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Verification of Determination of Hydraulic Conductivity for Coarse Soils by Empirical Formulas Based on the Density Index

Verification of Determination of Hydraulic Conductivity for Coarse Soils by Empirical Formulas... Acta Sci. Pol. Architectura 20 (2) 2021, 83–92 content.sciendo.com/aspa ISSN 1644-0633 eISSN 2544-1760 DOI: 10.22630/ASPA.2021.20.2.17 ORIGINAL P APER Received: 19.05.2021 Accepted: 08.06.2021 VERIFICATION OF DETERMINATION OF HYDRAULIC CONDUCTIVITY FOR COARSE SOILS BY EMPIRICAL FORMULAS BASED ON THE DENSITY INDEX Krystyna Jaśkiewicz , Tomasz Godlewski Building Structures, Geotechnics and Concrete Department, Building Research Institute, Warsaw, Poland ABSTRACT This paper examines the importance of empirical formulas for estimating the hydraulic conductivity of non- -cohesive soils, taking into account their compaction. Empirical formulas are often used in practice to quickly and cost-effectively determine hydraulic conductivity of soil. Verification of calculation of this parameter was performed for five formulas taking into account the characteristic diameters of grains and porosity. The results obtained by calculations were compared with the results of laboratory tests performed on soil samples with the same porosity coefficients (at different density index) as assumed in the calculation method. An empirical formula has been proposed to correct the hydraulic conductivity of soils obtained from the Hazen formula by taking into account the density index of a given soil. Key words: filtration, hydraulic conductivity, empirical formulas, density index INTRODUCTION open-pit mine drainage, as well as the stability of The soil filtration properties are very important in the slopes. The problem also concerns buildings in rela- engineering-geological, geotechnical and hydrogeo- tion to environmental protection, in waste landfills, logical assessment of the site. The hydraulic conduc- sewage treatment plants, etc. Currently, an increas- tivity (k) is a parameter which defines the ability of ingly serious problem during construction of excava- the soil medium to transport water in it. It depends on tions (below the groundwater table) is drainage of the such soil characteristics as: graining, porosity, mineral construction site. Due to the limitations of environ- composition, moisture, shape and surface texture of mental decisions, the inflow of groundwater into the particle, temperature of water (Wiłun, 1982; Head & excavation should be estimated in detail, and then the Epps, 2011; Zięba, 2016; Jiang et al., 2021). Hydraulic optimal method of drainage should be selected. conductivity determines the ability of the soil to pass There are many different methods to determine water subjected to water pressure difference. Accord- the hydraulic conductivity including field methods ing to the linear Darcy’s law, it expresses the relation- (Kozeny, 1953; Cheng & Chen, 2007; Hussain & ship between the hydraulic gradient and the water Nabi, 2016), laboratory methods and calculations from filtration rate (Myślińska, 1998; Head & Epps, 2011). empirical formulas (Kozerski, 1977; Twardowski & The correct determination of the hydraulic conduc- Drożdżak, 2006; Idris-Nda, 2013). The most common- tivity becomes important when assessing the filtration ly used method of field tests is pumping test, which in- conditions in the areas of hydrotechnical structures, volves pumping water out of a well to obtain a hydro- Krystyna Jaśkiewicz https://orcid.org/0000-0002-8948-6275; Tomasz Godlewski https://orcid.org/0000-0001-7986-5995 k.jaskiewicz@itb.pl © Copyright by Wydawnictwo SGGW Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 dynamic reaction of the subsoil. In situ tests based on ing from the genesis) on the obtained permeability co- pumping tests are the most accurate in describing the efficients are significant for non-cohesive soils from the practical point of view. Results from the literature actual filtration conditions in the subsoil, but due to time-consumption, the cost and scope of implementa- show that for the same soils but with different den- tion (construction of wells and piezometers), they are sity indexes, the permeability coefficient differs even rarely performed at the stage of geotechnical investi- several times (Wrzesiński, 2020). There are formulas gation (Wrzesiński, 2020). On the other hand, labora- in literature, based on porosity and other properties. However, their use requires taking additional samples tory tests for the estimation of permeability are less reliable. In the field of geotechnical tests, the hydrau- and conducting laboratory tests, which increase the lic conductivity for coarse-grained soils is most often time of execution and generate additional costs. The determined using empirical formulas based on the par- density index value is almost always obtained in field ticle size distribution curve. It is justified because the tests (dynamic sounding, static sounding) as part of geological or geotechnical investigations. particle size analysis is performed as standard test in most geotechnical investigations and the particle size The purpose of the research presented in the paper distribution is the main factor influencing the per- is to determine and compare the values of the perme- meability of coarse soils (Parylak, Zięba, Bułdys & ability coefficient in coarse soils determined with use Witek, 2013). Therefore, this method of determination of selected empirical formulas and simple laboratory tests, with focus on the impact of the density index is widely practiced despite its lower reliability of esti- mation of the hydraulic conductivity. change. There are many empirical formulas for calculating the hydraulic conductivity based on the particle size MATERIAL AND METHODS distribution. They have a limited scope of application The tests were conducted on samples of coarse-grained and limited accuracy of determinations related to the subjective interpretation of the particle size curve, (non-cohesive) soils from Poland. Sample soils ge- especially, in the case of sandy soils containing clay netically belong to fluvial formations of the Mazovian or silt admixtures. Empirical formulas can be divided interglacial and fluvioglacial formations of the Odra into three groups (Twardowski & Drożdżak, 2006): glaciation. The hydraulic conductivity of samples was determined by two methods: the first, based on labora- − Group I – formulas that only take into account characteristic grain diameters; tory tests, and the second, using empirical formulas. − Group II – formulas taking into account the char- The laboratory method of determining the conduc- acteristic grain diameter and porosity of soil; tivity is based on the principle of measuring the veloc- − Group III – formulas taking into account the gran- ity of lowering of the table of water freely flowing out of a tube containing a sample of the examined ground ulometric composition and porosity of the soil as well as the physical properties of the filtering (i.e. the Kaminski tube). The method allows for very water. simple and quick determination of approximate value The aim of this study was to determine if there is a of hydraulic conductivity of high permeable soils. relationship between hydraulic conductivity and den- The principle of the method is to measure the veloc- ity of lowering of the table of water flowing through sity index and if it is large enough to be used to de- termine the filtration coefficient by indirect methods the sample of specified height at variable (decreasing) (empirical formulas). The value of this index depends pressure of water column (Myślińska, 1998; Twar- among others on grain composition, porosity, grain dowski & Drożdżak, 2007). The formula for estimat- shape (Parylak et al., 2013). Porosity is one of the im- ing the hydraulic conductivity has the form: portant parameters determining the ability of soil to accumulate water. It is also closely related to the den- ls§· sity and shape of grains (Zięba, 2016). The impact of k=− ln 1 (1) ¨¸ tH ©¹ 0 the density index and the shape of soil grains (depend- 84 architectura.actapol.net Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 where: tory filtration test was carried out), the particle size k – hydraulic conductivity [cm], distribution was established according to PKN-CEN t – time for the water column to decrease in height [s], ISO/TS 17892-4:2008 (PKN, 2008). Based on the s – reduction of height of the water column [mm, cm], particle size curve, parameters d , d , d , d and 10 17 50 60 H – initial hydraulic height in the tube [mm, cm]. soil type were determined, where d , d , d , d , are 0 10 17 50 60 grain sizes [mm] corresponding to 10, 17, 50 and 60% In spite of its simplicity and some limitations, the by weight passing through the sieves. The soil type method has been widely used in practice as a simple was determined in accordance with PN-B-0248:1986 method of determining the hydraulic conductivity of (PKN, 1986) as well as PN-EN ISO 14688-2:2019 soils (Kozerski, 1977). Some studies show that esti- (PKN, 2019). The results (28 tests) are summarized mated filtration values reflect realistic results from test in Table 1. pumping (Żurek & Czudec, 2007). In order to determine the hydraulic conductivity by Testing of the hydraulic conductivity was carried the indirect method, some empirical formulas based out on samples with disturbed structure. The sam- on studies by Vukovic and Soro (1992) were used. The ples were dried in the oven at 105°C. According to general form of the formula is expressed as: PN-B-04481:1988 standard (Polski Komitet Normal- izacyjny [PKN], 1988) the maximum and minimum g ªº Kn =⋅[]βϑ⋅[ ( )]⋅[d ] (3) «» dry density volume of soil was tested in order to de- ¬¼ termine the parameters of forming samples at different where: degrees of compaction. Samples intended for filtration –1 K – hydraulic conductivity [cm·s ], testing were formed dry and then wetted by capillar- –2 g – the gravitational constant [cm·s ], ity. This was done from the bottom so that air could v = ν – kinematic viscosity, , where: μ – the tem- escape from the surface. For each sample, four filtration tests were per- perature-dependent dynamic viscosity of wa- formed using the laboratory method for a given com- –1 –1 ter [g·cm ·s ], ρ – the temperature-dependent paction level to determine the filtration coefficient –3 water density [g·dm ], at a given density and then the average of these four β – constant depending on characteristics of the measurements was taken. The tests were made for four porous medium, density index levels: loose – ln (I = 0.30), medium ϑ (n) – porosity function, dense – szg (I = 0.50), dense – zg (I = 0.70), very D D d – effective grain diameter [cm, mm], dense – bzg (I = 0.90). In total, 112 filtration tests were carried out. All results were related to tempera- To evaluate the applicability of the empirical for- ture 10°C using the empirical equation: mulas for determination of the hydraulic conductivity, k calculations of this parameter were carried out using k = (2) the following five formulas: 0.7 + 0.03T 1. Hazen (1892) according to Vukovic and Soro where: (1992) and Devlin (2015) k – hydraulic conductivity at the water temperature –1 of 10°C [m·s ], −42 ªº Kn =⋅ 6⋅10 ⋅ªº 1+10 − 0.26 ⋅d () (4) k – hydraulic conductivity at the temperature T, at t ¬¼ 10 ¬¼ –1 which the test was conducted [m·s ], T – water temperature at the time of testing [°C]. Hazen formula is used for uniformly graded sands; however, it could also be used for the range fine In aim to determine the hydraulic conductivity sand − gravel, provided the sediment has a uni- based on empirical formulas and to control the grain formity coefficient less than 5 and effective grain size distribution of each sample (for which the labora- size between 0.1 and 3 mm. architectura.actapol.net 85 Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 Table 1. Presentation of grain size distribution characteristic of analysed soil Particle size distribution Soil type acc. to Coefficient [mm] Density index Soil of uniformity Test (I ) sample (CU) PN-EN ISO [-] PN-B-0248 d d d d [-] 10 17 50 60 14688-2 1 Ps MSa 2 0.20 0.26 0.38 0.42 0.90 2 Ps MSa 2 0.17 0.23 0.38 0.42 0.70 3 Ps MSa 2 0.23 0.27 0.39 0.43 0.50 4 Ps MSa 2 0.19 0.26 0.39 0.43 0.30 5 Ps MSa 3 0.12 0.15 0.27 0.32 0.90 6 Ps MSa 3 0.12 0.15 0.27 0.32 0.70 7 Ps MSa 3 0.12 0.14 0.29 0.34 0.50 8 Ps MSa 3 0.12 0.15 0.28 0.34 0.30 9 Ps MSa 3 0.10 0.13 0.25 0.30 0.90 10 Ps MSa 3 0.12 0.15 0.28 0.33 0.70 11 Ps MSa 3 0.12 0.14 0.26 0.32 0.50 12 Ps MSa 3 0.13 0.16 0.31 0.36 0.30 13 Ps MSa 3 0.12 0.15 0.31 0.37 0.90 14 Ps MSa 3 0.11 0.14 0.29 0.35 0.70 15 Ps MSa 3 0.12 0.15 0.30 0.36 0.50 16 Ps MSa 3 0.11 0.14 0.29 0.34 0.30 17 Ps MSa 3 0.12 0.15 0.31 0.36 0.90 18 Ps MSa 3 0.12 0.16 0.32 0.37 0.70 19 Ps MSa 3 0.12 0.16 0.32 0.37 0.50 20 Ps MSa 3 0.13 0.16 0.31 0.37 0.30 21 Pr CSa 5 0.19 0.27 0.78 0.93 0.90 22 Pr CSa 5 0.19 0.27 0.78 0.94 0.70 23 Pr CSa 5 0.18 0.24 0.75 0.93 0.50 24 Pr CSa 5 0.19 0.27 0.78 0.93 0.30 25 Po grCSa 2 0.51 0.57 0.85 0.94 0.90 26 Po grCSa 2 0.47 0.55 0.85 0.94 0.70 27 Po grCSa 2 0.49 0.57 0.88 0.98 0.50 28 Po grCSa 2 0.50 0.57 0.87 0.97 0.30 Ps (MSa) – medium sand; Pr (CSa) – coarse sand; Po (grCSa) – coarse sand with gravel. 86 architectura.actapol.net Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 2. Sauerbrei (1932) according to Vukovic and Soro 5. Chapuis (2004) according to Vukovic and Soro (1992) and Devlin (2015) (1992) and Devlin (2015) 2 () 0.5504−0.2937 ξ ªº −52 n 1.291ξ−⋅ 0.6435ªº 0.510 ªº ªº Kd =⋅ 3.75⋅10 τ ⋅ ⋅ (5) Kd =⋅ 10 (8) «» () 17 10 2 ¬¼«» ¬¼ ¬¼ «» (1− n ) ¬¼ where: (9) ξ = –4 2 –2 τ ≅ 1.093⋅10 T + 2.102⋅10 + 0.5889, 1− n T – temperature of water [°C]. The Chapuis formula is applicable for 0.3 < n < 0.7, 3. Kozeny–Carman (1953) according to Vukovic and 0.10 < d < 2.0 mm, 2 < CU < 12, d /d < 1.4. 10 10 5 Soro (1992) and Devlin (2015) RESULTS AND DISCUSSSION ªº −32 n ªº Kd =⋅ 8.3⋅10 ⋅ ⋅ (6) «» ¬¼ 2 Based on the results obtained from particle size dis- «» (1− n ) ¬¼ tribution (Table 1), the soils were divided into the fol- The Kozeny–Carman formula is not appropriate for lowing groups: soils with effective size above 3 mm or for clayey A. Medium sand – MSa (Ps): A – CU = 2 (Sample 1) soils (Carrier, 2003). and A – CU = 3 (Samples 2, 3, 4, 5). B. Coarse sand – CSa (Pr); CU = 5 (Sample 6). 4. Zamarin (1928) according to Vukovic and Soro C. Coarse sand with gravel – grCSa (Po); CU = (1992) and Devlin (2015) = 2 (Sample 7). The division criterion was the soil type, the co- ªº efficient of uniformity (CU) and value of effective «» grain diameter. The change in the hydraulic conduc- «» tivity determined by a laboratory method was ob- «» ªº g «» −3 n 1 served depending on the density index for each of the ªº KC =⋅ 8.64⋅10 ⋅ ⋅ «»n «» ¬¼ 2 v soil groups. In the case of laboratory tests for coarse- §· «» (1− n ) ¬¼«» ln¨¸ -grained soils of loose density (density index I = 0.3) «» ¨¸ ©¹ i «» during the water permeability determination with use Δg i=1 «» g d dd − of a so-called the Kaminski tube, the consolidation ¬¼ ii of samples during the filtration test was observed, (7) which resulted in a change of the compaction state where: from loose to medium dense (Fig. 1). The cause of C – factor depending on the porosity, this phenomenon may arise from the temporary in- C = (1,275 − 1.5n) , duction of negative pore pressure during saturation ∆g – the fraction of mass that passes between of the dry-formed sample. sieves i and i + 1 where i is the smaller sieve, The determination of the hydraulic conductiv- d – the maximum grain diameter in fraction i, ity by the indirect method (empirical formulas) was d – the minimum grain diameter in fraction i. performed for each sample at different porosity val- ues corresponding to the density index at which the The formula is applicable for large-grained sands laboratory tests were performed. The results of calcu- with no fractions having d < 0.00025 mm. It can be lations with these formulas, for individual soil samples used for fine and medium-grained sands. and laboratory tests, are presented in Table 2. architectura.actapol.net 87 Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 WƐ;ĂD^Ϳ hϯс / ŵƉE ŵƉE ŵƉE ŵƉE ďnjŐ ͕Ϭ ϬϬ ϬϬϬϬ͘ϬϬ͘ϬϬϭϱϬ͘ϬϬϭϬ  Ϭ ϱ Ͳϭ Ŭ ΀ŵƐ ΁ ƵсϮ ƐnjŐ Ɖϭ njŐ ďnjŐ Ϭ ϬϬ͘ϰϬ Ͳϭ Ŭ ΀ŵƐ ΁ ĂͿĂͿ;;^^WƌWƌ ůŶ ƐnjŐ Ă^ŵƉůĞEŽ͘ϲ njŐ ďnjŐ Ϭ Ϭϭ Ϯ Ϭϯ ͕Ϭϰ Ŭ ΁ WŽ;Őƌ^ĂͿ / Ϭ ƐnjŐ / Ϭ Fig. 1. Changes in the hydraulic conductivity (k ) ŵƉE / Ϭ laboratory tests for Ps (MSa) – medium sand; Pr (CSa) – coarse sand; Po (grCSa) ďnjŐ – coarse sand with gravel (average of four / Ϭ determinations: ln – loose; szg – medium Ϭ ͕ϬϬϬϱ Ϭ ͕ϬϭϬϱ ͘Ϭ dense; zg – dense; bzg – very dense) de- Ͳϭ Ŭ ΀ŵƐ ΁ pending on the density index (I ) 88 architectura.actapol.net ϭϬ Ϭ͕Ϭϭϱ Ϭ͘ϬϭϬ Ϭ͘ϬϬϱϬϬϬ Ϭ͕Ϭϭ Ϭ͕ϬϬ сϬ͘ϵ сϬ͘ϳ njŐ ϳŽ͘ůĞ^Ă сϬ͘ϱ сϬ͘ϯ ůŶ ϭϬ ΀ŵƐ Ͳϭ Ϭ͘ϬϬϬ͘ϬϬϯ Ϭ͘ϬϬϮϬ͘ϬϬϭϬ͘ϬϬϬ ϬϬ ͕ϬϬ ϬϬϬ͕ ͕ϬϬ ϬϬϬ͕ сϬ͘ϵϬ сϬ͘ϳϬ сϬ͘ϱϬ сϬ͘ϯϬ ϭϬ ͘ϬϬϯϬ͘ϬϬϮϭϬ͘ϬϬϬϬϬϬ͘ ϰϬϬ͕ϬϬ ϯϬϬ͕ϬϬ ϮϬϬ͕ϬϬ ϭϬϬ͕ϬϬ ϬϬϬ͕ϬϬ сϬ͘ϵϬ сϬ͘ϳϬ Ž͘ůĞE^Ăŵ сϬ͘ϱϬ сϬ͘ϯϬ D^ĂͿƐ; ůŶ ϭϬ ͘ϬϬϮ Ϭ͘ϬϬϮϬϬ͘ϬϬϭϱ ϮϱϬϬϬ͕ ϮϬϬ͕ϬϬ ϭϱϬϬϬ͕ ϭϬϬ͕ϬϬ ϬϱϬ͕ ϬϬϬϬ сϬ͘ϵϬ Ž͘ϮůĞ^Ă сϬ͘ϳϬ Ž͘ϯůĞ^Ă njŐ Ž͘ϰůĞ^Ă Ž͘ϱůĞ^Ă сϬ͘ϱϬ Ɛnj сϬ͘ϯϬ ůŶ Table 2. Comparison of the hydraulic conductivity value obtained with use of empirical formulas and in laboratory tests –1 Estimation of hydraulic conductivity [m·s ] by Density Soil type acc. to Tested Porosity Soil index empirical formula laboratory test Test soil (n) sample (I ) D (average of four PN-EN ISO Kozeny– group [-] PN-B-0248 Hazen Sauerbrei Zamarin Chapuis [-] measurement) 14688-2 –Carman 1 Ps MSa 0.40 (ln) 0.30 5.67E-04 4.63E-04 8.46E-04 7.12E-04 4.28E-04 1.47E-03 2 Ps MSa 0.38 (szg) 0.50 5.20E-04 3.72E-04 6.79E-04 6.24E-04 3.19E-04 9.78E-04 A 1 3 Ps MSa 0.35 (zg) 0.70 4.49E-04 2.65E-04 4.83E-04 5.02E-04 2.10E-04 6.68E-04 4 Ps MSa 0.33 (bzg) 0.90 4.02E-04 2.09E-04 3.81E-04 4.28E-04 1.62E-04 4.69E-04 5 Ps MSa 0.41 (ln) 0.30 2.19E-04 1.71E-04 1.08E-04 2.74E-04 1.66E-04 1.53E-03 6 Ps MSa 0.39 (szg) 0.50 2.01E-04 1.37E-04 8.71E-05 2.41E-04 1.17E-04 1.28E-03 A 2 7 Ps MSa 0.36 (zg) 0.70 1.75E-04 9.82E-05 6.22E-05 1.96E-04 7.21E-05 9.21E-04 8 Ps MSa 0.33 (bzg) 0.90 1.49E-04 6.90E-05 4.37E-05 1.55E-04 4.57E-05 6.27E-04 9 Ps MSa 0.41 (ln) 0.30 2.66E-04 2.05E-04 4.29E-04 4.19E-04 2.07E-04 2.35E-03 10 Ps MSa 0.38 (szg) 0.50 2.34E-04 1.47E-04 3.08E-04 3.44E-04 1.25E-04 1.23E-03 A 3 11 Ps MSa 0.36 (zg) 0.70 2.12E-04 1.18E-04 2.46E-04 2.98E-04 9.12E-05 8.53E-04 12 Ps MSa 0.33 (bzg) 0.90 1.81E-04 8.27E-05 1.73E-04 2.36E-04 5.84E-05 6.61E-04 13 Ps MSa 0.39 (ln) 0.30 1.75E-04 1.25E-04 4.58E-05 1.95E-04 9.99E-05 7.82E-04 14 Ps MSa 0.36 (szg) 0.50 1.52E-04 8.92E-05 3.28E-05 1.58E-04 6.08E-05 6.52E-04 A 4 15 Ps MSa 0.34 (zg) 0.70 1.37E-04 7.07E-05 2.59E-05 1.36E-04 4.44E-05 3.91E-04 16 Ps MSa 0.31 (bzg) 0.90 1,14E-04 4.90E-05 1.80E-05 1.05E-04 2,85E-05 2.91E-04 17 Ps MSa 0.39 (ln) 0.30 2.20E-04 1.57E-04 1.06E-04 2.81E-04 1.30E-04 1.22E-03 18 Ps MSa 0.37 (szg) 0.50 2.01E-04 1.26E-04 8.45E-05 2.45E-04 9.37E-05 7.50E-04 A 5 19 Ps MSa 0.34 (zg) 0.70 1.72E-04 8.87E-05 5.97E-05 1.96E-04 5.91E-05 5.05E-04 20 Ps MSa 0.31 (bzg) 0.9 1.43E-04 6.15E-05 4.14E-05 1.52E-04 3.84E-05 2.96E-04 21 Pr CSa 0.39 (ln) 0.30 4.97E-04 4.42E-04 2.28E-03 1.38E-03 3.33E-04 3.04E-03 22 Pr CSa 0.37 (szg) 0.50 4.54E-04 3.54E-04 1.82E-03 1.21E-03 2.49E-04 3.24E-03 B6 23 Pr CSa 0.34 (zg) 0.70 3.89E-04 2.50E-04 1.29E-03 9.63E-04 1.65E-04 2.30E-03 24 Pr CSa 0.31 (bzg) 0.90 3.24E-04 1.74E-04 8.94E-04 7.48E-04 1.12E-04 1.91E-03 25 Po grCSa 0.38 (ln) 0.30 2.87E-03 1.71E-03 3.57E-03 3.26E-03 2.36E-03 1.20E-02 26 Po grCSa 0.36 (szg) 0.50 2.61E-03 1.36E-03 2.84E-03 2.83E-03 1.91E-03 1.22E-02 C7 27 Po grCSa 0.33 (zg) 0.70 2.22E-03 9.57E-04 2.00E-03 2.24E-03 1.42E-03 8.26E-03 28 Po grCSa 0.31 (bzg) 0.90 1.96E-03 7.48E-04 1.56E-03 1.88E-03 1.18E-03 5.20E-03 Ps (MSa) – medium sand; Pr (CSa) – coarse sand; Po (grCSa) – coarse sand with gravel ln – loose; szg – medium dense; zg – dense; bzg – very dense. ϬϭϰϬ ϬϭϮϬ ϬϭϬϬ ϬϬϴϬ ϬϬϲϬ ϬϬϰϬ ϬϬϮϬ ϬϬϬϬ ΀ŵ ϬϬϰϴϬϬϰϴϬ͘Ϭ͘ ϬϬϰϬϬϬϰϬϬ͘Ϭ͘ ϬϬϯϮϬϬϯϮϬ͘Ϭ͘ ϬϬϮϰϬϬϮϰϬ͘Ϭ͘ ϬϬϭϲϬϬϭϲϬ͘Ϭ͘ ϬϬϬϴϬϬϬϴϬ͘Ϭ͘ ϬϬϬϬϬ͘ ϬϬϬϬϬ͘ ΀ŵ Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 Data presented in Figure 1 show clear relation be- ratory tests. This comparison indicates the need for tween the changes in the hydraulic conductivity (k) individual evaluation of reliability of the formulas in and effective pore diameter caused by the increase in the assessment of the filtration considering the mate- the density index (I ). This points at the need of tak- rial type. An attempt was made to verify the hydraulic ing the state of the soil (density) into account. This conductivity determined according to the Hazen for- relationship is visible regardless of the grain size and mula (most commonly used in design practice) taking type of material. Generally, lower permeability coeffi- into account density index (corresponding to porosity) cients were obtained in soils characterized by a higher for each tested soils (Fig. 2). For the Hazen equation, density index. It should be noted that the value of the the filtration coefficients obtained are of lower order permeability coefficient is influenced by the shape of magnitude than the laboratory test results, depend- of soil particles and their mutual arrangement (Pary- ing on the density parameter. lak et al., 2013; Zięba, 2016; Shen, Zhu & Gu, 2019; Wrzesiński, 2020). This effect can be ignored in this CONCLUSIONS study, since all sands had the same origin – they are alluvial soils. Laboratory methods were used to evaluate the hydrau- When analysing the results given in Table 2, for- lic conductivity (k), which is a basic hydrogeological mulas with a better and worse match to the results ob- parameter determining the ability of soil to transport tained from direct measurements can be indicated. The water, and confronted with the values obtained from best representation for non-cohesive soils of group A empirical formulas for soils characterized by four was obtained with the Chapuis formula, and for group different density indexes. The results of the filtration A with the Zamarin formula. For soils of B and C coefficient calculations based on empirical formulae groups, the best results in comparison with laboratory are inaccurate and highly differentiated (in described tests were obtained by Kozeny–Carman formula. The cases from four to six times), which undermines their Hazen formula gave relatively good hydraulic con- reliability and excludes the possibility of using this ductivity values for each group relative to the labo- method in well-understood engineering practice. soil groups A , A , B soil group C 1 2 džсLJ džсLJ ϮƵс ϮWŽhс ϰdžϴ͘сϰLJͿ͕ƵсϮWƐ;ŶĞĂƌŝů LJ ĞĂƌ;WŽϮͿ͕ůŝŶhс ĂƌͲŬ ϰdžϬ͘сϱLJͿ͕ƵсϯWƐ;ŶĞĂƌŝů džϵ Ϳϲϱ͕ƵсW;ĞƌĂ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ͳϭ ͲŬŬƋƵĂƚŝŽŶĞ ͲŬŬĞƋƵĂƚŝŽŶ Ɛ Y Y Fig. 2. Relations between hydraulic conductivity obtained from empirical formula (k ) and in laboratory tests (k ) of soil Q L groups 90 architectura.actapol.net Ͳϭ ŬůĂďŽƌƚŽ Ͳϭ ͲŬŬůĂďŽƌĂƚŽƌLJ ΁ ΀ŵ ΁ ΀ŵƐͲ Ϭ͘ϬϬϬϬϬϬϬ͕ϬϬ ϬϬϬϬϬ͘ ϬϬϬ͕ϬϬ ůŝŶƌLJс͘ϯϯdž ϯ͘ϵLJс ϮϬϬ͕ϬϬ Ϭ͘ϬϬϮϬ ϬϴϬ͕ϬϬ ϬϬϬϴϬ͘ ϰϬϬ͕ϬϬ Ϭ͘ϬϬϰϬ Wƌhс ϭϲϬ͕ϬϬ ϬϬϭϲϬ͘ WƐhс ϲϬϬ͕ϬϬ Ϭ͘ϬϬϲϬ ϮϰϬ͕ϬϬ ϬϬϮϰϬ͘ WƐ ϴϬϬ͕ϬϬ Ϭ͘ϬϬϴϬ ϯϮϬ͕ϬϬ ϬϬϯϮϬ͘ ϬϬϬ͕Ϭϭ Ϭ͘ϬϭϬϬ ϰϬϬ͕ϬϬ ϬϬϰϬϬ͘ ϮϬϬ͕Ϭϭ Ϭ͘ϬϭϮϬ ϬϬϰϴϬ͘ ϰϴϬ͕ϬϬ Ϭ͘ϬϭϰϬ ϰϬϬ͕Ϭϭ Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 Massachusetts (pp. 539–556). Boston: State Board of In the case of empirical formulas, a randomly se- Health of Massachusetts. lected soil sample has been tested and the result de- Head, K. & Epps, R. (2011). Manual of soil laboratory test- pends in principle only on the particle size of the soil. ing. Vol. 2. Permeability, shear strength and compress- Laboratory methods almost always generate filtration ibility test. Dunbeath Mill: Whittles Publishing. factor values lower than those obtained by empirical Hussain, F. & Nabi, G. (2016). Empirical Formulae Evalu- formulas. The empirical formulas used often give per- ation for Hydraulic Conductivity Determination Based meability coefficient values several times smaller or on Grain Size Analysis. Pyrex Journal of Research in larger than the actual values observed in the field. Em- Environmental Studies, 3 (3), 26–32. pirical formulas give only approximate values of the Idris-Nda, A. (2013). Estimating Aquifer Hydraulic Prop- permeability coefficient, because they do not embrace erties in Bida Basin, Central Nigeria Using Empirical Methods. Earth Science Research, 2 (1). http://doi. real in-situ conditions. org/10.5539/esr.v2n1p209 The results, as an attempt to find relationship be- Jiang, R., Li, T., Liu, D., Fu, Q., Hou, R., Li, Q., Cui, S. tween filtration and density index, are promising; & Li, M. (2021). Soil infiltration characteristics and however, the research is preliminary in nature. The pore distribution under freezing-thawing conditions. proposal for verification of the formulas, taking into Cryosphere, 15 (4), 2133–2146. http://doi.org/10.5194/ account the degree of soil compaction, will be extend- tc-15-2133-2021 ed to other methods of testing the hydraulic conductiv- Kozeny, J. (1953). Das Wasser im Boden. Grundwasserbe- ity, e.g. with a constant head permeameter. wegung. In J. Kozeny (Ed.), Hydraulik (pp. 380–445). Vienna: Springer. Authors’ contributions Kozerski, B. (1977). Zasady obliczeń hydrogeologicznych ujęć wód podziemnych. Wytyczne określania współczyn- Conceptualization: T.G. and K.J.; methodology: K.J.; nika filtracji metodami pośrednimi i laboratoryjnymi. validation: T.G. and K.J.; formal analysis: T.G. and Warszawa: Wydawnictwa Geologiczne. K.J.; investigation: K.J.; resources: K.J.; data curation: Myślińska, E. (1998). Laboratoryjne badania gruntów. K.J.; writing – original draft preparation: K.J.; writ- Warszawa: Wydawnictwo Naukowe PWN. ing – review and editing: T.G. and K.J.; visualization: Parylak, K., Zięba, Z., Bułdys, A. & Witek, K. (2013). We- K.J.; supervision: T.G.; project administration: T.G. ryfikacja wyznaczania współczynnika filtracji gruntów All authors have read and agreed to the published niespoistych za pomocą wzorów empirycznych w ujęciu version of the manuscript. ich mikrostruktury. Acta Sci. Pol. Architectura, 12 (2), 43–51. Polski Komitet Normalizacyjny [PKN] (1986). Grunty bu- REFERENCES dowlane. Określenia symbole podział i opis gruntów (PN-B-0248:1986). Warszawa: Polski Komitet Norma- Chapuis, R. P. (2004). Predicting the saturated hydraulic lizacyjny. conductivity of sand and gravel using effective diam- Polski Komitet Normalizacyjny [PKN] (1988). Grunty bu- eter and void ratio. Canadian Geotechnical Journal, 41, dowlane. Badania próbek gruntu (PN-B-04481:1988). 787–795. Warszawa: Polski Komitet Normalizacyjny. Cheng, C. & Chen, X. (2007). Evaluation of Methods Polski Komitet Normalizacyjny [PKN] (2008). Badania for Determination of Hydraulic Properties in an Aq- geotechniczne. Badania laboratoryjne gruntów. Część 4: uifer-Aquitard System Hydrologically Connected to Oznaczanie składu granulometrycznego (PKN-CEN River. Hydrogeology Journal, 15, 669–678. http://doi. ISO/TS 17892-4:2008). Warszawa: Polski Komitet Nor- org/10.1007/s10040-006-0135-z malizacyjny. Devlin, J. F. (2015). HydrogeoSieveXL: an Excel-based Polski Komitet Normalizacyjny [PKN] (2019). Badania tool to estimate hydraulic conductivity from grain size geotechniczne. Oznaczanie i klasyfikowanie gruntów. analysis. Hydrogeology Journal. http://doi.org/10.1007/ Część 2: Zasady klasyfikowania (PN-EN ISO 14688-2: s10040-015-1255-0 2019). Warszawa: Polski Komitet Normalizacyjny. Hazen, A. (1892). Some physical properties of sands and Shen, C., Zhu, J. & Gu, W. (2019). Prediction Method for gravels, with special reference to their use in filtration. Hydraulic Conductivity considering the Effect of Sizes In 24th Annual Report of the State Board of Health of architectura.actapol.net 91 Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 of Ellipsoid Soil Particles from the Microscopic Perspec- Zamarin, J. A. (1928). Raschet dvizheniya gruntovykh vod tive. Advances in Civil Engineering, 7213094. http://doi. [Calculation of ground-water flow]. Moskva: Izdatel- org/10.1155/2019/7213094 stvo I.V.Kh. Twardowski, K. & Drożdżak, R. (2006). Pośrednie metody Zięba, Z. (2016). Influence of soil particle shape on satu- oceny właściwości filtracyjnych gruntów. Wiertnictwo rated hydraulic conductivity, Journal of Hydrology and Nafta Gaz, 23 (1), 477–486. Hydromechanics, 65 (1), 80–87. http://doi.org/10.1515/ Twardowski, K. & Drożdżak, R. (2007). Uwarunkowania johh-2016-0054 dotyczące laboratoryjnych metod oznaczania wodoprze- Żurek, A. & Czudec, Ł. (2007). Pionowa zmienność pra- puszczalności gruntów. Wiertnictwo Nafta Gaz, 24 (1), metrów hydrogeologicznych w czwartorzędowym 565–574. zbior niku wód podziemnych (GZWP 450 – Dolina Vukovic, M. & Soro, A. (1992). Determination of hydraulic rzeki Wisły) na przykładzie profilu studni badawczej conductivity of porous media from grain-size composi- z poletka doświadczalnego AGH [The vertical variabil- tion [trans. from Serbo-Croation by Dubravka Miladi- ity of the hydrogeological parameters in the quaternary nov]. Littleton, CO: Water Resources Publications. groundwater basin (MGWB 450 – the Vistula river val- Wiłun, Z. (1982). Zarys geotechniki. Warszawa: Wydawni- ley) illustrated by the example of the AGH University of ctwo Komunikacji i Łączności. Science and Technology Experimental Field Research Wrzesiński, G. (2020). Permeability coefficient tests in non- Well Profile]. In A. Szczepański, E. Kmiecik & A. Żurek -cohesive soils. Przegląd Naukowy. Inżynieria i Kształ- (Eds.), Współczesne problemy hydrogeologii. Vol. 13. towanie Środowiska – Scientific Review. Engineering Part 2 (pp. 389–399). Kraków: Wydział Geologii, Geo- and Environmental Sciences, 29 (1), 72–80. http://doi. fizyki i Ochrony Środowiska AGH. org/10.22630/PNIKS.2020.29.1.7 WERYFIKACJA WYZNACZANIA WSPÓŁCZYNNIKA FILTRACJI GRUNTÓW GRUBOZIARNISTYCH ZA POMOCĄ WZORÓW EMPIRYCZNYCH Z UWZGLĘDNIENIEM STOPNIA ZAGĘSZCZENIA STRESZCZENIE W pracy zbadano przydatność wzorów empirycznych do oceny współczynnika filtracji gruntów niespoi- stych z uwzględnieniem ich zagęszczenia. Wzory empiryczne są często stosowane w praktyce do szybkiego i taniego wyznaczania współczynnika filtracji. Weryfikację obliczeń współczynnika filtracji przeprowadzono dla pięciu wzorów uwzględniających charakterystyczne średnice ziarna oraz porowatość. Otrzymane wyniki porównano z wynikami badań laboratoryjnych wykonanych na próbkach gruntów o takich samych wskaź- nikach porowatości (przy różnych stopniach zagęszczenia), jakie przyjmowano w metodzie obliczeniowej. Zaproponowano formułę empiryczną pozwalającą skorygować współczynnik filtracji gruntów uzyskanych na podstawie wzoru Hazena, uwzględniając stopień zagęszczenia danego gruntu. Słowa kluczowe: filtracja, współczynnik filtracji, wzory empiryczne, stopień zagęszczenia 92 architectura.actapol.net http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Scientiarum Polonorum Architectura de Gruyter

Verification of Determination of Hydraulic Conductivity for Coarse Soils by Empirical Formulas Based on the Density Index

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Acta Sci. Pol. Architectura 20 (2) 2021, 83–92 content.sciendo.com/aspa ISSN 1644-0633 eISSN 2544-1760 DOI: 10.22630/ASPA.2021.20.2.17 ORIGINAL P APER Received: 19.05.2021 Accepted: 08.06.2021 VERIFICATION OF DETERMINATION OF HYDRAULIC CONDUCTIVITY FOR COARSE SOILS BY EMPIRICAL FORMULAS BASED ON THE DENSITY INDEX Krystyna Jaśkiewicz , Tomasz Godlewski Building Structures, Geotechnics and Concrete Department, Building Research Institute, Warsaw, Poland ABSTRACT This paper examines the importance of empirical formulas for estimating the hydraulic conductivity of non- -cohesive soils, taking into account their compaction. Empirical formulas are often used in practice to quickly and cost-effectively determine hydraulic conductivity of soil. Verification of calculation of this parameter was performed for five formulas taking into account the characteristic diameters of grains and porosity. The results obtained by calculations were compared with the results of laboratory tests performed on soil samples with the same porosity coefficients (at different density index) as assumed in the calculation method. An empirical formula has been proposed to correct the hydraulic conductivity of soils obtained from the Hazen formula by taking into account the density index of a given soil. Key words: filtration, hydraulic conductivity, empirical formulas, density index INTRODUCTION open-pit mine drainage, as well as the stability of The soil filtration properties are very important in the slopes. The problem also concerns buildings in rela- engineering-geological, geotechnical and hydrogeo- tion to environmental protection, in waste landfills, logical assessment of the site. The hydraulic conduc- sewage treatment plants, etc. Currently, an increas- tivity (k) is a parameter which defines the ability of ingly serious problem during construction of excava- the soil medium to transport water in it. It depends on tions (below the groundwater table) is drainage of the such soil characteristics as: graining, porosity, mineral construction site. Due to the limitations of environ- composition, moisture, shape and surface texture of mental decisions, the inflow of groundwater into the particle, temperature of water (Wiłun, 1982; Head & excavation should be estimated in detail, and then the Epps, 2011; Zięba, 2016; Jiang et al., 2021). Hydraulic optimal method of drainage should be selected. conductivity determines the ability of the soil to pass There are many different methods to determine water subjected to water pressure difference. Accord- the hydraulic conductivity including field methods ing to the linear Darcy’s law, it expresses the relation- (Kozeny, 1953; Cheng & Chen, 2007; Hussain & ship between the hydraulic gradient and the water Nabi, 2016), laboratory methods and calculations from filtration rate (Myślińska, 1998; Head & Epps, 2011). empirical formulas (Kozerski, 1977; Twardowski & The correct determination of the hydraulic conduc- Drożdżak, 2006; Idris-Nda, 2013). The most common- tivity becomes important when assessing the filtration ly used method of field tests is pumping test, which in- conditions in the areas of hydrotechnical structures, volves pumping water out of a well to obtain a hydro- Krystyna Jaśkiewicz https://orcid.org/0000-0002-8948-6275; Tomasz Godlewski https://orcid.org/0000-0001-7986-5995 k.jaskiewicz@itb.pl © Copyright by Wydawnictwo SGGW Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 dynamic reaction of the subsoil. In situ tests based on ing from the genesis) on the obtained permeability co- pumping tests are the most accurate in describing the efficients are significant for non-cohesive soils from the practical point of view. Results from the literature actual filtration conditions in the subsoil, but due to time-consumption, the cost and scope of implementa- show that for the same soils but with different den- tion (construction of wells and piezometers), they are sity indexes, the permeability coefficient differs even rarely performed at the stage of geotechnical investi- several times (Wrzesiński, 2020). There are formulas gation (Wrzesiński, 2020). On the other hand, labora- in literature, based on porosity and other properties. However, their use requires taking additional samples tory tests for the estimation of permeability are less reliable. In the field of geotechnical tests, the hydrau- and conducting laboratory tests, which increase the lic conductivity for coarse-grained soils is most often time of execution and generate additional costs. The determined using empirical formulas based on the par- density index value is almost always obtained in field ticle size distribution curve. It is justified because the tests (dynamic sounding, static sounding) as part of geological or geotechnical investigations. particle size analysis is performed as standard test in most geotechnical investigations and the particle size The purpose of the research presented in the paper distribution is the main factor influencing the per- is to determine and compare the values of the perme- meability of coarse soils (Parylak, Zięba, Bułdys & ability coefficient in coarse soils determined with use Witek, 2013). Therefore, this method of determination of selected empirical formulas and simple laboratory tests, with focus on the impact of the density index is widely practiced despite its lower reliability of esti- mation of the hydraulic conductivity. change. There are many empirical formulas for calculating the hydraulic conductivity based on the particle size MATERIAL AND METHODS distribution. They have a limited scope of application The tests were conducted on samples of coarse-grained and limited accuracy of determinations related to the subjective interpretation of the particle size curve, (non-cohesive) soils from Poland. Sample soils ge- especially, in the case of sandy soils containing clay netically belong to fluvial formations of the Mazovian or silt admixtures. Empirical formulas can be divided interglacial and fluvioglacial formations of the Odra into three groups (Twardowski & Drożdżak, 2006): glaciation. The hydraulic conductivity of samples was determined by two methods: the first, based on labora- − Group I – formulas that only take into account characteristic grain diameters; tory tests, and the second, using empirical formulas. − Group II – formulas taking into account the char- The laboratory method of determining the conduc- acteristic grain diameter and porosity of soil; tivity is based on the principle of measuring the veloc- − Group III – formulas taking into account the gran- ity of lowering of the table of water freely flowing out of a tube containing a sample of the examined ground ulometric composition and porosity of the soil as well as the physical properties of the filtering (i.e. the Kaminski tube). The method allows for very water. simple and quick determination of approximate value The aim of this study was to determine if there is a of hydraulic conductivity of high permeable soils. relationship between hydraulic conductivity and den- The principle of the method is to measure the veloc- ity of lowering of the table of water flowing through sity index and if it is large enough to be used to de- termine the filtration coefficient by indirect methods the sample of specified height at variable (decreasing) (empirical formulas). The value of this index depends pressure of water column (Myślińska, 1998; Twar- among others on grain composition, porosity, grain dowski & Drożdżak, 2007). The formula for estimat- shape (Parylak et al., 2013). Porosity is one of the im- ing the hydraulic conductivity has the form: portant parameters determining the ability of soil to accumulate water. It is also closely related to the den- ls§· sity and shape of grains (Zięba, 2016). The impact of k=− ln 1 (1) ¨¸ tH ©¹ 0 the density index and the shape of soil grains (depend- 84 architectura.actapol.net Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 where: tory filtration test was carried out), the particle size k – hydraulic conductivity [cm], distribution was established according to PKN-CEN t – time for the water column to decrease in height [s], ISO/TS 17892-4:2008 (PKN, 2008). Based on the s – reduction of height of the water column [mm, cm], particle size curve, parameters d , d , d , d and 10 17 50 60 H – initial hydraulic height in the tube [mm, cm]. soil type were determined, where d , d , d , d , are 0 10 17 50 60 grain sizes [mm] corresponding to 10, 17, 50 and 60% In spite of its simplicity and some limitations, the by weight passing through the sieves. The soil type method has been widely used in practice as a simple was determined in accordance with PN-B-0248:1986 method of determining the hydraulic conductivity of (PKN, 1986) as well as PN-EN ISO 14688-2:2019 soils (Kozerski, 1977). Some studies show that esti- (PKN, 2019). The results (28 tests) are summarized mated filtration values reflect realistic results from test in Table 1. pumping (Żurek & Czudec, 2007). In order to determine the hydraulic conductivity by Testing of the hydraulic conductivity was carried the indirect method, some empirical formulas based out on samples with disturbed structure. The sam- on studies by Vukovic and Soro (1992) were used. The ples were dried in the oven at 105°C. According to general form of the formula is expressed as: PN-B-04481:1988 standard (Polski Komitet Normal- izacyjny [PKN], 1988) the maximum and minimum g ªº Kn =⋅[]βϑ⋅[ ( )]⋅[d ] (3) «» dry density volume of soil was tested in order to de- ¬¼ termine the parameters of forming samples at different where: degrees of compaction. Samples intended for filtration –1 K – hydraulic conductivity [cm·s ], testing were formed dry and then wetted by capillar- –2 g – the gravitational constant [cm·s ], ity. This was done from the bottom so that air could v = ν – kinematic viscosity, , where: μ – the tem- escape from the surface. For each sample, four filtration tests were per- perature-dependent dynamic viscosity of wa- formed using the laboratory method for a given com- –1 –1 ter [g·cm ·s ], ρ – the temperature-dependent paction level to determine the filtration coefficient –3 water density [g·dm ], at a given density and then the average of these four β – constant depending on characteristics of the measurements was taken. The tests were made for four porous medium, density index levels: loose – ln (I = 0.30), medium ϑ (n) – porosity function, dense – szg (I = 0.50), dense – zg (I = 0.70), very D D d – effective grain diameter [cm, mm], dense – bzg (I = 0.90). In total, 112 filtration tests were carried out. All results were related to tempera- To evaluate the applicability of the empirical for- ture 10°C using the empirical equation: mulas for determination of the hydraulic conductivity, k calculations of this parameter were carried out using k = (2) the following five formulas: 0.7 + 0.03T 1. Hazen (1892) according to Vukovic and Soro where: (1992) and Devlin (2015) k – hydraulic conductivity at the water temperature –1 of 10°C [m·s ], −42 ªº Kn =⋅ 6⋅10 ⋅ªº 1+10 − 0.26 ⋅d () (4) k – hydraulic conductivity at the temperature T, at t ¬¼ 10 ¬¼ –1 which the test was conducted [m·s ], T – water temperature at the time of testing [°C]. Hazen formula is used for uniformly graded sands; however, it could also be used for the range fine In aim to determine the hydraulic conductivity sand − gravel, provided the sediment has a uni- based on empirical formulas and to control the grain formity coefficient less than 5 and effective grain size distribution of each sample (for which the labora- size between 0.1 and 3 mm. architectura.actapol.net 85 Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 Table 1. Presentation of grain size distribution characteristic of analysed soil Particle size distribution Soil type acc. to Coefficient [mm] Density index Soil of uniformity Test (I ) sample (CU) PN-EN ISO [-] PN-B-0248 d d d d [-] 10 17 50 60 14688-2 1 Ps MSa 2 0.20 0.26 0.38 0.42 0.90 2 Ps MSa 2 0.17 0.23 0.38 0.42 0.70 3 Ps MSa 2 0.23 0.27 0.39 0.43 0.50 4 Ps MSa 2 0.19 0.26 0.39 0.43 0.30 5 Ps MSa 3 0.12 0.15 0.27 0.32 0.90 6 Ps MSa 3 0.12 0.15 0.27 0.32 0.70 7 Ps MSa 3 0.12 0.14 0.29 0.34 0.50 8 Ps MSa 3 0.12 0.15 0.28 0.34 0.30 9 Ps MSa 3 0.10 0.13 0.25 0.30 0.90 10 Ps MSa 3 0.12 0.15 0.28 0.33 0.70 11 Ps MSa 3 0.12 0.14 0.26 0.32 0.50 12 Ps MSa 3 0.13 0.16 0.31 0.36 0.30 13 Ps MSa 3 0.12 0.15 0.31 0.37 0.90 14 Ps MSa 3 0.11 0.14 0.29 0.35 0.70 15 Ps MSa 3 0.12 0.15 0.30 0.36 0.50 16 Ps MSa 3 0.11 0.14 0.29 0.34 0.30 17 Ps MSa 3 0.12 0.15 0.31 0.36 0.90 18 Ps MSa 3 0.12 0.16 0.32 0.37 0.70 19 Ps MSa 3 0.12 0.16 0.32 0.37 0.50 20 Ps MSa 3 0.13 0.16 0.31 0.37 0.30 21 Pr CSa 5 0.19 0.27 0.78 0.93 0.90 22 Pr CSa 5 0.19 0.27 0.78 0.94 0.70 23 Pr CSa 5 0.18 0.24 0.75 0.93 0.50 24 Pr CSa 5 0.19 0.27 0.78 0.93 0.30 25 Po grCSa 2 0.51 0.57 0.85 0.94 0.90 26 Po grCSa 2 0.47 0.55 0.85 0.94 0.70 27 Po grCSa 2 0.49 0.57 0.88 0.98 0.50 28 Po grCSa 2 0.50 0.57 0.87 0.97 0.30 Ps (MSa) – medium sand; Pr (CSa) – coarse sand; Po (grCSa) – coarse sand with gravel. 86 architectura.actapol.net Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 2. Sauerbrei (1932) according to Vukovic and Soro 5. Chapuis (2004) according to Vukovic and Soro (1992) and Devlin (2015) (1992) and Devlin (2015) 2 () 0.5504−0.2937 ξ ªº −52 n 1.291ξ−⋅ 0.6435ªº 0.510 ªº ªº Kd =⋅ 3.75⋅10 τ ⋅ ⋅ (5) Kd =⋅ 10 (8) «» () 17 10 2 ¬¼«» ¬¼ ¬¼ «» (1− n ) ¬¼ where: (9) ξ = –4 2 –2 τ ≅ 1.093⋅10 T + 2.102⋅10 + 0.5889, 1− n T – temperature of water [°C]. The Chapuis formula is applicable for 0.3 < n < 0.7, 3. Kozeny–Carman (1953) according to Vukovic and 0.10 < d < 2.0 mm, 2 < CU < 12, d /d < 1.4. 10 10 5 Soro (1992) and Devlin (2015) RESULTS AND DISCUSSSION ªº −32 n ªº Kd =⋅ 8.3⋅10 ⋅ ⋅ (6) «» ¬¼ 2 Based on the results obtained from particle size dis- «» (1− n ) ¬¼ tribution (Table 1), the soils were divided into the fol- The Kozeny–Carman formula is not appropriate for lowing groups: soils with effective size above 3 mm or for clayey A. Medium sand – MSa (Ps): A – CU = 2 (Sample 1) soils (Carrier, 2003). and A – CU = 3 (Samples 2, 3, 4, 5). B. Coarse sand – CSa (Pr); CU = 5 (Sample 6). 4. Zamarin (1928) according to Vukovic and Soro C. Coarse sand with gravel – grCSa (Po); CU = (1992) and Devlin (2015) = 2 (Sample 7). The division criterion was the soil type, the co- ªº efficient of uniformity (CU) and value of effective «» grain diameter. The change in the hydraulic conduc- «» tivity determined by a laboratory method was ob- «» ªº g «» −3 n 1 served depending on the density index for each of the ªº KC =⋅ 8.64⋅10 ⋅ ⋅ «»n «» ¬¼ 2 v soil groups. In the case of laboratory tests for coarse- §· «» (1− n ) ¬¼«» ln¨¸ -grained soils of loose density (density index I = 0.3) «» ¨¸ ©¹ i «» during the water permeability determination with use Δg i=1 «» g d dd − of a so-called the Kaminski tube, the consolidation ¬¼ ii of samples during the filtration test was observed, (7) which resulted in a change of the compaction state where: from loose to medium dense (Fig. 1). The cause of C – factor depending on the porosity, this phenomenon may arise from the temporary in- C = (1,275 − 1.5n) , duction of negative pore pressure during saturation ∆g – the fraction of mass that passes between of the dry-formed sample. sieves i and i + 1 where i is the smaller sieve, The determination of the hydraulic conductiv- d – the maximum grain diameter in fraction i, ity by the indirect method (empirical formulas) was d – the minimum grain diameter in fraction i. performed for each sample at different porosity val- ues corresponding to the density index at which the The formula is applicable for large-grained sands laboratory tests were performed. The results of calcu- with no fractions having d < 0.00025 mm. It can be lations with these formulas, for individual soil samples used for fine and medium-grained sands. and laboratory tests, are presented in Table 2. architectura.actapol.net 87 Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 WƐ;ĂD^Ϳ hϯс / ŵƉE ŵƉE ŵƉE ŵƉE ďnjŐ ͕Ϭ ϬϬ ϬϬϬϬ͘ϬϬ͘ϬϬϭϱϬ͘ϬϬϭϬ  Ϭ ϱ Ͳϭ Ŭ ΀ŵƐ ΁ ƵсϮ ƐnjŐ Ɖϭ njŐ ďnjŐ Ϭ ϬϬ͘ϰϬ Ͳϭ Ŭ ΀ŵƐ ΁ ĂͿĂͿ;;^^WƌWƌ ůŶ ƐnjŐ Ă^ŵƉůĞEŽ͘ϲ njŐ ďnjŐ Ϭ Ϭϭ Ϯ Ϭϯ ͕Ϭϰ Ŭ ΁ WŽ;Őƌ^ĂͿ / Ϭ ƐnjŐ / Ϭ Fig. 1. Changes in the hydraulic conductivity (k ) ŵƉE / Ϭ laboratory tests for Ps (MSa) – medium sand; Pr (CSa) – coarse sand; Po (grCSa) ďnjŐ – coarse sand with gravel (average of four / Ϭ determinations: ln – loose; szg – medium Ϭ ͕ϬϬϬϱ Ϭ ͕ϬϭϬϱ ͘Ϭ dense; zg – dense; bzg – very dense) de- Ͳϭ Ŭ ΀ŵƐ ΁ pending on the density index (I ) 88 architectura.actapol.net ϭϬ Ϭ͕Ϭϭϱ Ϭ͘ϬϭϬ Ϭ͘ϬϬϱϬϬϬ Ϭ͕Ϭϭ Ϭ͕ϬϬ сϬ͘ϵ сϬ͘ϳ njŐ ϳŽ͘ůĞ^Ă сϬ͘ϱ сϬ͘ϯ ůŶ ϭϬ ΀ŵƐ Ͳϭ Ϭ͘ϬϬϬ͘ϬϬϯ Ϭ͘ϬϬϮϬ͘ϬϬϭϬ͘ϬϬϬ ϬϬ ͕ϬϬ ϬϬϬ͕ ͕ϬϬ ϬϬϬ͕ сϬ͘ϵϬ сϬ͘ϳϬ сϬ͘ϱϬ сϬ͘ϯϬ ϭϬ ͘ϬϬϯϬ͘ϬϬϮϭϬ͘ϬϬϬϬϬϬ͘ ϰϬϬ͕ϬϬ ϯϬϬ͕ϬϬ ϮϬϬ͕ϬϬ ϭϬϬ͕ϬϬ ϬϬϬ͕ϬϬ сϬ͘ϵϬ сϬ͘ϳϬ Ž͘ůĞE^Ăŵ сϬ͘ϱϬ сϬ͘ϯϬ D^ĂͿƐ; ůŶ ϭϬ ͘ϬϬϮ Ϭ͘ϬϬϮϬϬ͘ϬϬϭϱ ϮϱϬϬϬ͕ ϮϬϬ͕ϬϬ ϭϱϬϬϬ͕ ϭϬϬ͕ϬϬ ϬϱϬ͕ ϬϬϬϬ сϬ͘ϵϬ Ž͘ϮůĞ^Ă сϬ͘ϳϬ Ž͘ϯůĞ^Ă njŐ Ž͘ϰůĞ^Ă Ž͘ϱůĞ^Ă сϬ͘ϱϬ Ɛnj сϬ͘ϯϬ ůŶ Table 2. Comparison of the hydraulic conductivity value obtained with use of empirical formulas and in laboratory tests –1 Estimation of hydraulic conductivity [m·s ] by Density Soil type acc. to Tested Porosity Soil index empirical formula laboratory test Test soil (n) sample (I ) D (average of four PN-EN ISO Kozeny– group [-] PN-B-0248 Hazen Sauerbrei Zamarin Chapuis [-] measurement) 14688-2 –Carman 1 Ps MSa 0.40 (ln) 0.30 5.67E-04 4.63E-04 8.46E-04 7.12E-04 4.28E-04 1.47E-03 2 Ps MSa 0.38 (szg) 0.50 5.20E-04 3.72E-04 6.79E-04 6.24E-04 3.19E-04 9.78E-04 A 1 3 Ps MSa 0.35 (zg) 0.70 4.49E-04 2.65E-04 4.83E-04 5.02E-04 2.10E-04 6.68E-04 4 Ps MSa 0.33 (bzg) 0.90 4.02E-04 2.09E-04 3.81E-04 4.28E-04 1.62E-04 4.69E-04 5 Ps MSa 0.41 (ln) 0.30 2.19E-04 1.71E-04 1.08E-04 2.74E-04 1.66E-04 1.53E-03 6 Ps MSa 0.39 (szg) 0.50 2.01E-04 1.37E-04 8.71E-05 2.41E-04 1.17E-04 1.28E-03 A 2 7 Ps MSa 0.36 (zg) 0.70 1.75E-04 9.82E-05 6.22E-05 1.96E-04 7.21E-05 9.21E-04 8 Ps MSa 0.33 (bzg) 0.90 1.49E-04 6.90E-05 4.37E-05 1.55E-04 4.57E-05 6.27E-04 9 Ps MSa 0.41 (ln) 0.30 2.66E-04 2.05E-04 4.29E-04 4.19E-04 2.07E-04 2.35E-03 10 Ps MSa 0.38 (szg) 0.50 2.34E-04 1.47E-04 3.08E-04 3.44E-04 1.25E-04 1.23E-03 A 3 11 Ps MSa 0.36 (zg) 0.70 2.12E-04 1.18E-04 2.46E-04 2.98E-04 9.12E-05 8.53E-04 12 Ps MSa 0.33 (bzg) 0.90 1.81E-04 8.27E-05 1.73E-04 2.36E-04 5.84E-05 6.61E-04 13 Ps MSa 0.39 (ln) 0.30 1.75E-04 1.25E-04 4.58E-05 1.95E-04 9.99E-05 7.82E-04 14 Ps MSa 0.36 (szg) 0.50 1.52E-04 8.92E-05 3.28E-05 1.58E-04 6.08E-05 6.52E-04 A 4 15 Ps MSa 0.34 (zg) 0.70 1.37E-04 7.07E-05 2.59E-05 1.36E-04 4.44E-05 3.91E-04 16 Ps MSa 0.31 (bzg) 0.90 1,14E-04 4.90E-05 1.80E-05 1.05E-04 2,85E-05 2.91E-04 17 Ps MSa 0.39 (ln) 0.30 2.20E-04 1.57E-04 1.06E-04 2.81E-04 1.30E-04 1.22E-03 18 Ps MSa 0.37 (szg) 0.50 2.01E-04 1.26E-04 8.45E-05 2.45E-04 9.37E-05 7.50E-04 A 5 19 Ps MSa 0.34 (zg) 0.70 1.72E-04 8.87E-05 5.97E-05 1.96E-04 5.91E-05 5.05E-04 20 Ps MSa 0.31 (bzg) 0.9 1.43E-04 6.15E-05 4.14E-05 1.52E-04 3.84E-05 2.96E-04 21 Pr CSa 0.39 (ln) 0.30 4.97E-04 4.42E-04 2.28E-03 1.38E-03 3.33E-04 3.04E-03 22 Pr CSa 0.37 (szg) 0.50 4.54E-04 3.54E-04 1.82E-03 1.21E-03 2.49E-04 3.24E-03 B6 23 Pr CSa 0.34 (zg) 0.70 3.89E-04 2.50E-04 1.29E-03 9.63E-04 1.65E-04 2.30E-03 24 Pr CSa 0.31 (bzg) 0.90 3.24E-04 1.74E-04 8.94E-04 7.48E-04 1.12E-04 1.91E-03 25 Po grCSa 0.38 (ln) 0.30 2.87E-03 1.71E-03 3.57E-03 3.26E-03 2.36E-03 1.20E-02 26 Po grCSa 0.36 (szg) 0.50 2.61E-03 1.36E-03 2.84E-03 2.83E-03 1.91E-03 1.22E-02 C7 27 Po grCSa 0.33 (zg) 0.70 2.22E-03 9.57E-04 2.00E-03 2.24E-03 1.42E-03 8.26E-03 28 Po grCSa 0.31 (bzg) 0.90 1.96E-03 7.48E-04 1.56E-03 1.88E-03 1.18E-03 5.20E-03 Ps (MSa) – medium sand; Pr (CSa) – coarse sand; Po (grCSa) – coarse sand with gravel ln – loose; szg – medium dense; zg – dense; bzg – very dense. ϬϭϰϬ ϬϭϮϬ ϬϭϬϬ ϬϬϴϬ ϬϬϲϬ ϬϬϰϬ ϬϬϮϬ ϬϬϬϬ ΀ŵ ϬϬϰϴϬϬϰϴϬ͘Ϭ͘ ϬϬϰϬϬϬϰϬϬ͘Ϭ͘ ϬϬϯϮϬϬϯϮϬ͘Ϭ͘ ϬϬϮϰϬϬϮϰϬ͘Ϭ͘ ϬϬϭϲϬϬϭϲϬ͘Ϭ͘ ϬϬϬϴϬϬϬϴϬ͘Ϭ͘ ϬϬϬϬϬ͘ ϬϬϬϬϬ͘ ΀ŵ Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 Data presented in Figure 1 show clear relation be- ratory tests. This comparison indicates the need for tween the changes in the hydraulic conductivity (k) individual evaluation of reliability of the formulas in and effective pore diameter caused by the increase in the assessment of the filtration considering the mate- the density index (I ). This points at the need of tak- rial type. An attempt was made to verify the hydraulic ing the state of the soil (density) into account. This conductivity determined according to the Hazen for- relationship is visible regardless of the grain size and mula (most commonly used in design practice) taking type of material. Generally, lower permeability coeffi- into account density index (corresponding to porosity) cients were obtained in soils characterized by a higher for each tested soils (Fig. 2). For the Hazen equation, density index. It should be noted that the value of the the filtration coefficients obtained are of lower order permeability coefficient is influenced by the shape of magnitude than the laboratory test results, depend- of soil particles and their mutual arrangement (Pary- ing on the density parameter. lak et al., 2013; Zięba, 2016; Shen, Zhu & Gu, 2019; Wrzesiński, 2020). This effect can be ignored in this CONCLUSIONS study, since all sands had the same origin – they are alluvial soils. Laboratory methods were used to evaluate the hydrau- When analysing the results given in Table 2, for- lic conductivity (k), which is a basic hydrogeological mulas with a better and worse match to the results ob- parameter determining the ability of soil to transport tained from direct measurements can be indicated. The water, and confronted with the values obtained from best representation for non-cohesive soils of group A empirical formulas for soils characterized by four was obtained with the Chapuis formula, and for group different density indexes. The results of the filtration A with the Zamarin formula. For soils of B and C coefficient calculations based on empirical formulae groups, the best results in comparison with laboratory are inaccurate and highly differentiated (in described tests were obtained by Kozeny–Carman formula. The cases from four to six times), which undermines their Hazen formula gave relatively good hydraulic con- reliability and excludes the possibility of using this ductivity values for each group relative to the labo- method in well-understood engineering practice. soil groups A , A , B soil group C 1 2 džсLJ džсLJ ϮƵс ϮWŽhс ϰdžϴ͘сϰLJͿ͕ƵсϮWƐ;ŶĞĂƌŝů LJ ĞĂƌ;WŽϮͿ͕ůŝŶhс ĂƌͲŬ ϰdžϬ͘сϱLJͿ͕ƵсϯWƐ;ŶĞĂƌŝů džϵ Ϳϲϱ͕ƵсW;ĞƌĂ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ϭ͘ Ͳϭ ͲŬŬƋƵĂƚŝŽŶĞ ͲŬŬĞƋƵĂƚŝŽŶ Ɛ Y Y Fig. 2. Relations between hydraulic conductivity obtained from empirical formula (k ) and in laboratory tests (k ) of soil Q L groups 90 architectura.actapol.net Ͳϭ ŬůĂďŽƌƚŽ Ͳϭ ͲŬŬůĂďŽƌĂƚŽƌLJ ΁ ΀ŵ ΁ ΀ŵƐͲ Ϭ͘ϬϬϬϬϬϬϬ͕ϬϬ ϬϬϬϬϬ͘ ϬϬϬ͕ϬϬ ůŝŶƌLJс͘ϯϯdž ϯ͘ϵLJс ϮϬϬ͕ϬϬ Ϭ͘ϬϬϮϬ ϬϴϬ͕ϬϬ ϬϬϬϴϬ͘ ϰϬϬ͕ϬϬ Ϭ͘ϬϬϰϬ Wƌhс ϭϲϬ͕ϬϬ ϬϬϭϲϬ͘ WƐhс ϲϬϬ͕ϬϬ Ϭ͘ϬϬϲϬ ϮϰϬ͕ϬϬ ϬϬϮϰϬ͘ WƐ ϴϬϬ͕ϬϬ Ϭ͘ϬϬϴϬ ϯϮϬ͕ϬϬ ϬϬϯϮϬ͘ ϬϬϬ͕Ϭϭ Ϭ͘ϬϭϬϬ ϰϬϬ͕ϬϬ ϬϬϰϬϬ͘ ϮϬϬ͕Ϭϭ Ϭ͘ϬϭϮϬ ϬϬϰϴϬ͘ ϰϴϬ͕ϬϬ Ϭ͘ϬϭϰϬ ϰϬϬ͕Ϭϭ Jaśkiewicz, K., Godlewski, T. (2021). Verifi cation of determination of hydraulic conductivity for coarse soils by empirical formulas based on the density index. Acta Sci. Pol. Architectura, 20 (2), 83–92. doi: 10.22630/ASPA.2021.20.2.17 Massachusetts (pp. 539–556). Boston: State Board of In the case of empirical formulas, a randomly se- Health of Massachusetts. lected soil sample has been tested and the result de- Head, K. & Epps, R. (2011). Manual of soil laboratory test- pends in principle only on the particle size of the soil. ing. Vol. 2. Permeability, shear strength and compress- Laboratory methods almost always generate filtration ibility test. Dunbeath Mill: Whittles Publishing. factor values lower than those obtained by empirical Hussain, F. & Nabi, G. (2016). Empirical Formulae Evalu- formulas. The empirical formulas used often give per- ation for Hydraulic Conductivity Determination Based meability coefficient values several times smaller or on Grain Size Analysis. Pyrex Journal of Research in larger than the actual values observed in the field. Em- Environmental Studies, 3 (3), 26–32. pirical formulas give only approximate values of the Idris-Nda, A. (2013). Estimating Aquifer Hydraulic Prop- permeability coefficient, because they do not embrace erties in Bida Basin, Central Nigeria Using Empirical Methods. Earth Science Research, 2 (1). http://doi. real in-situ conditions. org/10.5539/esr.v2n1p209 The results, as an attempt to find relationship be- Jiang, R., Li, T., Liu, D., Fu, Q., Hou, R., Li, Q., Cui, S. tween filtration and density index, are promising; & Li, M. (2021). Soil infiltration characteristics and however, the research is preliminary in nature. The pore distribution under freezing-thawing conditions. proposal for verification of the formulas, taking into Cryosphere, 15 (4), 2133–2146. http://doi.org/10.5194/ account the degree of soil compaction, will be extend- tc-15-2133-2021 ed to other methods of testing the hydraulic conductiv- Kozeny, J. (1953). Das Wasser im Boden. Grundwasserbe- ity, e.g. with a constant head permeameter. wegung. In J. Kozeny (Ed.), Hydraulik (pp. 380–445). Vienna: Springer. Authors’ contributions Kozerski, B. (1977). Zasady obliczeń hydrogeologicznych ujęć wód podziemnych. Wytyczne określania współczyn- Conceptualization: T.G. and K.J.; methodology: K.J.; nika filtracji metodami pośrednimi i laboratoryjnymi. validation: T.G. and K.J.; formal analysis: T.G. and Warszawa: Wydawnictwa Geologiczne. K.J.; investigation: K.J.; resources: K.J.; data curation: Myślińska, E. (1998). Laboratoryjne badania gruntów. K.J.; writing – original draft preparation: K.J.; writ- Warszawa: Wydawnictwo Naukowe PWN. ing – review and editing: T.G. and K.J.; visualization: Parylak, K., Zięba, Z., Bułdys, A. & Witek, K. (2013). We- K.J.; supervision: T.G.; project administration: T.G. ryfikacja wyznaczania współczynnika filtracji gruntów All authors have read and agreed to the published niespoistych za pomocą wzorów empirycznych w ujęciu version of the manuscript. ich mikrostruktury. Acta Sci. Pol. Architectura, 12 (2), 43–51. Polski Komitet Normalizacyjny [PKN] (1986). Grunty bu- REFERENCES dowlane. Określenia symbole podział i opis gruntów (PN-B-0248:1986). Warszawa: Polski Komitet Norma- Chapuis, R. P. (2004). Predicting the saturated hydraulic lizacyjny. conductivity of sand and gravel using effective diam- Polski Komitet Normalizacyjny [PKN] (1988). Grunty bu- eter and void ratio. Canadian Geotechnical Journal, 41, dowlane. Badania próbek gruntu (PN-B-04481:1988). 787–795. 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Science and Technology Experimental Field Research Wrzesiński, G. (2020). Permeability coefficient tests in non- Well Profile]. In A. Szczepański, E. Kmiecik & A. Żurek -cohesive soils. Przegląd Naukowy. Inżynieria i Kształ- (Eds.), Współczesne problemy hydrogeologii. Vol. 13. towanie Środowiska – Scientific Review. Engineering Part 2 (pp. 389–399). Kraków: Wydział Geologii, Geo- and Environmental Sciences, 29 (1), 72–80. http://doi. fizyki i Ochrony Środowiska AGH. org/10.22630/PNIKS.2020.29.1.7 WERYFIKACJA WYZNACZANIA WSPÓŁCZYNNIKA FILTRACJI GRUNTÓW GRUBOZIARNISTYCH ZA POMOCĄ WZORÓW EMPIRYCZNYCH Z UWZGLĘDNIENIEM STOPNIA ZAGĘSZCZENIA STRESZCZENIE W pracy zbadano przydatność wzorów empirycznych do oceny współczynnika filtracji gruntów niespoi- stych z uwzględnieniem ich zagęszczenia. Wzory empiryczne są często stosowane w praktyce do szybkiego i taniego wyznaczania współczynnika filtracji. Weryfikację obliczeń współczynnika filtracji przeprowadzono dla pięciu wzorów uwzględniających charakterystyczne średnice ziarna oraz porowatość. Otrzymane wyniki porównano z wynikami badań laboratoryjnych wykonanych na próbkach gruntów o takich samych wskaź- nikach porowatości (przy różnych stopniach zagęszczenia), jakie przyjmowano w metodzie obliczeniowej. Zaproponowano formułę empiryczną pozwalającą skorygować współczynnik filtracji gruntów uzyskanych na podstawie wzoru Hazena, uwzględniając stopień zagęszczenia danego gruntu. Słowa kluczowe: filtracja, współczynnik filtracji, wzory empiryczne, stopień zagęszczenia 92 architectura.actapol.net

Journal

Acta Scientiarum Polonorum Architecturade Gruyter

Published: Jun 1, 2021

Keywords: filtration; hydraulic conductivity; empirical formulas; density index

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