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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Geoderma 159 (2010) Contents lists available at ScienceDirect Geoderma journal homepage: Validation of an analytical method for determining soil hydraulic properties of stony soils using experimental data DongHao Ma a,b,c,, MingAn Shao b, JiaBao Zhang a, QuanJiu Wang b a State Experimental Station of Agro-Ecosystem in Fengqiu, State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences, Nanjing , China b State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Chinese Academy of Sciences, Yangling , Shaanxi, China c Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing , China article info abstract Article history: Received 28 August 2009 Received in revised form 20 July 2010 Accepted 1 August 2010 Keywords: Stony soils Rock fragment content Soil water characteristic curve Hydraulic conductivity Soil unsaturated hydraulic properties are an important input for simulations of water and solute movement in the vadose zone. However, in the case of soils containing rock fragments, direct measurement of unsaturated hydraulic properties remains difficult. Recently, an analytical method was proposed (Ma et al., 2009) for determining soil hydraulic properties from horizontal water absorption experiments. Here, we test if this method could be used in the determination of the hydraulic properties of stony soils with a set of experiments. The results show that the method can predict accurately and quickly the hydraulic parameters of stony soils using the cumulative infiltration volume and the rate of wetting front advancement during water absorption into a horizontal soil column. The influence of rock fragment content on some soil hydraulic properties including air entry suction, saturated hydraulic conductivity and the shape coefficients of hydraulic functions was further evaluated. Both air entry suction and shape coefficient show a large range of variation with rock fragment content. Globally, the saturated hydraulic conductivities of stony soils decreased with increasing rock fragment content. However, when the volumetric rock fragment content is about 0.08 cm 3 cm 3, the stony soil displayed a greater saturated hydraulic conductivity compared to the fine earth at 95% confidence level. The relationship between saturated hydraulic conductivity and rock fragment content is not accurately estimated by different equations relating saturated hydraulic conductivity of stony soils to that of non-stony soils. These findings imply that other factors than the reduction of cross sectional area for water flow influence the hydraulic properties of stony soils Elsevier B.V. All rights reserved. 1. Introduction Understanding water and solute movement in soils and ground water has important implications for the determinations of hydrologic processes and management of field water and nutrient conditions. Accurate prediction of water flow and solute transport depends largely on reliable and accurate measurement of soil hydraulic properties (Wang et al., 2002). Many studies have been focused on the hydraulic properties of homogeneous soils and studies on the hydraulic properties of heterogeneous soils do not reach accurate predictions of water flow and solute transport, especially in soils with rock fragments. Soils containing rock fragments (N2 mm) are Corresponding author. State Experimental Station of Agro-Ecosystem in Fengqiu, State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences, Nanjing , China. Tel.: ; fax: addresses: dhma@issas.ac.cn (D. Ma), mashao@ms.iswc.ac.cn (M. Shao), jbzhang@issas.ac.cn (J. Zhang), wquanjiu@163.com (Q. Wang). common in many areas due to soil development processes and human actions (Poesen and Lavee, 1994). Rock fragments can reduce pore volume available for water flow and increase the tortuosity of soil water flow (Mehuys et al., 1975; Childs and Flint, 1990). On the other hand, rock fragments may also create new voids at the rock fragment fine earth interfaces (Fies et al., 2002; Tokunaga et al., 2003) and some rock fragment types (e.g. catogene, shale, ironstone and limestone) can hold water (Coile, 1953; Hanson and Blevins, 1979; Brouwer and Anderson, 2000; Cousin et al., 2003), and may provide pathways for water flow. Therefore, the existence of rock fragments in stony soils can lead to hydraulic properties that are highly different from those of non-stony soils (Mehuys et al., 1975; Sharma et al., 1993; Fies et al., 2002). Knowledge on the hydraulic properties of stony soils is rather limited. This is due, mainly, to the fact that no simple methods are available for determining the unsaturated hydraulic properties of soils containing rock fragments. The presence of rock fragments is problematic for the measurement of water content, water potential or water flow (Reinhart, 1961; Koshi, 1966; Fleming et al., 1993) /$ see front matter 2010 Elsevier B.V. All rights reserved. doi: /j.geoderma

3 D. Ma et al. / Geoderma 159 (2010) because of practical issues in inserting probes in soils (such as TDR probes, tensiometers) or installing lysimeters (Cousin et al., 2003) in such soils without altering the soil structure, especially when the content of rock fragments is great. In order to guarantee representative samples, the volume of soil sampled must be relatively large (Buchter et al., 1984; Flint and Childs, 1984) which involves considerable labour and extended times required for equilibrium when using pressure plate apparatus. Thus, although traditional methods (Bruce and Klute, 1956; Green et al., 1986; Klute and Dirksen, 1986) have proved reliable for determining the hydraulic properties of homogeneous soils, they may lead to difficulties for stony soils. For these reasons, many previous studies focused on the determination of saturated hydraulic conductivities of stony soils (Bouwer and Rice, 1984; Ravina and Magier, 1984; Brakensiek et al., 1986) and the relationships between the saturated hydraulic conductivity of stony soils and their homogenous counterpart (Bouwer and Rice, 1984; Brakensiek et al., 1986). Hydraulic properties of the fine earth are often assumed to be the same as those of soils without rock fragments. Nevertheless, it has been found (Mehuys et al., 1975; Fies et al., 2002; Ma and Shao, 2008) that the presence of rock fragments in soils can result in a pore structure of the fine earth that differs from that of soils without rock fragments. Until now, explicit unsaturated hydraulic conductivities of stony soils seemingly remained elusive for simulations of the infiltration into stony soils by deterministic models (Cousin et al., 2003). Methods for determining unsaturated hydraulic properties in stony soils from horizontal absorption experiments may be a promising approach, by avoiding direct measurements of water content or potential. Shao and Horton (1998) and Wang et al. (2002) used horizontal absorption experiments for estimating parameters of the van Genuchten (1980) and Brooks-Corey (1964) hydraulic functions respectively. Although the applicable soil types are limited, their methods are simple, requiring only data for cumulative infiltration, infiltration rate and wetting front advance versus time during horizontal absorption. In that case, measurements of the required data show the same difficulty for stony as well as for non-stony soils. Recently, Ma et al. (2009) further improved the method of Wang et al. (2002) for application to a wider range of soil textures. More experimental tests are however required, especially for soils containing rock fragments. The first objective of this paper was to test whether the method developed by Ma et al. (2009) could be used to measure the hydraulic properties of soils containing rock fragments. The second objective was to evaluate the influence of rock fragments on the soil hydraulic properties. 2. Theory 2.1. Model of water movement in stony soils Ma et al. (2009) proposed and compared several models including the non-equilibrium dual-porosity model (NDPM), the equilibrium dual-porosity model (EDPM) and the equilibrium single-porosity model (ESPM) to simulate water movement in stony soils. Their results indicated that the dual-porosity model could accurately simulate many phenomena especially non-equilibrium flows during water movement in stony soils. However, it is difficult to measure the hydraulic properties of fine earth and rock fragments separately to allow for the influence of rock fragments on soil pore structure. An alternative method is to consider the mixed fine earth and rock fragments as a homogeneous effective medium. Water movement theory for homogeneous soils (the ESPM model) can then be used to simulate water flow in stony soils. Although the exact water distribution cannot be described, in that case, for non-equilibrium flows, the single-porosity model could give good estimations of the cumulative infiltration and wetting front advance in soils with rock fragments. For one-dimensional horizontal absorption, the ESPM can be written as (Richards equation) θ t = x Kh ð Þ h ð1þ x θð0; xþ = θ i ð2þ θðt; 0Þ = θ s ð3þ θðt; Þ = θ i ð4þ where θ is the volumetric soil water content (cm 3 cm 3 ), θ i is the initial water content (cm 3 cm 3 ), θ s is the saturated water content (cm 3 cm 3 ), h is the soil water potential (cm), K is the soil hydraulic conductivity (cm min 1 ), x is the horizontal distance from the inlet (cm), and t is time (min). Soil water retention curves and unsaturated hydraulic conductivities can be described using the equations proposed by Brooks and Corey (1964) S = θ θ r θ s θ r = ðαhþ n h 1 = α S =1 h N 1 = α KS ðþ= K s ðαhþ m = K s S l +1+2= n ð6þ where θ r is the residual water content (cm 3 cm 3 ), S is the effective water saturation, α is an empirical parameter (cm l ) whose inverse is often referred to as the air entry value or bubbling pressure, n is the shape coefficient, K s is the saturated hydraulic conductivity (cm min 1 ), l is the soil pore tortuosity factor, and m=n (l+1) +2. The factor l can be any value, but 2 is applied to most soils (Brooks and Corey, 1964)and is also adopted here. For notational convenience, let h d = 1/α for the remainder of this article which is positive and still denote the air entry suction (cm) Method for estimating soil hydraulic properties Combining the power function flux concentration relationship (Kutilek, 1980) with the Boltzmann transformation method (Philip, 1960), Ma et al. (2009) deduced a simple approximate analytical solution to the problem of horizontal absorption (Eqs. (1) to (4)) and proposed a method for estimating hydraulic parameters of the Brooks-Corey model from horizontal absorption experiments and is designated as unimproved method (UM) in this paper. In the UM, Brooks-Corey model parameters can be obtained from the following formulas a n = ð7þ 1 ðl +1 βþa sd h d = 2K s b½1 ðl +1 βþaš where β is the shape coefficient of water flux distribution on soil profile and is assumed to be constant with no relation to soil texture. Ma et al. (2009) recommended the β value of when the UM was used. However, the β value was found to be close to 1 according to the measured water flux distributions for several soil types (White et al., 1979; Boulier et al., 1984). Thus, UM with β=1 and β=1.145 were tested here using experimental data to acquire an appropriate value of β. a and b are parameters concerning soil water content distribution which can be calculated by the two formulas as follows a = θ s θ r A + θ i θ r 1 ð5þ ð8þ ð9þ

4 264 D. Ma et al. / Geoderma 159 (2010) b =1 S 1 a i ð10þ b can be approximated to 1 because the initial water content (θ i )or initial water saturation (S i ) required for this method is very low. A, s and d are the average increase of profile water content (cm), the sorptivity (cm min 0.5 ) and the characteristic length of the wetting zone (cm), respectively, which can be obtained by fitting observed data series with the following equations I = A x f x f = d t 1 = 2 I = s t 1 = 2 ð11þ ð12þ ð13þ where I is the cumulative infiltration (cm) and x f is the wetting front advance(cm). Obviously, if β is known in advance, all the hydraulic parameters of the Brooks-Corey model can be easily estimated from Eqs. (7) (13). To further improve the estimation of soil hydraulic parameters, based on the experimental results from 19 typical soils, Ma et al. (2009) developed an improved method (IM) using the experimental relationship between the real hydraulic parameters and those estimated by UM with β=0. n = a 0 1 ðl +1Þa 0 ð14þ sda 0 h d = 2K s b a ½1 ðl +1Þa 0 Š where ð15þ a =0:77a 0:01 ð16þ a = a 0:028 ð17þ sand, 13.4% silt, and 0.2% clay, 0.1% organic matter) according to the particle size classification of USDA. The particle density of the fine earth was 2.59 g cm 3. The saturated water content of the fine earth was 0.42 cm 3 cm 3 at a bulk density of 1.5 g cm 3. The initial water contents of the rock fragments and the fine earth were cm 3 cm 3 and cm 3 cm 3, respectively. Rock fragments and fine earth were packed uniformly into Plexiglas columns with five different gravimetric rock fragment contents R m of 0, 10%, 20%, 30% and 40% which corresponded to volumetric contents R v of 0, 0.08, 0.17, 0.25 and The weight of fine earth was calculated to reach a bulk density of 1.5 g cm 3.Inordertofill rock fragments and fine earth into the columns as uniformly as possible, they were weighed separately for each layer of 10 cm and mixed in one container before being packed into columns. Horizontal absorption experiments were performed at zero water head maintained by Marriott tubes at the water inlet. The cumulative infiltration volume and wetting front advance versus time were measured during the experiments. At the completion of infiltration experiments, the soil columns were saturated and arranged vertically to determine the saturated hydraulic conductivity using a constant water head of about 10 cm. The soil columns were weighed before and after experiments to determine the total porosity. Each treatment was replicated three times, but for the relative standard errors of cumulative infiltration or wetting front advance were less than 4% for R m b40%, the treatment for R m =40% was replicated only twice. The analytical method of Ma et al. (2009) was used to estimate the hydraulic parameters of soils with different rock fragment contents. HYDRUS-1D software (Šimůnek et al., 2005) was used to calculate the cumulative infiltration and wetting front advance versus time for comparison with the observed values. To evaluate the influence of data series length on the stability of the estimated parameters, the experimental data from R m =0 with final times of 50, 100, 150 and 173 min were used to further test the analytical method of Ma et al. (2009). Finally, the average values of the estimated hydraulic parameters of the stony soils for each treatment were used to evaluate the influence of rock fragments on the soil hydraulic properties. b =1 S 1 a i ð18þ 4. Results and discussion The parameters a, A, s and d are same to those of UM. Similarly, b can also be approximated to 1 when a soil is initially very dry. But in the improved method, β becomes a function of the parameter n and the average water saturation of the wetting zone rather than a constant with no relation to soil texture. β = ðl +1+1= nþ 1 a 3. Materials and methods ð19þ One-dimensional water absorption experiments were performed using horizontal soil columns to test the analytical model and investigate how rock fragments affect soil hydraulic properties. Experiments were conducted using a horizontal cylindrical column, 50 cm long with an inner diameter of 11 cm. Soils containing rock fragments were sampled from the surface 0 20 cm soil layer at the Liudaogou Basin experimental station located in the Shenmu District of the Loess Plateau, Shaanxi Province in China ( N, E). The rock fragments were calcium concretions from sediments containing calcium salts. Samples were air-dried and rock fragments (N2 mm) were separated from the fine earth (b2 mm) by sieving. The rock fragments were sieved again to obtain rocks of mm equivalent diameter. The rocks were approximately spherical in shape. The particle density, bulk density and saturated water content of the rock fragments were 2.66 g cm 3, 1.94 g cm 3 and 0.27 cm 3 cm 3, respectively. The fine earth was a Sand (86.3% 4.1. Test of the methods for stony soils The UM with β=1, the UM with β=1.145 and the IM were all evaluated (Ma et al., 2009). Using the observed data for cumulative infiltration and wetting front advance versus time, the Brooks-Corey hydraulic model parameters for all replications were estimated from θ i, θ s, θ r, K s, A, s and d with Eqs. (7) (13) or Eqs. (14) (18). Average values of the estimated hydraulic parameters (h d and n) are shown in Table 1 as well as the measured saturated hydraulic conductivities (K s ). Parameters estimated by the three methods are not very different from each other but have obvious differences in their relative magnitudes. The UM with β=1 predicted slightly greater n values for all treatments than did the UM with β=1.145 which further predicted greater n values than did the IM. The air entry suction (h d ) values calculated by the UM with β=1 are greater than those predicted by the two other methods. Obviously, a lesser β value in the UM will result in greater h d and n values. This will result in a steeper soil water characteristic curve with greater air entry suction when β is treated as constant. As discussed earlier, β values are related to soil texture and initial soil water saturation (Eqs. (9), (17) and (19)). Since the initial soil water contents used in the testings are close to residual water contents, β values mainly change with soil texture (with rock fragment content). Using Eq. (19), β values were calculated and are also shown in Table 1. The results in Table 1 indicate that most of the β values are less than 1 that is conjectured to be the upper theoretical limit (Philip, 1973) and that β values change with soil texture. Thus,

5 D. Ma et al. / Geoderma 159 (2010) Table 1 Measured saturated conductivity and predicted Brooks-Corey hydraulic model parameters obtained by the horizontal absorption method for soils containing different rock fragment contents. R v (cm 3 cm 3 ) K s (cm min 1 ) IM UM β=1 β=1.145 β h d (cm) n h d (cm) n h d (cm) n ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.063 Eq. (19) may be more reasonable for describing the relationship between β and soil texture than using a constant β. To test the validation of the predicted soil hydraulic properties, the HYDRUS-1D software was used, with estimated parameters, to calculate cumulative infiltration and wetting front advance for comparison with observed values. The calculated and observed cumulative infiltration and wetting front advance are plotted in Figs. 1 and 2, respectively, and compared with 1:1 lines for the three methods. Root mean square errors (RMSE) were also calculated (Table 2) for the three different methods between the observed values for cumulative infiltration and wetting front advance and calculated values. The plotted data all agree well with the 1:1 lines (Figs. 1 and 2) except that the RMSE increases from the IM to the UM with β=1 and the UM with β= As shown in Figs. 1 and 2, the IM slightly improves the estimations of soil hydraulic parameters compared with the UM. The UM with β=1.145 seems to be a poorer predictor of soil hydraulic properties as when β=1. Although five different contents of rock fragments were mixed with fine earth, only one type of fine earth was used. The calculated values of β from Eq. (19) are very close to 1 for soils containing no rock fragments and are mostly in the range from 0.8 to 1 for soils with rock fragments (Table 1). The fact that β are close to 1 for all treatments, results in little differences of the calculated cumulative infiltration or wetting front advance by the IM from the UM with β=1. However, for soils under natural conditions with a wider range of textures, the β value may be far from 1. In such cases, the UM would not be valid for estimating soil hydraulic parameters. Moreover, using a uniform β value for typical soils covering large range of textures may not be applicable for a particular soil. Therefore, it can be concluded that the IM should have wider applicability than the other two methods and is expected to be an accurate and time saving method for determining the hydraulic properties of soils containing rock fragments. Sufficient data series acquisition time is necessary for obtaining confident hydraulic parameter values. Fig. 3 shows the observed and calculated cumulative infiltration and wetting front advance curves obtained from HYDRUS-1D while Table 3 presents soil hydraulic parameters for R v =0 estimated by the IM using data with different time length. The root mean square errors (RMSE) between the observed and calculated cumulative infiltration and wetting front advance are also shown in Table 3. A shorter time length of data leads to a greater h d or n value but not a greater RMSE (Table 3). The calculated results were significantly overestimated when data for times less than 50 min were used (Fig. 3) while the calculated cumulative infiltration and wetting front advance together are in good accordance with the observed values when the data time length is greater than 100 min. Thus, the IM is reliable as long as experimental data with sufficient length of time is available Influence of rock fragments on the soil water characteristic curve Air entry suction (h d ) and shape coefficient (n) are the two most important parameters of the Brooks-Corey hydraulic model. Fig. 4a and b show the mean and standard errors of air entry suction (h d ) and shape coefficient (n), predicted by the IM, as a function of the volumetric rock fragment content. The air entry suctions of stony soils exhibit no single increasing or decreasing relationship but show two significant turning points with increasing rock fragment content. Values of h d fall to a local minimum when the rock fragment content by volume increases from 0 to about 0.08 and then rise gradually to a maximum at a rock fragment content by volume of about The values of h d then decrease again with rock fragment content. In contrast, the shape coefficient n increases to a maximum when the rock fragment content is about 0.25 and then decreases. Both air entry suction and shape coefficient depend on soil particle size distribution and pore structure (total porosity and pore size distribution). If rock fragments were non-porous and did not change the pore structure of the fine earth fraction, h d and n would be constant and only a linear offset for the soil water characteristic curve would occur irrespective of rock fragment content of the soil. Fig. 4a and b show that this is obviously not the case. The results indicate that both h d and n vary with increased rock fragment content. Some studies (Mehuys et al., 1975; Brakensiek and Rawls, 1994) have reported that the main effects of rock fragments on the fine earth water characteristic curve occurred in the low and high suction regions. Air entry suction is associated with the high suction region while the shape coefficient of the soil water characteristic curve can be influenced by the whole region of suction. Several reasons may explain the variations of h d and n with rock fragment content shown in Fig. 4. First, rock fragments (N2 mm) will add new particle size grades and the ratio of them to finer solid particles (b2 mm) will increase with rock fragment content. Second, rock fragments may create some new voids especially big pores (Ravina and Magier, 1984) at the rock fragment fine earth interfaces (Fies et al., 2002; Tokunaga et al., 2003). Third, rock fragments may influence the ability of soils to resist local compaction (Ravina and Magier, 1984), hence resulting in more heterogeneity of bulk density and pore distribution within soils. As a result, a greater total porosity of stony soil was found in the experiments when R v =0.08 cm 3 cm 3 compared to R v =0.0 cm 3 cm 3 (Fig. 4c). Finally, some rock fragments contain considerable numbers of pores (Hanson and Blevins, 1979; Jones and Graham, 1993; Brouwer and Anderson, 2000; Cousin et al., 2003) rather than being non-porous rocks (Unger, 1971; Mehuys et al., 1975; Peck and Watson, 1979; Khaleel and Relyea, 1997). In these experiments, the average porosity of rock fragments can reach up to 0.27 cm 3 cm 3, which represents 64% of fine earth porosity (0.42 cm 3 cm 3 ). The pores within rock fragments are mainly small sized and then in the low water potential range, their porosity may make them the main contributor to water storage instead of fine earth pores within this suction range (Sharma et al., 1993; Tokunaga et al., 2003). With increasing rock fragments, the soil rock fragment mixture may undergo an intrinsic change from a soil containing rock fragments to a mixture with fine earth embedded into pore spaces among rock fragments (Ma and Shao, 2008). The influence of rock fragments on soil hydraulic properties is therefore of great complexity and the behavior of the soil water characteristic curve could not be attributed to only one of the factors discussed above.

6 266 D. Ma et al. / Geoderma 159 (2010) Fig. 1. Observed cumulative infiltration versus calculated cumulative infiltration from HYDRUS-1D with the estimated parameters by the (a) IM, (b) UM with β=1, and (c) UM with β= Fig. 2. Observed wetting front advance versus calculated wetting front advance from HYDRUS-1D with the estimated parameters by the (a) IM, (b) UM with β=1, and (c) UM with β=1.145.

7 D. Ma et al. / Geoderma 159 (2010) Table 2 Root mean square error (RMSE) between the observed values for cumulative infiltration and wetting front advance, and calculated values from HYDRUS-1D for all treatments using three different methods. Method Cumulative infiltration (cm) Wetting front (cm) IM UM (β=1) UM (β=1.145) Table 3 Estimated soil hydraulic parameters for R v =0 by the IM using data for different series length, and the root mean square error (RMSE) between the observed and calculated values of cumulative infiltration and wetting front advance from HYDRUS-1D. Time (min) h d (cm) n RMSE (cm) Cumulative infiltration Wetting front 4.3. Influence of rock fragments on soil hydraulic conductivity Unsaturated soil hydraulic conductivity usually can be expressed as a product of saturated hydraulic conductivity and a dimensionless function of water saturation with values between 0 and 1. Due to the difficulty of determining the unsaturated hydraulic conductivities of soils containing rock fragments, the dimensionless function or relative hydraulic conductivity is usually assumed to be that of fine earth. To simplify the calculation of unsaturated hydraulic conductivities of stony soils, attempts have been made to relate the saturated hydraulic conductivity of the soil containing rock fragments to that of fine earth (Peck and Watson, 1979; Bouwer and Rice, 1984; Ravina and Magier, 1984). Four main methods have been proposed. Using heat transfer theory as a basis, Peck and Watson (1979) derived a formula for a homogeneous medium containing non-porous spherical inclusions to calculate the hydraulic conductivity of a stony soil from the hydraulic conductivity of the fine earth and the volumetric rock fragment content K s;t = 21 R ð vþ ð2+r v Þ K s;fe ð20þ where K s,t and K s,fe are the hydraulic conductivities (cm min 1 ), and the subscripts s, T and fe denote saturated soil, total soil (i.e. stony soil) and fine earth, respectively. For easier application, Eq. (20) was simplified to a function of the rock fragment content by weight according to experiential relations (Brakensiek et al., 1986) K s;t = ð1 R m ÞK s;fe ð21þ Bouwer and Rice (1984) proposed the following equation that takes porosity of rock fragments into consideration K s;t = θ s;t θ s;fe K s;fe ð22þ where θ s,t and θ s,fe are the porosities or saturated water contents (cm 3 cm 3 ) and the subscripts mean the same to the above. Assuming that rock fragments were non-porous and did not exert an influence on the pore structure of the fine earth, Ravina and Magier (1984) considered that the relative hydraulic conductivity of a stony soil to fine earth could be approximated to the volumetric percentage of bulk fine earth. K s;t = ð1 R v ÞK s;fe ð23þ Fig. 3. Observed and calculated (a) cumulative infiltration curves and (b) wetting front advance curves from HYDRUS-1D with the estimated parameters by the IM using data with different series length. Fig. 5 shows the observed saturated hydraulic conductivities of stony soils (K s,t ) as a function of rock fragment content (R v ), as well as predicted values by Eqs. (20), (21), (22) and (23) for comparison between models. Fig. 5 indicates that the observed saturated hydraulic conductivities exhibit no consistent increase or decrease with increased rock fragment content. At 95% confidence level, statistical analysis by Mathcad software (Mathsoft, 2001) shows an overall decrease of the saturated hydraulic conductivity of the stony soils with increasing stone content, but a greater saturated hydraulic conductivity compared to the fine earth is observed when the rock fragment content is about With further increases in rock fragment content, the saturated hydraulic conductivity declines and then increases again. Zhu and Shao (2006), using different kinds of fine soil and stones from those used in this study, also observed this phenomena for soils containing 0.08 volumetric rock fragments in rain runoff experiments. In Fig. 4c, the soils with R v =0.08 cm 3 cm 3 show the maximum porosity. Clearly, factors enhancing water flow in stony soils, such as the generation of new voids and the change of the fine earth pore structure exert a greater influence on soil hydraulic

8 268 D. Ma et al. / Geoderma 159 (2010) Fig. 5. Influence of rock fragment content (R v ) on the saturated hydraulic conductivity (K s,t ), and comparisons among models relating the saturated hydraulic conductivity (K s,t ) of a stony soil to that of fine earth (K s,fe ). Error bars are standard errors of measured values. Fig. 4. Influence of rock fragment content (R v ) on (a) the air entry suction (h d ), (b) the shape coefficient (n) of the soil water characteristic curve predicted by the IM, and (c) the measured total porosities of stony soils. Error bars are standard errors. conductivity than factors reducing flow, such as the reduction of cross sectional area for water flow and the possible increase of tortuosity induced by rock fragments. The alternating dominance of these opposite factors can be responsible for the fluctuation of the measured saturated hydraulic conductivities with the rock fragment content. As shown in Fig. 5, values estimated from Eq. (22) are the greatest and the closest to the observed saturated hydraulic conductivities, while Eqs. (20), (21) and (23) give lower estimated values than observed. Brakensiek and Rawls (1994) also found that Eq. (22) gave the best estimations of saturated hydraulic conductivities of stony soils. In both Eqs. (22) and (23), the cross sectional area available for water flow is assumed to be directly proportional to the saturated hydraulic conductivity. However, the rock fragments examined by Ravina and Magier (1984) have very low porosity of 0.04 cm 3 cm 3 contrasted to 0.27 cm 3 cm 3 in this paper and thus the rock porosity may explain the discrepancy between the estimations of Eqs. (23) and (22). Eq. (20) was derived for non-porous spherical inclusions (Peck and Watson, 1979) but a perfect contact at the rock fragment fine earth interface was assumed and the reorganization of the fine earth pore structure was not considered. The change of fine earth pore structure and the non-perfect contact between rock fragments and fine earth are responsible for the discrepancy between Eqs. (20) and (23). As well as saturated hydraulic conductivity, air entry suction (h d ) and the exponent m are main parameters determining the unsaturated hydraulic conductivity curve (Eq. (6)). Mehuys et al. (1975) reported that the influence of rock fragments on unsaturated hydraulic conductivity was most important in the low and high suction regions. Given that a linear relationship exists between the parameters m and n, rock fragment content should have the same effect on both of them. This paper considered only disturbed soils. The field situation would be more complex than discussed here. Apart from their direct influence on soil porosity and pore structure, rock fragments may also affect soil structure development processes. For example, rock fragments can serve as a skeleton to resist compaction and provide many opportunities for soil burrowing animals, which may promote soil aggregate development (Ma and Shao, 2008). Rock fragments could force the plant roots to make morphological adaptations (Zwieniecki and Newton, 1995) which may also be an important contributor to soil aggregation. Therefore, further field experiments are required to determine the influence of rock fragments on soil

9 D. Ma et al. / Geoderma 159 (2010) hydraulic properties and to depict more clearly the processes affecting water movement in soils containing rock fragments. 5. Conclusions Few simple and valid methods are available to measure the unsaturated hydraulic properties of soils containing rock fragments. Consequently, it is almost impossible to accurately simulate water or solute transport in these kinds of soils using deterministic models which require explicit hydraulic functions. In this study, the horizontal absorption method proposed by Ma et al. (2009) was tested for determining the hydraulic properties of soils containing rock fragments. Using the estimated parameters, the effects of rock fragments on soil hydraulic properties were also evaluated. The results demonstrate that the Improved Method (IM) can give good estimations of the hydraulic parameters of stony soils as shown with the cumulative infiltration and wetting front advance calculated using the HYDRUS-1D software. Calculated cumulative infiltration and wetting front advance agreed favorably with observed values for soils with rock fragment contents ranging from 0 to 0.35 cm 3 cm 3. For the soil used, an Unimproved Method (UM) with β=1 or β=1.145 predicted the Brooks-Corey model parameters close to those calculated using the IM. All of the important hydraulic parameters of stony soils such as air entry suction, saturated hydraulic conductivity and curve shape coefficients vary with rock fragment content. The soil containing about 0.08 rock fragments displayed greater saturated hydraulic conductivity than the non-stony soil. The observed relationship between saturated hydraulic conductivity and rock fragment content was not well fitted by any of the four methods assessed. These findings suggest that rock fragments should not be treated as non-porous media in all situations. The hydraulic properties of the fine earth could not be approximated to those of soils without rock fragments especially when the fine earth contains great amounts of clay favorable to soil aggregation. Reduction of porosity with increased rock fragment content is one of the most important factors affecting the hydraulic properties of stony soils but other factors may also take effects. For example, existence of rock fragments in field soils may affect the actions of soil animals and microorganisms and the growth of plant roots, all of them affecting the development of soil pore structure. Although further experimental tests are required on the applicability of the horizontal absorption method to stony soils over a wider range of textures, it provides a good tool for studying unsaturated hydraulic properties and thus water and solute movements in soils containing rock fragments. Acknowledgments This work was supported by the National Nature Science Foundation of China (No ), National Basic Research Program of China (No. 2005CB121103), the Knowledge Innovation Program of the Chinese Academy of Sciences (No. kzcx2-yw-406) and the State Key Laboratory Foundation of Soil Erosion and Dryland Farming on the Loess Plateau (No ). We thank two anonymous reviewers and Claude Doussan in INRA for their valuable suggestions and efforts made in improving the quality of the manuscript. References Boulier, J.F., Touma, J., Vauclin, M., Flux-concentration relation-based solution of constant-flux infiltration equation: I. Infiltration into nonuniform initial moisture profiles. Soil Science Society of America Journal 48, Bouwer, H., Rice, R.C., Hydraulic properties of stony vadose zones. Ground Water 22, Brakensiek, D.L., Rawls, W.J., Soil containing rock fragments: effects on infiltration. Catena 23, Brakensiek, D.L., Rawls, W.J., Stephenson, G.R., Determining the saturated hydraulic conductivity of a soil containing rock fragments. Soil Science Society of America Journal 50, Brooks, R.H., Corey, A.T., Hydraulic properties of porous media. Hydrological Paper 3. Colorado State University, Fort Collins, Colorado, pp Brouwer, J., Anderson, H., Water holding capacity of ironstone gravel in a typic plinthoxeralf in southeast Australia. Soil Science Society of America Journal 64, Bruce, R.R., Klute, A., The measurement of soil moisture diffusivity. Soil Science Society of America Journal 20, Buchter, B., Leuenberger, J., Wierenga, P.J., Richard, F., Preparation of large core samples from stony soils. Soil Science Society of America Journal 48, Childs, S.W., Flint, A.L., Physical properties of forest soils containing rock fragments. In: Gessel, S.P., Weetman, G.F., Powers, R.F. (Eds.), Sustained Productivity of Forest Soil. University of British Colombia, Vancouver. Coile, T.S., Moisture content of small stone in soil. Soil Science 75, Cousin, I., Nicoullaud, B., Coutadeur, C., Influence of rock fragments on the water retention and water percolation in a calcareous soil. Catena 53, Fies, J.C., Louvigny, N.D., Chanzy, A., The role of stones in soil water retention. European Journal of Soil Science 53, Fleming, R.L., Black, T.A., Eldridge, N.R., Water content, bulk density, and coarse fragment content measurement in forest soils. Soil Science Society of America Journal 57, Flint, A.L., Childs, S., Development and calibration of an irregular hole bulk density sampler. Soil Science Society of America Journal 48, Green, R.E., Ahuja, L.R., Chong, S.K., Hydraulic conductivity, diffusivity, and sorptivity of unsaturated soils: field methods, In: Klute, A. (Ed.), Methods of soil analysis, 2nd ed. : Part 1. Agronomy Monographs, vol. 9. American Society of Agronomy and Soil Science Society of America, Madision, WI, pp Hanson, C.T., Blevins, R.L., Soil water in coarse fragments. Soil Science Society of America Journal 43, Jones, D.P., Graham, R.C., Water-holding characteristics of weathered granitic rock in chaparral and forest ecosystems. Soil Science Society of America Journal 57, Khaleel, R., Relyea, J., Correcting laboratory-measured moisture retention data for gravels. Water Resources Research 33, Klute, A., Dirksen, C., Hydraulic conductivity and diffusivity: laboratory methods, In: Klute, A. (Ed.), Methods of soil analysis, 2nd ed. : Part 1. Agronomy Monographs, vol. 9. American Society of Agronomy and Soil Science Society of America, Madision, WI, pp Koshi, P.T., Soil-moisture measurement by the neutron method in rocky wildland soils. Soil Science Society of America Journal 30, Kutilek, M., Constant-rainfall infiltration. Journal of Hydrology 45, Ma, D.H., Shao, M.A., Simulating infiltration into stony soils with a dual-porosity model. European Journal of Soil Science 59, Ma, D.H., Wang, Q.J., Shao, M.A., Analytical method for estimating soil hydraulic parameters from horizontal absorption. Soil Science Society of America Journal 73, MathSoft, Mathcad & Reference manual. MathSoft Inc, Cambridge, MA. Mehuys, G.R., Stolzy, L.H., Letey, J., Weeks, L.V., Effect of stones on the hydraulic conductivity of relatively dry desert soils. Soil Science Society of America Journal 39, Peck, A.J., Watson, J.D., Hydraulic conductivity and flow in non-uniform soil. Workshop on Soil Physics and Field Heterogeneity. CSIRO Division of Environmental Mechanics, Canberra, Australia. Philip, J.R., General method of exact solutions of the concentration-dependent diffusion equation. Australian Journal of Physics 13, Philip, J.R., On solving the unsaturated flow equation: I. The flux concentration relation. Soil Science 117, Poesen, J., Lavee, H., Rock fragments in top soils: significance and processes. Catena 23, Ravina, I., Magier, J., Hydraulic conductivity and water retention of clay soils containing coarse fragments. Soil Science Society of America Journal 48, Reinhart, K.G., The problem of stones in soil-moisture measurement. Soil Science Society of America Journal 25, Shao, M.A., Horton, R., Integral method for estimating soil hydraulic properties. Soil Science Society of America Journal 62, Sharma, P.P., Carter, F.S., Halvorson, G.A., Water retention by soils containing coal. Soil Science Society of America Journal 57, Šimůnek, J., van Genuchten, M.T., Šejna, M., The HYDRUS-1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media. Version 3.0, HYDRUS Software Series 1. Department of Environmental Sciences, University of California, Riverside, California, USA. Tokunaga, T.K., Olson, K.R., Wan, J., Moisture characteristics of Hanford gravels: bulk, grain-surface, and intragranular components. Vadose Zone Journal 2, Unger, P.W., Soil profile gravel layers: I. Effect on water storage, distribution, and evaporation. Soil Science Society of America Journal 35, Van Genuchten, M.Th., A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, Wang, Q.J., Horton, R., Shao, M.A., Horizontal infiltration method for determining Brooks Corey model parameters. Soil Science Society of America Journal 66, White, I., Smiles, D.E., Perroux, K.M., Absorption of water by soil: the constant flux boundary condition. Soil Science Society of America Journal 43, Zhu, Y.J., Shao, M.A., Processes of rainfall infiltration and sediment yield in soils. Transactions of the CSAE 22 (2), (In Chinese). Zwieniecki, M.A., Newton, M., Roots growing in rock fissures their morphological adaptation. Plant and Soil 172,