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Published online 16 December 2005
Published in Vadose Zone J 5:35-47 (2005)
DOI: 10.2136/vzj2005.0040
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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ORIGINAL RESEARCH

Saturated and Unsaturated Hydraulic Conductivities and Water Retention Characteristics of Weathered Granitic Bedrock

Shin'ya Katsura*, Ken'ichirou Kosugi, Nobuhiro Yamamoto and Takahisa Mizuyama

Lab. of Erosion Control, Dep. of Forest Science, Graduate School of Agriculture, Kyoto Univ., Kyoto 606-8502, Japan
* Corresponding author (katsura3{at}kais.kyoto-u.ac.jp)

Received 15 March 2005.



   ABSTRACT
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
As a first step toward describing water flow processes in bedrock, we determined the hydraulic properties of three trimmed samples of weathered granitic bedrock (referred to as Samples A, B, and C, in order of size) in the laboratory. Silicone rubber was used to fill the space between each sample and the surrounding cylinder wall, ensuring accurate measurement of hydraulic properties of the samples. All samples showed similar saturated hydraulic conductivity values of 1 x 10–4 cm s–1, with the saturated water flow in all samples obeying Darcy's Law. Unsaturated hydraulic conductivity and water retention functions of Sample A were determined by means of a multistep outflow experiment. Parameters in both functions were optimized by comparing observed and computed cumulative outflow rates. The resulting computed cumulative outflow rates using the optimized parameters showed a good match to the observed cumulative outflow data. Moreover, the derived water retention function agreed closely with the function measured by the pressure plate method. We conclude that the methods proposed in this study are effective for determining the hydraulic properties of weathered bedrock. The bedrock water retention curve exhibited small changes in volumetric water content throughout the measurement range where the pressure head, {psi}, was greater than –200 cm. The bedrock hydraulic conductivity function showed a small decrease in hydraulic conductivity in the very wet range of {psi} greater than –30 cm, and then declined gradually with decreasing {psi}.


   INTRODUCTION
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
RECENT RESEARCH in hillslope hydrology suggests that rainwater does percolate into bedrock, which had been conventionally treated as an impermeable layer, and that bedrock groundwater can influence both the water balance and material balance in headwater catchments. Terajima and Moroto (1990) and Onodera (1991) demonstrated bedrock groundwater flow during and after rainfall events by tensiometric and piezometric observations. Tracer experiments have also detected groundwater flow in bedrock (Noguchi et al., 1999; Frazier et al., 2002). Terajima et al. (1993) examined the water balance in two small catchments in granitic mountain areas, and demonstrated that at least 18% of annual precipitation percolated into bedrock. Groundwater that had infiltrated into bedrock then discharged very slowly, sustaining base flow (Mulholland, 1993; Burns et al., 1998). More recently, both sprinkling experiments performed at the CB1 catchment in Oregon (Montgomery et al., 1997; Anderson et al., 1997a, 1997b; Montgomery et al., 2002) and detailed hydrological, hydrochemical, and thermal measurements conducted at the Fudoji catchment in central Japan (Uchida et al., 2003a, 2003b; Asano et al., 2003, 2004) have shown that it is essential to take into account the contribution of bedrock groundwater to runoff generation and water chemistry in headwater catchments. Many researchers have also pointed out that bedrock groundwater flow plays a significant role in the occurrence of landslides (e.g., Everett, 1979; Wilson and Dietrich, 1987; Onda et al., 1999; Kato et al., 2000; Montgomery et al., 2002).

Although these studies have emphasized the importance of bedrock groundwater in headwater catchments, most have made no reference to the physical processes of bedrock groundwater movement based on the hydraulic properties of bedrock. The studies have addressed the phenomena occurring in headwater catchments and sometimes provided credible explanations, but few have numerically analyzed the water movement processes in bedrock that give rise to those phenomena. To evaluate the effect of bedrock groundwater on runoff generation and water chemistry, and to predict timing and locations of landslide occurrences, physical descriptions of water movement processes in bedrock are needed. These descriptions in turn require information on the hydraulic properties of bedrock such as saturated and unsaturated hydraulic conductivities and water retention.

Many recent environmental problems (e.g., oil and natural gas recovery, successful design of facilities for radioactive wastes disposal, and effective operation of geological CO2 storage) motivated the development of new techniques to measure the fluid flow properties in tight rock samples to assess and predict fluid flow in deep rock layers. For example, the transient-pulse method, introduced by Brace et al. (1968), is a well-established and widely conducted technique to determine the permeability of rock samples (e.g., Hsieh et al., 1981; Trimmer, 1982; Zhang et al., 2000). Gas is often used for measuring fluid transport properties in rocks since the viscosity of gas is much less than that of water (e.g., Lin et al., 1986; Finsterle and Persoff, 1997; Takeda et al., 2000). Lin et al. (1999) used the mercury intrusion porosimetry, which is an established technique in the petroleum industry, for predicting the permeability of tight rocks by evaluating pore radii distribution in them. Whereas these techniques are successfully conducted for materials with very low porosity (typically <10%) and permeability (10–15 to 10–7 cm s–1), it is questionable whether they are applicable for highly weathered bedrock, which is located just below the soil layer and contributes to hydrological processes in headwater catchments. For measuring the hydraulic properties of weathered bedrock, accepted soil physics methods can be more reasonable.

Among the hydraulic properties of weathered bedrock, the saturated hydraulic conductivity, Ks, was measured in situ in several earlier studies. Megahan and Clayton (1986) reported that the granitic bedrock that had weathered to different degrees in the Idaho batholiths had in situ Ks values varying from 0 to 2.0 x 10–3 cm s–1. Montgomery et al. (2002) conducted falling-head tests on piezometers installed in fractured Eocene sandstone and saprolite underlying the CB1 catchment and obtained Ks values ranging from 10–6 to 10–1 cm s–1. These in situ Ks values, however, essentially involve uncertainty in the boundary conditions and their effects on the measurements. On the other hand, the difficulty of taking undisturbed weathered bedrock samples has limited the number of studies on the laboratory Ks values of weathered bedrock (Ohta, 1990; Yoshinaga and Ohnuki, 1992; Johnson-Maynard et al., 1994; Flint, 2003). More knowledge of the Ks values, measured accurately under well-defined boundary conditions, is needed, since this is the most fundamental hydraulic parameter for characterizing the water dynamics in bedrock.

Besides the saturated hydraulic conductivity, unsaturated hydraulic properties are important when water flow in bedrock occurs under unsaturated conditions (e.g., Flint et al., 2003). The requirement is for unsaturated hydraulic properties consisting of water retention and unsaturated hydraulic conductivity curves. The former represents the water storage capacity of bedrock, and the latter characterizes the flow magnitude in unsaturated bedrock.

Because intact weathered bedrock samples are difficult to collect, less is known about the water retention characteristics of weathered bedrock than the saturated hydraulic conductivity. Weathered bedrock can serve as a rooting medium for plants (e.g., Hellmers et al., 1955; Zwieniecki and Newton, 1994; Sternberg et al., 1996), and studies on water retention of weathered bedrock have been conducted for the purpose of evaluating plant-available water capacity (Jones and Graham, 1993; Anderson et al., 1995). These studies did not focus on water movement in bedrock but rather plant-available water capacity, and often omitted detailed data in the very wet range. Flint (2003) developed a database of the water retention characteristics of many volcanic rock samples, for which there is also only scant information on the wet range. Johnson-Maynard et al. (1994) measured water retention of weathered granite in addition to saturated hydraulic conductivity, but they showed only effective pore size distributions of weathered granitic rock determined from the water retention data. The water retention curve of bedrock including weathered granite, describing the wet range in particular, is required to elucidate storm runoff processes in headwater catchments.

Much less is known about unsaturated hydraulic conductivity of bedrock. None of the conventional methods of measuring unsaturated hydraulic conductivity of soils, such as the steady-state head-control method and the instantaneous profile method, are readily applicable to weathered bedrock, since they require the insertion of tensiometers into samples. Therefore, the inverse method, which estimates unsaturated hydraulic conductivity by comparing numerical solutions of the Richards equation with readily measurable data such as the drainage hydrograph, can be an effective tool. While the inverse method has been intensively studied for the determination of soil hydraulic properties (van Genuchten et al., 1999), it has rarely been applied to bedrock.

Moreover, although the entire set of saturated and unsaturated conductivities and water retention characteristics is indispensable for simulating saturated–unsaturated water movement in bedrock, previous studies have not supplied the complete set of measurements for the same bedrock sample.

The objective of this study was to determine the saturated and unsaturated hydraulic conductivities and water retention of weathered granitic bedrock by using accepted soil physics methods as a first step toward clarifying the physical processes of water movement in bedrock. We determined these hydraulic properties in the laboratory under well-defined boundary conditions. The unsaturated hydraulic conductivity and water retention functions were determined by the inverse method, and the performance of the method is discussed on the basis of an examination of solution uniqueness and a comparison with water retention data observed by the conventional steady-state method.


   MATERIALS AND METHODS
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Study Site and Hydrological Observations
Bedrock samples were taken from the Kiryu experimental basin (5.99 ha) in Shiga Prefecture, central Japan (34.58° N, 136.00° E) (Fig. 1 ). The mean annual air temperature was 13.6°C (1997–2004), with the highest average monthly temperature (24.9°C) in August and the lowest (2.9°C) in January. The mean annual precipitation was 1645.4 mm (1972–2004), most of which fell as rain. Annual evapotranspiration in the Kiryu experimental basin ranged from 609.4 to 944.0 mm, equivalent to 35.4 to 65.6% of the annual precipitation (1972–2003).



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  		Fig. 1. Topography of the Akakabe catchment (right). The bedrock sampling point and locations of hydrological observations are also shown. The map of the Akakabe catchment has a contour interval of 1 m. A and B in the map correspond to those in Fig. 2.

 


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  		Fig. 2. Longitudinal section of the hillslope plot and the results of the cone penetration tests. A and B correspond to those in Fig. 1.

 
The Akakabe catchment, located in the southeastern part of the Kiryu experimental basin, was chosen for this study (Fig. 1). The catchment has an area of 0.086 ha and a mean gradient of 22.0°; it is predominantly covered with Japanese cypress [Chamaecyparis obtusa (Siebold & Zucc.) Siebold & Zucc. ex Endl.] planted in 1959. The catchment is underlain by granitic bedrock. The granite underlying the study site is called Tanakami Granite (Collaborative Research Group for the Granites around Lake Biwa, 2000), which has a primary mineral composition that mainly consists of quartz, alkali feldspars, plagioclase feldspars, and biotite (Torii, 1996).

We delineated a hillslope plot in the northeastern part of this catchment (Fig. 1) and conducted detailed hydrological observations there. The soil depth to bedrock in this plot was determined using a cone-penetrometer with a cone diameter of 30 mm, a weight of 5 kg, and a fall distance of 50 cm. The results of the cone penetration tests along the hollow in the plot are shown in Fig. 2 . The Nc value in Fig. 2 denotes the number of blows required for a 10-cm penetration. Many previous studies have suggested that bedrock be defined as the layer with Nc exceeding 50 for granitic regions (Okunishi and Iida, 1978; Okimura and Tanaka, 1980; Mochiduki and Matsumoto, 1986); we also adopted this definition. Soil depth to bedrock in the plot was determined as ranging from 20 to 126 cm, averaging 70 cm (Katsuyama et al., 2004).

We excavated a trench to the bedrock surface by removing the soil layers at the plot outlet (Figs. 1 and 2) and monitored the occurrence of saturated lateral flow generated on the soil–bedrock interface. The rate of the saturated lateral flow (referred to hereafter as "plot runoff") was measured with a tipping bucket. The plot runoff consisted entirely of saturated water flow from the soil layers.

We also monitored the volumetric water content profile from the soil through the bedrock at a point indicated by a blue circle in Fig. 1. The soil depth at this point was approximately 50 cm. Profile moisture sensors (EasyAG, Sentek, Stepney, SA, Australia) were installed in the soil layer to monitor soil moisture at depths of 10, 20, 30, and 40 cm from the ground surface. Coil-type TDR probes (made by the authors) were installed in the bedrock to monitor bedrock moisture at depths of 3, 7, and 11 cm from the bedrock surface. These sensors and probes were installed carefully so that water flow along the walls of the sensors and probes was inhibited. The observations continued from June 2003 to June 2004, and the sensors and probes were subsequently calibrated individually in the laboratory.

Sample Collection and Preparation
The bedrock sampling point was located just below the trench excavated for plot runoff measurement (Fig. 1). Figure 3 shows the correspondence between the Nc value and the photograph of the soil–bedrock profile observed at a pit dug for bedrock sampling. The Nc value at the sampling point sharply increased to more than 50 at a depth of approximately 35 cm. According to the definition of bedrock given above, a layer with Nc value exceeding 50 was considered the bedrock. The depth of 35 cm at the sampling point corresponded to the soil–bedrock interface that could be recognized relatively clearly by visual estimation. The {square} surface of the bedrock was not sufficiently weathered to be considered saprolite and could be crushed into small fragments with bare hands while it retained rock fabric and structure.



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  		Fig. 3. Change of the Nc value with depth at the bedrock sampling point (left), corresponding to the photograph around the soil–bedrock interface (right).

 
A mass of weathered granitic bedrock (approximately 20 cm in diameter and 15 cm in height) was dug out using a combination of a handsaw and an electric drill to achieve minimum sample disturbance. In the laboratory, three bedrock samples were separated from the collected mass of bedrock. Each sample was trimmed into a column with the same cross-sectional area throughout. These trimmed bedrock samples are referred to as Samples A, B, and C, in order of size (Table 1). Samples A and B were individually placed in the center of PVC cylinders that were approximately 20 and 50% higher and 27 and 31% larger in diameter than the samples, respectively. Sample C was placed in the center of a stainless-steel cylinder with the same height and a 35% larger diameter than the sample. Liquid silicone rubber (TSE350, GE Toshiba Silicones, Tokyo, Japan) was then poured into the space between each bedrock sample and the cylinder wall to the top of the bedrock sample (Fig. 4 ). After 1 d, when solidification of the liquid silicone rubber was complete, any silicone rubber adhering to the bottom of the samples was removed. Because infiltration of the silicone rubber into pores of the bedrock samples was not observed, and the solidified silicone rubber does not allow water to pass through it, accurate measurement of hydraulic properties of the bedrock samples was ensured.


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  		Table 1. Outline and the Ks value of each sample.

 


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  		Fig. 4. Photographs of bedrock Samples A, B, and C. Silicone rubber filled the space between each sample and the surrounding cylinder walls.

 
Saturated Hydraulic Conductivity Test
Samples A, B, and C were gradually (over 72 h) saturated with water from the bottom up to minimize air entrapment.

The constant-head tests (Reynolds et al., 2002) were conducted on Samples A and B. We applied various hydraulic gradients to the samples and measured the outflow rate when a steady state was established. The relationship between the hydraulic gradient and the water flux was then examined to evaluate the applicability of Darcy's Law and to calculate the values of saturated hydraulic conductivity, Ks.

The falling-head test (Reynolds et al., 2002) was conducted on Sample C. The time (ti) for the water level to fall from the initial water level (h0 = 11.7 cm) to the predetermined water levels (hi) was recorded (i = 1 to 4). To evaluate the applicability of Darcy's Law and calculate the Ks value, the following equation, derived theoretically from Darcy's Law (Reynolds et al., 2002), was applied to the observed data:

[1]
where t is the time, h is the water level, a is the cross-sectional area of the falling-head standpipe (0.5 cm2), and S and L are the cross-sectional area (11.0 cm2) and height (5.0 cm) of Sample C, respectively. The value of Ks was optimized by minimizing the residual sum of squares, RSS, defined as follows:

[2]
By examining how well the water level curve obtained from Eq. [1] fit the observed water levels, we tested the applicability of Darcy's Law to the saturated water flow occurring in Sample C.

Water Retention Test
The water retention test was conducted on Sample A by the pressure plate method (Dane and Hopmans, 2002). After being fully saturated over 72 h, Sample A was placed on a previously saturated, porous ceramic plate (0675B0.5M2, Soilmoisture Equipment, Santa Barbara, CA). The porous plate was 0.9 cm thick, with an air-entry value of 50 kPa ({approx}510 cm) and a saturated hydraulic conductivity of 3 x 10–5 cm s–1. Because there were spaces between the bottom of the bedrock Sample A and the porous plate, saturated quartz sand (0.17–0.32 mm in diameter) was used to fill the space, ensuring continuous water movement from the sample to the porous plate. We measured the water retention characteristics of the combination of the bedrock sample and the quartz sand by setting the air pressure at 10, 20, 50, 90, and 200 cm. The measured data were corrected to obtain the water retention characteristics of the bedrock sample by using an independently measured water retention curve of pure quartz sand (Fig. 5 ).



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  		Fig. 5. Water retention curves of pure quartz sand.

 
In addition, the water retention characteristics of the soil samples (100 mL) taken from depths of 15 and 30 cm from the ground surface at the bedrock sampling point were measured by the pressure plate method for comparison with the bedrock.

Multistep Outflow Experiment
After the water retention test, Sample A was brought back to complete saturation by soaking in water for 72 h. It was again placed on the previously saturated porous plate, and the same saturated quartz sand as used for the water retention test was applied between the sample and the porous plate to ensure continuous water movement from the sample to the porous plate. The sample was then placed in a pressure chamber. The bottom of the porous plate was sealed and connected to the outside of the chamber by tubing. The water dropping point (i.e., the outlet of the tubing) was fixed 3.75 cm below the bottom of the porous plate (Fig. 6 ). This outlet was fed into a container on a digital balance for measurement of outflow. The container was placed so that water drained at atmospheric pressure, and it was loosely covered with plastic film to prevent evaporation.



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  		Fig. 6. Equipment for the multistep outflow experiment.

 
After the tubing was filled with water and the pressure chamber was closed, the chamber was left until the discharge from the tubing stopped. With this initial condition, air pressure (20 cm) was applied to the surface of Sample A, and the cumulative outflow drained from the bedrock sample coupled with the quartz sand was measured. Once the outflow had nearly stopped, the air pressure was raised to the next step. This procedure was repeated for four steps of applied air pressure: 20, 50, 90, and 200 cm. Measurement of the cumulative outflow was continued throughout the experiment (Hopmans et al., 2002).

To describe water movement in Sample A and the quartz sand during the experiment, the one-dimensional vertical flow equation (Richards equation) was applied. This equation can be expressed as follows:

[3]
where t is time, z is the vertical distance taken positive upward, C({psi}) = d{theta}/d{psi} is the water-capacity function, {theta} is the volumetric water content, {psi} is the pressure head, and K({psi}) is the hydraulic conductivity function. Equation [3] can be solved if hydraulic properties C({psi}) and K({psi}) are given, and the initial and boundary conditions are specified.

Kosugi (1996) developed the following model equation for water retention by assuming the pore radii to be lognormally distributed:

[4]
where Se represents the effective saturation, {theta}s and {theta}r are the saturated and residual volumetric water contents, respectively, {psi}m is the pressure head at Se = 0.5, {sigma} is a dimensionless parameter characterizing the width of the pore-size distribution, and Q is the complementary normal distribution function defined as

[5]

By differentiating Eq. [4], the following water-capacity function was obtained:

[6]

Kosugi (1996) derived the unsaturated hydraulic conductivity function by combining Eq. [4] with Mualem's (1976) model:

[7]
where Ks is the saturated hydraulic conductivity.

The water retention and hydraulic conductivity functions expressed by Eq. [4] and [7] adequately describe the observed hydraulic properties of many kinds of soils (Kosugi, 1996). We assumed that the hydraulic properties of Sample A and the quartz sand could also be described by Eq. [4] and [7].

Using Eq. [3], [6], and [7], the one-dimensional vertical flow in bedrock Sample A and the quartz sand during the experiment was calculated. Four parameters, {theta}s – {theta}r, {psi}m, {sigma}, and Ks, are required to characterize their hydraulic properties. Fitting the model Eq. [4] to the water retention curves of pure quartz sand measured individually by the pressure plate method (Fig. 5) yielded the parameters of {theta}s – {theta}r = 0.392, {psi}m = –63.7 cm, and {sigma} = 0.33. The value of Ks of the same pure quartz sand (1.3 x 10–2 cm s–1) was measured by the falling-head test. Sample A's Ks was held at the value measured by the method described above, and the remaining parameters (i.e., {theta}s – {theta}r, {psi}m, and {sigma}) of Sample A were treated as parameters to be fitted.

These three parameters were obtained by minimizing the residual sum of squares (RSS):

[8]
where Qobs,i is the cumulative outflow observed at t = Tobs,i, Qcal,i is the cumulative outflow at t = Tobs,i calculated from Eq. [3], [6], and [7], and n is the number of observations. To compute Qcal,i, Eq. [3] was numerically solved using a fully implicit finite difference scheme with equally spaced nodes (element lengths 0.3 cm) and a variable time step of 1 to 10 s.

Since only the difference {theta}s – {theta}r was obtained from the optimization, the individual values of {theta}s and {theta}r to describe the water retention curve of Sample A were unknown. Their separate values were determined by requiring that the derived water retention curve produced the same volumetric water content at {psi} = –210.65 cm as the measured water retention curve (the result of the water retention test for bedrock Sample A discussed above).


   RESULTS
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Hydrological Observations
Figure 7 shows the relationship between the total rainfall and the total storm runoff from the hillslope plot for individual rainfall events. Because the plot runoff occurred only during rainfall events, the total storm runoff is equivalent to the whole discharge from the hillslope plot. Since the annual evapotranspiration in the Kiryu experimental basin ranges from 35.4 to 65.6% of the annual rainfall, the annual discharge should be 34.4 to 64.6% of the annual rainfall. However, the figure demonstrates that the total storm runoff was always less than about 5% of the total rainfall. The extremely small runoff ratio observed at the trench of the hillslope plot suggests a large amount of infiltration into the weathered bedrock.



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  		Fig. 7. Relationship between the total rainfall and the total storm runoff from the hillslope plot.

 
The results of the bedrock volumetric water content measurements provided evidence of rainwater infiltration into the bedrock. The temporal variations in volumetric water content during the largest rainfall event (total rainfall 160.6 mm) are shown in Fig. 8a . The event produced a rise in the volumetric water content from the shallower soil layer to the deeper bedrock layer. During a small rainfall event (total rainfall 18.3 mm, Fig. 8b), the volumetric water content again rose from the shallow layer progressively with depth, but the increment in the volumetric water content was reduced as the depth increased. Consequently, the deeper bedrock layers (7 and 11 cm from the soil–bedrock interface) showed little response to rainfall. Thus, rainwater does infiltrate from the soil surface progressively with depth into the bedrock, and unsaturated water flow in the bedrock is very important for hydrological processes in the Akakabe catchment.



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  		Fig. 8. Temporal variations in volumetric water content for (a) the largest rainfall event and (b) a small rainfall event.

 
Saturated Hydraulic Conductivity and Water Retention Tests
Figure 9 indicates that water flux was proportional to the hydraulic gradient for both Samples A and B, suggesting that Darcy's Law can be applied to the saturated water flow occurring in both samples. The saturated hydraulic conductivity of Samples A and B, computed as the slopes of the regression lines in Fig. 9, were 9.7 x 10–5 and 9.5 x 10–5 cm s–1, respectively (Table 1).



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  		Fig. 9. Results of the constant-head tests for measuring the saturated hydraulic conductivities of Samples A and B.

 
The result of the saturated hydraulic conductivity test for Sample C is shown in Fig. 10 . The value of Ks = 1.2 x 10–4 cm s–1 is the parameter value that best relates the calculated water level to that observed, and the agreement between them was satisfactory. This indicates that the saturated water flow occurring in Sample C obeyed Darcy's Law with a saturated hydraulic conductivity of 1.2 x 10–4 cm s–1 (Table 1). When the values of Ks = 9.7 x 10–5 cm s–1 and Ks = 9.5 x 10–5 cm s–1 (i.e., the Ks from Samples A and B, respectively) are applied to Eq. [1], the calculated water level drops slightly slower than the observed and calculated water levels. On the other hand, the value of Ks = 2.4 x 10–4 cm s–1, which is twice as large as the optimal value, produces a much quicker fall of the calculated water level than that observed, whereas the value of Ks 6.0 x 10–5 cm s–1, which is half as large as the optimal value, generates too slow a fall of the calculated water level. These analyses suggest that this method of determining the Ks value produces a remarkably small error in the determined Ks value, which emphasizes the fairly small difference in the Ks value between the samples.



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  		Fig. 10. Result of the falling-head test for measuring the saturated hydraulic conductivity of Sample C. Water level curves generated by various Ks values are also shown.

 
The measured water retention curve of bedrock Sample A is shown by the brown circles in Fig. 11 . The curve exhibits a very gentle decline in volumetric water content with decreasing pressure head, displaying small water capacity values for the measured range of pressure head.



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  		Fig. 11. Water retention curves of Sample A (measured and estimated), soils (15 and 30 cm), and weathered granite measured by Jones and Graham (1993; their WC5 and WC6).

 
Multistep Outflow Experiment to Obtain Unsaturated Hydraulic Properties
We used 94 representative data values of the observed cumulative outflow (Qobs,i) for the parameter optimization runs (i.e., n = 94), which resulted in {theta}s – {theta}r = 0.073, {psi}m = –39.8 cm, and {sigma} = 0.45. We obtained excellent agreement between the observed and computed cumulative outflow values using these optimized parameters (Fig. 12 ).



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  		Fig. 12. Observed cumulative outflow and that calculated by optimization during the multistep outflow experiment.

 
The uniqueness of the solution from the optimization runs is examined in Fig. 13 . Figure 13A shows contour lines of RSS on a coordinate system with {psi}m on the abscissa and {sigma} on the ordinate for the fixed value of {theta}s – {theta}r = 0.073. Likewise, Fig. 13B shows {theta}s – {theta}r on the abscissa and {sigma} on the ordinate for the fixed value of {psi}m = –39.8 cm, and Fig. 13C has {theta}s – {theta}r on the abscissa and {psi}m on the ordinate for the fixed value of {sigma} = 0.45. In these figures, the {theta}s – {theta}r, {psi}m, and {sigma} domains were discretized into 9, 21, and 19 discrete points, respectively. All figures show well-defined global minima. Detailed contour lines of RSS around the optimized values of each parameter are shown in Fig. 13a through 13c, where {theta}s – {theta}r, {psi}m, and {sigma} domains were discretized into 11, 21, and 11 discrete points, respectively. All figures again show well-defined global minima, which correspond to the optimized values of each parameter.



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  		Fig. 13. Contour lines of RSS comparing the observed vs. computed cumulative outflow for the multistep outflow experiment. Pluses indicate the optimized parameter values.

 
The estimated water retention function of bedrock Sample A using model Eq. [4] with the optimized parameters is shown in Fig. 11. As described in Materials and Methods, the observed value of {theta} = 0.275 at {psi} = –210.65 cm was used as the point at which the estimated and measured water retention curves were to be matched. The estimated water retention curve adequately reproduced the measured curve, and both exhibited small change in volumetric water content throughout the measured range of pressure head.

The estimated hydraulic conductivity function of bedrock Sample A using model Eq. [7] with the optimized parameters is shown in Fig. 14 . The saturated hydraulic conductivity is relatively low (9.7 x 10–5 cm s–1), but does not drop sharply, especially in the very wet range, gradually decreasing to about 10–15 cm s–1 at {psi} = –200 cm.



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  		Fig. 14. Hydraulic conductivity curves of Sample A (estimated) and the soils collected in (a) the Kiryu experimental basin and (b) the Aichi experiment forest.

 

   DISCUSSION
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
Usefulness of the Inverse Method to Determine Hydraulic Properties of Bedrock
The calculated cumulative outflow using the optimized parameters resulted in a good match to the observed cumulative outflow (Fig. 12), suggesting that model Eq. [4] and [7] can be applied to the hydraulic properties of both the bedrock sample and the quartz sand and that the Richards equation can successfully describe unsaturated water flow during the experiment. In addition, the water retention function of Sample A derived from the inverse method displays good agreement with the water retention curve measured by the pressure plate method (Fig. 11). Hence we conclude that the inverse method is a very effective technique to determine the hydraulic properties of highly weathered bedrock. It should be noted that, for using the proposed outflow technique for weakly weathered bedrock samples with lower permeability, more accurate measurement of the cumulative outflow and application of higher air pressure would be required.

Comparison Between Soil and Bedrock Hydraulic Properties
Figure 11 shows water retention curves of the soils overlying the bedrock measured by the pressure plate method. The bedrock has a much smaller value of the saturated volumetric water content than the soils, but the decrease in volumetric water content with decreasing pressure head is less for the bedrock than for the soils, particularly in the wet range ({psi} > –50 cm). Consequently, the volumetric water content of the bedrock is about 10% higher than that of the soils at {psi} = –200 cm.

Figure 14 also includes soil hydraulic conductivity curves for comparison with the estimated bedrock hydraulic conductivity curve. Hydraulic conductivity curves measured for soil samples (100 mL) collected from depths of 5, 15, 25, and 35 cm from the ground surface in a catchment adjacent to the Akakabe catchment by the steady-state head-control method (Hendrayanto, 2005, personal communication) are shown in Fig. 14a. To supplement the lack of data in the dry range ({psi} < –60 cm), we also show hydraulic conductivity curves measured by the steady-state head-control method for soil samples (100 mL) collected from depths of 40, 70, and 100 cm from the ground surface in the Aichi experiment forest in central Japan (Shinomiya, 2005, personal communication), where the parent materials are also weathered granite (Fig. 14b). These hydraulic conductivity curves show a tendency similar to the water retention curves in the wet range. Although the saturated hydraulic conductivity value of the bedrock is three orders of magnitude less than those of the soils, the soils exhibit a steep decline in hydraulic conductivity in the very wet range, resulting in similar values of the hydraulic conductivity between the bedrock and the soils in the range of –50 < {psi} < –30 cm. However, the hydraulic conductivity of the soils does not drop as sharply as that of the bedrock in the dry range of {psi} < –50 cm. Hence, the hydraulic conductivity value of the soils is again larger than that of the bedrock by several orders of magnitude in the dry range.

Figures 11 and 14 provide an indication of pore radii distribution in the bedrock and the soils. The larger values of the saturated volumetric water content and saturated hydraulic conductivity of the soils are due to more pores in the soils than in the bedrock. From the steep decrease in volumetric water content and hydraulic conductivity of the soils in the very wet range (–50 < {psi} < 0 cm), it follows that most of the pores in the soils are relatively large, whereas the bedrock contains few fractures. On the other hand, the lower hydraulic conductivity (Fig. 14b) of the bedrock in the dry range ({psi} < –50 cm), despite higher volumetric water content (Fig. 11), implies that the bedrock contains more micropores, most of which, however, do not contribute to water movement.

Comparison with Hydraulic Properties of Weathered Granitic Bedrock in Other Sites
The Ks values of weathered granitic bedrock measured in previous studies are summarized in Fig. 15 . The bedrock samples whose Ks values are shown in Fig. 15 have similar characteristics to those of the bedrock at our site; that is, they can easily be crushed into small fragments while retaining rock fabric and structure. Note that Fig. 15 includes Ks values measured both in the laboratory and in situ. The Ks value measured in this study lies in the lowest range, reflecting less contribution of fractures to saturated water flow. Figure 15 also shows no apparent relationship between the porosity and the Ks value, indicating that it is impossible to predict the Ks value from the porosity, probably because pore volume and pore shape and continuity have important effects on the Ks value. In addition, bedrock may include micropores that do not contribute to water movement, as discussed in the section above. It is possible that the ratio between open and closed micropores also affects the Ks value.



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  		Fig. 15. Relationship between the Ks value and the porosity of weathered granitic bedrock measured in various sites (Johnson-Maynard et al., 1994; Graham et al., 1997; Frazier et al., 2002). {dagger} Measured in the laboratory. {ddagger} Measured in situ. § Final infiltration rate is regarded as the Ks value. ¶ {theta}s substituted for the porosity.

 
Next we compare the water retention characteristics of weathered granitic bedrock. Jones and Graham (1993) measured water retention of granitic bedrock weathered to various degrees; their results for bedrock samples (WC5 and WC6) that had very similar structural characteristics to those of our bedrock are shown in Fig. 11. Compared with WC5 and WC6, our Sample A holds more water over the range of pressure head measured in this study, but the water retention curves are nearly parallel to each other. In other words, WC5, WC6, and Sample A have comparable water capacities in the range of {psi} > –200 cm. This is of great importance in describing water movement processes in bedrock because it is not the water retention curve itself but the water-capacity function that controls unsaturated water movement, as indicated by Eq. [3]. The difference in absolute values of volumetric water content may result from the difference in the volume of micropores that do not contribute to water movement. The similarity in shapes of the water-capacity function of bedrock samples taken from different sites suggests the possibility that similar characteristics of weathered granitic bedrock can lead to similar water storage capacity regardless of the relatively large variation in the Ks values.

Importance of Bedrock Hydraulic Properties in Storm Runoff
Figure 16 suggests the importance of determining hydraulic properties of the bedrock to clarify the hydrological processes at our study site. As shown in Fig. 7, we did not observe the plot runoff for some rainfall events. Figure 16 shows the relationship between the cumulative rainfall and the maximum 1-h rainfall intensity before plot runoff was observed. For each of the rainfall events that did not produce plot runoff (indicated by the blue circles), the x- and y-axes represent the total rainfall and the maximum 1-h rainfall intensity during the whole rainfall event. The figure shows that the plot runoff was not generated when the cumulative rainfall was <3.2 mm, but was always generated when the cumulative rainfall was >10 mm. In the region where the cumulative rainfall was >3.2 mm and <10 mm, the cumulative rainfall could not explain the generation of plot runoff. In this region, it seems that the maximum 1-h rainfall intensity is a better indicator of whether plot runoff occurred. That is, the maximum rainfall intensity of 3.6 mm h–1 seems to be the threshold for the occurrence of plot runoff. The intensity of 3.6 mm h–1 is equivalent to 1 x 10–4 cm s–1, which corresponds to the Ks value of the bedrock samples measured in this study. This indicates that bedrock permeability controlled the storm runoff processes, and that rainfall intensity greater than the Ks value of the bedrock was required for plot runoff generation. In this discussion, we have neglected water storage by unsaturated soil layer and assumed that the water infiltration rate at the soil–bedrock interface was similar to the rainfall intensity. The assumption is based on the small soil thickness ({approx}20 cm) around the trench as shown in Fig. 2, which results in a small water storage capacity of the soil layer that makes the infiltration rate similar to the rainfall intensity after some continuation of rainfall. Thus, the simple comparison between bedrock permeability and the rainfall intensity would explain the occurrence of the plot runoff. For more detailed analyses of the discharge rate and trench hydrograph formation, this simplified discussion would have to be supplemented by two- or three-dimensional numerical evaluation of unsaturated water movement in soil and bedrock layers. Nevertheless, Fig. 16 does imply the importance of the hydraulic properties of bedrock for describing storm runoff processes in headwater catchments underlain by weathered bedrock.



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  		Fig. 16. Relationship between the maximum 1-h rainfall intensity and cumulative rainfall before the plot runoff was observed.

 

   CONCLUSIONS
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
As a first step toward understanding the physical processes of water movement in bedrock, the hydraulic properties of weathered granitic bedrock were determined in the laboratory. Three trimmed samples (referred to as Samples A, B, and C, in order of size) were excavated from a mass of weathered granite in the Kiryu experimental basin, central Japan. Silicone rubber was used to fill the space between each bedrock sample and the surrounding cylinder wall, ensuring accurate measurement of hydraulic properties of the bedrock samples.

To measure saturated hydraulic conductivity, constant-head tests were conducted for Samples A and B, and a falling-head test was conducted for Sample C. All bedrock samples had very similar saturated hydraulic conductivity values of 1 x 10–4 cm s–1 (the average was 1.0 x 10–4 cm s–1 with a standard deviation of 1.4 x 10–5 cm s–1), and we confirmed that Darcy's Law can be applied to the saturated water flow occurring in all samples.

Unsaturated hydraulic conductivity and water retention functions of Sample A were determined by a multistep outflow experiment. Parameters of both functions were optimized by comparing the observed versus computed cumulative outflow. The cumulative outflow computed using the optimized parameters showed good agreement with the observed cumulative outflow, indicating that the model equations based on the lognormal pore-size distribution (i.e., Eq. [4] and [7]) can be applied to hydraulic properties of bedrock and that the Richards equation can successfully describe the unsaturated water flow during the experiment.

The derived bedrock water retention function compared well with that measured by the pressure plate method. Both curves exhibited small change in volumetric water content throughout the measured range of {psi} > –200 cm, while volumetric water content of the soil layer overlying the bedrock sharply decreased in the wet range ({psi} > –50 cm). The derived bedrock hydraulic conductivity function showed a much smaller decrease in hydraulic conductivity in the very wet range ({psi} > –30 cm) than that of the soil layer. In the dry range ({psi} < –50 cm), the bedrock had higher volumetric water content and lower hydraulic conductivity than the soils.

In this study, we successfully determined hydraulic properties of weathered granitic bedrock. The method used has the potential to elucidate the hydraulic properties of various kinds of weathered bedrock. Spatial variability and vertical distribution of hydraulic properties of bedrock in the study site should be investigated next to describe water movement processes in bedrock; this will make it possible to evaluate the roles of bedrock in runoff generation, water chemistry, and landslide occurrence in headwater catchments.


   ACKNOWLEDGMENTS
 
The authors wish to thank two anonymous reviewers for their helpful comments. This research was partly supported by a grant from the Fund of Monbusho for Scientific Research (16780114).


   REFERENCES
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 





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