate cryostructure - 3.5 and 3.9 m: massive cryostructure

100000 E" t-O

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Stratified .~ cryostructure " ~

.

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if)

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I \ ~ 2.0,

10000

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/

m

I i

Saturated sand gravel i(Hoekstra and McNeil, 1973)

1000 E

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C)..

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\

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l

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I I

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I I

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t .... L .... 0 5 Temperature (°C)

and --

--

1973)

McNeil, r-

I

10

1973)

. . . . .

....

15

Fig. 12. Fieldmeasurementof apparent electricalresistivity (Wennerarray) of active layer and permafrost as a function of groundtemperatureand cryostructure.Comparisonwith other results. electrical resistivity increases abruptly (from 1 to 5 k ~ - m for the same range of temperature). Silty soils exhibit an intermediate behavior. Variation of electrical resistivity observed in the thawed active layer at depths of 0.3 and 0.8 m is linked to wetting-drying cycles in the active layer (Fig. 12).

The effect of cryostructure on apparent electrical resistivity For a given temperature below the freezing point, significant variations of apparent electrical resistivity of the studied silty permafrost are noticed (Fig. 12 ). These variations are linked to both unfrozen water content and ground ice

cryostructures. Structural effects on the apparent electrical resistivity of frozen ground was pointed out by Bogolyubov (1973) who recognized two major types of cryostructure affecting resistivity (Fig. 12). The first group is characterized by a massive cryostructure in which interstitial ice is predominant (Fig. 10). A change of electrical resistivity values in such frozen ground is mainly due to a variation of unfrozen water content. Interstitial ice has relatively little effect on electrical resistivity because unfrozen water films are continuous in pores and interconnected passages. The second group is characterized by a stratified cryostructure where segregated ice lenses (of varying thickness) alternate

R. Fortier et al. / Cold Regions Science and Technology 22 (I 994) 361-384

with frozen soil layers (Fig. 7 ). The resistivity of such frozen ground is linked to the spacing between ice lenses, the thickness of ice lenses, and the dependence of electrical resistivity of ice on temperature (Bogolyubov, 1973). In this case, unfrozen water films are discontinuous, cut by ice lens barriers, and current flow through ice lenses is impeded since ice is a good insulator. Contrary to interstitial ice in a massive cryostructure, ice lenses in stratified cryostructure cause a resistivity increase. In silty permafrost at Umiujaq, apparent electrical resistivity can vary by a factor of 10 to 30 depending on depth of measurement and cryostructure (Fig. 12). For example, at a temperature of - 5 ° C (Fig. 12), permafrost at depths greater than 3.3 m and characterized by a massive cryostructure (Fig. 10) has lower resistivity values (about 104 f~-m) than permafrost with a reticulated or erratic cryostructure (Figs. 8 and 9) at depths between 2.2 and 3.3 m (about 10s t2-m). Frozen ground with a stratified cryostructure (Fig. 7 ) between 1.1 and 2.2 m in depth has an intermediate value (about 5 × 104 t2-m). The reticulated cryostructure obstructs the current flow in all directions while the stratified one only blocks the current flow perpendicular to the ice lenses. Hence, resistivity of layered ice is lower than one of reticulated cryostructure. For tern-

375

peratures between - 2 and - 7 oC (Fig. 12 ), the electrical resistivity gradients with temperature (the slopes of curves) are quite similar independent of cryostructure, ice content or depth of measurement because the variation of unfrozen water content with temperature is the same for the whole conditions.

Unfrozen water and ice contents as functions of apparent electrical resistivity Correlations of the mass proportions of unfrozen water and ice with apparent resistivity for the three arrays are illustrated on Fig. 13. Circles and squares represent the mass proportions of unfrozen water and ice respectively. The error estimates of mass proportion determination with the calorimetric method are given by an I-shaped symbol for each value. The curves represent nonlinear regressions between physical properties and electrical resistivities of the silty frozen ground at Umiujaq. The results of non-linear regression are explicitly given in Table 1 and are valid only for the specific intervals of apparent resistivity indicated below: 200 f~-m
Table 1 Non-linear regressions between physical and electrical properties Relation

Y= aX b

Variables

Y= Muw

Constants

a

b

r

a

b

r

a

b

r

X=pw

31.497

-0.285

0.708 (0.365)

22.574

-0.203

0.586

11.163

- 15.911

0.620

10.476

-0.154

0.648 (0.385)

10.286

-0.108

0.578

7.209

0.053

0.579

6.479

-0.123

0.822 (0.430)

5.287

-0.048

0.826

9.915

-3.808

0.721

Y= alogmX+ b

Y= Wu~

n=49

X=p~ n=44

X=~o n=35

Y= Mi

Values in parentheses are the critical values of correlation coefficient r at the 1% level of significance for the number of degrees of freedom v considered (v = n - 2 ; n is the number of observations). The null hypothesis is rejected when the correlation coefficient is larger than the critical value, in which case the correlation is significant.

376

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

70

v

.o_

[

t

I

70

60A

60

I

I

I

B

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~:

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o

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30-

-'I O ¢--

0 t-"

20

.o_ 1= O

£

20

.£ oo

er

oQ..

10

m

0

Unfrozen water

£

ta (/}

(Wenner array, a=0.10 m) -10 , , , 100 1000 10000 100000 1000000

(double-dipole array, a=0.10 m, n=4) -10 , ~ , 100 1000 10000 100000 10( 0000

Apparent electrical resistivity (Ohm-m

Apparent electrical resistivity (Ohm-m)

I

70

v(l)

60

r

I

C

._o

50 ~

c'-

40

N

~e-tO

o 9

30 20 10

S!enwaer

c~

(n

0 (lateral dipole array, a=0.10 m) I I I -10 100 1000 10000 100000 1000000 Apparent electrical resistivity (Ohm-m)

Fig. 13. Correlations between mass proportion of unfrozen water or ice and apparent electrical resistivity for three different arrays. (A) Wenner, (B) double-dipole, (C) lateral dipole.

R. Fortier et aL I Cold Regions Science and Technology 22 (I 994) 361-384 ,

100

I

,

metric tests and the soil porosity was evaluated by adding the densities of each constituent parts of the samples. Due to the presence of few air voids in some samples, the estimation of porosity could be erroneous, therefore affecting the quality of the correlations. However the correlation trends are obvious despite the scattering of data points. Fig. 14 shows the distribution range of mass proportion of unfrozen water (A) or ice (B) in the silty permafrost as a function of apparent electrical resistivity (Wenner) and temperature. The circles and squares indicate the intersection of temperature and apparent electrical resistivity where values of mass proportion of unfrozen water and ice respectively are available. These graphs characterize the distribution range of physical properties of silty permafrost with two geophysical parameters. For example, for a resistivity of l03 D-m and a temperature of - 1°C, the mass proportions of unfrozen water and ice are 4.8 (Fig. 14A) and 12% (Fig. 14B) respectively. However, a resistivity of l05 D-m and a temperature of - l °C cannot define unfrozen water and ice contents. Intersection of these values extends beyond the distribution range of the mass proportions of unfrozen water and ice for the material. In addition, a combination of two variables can provide a third. For instance, a temperature of - 3 oC and a mass proportion of unfrozen water of 1% yield a resistivity value of 105 D-m (Fig. I4A) and an ice content of about 42% (Fig. 14B).

,

'

A,

E tO

1ooo

-

-

, ~ - %,-

2

o-2T.-~

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o ~=~

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_

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,--

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J

I

Mass proportion of unfrozen water ()% I i I I "" -5 -4 -3 -2 -1 Temperature (°C)

100

g

E e,-

o

I

I

I

P

' ~

I

r

I

~/D

I

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._> 10000 .-

e-

~

100000

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I

1000000

Mass proportionof ice (~/o) -5

-4

I

i

-3 -2 -1 Temperature (°C)

377

0

Fig. 14. Distribution range of mass proportion of unfrozen water (A) or ice (B) as a function of apparent electrical resistivity (Wenner array) and ground temperature.

The large scattering of mass proportions of unfrozen water and ice around the regression curves and the low correlation coefficients are linked to the effect of cryostructure on electrical resistivity, the accuracy of calorimetric method, and some other undetermined parameters such as salinity which was not measured. Moreover, only the mass of sample was measured for the calori-

4.4. Estimation of u n frozen water and ice content variation with apparent electrical resistivity Typical contour lines s h o w i n g the temperature variation as a function of depth below ground surface and time are drawn in Fig. 15 for Site 1. These contour lines were drawn from daily measurement of ground temperature. Air temperature variation is also plotted on this figure. The thawing front position at 0 °C is underlined by a thick contour line (Fig. 15). The 1990 thawing period began on May 18. The thawing front in the active layer progressed rapidly dur-

378

=.?,

R. Fortier et al. / CoM Regions Science and Technology 22 (1994) 361-384

20 10 0 0.0

?-

<

0.5 1.0 1.5

v

E

.E I1) El

2.0 2.5 3.0 3.5 4.0 30/04

20/05 Time

09/06

29/06

(dd/mm/90)

Fig. 15. Ground temperature distribution as a function of depth and time.

ing the first 12 days and reached a depth of 0.4 m on May 30. Its progression then slowed to about 1.3 cm per day. At the end of the study period (July 9), the thawing front at a depth of 1.0 m had not yet reached its maximum depth as the permafrost table is about 1.1 m deep. Heat wave penetration in permafrost during the study period was dearly perceptible through a temperature increase. For instance, at a depth of 3 m, the temperature warming was about 4°C (from - 7 to - 3 ° C ) over 70 days (from May 30 to July 9). Variations of apparent resistivity, mass proportion of unfrozen water, unfrozen water content and mass proportion of ice as a function of depth and time are given for the three arrays in Figs. 16 (Wenner), 17 (double-dipole), and 18 (lateral dipole) at Site 1. Non-linear regressions used to make the evaluations appear in Table 1. The contour lines were drawn from daily (Wenher array) or weekly (double-dipole and lateral dipole arrays) measurements of apparent resis-

tivity logging and from calculated physical properties of frozen ground. For the double-dipole array (Fig. 17A), the spacing L between dipoles was kept constant (n = 4, L = 60 cm). In the graphs of apparent resistivity (Figs. 16A, 17A, and 18A), the thawing front position is underlined by a thick contour line. An electrical resistivity value of 400 f~-m for logs using the Wenner array defines roughly the thawing front position in the active layer. This value characterizes the boundary between unfrozen and frozen silts. The boundary was established from the comparison between the temperature profile (Fig. 15) and the apparent resistivity logging (Fig. 16A). Boundary values, for logs with double-dipole and lateral dipole arrays, are about 160 and 250 fl-m respectively. These boundary values are valid for the other sites in similar material. In the active layer, above a depth of 1 m, apparent resistivity decreased by a factor of 10 or more during the study period (Figs. 16A, 17A, and 18A). This reduction is due to phase composition change. The active layer-permafrost interface at a depth of about 1.1 m is well delineated by a sharp increase in electrical resistivity highlighted by a densification of contour lines. In permafrost, at a depth of 3 m for instance, temperature warming from - 7 to - 3 ° C during the study period produced a decrease in apparent resistivity from 9 × 104 to 6 × 104 fl-m (Fig. 16A). This decrease is due to an increasing in unfrozen water content. At depths greater than 3 m, apparent resistivity stayed approximately stable. A layer of high apparent resistivity between 2.0 and 3.0 m (Figs. 16A and 17A) is correlated with both a high ice content and a reticulated cryostructure. In this layer, apparent electrical resistivity logging with the double-dipole array has higher values (about 4X l0 s f~-m, Fig. 17A) than logging with the Wenner array (about l0 s fl-m, Fig. 16A). The former array integrated a larger volume of soil than the latter because the radial depth of investigation is larger ( 15 cm versus 5.1 cm, see Eqs. 1 and 2). The disturbed zone around the electric cable, created by freeze-up of filling mud in the drill hole, had a radius of 7.5 era. After a fast refreeze, the cryostructure of the frozen

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

_~

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30/04

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.

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T i m e (dd/mm/90) 2

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20/05

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30/04

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Mass propo~ion of ice (Vo)

30/04

20/05

I ,

09/06

~ ,,~

29/06

Time (dd/mm/90)

Fig. 16. Apparent electrical resistivity (A), calculated mass proportion of unfrozen water (B) or ice (D), and calculated unfrozen water content (C) of frozen ground as a function of depth and time ( Wenner array, a = 0.1 m).

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

380

:3 ~

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.0

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Mal propo?ion of unfrozen water ( '/o! Mass 4.0 30/04 20/05 09/06 29/06

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o.o <

r

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.m

/

I~

E

v

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~

3

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3.5 Mass ]propo/ion 2 8 ~ t ~ ~ 4.0 30/04 20•05 09•06 29•06 I

1

I

I

I

I

1

Time (dd/mm/90)

Fig. 17. Apparent electrical resistivity (A), calculated mass proportion of unfrozen water (B) or ice (D), and calculated un frozen water content ( C ) of frozen ground as a function of depth and time (double-dipole array, a = 0.1 m, n = 4 ).

R. Fortier et al. / Cold Regions Science and Technology 22 (I 994) 361-384

381

m 20

® <

Site '1

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~.~ 2o lo

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i I i <:~-'~_( j Apparent electrical resisti~ty~Ohm-m), ..~

4.0 30/04

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09/06

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09/06

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i

i

Unfrozen water content (%)

30/04

1.5 v

~"---r---

pof_~

0.5

1

i

09/06

Time (dd/mrn/90)

I

i

29/06

4.0 30/04

20/05

09/06

29/06

Time (dd/mm/90)

Fig. 18. Apparent electrical resistivity (A), calculated mass proportion of unfrozen water (B) or ice (D), and calculated unfrozen water content (C) of frozen ground as a function of depth and time (lateral dipole array, a-- 0.1 m).

382

R. Fortier et aL / Cold Regions Science and Technology 22 (1994) 361-384

filling mud was massive. Resistivity of frozen mud was lower than those of undisturbed permafrost. The double-dipole array is therefore more representative of the undisturbed permafrost resistivity. Apparent electrical resistivity logging in the lateral-dipole array showed lower values in this layer (about 4 X 104 f~-m, Fig. 18A ) than the two other arrays. In the lateral dipole array, current flow close to the potential dipole is parallel to the ice layers and induces lower resistivity. The active layer-permafrost interface is characterized by a decrease of 2% for the mass proportion of unfrozen water over a 0.25 m interval (from I to 1.25 m). In the upper permafrost section, the mass proportion of unfrozen water increased less than 0.5% with time and remained stable at depths greater than 3.0 m, as was the case for the apparent electrical resistivity. The unfrozen water content (Figs. 16C, 17C, and 18C), a more appropriate definition than the mass proportion of unfrozen water from the geotechnical engineering point of view, shows similar trends with the permafrost warming. Values of mass proportion of ice of 14% (Fig. 16D), 16% (Fig. 17D), and 20% (Fig. 18D) approximate the thawing front position at Site 1. These values delimit a sharp increase in ice content in a short gradient between unfrozen and frozen layers. The active layer-permafrost interface is well indicated by an increase in mass proportion of ice by 10% from 24 to 34%. During the study period, at a depth of 2.5 m, the ice content decreased by 2% (Fig. 16D and Fig. 17D ) or 4% (Fig. 18D). Consequently, the ice content reduction appears to be higher than the unfrozen water content increase. The effect of cryostructure on apparent electrical resistivity increases the gradient between mass proportion of ice and electrical resistivity. This increase produced an overestimation of the ice content variation with time from the variation of electrical resistivity. The indirect relation between ice content and apparent electrical resistivity is linked to the direct relation between thickness of the adsorbed water film around soil grains (mass proportion of unfrozen water) and space occuped by ice in soil pores (mass proportion of ice). As a result,

Pearson's correlation coefficient between mass proportions of unfrozen water and ice is relatively high and equal to -0.608 (Fig. 11 ). Thus, the estimation of mass proportion of unfrozen water with apparent electrical resistivity is probably more realistic than the estimation of mass proportion of ice.

5. Conclusion Long-term measurements of the variation of temperature and apparent resistivity with time using thermoelectric cables can be useful for monitoring natural climatic variation or humaninduced disturbance on permafrost. It appears from this study that unfrozen water content, and its corresponding ice content, best correlate with the apparent resistivity in permafrost in frozen silts. Numerical analysis highlights the relationship between permafrost conditions and electrical resistivity. This offers the possibility of estimating the time variation of unfrozen water content in fine-grained permafrost by using electrical resistivity measurements. This methodology can eventually be used for evaluating the impact on permafrost of infrastructure construction such as buildings, roads or airfields.

Acknowledgments The authors would like to express their sincere thanks to the Inuit community of Umiujaq for their hospitality and friendly support. We gratefully acknowledge the Centre d'~tudes nordiques of Universit~ Laval for its logistical support, and Energy, Mines and Resources Canada for the loan of an all-terrain vehicle and a CRREL coring auger kit. Thanks are also due to Jocelyn Lauzon for his help in the field and to Jean Pilon from the Geological Survey of Canada for his logistical support. The comments of Dr. P. Sellmann and Dr. A.K. Sinha, the journal's reviewers, were very helpful for improving the paper. The research was supported by the grants from the National Sciences and Engineering Research Council of Canada (NSERC), the Quebec "Fonds

R. Fortier et al. / Cold Regions Science and Technology 22 (1994) 361-384

pour la Formation de Chercheurs et l'Aide/t la Recherche" (Fonds FCAR), and the Indian and Northern Affairs Canada.

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