Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1 − m s 12 − 0.70 for clayey-siltey = 2 R 0.97, for total sum of 175 = 2 R ect of forces operating fluid movement ff 6676 6675 *, ** cient of correlation Sr. ffi ć ([email protected]) ective (flow) porosity result with parameters that reliably ć ff ective porosity, permeability and specific surface area distribution, 0.99 for sandy and gravelly materials and ff = ) presents coe 1 2 and K. Urumovi − R ective porosity and grain size 1 ć m s ff 2 − ective porosity in function of referential mean grain size has been calibrated ective porosity and the referential grain size are presented as fundamental ff ff retired This discussion paper is/has beenSciences under (HESS). review Please for refer the to journal the Hydrology corresponding and final Earth paper System in HESS if available. Croatian Geological Survey, Sachsova 2, P.O. Box 268, 10001 Zagreb, Croatia formally at: University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, up to 10 samples of variousporous deposits. material’s These e resultssince present these the three new parametersmodelling road are and to critical researches contaminant conditionsimportant for of to transport. be successful able From groundwater to flow identify the these parameters practical swiftly, cheaply point and very of accurately. view, it is very of an e within range from 1.5 µmmodel to was 6.0 confirmed mm. by Reliability veryconductivity of – high these correlation parameters between predicted applicationmaterials. and in Group tested KC hydraulic representation of hydraulic conductivity (ranged from 10 of permeability and specificof surface various area sediments as –The a from e function siltey of claysgranulometric granulometric parameters composition to which very express well anthrough e the graded saturated gravels porous aregrain media. size presented. Suggested and procedures determining for e determine calculating specific referential surface area and permeability.appliance These of procedures Kozeny–Carman ensure model successful up to the limits of validity of Darcy’s law. The value Hydrogeological parametersdependent of of their coherentformulas and granulometric defaultly and used characteristics. forfor calculation These uniform incoherent of incoherent hydraulic relations conductivity, materials, deposits and were mostly are sands. valid shaped are only In in this deeply paper, the results of analyses Abstract Published by Copernicus Publications on behalf of the European Geosciences Union. 1 * Zagreb, Croatia ** Received: 5 April 2014 – Accepted: 21Correspondence May to: 2014 K. – Urumovi Published: 24 June 2014 Hydrol. Earth Syst. Sci. Discuss.,www.hydrol-earth-syst-sci-discuss.net/11/6675/2014/ 11, 6675–6714, 2014 doi:10.5194/hessd-11-6675-2014 © Author(s) 2014. CC Attribution 3.0 License. relations in permeability functions K. Urumovi The e 5 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | cient and ffi et al., 2010). Covering ć erent from mean grain size. ff ective grain size is very widely ff is not much di 6678 6677 erent sizes provided the range of sizes is not ff 10 D ). Northern parts of the Republic of Croatia are covered by 1 ect on water flow in porous media. Even so, in hydrogeological ff ective grain size ff culty to determine the deposit specific surface area that can be either ffi cient used in most of experimental methods. Diversity of immanent grain ective porosity in function of permeability and specific surface area for ffi ff – soil particle diameter (mm) that 10 % of all soil particles are finer (smaller) ective porosity, generates harmonious parametric concept of porous media 10 ff ect of granular porous media granulometric composition on its transmissivity, D ff ective grain size. In such calculations, many authors (Kovács, 1981; Vukovic and The objective of this article is to research relations between average mean grain ff geometrics impact on its transmission capacity. 2 Study area and analyzed deposits For the purpose ofclayey-siltey deposits this was work, collected. data AllRepublic on of of researches the Croatia study of (Fig. sites sandy are and located gravely in aquifers plain and areas of size and e a wide rangehydraulic of conductivity grain calculations Kozeny–Carmanto size equation discover and was the uniformity used,with algorithm of with e for means particles calculating in the various referential mean soil grain samples. size In that, along Validity of the KCof equation clayey was particles. also That fact impairedthe was in accredited soil case to particles an deposits electrochemical andequation with correlation between a the between hydraulic higher water conductivity content (Carrier,soils and is 2003). gradation not On yet incorporating available the a (Boadu,Aubertin 2000). whole, wide (2003) In a range recommend means of of general determinationincorporating fine correlation of gained grain deposits, value specific Champuis in surface and the area KC in equation. laboratory and too wide (Bear et al.,sample 1968). that Errors can were caused distort byan arithmetic grains error mean of in value extreme calculating size (Arkin specific in surface andsize area, the Colton, composition. especially whole 1956). in These cases That problems of leadsgrain a have to deposits, wide been range distortion explained of was grain in accredited literature. to In non-linear case loss of due to large higher flow velocity. grain size in a mixture of spheres of di measured or estimated. Calculations of specific surface area using arithmetic mean of Even so, that practicerange did not of enhance grain the sizevarious validity and granulometric of uniformity. experimental composition More modelswater can for realistic flux be a and wide facilitated in complete1939) through porous correlation on theoretical between media, a analysisspecific laboratory as of surface area scale. conducted in Kozeny the by flowgeometric and model, properties Kozeny using Carman e them (1927) as have theoreticallypractice, and included exact the parameters Kozeny–Carman both Carman of (KC) porosity equation (1937, isto and not lie frequently in used. the The reason di seems sand, Hazen’s e Porosity of allunique uniform coe sandy depositssize distorts is such rather relations.(1902) level, Since and and Terzaghi natural (1925) materials can have are incorporated be mostly porosity incorporated function non-uniform, in Slichter in a hydraulic model. are used toe calculate hydraulic conductivitySoro, as 1992; a Cheng function andused of Chen, 2007; certain Odong, coe by 2008; weight Koch et (Hazen, al.,used 1892). 2011) lately, Such although have some application regulary ofas of the defined an authors by of e Slichter usedlimited (1902). models for Proper calculating have used use hydraulic conductivity mean of of grain the uniform size mentioned sand. experimental In methods case of is highly uniform An e accumulation and suctiona parameters practical is issue.conductivity. Several both experimental In methods (Hazen, permanent hydrogeology, Slichter, Beyer, attention Terzaghi scientific methods) is challenge particularly and devoted to a hydraulic 1 Introduction thick quaternary deposits with sandyaquitards and are gravely aquifers composed (Brki of siltey-clayey deposits. 5 5 25 20 10 15 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | in (2) and ); 19 ρg 1 that is δs δs in direction of s r ] inside the porous 1 − makes with its projection , [L is measured as a volume p a δs ect on water retention. Such n ff ∂s ∂h and its parallel exit plane, and , 2003): of water flow in direction µ ć . These two driving forces are, in have on fluid movement in porous ρg s δA s q [L]. Since, in isotropic environment, a . A component of gravity force k ect of driving forces of pressure and . The force of viscosity is proportional H − ff τ R ]. Porosity = 2 [L δp/δs ∂s ∂h s s k 6680 6679 k evac well field (marked as GW on Fig. , s − ž . ect of void geometry on the amount of viscosity 0 (1) = ρgnδAδs∂z/∂s ff n/r δA ) in the direction of elementary length = 2 s = ∂s ∂h , average velocity q s µ s µ k between entry plane s r nρg (Fig. δs − δV µr and specific surface area = − n ) , (3) z 2 δAδs H expresses an e ∂s ∂z is proportional to sine of the angle that + = s r cient of water ice (marked as CI/MI3) loess and aquatic loess like sediments were ∂ s C nR š δV ffi = p/ρg ( nδV ρg nδAδs 2 p ∂ n ) given by relation a − , 2013). 2 ć µ C s permeability is: r ∂s ∂p ect that porosity = nρg ect of geometry of void space given by drag resistance constant 2 p ff s ff − n a r and proportional to specific surface area. When the water is flowing, these forces = nδV ∝ Motion of fluid in pores is caused by forces of pressure and gravity. A force of Coherent deposits were investigated on 3 sites. Soil samples from exploration Analyses of non-coherent deposits were conducted on 36 gravel test samples from = s s − to viscosity coe the e δs are in balance and whence (Hantush, 1964; Urumovi pressure is transferred on the total amount is proportionalfluid to volume gradient on the horizontal planefluid and motion, equals confronted by the force of viscosity six investigation boreholes on the Ður or: q These relations express Darcy’s law,(1956). as The theoretically attention rigorously is here describedis given by (in to Hubbert Eq. permeability, as a property of porous media that r k forces, and represents specific amount ofspecific void geometry amount e ismedia, equivalent i.e. to to a avoid specific relation volume that of surface transfers solid the area flow grainis driving surface force. inversely Following proportional that the to Hagen confronts Poiseulle the water law, that hydraulic flow radius and saturated volume (REV) of moving fluid andgravity. is Constant connected with specific e 3 Methodology 3.1 Hydraulic model The e media can be illustrated by analyzing force field in the representative elementary of the mentioned analysis werevarious conducted types for of every soil singleCI/MI2) were soil and analyzed. sample. 65 On Na samples secondinvestigated. of and Laboratory third analyses test were sites conductedboreholes. on – Particular 21 analyses Ilok were samples (marked conducted from on as depths, 8 samples and investigation from this that test fact site was at(Urumovi the various reason to correlate mean values for individual boreholes perpendicular to elementary plane aquifers. boreholes (depthcomposition 1.0–30.0 m) (grain size were distribution),used. hydraulic laboratory On conductivity the tested. and first Atterberg test Analysis limits field were (route of of granulometric Danube–Sava channel – marked as CI/MI1) all uniform sand testManastir samples (marked from as SU1) the andmade Donji investigation from Miholjac boreholes siltey (marked material as on– test SU2); 2 Ravnik samples 28 (marked from sand well as with 2 fields laminas tests FS/SU1) investigation boreholes and were – on Osijek conducted Beli 2 (marked on well as this fields FS/SU2). Appropriate test pumping fields to determine the average hydraulic value of 5 5 10 15 25 20 20 10 15 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) 5 (4) (6) (5) ) from ect the s ; m ff T ρ 0.2. That ; in Eq. ( V p /D = V 2 s 6 a C = s ective grain size a pores) ff cient + of density ffi s V ; s instead of M 2 m D erence is not significant. Todd 0.2 in Eq. (3). ff = C , so it does not vary with the porosity. cient of proportionality that is dependent m ffi H a from mean straight trajectory. The best fit 1 R ◦ 6682 6681 = s [L] is the largest grain in segment. In all cases, a . However, the di ) , has direct impact on the amount of driving forces . He developed a theory for a bundle of capillary > ective voids specific surface area. i e n )]. (9) T i, a ff d n > a i n − represents the hypothetical hydraulic radius of porous ective porosity an active factor only to pores through < d ] as: ff /d (1 p 2 2 (1 i, g = 0.2. This solution of the Kozeny–Carman equation (Bear, [L /a 2, (7)  , (8) ) with 1 + s / (in form of porosity function) and certain e m = > 4 ) m i ) < d A a = > n < d i D C ) i 180 H d n ) i, h × e /d R d + < − i n n e < d ective porosity i [(1 (1 n − 2 ff m / d s . Their mutual conversion is expressed by following relations: q ( 2 D ρ (1 H = = 2 = R  ) = ] – specific surface based on the mass of solids e n i, g i, a 1 T i, h n n d − d a − [L] is the smallest, and 3 d ective porosity ] – specific surface area based on the total volume (solids ] – specific surface area based on the volume of contented pores ] – specific surface area based on the volume of solids = n M represents the non-dimensional coe < ff 1 = 1 i 1 2 e 2 p − − − d C s p ) into Eq. (3) with a n [L [L V [L A [L 4 180(1 C the critical factors of porous media transmissivity. By grouping them functionally: p T m s . Permeability is given by the relation: = ective mean grain which is the carrier of drag resistance. Both forces a In hydrogeology, specific surface area is often substituted with mean grain diameter a a a a All of the mentioned forms of specific surface are related to the hydraulic radius of = = m m p ff Eq. ( This relation has been achieved by inserting solids specific surface ( a There are fourexpressing surface ways area, of expressing specific surface area based on solid volume porous media of the particle shape. media representing the impact of e 3.2 Geometric parameters of permeability where where it can be shown(1959) that recommends the useand of recent geometric authors mean, often Bear follow (1972) their recommendations. prefers harmonic mean arithmetic, geometric, harmonic, without the wholeengineering indication practice, of there howadjacent are sieves: to three calculate ways this to equivalent calculate mean diameter. mean In of the rated size of 1972) is given for uniform spheremakes particles e and for the CarmanD coe k It is obvious that e and indirectly participates ine the conversion ofmoving specific fluid surface and value thatwhich into makes the a e water flows. value of 3.3 Referential grain size Many authors present the Kozeny–Carman equation with k Furthermore, Carman (1939) triedby to introducing take tortuosity an of angularwith the deviation experimental porous results of media he 45 into obtained with account a factor D Kozeny (1927) used Eq.tubes ( of equalthe length. specific Carman surface (1937) per verified unit the mass Kozeny of equation solid end expressed 5 5 20 25 15 10 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (10) (11) (12) ective . That ff aa > D lng D ) for samples with 10 erence between e [M] represents the mass ff i ective porosity controls the m ff ). Following that fact, it was 2 , and second, median size is e ) for two reasons. First, porosity n 6 impact on a mean grain (Bear, 1972) ect on the value of mean grain size. An i ff d . It can be shown that /M 6684 6683 i m ective porosity ff 100 = i P i )  ective porosity is not the same as specific yield which is, ) ), according to the data from the US Geol. Survey Water ). The above mentioned “parameter collaboration” requires ff of the sample are: 4 i, g 6 i, g d d lng ln( D i ln( 1 i P − ), according to the data from the US Geol. Survey Water Supply ), applies only to flow pores (Eq. m  ective porosity in function of referential grain size as it is presented i 4 6 ff X /d X i P 1 M 0.01  h X [M] represents the mass of the sample, and ective porosity. E  ff is a percentile of the sieve residue mass in the total mass of the sample. M i EXP EXP P 100 = = = erence is very small when calculated for uniformerence deposits, may but reach rapidly up grows to 2 when orders of magnitude. ective porosity is slightly lower than the value of specific yield. This value is related Starting values of porosity used in this procedure were ranges of an average specific The algorithm of integration of all the mentioned grain sizes (Eqs. 7–9) in sieve ff ff lng lng a ff appropriate to use in permeability equations (Eq. In a permeabilityparameters model, (Eq. porositynamed function, e expressed byas draining factors porosity, determined of in aporosity laboratory. porous Numerical and di media specific yieldcan may significantly not rise be whensize discernible analyzing (clay, samples when silt) containing analyzing particles. greater uniformaggregates Presentations percentage sand, (Eckis, of of but 1934) a small specific or yield median in grain function size of (Davis granulometric and De Wiest, 1966) are not calculating mean graindi of poorly sorted deposits.3.4 In Porosity case factor of gravelly sediments, di where of particular sieve residues, arithmetic scale. The generalparticle mathematical size expressions diameter for calculating the geometric D D and soil science researches.mean Arkin may and be Colton greatlyIrani (1956) and distorted pointed Callis by out (1963) advocated extreme thatproperties the values the use for and of soil arithmetic geometric samples. therefore rather Thewide may than reason, range not arithmetic in of statistical part, be particle is sizes typical. that making the in geometrical a scale natural much soil more sample suitable there then is the or D Here The arithmetic mean wasa used wide because variety of ofspecific the uses surface ease to were of achieved which only computation itAubertin, for and can uniform 2003). deposits because be Major of applied. of sand errorsa Correct and wide were results range silt of results of (Chapuis particle and of permeability sizes. Equivalent applying and annotations were the registered Eq. in sedimentology ( residue in the wholeoverview sample of related has expert and a scientific crucialsum literature has e regularly of confirmed mean the arithmetic (Freeze grain and sizes Cherry, 1979; in Kasenow, 2010) sieve as residue follows: of analyses (33a samples high of quality base gravel, fore 287 identification of of mean value sand of and specific yield 266 range. The of value silt of and clay) provided specific yield values (Fig. Supply Paper (Morris and Johnson, 1967). yield values (Fig. Paper (Morris and Johnson, 1967). Reputation of the laboratory and a large number used in thenot presentation referential mean is grainvalue not of size, permeability e paired (Eq. withidentification which of e the e in this paper, basedto on gravel. the Starting analysis values of of porosity numerous used data in on this procedure various were deposits, ranges from of clay an average 5 5 25 20 15 10 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , C) ect ◦ ff using 3 and by the / K K erent types ff ) is: 6 C. Hazen’s (1892) ◦ – temperature in T ( ) was ensured through 5 T ] represents the viscosity of 0.03 1 − + 2 and 2 times the mean value value that is between 1 T / 1 ), (13) K − École Polytechnique de Montréal 1 ). These relations simultaneously 0.70 − erence, ensuring error less than 2 % 12 = ff , Fig. 3). 20 %) can be reached with sand and τ 6 (m s ± 2 m D value, should not be equal for di cient 0.0625 is correct for a diameter of the 2 ) ffi 6686 6685 K e ), forming the function of drag resistance e 3 e n n lng − ective porosity range (Fig. D (1 ff value within K values ranging between 1 ect of temperature di 0.0625 for clayey materials is a value, which is within the expected margin of variation for ff = K K K 2 m D ] being gravity. Coe ective porosity rate has been achieved due to reliable guidelines- ] given through the KC equation (according to Eq. 2 2 ff 1 ) − , obtained from the grain size distribution analysis, were averaged. − e K n expressed in mm and a water temperature of 10 ] represents the density and µ [M L [LT 3 3 e − m [MLT − n K D g C. ◦ [M L 180(1 30 ρ µ ρg T < = Criteria for evaluating the acceptable accuracy of predicted hydraulic conductivity, Identification of e The Kozeny–Carman equation is, actually, a special form of Darcy’s law, so it The reliable reconstruction of e criteria were accepted for hydraulic conductivity calculation using the KC equation by of a predicted value3 of times the measured the laboratory permeabilityKozeny–Carman test. equation That using a relationSuch specific referred criteria surface can to area definitely determined a bereferential in an calculation grain the acceptable size. of laboratory. accuracy limit Insame for the sample calculating the case may give ofand siltey, an non-plastic excellent soils,gravel precision three when specimens ( the of special the procedure is applied (Chapuis and Aubertin, 2003). These were, both literally and functionally, on a laboratory scale. expressed by its correlation with a tested of materials. Chapuishave and disclosed Aubertin a very (2003) interesting study. of They have the concluded that acceptable accuracy 100 % natural lithological compound,conducted and on analysis the core of samples. particle Iftested exploration size well, borehole distribution hydraulic was conductivity must located of in be local theon scale vicinity was a of used. greater the If distance there were fromwas more the determined boreholes pumped and well, used hydraulicof conductivity for the of correlation. predicted a Congruously regionalSiltey to scale and the clayey samples test were processed dataanalyzed in scale, in a values specific the way. laboratory If one (grain specific size sample analysis was and hydraulic conductivity), the results Non coherent depositscontent make and it distributionnatural, almost of undisturbed state. impossible particles Identification of to average asanalyzing hydraulic the conductivity ensure well calculated pumping by as laboratory testsTest the data testing sites was consolidation of used were of for chosen correlation material in to in non-coherent its fulfill deposits. the following criteria: borehole core must be of testing of natural deposits represents a specific question in correlation investigations. in the water flow through a porous media (Eq. to the referential mean grain size ( Reliable verification of analyzed parametercomposition relations was for conducted a wide byresearched range using deposits of hydraulic the granulometric conductivity in Kozeny–Carman situconductivity equation as well and as analyses in the of laboratory. Hydraulic K was used to presentfor an e should be applicable for every possible natural sample of porous media. Hydraulic test fields forlaboratory analysis non-coherent of hydraulic deposits conductivity was were conducted on numerous properly soil samples. studied and4 investigated, and Results and verification where water, with mean grain non-dimensional temperature correction factor strong impact ofof discussed referential form of meanverified porosity the grain applicability function size of (Fig.composition. Kozeny–Carman (Eqs. 3) equation for and 11 wide exact and range calculation of granulometric 5 5 25 20 10 15 15 10 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | K 40 40 D D and ah D , ective porosity ff values of sandy aa results in a mild D erent depths, and K , ff value in correlation. ah lng D K D and with mild overestimating of ag lng present hydraulic properties of D D , 50 aa D D erent depths. ff values based on ) and total geometric mean (Eqs. 8 and 11). values. Laminas of silt were so thin that it K or even 10 6688 6687 K 40 D ) is commonly used to calculate the mean grain 10 is used in the calculations. lng D values for the gravelly aquifer is of a regional scale, since the cult to avoid a washout of the core while drilling through the ffi K ) provided remarkable results with practically negligible error. 6 values of the gravelly aquifer were analyzed at the same level as those ective porosity and referential mean grain size. The accepted criteria require K erent methods: arithmetic sum of arithmetic, geometric and harmonic mean ff values were customized. ff values of coherent materials were analyzed. The hydraulic conductivity values K K ). 6 A high quality drilling core from six exploration boreholes as well as a particle size Analyses of samples from fine sandy aquifers with siltey laminasIn such (Figs. specific 7 cases, and grain 8) size It is interesting to point out that the use of Predicted hydraulic conductivity was calculated using mean grain size determined In the process of verification, the results acquired using the KC equation were by four di between each pair of sieve sizes (Eqs. 7– 4.1 Incohesive deposit Validity limits of the Eq.sum (13) are of rarely proportions discussed of ineach hydrogeological arithmetic, pair circles. geometric Arithmetic of or sieve harmonic sizes mean (Eqs. size 7– of grain between value. Verification of boreholes that providedfrom high the quality pumped core well.analyzing were The a series located tested of value at successive steady ofwhere a states. The hydraulic distance third conductivity case of was was ofof determined 150–500 a siltey-clayey m samples laboratory by as scale well as granulometrictesting. parameters These were a were result the oftested laboratory procedures to which the criteria for correlating predicted and a high level of accuracy ofconcerning determining referential their mean role grain in size and Eq. e (13). matched with the resultsaquifers of were the identified hydraulic (pumping tests. test The data) average and local compared to the average sample applying e distribution analysis data of relevant corewere samples scattered was around at disposal. the Allon pumped of the the well border boreholes at part test ofthat well field is field GW. the where Borehole reason a SPB-2 why part that is of data situated an is aquifer is not of incorporated sandy in development average and Predicted of the sandy aquifer.(Table 2, Due Fig. to 9) are clarity, presented. only resulted with regularly underestimated was not possible to isolate content of sand in thesand samples much (Fig. 8). betterlaminas than of silt, the through calculated whichgrain horizontal mean size flow distribution is grain negligible, curve.geometric have size These a mean of grain strong distortions size, impact the are on the whole considerably weaker sample. if4.1.2 Thin referential Gravelly aquifer hydraulic conductivity value. Thatsample, can since be it interpreted islayers by of a di uniform slight sand. washout(Table An 1, of especially Fig. the interesting core fact is that the use of grain size In the case ofFig. uniform, mid-grain sands, a very high accuracy wasunderestimating achieved (Table of 1, hydraulic conductivity value, and Results ofsubheading. the Two of analysis thosetwo for consist aquifers of consist fine four sand of with specific uniform siltey laminas sand of sandy of di di aquifers are presented in this commonly represents the(Carrier, lower 2003; validity Odong, limit.analyzing The 2008). uniform sands. upper Common validity view limit is is that4.1.1 3 mm best grain results Sandy aquifer are achieved for size of a sample. In papers and reports on applying the KC formula, non-plastic silt 5 5 25 20 10 15 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) ) t ), K lng 40 i, min D D ( D ( ective ff K K )) and the tested ( ) of borehole SPB-3 is lng lng . Accordingly, in all types t D D ( K ( represents the real e . K K 40 1.000 (Table 4). lng D is identified by analyzing series = D t values of incoherent deposit 2 . However, the most important fact t ) is of the same order of magnitude K R ). K very correctly represents the true K lng 10 D ( 40 ) value is recorded in the borehole SPB- ect the mean grain size. The question is: cient D K lng ff ffi D ( ect in gravel, where extremely wide range of 6690 6689 ff K , and in clay sample, there can be a relatively min ) show lower values by 2–3 orders of magnitude, d ) of all boreholes (Table 2) in the tested area is only ah ) only slightly defers from D lng ective grain ( lng ff D D K ( represents the correct size of a referential mean grain. ( K ective porosity and referential mean grain with its size and K ff ect of the mentioned factors? lng ff D ) is 71 % higher value than ) and aa lng D D ( ( . Both values are of the same regional significance. Namely, t K K K 0.998. Also, it is interesting to register a very high accuracy of 3. (14) / = values of particular samples and two boreholes (SPB-3, SPB-5) mean 2 2 min R K d ective porosity, and some of them a q ff = cient . The numerical correlation between the predicted ( t ffi K ect e The first problem is determining mean grain from the granulometric data, especially It can be assumed that e The highest deviation of the predicted i,min ff D does (and/or how much) e distribution incorporate e since the sizea of minimal the measurable particle smallestlarge size content grain of particles is smaller than(size unknown. the corresponding measurable The one. to As grain anrespect mean equivalent size to size size specific curve surface of and always particles permeability, Chapuis has smaller and Légaré than (1992) used the relation: minimum size), with using particle size has frequentlyreasons been being: varied disputed particle in size, numerous highand papers proportions and Mulligan, of reports. fine 2004), fractions The inlarge electrochemical deposits content reaction (Young of between particlesa the such soil as particles mica and (Carrier, water, 2003) etc. All of these factors also achieving an extremely high correlation coe referential grain sizelaminas of of silt. incoherent deposits, even in4.2 case of Cohesive sand deposit intercalated by Use of the KC equation for calculating hydraulic conductivity of cohesive materials Depletion occurs only inYet, the case analyses of of those sandy samples samplesas show that intercalated with thinhydraulic laminas conductivity of for all silt. analyzed incoherentcoe deposits show a very high correlation of incoherent deposits, value are presented graphically inonly Fig. 9. 10 % Mean predicted smaller thana core the segment tested from value. 23.0 This to 30.0 borehole’s m core depth quality (Fig. is presented by Predicted Fine particles have theparticle most sizes intensive occurs. e This widea range of natural particle state, and sizes in ingrain gravel that deposits size, case, so is only the a mean product predicted grain of size illustrates accordance ofgrain results sandy of deposits. these Inanalyzed, methods this and only example, relations in relativelyrange the would homogenous of case probably mid-grain uniform, of be sands homogenous,in uniform of incoherent were small-grain mid- deposits. similar sandy An accuracy samples occurrence in excessively of reduces a siltey arithmetic wide laminas mean grain of size the grain size. opposed to that, manifestly showing the degeneration ofsize arithmetic for algorithm a for wide calculating range meanis of grain particle that very sizes. From good a results practical are point achieved of using view, grain4.1.3 an size interesting fact The correlation of predicted andThe tested graphicalconductivity correlation calculated between by using hydraulically specific tested methods and of mean predicted grain hydraulic size calculation, 5 % higher than presents: (1) the result(2) of hydraulic conductivity total of geometricon all mean the the size test samples of field. inof all The the successive tested the borehole cones hydraulic grains and of conductivity in (3) depression all achieved the in the sample, that boreholes area during the pumping test. As 5 core – average is that the geometric mean 5 5 25 15 20 10 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . However, ective grain 10 ff D ective porosity. ff , and most of the results t K values of the same single K ective grain size ff values. However, a few problems K ective porosity and referential mean ff 6692 6691 values was analyzed by using geometrical and . The numerical correlation confirms their high ective mean grain of the siltey-clayey deposits. t ff cient, the above mentioned formulation becomes K K 3 ffi proved to be the closest value to an referential grain < ) 40 . ). In this process, problems are related only to credibility 5 D lng D 12 ( ective grain size as various percentages of particles passing ff < K t K ) values in the vicinity of the tested value 3 / lng 0.696. That is a very high value, especially concerning the fact that truly represents an e D ( = 2 K lng R D ), presented in Fig. ective grain size formulation is simple only in the case of very uniform deposits lng ff D ( f grain-size = Pearson’s correlation was conducted for numerical and logarithmic values of The e Validity of the aquitard’s predicted Good results were achieved by using referential geometrical mean grain size – the Total sum of 86 samples of clayey-siltey deposits from three exploration fields were e was conducted for 8 more samples from the USGS laboratory (Morris and Johnson, of the sampleespecially for present grain with samples size ofthe distribution cause incoherent for materials analysis. searching from e Such boreholethrough the logs. technological sieves. That Grain problems was size are size and was incorporated in the final correlations. hydraulic conductivity of allnon-coherent materials samples, (gravel grouped and inall sand); coherent the three materials analyzed basic (silt samples. data and Verification groups of clay); group the (Table of 4): results for non-coherent materials group defined by percentage of particlesof that, that many pass authors recommend through thealong the use with sieve of the is Hazen’s rise e very of small.inappropriate. uniformity This Because coe problem is universallyvalue solved of by grain applying diameter the (Eq. total geometric mean model was tested multiple times onunavailability many of occasions, the but specific its surface use area was andby primarily porosity, and the limited was by also conversion further between complicated size. specific In that surface sense, areaversatility the and of verification the diameter referential of grain of size the formulation the and KC its e model connection to universality e isof conditioned sand by and the coarseof silt, when extreme the uniformity arithmetic of mean is sand, successfully divergence used. In between the the cases mean grain and the grain Universality of the hydraulicflow conditions model from is large to realized imperceptible.and That only credibility is when of conditioned by the it its used theoretical presents parameters. validity a The theoretical continuum validity of of the Kozeny–Carman 5 Verification of the KC model using e concentrating are within range 1 correlativity, some of deviations may havepermeability been test. a Achieved result results of confirmmean an earlier grain error conclusions in that conducting theAlso, of total it the geometric laboratory was usedn as reliable point of reference for verification of the porosity curve hydraulic conductivity values oneaverage, arithmetical order mean of values are magnitude outside lower acceptable than limits of the accuracypredicted tested (Table 3). values one. On ofwithin hydraulic the conductivity set were limits very of the close accuracy to criteria. the Graphical tested correlation (Fig. value, 13) e.g. illustrates deposits (test fields CI/MI2were and excluded. CI/MI3), In boreholes correlation with ofsample, less the samples than predicted with two and tested anomalies tested samples samples connected etc. to were the alsovarious short clayey excluded. period deposits The sampled of correlation fromCI/MI1). testing, the was laminated Danube–Sava conducted channel for boreholes 61 (test field samples of three forms of arithmetical mean value. All of the arithmetical mean values provided analyzed. All thethere samples was were no permeability controlwere of tested acceptable the in for test correlating the accuracy. withremained Yet, laboratory the concerning due selecting predicted to only appropriate a samples once,correlation large for correlation. so number of In of the samples mean tests, values from results the individual boreholes in loess and aquatic loess-like 5 5 25 20 10 15 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ć = e uni n Ž , unambiguously cients have been lng ffi in a range between D (read from grain size lng 40 D D eljko Miklin and Ivana Ž , . Simultaneously, the value of ć ective porosity presents flow 1 ff − . Correlation has provided very m s 2 40 − eljka Brki D Ž ective grain size ff and 10 6694 6693 12 − ) in a wide range of flow conditions. Very high values e ective porosity in function of referential grain size n ective grain size ff (Table 4) confirm its relations in porous media conditions, ff 2 R cients. The lowest values of correlation coe ffi The writers greatly appreciate cients ffi represents the referential grain size of the sample. ective porosity lng ff D ) is presented graphically for all types of clastic deposits. The graph was ective porosity and its relative referential grain size ff lng ects its permeability and specific surface area of coherent and non-coherent D ff ( Value of thesamples, referent very close mean to graindistribution the curve). value size of is, e in cases of analyzed non-coherent porosity and is slightlystandard lower literature. than the specific yield whichSuccessful is commonly appliance stated of in hydraulic the conductivity between KC 10 flowan model e confirms its1.5 µm validity up to in 6 mmparameters, a has been range the verified. of It range canpermeability be of and concluded specific applying that, surface through the areavalidity. presented is Kozeny–Carman extended up model to for the limits calculating of Darcy’s law constructed following literature data andbetween was the calibrated according tested to hydraulicapplying congruence conductivity the and Kozeny–Carman equation. its So, predicted this value e calculated by Geometric mean size of all particlesa contained in the sample deposits, regardless of the grainsense, size and distribution of specific particles.The In distribution that of anf e and an e Graphical correlation between the tested and the predicted hydraulic conductivity Separate sub-group was formed by non-coherent material data from all five CRO Publ. No. XXXIX, UNESCO, Arid Zone Research, Paris, 1968. Geotech. Geoenviron., 126, 739–746, 2000. 1956. 4. 3. 1. 2. lng on a laboratory scale. 6 Conclusions The following conclusions can be drawn from this study: achieved for siltey-clayey materials group,validity but of their the values presentedin (Table relations. 4) this It certainly research is confirm very referresult important to in to standard, even stronger point serial correlativity. out tests, that and test that data specific(Fig. used tests 14) illustrates would universality probably ofD the KC model (if applying referentialof mean correlation grain coe size two more samples from thegroup USGS are laboratory. presented Correlation in results of Fig. the 14. last mentioned test fieldshigh by correlation using coe the e 1967). Verification of the results for coherent materials was conducted by analyses of Boadu, F. K.: Hydraulic conductivity of soils from grain-size distribution: new models, J. Bear, J., Zaslavsky, D., and Irmay, S.: Physical Principles of Water Percolation and Seepage, Bear, J.: Dyinamics of Fluid in Porous Media, Elsevier, New York, 1972. Arkin, H. and Colton, R. R.: Statistical Methods, 4th Edn., Barnes and Noble Inc., New York, Vrbanek for their prevenance and helpstudy. This in collecting study large was number supported ofof by laboratory Croatia the data (Basic used Ministry Hydrogeological in ofproject Map this Science, of of Education Croatian the and Geological Republic Sports Survey). of of Croatia Republic 1 : 100000 – basic scientific References Acknowledgements. 5 5 25 20 10 15 20 25 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ˙ Ecole s, New Jersey, ff , 2011. ects of Aggregates and Mineral Filters cient of Permeability of Soils Using the ff ffi 6696 6695 10.5194/hess-15-1785-2011 , K.: The quantitative status of groundwater in alluvial aquifers ć Sr., K.: Physical Principles of Groundwater Dynamics, Faculty of Mining, Geology , K.: Parameter quantification of clastic sediments hydrogeologic properties based on ć ć ., Larva, O., and Urumovi Ž , ć Publishers, Boca Raton, 2004. Size Composition, Water Resources Publications, Littleton, Colorado, 1992. test fields in northernpp., Croatia, July Ph.D. 2013. thesis, unpubl, Univrsity of Zagreb, Zagreb, RGNf,and 164 Oil Engineering, Zagreb, 2003 (in croatian). Publications, LLC, Highlands Ranch, Colorado, 1997. Petroleum Transactions, 207, 222–239, 1956. Wiley & Sons, New York, 1963. on grain-size analysis, J. Am. Sci., 3, 1–6, 2008. Geological Survey, Washington, 1902. 27, pp. 742–746, 796–800, 832–836,1925. 874–878, 912–915, 987–990, 1026-1029, 1064–1068, Use in Filtration, Pub. Doc. No 34, 539–556, Massachusetts State Board of Health, 1892. Soil Materials, as Analyzed byWater the Supply Hydrologic Paper Laboratory 1839-D, of US US Geological Geological Survey, Survey Washington, 1948–60, 42 pp., 1967. of Valley Fill, California Division of Water Resources Bulletin, Sacramento,1979. 45 pp., 1934. on the hydraulic conductivityEarth Syst. and Sci., spectral 15, 1785–1794, induced doi: polarization response ofAmsterdam, 1981. sand, Hydrol. 1927 (in German). Resources Publications, LLC, Highlands Ranch, Colorado, 2010. aggregates and fillers inon bituminous Asphalt mixtures, Mixture in: Performance, E STP 1147, edited 177–186, by: 1992. Meininger, R. C., ASTM,aquifer-aquitard Philadelphia, system hydrologically ASTM connected to river, Hydrogeol. J., 15, 669–678, 2007. Kozeny–Carman Equation, Département desPolytechnique de génies Montréal, civil, Montreal, géologique 2003. et des mines, Engineering, 15, 150–166, 1937. 29, 263–273, 1939. 1054–1056, 2003. in norther Croatia,Croatian Geologia Geological Society, Croatica, 63, 283–298, Jornal 2010. of the Croatian Geological Survey and the Young, R. N. and Mulligan, C. N.: Natural Attenuation of Contaminants in Soils, Lewis Vukovic, M. and Soro, A.: Determination of Hydraulic Conductivity of Porous Media from Grain Urumovi Urumovi Kasenow, M.: Applied Ground-Water Hydrology and Well Hydraulics, Water Resources Todd, D. K.: Ground Water Hydrology, John Wiley & Sons, New York, 1959. Terzaghi, K.: Principles of soil mechanics. Engineering News-Record, 95, Nos. 19–23, 25– Irani, R. R. and Callis, C. F.: Particle Size: Measurement, Interpretation and Application, John Slichter, C. S.: The Motions of Underground Waters, Water Supply and Irrigation Paper, US Hubbert, M. K.: Darcy’s law and the field equations of the flow of underground fluids, AIME Odong, J.: Evaluation of empirical formulae for determination of hodraulic conductivity based Hazen, A.: Some Physical Properties of Sands and Gravels, With Special Reference to Their Morris, D. A. and Johnson, A. I.: Summary of Hydrologic and Physical Properties of Rock and Hantush, Mahdi S.: Hydraulic of wells, Academic Press, New York, 1964. Freeze, R. A. and Cherry, J. A.: Groundwater, Prentice-Hall Inc., Engelwood Cli Kozeny, J.: Uber Kapillare Leitung des Wassers im Boden, Akad. Wiss. Wien, 136, 271–306, Eckis, R. P.: South Coastal Basin Investigation, Geology, and Ground Water Storage Capacity Koch, K., Kemna, A., Irving, J., and Holliger, K.: Impact of changes in grain size andKovacz, G: pore space Seepage Hydraulics, Developments in Water Science, Elsevier Science Publishers, Davis, S. N. and De Wiest, R. J. M.: Hydrogeology, John Wiley & Sons, New York, 1966. Kasenow, M.: Determination of Hydraulic Conductivity from Grain Size Analysis, Water Cheng, C. and Chen, X.: Evaluation of methods for determination of hydraulic properties on an Chapuis, R. P. and Légaré, P.-P.: A simple method for determining the surface area of fine Chapuis, R. P. and Aubertin, M.: Predicting the Coe Carman, P.C.: Permeability of saturated sand, soil and clay, The Journal ofCarrier Agricultural Science, III, W. D.: Goodbye, Hazen, hello, Kozeny–Carman, J. Geotech. Geoenviron., 129, Carman, P. C.: Fluid flow through granular beds, Transactions of the Institute of Chemical Brki 5 5 25 20 30 15 25 10 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | t K 3 − ) 1 − 10 Kind of sand × (m s 1.8 ) 1 conductivity − K 3 3 3 3 3 4 − − − − − − (m s 4 10 10 10 10 10 10 − × × × × × × ) 10 2.5 2.0 1.6 1.1 4.6 8.8 40 × D ( 3 4 4 4 3 4 K − − − − − − 10 10 10 10 10 10 × × × × × × lng D 1.1 8.8 6.4 5.2 1.6 7.1 32.218.9 1.16 1.40 Fine to medium − − 6 6 6 6 6 6 − − − − − − ah 7.8 16.6 2.55 Medium uniform 10 10 10 10 10 10 D 88.4 52.1 14.0 12.0 2.78 − × × × × × × − − − ) 9.1 4.4 3.3 1.8 8.3 2.4 ah D ( 6 6 6 6 6 6 ag K − − − − − − 9.7 4.2 D 86.9 47.8 10 10 10 10 10 10 − − − − × × × × × × 7.2 3.0 2.2 1.5 5.7 2.2 aa 6698 6697 5.3 0.7 D 85.3 43.4 ective mean grain-size in samples Tested hydraulic − − ff 5 6 6 6 5 6 − − − − − − − − 10 10 10 10 10 10 × × × × × × ) 1.1 5.5 4.1 2.1 1.0 2.9 aa 50 D ( D 6 6 6 6 6 6 12.1 K − − − − − − − 10 10 10 10 10 10 erence between predicted and ff × × × × × × tested hydraulic conductivity (%) Di 9.0 3.6 2.7 1.8 6.9 2.7 40 7.8 18.1 0.5 25.8 0.1 14.3 D 32.7 − − − − 3 3 3 3 3 3 − − − − − − 10 10 10 10 10 10 30 × × × × × × distribution curves D ) 52.4 34.8 17.6 16.5 erence between predicted hydraulic conductivity calculated using Kozeny– Calculation manner of the predicted average hydraulic conductivity in the borehole 3.5 2.8 2.5 2.2 4.1 1.4 lng − − − Diameter form grain-size Mean grain size − ff D ( 3 3 3 3 3 3 − − − − − − K 10 10 10 10 10 10 × × × × × × Geom. Arithm. Geom. Arithm. Geom. Arithm. Geom. Arithm. 1.05 1.59 0.0021 0.0031 0.0017 0.0025 0.50 1.11 FS/SU-2 FS/SU-1 SU-2 Mean hydraulic conductivity of gravelly aquifer (test field GW). Average di t SPB-1 2.5 Aver. 1.8 Borehole Calculation manner of the e SPB-3 1.6 K/K SPB-4 1.3 SPB-5 3.0 SPB-6 1.2 grain size Variety of equivalent Predicted hydraulic conductivity calculated usingWell fields SU-1 Tested Table 2. Carman equation end tested one on well fields. Table 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | )) D 2 ( K ecients calculated ff RR K 2 aa 1046 D − RR 0.999 0.9981.0000.997 1.000 0.9940.74 0.9980.999 0.976 0.547 0.995 0.9990.997 0.993 0.990 0.995 0.985 0.834 0.971 0.696 0.942 0.985 0.971 ) and the predicted ( t K 1 2 3 4 5 6 ag Mark Nominal valuesR Log values R R R R R 1078 D − ah 1087 D ective grain size Pearson’s correlation coe lng 40 lng lng lng lng ff − D D D D D D 6700 6699 lng 44 D − 0.69 0.084 0.085 0.087 Geometric mean Arithmetic mean rence between the tested ( ff Gravel, sand Gravel, sand, silt, clay t erence ff /K ) erence % D ff ( Di K Average relationand di Used mean grain USGS lab. Gravel, sand, silt, clay + USGS lab. Gravel, sand + Average relations and di Numerical results of correlations between the tested and the peredicted Togeather CRO CRO test filedsAll togeather CRO Silt, clay CRO test fileds Gravel, sand Sample locations Materials E using the Kozeny–Carmansamples equation from US (for Geol. all Survey laboratory, Morris samples and from Johnson, 1967). test fields in Croatia and a few Table 4. Table 3. hydraulic conductivity depending on used mean grain of coherent deposits. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 6702 6701 Definition sketch of liquid driving and opposed viscous forces for elemental volume. Situation map of Northern Croatia with test sites locations. Figure 2. Figure 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) factor on porosity function 2 ) n − (1 / 2 n 6704 6703 ) and drag resistance ( n ). Efect of driving ( 2 Range and arithmetic mean of specific yield values for 586 analyses in the Hydrol. ) n − (1 / 3 n Figure 4. Lab. of the US Geol. Survey (from Morris and Johnson, 1967). ( Figure 3. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 20)

U >

<20. <20.

U U coefficient Uniformity 10 1

. Carman equation for for equation Carman 95 - lng D 2, and medim uniform grain

2 - < K(Dah) U=D60/D10 10 75

. /D lng >20) lie below full line the Aquifer SU 60 U

D = U <2 , and medim uniform grain deposits 2< 55 10 K(Daa) Kt Depth (m) /D 6706 6705 60

1 35 - K(D40) K(Dlng) ) in function of referential mean grain

e n ) in function of referential mean grain D mean of referential function ) in Aquifer SU e n uniform grain deposits of sand and gravel ( gravel and sand of deposits grain uniform 15

20. Verified samples of non-uniform grain deposits of sand and gravel ( Hidraulic conductivity K(m) conductivity Hidraulic 1,E-04 1,E-03 Effective porosity ( Effective porosity ective porosity (

Results of predicted hydraulic conductivity calculated using Kozeny–Carman 5 ff < U < Results of predicted hydraulic conductivity calculated using Kozeny E

6 Verified samples of non- Figure Figure Note: Dot line devides uniform grain deposits U D =

5 samples fromsamples medium uniform sandyaquifers Figure Figure Figure 6. equation for samples from medium uniform sandy aquifers. Figure 5. Note: dot line devides uniform grain deposits lie below the full line. deposits 2

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

SF/SU1 (see Fig. ( 7)) Fig. (see SF/SU1

Uniformity coefficient U coefficient Uniformity 100 10 1 125 U=D60/D10

2 - 105 K test Aquifer SF/SU

85 K(Dlng) Depth (m)

6708 6707 65 K(Dah)

1 -

45

K(Daa) Aquifer SF/SU 25 K(D40)

1,E-03 1,E-04 1,E-05 1,E-06 1,E-07 Hydraulic conductivity K(m/s) conductivity Hydraulic

Fine sand sample with thin silty laminas from test field

8 Results of predicted hydraulic conductivity calculated using KC equation for samples from fine Fine sand sample with thin silty laminas from test field SF/SU1 (see Fig. 7). Results of predicted hydraulic conductivity calculated using KC equation for samples

7 Figure Figure Figure Figure sandy aquifers with thin siltey laminas Figure 8. Figure 7. from fine sandy aquifers with thin siltey laminas. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (9)) Fig. 3 (see -

60 5 3 - - Ktest K test 55 GW, SPB GW, SPB 50 KC(D40) K(D40)

45

KC(Dah) from 23 to 30 m depth et borehole SPB borehole et depth 30 m 23 to from K(Dah) 40 35 Aquifer depth d (m) 6710 6709

KC(Daa) Aquifer depth d (m) K(Daa)

30 25 core borehole Gravel KC(Dlng) K(Dlng) 10 20 15 Results of predicted hydraulic conductivity calculated using KC equation for from samples

9

Figure Figure

Hydraulic conductivity K (m/s) K conductivity Hydraulic

Hydraulic conductivity, K (m/s) K conductivity, Hydraulic 1,E-04 1,E-05 1,E-06 1,E-07 1,E-02 1,E-03 1,E-03 1,E-04 1,E-05 1,E-06 1,E-01 1,E-02 gravely aquifer (test field GW) (test field gravelyaquifer Figure Figure

5 Gravel borehole core from 23 to 30 m depth et borehole SPB-3 (see Fig. 9). Results of predicted hydraulic conductivity calculated using KC equation for samples Figure 10. Figure 9. from gravely aquifer (test field GW). Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

clayey samples clayey - )) mean grain size 1,E-07 of sand and gravel ah t D ( K

K(Dah) K 1,E-02 1,E-02 1,E-08

) and the predicted hydraulic ) and t K(Dlng) and the predicted hydraulic conductivity using K aa K(Daa) well graded well gravel K(Dlng) and tested D

mean grain size for siltey grain size mean ( 1,E-03 (Kt) (Kt) ))

K K

ah

1,E-03 2 1,E-09 - GW

(D 1,2Kt 1,2Kt K(D40) 2

- SU uniform 1 - K(Dlng)

1,E-04 and K SF/SU

SF/SU ) 0,8Kt fine sand

aa Tested Kt (m/s) 1 6712 6711 Tested, Kt (m/s) - 0,8Kt K(Daa) Tested Kt (m/s) 1,E-10 SU K(D

1,E-04

K=Kt Kt/3 1,E-05

), and arithmetic ( silt K=Kt K(Dah) lng D 1,E-11 ( 3Kt all Nominal values: R²=0,998 Log values R²=0,976

- K 1,E-06 Graphical correlation between predicted K and tested Kt of sand and gravel deposits gravel Kt and of tested K and correlation sand between predicted Graphical 1,E-05 11

, and arithmetic ( arithmetic , and

) 1,E-04 1,E-05 1,E-06 1,E-02 1,E-03

(m/s) K Predicted

1,E-03 (m/s) K 1,E-04 Predicted 1,E-05 1,E-02 CI/MI lng Kt Figure Figure

Graphical corelation between tested the Graphical K(D 1,E-12

5 12

1,E-07 1,E-08 1,E-09 1,E-10 1,E-11 1,E-12

(m/s) K Predicted, Figure Figure geometric geometric

Graphical correlation between the tested ( Graphical correlation between predicted Figure 12. conductivity using geometric for siltey-clayey samples. Figure 11. deposits. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

) and the ) and the and the predicted t t

K K siltey samples -

) for all samples. the predicted 1,E-01 lng and 1,E-07 D

( K

1,E-02 1,E-03 3Kt 0,8Kt lab.) K(USGS 1,E-08 K(Dlng) 1,E-04 for all samples

) lng

1,E-05

Kt/3 1,E-09 1,E-06 1/3Kt 2Kt K(CROsamples) 3Kt 1,E-07 Tested, Kt Kt Tested, (m/s)

6714 6713 Tested K (m/s) 1,E-10

1,E-08 ):

Kt lng ) using referential geometric mean grain size for clayey- using referential geometric mean grain size for clayey grain size geometric referential using mean

) lng

1,E-09 lng D ( 1,E-11 K

1,E-10 Kt 1/2Kt 1,2Kt R²=0,547 Log values: R²=0,696 Nominal values: 1,E-11 Nominal values of K(D of values Nominal R²=0,999 CRO CRO R²=0,999 samples Log values: CRO R²=0,942 samples R²=0,995 CRO+USGS sampesCRO+USGS R²=0,995 sampesCRO+USGS R²=0,971 1,E-12 Verification of graphical and and correlationofnumerical (Kt) betweenVerification tested graphical the 1,E-12 Verification of graphical and and correlation (Kt) ofnumerical Verification between tested graphical the 13

1,E-07 1,E-08 1,E-09 1,E-10 1,E-11 1,E-12

1,E-01 1,E-02 1,E-03 1,E-04 1,E-05 1,E-06 1,E-07 1,E-08 1,E-09 1,E-10 1,E-11 1,E-12 14

(m/s) K Predicted (m/s) K Predicted Figure Figure hydraulic conductivity K(D hydraulic conductivity using referemtial geometric mean size K(D size geometric mean using referemtial conductivity hydraulic Figure Figure Verification of graphical and numerical correlation between the tested ( Verification of graphical and numerical correlation between the tested ( Figure 14. siltey samples. Figure 13. predicted hydraulic conductivity using referemtial geometric mean size predicted hydraulic conductivity