Comparison of Hydraulic Conductivity Estimation using Falling Head and Mini Disk Infiltrometer in Gypsiferous Soil

Hydraulic conductivity (K) was calculated using falling head (FH) and Mini Disk Infiltrometer (MDI) for 15 Gypsiferous soil. In this study the hydraulic conductivity was predicted by basic infiltration rate (BIR) and using two methods, Wooding-Gardner (W-G) and van Genuchten-Zhang (V-Z). Hydraulic conductivity was measured using a falling head permeability test, and the results were compared to the expected values. A statistical analysis (t-test) was performed to show the significant differences between the two methods and the falling head. The results showed high agreement between (K) values estimated by (FH) and (BIR) for different gypsum content, the results showed that Both methods did not succeed in estimating the hydraulic conductivity for different gypsum content. Values derived from (W-G) method are exaggerated and the values derived from the (V-Z) method are very low compared to the values derived from (FH).


Introduction
The ability of soil to convey water is measured by a property called hydraulic conductivity (K).For a given area and time period, this constant is typically indicated when the soil is saturated.It plays a crucial role in numerous geotechnical, environmental, and agricultural uses.When it rains, water either runs off the soil's surface into nearby bodies of water or soaks into the ground below.It is ecologically significant for predicting flood damage.In addition to predicting runoff in channels and streams, these measures shed light on the efficacy of irrigation, infiltration rates, and vegetation.The rate at which groundwater can percolate into drainage lines below the water table is determined by the saturated water conductivity [1].There is always a discrepancy between laboratory data and outdoor measurements.Since field measurements are taken in more realistic settings, they are more likely to be accurate than those made in a lab [2,3].Measurements of (K) made using the falling head permeability method are generally accepted as representative of the saturated hydraulic conductivity of the soil.The Mini Disc Infiltrometer (MDI) is one of the often-employed tools for in-situ measuring hydraulic conductivity [4].The testing gear is portable and quite simple to put together and use for the field test.The sampled depth is relatively shallow and only a tiny region is measured by this method due to the mechanical restrictions of the disc size.It is mostly used to gauge the soil's surface layer's hydraulic characteristics.While certain instruments (such double ring permeameters) can only measure flow in 1259 (2023) 012017 IOP Publishing doi:10.1088/1755-1315/1259/1/012017 2 ponded or saturated conditions, MDI can measure the soil's unsaturated hydraulic conductivity.Unsaturated hydraulic conductivity is a better indicator of true soil properties in connected macroporous soils with predominately favored flow.In order to measure the unsaturated hydraulic conductivity, a negative potential (Suction) must be applied to the soil's surface.Since macropores are not a part of the flow process, this just gauges the flow in the soil matrix [3,5].Despite their flaws, MDI have been demonstrated to be quite effective at determining the hydraulic properties of soil in the field, particularly because they are quicker and easier to use than other techniques [6].
A number of studies have used MDI, MDI to ascertain the hydraulic conductivity of soils [7][8][9].In the case of MDI, macropore flow is inhibited by the applied negative potential during infiltration measurements [10].When compared to other methods like Warrick's method [11] and Haverkamp's method [12] and when validated using small plot-scale rainfall simulations [13], MDI produces better findings for hydraulic conductivity [14].
According to [15] There are three primary parts of MDI: the bubble tower, the water tank, and the disc.A tube that draws air into the bubble tower is removable.To create the necessary negative water pressure at the disc's base, a change in air pressure is facilitated through this air intake tube.The height above sea level that the air can enter A water tank with a level gauge sits in the other huge tube next to the bubble tower.Manual or automatic tank level readings are used to calculate the amount of water absorbed into the soil in response to varying negative water pressures[16The disc is used to connect the soil and water supply.This is a plate of plexiglass with 1.5 mm diameter holes drilled into it, allowing water to freely flow through the disc's nylon film (400 network) cover.the goal of study is comparing the hydraulic conductivity values estimated by falling head and mini disc infiltrometer using two equations, Wooding-Gardner (W-G) and Van Genuchten-Zhang (V-Z).

Theory
Measuring the amount of water that percolates through the soil on a regular basis allows one to determine its infiltration rate.The infiltration rate in a one-dimensional water flow (like the Double Ring Infiltrometer) is nearly similar to the hydraulic conductivity at very large times.However, a formula is needed to figure out how much water would be absorbed laterally during a threedimensional infiltration process utilizing a Mini disk infiltrometer.Water-supply reservoir levels can be used to estimate steady-state infiltration rates, which are then used in the calculation of soil hydraulic properties.However, the hydraulic conductivity of the soil can be calculated using the data from transient infiltration using alternative methods [17].Multiple methods existed for deriving soil hydraulic conductivity from infiltration measurements.Two widely used methods were used in this research, and the accuracy of each was evaluated by determining the basic infiltration rate.

Wooding-Gardner Method
[18] discovered that, It is possible to make a reasonable approximation of the steady-state flow, Q (LT - 1 ), from a shallow circular pond of radius, r (L), at a supply tension, h (L), based on the properties of three-directional axisymmetric infiltration: Where is the hydraulic conductivity as a function of soil water potential (h) and is the macroscopic capillary length (L).The vertical flow under the disc caused by gravity flow is taken into account in the first part of the equation (as in one-dimensional infiltration), and the capillary absorption is considered in the second term.
Where is the saturated hydraulic conductivity (LT -1 ).The following equation, which combines the Wooding's and Gardner's equations, can be used to determine saturated hydraulic conductivity: where is the steady-state flow rate (L 3 T -1 ) under a given supply potential h (L).The observations with a constant disk radius at various supply potentials or at a fixed potential with disks of varied radii may be used to solve the equation because the only unknowns are K S and [18].However, the constrained assumptions that underlie Wooding's solution, namely that the soil is homogenous, isotropic, and has a constant starting moisture content, may result in absurd results, such as negative values for K [20].

Van-Genuchten Zhang Method
[21] suggested a very easy approach that is effective for measuring hydraulic conductivity from infiltration data into dry soil.To use the technique, you must plot cumulative infiltration against time and use the [14] equation to fit the findings.

Zhang Equation
Where C 1 (LT -0.5 ) and C 2 (LT -1 ) are parameters.C 1 is the soil sorptivity, and C 2 is related to hydraulic conductivity.The soil's hydraulic conductivity (k) is then calculated using: The van-Genuchten parameters for a specific soil type are connected to the suction rate and the infiltrometer disk radius by a value labeled A, and CT can be determined by fitting a second-order polynomial to the cumulative infiltration data against the square root of time.Calculating A involves: where r is the diameter of the disc, h is the suction at the disc surface, and n and are the soil's Van Genuchten parameters.The Van Genuchten parameters can be obtained through the Soil water retention curve.

Materials and Methods
The study area is the agricultural research department in the city of Tikrit-Iraq, with its geographic location between 43 38 ʹ 10 ʺ N 34 39 ʹ 05 ʺ E. The soils in the study area are gypsiferous Soils, 15 samples underdisturb were taken from 15 sites in the study area for measure K by using FH, another 15 samples underdisturb were taken and used to measure K by MDI under two suction rates.And other samples were taken from the field to measure different physical properties.The gypsum content at the study site ranged between 5.9 to 15.97 g. kg -1 .The water retention curve was calculated for all point in the study area and using application RETC to get van Genuchten parameters.Soil saturated vertical hydraulic conductivity was calculated using the falling head permeability technique, FH.The application of Darcy's equation to the study of FH is seen in Equation 8, according to [23].The purpose of this test was to provide an accurate estimate of saturated hydraulic conductivity for comparison with other suggested techniques.
a and A are the input water valve and specimen cross sectional areas (L 2 ), L is the specimen height (L), and is the time required for the total head to drop from clearly indicated graduations H1 to H2.A 2.25-cm-diameter MDI disc was used to determine the soil's hydraulic conductivity.We can learn more about the soil by eliminating macropores with air entry values less than the infiltrometer's 1259 (2023) 012017 IOP Publishing doi:10.1088/1755-1315/1259/1/0120174 suction, which may be adjusted from 0.5 to 7 cm.Laboratory testing was carried out using MDI (Fig. 1) at suction rates of 1 and 2 cm.For each suction rate, we ran two sets of tests to determine the corresponding hydraulic conductivities.The water level in the reservoir was monitored every 90 seconds, and its total water volume was calculated before and after each test.The steady-state infiltration rate, calculated by averaging the infiltration rates at the end of each test, was used to calculate hydraulic conductivity values.After collecting data on infiltration rates over long periods of time, we used linear regression to estimate steady-state values.
The infiltration rates for two alternative suction values at a constant disk size are required for forecasting hydraulic conductivity using the W-G technique [18].Since we were always working with the same sized disk, we could utilize the negative pressure rates of 1 and 2 cm to get a good idea of the hydraulic conductivity.Basic infiltration rate is estimated by the equation:

Results and Discussion
Several infiltration experiment outcomes using MDI are presented in Table 1.This table displays the recorded time-dependent changes in reservoir volume at suction rates of 1 and 2 cm for the purpose of calculating hydraulic conductivity.The rate of infiltration reduced over time for both suctions, as seen in the table.For hydraulic conductivity measurements, the van Genuchten-Zhang method called for plotting cumulative infiltration against the square root of time.The cumulative infiltration curve as a function of square root of time is seen in Figure 2. As can be seen in the image, increasing suction from 1 to 2 cm results in a decreased cumulative infiltration.Table 2. shows the saturated hydraulic conductivity values estimated by FH method, W-G method at two suction rates and the BI R which is almost equal to the saturated hydraulic conductivity at long times.The table also shows the value of the unsaturated hydraulic conductivity, which were estimated by the V-Z method at two suction rates.3 when comparing the average values that BI R was almost equal to the saturated hydraulic conductivity values estimated by FH, also when comparing the calculated ttest value 1.46 with the tabular t-value (2.04), we find that there are no statistical evidences for the presence of significant differences between the values estimated by FH and BI R values.While W-G method overestimated the saturated hydraulic conductivity at the two suction rates, as the highest value for the suction rates 1 and 2 cm was 527.29 cm.day -1 and 532.64 cm.day -1 , while the lowest value was 54.32 cm.day -1 and 34.94 cm.day -1 respectively, and the t values of 2.68 and 2.67 for the two suction rates indicate that there are significant differences between the W-G method and FH method.Table 2 also shows that V-Z method gave very few values for the two suction rates compared to the reliable K values estimated by FH, as the highest value of K was reached for two suction rates 42.37 and 10.84 cm.day -1 and the lowest value 2.31 and 0.49 cm.day -1 respectively.This is confirmed by the calculated t values, which showed high significant differences between the V-Z and FH methods, amounting to 7.15 and 8.28, respectively, for the suction rates 1 and 2 cm.  Figure 4 shows the spread of the hydraulic conductivity values estimated by different methods.The low values estimated by the V-Z method may be due to the type of soil, if the study soil is a soil with a high content of gypsum, if the gypsum content ranges from 5.9 to 15.97 g. kg -1 at the study site, and the parameters of van Genuchten has a correlation with the type of soil and therefore has an effect on the K value, in addition to that the V-Z method estimates the unsaturated hydraulic conductivity (under negative pressures), which means that the Macro pores will have a very little effect on the transport of water, This applies to the W-G method, which assumes that the soil is homogeneous, and this condition is not available in gypsum soils, which are characterized by being heterogeneous and without construction, this is consistent with what he found [20].

Conclusion
The hydraulic conductivity of Gypsiferous soil was determined in this work utilizing the Mini Disk Infiltrometer methodology in two different ways.Laboratory tests were used to generate cumulative infiltration curves at two different suction rates, and hydraulic conductivities were then calculated using the data.If the values derived from the Wooding-Gardner method are inflated and the values derived from the van Genuchten-Zhang method are very low compared to the values derived from falling head test, then it is clear that neither of the two methods used was successful in estimating the hydraulic conductivity.This could be because of the soil's high gypsum content, which modifies its physical characteristics and, in turn, its parameters.That both methods' equations incorporate to a significant extent.Findings from this research can guide our selection of Mini Disk Infiltrometer methods more suited to Gypsiferous soils.

Figure 2 .
Figure 2. Cumulative infiltration with the square root of time.

Figure 3 .
Figure 3. Methods for measuring hydraulic conductivity are compared and averaged.

[ 1 ]
Amoozegar, A and Wilson G V 1999 Methods for measuring hydraulic conductivity and drainable porosity p 1149 1205 In R W Skaggs and J van Schilfgaarde ed Agricultural Drainage Monograph No 38 ASA CSSA SSSA Madison WI [2] Scott, D F 2000 Soil wettability in forested catchments in South Africa as measured by different methods and as affected by vegetation cover and soil characteristics J Hydrol 231 232 87 104 [3] AL-Taiey, Emad Tarar Daham 2022 The Prediction of field soil water Infiltration Using some of methods and mathematical models for gypsiferous soils cultivated and un cultivated thesis submitted College of Agriculture Tikrit University [4] Vandervaere, J P, Peugeot C, Vauclin M , Angulo Jaramillo R. and Lebel T 1997 Estimating hydraulic conductivity of crusted soils using disc infiltrometers and minitensiometers J Hydrol 188 189 203 223 [5] Naik, Aparimita Priyadarshini, Biplab Ghosh and Sreeja Pekkat 2018 Estimating soil hydraulic properties using mini disk infiltrometer.ISH Journal of Hydraulic Engineering DOI 10 1080 09715010 2018 1471363 [6] Angulo Jaramillo, R, Vandervaere J P, Roulier S, Thony J L, Gaudet J P and Vauclin M 2000 Field measurement of soil surface hydraulic properties by disc and ring infiltrometers A review and recent developments Soil and Tillage Res 551 1 29 doi 101016S0167198700000982 [7] Fatehnia, M, Tawfiq K and Abichou T 2014 Comparison of the Methods of Hydraulic Conductivity Estimation from Mini Disk Infiltrometer Electron J Geotech Eng 19 E 10471063 [8] Schacht, K and Marschner B 2015 Treated wastewater irrigation effects on soil hydraulic conductivity and aggregate stability of loamy soils in Israel J Hydrol Hydromech 6314754 doi 10 1515johh 20150010 [9] Gadi, V.K, Tang Y R, Das A, Monga C, Garg A, Berretta C and Sahoo L 2017 Spatial and temporal variation of hydraulic conductivity and vegetation growth in green infrastructures using infiltrometer and visual technique CATENA 1552029 doi 101016jcatena 201702024 [10] Minasny, B and George BH 1999 The measurement of soil hydraulic properties in the field Science 22 26th [11] Warrick, A W 1992 Models for disc infiltrometers Water Resour Res 285 1319 1327 doi 10 1029 92WR00149 [12] Haverkamp, R, Ross P J Smettem K R J and Parlange J Y 1994 Three dimensional analysis of infiltration from the disc infiltrometer 2 Physically based infiltration equation Water Resour.Res 3011 2931 2935 doi 10102994WR01788 [13] Li, X Y, González A, Solé Benet A 2005 Laboratory methods for the estimation of infiltration rate of soil crusts in the Tabernas Desert badlands Catena 603255266.doi101016 j catena 200412004 [14] Zhang, R 1997b Infiltration models for the disk infiltrometer Soil Sci Soc America J 61615971603 doi 102136 sssaj199703615995006100060008x [15] Perroux, K M and White I 1988 Designs for disc permeameters Soil Sci Soc America J 52512051215doi 102136 sssaj198803615995005200050001x [16] Ankeny, M D, Ahmed M, Kaspar T C and Horton R 1991 Simple field method for determining unsaturated hydraulic conductivity Soil Science Society of America Journal 55 467470 [17] Wooding, R A 1968 Steady infiltration from large shallow circular pond Water Resources Research 4 1259 1273 [18] Wang, D., Yates S R, Lowery B and van Genuchten M T 1998 Estimating soil hydraulic properties using tension infiltrometer with varying disk diameters Soil Science 163 5 356361 [19] Gardner,W R 1958 Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table Soil Science 85 228232 [20] Hussen, A A and Warrick A W 1993 Alternative analyses of hydraulic data from the disc tension infiltrometers Water Resources Research 29 41034108 [21] Zhang, R 1997a Determination of soil sorptivity and hydraulic conductivity from the disc infiltrometer Soil Sci Soc America J 6110241030doi 102136sssaj1997 03615995 006 10 0040005x [22] Zhang, R 1998 Estimating soil hydraulic conductivity and macroscopic capillary length from the disk infiltrometer Soil Science Society of America Journal 62 15131521

Table 1 .
Volumetric water changes over time in Mini Disk Infiltrometer.

Table 2 .
Hydraulic conductivity values estimated by different methods.