A Knowledge Base (KB) in knowledge engineering is a commonly accepted information structure over a discipline that combined with artificial intelligence and expert systems, where information can be easily retrieved in a rapid way and deployed in numerous applications, outlining the relationship with the software engineering, information integration and knowledge management (Studer et al., 1998). KBs form ontological mappings (Ontologies) by employing concepts (semantics) and rigid internal relationships amid its network corpus. Clearly defined concepts (conceptualization—explicitly or implicitly), shared (controlled) vocabulary and leveled up/down generations/classes (taxonomies) have to be built up inconsequential hierarchies (Genesereth & Nilsson, 1987; Gruber, 1995; Guarino, 1995; Uschold & Grüninger, 1996; Borst, 1997; Roche, 2003) to support such a structure.
Ontology-Based Knowledge Networks gradually are being applied to a vast range of disciplines, such as in soil science, by describing soil properties, processing and their interaction (Du et al., 2016; Heeptaisong & Srivihok, 2010). Ontologies as a formal description of knowledge set, with suitably placed concepts within a domain strictly bound by well-defined relationships are applied in artificial intelligence in order to provide to all users an interaction framework with various application systems i.e. communication models between (KB) users and machines (Weng & Chang, 2008).
In soil science, pollutant’s fate via infiltration/percolation is considered to be a multi-stage processing and undoubtedly a major concern in industrial ecology. Precipitated water runoffs could arise contamination problems on account of their penetration from humic topsoil to lower surface layers. Mikkelsen et al. (1997) presented a case of heavy traffic roads. Soil crust rehabilitation in the aftermath of a pollution incident, could be remarkably aided by already building up ontological structures dedicated to infiltration phenomena applied to various accidental cases (Du & Cohn, 2016).
Infiltration is approached as a complex both biological & physicochemical process during which an aquatic solution (potentially contaminated with insoluble/dispersed particles or micelles), penetrates the ground under the gravity force and/or the capillary action. The partial sub-processes which are taking place until the infiltration water reaches the groundwater table are, inter alia, common filtration, chemical reaction (depending on the layers of sedimentary rock/soil the water is passing through), biochemical conversion, sedimentation, coagulation, flocculation (Lassabatere et al., 2010).
In general, the infiltration rate depends mainly on 1) ground surface loading with (waste) water; 2) the soil porosity; and 3) the vegetation coverage. Αn introspection reveals interdependences of numerous parameters among others, type, bulk density and texture of the soil, canopy coverage and topsoil biomass production (Wang et al., 2017; Patle et al., 2018; Wood et al., 1987; Tejedor et al., 2013). The given physicochemical parameters are of variant importance/gravity in terms of inducing the evolution of the ongoing phenomenon.
In the present paper, an Ontology-Based Knowledge Network is developed of soil/water physicochemical & biological properties (soil/water concepts), derived from ASTM standards and published scientific references in order to describe the infiltration/percolation process of contaminated water. The developed/proposed Ontology-Based Knowledge Network can be adopted as a tool for the semantic representation of infiltration/percolation process of contamination water through soil structure and porous media.
In this section, a comprehensive Ontology-Based Knowledge Network design and construction is described/summarized by the below presented steps.
1) Determination of the initial ontology concept.
2) Determination and proper selection of other sub-concepts, which could be fitted in the ontology network, and correspond to soil/water physicochemical & biological properties.
3) Identification of soil/water physicochemical & biological properties through an extensive research of ASTM Standards and scientific published references.
4) Documentation of three possible ways that could justify the interconnections between all the ontology sub-concepts of our interest and relevant soil/water physicochemical & biological properties.
As regards the first step, the “infiltration rate” of contaminated water in the soil (porous medium), it was established as the initial conceptual property of our ontology network. Interconnection of the afore-mentioned properties is achieved by adopting a framework of concepts interrelated with soil/water properties and partial sub-processes which are taking place during the process.
The infiltration rate could be measured and monitored by well-established techniques fully described by standard methods and practices recommended by a widely recognized standardization organization such as the American Society for Testing & Material (ASTM) and relative scientific published papers. This is indispensable for obtaining results comparable with the ones obtained in similar experimental models, under similar conditions, since some of these observations are obtained with more precise measurements that are described through standardized methods i.e. ASTM standards and scientific published papers.
According to the structure of the network, all the nodes/concepts/physicochemical and biological properties are interconnected by using the principles set by dependent and independent variables. This set of dependent and independent variables justified and documented by three possible ways, as they are describing below:
1) Dependent and independent variables interconnected by using the logical operator “depends on” quoting existent explicit functions and equations;
2) Dependent and independent variables interconnected by using the logical operator “depends on” quoting produced implicit functions, by implementing Rayleigh’s method of indices;
3) Dependent and independent variables interconnected by using the logical operator “related to” based on a logical dependence between the examined nodes-concepts-variables.
The last Rayleigh’s method of indices is based on the fundamental principle of dimensional homogeneity of physical variables involved in this problem. The dependent variable is identified and expressed as a product of all the independent variables raised to an unknown integer exponent. Equating the indices of n fundamental dimensions of the variables involved, n independent equations are obtained. Finally, these n equations are solved to obtain the dimensionless groups.
Under the form of the directed/developed ontology network, shown in FigureA2 of the Appendix, it can be easily supported by a computer program through several ready-to-use packages already available in the market. All these nodes/concepts/properties are represented by ASTM standards and scientific published papers in an integrated Ontology-Based Knowledge Network, FigureA1 of the Appendix, a part of which is shown in Figure1 of the current page.
Each node of ASTM standard and published paper has a set of references to other ASTM standards or/and published papers. All the nodes of scientific published papers and ASTM standards are symbolized as PPi,n and ASTMi,n respectively, where i denotes the generation number, and n denotes the member number of each generation. Starting from a certain ASTM standard, related with the topic under consideration (e.g. “Infiltration Rate Determination Using Double-Ring Infiltrometer with Sealed-Inner Ring”, according to D5093-15 ASTM Standard Test Method, in the case of the present work), we may represent it as well as its references with points or vertices or nodes interconnected with arcs directed from the initial standard to its references. These references are all members of the first generation with the initial standard as unique parent. Each member of the first generation has other referenced ASTM standards or/and published papers of its own, creating a second generation, and so forth until the seventh generation is achieved in our case. Evidently, the initial standard as well as any
Figure 1. Part of the ontology-based knowledge network of ASTM standards and scientific published papers for estimating the infiltration rate of contaminated water.
member of the i generation may be a member of one or more generations i.e. a member of the i (i = 0, 1, 2, …) generation may also appear as a member of the j generation, provided that j ≥ i + 2.
Values, indicating dependence of applying a standard or/and published paper (especially of carrying out a standard test) on the previous application of another standard or/and published paper of the next generation, are assigned to each arc, so that a network is obtained from the directed multi-graph. These values vary from zero, indicating no dependence whatsoever, up to one, indicating full dependence (e.g. Table 1 & Table 2). Dependence concerning only knowledge that must be acquired for carrying out successfully a standard test is considered to be zero. Dependence of carrying out a standard test on the provision of a material with certain specifications varies from one to zero.
In the application example of current page, the selected initial “Standard Test Method for Field Measurement of Infiltration Rate Using Double-Ring Infiltrometer with Sealed-Inner Ring”, under the code number ASTM D5093-15 (2015), has four arcs leading to corresponding referenced scientific published papers (PP1,1 & PP1,2) and ASTM standards (ASTM1,3 & ASTM1,4) as shown in Figures 1-3. The same procedure continues to the next generation and so forth until the seventh generation is formed. The integrated Ontology-Based Knowledge Network with all its ASTM standards and scientific published papers is presented in FigureA1 of the Appendix. However, a partial network that includes all the nodes of the first three generations is presented in Figure1.
The dependence indices are considered as Boolean parameters, obtaining the values one or zero (meaning “referenced” or “not referenced”, respectively) for sake of simplicity.
The interconnections between all nodes/concepts which represents soil/water physicochemical and biological properties and sub-processes of the integrated
Table 1. Adjacency matrix for first generation relations, in accordance with part of the ontology-based knowledge network shown in Figure 2.
Table 2. Adjacency matrix for second generation relations, in accordance with part of the ontology-based knowledge network shown in Figure 2.
Figure 2. A tree representation of merely a part of the network of scientific published papers and ASTM standards for estimating the infiltration rate of contaminated water.
Ontology-Based Knowledge Network of FigureA2 of the Appendix, are presented and depicted with arcs. Each single arc consists of a starting point and a final point edge. In order to find and justify the correlations between all the nodes/concepts of FigureA1 & FigureA2 of the Appendix, the selected concepts are corresponding to dependent and independent physical variables. According to the structure of the network, a dependent physical variable is the starting point of an arc that ends up (final pointed arc edge), to an independent variable. All these interconnections are documented according to the below three ways: 1) dependent and independent variables interconnected by using the logical operator “depends on” quoting existent explicit functions and equations, 2) dependent and independent variables interconnected by using the logical operator “depends on” quoting produced implicit functions, according to Rayleigh’s method of indices, presented in Tables A1-A7 of the Appendix 3) dependent and independent variables interconnected by using the logical operator “related to” based on a logical dependence between the examined nodes-concepts-variables. All the above-described methods are detailed presented in the “contribution” column of Tables A1-A7 in the Appendix along with a Terminology Tablein (SI units) of TableA8.
PP1,1: Lassabatere et al. (2010), Effect of the settlement of sediments on water infiltration in two urban infiltration basins, Geoderma, 156(3-4), 316-325.
PP1,2: Assouline (2013), Infiltration into soils: Conceptual approaches and solutions, Water resources research, 49(4), 1755-1772.
ASTM1,3: ASTM C1585-20 (2020), Standard Test Method for Measurement of Rate of Absorption of Water by Hydraulic-Cement Concretes.
ASTM1,4: ASTM D3385-18 (2018), Standard Test Method for Infiltration Rate of Soils in Field Using Double-Ring Infiltrometer.
ASTM2,1: ASTM D3385-18 (2018), Standard Test Method for Infiltration Rate of Soils in Field Using Double-Ring Infiltrometer.
ASTM2,2: ASTM D5126-16e1 (2016), Standard Guide for Comparison of Field Methods for Determining Hydraulic Conductivity in Vadose Zone.
ASTM2,3: ASTM C1792-14 (2014), Standard Test Method for Measurement of Mass Loss versus Time for One-Dimensional Drying of Saturated Concretes
PP2,4: Di Prima et al. (2016), Testing a new automated single ring infiltrometer for Beerkan infiltration experiments, Geoderma, 262, 20-34.
The network presented on FigureA1 of the Appendix is structured by using all relevant ASTM standardization available to build up rigid constructed generations. Nonetheless, no other international fully approved standardized methodology was adopted (e.g. ISO, DIN, BS, EN etc.). A terminology Tableis an integral part of the Ontology-Based Knowledge Network and is a very useful medium to avoid scientists of boundary disciplines misapprehension/misleading to even basic concepts.
The following presented paradigm could be a characteristic one to hydraulic engineers and earth scientists that their activities are located in between interdisciplinary knowledge areas. The term “infiltration” forms a continuum with “percolation” and “seepage” terms, so that several authors use them interchangeably, as quasi synonyms. From a topological point of view infiltration is considered to be the water movement into the soil while percolation refers to the water path within/through the soil until it reaches the water table. Consequently, it seems that there is a first interface between the infiltration and percolation zones as well as another subsequent interface between percolation zone and water table. On the other hand, seepage is the slow escape/leakage of water on or near the earth surface simulating a downhill route possible formed by natural phenomena or local constitution of earth, implying difference in permeability enhanced by the presence of clay-loam soils and certain minerals.
The presented multi-generation ontological network, which employs standardization of techniques/methods relevant to sedimentation during and after infiltration, is merely the beginning of a forthcoming profound interdisciplinary expansion. The corresponding network of standards and recommended practices might receive further enrichment, incorporated e.g. ISO/EN standards and more profound phenomenological knowledge related to porous media infiltration. This could be achieved by presented new interconnections among conceptual levels and deeper generation formation analysis upon the already proposed structure.
Figure A1. The integrated ontology-based knowledge network that represents the interconnections between ASTM standards (ASTMi,n) and scientific published papers (PPi,n) formed in accordance with the third column named “node” of each Tables A1-A7 of the Appendix.
Figure A2. The integrated ontology-based knowledge network that represents the interconnections between soil/water concepts/properties formed in accordance with the fifth column named “concept” of each Tables A1-A7 of the Appendix.
Table A1. Description of all nodes (see Figure A1) under the form of Standards or published papers and the corresponding concepts (see Figure A2) which are included in the first generation.
Table A2. Description of all nodes (see Figure A1) under the form of standards or published papers and the corresponding concepts (see Figure A2) which are included in the second generation.
Table A3. Description of all nodes (see Figure A1) under the form of Standards or published papers and the corresponding concepts (see Figure A2) which are included in the third generation.
Table A4. Description of all nodes (see Figure A1) under the form of Standards or published papers and the corresponding concepts (see Figure A2) which are included in the fourth generation.
Table A5. Description of all nodes (see Figure A1) under the form of Standards or published papers and the corresponding concepts (see Figure A2) which are included in the fifth generation.
Table A6. Description of all nodes (see Figure A1) under the form of Standards or published papers and the corresponding concepts (see Figure A2) which are included in the sixth generation.
Table A7. Description of all nodes (see Figure A1) under the form of Standards or published papers and the corresponding concepts (see Figure A2) which are included in the seventh generation.
Terminology Table—SI Units
Table A8. All the term and the soil/water physicochemical & biological properties that are being used in the above Appendix tables, including their symbols and dimensions.
 ASTM C714-17, Standard Test Method for Thermal Diffusivity of Carbon and Graphite by Thermal Pulse Method.
 ASTM C1585-20, Standard Test Method for Measurement of Rate of Absorption of Water by Hydraulic-Cement Concretes.
 ASTM C1792-14, Standard Test Method for Measurement of Mass Loss versus Time for One-Dimensional Drying of Saturated Concretes.
 ASTM D653-20, Standard Terminology Relating to Soil, Rock, and Contained Fluids.
 ASTM D3385-18, Standard Test Method for Infiltration Rate of Soils in Field Using Double-Ring Infiltrometer.
 ASTM D4612-16, Standard Test Method for Calculating Thermal Diffusivity of Rock and Soil.
 ASTM D5093-15e1, Standard Test Method for Field Measurement of Infiltration Rate Using Double-Ring Infiltrometer with Sealed-Inner Ring.
 ASTM D5126-16e1, Standard Guide for Comparison of Field Methods for Determining Hydraulic Conductivity in Vadose Zone.
 ASTM D5334-14, Standard Test Method for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe Procedure.
 ASTM D5856-15, Standard Test Method for Measurement of Hydraulic Conductivity of Porous Material Using a Rigid-Wall, Compaction-Mold Permeameter.
 ASTM D7100-11 (2020) Standard Test Method for Hydraulic Conductivity Compatibility Testing of Soils with Aqueous Solutions.
 ASTM E1461-13, Standard Test Method for Thermal Diffusivity by the Flash Method.
 ASTM E2585-09 (2015) Standard Practice for Thermal Diffusivity by the Flash Method.
 ASTM F316-03 (2019) Standard Test Methods for Pore Size Characteristics of Membrane Filters by Bubble Point and Mean Flow Pore Test.
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 Camara, J., et al. (2017) Lithologic Control on Soil Texture Heterogeneity. Geoderma, 287, 157-163. https://doi.org/10.1016/j.geoderma.2016.09.006
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 Di Prima, S. (2016) Testing a New Automated Single Ring Infiltrometer for Beerkan Infiltration Experiments. Geoderma, 262, 20-34. https://doi.org/10.1016/j.geoderma.2015.08.006
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 Haverkamp, R., Parlange, J.Y., Starr, Y.L., Schmitz, G. and Fuentes, C. (1990) Infiltration under Ponded Conditions. 3. A Predictive Equation Based on Physical Parameters. Soil Science, 149, 292-300. https://doi.org/10.1097/00010694-199005000-00006
 Haverkamp, R., Ross, P.J., Smetten, K.R.J and Parlange, J.Y. (1994) Three-Dimensional Analysis of Infiltration from the Disc Infiltrometer: 2. Physically Based Infiltration Equation. Water Resources Research, 30, 2931-2935. https://doi.org/10.1029/94WR01788
 Jaynes, R.A. and Gifford, G.F. (1981) An In-Depth Examination of the Philip Equation for Cataloging Infiltration Characteristics in Rangeland Environments. Journal of Range Management, 34, 285-296. https://doi.org/10.2307/3897853
 Jindaluang, W., et al. (2013) Influence of Soil Texture and Mineralogy on Organic Matter Content and Composition in Physically Separated Fractions Soils of Thailand. Geoderma, 195-196, 207-219. https://doi.org/10.1016/j.geoderma.2012.12.003
 Kosugi, K. (1997) A New Model to Analyze Water Retention Characteristics of Forest Soils Based on Soil Pore Radius Distribution. Journal of Forest Research, 2, 1-8. https://doi.org/10.1007/BF02348255
 Lassabatere, L., et al. (2010) Effect of the Settlement of Sediments on Water Infiltration in Two Urban Infiltration Basins. Geoderma, 156, 316-325. https://doi.org/10.1016/j.geoderma.2010.02.031
 Leverett, M.C. (1941) Capillary Behavior in Porous Solids. Transactions of the AIME, 142, 159-172. https://doi.org/10.2118/941152-G
 Liu, Y., et al. (2014) Effects of Capillary Pressure—Fluid Saturation—Relative Permeability Relationships on Predicting Carbon Dioxide Migration during Injection into Saline Aquifers. Energy Procedia, 63, 3616-3631. https://doi.org/10.1016/j.egypro.2014.11.392
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Glossary and Terms
 American Geosciences Institute AGI (2020) Glossary of Geology. Fifth Edition, Revised. https://www.americangeosciences.org/pubs/glossary
 Schluberger Oil Field (2020) The Oilfield Glossary. https://www.glossary.oilfield.slb.com
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1No model/function or quantitative path exists, interconnecting the concepts, though experimentally proven.
2No model/function or quantitative path exists, interconnecting the concepts.
3No model/function or quantitative path exists, interconnecting the concepts.
4No model/function or quantitative path exists, interconnecting the concepts.
5No model/function or quantitative path exists, interconnecting the concepts.
4No model/function or quantitative path exists, interconnecting the concepts.
5No model/function or quantitative path exists, interconnecting the concepts.
 Borst, W. N. (1997). Construction of Engineering Ontologies for Knowledge Sharing and Reuse. Enschede: Centre for Telematics and Information Technology (CTIT).
 Guarino, N. (1995). Ontologies and Knowledge Bases: Towards a Terminological Clarification. In Towards Very Large Knowledge Bases (pp. 25-32). Amsterdam: IOS Press.
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 Lassabatere, L. et al. (2010). Effect of the Settlement of Sediments on Water Infiltration in Two Urban Infiltration Basins. Geoderma, 156, 316-325.
 Mikkelsen, P. S. et al. (1997). Pollution of Soil and Groundwater from Infiltration of Highly Contaminated Stormwater—A Case Study. Water Science and Technology, 36, 325-330.
 Patle, G. T. et al. (2018). Estimation of Infiltration Rate from Soil Properties Using Regression Model for Cultivated Land. Geology, Ecology & Landscapes, 3, 1-13.
 Tejedor, M. et al. (2013). Soil Properties Controlling Infiltration in Volcanic Soils (Tenerife, Spain). Soil Science Society of America Journal, 77, 202-212.
 Wang, P. et al. (2017). Effects of Urbanization, Soil Property and Vegetation Configuration on Soil Infiltration of Urban Forest in Changchun, Northeast China. Chinese Geographical Science, 28, 482-494.
 Weng, S. S., & Chang, H. L. (2008). Using Ontology Network Analysis for Research Document Recommendation. Expert Systems with Applications, 34, 1857-1869.
 Wood, J. C. et al. (1987). Important Factors Influencing Water Infiltration and Sediment Production on Arid Lands in New Mexico. Journal of Arid Environments, 12, 111-118.