J. Cent. South Univ. (2012) 19: 222-230

DOI: 10.1007/s11771-012-0995-4

Hysteresis of saturation-capillary pressure relations under consecutive drainage-imbibition cycles in fine sandy medium

XIE Xiao-xi(谢小茜)¹, LI Yan(李雁)2, XIA Bei-cheng(夏北成)¹,

XU Li-min(许丽敏)³, SU Yu(苏钰)⁴, GU Qing-bao(谷庆宝)⁵

1. School of Environmental Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China;

2. School of Marine Sciences, Sun Yat-sen University, Guangzhou 510275, China;

3. Guangdong Huizhou Environmental Protection Agency, Huizhou 516001, China;

4. Guangdong Environmental Protection Engineering Research and Institute, Guangzhou 510635, China;

5. Chinese Research Academy of Environmental Sciences, Beijing 100012, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: The hysteresis of saturation-capillary pressure (S-p) relations was investigated in a fine sandy medium under consecutive drainage-imbibition cycles, which resulted from scheduled water level fluctuations. A drainage-imbibition cycle starts with a drainage process and ends with an imbibition process in sequence. The saturation and capillary pressure were measured online with time domain reflectometry (TDR) probes and T5 tensiometers, respectively. Results show that the relation between the degree of hysteresis and the number of the drainage-imbibition cycles is not obvious. However, the degree decreases with the increase of the initial water saturation of the imbibition processes in these drainage-imbibition cycles. The air-entry pressure of a sandy medium is also found to be constant, which is independent of the drainage-imbibition cycles and the initial water saturation of the drainage process. In all the imbibition processes, parameter α of the van Genuchten (VG) model decreases with the increase of the initial water saturation, which corresponds positively to the magnitude of the hysteresis.

Key words: S-p relation; hysteresis; drainage; imbibition; van Genuchten model

1 Introduction

It is an effective method to obtain the saturation and capillary pressure (S-p) relation for the study of the migration of a fluid in a porous medium. The phenomenon that the S-p relation curve of an imbibition process does not coincide with that of its former drainage process is called the hysteresis of a porous medium. Due to hysteresis, the S-p relation curve is fluid flow-path dependent and drainage-imbibition history dependent, which results in various S-p relation curves in a porous medium [1]. Accordingly, a fluid saturation of the medium could correspond with numberless capillary pressures. Likewise, a capillary pressure could also correspond with numberless saturations [2].

When a numerical simulation is conducted for the migration of a non-aqueous phase liquid (NAPL) in a porous medium, neglect of the hysteresis leads to obvious errors between the measured and the simulated saturations [3-4]. A hysteretic model provides a better description of a NAPL migration in a porous medium in comparison with a non-hysteretic model [5-9]. The hysteresis effects were shown to be crucial to the accuracy of the numerical simulation of the temporal-spatial distribution of petroleum pollutants in porous media.

Frequent fluctuation of the groundwater table will lead to consecutive drainage and imbibition processes in the medium of the subsurface. Therefore, the hysteresis behavior is popular in the subsurface with water table fluctuation. It is necessary to take into a full consideration of the hysteresis effect for the accurate description of the S-p relations and the prediction of the temporal and spatial distribution of a pollutant in the subsurface.

Many researches have been performed on the hysteresis phenomenon of soil water retention curves and the development of various models for a good description of the hysteresis [10-16]. Moreover, researches on hysteresis of the S-p relation between drainage and imbibition are also carried out in the field of the multiphase flows in porous media [17-18].

Long term seasonal rainfall or groundwater exploitation may cause the groundwater table fluctuation, which results in consecutive drainage-imbibition cycles in the subsurface. SHEN [19-20] investigated the hysteretic phenomenon of the scanning displacement processes under several drainage-imbibition cycles by the measurement of the soil water retention curves and the hysteresis of fluid migration in numerical simulation. LI [18] conducted a series of column tests to characterize the migration of liquid paraffin in a fine sandy medium under two cycles of water level fluctuation by an online detection method of the S-p relation with electrical conductivity probes and T5 tensiometers. All these researches indicate that the hysteresis plays an important role during the fluctuation of water table.

So far, most of the experiments were carried out under limited drainage-imbibition cycles. The researches on the hysteresis or hysteretic models under multiple consecutive drainage-imbibition cycles induced by the long term water level fluctuation in the subsurface were not sufficient.

In this work, a series of column tests were applied along two test routes to systematically characterize the effects of the initial water saturation on the hysteresis of the S-p relation in a sandy medium. One route was designed for the effects of initial water saturation on the hysteresis when the initial water saturation changed from a lower value to a higher one, and the other from a higher value to a lower one. The difference in the hysteresis between the two routes was also characterized.

2 Constitutive equations

2.1 Capillary pressure head

Capillary pressure head, h_c, is defined on an equivalent water height basis by [21]

                                                                  (1)

where ρ_w is the water density; P_c is the capillary pressure; and g is the scalar magnitude of gravitational acceleration.

2.2 VG model for S-p relations

In an air-water two phase porous medium, the relation between the water saturation and the capillary pressure head (h_c) is referred as the water retention curve or the S-p relation. The S-p relationship is generally measured through laboratory methods, and the parameters of the S-p models are obtained by the fitting methods [22]. It is thus crucial to choose a feasible method for the measurement of the S-p relation and an appropriate empirical formula for the description of the relation. A widely accepted empirical parameter form is as follows [23]:

h_c>0                                            (2)

Equation (2) refers to the van Genuchten (VG) model, where  and n are fitted parameters, m=1-1/n, and S_we is the effective water saturation, which is defined as

S_wr≤S_w≤1-S_ar                                (3)

where S_w is the water saturation; S_wr is the residual water saturation and S_ar is the residual air saturation.

The VG model was initially applied to describe a single drainage process. It was then extended to describe complex drainage and imbibition processes, in which the features of hysteresis were embedded [6]. As it is well known, hysteresis is mainly attributed to two factors, the fluid entrapment and the saturation hysteresis [3]. In the VG model, the fluid entrapment is characterized by the parameters of S_wr and S_ar, and the saturation hysteresis is mainly characterized by the parameter  All these parameters are path dependent and history dependent.

2.3 Degree of hysteresis

Based on the definition of hysteresis, two ways are selected to calculate the degree of hysteresis: The first one is defined as the difference in the capillary pressure between the drainage curve and the imbibition curve at an intermediate saturation of the whole drainage span [17]; The second one is defined as the ratio of the maximum difference of the two water contents at a particular capillary pressure between the drainage curve and the imbibition curve to the difference between the water content under the air-dried condition and that under the saturated condition. The equation is written as [16]:

                                                                     (4)

where r is the degree of hysteresis; θ_r and θ_s are the water contents under the air-dried condition and that under the saturated condition, respectively; ?θ_max is the maximum difference in water content between the drainage curve and the imbibition curve at a particular capillary pressure. In a soil, Eq. (4) also equals

                                                                    (5)

where S, S_s and S_r, similar to  are the water saturation, the water saturation in saturated condition, and the residual water saturation, respectively.

3 Experimental

3.1 Experimental design

The schematic for measuring the S-p relation in an air-water system is shown in Fig. 1. A polymethyl methacrylate column (7.0 cm in inner diameter and   100 cm in length) was applied, with a time domain reflectometry (TDR) probe (Trime-IT) assembled on one side and a tensiometer (SWT5, Delta-T Devices Ltd) on its opposite side. The signals of water pressure and saturation were recorded by a data logger (DT80 datataker). A spillway was located 3.5 cm from the top of the column to keep a constant water pressure when saturated.

Fig. 1 Schematic diagram of measurement of S-p relations in air-water two phase sandy medium

3.2 Sample preparation

Natural river sand, with particle density of     2.64 g/cm³, compacted-state void ratio of 0.74, and dry bulk density of 1.52 g/cm³, was used as a porous medium for the column tests. The grain size distribution of the river sand is displayed in Fig. 2.

Fig. 2 Grain size distribution of sand sample

The river sand was filled into the column with the underwater falling method to achieve a fully saturated condition [24-25]. In the process of sand-filling, deaerated water was induced into the column gradually from the bottom. The sand was poured into the column from the top via a funnel in uniform layers. The water level was all the while controlled about 5.0 cm above the sandy medium in the column. The redundant pore water in the column was induced out via the spillway at the top of the column.

3.3 Water level fluctuation and resulting drainage and imbibition processes

The hysteresis is defined to describe the difference between the drainage curve and the imbibition curve in a drainage-imbibition cycle. The initial fluid saturation is such a value from which a drainage or imbibition process starts, and therefore decides the flow path and flow history in a sandy medium. The initial fluid saturations of both the drainage process and the imbibition process may be the influencing factors on the hysteresis in a drainage-imbibition cycle. The initial fluid saturation of the imbibition process is both the end of the drainage process and the beginning of the subsequent imbibition process, which may play a more important role in the degree of the hysteresis. In this work, the initial water saturation is defined as the initial water saturation of the imbibition process in a drainage-imbibition cycle, and it can be also considered as the maker saturation/maker point of the drainage-imbibition cycle different from the other one.

Two test routes were designed based on the marker saturation, as shown in Fig. 3. Each route is composed of a series of consecutive drainage-imbibition cycles. The point A, B, C, D and E are the marker saturations of  these cycles. Route I (from A to E) is to investigate the effects of the initial water saturation on the hysteresis while the initial water saturation is changed from a low —Non-wetting phase residual saturation; S_wr—Wetting phase residual saturation; P_d—Air entry pressure) value to a high value, and Route II (from E to A) is to investigate the effects when the initial water saturation is changed from a high value to a low value

Fig. 3 Test routes for measurement of S-p relation curves (Route I refers toe test sequence from A to E, and Route II from E to A; S_ar

Along each route, three parallel column tests were conducted. Test 1, Test 2 and Test 3 belong to Route I. Each column test includes four levels of drainage- imbibition cycle based on the marker saturation. The marker saturations in these cycles are about 13%, 25%, 44% and 65%, respectively. Each marker saturation of the drainage-imbibition cycle was performed twice. The difference in the initial water saturation between every two imbibition processes of one level was controlled as small as possible. Test 4, Test 5, and Test 6 belong to Route II. Each column test includes 6-8 levels of drainage-imbibition cycle. The marker saturations in these cycles decrease from 80% to 10% gradually.

Before the column tests began, the sand was originally saturated with deaerated water, and the water level was controlled to be 16.3 cm above the top surface of the sand medium in the column, and 147.3 cm above the bottom of the column. During the water level falling, the water in the sand flowed out of the column in an adjusted flux rate by a rotary pump or a suction pump to obtain the scheduled water saturation, which resulted in a drainage process. During the subsequent water level rising, the water level of the water tank was maintained at a fixed height of 147.3 cm above the bottom of the column. The water in the water tank was induced into the column from its bottom in a controlled low flux for quite a long time (e.g., 48 h or more) to obtain the residual air saturation, which resulted in an imbibition process. The imbibition process did not terminate until the stable residual air saturation was obtained. The redundant water in the column flowed out from the top spillway.

All the drainage-imbibition cycles propagated in an uninterrupted sequence. The end point of one drainage process was the starting point of the subsequent imbibition process, and vice versa.

3.4 Calibrations of TDR probe and T5 tensiometer

Trime-IT TDR probes (IMKO, Micromodultechnik GmbH, Germany) and T5 tensiometers (UMS Gmbh, Munich) were used to measure the water saturation and capillary pressure, respectively. They were both calibrated before and after the column tests to investigate their accuracies and drifts during the whole column tests.

In order to obtain the water saturation and its corresponding output signal from a TDR probe in the sand, a suction pump was applied to extract pore water out of the sand medium to produce drainage processes. When there was no more water flowing out of the sand medium, the sand sample located around the probe was excavated as a specimen and then dried to determine the water saturation. Simultaneously, the corresponding output signal was collected with the data logger. In order to obtain different water contents and their corresponding output signals in the sandy medium, this procedure was conducted under different suction pressures or draining durations.

The above process was the anterior calibration of the TDR probe before the column tests. At the end of each formal column test, a drainage process was also imposed to a scheduled level to obtain the sampling for the posterior calibration of TDR probes. The calibration results of the TDR probe before and after the column tests are given in Fig. 4. The absolute errors in saturation between the measured value with TDR and that with gravimetric method are all less than 1%, and their relative errors are in the range of 0.81%-6.81%.

Fig. 4 Calibration results of TDR probe (a) and T5 tensiometer (b) before and after column tests

The ambient temperatures of column tests 1-6 are (23±2) °C, (18±2) °C, (18±2) °C, (21±2) °C, (24±2) °C and (24±2) °C, respectively. Depending on the manual from the IMKO Company, the maximum drift of Trime-IT probe caused by the temperatures is about ±0.4% in the range from -15 °C to 50 °C. The influence of temperature on the TDR probes is considered to be unconspicuous.

In order to obtain a pressure-output signal relation of T5 tensiometer, deaerated water was filled to a column in steps. T5 tensiometer was applied to measuring the hydrostatic pressures at each water level. The relation between pressure and output signal was then obtained.

In order to understand the difference in pressure between the hydrostatic and the dynamic conditions, the signal of T5 was also analyzed when the water level moved at a low speed but much higher than the magnitude of the water flow speed in the sandy medium. It is clear that the difference in the signal was unconspicuous [26].

The calibration results of T5 tensiometer before and after the experiments are shown in Fig. 4. The pressure drifts of T5 tensiometers in about one year were less than 0.8 cm water column. The drifts were mainly due to the changes of the ambient temperatures during the column tests.

Thus, the drifts of TDR probes and tensiometers during the total column tests are small and acceptable.

4 Results and discussion

4.1 Hysteresis under consecutive drainage and imbibition cycles

The test conditions and test results are almost the same as one another among the three parallel column tests along each route. Therefore, only the S-p relations of Test 1 and Test 5 are illustrated in Fig. 5, representing Route I and Route II, respectively.

It is found that the S-p relation curves of both the drainage and the imbibition in every drainage-imbibition cycle form a close loop, which is defined as the S-p curve loop in this work. All these loops show that the drainage curve and imbibition curve are not the same, which is referred as the hysteresis phenomenon in the porous medium. At a given saturation, the capillary pressure of the drainage process is larger than that of the imbibition in a drainage-imbibition cycle. It is concluded that there is no uniform relation between the saturation and capillary pressure in a porous medium, which is similar to the research results that a given saturation corresponds to various capillary pressures, and vice versa in a porous medium [2].

There are four levels of drainage-imbibition cycle in each parallel test of Route I. As mentioned above, each level of drainage-imbibition cycle was performed twice. The obtained two S-p curve loops almost overlap with each other, which means that the two drainage- imbibition cycles possess the same degree of hysteresis. Thus, when the initial water saturation of one drainage- imbibition cycle is close to the initial water saturation of the other cycle, the difference in the degree of hysteresis between the two cycles is not obvious, which suggests that the degree of hysteresis is not affected by the cycle number in a porous medium (in Fig. 5). This does not agree with the research by SHARMA [27] that the degree of hysteresis was affected by the number of cycle.

Fig. 5 S-p relation curves in Test 1 and Test 5: (a) Anterior part of Test 1; (b) Posterior part of Test 1; (c) Anterior part of Test 5;    (d) Posterior part of Test 5

The S-p relations of each level of initial water saturation in Test 1 and Test 5, which represent Route I and II, respectively, are shown in Fig. 6. In the drainage- imbibition cycle of the sandy porous medium, when the two drainage processes start with the same level of initial water saturation, but their succedent imbibition processes start with different initial water saturations, the obtained S-p curve loops and their degrees of hysteresis are found to be different from each other. With the increase of the initial water saturation of the imbibition processes in these drainage-imbibition cycles, the S-p curve loop resulting from the larger initial water saturation is surrounded by the one from the smaller initial water saturation. This phenomenon exists in both Route I and Route II (Fig. 6). It is concluded that, it is not history- dependent and flow-dependent for the S-p curve loops from the larger initial water saturation to be surrounded by the one from the smaller initial water saturation.

The hysteresis corresponding to the initial water saturation of each level was calculated with two methods. One is given by SHARMA and MOHAMED [17] and the other by KONYAI et al [16]. The drainage- imbibition cycle of interest and the primary drainage- main imbibition cycle were both taken into consideration in the KONYAI method, rather than only the former cycle in the SHARMA method. The KONYAI method is thus considered to be better. It is found that an obvious phenomenon exists that the degree of hysteresis decreases gradually with the increase of the initial water saturation of the imbibition process in both Route I and Route II, whether the degree of hysteresis is calculated by the SHARMA method or the KONYAI method (as shown in Fig. 7). It could be concluded that the degree of hysteresis is not obviously correlated to the number of drainage-imbibition cycle which happens in the porous medium, but is influenced by the initial water saturation from which the imbibition process in a drainage- imbibition cycle starts.

In a drainage process of a porous air-water two phase system medium, the air-entry pressure is such a value that only when the capillary pressure of the medium exceeds this value, the wetting phase fluid water can be displaced by the non-wetting phase fluid air, and the wetting phase saturation in the medium begins to decrease gradually with the increase of the capillary pressure. Based on the two test routes shown in Fig. 5, the air-entry pressures of all the drainage processes are about 2.2-2.3 kPa. This indicates that, in an air-water two phase porous medium, the air-entry pressure is almost a constant, which is independent of the initial water saturation or initial air saturation, history and flow-path of a drainage process.

Fig. 6 S-p relationships under different levels of initial water saturation: (a) Test 1; (b) Test 5

Fig. 7 Degree of hysteresis corresponding to initial water saturation in each cycle of all tests: (a) SHARMA and MOHAMED method; (b) KONYAI method

4.2 Description of S-p relation with VG model

The VG model was selected to describe the S-p relation data measured in these column tests. The parameters of the model were obtained by the combination of two methods. One is the function lsqcurvefit in optimization toolbox of the MatLab software developed by American Math Works Company [28-29]. The other is 1stopt software, an integrated tool package for the mathematical optimization, which was developed by the 7D-Soft High Technology Inc. The latter does not need the users to offer the initial value, and can obtain the optimal solution through universal global optimization method. Between the two methods, the one with higher correlation coefficient was chosen to calculate the parameters of the VG model.

The S-p relations measured in Test 1 and Test 5 and fitted with the VG model are shown in Fig. 5. In Test 1, the S-p relation curves described by the VG model coincide well with the measured S-p relation data. In Test 5, there are not enough data for the VG model fitting in the former cycles. However, in the later cycles, the S-p curves are well described by the VG model. The correlation coefficients resulting from the fitting of the VG model in each drainage-imbibition cycle are shown in Table 1. As mentioned above, the test for each level  of initial water saturation was conducted twice, which resulted in two drainage-imbibition cycles. For simplicity, only one cycle is summarized in the table. These correlation coefficients are all higher than 0.940. All these suggest that the VG model could be applied successfully to describe the S-p relations of these complicated drainage and imbibition processes of the present tests.

Table 1 Parameters of S-p relations fitted with VG model

4.3 Changes of parameters of VG model in drainage- imbibition cycles

4.3.1 Parameter α of VG model

In Table 1, it shows that the parameter α is in the range of 0.036-0.040 in all the drainage processes of Route I, and in the range of 0.033-0.042 in Route II. The values of parameter α in all the drainage processes of the two test routes are almost equal to one another, and they are all approximately equal to the inverse of the air-entry value, which is 2.2-2.3 kPa in these column tests. This successfully explains that parameter α is approximately equal to the inverse of the air-entry pressure (P_d) in a drainage process [23].

In Table 1 and Fig. 8, it is also found that the value of parameter α decreases with the increase of the initial water saturation in all the imbibition processes of the two group experiments. A significant negative linear relation exists between parameter α and the initial water saturation in these imbibition processes. Furthermore, between every two close initial water saturations, namely, the same level of initial water saturation, the two parameters α are close to each other. This thus suggests that parameter α of an imbibition process is obviously affected by the initial water saturation, but not the numbers of drainage-imbibition cycle which happens in the porous medium.

Fig. 8 Parameter a and n of S-p relations fitted with VG model in both test routes: (a) Parameter α; (b) Parameter n

4.3.2 Parameter n of VG model

Parameter n of the VG model is considered to be related to the pore distribution of a porous medium [30]. In all the tests, the pore structure of the sand was difficult to be kept the same as one another. Structure difference should exist between every two of the six column tests, but the structure could be considered the same from the beginning to the end within one test, and parameter n of all the drainage processes or the ones of all the imbibition processes in this test should thus be constant. Anyway, it is found that, in Table 1 and Fig. 8, values of parameter n are different even within one test. The parameter n increases with the increase of the initial water saturation in all the drainage processes, and decreases with the increase of the initial water saturation in all the imbibition processes. It could be concluded that parameter n of an imbibition process is also obviously affected by the initial water saturation. The statement that parameter n of the VG model is related to the pore distribution in porous media [30] may need to be verified with more tests.

The parameters α of the VG model in all the drainage processes are almost the same as one another. However, the parameter α in all the imbibition processes, and n in all the drainage processes and the imbibition processes are obviously influenced by the initial water saturation.

It could be found that the VG model is capable to offer a good description for the S-p relations in these complicated drainage-imbibition cycles of the present tests. It also should be noted that further study will be needed on the sensitivity and simulation precision of the VG model and the uncertainty of its parameters if it is applied at any situation.

5 Conclusions

1) The degree of hysteresis decreases with the increase of the initial water saturation in a drainage- imbibition cycle happening in a porous medium. The influence factor is the initial water saturation of the imbibition process.

2) The air-entry pressure is a constant, and it is not dependent on the flow history and flow path in a sandy medium.

3) The VG model is a useful tool for the description of the S-p relations under complicated drainage- imbibition cycles. The parameter α is proved to be approximately equal to the inverse of the air-entry pressure in a drainage process. However, the parameter n of the VG model may not be related to the pore distribution of a porous medium whether in a drainage process or an imbibition process.

References

[1] DANE J H, WIERENGA P J. Effect of hysteresis on the prediction of infiltration, redistribution and drainage of water in a layered soil [J]. Journal of Hydrology, 1975, 25(3/4): 229-242.

[2] POULOVASSILIS A. The effect of the entrapped air on the hysteresis curves of a porous body and on its hydraulic conductivity [J]. Soil Science, 1970, 100(3): 154-162.

[3] van GEEL P J, SYKES J F. The importance of fluid entrapment, saturation hysteresis and residual saturations on the distribution of a lighter-than-water non-aqueous phase liquid in a variably saturated sand medium [J]. Journal of Contaminant Hydrology, 1997, 25(3/4): 249-270.

[4] BASILE A, CIOLLARO G, COPPOHA A. Hysteresis in soil water characteristics as a key to interpreting comparisons of laboratory and field measured hydraulic properties [J]. Water Resources Research, 2003, 39(12): 1301-1312.

[5] KOOL J B, PARKER J C. Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties [J]. Water Resources Research, 1987, 23(1): 105-114.

[6] LUCKNER L, VAN GENUCHTEN M T, NIELSEN D R. A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface [J]. Water Resources Research, 1989, 25(10): 2187-2193.

[7] LENHARD R J, JOHNSON T G, PARKER J C. Experimental observations of non-aqueous-phase liquid subsurface movement [J]. Journal of Contaminant Hydrology, 1993, 12(1): 79-101.

[8] OSTROM M, LENHARD R J. Comparison of relative permeability- saturation-pressure parametric models for infiltration and redistribution of a light nonaqueous-phase liquid in sandy porous media [J]. Advances in Water Resources, 1998, 21(2): 145-157.

[9] MILLER C D, DUMFORD D S, FOWLER A B. Equilibrium nonaqueous phase liquid pool geometry in coarse soils with discrete textural interfaces [J]. Journal of Contaminant Hydrology, 2004, 71(1/2/3/4): 239-260.

[10] XU Yan-bing, WEI Chang-fu, CHEN Hui, LUAN Mao-tian. A model of soil-water characteristics for unsaturated geotechnical materials under arbitrary drying-wetting paths [J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(5): 1046-1052. (in Chinese)

[11] MUALEM Y. A modi?ed dependent domain theory of hysteresis [J]. Journal of Soil Science, 1984, 137 (5): 283-91.

[12] BRADDOCK R D, PARLANGE J Y, LEE J. Application of a soil water hysteresis model to simple water retention curves [J]. Transport in Porous Media, 2001, 44(3): 407-420.

[13] MAQSOUD A, BUSSIERE B, MBONIMPA M, AUBERTIN M. Hysteresis effects on the water retention curve: A comparison between laboratory results and predictive models [C]// Proceedings of the 5th Joint IAH-CNC and CGS Groundwater Specialty Conference and 57th Canadian Geotechnical Conference. Quebec, 2004: 8-15.

[14] WITKOWSKA-WALCZAK B. Hysteresis between wetting and drying processes as affected by soil aggregate size [J]. International Agrophysics, 2006, 20(4): 359-365.

[15] LIKOS W J, LU N. Hysteresis of capillary cohesion in unsaturated soils [C]// Proceedings of the 15th ASCE Engineering mechanics Conference. New York: Columbia University, 2002: 1-8.

[16] KONYAI S, SRIBOONLUE V, TRELO-GES V. The effect of air entry values on hysteresis of water retention curve in saline soil [J]. American Journal of Environmental Sciences, 2009, 5(3): 341-345.

[17] SHARMA R S, MOHAMED H A. An experimental investigation of LNAPL migration in an unsaturated or saturated sand [J]. Engineering Geology, 2003, 70(3/4): 305-313.

[18] LI Yan. Mechanism of LNAPL migration in conjunction with groundwater fluctuation [D]. Japan: Kyoto University, 2005: 1-167.

[19] SHEN Rong-kai. Experiment study on hysteresis mechanism of water movement in soil [J]. Journal of Hydraulic Engineering, 1987, 4: 38-45. (in Chinese)

[20] SHEN Rong-kai. Effect of hysteresis on water movement in unsaturated soils [J]. Acta Pedologica Sinica, 1993, 30(2): 208-216. (in Chinese)

[21] LEVERETT M C. Capillary behavior in porous solids [J]. Transactions of the American Institute of Mining, Metallurgical, and Petroleum Engineers, 1941, 142: 152-169.

[22] XING Wei-wei. Study on migration behavior of LNAPLs in soils [D]. Beijing: Tsinghua University, 2005: 1-130. (in Chinese)

[23] van GENUCHTEN M T. A closed form equation for predicting the hydraulic conductivity of unsaturated soils [J]. Soil Science Society of America Journal, 1980, 44(5): 892-898.

[24] KAMON M, ENDO K, KATSUMI T. Measuring the k-S-p relations on DNAPLs migration [J]. Engineering Geology, 2003, 70(3/4): 351-363.

[25] LI YAN, ZHOU Jin-feng, XU Jun, KAMON M. Online dynamic measurement of saturation-capillary pressure relation in sandy medium under water level fluctuation [J]. Journal of Central South University of Technology, 2010, 17(1): 85-92.

[26] XIE Xiao-xi, LI Yan, XU Jun, XIA Bei-cheng, SU Yu. Response of saturation-capillary pressure relationship to the water table fluctuation in a sandy medium [J]. Acta Scientiae Circumstantiae, 29(11): 2331-2338. (in Chinese)

[27] SHARMA R S. Mechanical behaviour of unsaturated highly expansive clays [D]. UK: University of Oxford, 1998: 1-250.

[28] WEI Yi-chang, LIU Zuo-xin, KANG Ling-ling, WANG Yun-zhang, SHI Ming-li. Parameters estimation of van Genuchten model for soil water retention curves using Matlab [J]. Acta Pedologica Sinica, 2004, 141(13): 380-386. (in Chinese)

[29] PENG Jian-ping, SHAO Ai-jun. Determination of parameters of soil water characteristic carve by Matlab [J]. Soils, 2007, 39(3): 433-438. (in Chinese)

[30] van GENUCHTEN M T, NIELSEN D R. On describing and predicting the hydraulic properties of unsaturated soils [J]. Annales Geophysicae, 1985, 3: 615-628.

(Edited by HE Yun-bin)

Foundation item: Project(41072182) supported by the National Natural Science Foundation of China; Project(2010Z1-E101) supported by the Science and Technology Program of Guangzhou City, China; Project(200809095) supported by the Special Funds for Environmental Nonprofit Research, China; Project(8151027501000008) supported by the Natural Science Foundation of Guangdong Province, China

Received date: 2011-02-21; Accepted date: 2011-05-10

Corresponding author: LI Yan, PhD; Tel: +86-13925090686; E-mail: eesly@mail.sysu.edu.cn