Characterizing the hydraulic conductivity of soil based on the moving average of precipitation and groundwater level using a regional database

Hydraulic conductivity is an important geological and geotechnical characteristic that is required for various flow-related problems, the design of underground structures and the selection of dewatering and waterproof methods for excavation (Boadu 2000; Lobbezoo & Vanapalli 2002; Ranaivomanana et al. 2017; Singh et al. 2019; Rehman et al. 2022). The hydraulic conductivity of soil is influenced by various factors such as soil type, grain size distribution, in situ void ratio, and inner particle configuration (Elhakim 2016; Fujikura 2019). Despite the importance of soil hydraulic conductivity in geological and geotechnical characterization, the evaluation of soil hydraulic conductivity remains a challenging task due to the heterogeneity of soil, difficulties in soil sampling and subsequent experimental procedure, and the large extent of flow area within soil deposit (López-Acosta et al. 2019).

The hydraulic conductivity of soil can be determined experimentally or empirically using a property-based correlation. Experimental methods include laboratory tests using soil samples and in situ tests, all costly and subjected to uncertainties associated with experimental procedure and variability of local soil conditions (Jabro 1992; Sahin 2016; López-Acosta et al. 2019; Singh et al. 2019; Sadeghi & Alipanahi 2020). Empirical correlation methods have also been often used in practice (Kozeny 1927; Carman 1956; Kenney et al. 1984; Boadu 2000; Chapuis 2004; Rosas et al. 2014; Wang et al. 2017). The empirical approach is cost-effective and has produced reasonable estimates in many practical cases, while limitedly valid and applicable for considered target soil type and grain size (Boadu 2000; Odong 2008).

Groundwater level (GWL) fluctuates owing to natural or anthropogenic reasons with characteristics that vary depending on hydrological, geological, and topographical conditions in a given area. The response rate of GWL fluctuation can also change depending on the duration and magnitude of precipitation and soil hydraulic conductivity (Hoque et al. 2007; Kim & Lee 2018). According to Kim & Lee (2018), in areas with a largely exposed ground surface, GWL is well correlated to precipitation due to the direct infiltration of rainfall into the ground. For such cases, a time lag occurs until GWL starts showing a response and actual fluctuation from the rainfall infiltration, which is all affected by soil hydraulic conductivity within the area.

In many countries, databases for hydrological and geological parameters are well established, often provided in a compiled format open to the public. However, such databases have not been sufficiently and effectively utilized in practice for the characterization of the hydraulic conductivity of soil, and few methods are currently available for the direct estimation of soil hydraulic conductivity using the databases. The hydraulic conductivity of soil is usually introduced as a regional-based property, rather than an individual elementary property, in the flow-related design and analysis. Therefore, it would be beneficial and could further enhance soil characterization if a method based on a regionally established database for estimating the hydraulic conductivity of soil is available.

In this study, a method for estimating the hydraulic conductivity of soil is proposed, focusing on the utilization of a regionally established database. For this purpose, databases at 68 different regions with hydraulic conductivity, precipitation, GWL, and other geographical parameters were established and adopted for the investigation. Based on the moving average (MA) and GWL response to precipitation at each region from the database, a correlation model of the soil hydraulic conductivity to the optimal MA period was proposed. 14 additional case examples were collected and adopted to check the validity of the proposed method.

The hydraulic conductivity of soil can be directly measured using laboratory tests such as constant or falling head tests, provided that a proper soil sample is available. However, results from laboratory tests indicate only the local hydraulic conductivity characteristics of sampled soil elements, which may not be valid for representing regionally applicable hydraulic conductivity characteristics (Lopez-Acosta et al. 2019). The procedure of soil sampling inevitably required for an experimental testing procedure is also always a challenging task. The hydraulic conductivity obtained from the laboratory tests is scale-dependent often exhibiting a larger range of variability than any other soil parameters (Boadu 2000; Elhakim 2016; Wang et al. 2020). In situ pumping tests with a monitoring well may be more suitable to obtain regionally applicable soil hydraulic conductivity characteristics as confirmed by El-Daly & Farag (2006) and Sahin (2016). However, it is obvious that the testing procedure is costly and time-consuming.

The empirical approach based on a correlation model to soil property is also often employed in practice (Hazen 1911; Kozeny 1927; Carman 1937, 1956; Kenney et al. 1984; Vukovic & Soro 1992; Kresic 1997; Boadu 2000; Chapuis 2004; Rosas et al. 2014; Wang et al. 2017). Table 1 summarizes various empirical correlation models commonly adopted to estimate hydraulic conductivity. Among these, the correlations proposed by Hazen (1911), Kozeny (1927) and Carman (1937, 1956) are popular in practice, due to the simplicity and the reasonableness of predicted results (Odong 2008; Elhakim 2016). The Kozeny-Carman equation was originally proposed by Kozeny (1927) and later modified by Carman (1937, 1956) to become the Kozeny-Carman equation (Chapuis & Aubertin 2003; El-Daly & Farag 2006). It is noted that each correlation model targets certain soil conditions, but does not cover all possible variable conditions in porous media (Odong 2008).

Table 1

Correlation models for k based on grain size configuration

.	Correlation equation .	Remarks .
Hazen (1911)		CH = Hazen coefficient; D10 = effective grain size (0.1 mm < d10 < 3 mm)
Kozeny-Carman (Kozeny 1927; Carman 1937, 1956)		n = porosity; g = acceleration of gravity; υ = kinematic viscosity; D10 = effective grain size; ρw = fluid density
Breyer (1964)		1 < uniformity coefficient < 20, 0.06 mm < effective grain size < 0.6 mm
Kenney et al. (1984)		D5 = grain diameter for 5% passing
Vukovic & Soro (1992)		g = acceleration of gravity; v = viscosity; C = dimensionless coefficient; f(n) = porosity function; De = effective grain diameter; n = porosity
Alyamani & Sen (1993)		Io = intercept in mm of the line by D50 and D10 with the grain size axis.
Carrier (2003)		fi = particle fraction between two sieves; SF = shape factor; Davg = average particle size; e = void ratio
Chapuis (2004)		D10 = effective grain size (0.03 mm < D10 < 3 mm); e = void ratio

.	Correlation equation .	Remarks .
Hazen (1911)		CH = Hazen coefficient; D10 = effective grain size (0.1 mm < d10 < 3 mm)
Kozeny-Carman (Kozeny 1927; Carman 1937, 1956)		n = porosity; g = acceleration of gravity; υ = kinematic viscosity; D10 = effective grain size; ρw = fluid density
Breyer (1964)		1 < uniformity coefficient < 20, 0.06 mm < effective grain size < 0.6 mm
Kenney et al. (1984)		D5 = grain diameter for 5% passing
Vukovic & Soro (1992)		g = acceleration of gravity; v = viscosity; C = dimensionless coefficient; f(n) = porosity function; De = effective grain diameter; n = porosity
Alyamani & Sen (1993)		Io = intercept in mm of the line by D50 and D10 with the grain size axis.
Carrier (2003)		fi = particle fraction between two sieves; SF = shape factor; Davg = average particle size; e = void ratio
Chapuis (2004)		D10 = effective grain size (0.03 mm < D10 < 3 mm); e = void ratio

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GWL fluctuates for a variety of reasons, including changes in annual precipitation, river stage, groundwater pumping, and other local activities, all possibly affecting the geotechnical stability of underground structures and foundations (Guttman 1999; Healy & Cook 2002; Almedeij & Al-Ruwaih 2006). Dominant influencing factors on GWL become different depending on the geotechnical, geological and geographical conditions in a given region, such as the hydraulic conductivity of soil, proximity to rivers, and ground surface conditions. In urban areas located near rivers, changes in river stage affect most significantly the fluctuation of GWL (Hoque et al. 2007; Kim & Lee 2019). In rural areas where ground surfaces are largely exposed, precipitation becomes the major influence factor on GWL, and the MA reflecting accumulated preceding rainfall is known to better describe the fluctuation of GWL (Kim & Lee 2022).

The methods for estimating GWL can be categorized into knowledge-based and data-based approaches (Coppola et al. 2005; Sahoo & Jha 2013; Guzmán et al. 2016). The knowledge-based approach employs analytical and numerical models, explaining mathematically the flow of groundwater through soil (Serrano & Workman 1998; Batelaan et al. 2003; Trichakis et al. 2011; Sahoo & Jha 2013; Kim & Lee 2018, 2019). The data-based approach involves statistical correlation and calculation algorithm between selected influencing factors and GWL (Daliakopoulos et al. 2005; Fallah-Mehdipour et al. 2013; Sahoo & Jha 2013; Suryanarayana et al. 2014; Wen et al. 2015). It is noted that results predicted using the data-based approach are largely affected by datasets adopted in the calculation procedure for statistical calibration and training.

A time lag occurs in the GWL response to precipitation, due to the infiltration time of rainfall into soil, which varies depending on the permeable characteristics of soil and ground surface conditions. It is indicated that accumulated precedent precipitation would be more dominant in changes in GWL, rather than simple daily precipitation. In that sense, MA is an effective parameter that can reflect the effect of precedent precipitation on GWL, for areas where the rainfall infiltration governs changes in GWL.

MA_t has been frequently adopted to describe the effect of preceding precipitation as an operating index for underground dams (Guttman 1999) and to analyze the correlation between precipitation and GWL (Yang & Kim 2011; Kim & Lee 2022). As MA reflects the actual infiltration time of rainfall into the ground to reach GWL, it is largely affected by the hydraulic conductivity of the soil. This implies that differences in MA_t in different regions are closely related to differences in soil type and hydraulic conductivity.

To investigate the correlation between t_opt and the hydraulic conductivity, a database was established, which contains various geological and hydrological information including the hydraulic conductivity, daily measured precipitation, changes in GWL, proximity to the river, and surface pavement ratio. A total of 68 different regions in Korea were selected and adopted in the database. The average time period for the collected data from the selected regions was 11.3 years. GWL and hydraulic conductivity (k) data were obtained from the National Groundwater Information Center (GIMS) and precipitation data were obtained from the Korea Meteorological Administration (KMA).

As Δt and t_opt both represent the time delay characteristics of GWL response to precipitation, it is likely that these parameters are related to the hydraulic conductivity of the soil. Due to the differences between Δt and t_opt described previously, data scatters were observed from Figure 8(b), showing different magnitude scales for Δt and t_opt. Nonetheless, it is indicated that the smaller the hydraulic conductivity, the longer the values of Δt and t_opt, implying the slower response of GWL to precipitation. These two components will be further examined and considered for the correlation analysis of the hydraulic conductivity.

It is noted that the newly proposed correlation of Equation (2) was established based on the regional-based hydrological and geological characteristics, which were not specifically considered in the existing experimental and empirical approaches. The hydraulic conductivity of soil is spatially distributed in complex ways. The use of databases for piezometric level and precipitation would be effective to reflect the spatial variability of hydraulic conductivity. The proposed method is expected to further enhance the soil characterization process with a more efficient application of the regional database, leading to improved reliability of estimated results. It is also noted that the proposed k correlation model based on the GWL response time of t_opt can provide an effective tool for the input system of hydraulic conductivity, which would particularly benefit the widely adopted GIS-based regional analysis of flow and seepage problems. Cost effectiveness is another advantage as no experimental or testing procedure is involved.

The hydraulic conductivity of soil is closely related to the grain configuration of soil such as the constitution and distribution of particle and pore size as indicated in Table 1. This implies that t_opt may be a possible indicator of soil type provided that t_opt is well correlated to k. It also implies that the portion of granular materials in the soil is larger if the value of t_opt is small. It should also be noted that t_opt can be affected by morphological factors such as terrain slope, water table depth, and land cover.

To check the validity of the proposed correlation model for the estimation of k, 14 additional case examples in Korea were collected and obtained from the same sources as those used for the database previously described. Considered necessary parameters were then obtained from the 14 cases and adopted for comparing measured and predicted values of k. The collected case examples are summarized in Table 2. For the selection of the newly introduced case examples in Table 2, the similar geographical conditions of low surface paved ratio as those for the previous database were considered to maintain the consistency of the prediction. For GWL and precipitation data at each case region, the values of t_opt were obtained following the same procedure described in Figure 5 and adopted in the prediction.

The hydraulic conductivity (k) is an important geological and geotechnical characteristic that is required for soil characterization, design of underground structures and other flow-related problems. In this study, a method for estimating hydraulic conductivity was proposed, focusing on the utilization of a regionally established database of hydrological and geological parameters. The time response of GWL to precipitation was considered as a key influencing factor on the regional characteristics of the hydraulic conductivity, which was considered based on the optimum time period (t_opt) of moving average (MA_t).

To investigate the correlation between t_opt and k, a database of 68 different regions was established, which contains various geological and hydrological parameters. The values of MA_t and t_opt that gave the best correlation to GWL were obtained for all regions from the database. It was shown that MA_t was well correlated to GWL whereas the daily measured precipitation showed no meaningful correlation to GWL, indicating that the effect of preceding precipitation was important. It was found that the smaller the hydraulic conductivity at a given region, the longer the t_opt with the slower response of GWL.

Based on the findings and matches of the considered parameter from the database, a correlation model between t_opt and the hydraulic conductivity (k) was established. The overall trend of the proposed correlation was sufficiently consistent, showing that the values of k decreased as t_opt increased. Such a trend was reasonable because a soil condition with lower hydraulic conductivity would produce a longer time of rainfall infiltration into the ground and thus a longer response time of GWL. The newly proposed correlation model was beneficially effective and advantageous, in that an experimental and empirical procedure is not required whereas the applicability and utilization of the regional database is further enhanced. For the general applicability of the proposed method, the correlation coefficients of the proposed model can be further updated if additional datasets are available, or databases of other regions are targeted. Once the correlation model is established for a given region, the correlation is valid for estimating k using t_opt in areas within the region or neighboring regions unless geological and geotechnical conditions are not dramatically different.

To check the validity of the proposed correlation model, 14 additional case examples were collected and adopted in the comparison between measured and predicted values of k. The predicted values of k using the proposed method showed a consistent level of prediction, compared to those obtained using other existing methods, indicating that the proposed method is sufficiently effective and applicable in practice.

This work was supported by the Basic Science Research Program through the National Research Foundation of Korea and the Korea Agency for Infrastructure Technology Advancement with grants funded by the government of Korea (Nos 2020R1A2C201196614 and RS-2020-KA156488).

Groundwater level and Hydraulic conductivity data: National Groundwater Information Center. (https://www.gims.go.kr/micro1.do). Precipitation data: Korea Meteorological Administration. (https://data.kma.go.kr/stcs/grnd/grndRnList.do?pgmNo=69/).

The authors declare there is no conflict.