Sensitivity of Infiltration Models in Rural Soils Overlying Unsteady Shallow Groundwater

Abstract


Introduction
Hydrologists and agricultural engineers used to assess the infiltration depth by measuring it by means of a double ring infiltrometer without taking into account the depth of the shallow groundwater (SGW) under the soil surface, which was found to greatly affect the value of the infiltration rate, accumulated depth of infiltration, Wu and Selvadurai (2016); Wu et al. (2018) and most of the previous studies dealt with the rise of groundwater after rainstorms as a result of the infiltration of rain or irrigation water, and the rare ones deal with the sensitivity of the infiltration process with the depth of the groundwater.According to the shortcoming in the understanding this, the infiltration rate evaluation was reconsidered by conducting several tests in the laboratory for different types of soils by means what is called infiltration box, Ali et al. (2021) through which the infiltration rate can be measured through virtual SGW depths to identify the sensitivity and response of the double ring infiltrometer readings and the infiltration models to the depth of SGW variations.Many researchers studied the infiltration losses within the basins around the worldwide, among them Tu et al. (2011) studied the gradual decrease in the value of infiltration rate over the years from 2003-2007 without indicating the real reasons for its decrease.It was mentioned that the presence of a sandy layer in the Wanglong Lake, Pingtung, Taiwan was the main cause for this descent.Infiltration depth through flood plain was decreased with increasing GW gradient which was positive toward the river.An analytical equation was derived for infiltration depth estimation to compensate the inapplicable full complex modeling.A new modeling technique to simulate soakaways infiltration over SGW mound of small-scale schemes.The output results were compared to the 2D saturated and unsaturated model which derived from Richard's Equation.Results reveal that emptying times of soakaway obtained by the new model were higher by 13% than the emptying times of the 2D model.The study proved to be a good tool for the simulation of small-scale infiltration over SGW schemes, (Roldin et al. 2013), while the trenches of infiltration were used widely in the basins managements to drain excess surface water but these infiltration trenches endure infiltration rate reduction when installed in areas over SGW, a simulation of such infiltration trenches during rainstorm runoff shows that infiltration trenches are severely response to SGW underneath unsaturated zone of thickness 1.5-3m in sandy soils, 6.5-8m in silty soils and 11-12m in silty clay soils.Below the forgoing values of the unsaturated depths, the dissipation of water by infiltration trenches becomes dominant phenomenon, Ocatelli et al (2015).Infiltration rate slowed lately due to K reduction and (or) clogging as results of SGW rise.The modeling results of infiltration trenches indicate an increasing of infiltration rate with high k and deeper GW.An empirical equation was derived for estimating infiltration rate as a function of k and GW, a relationship between the flood water depth in the Tarim River, north-China and the depth of groundwater corresponding to the induced infiltration with correlation factor of .The vegetable filter strips (VFS) of surface runoff pollution protection is usually used in agricultural watersheds.Its efficiency was extremely dependable on subsurface hydraulic conductivity of soil and GW depth.The experimental works and mathematical modeling by SWINGO and VFSMOD which were applied on two field cases of soils in France (sandy loam in Mediterranean weather and silty clay in oceanic climate).The results indicate that VFS efficiency considerably reduced when the SGW depth 0 to1.5mbelow the surface.This is attributed to the infiltration rate reduction due to GW rise which increases surface runoff, Lauvernet and Munoz (2018).The continuous measuring of soil moisture may provide a good estimate to infiltration rate reduction by which the basin could be managed, (Barquero et al. 2019).By the way, it was found that the permeability coefficient of the unsaturated layer is equal to the value of the final filtration rate ( ) multiplied by a constant of 1.15, (Jabbar et al., 2021).Wu et al. (2021) Modified smith et al. (1993) infiltration model to simulating rainfall-infiltration-runoff in shallow GW.The model was examined under two cases of inflow rates and SGW depths.The results reveal that there is a considerable reduction in the surface runoff with increasing of infiltration rates.
This study is considered as a platform to re-evaluate groundwater recharge and the increase in GW storage, which is very important for preparing the water budget for any region in the world.The results proved that the infiltration water depth added to the SGW changes with the change of SGW depth.
The aim of this study is to find the effect of the SGW fluctuation on the accumulated infiltration and how to be corrected accordingly by the hydrologist and agricultural engineers, since the GW depth is seasonally fluctuated for many reasons including; seasonal temperature in cold climate variation, excessive GW depletion and irrigation, river embankment infiltration, etc.For example, if three consecutive rainstorms of the same duration and equal intensity have been occurred, it is expected that the amount of accumulated infiltration depth for each rain storm has been varied due to a change in the GW depth.

Theoretical Consideration
When the double ring infiltrometer is setup a saturated water plume is originated under the base of the infiltrometer which is enlarged spherically in 3D with time proceeding.The saturated plume boundary proceeds toward GW as shown in the lab arrangement of an infiltration box of Fig. 1a, (Arkan, 2021).Hydrologists usually does not undertake the effect of GW depth during the evaluation of water infiltration into the soil which is indeed greatly affected by the depth of GW beneath the infiltrometer.Naturally GW level usually fluctuates permanently during annum, Tabari et al. (2012); Nygren et al. (2020); Kyoochul et al. (2021).Water infiltration normally starts with a spherical plum under the infiltrometer and enlarges spherically outward which is associated with increasing in water leach from the infiltrometer as demonstrated in Fig. 1b.The infiltration capacity (rate) begins to decreasing at the moment when the infiltration plume touches the GW surface because the infiltrometer is very sensitive to SGW as shown in Fig. 1c.Experiments through this research indicate that further rising in GW level will reduces the infiltration rate correspondingly and then will be stopped when GW becomes in contact with the soil surface.For instance, Swamps are a natural phenomenon to indicate a decline or cessation of infiltration process.The current study considers the behaviors of infiltration rate amount due to GW level fluctuation.During conductance of series of infiltration field tests, it was noticed that the water leaching from the infiltrometer decreases a lot as the GW level converges from the soil surface, and it is normally expected that water percolation is stopped when the GW appears on the surface of the earth, i.e. when the soil surface turns into a swamp.Laboratorial experiments proved that the infiltration rate curves shapes for the same soil test vary with GW level, (Ali et al., 2021).The infiltration box model of Fig. 1d was currently employed to investigate the effect of GW level on the water infiltration rate behavior.The model consists of a glass box with length, width and height of 100 cm, 50 cm and 80 cm, respectively.The box is equipped with four side taps to control the level of GW and the infiltrometer device should be installed at the top of the box as shown in Fig. 1d.A continuous water supply is used to maintain a constant water level in base of the box to simulate GW category.
It is self-evident to hydrologists that the ground water fluctuates seasonally depending on the inflow of the ground water, Todd (1980); Tabari et al. (2012); Nygren et al. (2020); Kyoochul et al. (2021).Accordingly, it takes different levels annually as shown in Fig. 2 which is significantly affected the infiltration capacity of the unsaturated zone of the soil.
It was found experimentally that the GW when it is fixed at level Z1 in Fig. 2, produces the infiltration rate curve Z1 and when it is at level Z2 produces the infiltration rate curve Z2 and so on for levels Z3, Z4 …etc.Correspondingly, the main goal in this study is that if GW level has a significant effect on the rate of infiltration rate during a rainstorm which is not taken into consideration previously by the hydrologists and engineers who work in the agricultural aspects relating water allocation for irrigation losses.

Lab infiltration test methodology
The infiltration measurement test by using the infiltration box is conducted through filling the box with a soil and stacking it in the form of layers up to a field density.Then the water is adding constantly by means of tap as shown in Fig1d.After opening the bottom water exit valve (at level z1) to ensure the stability of the water level in the box as in the figure.This is ensured when water begins to come out from the outlet valve in continuous and constant discharge.At this time, the infiltration measurement begins by installing the double ring infiltrometer on the top of the soil surface, and the test is conducted according to ASTM D3385.When the test is completed, the bottom water outlet valve is locked, the one above it is unlocked (at level Z2), and the filtration measurements are repeated in the same way as before, until infiltrometer tests for all valves Z3 and Z4 are sequentially carried out.After the test has been completed, a sample of the soil is taken for additional physical tests in the lab.
In this way, the infiltration rate curve for each depth (Z) starting from the bottom up can be obtained as illustrated in graphical representation of Fig. 2.

Infiltration Models
The main work depends on the most famous models including Horton model (1940), of the form: Al Maimuri et al. (2017) and Al Maimuri (2018), where,  () is the water infiltration rate,   is the infiltration rate at the end of a rainstorm,   is an initial infiltration rate, t is the time, a and  are arbitrary constants and   () is the accumulated infiltration depth after time (t).

Additional Lab Tests
The soil samples were brought to the laboratory, the grain size distribution test of soil samples according to ASTM D7928 -17, and variable head test of undisturbed soil samples according to BS 1377-5:1990 were achieved then a deep penetration test was conducted on each model with four levels of GW.The uniformity and concavity of the soils were used to indicate the soil gradation of each soil.These parameters may be estimated by the following equations: WhereC u and C c are the coefficients of uniformity and concavity respectively, D 10 , D 30 , andD 60 are the soil grains diameters in millimeters at percentage finer by weight 10%, 30%and60% respectively.

Practical Measurement of a Case Study
For the purpose of practical test, a square trench of 0.4m in width was constructed with horizontal dimensions of 3 m * 3 m and a depth of 2.5 m in a clayey soil of 3.3m GW depth.The trench is connected to a drainage ditch by means of pipes for the purpose of removing excess water to control the artificial GW at a certain level as shown by the sketch of Fig. 3.A double infiltrometer ring is then installed in the center of the square trench and the test according to (ASTM D3385 -18 specification) is conducted at each GW level to monitor the effect of its level on the response of the infiltrometer readings and infiltration rate curve.The experiment may begin with adding water to the trench by means of a water supply pipe to raise the artificial GW to the level Z1, and the pipe connecting the trench to the drainage ditch to drains the excess water is opened.The system is left for suitable period depending on soil texture (may be 1 hours) to ensure the stability of the artificial GW level inside the square trench and then the double ring infiltrometer test is then conducted.Then the pipe of Z1 level is closed by mean of valve to allowing the artificial GW raise to the level Z2 and the pipe of level Z2 is opened and the infiltration test is conducted again and so on for the level of Z3, Z4…etc.

Practical Measurement of a Case Study
For the purpose of practical test, a square trench of 0.4m in width was constructed with horizontal dimensions of 3 m * 3 m and a depth of 2.5 m in a clayey soil of 3.3m GW depth.The trench is connected to a drainage ditch by means of pipes for the purpose of removing excess water to control the artificial GW at a certain level as shown by the sketch of Fig. 3.A double infiltrometer ring is then installed in the center of the square trench and the test according to (ASTM D3385 -18 specification) is conducted at each GW level to monitor the effect of its level on the response of the infiltrometer readings and infiltration rate curve.The experiment may begin with adding water to the trench by means of a water supply pipe to raise the artificial GW to the level Z1, and the pipe connecting the trench to the drainage ditch to drains the excess water is opened.The system is left for suitable period depending on soil texture (may be 1 hours) to ensure the stability of the artificial GW level inside the square trench and then the double ring infiltrometer test is then conducted.Then the pipe of Z1 level is closed by mean of valve to allowing the artificial GW raise to the level Z2 and the pipe of level Z2 is opened and the infiltration test is conducted again and so on for the level of Z3, Z4…etc.

Field Test Facilities
To facilitate the process of conducting the field infiltrometer test at different levels of artificial GW, the testing site was chosen adjacent to main drain which has a conjunctive use, it is use in water supplying of the trench and also to drain the excess GW instead of the drainage ditch shown in Fig. 3.It is worth noting that to facilitate the implementation of the infiltrometer test, the drainage ditch can be excavated to a depth so that the water level in it is the same as the GW.The test site was chosen in Abu-Gharaq area, west of Babylon Governorate, Iraq with coordinates of latitude 32 0 32 ′ 40.66 "  44 0 19 ′ 52.47 " adjacent to a main drain to facilitate the process of water supply and drainage as shown in the location map of Fig. 4. The field work included conducting some surveying measurements to determine the levels of natural and artificial GW and the global coordinates of the test site and taking undisturbed soil sample for physical tests purposes.

Fig. 4. Location map of the testing site
There are a number of obstacles that accompanied the drilling process of the trench, which represented by the collapse of the sides of the excavated soil, especially during the operation of the water supply system and the artificial drainage.This difficulty was overcome by filling the ditch with boulders and cobbles to stabilize the sides of the excavation.The drilling and construction processes of the infiltration trench were presented in Fig. 5a.The testing process by double ring infiltrometer was shown in Fig. 5b.Although the field work was financially costly, it is useful to check the validity of laboratory results.

Lab Work Results
A nature field soil sample and four types of soils were randomly selected for laboratory testing by infiltration box.Before starting the tests, the soil texture was tested to identify the fractions of its components, coarse and fine, which represent a key indicator of deep infiltration processes and k value.The grain size distribution was represented for all soil's types in Fig. 6.The coarse fractions of the four soil samples (sand and gravel), the coefficients of uniformity and concavity, and the lab initial and final infiltration rates at different GW depths and k values were summarized in Table 1.The bulk, dry density and the moisture content of the field soil sample were found to be 17KN/m2, 15KN/m2 and 12.6% respectively.The infiltration rate curves of soil samples No.2, No.3, and No.4 were represented graphically in Figs.(7a, 8a and 8b) respectively.It is worth noting that for Soil (No. 1), the infiltration test couldn't be conducted because of its fineness.Moreover, for comparison purposes, the soil samples were classified according to the Unified Soil Classification System (USCS) as Sandy clay for soil sample no.1 and Abu-Gharaq soil sample, whereas soil samples no.2, 3 and 4 were classified as Clayey sand.

Field Work Results
The infiltration test was conducted in the study area on Dec/2021 shown in Fig. 5 for several depths.The double ring infiltrometer was installed in the middle of the square trench and the test was conducted for each depth for a period of 4 hours.Typical readings were taken and as expected from the laboratory results.The infiltration rate curves obtained from the practical work were represented in Fig. 10a.The experiment was conducted five times at the levels; NaturalGWlevelencounteredat3.3mdepth,Z1 = 2m, Z2 = 1.5m,Z3 = 1m, Z4 = 0.5mbelowsoilsurface.
The initial and final infiltration rates versus the GW depths were represented graphically in Fig. 10b.It was concluded that there is a linear relationship between the initial and final infiltration rate and the depth of GW.This shown in the lab results of Figs.7b, 8b and 9b and the field results of Fig. 10b.An acceptable correlation coefficient was found for both the initial and final infiltration rate of  4 = 0.9984 and  2 = 0.9521respectively.Table 2 includes the field results.

Infiltration Correction to Annual GW Fluctuation
According to the current study, the hydrologist and engineer who are concerned with the issue of infiltration losses in modern agriculture, especially countries that suffer from drought and water scarcity, must conduct the infiltration test using the infiltration box of a undisturbed soil sample or carrying out a field infiltration test by square infiltration trench and then prepare diagrams for his farm like Figs.10a and 10b and thus be able to calculate the amount of accumulated infiltration during the agricultural season by the following procedure; The assessment of accumulated infiltration (irrigation losses) begins by measuring the depth of the GW by means of a piezometric well, and then accessing Fig. 10b to read the value of     .The next step is to use Eq.1 or Eq.4 to draw the infiltration rate curve after estimating the factor k by using Eq.2 or Eq.4 and then estimate the accumulated infiltration depth by using Eq.3 or Eq.6.
As an example, by excessing Fig. 10b to get the initial and final infiltration rates     and then estimate the k coefficient for each depth namely; Z=0.5, 1, 1.5, 2 and 3.3m.The results were included in Table 2. Accordingly, the accumulated infiltration depth can be estimated by using Eq.3 or Eq.6.The accumulated infiltration depth or the irrigation losses for irrigation interval 1hr, 2hr…5hrs were correspondingly estimated and listed in Table 2 and shown graphically in Fig. 11.It is observed the accumulated infiltration depth values were increased linearly and proportionally with GW depth increasing.Fortunately, it was observed in Fig. 11 that the relationships between the accumulated infiltration depths and the GW depth offer acceptable correlation coefficients exceeding 0.99.

Conclusions
It is concluded that the water amount of the accumulated infiltration depth is usually unsteadily depending upon the occurring fluctuation of GW depth.This variation is certainly depended on both the depth and application duration of a single rainstorm and/or irrigation event.It is also found the accumulated infiltration is directly proportional to the GW depth and soil permeability in the unsaturated zone.There is a linear relationship between the accumulated infiltration and the GW depth for a specified rainstorm or irrigation event with a correlation coefficient of more than 0.99.

Recommendations
Since the accumulated infiltration depth increases directly as the depth of the GW increases beneath the soil surface, it is recommended that, the hydrologists and the agricultural engineers must correct this seasonally, due to the GW fluctuation.

Fig. 5 .
Fig. 5. Construction of infiltration trench and testing methodology; (a) Drilling and construction of infiltration trench; (b)Double ring infiltrometer test at the center of the artificial square trench

Fig. 6 .
Fig.6.Grain size distribution of the soils

Fig. 11 .
Fig.11.Accumulated infiltration depth versus GW depth for the case study

Table 1 .
Some physical properties, initial and final infiltration rates of lab and field soil samples

Table 2 .
Field infiltration rates versus depth of artificial and natural GW