240 Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 Journl of Zhejing University-SCIENCE A (Applied Physics & Engineering) ISSN 1673-565X (Print); ISSN 1862-1775 (Online) www.zju.edu.cn/jzus; www.springerlink.com E-mil: jzus@zju.edu.cn Study on clibrtion eqution for soil wter content in field tests using time domin reflectometry * Yun ZHAO 1,2, Do-sheng LING 1,2, Yun-long WANG 1,2, Bo HUANG 1,2, Hn-lin WANG 1,2 ( 1 MOE ey Lbortory of Soft Soils nd Geoenvironmentl Engineering, Zhejing University, Hngzhou 310027, Chin) ( 2 Institute of Geotechnicl Engineering, Zhejing University, Hngzhou 310058, Chin) E-mil: dsling@zju.edu.cn Received Mr. 24, 2015; Revision ccepted July 8, 2015; Crosschecked Feb. 29, 2016 Abstrct: The crucil point in clibrting soil wter content using the technology of time domin reflectometry (TDR) is to estblish the reltionship between the pprent dielectric constnt nd the wter content. Bsed on dtbse, which included 45 kinds of soil smples nd 418 dt points from our own test dt nd relevnt literture, n empiricl clibrtion eqution is proposed. Additionlly, the influence of soil type, dry density of soil, compction energy, pore fluid conductivity, nd temperture on the clculted result for wter content ws lso nlyzed. Results show tht the eqution cn offer n error of ±0.05 g/g for most soils encountered in geotechnicl engineering. However, the estimtion error given by the empiricl eqution becomes significnt for soils with dry density less thn 1.3 g/cm 3, so the eqution ws modified to consider the influence of dry density. Both of the empiricl equtions cn be used to test grvimetric wter content using the TDR method conveniently nd efficiently without clibrtion. ey words: Soil, Grvimetric wter content, Time domin reflectometry (TDR), Empiricl clibrtion eqution http://dx.doi.org/10.1631/jzus.a1500065 CLC number: TU413 1 Introduction Wter content is bsic prmeter of the threephse-system of soil nd ffects soil behvior notbly in geotechnicl engineering. Obviously, therefore, it is of gret significnce to be ble to test the wter content of soil efficiently. The time domin reflectometry (TDR) method hs been widely used to mesure wter content in griculture, hydrulic engineering, geotechnicl engineering, etc., for its dvntges of speed, relibility, nd the possibility of utomtic monitoring (Drnevich et l., 2001; Noborio, 2001; Imhoff et l., 2007; Cui et l., 2013; Chen, 2014). Corresponding uthor * Project supported by the Ntionl Bsic Reserch Progrm (973 Progrm) of Chin (No. 2014CB047005) ORCID: Yun ZHAO, http://orcid.org/0000-0002-7247-9968; Dosheng LING, http://orcid.org/0000-0002-0604-1175 Zhejing University nd Springer-Verlg Berlin Heidelberg 2016 The crucil point in clibrting soil wter content using TDR technology is to estblish the reltionship between the dielectric constnt nd the wter content, which is usully referred to s the clibrtion eqution. At present there re minly two pproches to set up the eqution. One is the volumetric mixing model, which cquires the dielectric constnt of mixture by tking weighted verge of the dielectric constnt of ech component in the mixture ccording to their volumetric proportions. Since this theoreticl model is usully bsed on some ssumptions, it hs limittions in prcticl use (Birchk et l., 1974; Dobson et l., 1985; Heimovr et l., 1994; Chen et l., 2003). The other pproch is to find purely empiricl eqution to fit the experimentl dt points. Among these empiricl equtions, Topp s eqution is widely used (Topp et l., 1980). This eqution shows tht the reltionship between pprent dielectric constnt nd volumetric wter content is not sensitive to soil
Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 241 texture, soil bulk density, temperture, slt content, etc. Mny studies found tht this empiricl eqution hd high ccurcy for inorgnic soils but ws inpplicble to orgnic soils, fine texturl soils, nd cly soils (Herkelrth et l., 1991; Jcobsen nd Schjønning, 1993; Dirksen nd Dsberg, 1993; Ponizovsky et l., 1999). There re lso other types of empiricl equtions including liner reltionship between volumetric wter content nd the squre root of the pprent dielectric constnt (Hook nd Livingston, 1996; Yu et l., 1997; Msbruch nd Ferré, 2003). There re lso equtions considering the effect of soil density (Ledieu et l., 1986; Mlicki et l., 1996). However, in geotechnicl engineering, grvimetric wter content is used more extensively. According to the theory of TDR, two physicl quntities, dielectric constnt nd bulk electricl conductivity, of soil cn be obtined through the TDR wveforms. The two prmeters re used in n empiricl reltionship relting grvimetric wter content nd dry density. Siddiqui nd Drnevich (1995) proposed liner clibrtion eqution to relte dielectric constnt with grvimetric wter content nd dry density. Then the corresponding two-step method ws performed to obtin grvimetric wter content nd dry density from field mesurements. Yu nd Drnevich (2004) estblished liner empiricl clibrtion eqution to relte bulk electricl conductivity to grvimetric wter content nd dry density. Using this eqution with Siddiqui nd Drnevich (1995) s eqution, only one TDR test is required to obtin the prmeters of soil in situ. This method is clled the one-step method. Since the reltionship between soil bulk electricl conductivity nd grvimetric wter content is not liner (Abu-Hssnein et l., 1996; Zmbrno, 2006), Jung (2011) proposed voltge normliztion method nd developed clibrtion eqution between the voltge drop prmeter nd the pprent dielectric constnt to replce the bulk electricl conductivity eqution in the one-step method. It is importnt tht lbortory tests should be conducted to obtin the constnts in the equtions before using the one-step method nd the two-step method. Generlly, fter clibrtion of the constnts of the empiricl equtions, wter content cn be mesured in the lbortory nd in the field by the TDR method conveniently nd efficiently with high ccurcy. But for the resons listed below, there re some constrints on pplying these clibrtion equtions in field tests: 1. The two-step method tkes time nd energy to obtin the mesurements for the field test. In prticulr, when continuous testing t different depths is required, this method will be invlid since it is difficult to perform the second TDR test. 2. For both the one-step method nd the twostep method, the constnts of the clibrtion equtions re soil-dependent. As the soil is usully heterogeneous in the field nd not of single soil type, the clibrtion of ech soil s constnts is difficult. Hence, it is of gret significnce to propose clibrtion eqution tht is pplicble to vrious soils nd correltes grvimetric wter content with pprent dielectric constnt directly in geotechnicl prctice. The object of this study is to estblish such clibrtion eqution through nlyzing TDR dt points from lbortory tests nd the literture. 2 A new empiricl clibrtion eqution Herein, the soil-wter-ir three phse system of soil is described ccording to Hook nd Livingston (1996) (Fig. 1). Solid prticles re considered s n impervious lyer with thickness l s nd dielectric constnt s tht cn hve dsorbed moisture. Liquid nd ir phses re lso treted s liquid lyer nd n ir lyer with thicknesses l w nd l, nd dielectric constnts w nd, respectively. X 1 nd X 2 represent the positions of the probe inserted into the soil. The reltionship between the volumes of ech phse is: Coxil cble l l l l. (1) w s Solid s Air l s l l w Probe Liquid l X 1 X 2 Fig. 1 Soil-wter-ir trnsmission line model (Reprinted from (Hook nd Livingston, 1996), Copyright 1996, with permission from ACSESS) w
242 Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 It is ssumed tht the totl trvel time of the TDR wveform through the tested soil smple is equl to the sum of the time in ech phse, which cn be given by t t t t, (2) s w where t, t s, t w, nd t represent the time of TDR wveform trvel in the system, solid prticles, wter, nd ir, respectively. Topp et l. (1980) showed tht the velocity of n electromgnetic wve trvelling through the medium could be described by n pprent dielectric constnt : c v, (3) where v is the velocity of electromgnetic wve tht trvels through the medium, nd c is the velocity of n electromgnetic wve in free spce (the pprent dielectric constnt is lso clled the dielectric constnt, so the two concepts re the sme in this study). The velocity of the TDR wveform in ech phse cn lso be described by i 2 li vi, (4) t where i represents s, w, or. Combining Eqs. (2) (4) leds to the eqution: l ls s lw w l. (5) Define α s the vlue of the volume of the ir phse compred to the volume of the solid phse, i.e., l, (6) ls the grvimetric wter content of soil cn be expressed s w l w, (7) Gl s s where G s is the specific grvity of the solids. Combining Eq. (1) nd Eqs. (5) (7) leds to Eq. (8): w 1 w Gs Gs 1 1 s. (8) As shown in Eq. (8), the reltionship between grvimetric wter content nd pprent dielectric constnt is influenced by the dielectric constnt of ech component, the vlue of α, etc. For most nturl soils, the typicl vlues of the dielectric constnts of the solid phse s, ir phse, nd liquid phse w re 3 5, 1, nd 81, respectively. The vlue of the specific grvity of solids G s is usully round 2.6 2.8. The prmeters bove cn be regrded s constnts. According to the definition of α, α is less thn the void rtio, which vries between 0.4 1.5 (Chen Y., 2011). Then, the rnge of 1/(1+α) is limited between 0.4 0.71, which represents the degree of compction of the soil. Therefore, it ssumes tht treting 1/(1+α) s constnt will introduce negligible errors for soils of different types nd compction. From Eq. (8), the clibrtion eqution between grvimetric wter content nd pprent dielectric constnt hs the form of A w B C, (9) where A, B, nd C re empiricl constnts. Vlues of them re obtined through regression nlysis of rel tests. 3 Dt collection To obtin the prmeters in Eq. (9) through regression nlysis, totl of 418 dt points from TDR tests of 45 soil smples from our experiments nd from the literture were collected. 3.1 Dt from lbortory test Three types of soils commonly used in engineering were used to conduct the lbortory tests: Fujin snd, Qintng silt, nd one cly soil. The
Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 243 properties of these soils, including the specific grvity of solids (G s ), liquid limit (L L ), plsticity index (P I ), grin-size distributions, nd the clssified types by the Unified Soil Clssifiction System (USCS) re shown in Tble 1. Tble 1 Physicl properties of soils in the lbortory tests USCS GSD (%) Soil G type s L L P I Snd Silt Cly Fujin snd SP 2.64 100.0 0 0 Qintng silt ML 2.69 31.7 9.1 11.2 83.0 5.8 Cly snd CL 2.66 48 15.4 11.4 51.9 36.7 SP: poorly grded snd soils; ML: silt soils; CL: low plsticity cly soils; GSD: grin-size distribution The TDR tests were conducted with the Cmpbell Scientific TDR 100 pprtus nd its PCTDR softwre. The TDR wveforms re nlyzed to obtin the dielectric constnt (Bker nd Allmrs, 1990). The probe used here is the sme s the one recommended by ASTM (2012) with height of 116 mm for the compct mold. Before the test, the soil smples were oven dried, pulverized, sieved first, nd mixed with tp wter to pproch the trgeted wter contents. After being plced in room with constnt temperture round 20 C in seled plstic bg for 24 h, the soil smples were then compcted in the mold ccording to ASTM (2012b) nd TDR test ws performed. Finlly the soil smples were oven dried to obtin the rel grvimetric wter content. Through this method, the dielectric constnt nd the dry density of the snd, silt, nd cly soil smples with seven, seven, nd six different wter contents, respectively, were obtined. 3.2 Dt from the field test Bsed on the pvement mintennce project of n irport in the west of Chin, TDR tests for soils of different depths t the pvement re nd soil surfce re were performed. Soil smples t trgeted depths were tken by the dry drilling method. Prt of the soil ws seled in plstic bgs nd tested by oven dry method while the rest ws compcted in the mold for TDR test. The properties of field soils re shown in Tble 2. As the test condition in the field ws complex nd time ws limited, twelve dt points were obtined. Tble 2 Physicl properties of the field soils Soil USCS GSD (%) G type s L L P I Snd Silt Cly Airport-1 CL 2.61 47.3 33.4 7.1 74.0 18.9 Airport-2 CL 2.64 35.9 11.8 15.6 65.2 19.2 Airport-3 CL 2.75 35.1 14.9 23.8 60.7 15.5 3.3 Dt from the literture Informtion from the literture on 39 soil smples nd 386 TDR dt points, including the vlues of dielectric constnt, dry density, nd grvimetric wter content by the oven dry method, ws used for re-nlysis in this study. In this dtbse, the number of smples for sndy soils, silt soils, nd cly soils re 9, 8, nd 22, respectively. The rnge of grvimetric wter content is 0 0.55 g/g nd dry density is 1.07 2.3 g/cm 3. Temperture vries from 4 C to 40 C. Properties of soils from the literture re shown in Tble 3. According to their properties, the soils collected re clssified into four types: sndy soils (S), silt soils (ML), low plsticity cly soils (CL) nd high plsticity cly soils (CH). According to USCS, S soils include SW, SP, SM, SM-SC, nd SM-SW soil types. CL soils include CL nd CL-ML soil types. CH soils include CH nd CH-CL soil types. The compction energy levels used in Jung (2011) on ASTM Reference Soils (ASTM, 2010) were 360, 600, nd 2700 kj/m 3 for compction methods of reduced compction (RC), stndrd compction (SC), nd modified compction (MC), respectively (ASTM, 2007; 2009). Lin (1999) used the sme compction methods to conduct compction test for M1 M5 soils. The vlues of electricl conductivity used by Jung (2011) to perform TDR test on ASTM Reference Soils (ASTM, 2010) re bout 62 ms/m for tp wter nd 130 ms/m for sline wter. 4 Results nd discussion 4.1 Regression nlysis The dt bse collected bove ws used to obtin the prmeters in Eq. (9) through regression nlysis. As shown in Fig. 2 (p.245), ten points lbeled with squres show gret disprity, nd these
244 Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 Soil USCS type Tble 3 Properties of the soils from litertures GSD (%) Compction Temperture G s L L P I Snd Silt Cly method ( C) Pore fluid NDS Reference A1 SW SC Room CCl 2 6 Chen et l. (2014) A2 ML SC Room CCl 2 7 Chen et l. (2014) A3 CL SC Room CCl 2 7 Chen et l. (2014) Silt ML 2.67 5.7 93.7 0.6 SC Room TAP 6 Xu (2008) Xioshn CL 2.69 34 23 0 69.6 30.4 SC Room TAP 5 Xu (2008) cly Bentonite CH 2.82 60 45 29.5 39.8 30.7 SC Room TAP 5 Xu (2008) Crosby till CL-ML 41 23 16 50 34 SC 4, 10, 20, 30, 40 TAP 31 Drnevich et l. (2001) olinite CL 30 6 0 0 100 SC 4, 20, 30 TAP 8 Drnevich et l. (2001) Illite CH-CL 50 28 0 0 100 SC 4, 20, 30 TAP 7 Drnevich et l. (2001) Concrete SW 100 0 0 SC 4, 20, 40 TAP 6 Drnevich et l. (2001) snd Fine snd SP 2.65 100 0 0 SC 4, 20, 40 TAP 6 Drnevich et l. (2001) Houston CH 54 31 0 5 * 95 * SC 4, 10, 20, TAP 30 Drnevich et l. (2001) cly 30, 40 Grde snd SW SC Room TAP 4 Yu nd Drnevich (2004) Silt ML 2.69 32 9 11.2 83.0 5.8 SC Room 5 Chen W. (2011) Silt snd SM 2.66 28.1 5 SC Room 6 Chen W. (2011) Silt ML 2.68 28.9 6 SC Room 5 Chen W. (2011) Mucky soil CL 2.73 33.4 14.9 SC Room 7 Chen W. (2011) Silt cly CL-ML 2.72 30.3 13.4 SC Room 7 Chen W. (2011) Vigo CL 36 12 SC, MC Room 9 Feng et l. (1998) Hendricks І CL 37 13 SC, MC Room 5 Feng et l. (1998) Indinpolis ML 15 SC, MC Room 9 Feng et l. (1998) Hendricks II CL 32 11 SC, MC Room 10 Feng et l. (1998) Bloomington CL-CH 50 24 SC, MC Room 9 Feng et l. (1998) ASTM-CH CH 2.72 59.8 39.2 1.2 42.5 56.3 SC, MC, RC 20 TAP, DI, SAL 29 Jung (2011) ASTM-CL CL 2.67 33.4 13.6 11.5 42.5 46 SC, MC, RC 20 TAP 15 Jung (2011) ASTM-ML ML 2.73 27.4 4.1 1 94 5 SC, MC, RC 20 TAP 15 Jung (2011) ASTM-SP SP 2.66 99 SC, MC, RC 20 TAP 19 Jung (2011) M1 SM-SC 2.76 55 35 10 SC, MC, RC 20 TAP 12 Jung (2011) M2 ML 2.77 16.2 5.7 37.5 45.0 17.5 SC, MC, RC 20 TAP 14 Jung (2011) M3 CL 2.83 28.5 16.2 20 55 25 SC, MC, RC 20 TAP 12 Jung (2011) M4 CL 2.83 33.7 14.8 12.5 47.5 40 SC, MC, RC 20 TAP 13 Jung (2011) M5 CL 2.82 41 21.1 5 40 55 SC, MC, RC 20 TAP 13 Jung (2011) GRP CL 2.68 31.1 15.8 12 60.5 27.5 21 23 6 Jung (2011) SAG SM-SW 2.72 65.3 16.4 9 21 23 5 Jung (2011) DFA CL-ML 2.62 17.6 5.3 35 50.4 14.6 21 23 5 Jung (2011) Poor snd SP 98.7 1.34 SC, MC 11 Rthje et l. (2006) Tylor cly CH 4.17 95.8 SC 5 Rthje et l. (2006) Cly CL 12.2 77.9 SC 6 Rthje et l. (2006) Sndy cly CH 37.2 62.9 SC 6 Rthje et l. (2006) SW: well-grded snd soils; SM: silt snd soils; NDS: number of dt smples; TAP: tp wter; DI: deionized wter; SAL: sline wter (bout twice pore fluid conductivity of TAP); * : the dt is estimted; Room: room temperture, usully round 20 C
Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 245 points were omitted during dt fitting. At the sme time, only the dt points t 20 C given by Drnevich et l. (2001) were dopted for the regression nlysis. It should be pointed out tht the subsequent sttisticl nlysis covered the ten omitted scttered points. The results of regression nlysis re shown in Fig. 2 nd the empiricl clibrtion eqution is given in Eq. (10). The correltion coefficient R 2 is 0.9019, showing good correltion between the regression results nd the dt points. 1.4637 w 22.1373 1.4606. (10) N ( ) 2 w 1 (14) SEE, N 2 where w o is grvimetric wter content obtined by the oven dry method nd N is the number of dt points. 4.2 Soil type effects Error vritions long with wter content for different soil types re shown in Fig. 3. Vlues of E, SE, SEE, nd the distribution of errors re shown in Tble 4. Fig. 2 Result of regression nlysis by Eq. (10) Eq. (10) ignores the influence of soil type, dry density, compction energy, pore fluid conductivity, temperture, etc. To quntify nd evlute the effect of these elements on the ccurcy of Eq. (10), sttisticl quntittive evlution indexes re dopted s follows: (1) errors (Δw) reflecting the difference between wter contents clculted by Eq. (10) nd by the oven dry method; (2) verge errors (E); (3) stndrd errors (SE); (4) stndrd errors of estimte (SEE). E is used to evlute the degree of devition of the clculted result from the rel vlue nd SE indictes the discrete extent of E. SEE estimtes the dispersion of the overll errors (Jung, 2011). The definitions of ech prmeter re shown s follows: w w w, (11) o N w 1 E, (12) N N ( ) 2 w E 1 SE, (13) N Fig. 3 Errors of wter content by Eq. (10) vs. grvimetric wter content for different soil types As shown in Fig. 3, errors tend to increse with the incresing of wter content. The reson is tht the vlues of A, B, nd C re ssumed constnt in the proposed Eq. (9) nd obtined through regression nlysis, which mens the vrition of wter content with dry density is ignored. As shown in Tble 4, the vlues of sttistic prmeters for S, ML, nd CL soils re smll nd the rtio of errors within ±0.03 g/g re lrge, which indictes tht Eq. (10) hs good ccurcy for these soils. But for CH soils, it shows reltively poor result, which cn be ttributed to ignornce of the effect of bound wter for soils with high cly contents. In generl, errors of most dt points of ll soil types re within ±0.05 g/g. 4.3 Dry density effects Errors vrying with dry density re shown in Fig. 4. Vlues of E, SE, SEE, nd the distribution of errors re shown in Tble 5. As shown in Fig. 4, errors show reltively obvious dependency on the chnge of dry density. With
246 Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 the incresing of dry density, errors grdully vry from negtive to positive, mening tht Eq. (10) underestimtes the result in cses of low dry density nd overestimtes the result in cses of high dry density. Note tht errors re lrge for low dry density soils. The reson cn lso be ttributed to the neglect of vrition of A, B, nd C. As shown in Tble 5, when dry density rnges round 1.3 2.3 g/cm 3, the sttistic prmeters E nd SEE re round 0.01 0.03 g/g nd errors within ±0.05 g/g re t high level, indicting tht Eq. (10) hs good ccurcy for wide scope of dry density 0.15 0.10 0.05 0.00-0.05-0.10-0.15-0.20 S ML CL CH -0.25-0.30 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Dry density (g/cm 3 ) Fig. 4 Errors of wter content by Eq. (10) vs. dry density cses. However, for dry density of 1.0 1.3 g/cm 3, it shows poor result, which indictes tht t this condition, the effect of dry density on the result of Eq. (10) cnnot be ignored. Therefore, it is necessry to correct Eq. (10) to consider the effect of dry density. In Eq. (9), prmeters A, B, nd C re ssumed to be constnts. Actully, they re vribles nd hve reltionship with dry density, etc. Herein, vlues of A, B, nd C re ssumed to hve simple liner reltion with dry density nd then Eq. (9) becomes d b w w d d c d f g w w, (15) where, b, c, d, f, nd g re modified constnts, ρ d is the dry density, nd ρ w is the density of wter. The dt points collected in this reserch re used to mke regression nlysis of the prmeters in Eq. (15). The result empiricl clibrtion eqution is given in Eq. (16). The vlue of R 2 is 0.9413. Tble 4 Errors for wter content by Eq. (10) vs. different soil types Soil type dt smples S 74 0.019 0.023 0.031 40.5 66.2 83.8 91.9 94.6 ML 68 0.017 0.013 0.022 39.7 67.7 83.8 89.7 100.0 CL 148 0.022 0.022 0.031 34.5 62.2 75.7 81.8 89.2 CH 62 0.036 0.041 0.056 22.6 37.1 56.5 71.0 80.7 For distribution of error, the ±0.01 column represents the percentge of errors within ±0.01 g/g, the menings of the rest columns re nlogous, nd the sme below Density (g/cm 3 ) Tble 5 Errors for wter content by Eq. (10) vs. different dry densities dt smples 1.0 1.3 12 0.093 0.065 0.124 0.00 0.00 0.00 25.00 41.70 1.3 1.4 25 0.036 0.024 0.045 4.00 28.00 52.00 64.00 76.00 1.4 1.5 40 0.028 0.02 0.035 20.00 45.00 62.50 70.00 87.50 1.5 1.6 72 0.018 0.015 0.024 37.50 63.90 79.20 90.30 95.80 1.6 1.7 62 0.018 0.025 0.031 56.50 75.80 82.30 87.10 90.30 1.7 1.8 63 0.013 0.018 0.022 57.10 81.00 93.70 95.20 95.20 1.8 1.9 35 0.015 0.016 0.023 4.00 82.90 91.40 94.30 94.30 1.9 2.0 14 0.021 0.009 0.025 7.14 57.10 85.70 92.90 100.00 2.1 2.3 29 0.029 0.009 0.032 0.00 13.80 58.60 75.90 100.00
Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 247 w d 0.3039 2.1851 w d d 18.0283 17.9531 0.6806 1.8351 w w. (16) Vlues of E, SE, SEE, nd the distribution of errors fter considering the effect of dry density by Eq. (16) re shown in Tble 6. Through Tble 6, sttistic prmeters of soil smples with 1.0 1.3 g/cm 3 dry densities show obvious improvement. In relity, if informtion on dry density is vilble, Eq. (16) cn offer better ccurcy. Considering totl density ρ t, which is more vilble in geotechnicl engineering prctice, Eq. (16) cn be combined with the following eqution: t d. (17) 1 w Combining Eq. (16) nd Eq. (17), we cn obtin the following eqution: where 2 f2 f2 4 f1f3 w, (18) 2 f f 17.9531 1.8351, 1 f 18.0283 0.6806 0.8351 15.768, 2 t t 3 t 1 f 0.3039 2.1851. Eq. (18) cn offer the sme ccurcy s Eq. (16). As it is expressed in terms of totl density, it cn be more prcticl. 4.4 Compction energy effects For unit soil with certin wter content, when compcted with different compction energy levels, the smple obtined will hve different structures nd compctness, which will influence the dielectric constnt by the TDR test. For brevity, only comprisons of wter content by Eq. (10) nd the oven dry method for ASTM-CH soil re plotted in Fig. 5. Vlues of E, SE, SEE, nd the distribution of errors for soil smples of ASTM Reference Soils nd M1 M5 soils with three compction energy levels re shown in Tble 7. Fig. 5 nd Tble 7 show tht, with the compction energy incresing, E nd SEE hve n incresing trend nd the rtios of errors within ±0.03 g/g nd ±0.05 g/g decrese correspondingly. This mens w (g/g) 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 1:1 line +0.03 line 0.03 line CH, modified compction CH, stndrd compction CH, reduced compction 0.1 0.2 0.3 0.4 w o (g/g) Fig. 5 Comprisons of wter content by Eq. (10) nd the oven dry method for ASTM-CH soil t different compction energy levels Density (g/cm 3 ) Tble 6 Errors for wter content by Eq. (16) vs. different dry densities dt smples 1.0 1.3 12 0.029 0.021 0.039 33.30 41.70 50.00 75.00 91.70 1.3 1.4 25 0.020 0.018 0.028 48.00 52.00 68.00 88.00 92.00 1.4 1.5 40 0.026 0.021 0.035 25.00 40.00 67.50 80.00 90.00 1.5 1.6 72 0.016 0.014 0.021 48.60 75.00 83.30 93.10 97.20 1.6 1.7 62 0.017 0.017 0.025 45.20 64.50 82.30 88.70 93.60 1.7 1.8 63 0.009 0.008 0.012 66.70 90.50 96.80 100.00 100.00 1.8 1.9 35 0.007 0.007 0.010 77.10 94.30 97.10 100.00 100.00 1.9 2.0 14 0.008 0.004 0.010 71.40 100.00 100.00 100.00 100.00 2.1 2.3 29 0.009 0.007 0.011 69.00 93.10 100.00 100.00 100.00
248 Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 tht the errors of Eq. (10) increse with the incresing of compction energy. 4.5 Pore fluid conductivity effects Soils with different pore fluid conductivities will cuse different energy losses under the TDR wveform, which will influence the vlue of their dielectric constnts. Comprisons of wter content by Eq. (10) nd the oven dry method for ASTM-CH soil re shown in Fig. 6. Vlues of E, SE, SEE, nd the distribution of errors for ASTM-CH soil with different pore fluid conductivity re shown in Tble 8. As shown in Fig. 6 nd Tble 8, with the pore fluid conductivity incresing, the sttisticl prmeters E nd SEE hve n incresing trend nd the rtio of errors within ±0.03 g/g nd ±0.05 g/g decrese Fig. 6 Comprisons of wter content by Eq. (10) nd the oven dry method for ASTM-CH soil t different pore fluid conductivities correspondingly, which indictes tht errors of Eq. (10) increse with the incresing of pore fluid conductivity. Note tht the prmeters for soil with deionized wter s pore fluid seem not to be in ccordnce with the conclusion bove, which my be becuse the constnts in Eq. (10) re obtined minly from soil smples with tp wter s the pore fluid. In ddition, s the smples re smll nd the slinity is t low level, the conclusions bove need to be further discussed. 4.6 Temperture effects Temperture hs different effect on the vlue of dielectric constnt for different soil types (Writh nd Or, 1999; Robinson et l., 2003; Schnz et l., 2011). Pepin et l. (1995) nd Persson nd Berndtsson (1998) found tht for sndy soils, dielectric constnt decreses with the incresing of temperture. Drnevich et l. (2001) pointed out tht due to lrge content of cly prticles, the dielectric constnt of cohesive soils increses with the incresing of temperture. Drnevich et l. (2001) performed TDR tests on cohesive nd cohesionless soils with tempertures rnging from 4 C to 40 C. For brevity, only comprisons of wter content by Eq. (10) nd the oven dry method for Crosby Till soil re plotted in Fig. 7. Vlues of E, SE, SEE, nd the distribution of errors for soil smples with different tempertures re shown in Tble 9. Compction method Tble 7 Errors for wter content by Eq. (10) t different compction energy levels dt smples MC 45 0.020 0.017 0.027 28.90 57.80 77.80 91.10 95.60 SC 43 0.013 0.008 0.016 34.90 74.40 100.00 100.00 100.00 RC 44 0.011 0.009 0.014 56.80 77.30 97.70 100.00 100.00 Pore fluid Tble 8 Errors for wter content by Eq. (10) t different pore fluid conductivities dt smples DI 5 0.026 0.013 0.038 20.00 20.00 40.00 100.00 100.00 TAP 6 0.020 0.007 0.026 16.70 50.00 100.00 100.00 100.00 SAL 5 0.032 0.017 0.047 0.00 40.00 60.00 60.00 80.00 DI: deionized wter; TAP: tp wter; SAL: sline wter (bout twice pore fluid conductivity of TAP). For distribution of error, the ±0.01 column represents the percentge of errors within ±0.01 g/g, nd the menings of the rest columns re nlogous
Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 249 As shown in Fig. 7 nd Tble 9, the sttisticl prmeters E nd SEE re reltively lrge, which is minly due to the presence of some scttered dt, specificlly, the dt points bove 0.4 g/g with low dry density. Errors trend to decrese with the incresing in temperture. When the temperture is within 4 30 C, it hs no significnt influence on the result of Eq. (10). Drnevich et l. (2001) pointed out tht the effect of tempertures from 5 C to 20 C cn be ignored since their influence is smll. ASTM (2012) presents the equtions used to modify the effect of temperture. 4.7 Comprison of Topp s eqution nd twostep method eqution Topp et l. (1980) proposed widely used empiricl clibrtion eqution: 4.3 10 5.5 10 2.92 10 5.3 10, 6 3 4 2 2 2 (19) where θ is the volumetric wter content. Grvimetric wter content (w) nd volumetric wter content (θ) re relted s follows: Fig. 7 Comprisons of wter content by Eq. (10) nd the oven dry method for Crosby Till soil t different tempertures w w. d (20) Combining Eqs. (19) nd (20), the grvimetric wter content clculted by Topp s eqution is obtined. Siddiqui nd Drnevich (1995) performed the two-step method to test the wter content nd dry density of soil. The empiricl clibrtion eqution they developed is bw, (21) w 1 1 d where 1 nd b 1 re clibrtion constnts. Drnevich et l. (2005) pointed out tht lthough clibrtion constnts in Eq. (21) re soil-dependent, uniform clibrtion constnts cn be used within cceptble limits for engineering prctice. Herein, the vlues of 1 nd b 1 re 1 nd 8.5 for cohesionless soils nd 0.95 nd 8.8 for cohesive soils, respectively, s recommended by Drnevich et l. (2005). Comprisons of wter content clculted by Eq. (10), Topp s eqution, Eq. (21), nd Eq. (16) re shown in Tble 10. As shown in Tble 10, results clculted by Topp s eqution, Eq. (21), nd Eq. (10) re very close. Compred with Topp s eqution which expresses wter content in volumetric form nd the two-step method eqution which considers the influence of dry density, the sttisticl prmeters E nd SEE of Eq. (10) re slightly lrger thn those in the two other methods. After being modified by considering the dry density effects, Eq. (16) hs better ccurcy. Through the nlysis bove, Eq. (10) shows good ccurcy for most of soil types nd slight influence by wide rnge of dry densities, compction energy levels, nd pore fluid conductivity, t Temperture ( C) Tble 9 Errors for wter content by Eq. (10) t different tempertures dt smples 4 23 0.056 0.066 0.090 21.70 34.80 47.80 56.50 65.20 10 11 0.053 0.080 0.106 27.30 54.60 72.70 72.70 72.70 20 22 0.048 0.061 0.081 22.70 40.90 63.60 68.20 68.20 30 15 0.049 0.065 0.087 26.70 53.30 53.30 66.70 66.70 40 17 0.034 0.047 0.062 23.50 58.80 70.60 82.40 82.40
250 Zho et l. / J Zhejing Univ-Sci A (Appl Phys & Eng) 2016 17(3):240-252 Tble 10 Comprison of wter content obtined by Eq. (10), Topp s eqution, Eq. (21), nd Eq. (16) Eqution dt smples Eq. (10) 352 0.023 0.026 0.035 34.70 59.70 75.60 83.50 90.90 Topp s eqution 352 0.020 0.018 0.027 29.60 65.30 81.50 89.20 93.20 (Topp et l., 1980) Eq. (21) 352 0.018 0.021 0.028 45.50 75.60 82.70 88.10 92.30 Eq. (16) 352 0.015 0.016 0.022 53.40 73.60 84.90 92.60 96.30 tempertures commonly encountered in engineering prctice. 5 Conclusions From the dtbse including 45 kinds of soil smples nd 418 dt points, n empiricl clibrtion eqution hs been developed to relte grvimetric wter content directly with pprent dielectric constnt. The min conclusions re s follows: 1. The ccurcy of the new empiricl clibrtion eqution is within ±0.05 g/g for commonly encountered soils. 2. The new empiricl clibrtion eqution underestimtes the result in low dry density nd overestimtes the result in high dry density. For dry density rnging between 1.3 nd 2.3 g/cm 3, the new empiricl clibrtion eqution shows good ccurcy. 3. Errors of the new empiricl clibrtion eqution tend to increse with the incresing of compction energy nd pore fluid conductivity. However, for the commonly encountered rnges of compction energy nd pore fluid conductivity, the new empiricl clibrtion hs good ccurcy. 4. Temperture hs no sensible influence on the results from the new empiricl clibrtion eqution when it is used within 4 30 C. 5. This empiricl clibrtion eqution cn be used to mesure wter content by the TDR method conveniently nd efficiently in engineering prctice without clibrtion. References Abu-Hssnein, Z.S., Benson, C.H., Blotz, L.R., 1996. Electricl resistivity of compcted clys. Journl of Geotechnicl Engineering, 122(5):397-406. http://dx.doi.org/10.1061/(asce)0733-9410(1996)122:5 (397) ASTM, 2007. Stndrd Test Methods for Lbortory Compction Chrcteristics of Soil Using Stndrd Effort, D698-07. Americn Society for Testing nd Mterils, West Conshohocken, USA. ASTM, 2009. Stndrd Test Methods for Lbortory Compction Chrcteristics of Soil Using Modified Effort, D1557-09. Americn Society for Testing nd Mterils, West Conshohocken, USA. ASTM, 2010. Stndrd Prctice for Clssifiction of Soils for Engineering Purposes, D2487-10. Americn Society for Testing nd Mterils, West Conshohocken, USA. ASTM, 2012. Stndrd Test Method for Wter Content nd Density of Soil in situ by Time Domin Reflectometry (TDR), D6780-12. Americn Society for Testing nd Mterils, West Conshohocken, USA. ASTM, 2012b. Stndrd Test Methods for Lbortory Compction Chrcteristics of Soil Using Stndrd Effort, D698-12. Americn Society for Testing nd Mterils, West Conshohocken, USA. Bker, J.M., Allmrs, R.R., 1990. System for utomting nd multiplexing soil moisture mesurement by timedomin reflectometry. Soil Science Society of Americ Journl, 54(1):1-6. http://dx.doi.org/10.2136/sssj1990.03615995005400010 001x Birchk, J.R., Grdner, C.G., Hipp, J.E., et l., 1974. High dielectric constnt microwve probes for sensing soil moisture. Proceedings of the IEEE, 62(1):93-98. http://dx.doi.org/10.1109/proc.1974.9388 Chen, W., 2011. The Design of TDR Probe nd Monitoring Technology of Wter Content nd Dry Density. MS Thesis, Zhejing University, Hngzhou, Chin (in Chinese). Chen, Y., 2011. Study on Dielectric Constnt nd Wter Content Mesurement of Highly Conductive Geomterils by TDR Technique. PhD Thesis, Zhejing University, Hngzhou, Chin (in Chinese). Chen, Y.M., 2014. A fundmentl theory of environmentl geotechnics nd its ppliction. Chinese Journl of Geotechnicl Engineering, 36(1):1-46 (in Chinese). http://dx.doi.org/10.11779/cjge201401001 Chen, Y.M., Bin, X.C., Chen, R.P., et l., 2003. Propgtion of electromgnetic wve in the three phses soil medi. Applied Mthemtics nd Mechnics, 24(6):691-699. http://dx.doi.org/10.1007/bf02437870
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