A concept of time-density reducibility for soil samples, analogous to time-temperature and time-moisture simplicity is presented. Stress relaxation tests were conducted to determine the time-dependent relaxation modulus and the time-density shift function of one soil sample. The hypothesis that the concept of time-density reducibility is valid was verified for one soil sampl

Awadhwal, N K

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Geoderma, 44 (1989) 329-334 329 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands A Concept of Time-Density Reducibility for Soil N.K. AWADHWAL International Crops Research Institute for the Semi-Arid Tropics (ICRISAT), P.O. Patancheru 502 324, A ndhra Pradesh (India) (Received May 30, 1988; accepted after revision January 25, 1989 )ABSTRACT Awadhwal, N.K., 1989. A concept of time-density reducibility for soil. Geoderma, 44: 329-334. A concept of time-density reducibility for soil samples, analogous to time-temperature and time-moisture simplicity is presented. Stress relaxation tests were conducted to determine the time-dependent relaxation modulus and the time-density shift function of one soil sample. The hypothesis that the concept of time-density reducibility isvalid was verified for one soil sample. INTRODUCTION The concept of time-temperature equivalence for polymers is that, in addi- tion to time effects, the viscoelastic functions of polymers are sensitive to tem- perature variations and are affected to the same extent for each unit of tem- perature change (Ferry, 1961). This concept was developed empirically in advance of the theories which now support it. The concept of a moisture shift factor for samples of clay soils was developed on the basis of the argument that increasing the moisture content of clay is analogous to increasing the temperature of polymers (Krizek, 1968). Rao and Hammerle (1973) applied the concepts of time-moisture and time-tempera- ture shift functions to the relaxation modulus of soil samples and found that the samples were hydro-rheologically as well as thermo-rheologically simple. In this paper a concept of time-density reducibility is proposed and its appli- cability to one soil sample is verified. THEORETICAL CONSIDERATIONS Krizek (1968) discussed several phenomenological soil-polymer parallels, stating that the variations in temperature affect he mobility of molecular seg- ments of polymers and hence influence their viscoelastic functions. A change in the density of a soil sample changes ~he orientation and spacing of particles. 0016-7061/89/$03.50 © 1989 Elsevier Science Publishers B.V. 330 E( t  t i i i togt  Iogt . f (D)  Log t Fig. 1. Illustration ofthe shift principle. This alters interlocking and attractive forces between particles, leading to changes in soil strength and viscoelastic functions. Thus, changes in density of a soil and changes in the temperature of a polymer should affect he respec- tive viscoelastic functions in a qualitatively similar manner. This leads to the concept of time-density reducibility (shift function ) for soil and to postulation of the hypothesis that for soils, in addition to time-temperature and time- moisture shift functions, there also exists a time-density shift function and like thermo- and hydro-rheological simplicity, the time-density reducibility is also an inherent property of soils. The time-density reducibility, analogous to a time-temperature shift func- tion, implies that the effect of density on viscoelastic properties of soil can be offset by shifting the curve horizontally along the time axis. Considering the plot of relaxation modulus of soil as a function of log t for densities Do and D (Fig. 1 ), the following relationship can be derived (Seed et al., 1960; Hammerle and Mohsenin, 1970): ED (log t) =ED,, [log t + [(D)] (1) where t is time, E~ and ED,, are relaxation modulus functions at densities D and Do, respectively, and f(D ) is measured horizontally relative to Do as shown in Fig. 1. Let: logAD(t) =f(D) (2) where A D is a density shift factor and a function of density. Substituting eq. 2 in eq. 1 and defining reduced time, Z, as: Z=tAD (3) it can be written as: Eo(t) =E~,, (Z) (4) Hence, tunits of time at density D are equivalent to tA  D units of time at density Do. Mathematically it can be expressed as: 331 t~ A - (5) to where t D is the time required to observe some phenomenon atdensity D, and to is the time required to observe the same phenomenon atreference density Do. This expression is similar to the time-temperature shift function for poly- mers (Ferry, 1961). If the time-density reducibility is applicable to soil, then shifting a series of its property curves, measured at different densities but at one temperature and one moisture content, should produce a single master curve. MATERIALS AND METHOD Tests were conducted on a sample of silt loam to verify applicability of time- density reducibility to its time-dependent deformation modulus. The soil was classified according to USDA Soil Texonomy as a fine-loamy, mixed, hyper- thermic Aeric Fluvaquent. The soil sample was taken of a surface layer of 20 cm thickness. It was oven-dried and passed through a 2 mm sieve. The sieved sample contained 34.3% sand, 52.5% silt and 13.2% clay as per the interna- tional classification. Its maximum void ratio (era,x) and minimum void ratio (emi n) were 1.93 and 0.51, respectively. The soil sample was mixed with ade- quate water in a mixer to obtain a moisture content of 8% on a dry weight basis. The mixture was then placed in cylindrical plastic moulds (15 cm in diameter and 10 cm deep) and was compacted with a rammer to obtain speci- mens of predetermined density. The specimens were prepared within a half hour of testing. The samples were sealed in containers and kept in an environ- ment chamber at 90% relative humidity to prevent drying. The densities of the soil specimens used in this study were 1.28, 1.39, 1.45 and 1.52 Mg/m 3. The corresponding relative densities of the samples were 62.36, 73.75, 79.22 and 85.22 percent, respectively. The relative density (Dr) is defined as: (em,x -e )  Dr - (ema x __ emin)  (6) where e is the void ratio of the specimen and emax and emin are the maximum and minimum attainable void ratios, respectively. Die loading tests were con- ducted on the soil samples using the Instron Universal Testing Machine (Model TM-M) to determine their force deformation and relaxation responses. A cross head speed of 10 cm/min was used for die loading and a constant deformation of 1.6 mm was maintained while the stresses relaxed. The tests were repeated three times on each sample. A computer programme, developed on the basis of an analytical method for determining viscoelastic constants presented by Chen and Fridley (1971), was used for calculation of the time-dependent deforma- tion modulus function from the test data. Determination f the time-density 332 shift function was done on the basis of the method for determination of time- temperature shift functions outlined by Ferry (1961). RESULTS AND DISCUSSION The time-dependent deformation modulus decreases with decrease in den- sity of the soil sample (Fig. 2). To relate time to density the dimensionless values of time-density shift factors, AD, (Table I) were estimated using eq. 2. The regression equations for the shift factor with both density difference (Do  - D i  ) and the relative density difference (Dr,o - Dr,i ) were obtained. These relationships are: AD =exp {--29.285 (Do-Di )}  (7) and AD,=exp {--0.3166 (Dr,o-D~,i)} (8) where Do and D,,o are the reference density (1.52 Mg/m 3) and reference rela- tive density (85.23%), respectively. The parameters Di and Dr,i are  the inter- mediate densities (1.28<Di<1.52) and intermediate relative densities (62.30 < Dr,i < 85.23 ), respectively. DENSITY (tvlg/m 3 ) 3000 + 1,52 2000 ~ 1.45 --e-- 1.39 e ' - ' - '~""e '~- - -~ ~ 1.28 1000 ~ ~ . ~  800 o 600 - &00 w 300 ~ 200 o 100  , L i , , , , , I  i , ~ i . . . .  , I  -2 ,3 "4,5 1 2 3 4 5 10 TIME t,(Seconds) Fig. 2. Deformation modulus as a function of time for specimens of silt loam. TABLE I Time-density shift factor of the silt loam samples Soilsample Density Relative t (s) t,, (s) A logA= No. (Mg/m :~) density (%) log t - log  to YAlog A = log A D AD 1 1.52 85.22 0.25 0.25 0.00 2 1.45 79.22 0.25 1.5 --0.7781 3 1.39 73.75 0.25 3.4 -- 1.1335 4 1.28 62.36 0.25 2.55 - 1.0008 0.00 -0.7781 --1.9116 --2.9202 1.0000 0.1666 0.0122 0.0012 333 10000 5000 o ~1ooo  3oo I200[ 100 / .1 - -  MASTER CURVE OBSERVED VALUES OF MODULUS J i J i , , l l  , , i , ~ i J i I  , h J L i ~ , , I  . . . . . . . .  , .2 .3 "4-5 1 2 3 4 5 10 20 304050 100 200 500 1000 REDUCED TIME Z,(Seconds) Fig. 3. Master curve for deformation modulus of the subsamples ofsilt loam. The time-dependent deformation modulus E(t), expressed in kilopascals (kPa), was plotted against test time t, expressed in seconds (s), for all the soil specimens at different densities. The modulus curves at different densities were shifted horizontally to higher times until coincidence with the upper curve was obtained and a single master curve at the reference density Do of 1.52 Mg/m 3 was achieved. The method for obtaining a master curve by graphical shifting is explained by Hammerle and Mohsenin (1970). The reduced time Z was calculated using eq. 3. The observed values of deformation modulus, when plot- ted as a function of reduced time, almost coincided with the master curve (Fig. 3). The paired t test applied to observed values of the deformation modulus and the corresponding values obtained from the master curve shows that the differences are not significant at 5% level of probability. This indicates that the concept of time-density reducibility is valid and applicable to the soil sample. CONCLUSION An expression for a time-density shift factor analogous to the time-temper- ature shift factor has been derived. Experimental evidence indicates that the concept of time-density reducibility isapplicable to samples of a silt loam rep- resenting a fine-loamy, mixed, hyperthermic Aeric Fluvaquent. ACKNOWLEDGEMENTS The author thankfully acknowledges the facilities provided by the Depart- ment of Processing and Agriculture Structures, P.A.U. Ludhiana, for conduct- ing tests on the Instron Testing Machine. 334 REFERENCES Chen, P. and Fridley, R.B., 1971. An Analytical Method for Determining Visco-elastic Constants of Agricultural Materials. Paper No. 71-339, American Society of Agricultural Engineers, St. Joseph, Mich., 15 pp. Ferry, J.D., 1961. Viscoelastic Properties of Polymers. Wiley, New York, N.Y., 241 pp. Hammerle, J.R. and Mohsenin, N.~N., 1970. Tensile relaxation modulus of corn horny endosperm as a function of time, temperature and moisture content. Trans. ASAE, 13: 372-375. Krizek, R.J., 1968. Phenomenological soil-polymer parallels. Am. Sci., 56: 279-287. Rao, V.N.M. and Hammerle, J.R., 1973. Some viscoelastic properties of Hickory clay and Ottawa sand. J. Agric. Eng. Res., 18: 253-259. Seed, H.B., Mitchell, J.K. and Chan; C.K., 1960. The strength of compacted soils. ASCE Res. Conf. Shear Strength of Cohesive Soils, Colo., pp. 877-964. 

A concept of time-density reducibility for soil

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A concept of time-density reducibility for soil

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