Effect of Mixed Na-Ca Solutions on the Hydraulic Properties of Unsaturated Soils1

DAVID Russo AND ESHEL BRESLER2

ABSTRACTThe effects of mixed Na-Ca solutions on soil water diffusivity and

unsaturated hydraulic conductivity were tested for a loamy soil fromGilat, Israel. Soil water diffusivity functions, D(ff), were determinedby the horizontal infiltration method. Unsaturated hydraulic conduc-tivity functions, K(ff), were determined both directly (by vertical infil-tration for suction heads of 0-50 cm H2O) and indirectly (from dif-fusivity functions and soil water retention curves). Prior todeterminations, soil samples were equilibrated with solutions contain-ing a given concentration and composition of Ca and Na. The resultsshow that D(ff) and K(0) are independent of solution concentrations ina Ca-saturated system. In mixed Na-Ca systems, hydraulic conduc-tivity and soil water diffusivity functions are highly dependent on thecomposition and concentration of the soil solution, in addition to theirdependence on soil water content, 0. For any given 0, both K(0) andD(0) decrease as either soil solution concentration decreases or the so-dium fraction in the soil solution increases. The negative effect of acombination of high Na-to-Ca ratio and low soil solution concentrationon K(ff) is directly related to the degree of water saturation of the soil.Low values of 0 can compensate for the negative effects of high Na-to-Ca ratio and low solution concentration.

Additional Index Words: Unsaturated hydraulic conductivity, soilwater diffusivity, soil-water retentivity, exchangeable Na percentage(ESP), soil solution concentration, diffuse layer theory.

A SHORTAGE of rain and water resources exists in aridand semiarid zones, necessitating the common use of

marginal waters for irrigation. Such water may containlarge quantities of soluble salts, predominantly Ca and Naions. Considerable effort has been directed toward the studyof the effect of concentration and composition of solublesalts upon transport of water and solutes in soil (e.g., Quirkand Schofield, 1955; Emerson, 1963; McNeal and Cole-man, 1966; El Swaify and Swindale, 1968; Rowell et al.,1969; Shainberg and Caiserman, 1971). Most investigationswere limited to steady-state, saturated, flow conditions al-though, in the field, transport of solutes and water takesplace under transient, unsaturated flow conditions. Solu-tions of unsaturated, nonsteady flow problems require theknowledge of the hydraulic properties of the soil whichincludes the functional relationships between soil water suc-tion (h), soil water content (6), and hydraulic conductivity(K), or soil water diffusivity (D). This information is ratherlimited.

Effects of exchangeable sodium percentage (ESP) andelectrolyte concentration on soil water diffusivity functionD(6) was studied by Gardner et al. (1959). They found that,in soils with ESP < 15, the weighted mean soil water dif-fusivity was slightly increased as the solution concentration

'Contribution from the Agricultural Research Organization, The Vol-cani Center, Bet Dagan, Israel. 1976 Ser. no. 221-E. This research wassupported by a grant from the United States-Israel Binational ScienceFoundation (BSF), Jerusalem, Israel. Received 9 Sept. 1976. Approved 30March 1977.

2Research Assistant and Soil Physicist, Div. of Soil Physics, ARO, BetDagan, respectively E. Bresler is also Associate Professor of Irrigation,The Hebrew Univ. of Jerusalem, Faculty of Agriculture, Rehovot, Israel.

was raised from 0.002A7 to 0.10(W, whereas soils high inexchangeable Na (ESP > 25) had diffusivities which wereincreased by three orders of magnitude over the same con-centration range. Most of the effects took place within therange of soil water contents near saturation. Christensonand Ferguson (1966) studied the effect of ESP, electrolyteconcentration, and type of the dominating clay mineral onthe soil water diffusivity and found that changes of dif-fusivity with ESP and CaCl2 concentration were larger in amontmorillonitic soil than in a kaolinitic soil. Scotter andLoveday (1966) found that, for a given water suction, theporosity available for solution flow increased as the concen-tration of solutes in the irrigation water rose. Kutilek (1974)found for a montmorillonitic soil that, for any given watersuction, soil water diffusivity and hydraulic conductivity ofthe soil were lower for an ESP of 27.5 than for Ca-saturatedsoil. The difference between the K(0) functions was gener-ally observed within the range of soil water suctions be-tween 0 and 800 cm H2O.

This paper presents the results of an investigation on theeffects of composition and concentration of Na and Ca ionsin the soil solution on the h(0), D(6), and K(ff) functions.These functional relationships were determined over a widerange of water contents, soil solution concentrations, andNa/(Ca)1/2 ratios for Gilat loam soil.

MATERIALS AND METHODSPreparation of Soil Columns

Samples of the loam soil from Gilat, Israel (20% clay, 48%sand) were equilibrated with solutions containing a given composi-tion of Na and Ca ions. Soil samples used for the equilibratingprocess were first leached with I/V solution and containing anamount of Na+ -I- Ca2+ equivalent to 50 times the cation exchangecapacity (CEC) of the soil sample and with a given equivalent cat-ionic ratio R = Na/(Ca)1/2, where Na and Ca concentrations are inmeq/liter. Each soil sample was then leached with a series of grad-ually decreasing solution concentrations which contained the cor-responding Na-to-(Ca)1'2 ratio. When the electrical conductivity ofthe effluent reached a value equivalent to that of 0.01/V (which wasidentical to the lowest influent concentration), the inflow solutionwas replaced by a salt-free aqueous solution of 70% ethanol.When a steady low effluent concentration (corresponding to anelectrical conductivity of about 20 jumhos/cm) was obtained, thesoil sample was air dried for 5 days in equilibrium with 75%± 5%relative humidity at a temperature of 22 ± 1°C. At the end of theabove-mentioned procedure, the soil sample was free of excesssoluble salts and had an exchangeable sodium percentage (ESP) inapproximate equilibrium with the cationic ratio, R, used to equili-brate the appropriate soil sample. It was found that, approxi-mately, ESP = 100[0.0127fl/(l + 0.0127 /?)]. The dry soil wasthen passed through a 2-mm sieve and packed into lucite cylinders[35-cm length, 5-cm inside diameter (ID)] or cylindrical brasspressure cells (3-cm length, 5.5-cm ID) as uniformly as possible,to an average bulk density of 1.40 g/cm3. The packing method ofYaron et al. (1966) was used.

Determination of Soil Water Parametersa) Estimation of Soil Water Diffusivity Function D(0)—The dif-

fusivity functions D(0) were determined according to the methodsuggested by Bruce and Klute (1956) from the relationship

713

714 SOIL SCI. SOC. AM. J . , VOL. 41, 1977

10'.20 .30 .40

VOLUMETRIC WATER CONTENT, 0(cm3/cm3)Fig. 1—Soil water suction head (h) as a function of volumetric water

content (0) and solution concentration (C), for three cationic ratios(R). Note that the point h = 10 cm (indicated by the arrows) isshifted and the data are translated along the h-axis.

.040-

1 2 5 10 20 5 0SOLUTION CONCENTRATION, C(MEO/L)

Fig. 2—Hydraulic conductivity (K) as a function of the solution con-centration (C) for three values of soil water suction heads (h) andseven values of cationic ratio (R).

D ( f l ) = l / 2 — \(9)d6 [1]

with numerical evaluation of the integral and the derivative, andwith X = xl(t)'1*, where x is distance, t is time, and 00 is air-drywater content. For each combination of/? = 0, 10, 15, 20, 25, 50,and oo, and of C = 0.002, 0.005, 0.010, 0.020, and 0.0507V, aunique D(B) function was obtained.

b) Estimation of the Hydraulic Conductivity Function K(9) atHigh Water Contents—Hydraulic conductivity measurements atrelatively high water contents (i.e., suction heads lower than50-cm H2O) were performed using the method suggested byYoungs (1964), by recording the distance to the wetting front aswell as the cumulative amount of solution (of given R and C) en-tering a vertical column. Values of saturated hydraulic conduc-tivity (h=Q) and of hydraulic conductivity corresponding to h = 25and h=50 cm H2O were determined for each of the above combi-nations of/? and C values. The porous plate separating the soil col-umn from the solution was a brass perforated disc with holes ofabout 1 mm in diameter, or a sintered polyethylene plate with anair entry value of about 70 cm H2O, for saturated and unsaturatedsoil, respectively.

c) Estimation of K(6) at Low Water Contents—At low watercontents (i.e., h > 50-cm H2O), direct measurements of thehydraulic conductivity function K(ff) are no more reproduciblethan the method for determination of D(ff) and the relationship be-tween soil water content and water suction [h(0)]. Thus, we preferto estimate K(0) indirectly in this range from the soil water dif-fusivity function D(0), and from the function h(ff) obtained underwetting conditions.

The functional relationship between h and 0 for the range 0.01< h < 1.0 bar was obtained by a pressure cell technique similar tothat of Reginato and Van Bavel (1962), as described in a previouspaper (Russo and Bresler, 1977). The function h(6) was obtained

for each combination ofR = 0, 20, and 50, and C = 0.002, 0.005,0.010, and 0.050/V.

The h(6) curves used to calculate the hydraulic conductivityfunction K(ft) for each R-C combination are given in Fig. 1. In-terpolation was used to estimate h(9), for those combinations of Rand C which are missing in Fig. 1. The resultant K(ff) functions atwater contents below 0.38 were obtained from calculation of K(ff)= D(6/(dh/d0).

RESULTS

Hydraulic Conductivity at High Water Contents

The functional relationships between the hydraulic con-ductivity, K, equilibrium solution concentration (C =0.002, 0.005, 0.010, 0.020, and 0.050/V), Na-to-(Ca)1'2ratio (R = 0, 10, 15, 20, 25, 50, andoo), and soil water suc-tion head, h, are given on a semilog scale in Fig. 2, wherethe lines represent a visual fit between the measured points.In general, for each of the K(C) curves in Fig. 2 there is arange of concentrations in which the hydraulic conductivityincreases with C, and another range in which the hydraulicconductivity is practically independent of the solution con-centration. The value of C between these two ranges in-creases with both h and R. It is also seen in Fig. 2, that theslope dK/dC decreases as h increases, but does not changewith R.

The data given in Fig. 2 do not agree with the results of J.D. Oster and J. Wesseling (1972)3 and of Kutilek (1974).

3J. D. Oster, and J. Wesseling. 1972. Unsaturated hydraulic conduc-tivity and water retentivity of undisturbed soil cores as affected by soilsolution composition. Agron. Abstr. p. 76.

RUSSO & BRESLER: EFFECT OF Na-ca SOLUTIONS ON HYDRAULIC PROPERTIES 715

10

10

-,«o

10"'

10"

§10-

10

0.0 0.20 0.40VOLUMETRIC WATER CONTENT, 6 ( c m 3 / c m 3 )

Fig. 3 — Soil water diffusivity (DJ as a function of volumetric water content (0) and solution concentration (C), for seven cationic ratios (R). Note thatthe point 9 = 0.0 (indicated by the arrows) is progressively shifted and the data are translated along the 0-axis.

They found that the effect of soil solution composition andconcentration on the hydraulic conductivity is generally in-dependent of the soil water suction for ranges of soil suctionof 0 to 240 (Oster and Wesseling, 1972) and 0 to 800 cmH2O (Kutilek, 1974).

Soil Water DiffusivityBruce and Klute (1956) pointed out that the propor-

tionality constant, X = x/(t)>l2 (Eq. [1]) is necessary forcalculation of the soil water diffusivity from measuredwater content—distance profiles developed in semiinfinitehorizontal columns. The proportional relationship betweenx and (t)'12 was maintained throughout our study for all theexperimental range of R and C. It was found that X increasesas R becomes smaller and as C becomes larger. Based onpublished data of Reichardt et al. (1972), Miller and Bresler(1977) showed that the function D(0) for a so-called"stable" soil is directly related to X and can be approxi-mately expressed as:

0(0) = 1.04 x 10-3X2 exp [8.06[(0 - 00)/(0i - 0o)]} [2]

where 00 and 6l are the air dry and "saturated" water con-tents, respectively.

Calculations of D(6) for various combinations of R andC, using our experimental values of XfC,/?), 00(C,R), and9i(C,R) from Eq. [2] showed that the agreement betweenthe calculated and the measured D(6) functions is relativelygood for all values of C in which 7? < 10, and for combina-tions of/? and C which are: (R = 15, C > 0.0057V), (R =20, C > 0.01AO, (R = 25, C = 0.02N), and (R > 50, C >0.05N). It seems that as long as the soil does not undergosignificant and progressive changes in pore structure, Eq.[2] is a good approximation to the D(ff) functions. If oneuses the agreement between calculated (Eq. [2]) and mea-sured D(ff) as a first-order estimate to soil "stability", thenGilat soil may be considered as a "stable" soil as long as Rand C are within the aforementioned range.

The quantitative relationships between D(ff), Na-Ca com-position (R), and concentration (C) of the equilibrium solu-tion are given in Fig. 3. The solid lines represent the visual

fit between the measured points. To facilitate the compari-son, the abscissa scale is shifted to the right and the data areaccordingly translated along the 0-axis to distinguish be-tween the different sets of concentrations. In general, eachof the D(ff) curves can be represented by a single continuouscurve. When the solution concentration exceeds 0.050N, asingle-valued D(ff) function is obtained for any value of 10< R < 50. The same is seen for R = 0 and 0.002 < C <0.050N. For a given water content, 6 (from air dry to satu-ration), values of D(Q) become smaller asR increases and asC decreases. The differences between various D(6,C,R)functions become smaller as C increases and as 6 and Rdecrease. The experimental data in Fig. 3 are in qualitativeagreement with the data of Gardner et al. (1959) and ofChristenson and Ferguson (1966), in spite of the differencesin mineralogical and mechanical compositions of the dif-ferent soils.

The Complete K(8) FunctionThe functional relationships between K(Q) and the Na-Ca

composition (R) and concentration (C) are given in Fig. 4.

0 .10 .20 .30 .40 .50VOLUMETRIC WATER CONTENT, 0 (cm 3 / cm 3 )

Fig. 4—Hydraulic conductivity (K) as a function of volumetric watercontent (0) and solution concentration (C) for seven cationic ratios(R). Note that the point 0 = 0.0 is shifted, as indicated by the ar-rows.

716 SOIL SCI. SOC. AM. J . , VOL. 41, 1977

Table 1—Maximum values of R (i.e., Rmax) required to maintaintf*>0.50 for various values of C and O.

20 30 40 50 10CATIONIC RATIO, R in (MEQ/L)"

Fig. 5—Relative hydraulic conductivity K* = K(R,C, Q)/KCz(6) as afunction of cationic ratio (K) and the solution concentration (C), forsix values of reduced water contents, © = (0—00)/(Os—00). Notethat Afca (O) = K (B,R=0, C =0.05(W).

Here, again, the solid lines represent the best visual fit be-tween the measured and calculated points. Once again, theabscissa scale has been shifted to the right and the data areaccordingly translated along the 0-axis to distinguish be-tween different sets of concentrations.

In general, each of the K(B) functions can be representedby a single continuous curve. Furthermore, for the calcium-saturated system (R = 0 and 0.002 < C < 0.050AO, asingle-valued K(ff) is obtained. In the mixed Na-Ca system,however, values of K decrease with both 0 and C for a givencationic ratio, R. The differences between the various func-tions increases as 6 becomes larger and as C becomessmaller. These differences are pronounced when R and 9 aregreater than 15 and 0.25, respectively, and when C is equalto or less than 0 .0 ION.

To express the combined effects of 6, R, and C on soilhydraulic conductivity, relative to a condition in which thehydraulic conductivity can be considered a unique functionof water content, let us define

= K(R,C, Q)/KCa(Q) [3]

where KCa (9) is the hydraulic conductivity function of asoil in equilibrium with 0.05W CaCl2, and 0 = (0 - 00)I(0S— 60), with &0 and Bs being the air dry and the saturatedwater contents, respectively. The K* (R) functions are givenin Fig. 5 for selected 0 and C values. The value of R (i.e.,/?max) above which K* decreases is larger as C rises and as 9decreases. These tendencies for K* > 0.5 are clear in Table1. Here, again, low values of soil water content compensatefor the negative effects of high ^? and low C on hydraulicconductivity.

content, 0

1.00.80.60.40.2

Concentration (C)0.002JV

10.011.012.113.514.3

O.OQSN

11.313.014.315.117.2

O.OlOAr

12.414.020.022.023.0

0.020JV

14.015.635.043.045.0

0.050AT

15.818.350.<50.<50.<

DISCUSSIONThe experimental results given in Fig. 1 through 5 show

that an increase in the Na to Ca ratio (R) and a decrease insoil solution concentration (C) greatly affect soil water dif-fusivity, D(d), soil hydraulic conductivity, K(ff), and soilwater-suction relationships, h(6). These effects becomesmaller as soil water content decreases. Although thesefindings are partly in contrast with data of Oster and Wes-seling (1972) and Kutilek (1974), they can be explained inthe light of the nature of soil as an electrically chargedporous material.

The unsaturated hydraulic conductivity function K(ff)depends upon the size distribution of water-filled pores andthe total water-filled porosity (cf. e.g. equation [5.10.7] ofBear, 1972). The double-layer theory in mixed electrolytessystem (Bresler, 1972) predicts that for a given pore watersuction, the space between clay platelets increases as thevalue of R increases and as C decreases. This, in turn,results in an increase in the amount of water retained by theclay as the pore water suction decreases. For a constant-volume system, changes in the volume of the clay mass areat the expense of the quantity and distribution of the soilpores. Thus, at a given pore water suction, the amount ofwater retained by the soil increases (Fig. 1) and the hydrau-lic conductivity decreases (Fig. 4) as R becomes larger andsolution concentration is more diluted. Since the swelling ofclay decreases as the pore water suction increases, theincrease in amount of water retained and the decrease inhydraulic conductivity become smaller as the soil-watersuction increases. In addition, increasing soil-water suctionmay reduce the movement of clay particles and hence theblocking of pore space available for water flow.

Combinations of concentration, composition, and soilwater content which permit a specified reduction in thehydraulic conductivity of Gilat loam soil are given in Fig. 6.The reduced variable, R*, is defined by R* = RQK*, whereR, Q, and K* are as previously defined. The informationgiven in Fig. 6 covers the ranges of 6, C, and R valueswhich are important from a practical point of view. The fig-ure enables one to estimate the value of threshold R (i.e.,R max) in the soil solution at which a given prescribed K* ismaintained for given values of R, C, and G. For example: insaturated soil 9 = 1 and therefore R = R*, and if we take C= 0.02/V (which is common to irrigated field soil) then it ispossible to maintain K* > 0.5 as long as R = R* < 14(equivalent to ESP < 15 in our soil). It is clear that when Ris greater than 14, the soil solution concentration mustexceed 0.02jY to maintain the same value of A"*. However,under the same conditions, but in unsaturated soil, the valueof R can be higher to maintain the same K*. For example,for C = 0.020N and K* > 0.5, the corresponding value of

RUSSO & BRESLER: EFFECT OF Na-Ca SOLUTIONS ON HYDRAULIC PROPERTIES 111

~_ ! ! ' ~ that for practical purposes a maximum permissible value ofT ESP = 15 may be generally applicable for Gilat loam soil as

j!i I long as the soil solution concentration exceeds 0 .0 IN.^ K"».75 JK"»50 K**&''' Maintaining the soil surface under unsaturated conditions| 40- J' '/' - permits a higher ratio of Na to Ca for any given soil solutiono I ,' concentration. The extent to which this ratio can be in-g" ' ' creased depends upon the degree of water saturation of the§ J I / soil. The data of Fig. 6 suggest that the properties of the soilt; 30 ~ | I f ~ solution alone are not sufficient to enable characterization ofB | I / the relative hydraulic conductivities of different soils.§ / /'| 20- * f / ^3 / ' / ^^V> Doneen / / ' ^^f K«S.85 // / l^\D .ft. i nn / / / ^^ *- | Q_o i.yu /i i, ^£ Quirk and Schofield

3 y 'JrS K*s-853 /Jr<L / S'1-00kl ,x^ _^^/ / /

^jt^^So ̂ ^£~.<--+^_____i______i___0 10 20 30

REDUCED CATIONIC RATIO, R* in (MEQ/L)"2

Fig. 6 — Combinations of solution concentration (C), cationic ratio(« = R*/QK*) and reduced water content (&), at which 25%,50%, and 75% reduction in relative hydraulic conductivity,K* = K(R,C,Q)/KCa (9), occurs. (KCa(B) = K(Q, R=O,C =0.050 W)).

R* (see Fig. 6) is 14. Taking 9 = 0.5 then R = R*/QK* =14/(0.5)'/2 = 20 rather than 14 in the saturated soil. Thus,water of poorer quality can be applied when unsaturatedconditions are maintained during irrigation than when soilsurface is saturated while infiltration takes place.

We also include in Fig. 6 data of Doneen (Lunt, 1963)which are based on the relative effect of various irrigationwaters applied to montmorillonitic Yolo soil and data ofQuirk and Schofield (1955) for a threshold (15%) reductionin hydraulic conductivity on the illitic Sawyers soil. As isevident from Fig. 6, a considerable discrepancy exists be-tween the data of these two groups of workers which maystem from the differences in mineralogical and mechanicalcompositions between the two soils. The discrepancy be-tween our curves and those of these other workers may stemfrom the same reasons. The more optimistic picture ofQuirk and Schofield (1955) as compared with ours mayreflect the more stable nature of their illitic soil. The exag-geration of the adverse effects of high R for C < O.OW inDoneen's curve probably reflects, as indicated by McNealand Coleman (1966), "the fact that he selected the Na per-centage of the solution rather than the SAR, as a salt com-position parameter. The former is a relatively insensitiveindex of Na hazard in the concentration range where mostsalt-associated hydraulic conductivity decreases occur."

CONCLUSIONSThe experimental data presented here can be explained

qualitatively by soil-water-clay interactions and by theporous nature of the soil. The experimental results show