Estimation of the water retention curve for unsaturated clay

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1 Estimation of the water retention curve for unsaturated clay Seid Majdeddin Mir Mohammad Hosseini, Navid Ganjian, and Yadolah Pashang Pisheh Civil and Environmental Engineering Department, Amirkabir University of Technology, Tehran, Iran ( and Civil Engineering Department, University College of Engineering, University of Tehran, Iran. Received January 00, accepted March 0. Can. J. Soil. Sci. Downloaded from by on 0/3/8 Mir Mohammad Hosseini, S. M., Ganjian, N. and Pashang Pisheh, Y. 0. Estimation of the water retention curve for unsaturated clay. Can. J. Soil Sci. 9: Extensive laboratory tests are essential in order to determine the soil water retention curve, defined as the relationship between water content and suction, in an unsaturated soil. These laboratory tests are usually costly and time consuming. Moreover, for most practical problems, it has been found that approximate unsaturated soil properties are adequate for analysis. Thus, empirical procedures for predicting unsaturated soil parameters would be invaluable. The water retention curve can be estimated using soil properties to avoid the costs of experimental methods. Estimation of the water retention curve based on index properties is highly desirable due to its simplicity and low cost. Here, a model for the estimation of the soil water retention curve for fine soils is introduced, which takes the plasticity index and fine content into account, and is based on the and equations. The proposed equations are validated by comparing measured and simulated results. The curves predicted with these models were found to be in good agreement with the experimental results. Key words: Water retention curve, unsaturated soils, matric suction, index properties Mir Mohammad Hosseini, S. M., Ganjian, N. et Pashang Pisheh, Y. 0. Estimation de la courbe de re tention d eau des sols argileux insature s. Can. J. Soil Sci. 9: Il faut entreprendre de vastes essais de laboratoire pour établir la courbe de re tention d eau, c est-a` -dire le lien entre la teneur en eau et la succion dans un sol insature. Habituellement, de tels essais sont aussi one reux que laborieux. Par ailleurs, on a constaté que les proprie tés approximatives du sol insature suffisent pour analyser la plupart des proble` mes d ordre pratique. Des me thodes empiriques permettant de pre voir les parame` tres du sol insature s avéreraient donc d une utilite inestimable. Pour e pargner le couˆt des méthodes expérimentales, on peut estimer la courbe de re tention d eau a` partir des proprie tés du sol. Il serait fort souhaitable d estimer cette courbe à partir des proprie tés caracte ristiques, en raison de la simplicite et du couˆt modique de la me thode. Les auteurs proposent un modèle pour estimer la courbe de re tention d eau des sols a` fine granulome trie à partir de l indice de plasticite et de la teneur en particules fines. Ce modèle repose sur les équations de et de equations. Ces dernie` res ont e té valide es par la comparaison des re sultats mesure s aux résultats de la simulation. Les courbes prévues graˆces a` ce mode` le concordent bien avec les résultats des expériences. Mots clés: Courbe de rétention d eau, sols insature s, succion de la matrice, proprie tés caracte ristiques The investigation of unsaturated soil behavior requires the evaluation of particular behavior parameters in these soils. The constitutive equations for volume change, shear strength, and flow through unsaturated soil have become generally accepted in geotechnical engineering (Fredlund and Raharjo 993). The fundamental accepted principal in this theory is that unsaturated soil behavior cannot be described by making use of only one stress state variable. In other words, both the net normal stress (s u a ), where s is the total stress and u a is the pore-air pressure, and the matric suction (u a u w ), where u w is the pore-water pressure, are generally required for the constitutive models. As a result, the evaluation of suction is essential in assessing unsaturated soil behavior. The soil water retention curve (SWRC), which defines the degree of saturation corresponding to a particular suction in a soil, is widely used to estimate unsaturated soil properties. Evaluation of the SWRC based on direct measurement methods is time consuming and necessitates numerous laboratory tests. Equations to approximate the general form of the SWRC have been suggested. These equations consist of two or three fitting parameters evaluated by making use of either suction laboratory results at various water contents or statistical relationships based on other soil properties. Because of difficulties in evaluating these curves, i.e., the necessity to perform experimental tests, and the existence of noticeable variability in the test results, such parameters are often estimated. Statistical approaches have been followed by many researchers, for example Tomasella and Hodnett (998). Zapata et al. (000) proposed relationships to predict the constants of the equation based on soil index properties. Among the proposed equations, those derived by Van Genuchten (980) and Fredlund and Xing (994) seem to be the most accurate. In the current study, some correlations have been proposed for fine soils to Abbreviations: PI, plasticity index; SWRC, soil water retention curve Can. J. Soil Sci. (0) 9: doi:0.44/cjss

2 Can. J. Soil. Sci. Downloaded from by on 0/3/8 544 CANADIAN JOURNAL OF SOIL SCIENCE evaluate the fitting parameters of equations suggested by and Fredlund and Xing based on well-known soil index parameters. These parameters are chosen, however, based on the plasticity index (PI) and the proportion of material passing a #00 U.S. Standard Sieve (W). The SWRC shows the relationship between soil suction and either the degree of saturation or the volumetric water content. In soil science, the volumetric water content is most commonly used, and in most research the SWRC has been suggested as a relationship between volumetric water content and matric suction. The volumetric water content is the ratio of the volume of water in the soil to the total volume as shown below: us n S e () e where u is volumetric water content, S is the degree of saturation, n is the porosity ratio, and e is the void ratio of the soil. PROPOSED MODEL FOR PREDICTING THE SWRC In the current study, and Fredlund- Xing equations were selected as the base, and their fitting parameters (a, b, and c) were correlated with the index properties of fine soils with PI greater than zero. Using these relationships, one can predict the SWRC without carrying out expensive and time-consuming tests. It must be noted that by using the Fredlund- Xing equation, the water content of soil always tends to be zero at a matric suction equal to 0 6 kpa. By ignoring the residual water content at high matric suctions compared with the water content of soil, the basic equation proposed by can be rewritten as: S c b c () a Furthermore, the equation used in this study can be rewritten as: S C(c) (3) fln[exp() ( c a )b ]g c where C(c) ln( c c r ) ln( 0 6 ) c r To establish the relationships, a database characterizing approximately 60 soils with PI greater than was assembled from a knowledge-based program developed (4) by SoilVision Systems Ltd. (997). The proportion of material passing through a #00 U.S. Standard Sieve and the PI of the soils are presented in the database. For fine soils, the proportion of material passing a #00 U.S. Standard Sieve, W, expressed as a fraction of, was multiplied by PI in percentage, to form the weighted PI, W.PI. This parameter was selected as the main index soil property for the correlation. The reason behind this choice may be described as follows: The equilibrium soil suction at a given degree of saturation was expected to be proportional to the specific surface area of the soil. The PI is a fair indicator of surface area, and the use of PI alone can be considered. However, a soil with a small percentage of highly active clay would have a high PI but only a moderate specific surface area. Therefore, the weighted PI, W.PI, was considered to be a better index of soil particle surface area for predicting the SWRC. Using the database, and fitting the equation for the SWRC to the experimental results for each soil, the parameters a, b, and c were correlated with the weighted PI as the main index parameter. The relationships developed here are as follows: a0:005(w:pi) 3 0:08(W:PI) 0:587(W:PI) :83 (5) b0:000(w:pi) 0:0358(W:PI):76987 (6) c50 6 (W:PI) 0:0004(W:PI) 0:4745 (7) Moreover, in order to obtain the fitting parameters by making use of the equation, the corresponding relationships were similarly found to be: a0:09(w:pi) 3 0:95(W:PI) 6:40(W:PI) 7:70 (8) b0:00034(w:pi) 0:0874(W:PI):4735 (9) c9:60 5 (W:PI) 0:00984(W:PI) 0:5504 (0) (c r =a) b 0:0055(W:PI) 0:306(W:PI) 6:834 () where W is the proportion of material passing through a #00 U.S. Standard Sieve expressed as a fraction of, and PI is the plasticity index of the soil in percent. It must be noted that the correlation coefficients, R, for the fitting parameters are generally greater than The SWRCs achieved using the proposed models for and in various soils with distinct W.PI between and 40 are illustrated in Figs. and, respectively. As expected, with increasing W.PI, the air-entry value of suction increases. COMPARISONS To evaluate the accuracy of the proposed models in estimating the SWRC, some comparisons have been

3 HOSSEINI ET AL. * ESTIMATING THE WATER RETENTION CURVE FOR CLAY 545 Can. J. Soil. Sci. Downloaded from by on 0/3/8 Fig.. Predicted soil water retention curves using the proposed model based on the equation. made between laboratory suction test results and those of published models for various fine soils. Figures 3 through 6 illustrate the results for four different types of soils. The soil characteristics and corresponding fitting parameters that were predicted with the proposed models are shown in Table. As can be seen in Figs. 3 and 4, for clay soil samples (Madrid gray clay and Fountain Hills clay) with high degrees of saturation and, consequently, low suction levels (less than 5000 kpa), the curves resulting from the and equations are generally in good agreement with each other, and show a proper compatibility with experimental results, so the mean of squared errors (s ) for this series of data is about 0.0. However, for soil types at higher suctions, the proposed model based on the equation results in closer agreement with the measured data. In other words, these 4 W.PI = W.PI = 5 W.PI = 0 W.PI = 5 results could confirm the accuracy of the modified method proposed by Fredlund and Xing. On the other hand, the predicted curves based on the and equations in the cases of silty or sandy samples (red silty clay and Madrid clayey sand) were not in agreement with measured data (Figs. 5 and 6). However, the equation leads to better agreement with experimental results at low suctions. This would be expected considering the soil type (i.e., low fine contents and PI). The empirical test results for some of the soils considered in this research and the resulting curves of the proposed models are shown in Fig. 7 through 0. In these figures, the points are representative of test results and the curves are the result of the SWRC for the equation in an assessed domain. It should be noted that in the present study, a database W.PI = 40 W.PI = 30 W.PI = 0.E-0.E+00.E+0.E+0.E+03.E+04.E+05 Soil Suction, kpa.e+06 Fig.. Predicted soil water retention curves using the proposed model based on the equation.

4 546 CANADIAN JOURNAL OF SOIL SCIENCE Table. Soil characteristics and computed parameters Constant parameters () Constant parameters () Proportion passing Plasticity through # 00 US index Dry density Reference C r (kpa) c b a c b a standard sieve (% PI) (g cm 3 ) Soil type Escario and Juca Madrid gray clay (989) Zapata (999) Fountain Hills clay Escario and Juca Red silty clay (989) Escario and Juca (989) Madrid clayey sand Can. J. Soil. Sci. Downloaded from by on 0/3/8 4 = = E+03 = E-0.E+00.E+0.E+0.E+03.E+04.E+05.E+06 Fig. 3. Comparison between soil water retention curves resulting from the proposed models with laboratory results for Madrid gray clay. 4 =0.0 =0.04 = E+03.E-05.E-04.E-03.E-0.E-0.E-00.E+0.E+0.E+03.E+04.E+05.E+06 Fig. 4. Comparison between soil water retention curves resulting from the proposed models with laboratory results for Fountain Hills clay.

5 HOSSEINI ET AL. * ESTIMATING THE WATER RETENTION CURVE FOR CLAY = = Can. J. Soil. Sci. Downloaded from by on 0/3/8.E-0.E+00.E+0.E+0.E+03.E+04.E+05.E+06 Fig. 5. Comparison between soil water retention curves resulting from the proposed models with laboratory results for red silty clay. 4 =0.06.E-0.E+00.E+0.E+0.E+03.E+04.E+05.E+06 =0.003 Fig. 6. Comparison between soil water retention curves resulting from the proposed models with laboratory results for Madrid clayey sand. 4 W.PI = W.PI = 3.0 Fredlund - Xing, W.PI = 0. Fredlund - Xing, W.PI = 3.0.E-0.E+00.E+0.E+0.E+03.E+04.E+05.E+06 Fig. 7. The experimental results and soil water retention curves for soils with 0.BW.PIB3.

6 548 CANADIAN JOURNAL OF SOIL SCIENCE 4 W.PI = 3.0 W.PI = 0 Fredlund - Xing, W.PI = 3.0 Fredlund - Xing, W.PI = 0 Can. J. Soil. Sci. Downloaded from by on 0/3/8.E-0.E+00.E+0.E+0.E+03.E+04.E+05.E+06 Fig. 8. The experimental results and soil water retention curves for soils with 3BW.PIB0. Fredlund - Xing, W.PI = 0 Fredlund - Xing, W.PI = 30 W.PI = 30 4 W.PI = 0.E-0.E+00.E+0.E+0.E+03.E+04.E+05.E+06 Fig. 9. The experimental results and soil water retention curves for soils with 0BW.PIB30. 4 W.PI = 30 Fredlund - Xing, W.PI = 30 Fredlund - Xing, W.PI = 50 W.PI = 50.E-0.E+00.E+0.E+0.E+03.E+04.E+05.E+06 Fig. 0. The experimental results and soil water retention curves for soils with 30BW.PIB50.

7 HOSSEINI ET AL. * ESTIMATING THE WATER RETENTION CURVE FOR CLAY 549 Can. J. Soil. Sci. Downloaded from by on 0/3/8 of 60 sets of various soil types was used. As can be seen in Fig. 7, for soils with low PI (i.e., silts) and W.PIB3, the existing variations between the proposed models and the suction test results are considerable. This may be due to the greater effect of aggregate distribution on the SWRC in these materials. For cohesive soils with 3B W.PI B50 (Figs. 8 through 0), the proposed model predicts the SWRCs precisely. CONCLUSIONS According to extensive practical usage of water retention curves and existing difficulties in direct evaluation of these curves using laboratory tests, approximating models for fine soils have been developed based on a soil quality index. The laboratory tests have shown that for fine soils, the product of the PI in the percentage passing a #00 sieve, W, is an appropriate parameter for estimating the SWRC. Therefore, while investigating the empirical data of more than 60 types of soils, some relationships have been developed to approximate the fitting parameters of the and Fredlund- Xing equations based on W.PI. The main results of this research are: By increasing the parameter W.PI, the air-entry value will be enhanced, and the tendency of soil to retain water will be increased. With respect to the requirement of numerous suction laboratory tests to derive the SWRC, and the variability in test results, the use of approximating procedures similar to the methods described in this study is appropriate. There was good agreement between the measured water retention curves and those derived using empirical methods for most of the soils examined. The curves resulting from the and equations for clay soils were in good agreement with measured values at low suctions. However, at higher suctions, the proposed model based on the equation leads to better results. For soils with W.PIB3, the effect of this parameter on SWRCs and consequently on the proposed models accuracy is insignificant; thus, other parameter effects, such as soil classification, would be greater. Escario, V. and Juca, J Strength and deformation of partly saturated soils, Proceedings of the th International Conference on Soil Mechanics and Foundation Engineering. Rio de Janerio, Brazil. Vol., pp Fredlund, D. G. and Raharjo, H Soil mechanics for unsaturated soils. Wiley Interscience, Hoboken, NJ. Fredlund, D. G. and Xing, A Equations for the soil-water characteristic curve. Can. Geotech. J. 3: 553. SoilVision Systems Ltd User s guide. Version.. [computer software]. Soil Vision System, Ltd., Saskatoon, SK. Tomasella, J. and Hodnett, M. G Estimating soil water retention characteristics from limited data in Brazilian Amazonia. Soil Sci. 63: 900., M. T A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44: Zapata, C. E Uncertainty in soil-water characteristics curve and impact on unsaturated shear strength predictions. Ph.D. dissertation. Arizona State University, Tempe, AZ. Zapata, C. E., Houston, W. N., Houston, S. L. and Walsh K. D Soil water characteristic curve variability. Pages 844 in C. D. Shackleford, S. L. Houston, and N.-Y. Chang, eds. Advances in unsaturated soil mechanics, Geotechnical Special Publication No. 99. Geo-Institute of the ASCE, Reston, VA.

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