Variably Saturated Water Flow Across Soil-Bedrock Interface on Conceptual Hillslopes
Huade Guan and John L. Wilson, Earth and Environmental Science, New Mexico Institute of Mining & Technology
Introduction
Groundwater hydrologists commonly consider and study the contribution of mountains to groundwater
basin recharge at the mountain-front, while hillslope hydrologists often only focus on the thin soil layer
above the bedrock surface. At mountain hillslopes, few studies have examined the partitioning of water
between shallow processes (ET, interflow, etc) and deep percolation to the mountain block (Figure 1). Very
often, vertical water movement across the soil bedrock interface is neglected either based on the estimated
low bedrock permeability or the low permeable soil layer present on the bedrock surface. However, at least
in some cases, the mountain bedrock carries a significant amount of water to adjacent basins (Tiedeman et
al., 1998; Maurer and Berger, 1997). Variably saturated numerical simulations are conducted on conceptual
hillslopes (Figure 2) to help understand how water partitions at the soil-bedrock interface.
Results
Each of four depression types (Figure 5) was applied at three 10-meter intervals (40-50,
60-70, 80-90m) on a hillslopes (slope=0.3). Two different depression magnitudes were employed
for Step, V-notch, and Trough types.
1. Bedrock permeability threshold
The steady state simulations (Figure 6) inform a
permeability threshold between 1.0E-16 and 1.0E-17 m^2
above which percolation into bedrock becomes significant.
This value is lower than most reported permeability of
fractured rocks, but larger than those of crystalline rocks
without fractures. For example, Snow (1979) reported a
permeability around 1.0E-14 m^2 for most of the 5862 tests
on fractured crystalline rocks. Gimmi et al. (1997) estimated
a permeability of 1.0E-18 m^2 for a granodiorite lacking in
fractures at investigation scale.
For further simulations, a permeability of 1.0E-18 m^2 is
applied to the bedrock matrix, and1.0E-16 m^2 is used for
the composite permeability of the fractured bedrock.
2. Slope effect on water partitioning
Figure 1 Conceptual picture of water partitioning along hillslopes
Figure 2 Conceptual hillslope and some notations (ET and
surface runoff not modeled here)
From the simulations, we try to answer three questions: (1) What is the permeability threshold above
which percolation through bedrock becomes significant, and how is this compared to the actual fractured
rock permeability? (2) What is the effect of bedrock surface topography (slope and depression) on water
partitioning at the soil-bedrock interface? (3) What is the effect of soil characteristics on water partitioning?
Simulations of six slopes (0.05~0.3) with two types of soil
cover were conducted. The results are shown in Figures
7,8,and 9.
Figure 6 Percentage of infiltration water percolating into bedrock
as a function of bedrock permeabilities, shown are vectors
of specific discharge
Figure 14 Water partition indexes of various depression types and magnitudes at 80-90m interval for sandy loam-cover slope
(a) and silt-cover slope (b), at 40-50m interval for sandy loam-cover slope (c) and silt-cover slope (d).
Numerical simulations
Hillslopes of 100-meter length and 2-meter thickness are simulated in two dimensions using HYDRUS2D. Fractured bedrock is represented as a composite continuum with a Durner's type function (Figure 3).
In this model, water tends to flow through fractures when the fractured rock is saturated or near saturated,
and through rock matrix when the water potential is far away from the saturated condition. The composite
continuum model is a typical numerical method to simulate water flow in variably saturated fractured
media. Simulation is conducted in steady-state, with prescribed constant and uniform infiltration on the top.
No flow condition is assigned to the upslope side, free drainage (or unit downward hydraulic gradient) for
the bottom boundary, and seepage face for the downslope side. Later simulations will consider episodic
and spatially variable infiltration, evapotranspiration, anisotropic conditions, and use dual-permeability
model.
Inclines with various slopes (0.05~0.3) and soil types (Table 1 and Figure 4) were simulated. The
bedrock surfaces were made into various depressions to investigate their effects on water partitioning
(Figure 5). The hydrological functions of fractured rock and soils are shown in Table 2.
Discussion
4. Bedrock surface depression effect ( Fig. 14,15,16)
Figure 8 Water pressure head (matrix potential) in rock near the soil
-bedrock interface changes with slope for hillslopes covered
with sandy loam (a) and silt (b). The dash line shows a critical
water pressure head above which the slope effect on PI
shown in Figure 7 becomes insignificant.
Figure 7 Partition indices (PI) for three 10-meter intervals along the slope, measured
horizontally from the bottom (see Fig. 6). The PI changes with slope for two
hillslopes covered with sandy loam (a) and silt (b), showing that PI decreases
with an increase of the slope. However, this relationship is not held for siltcover slope at two downslope 10-meter intervals.
3. Soil characteristics effect (Fig. 10,11,12,13)
Figure 9 The role of water pressure head at soil-bedrock interface
on water partitioning
Figure 15 Water partition index (PI) as a function of depression
index (DI) for V-notch and Trough depression types.
Figure 16 Water pressure head (matrix potential) profiles at selected
locations of depression and non-depression intervals.
Water partitioning at the soil-bedrock interface along hillslopes depends on various conditions, such as water availability,
bedrock characteristics, soil characteristics, evapotranspiration, etc. It is often assumed that most bedrocks are not
permeable enough to allow water percolation. However, our simulation results show that the threshold permeability for
bedrock percolation is conservatively1.0E-16 m^2 (Figure 6). Permeability of fractured rocks is frequently reported above this
threshold value (Snow, 1979; Caine et al., 2002). In addition to tectonic factors, weathering and unloading often cause more
fractures in rocks near the surface, which increase bedrock permeability. Thus, detailed studies are required to look at the
mechanism of water partitioning at the soil-bedrock interface in detail, instead of simply neglecting the possible bedrock
percolation process. Given a fractured bedrock with a permeability exceeding the threshold value, the effects of slope, soil
types and thickness, bedrock topography on water partitioning are all observed from the simulation results.
Due to the gravitational force, more water becomes interflow when the slope increases. As shown in Figure 7 the partition
index (PI) decreases with the slope. The relationship between PI and the slope fits a power function very well for the
simulation cases in which water pressure at the soil-rock interface is below -5 cm, while this relationship is not held when
water pressure is above -5cm (Figures 7 and 8). This indicates that soil water pressure distribution is another important factor
affecting water partitioning, which is evident in Figure 9. For hillslopes covered with sandy loam (Figure 7a), PI of each slope
at three intervals increases downslope, even though the slope doesn't change. Water pressure at the soil-bedrock interface
increases downslope, increasing the fractured bedrock unsaturated conductivity to a larger magnitude than that of the soil,
thus increasing PI. For hillslopes covered with silt, the water pressure at soil-rock interface also increase downslope.
However, the difference of PI between intervals (40-50m) and (60-70m) for each slope is not observed for the slopes below
0.2. At these points the soil-bedrock interface is saturated (Figure 8), thus the pressure change doesn't result in actual
hydraulic conductivity change of the rock and soil at the interface. For the same reason, the slope effect becomes negligible
when the soil-bedrock interface is saturated, as shown in the PI of two downslope intervals in Figure 7b. Since the slope
effect on water partitioning is controlled by water pressure distribution at the soil-bedrock interface, the slope of bedrock
surface, rather than that of ground surface, is the agent affecting water partitioning.
The effect of soil characteristics on PI is observed between silt and sandy loam (Figure 7). Further simulation results of
hillslopes with single-layer and double-layer soil covers are shown in Figure 10. Double-layer soils allow more percolation
into bedrock for most cases, especially at upslope intervals. The most interesting result is that clay doesn't work as a barrier
for percolation except for the case at the interval (40-50m) of the slope (0.1). Due to space limitations the following analysis
only focuses on the simulations with a slope of 0.2. Comparison of the slope with sandy loam cover and sandy loam + clay
cover shows that clay increases the water pressure in the double-layer soils (Figure 12), resulting in an increase of
unsaturated bedrock hydraulic conductivity. Although the unsaturated conductivity of clay and sandy loam layer also
increases, the absolute hydraulic conductivity of clay layer is still lower than that in the slope of single sandy loam layer
(Figure 13). The barrier effects of clay is evident in Figure 13. But this barrier is not for percolation but for interflow because
the lowest hydraulic conductivity in clay layer is still larger than the saturated bedrock hydraulic conductivity (1.0E-9 m/sec). If
this is the case, a thicker clay layer on the bedrock surface will lead to a larger percolation given that the soil is unsaturated.
The slope with silt + sand cover has a different story. Sand layer decreases the water pressure in the soil layer at intervals
(40-50m) and (60-70m) (Figure 12), resulting in a decrease of unsaturated hydraulic conductivity of both soil layers (Figure
13). This is somewhat but not completely traded off by the decrease of bedrock unsaturated hydraulic conductivity. At the
interval (80-90), sand increases the water pressure head in the soil, leading to a similar situation of the slope with sandy loam
+ clay cover.
The effect of soil thickness is not so obvious between the slopes covered with the same soil (Figure 10). Much higher
water pressure (Figure 12) in thin soil than thick soil without resulting a low PI (Figure 10) indicates that the bedrock
unsaturated hydraulic conductivity may be the primary factor determining water partitioning.
The effect of bedrock surface depression on water partitioning is more evident at upslope intervals (more unsaturated)
than downslope intervals (more saturated) (Figure 14). The depression effect also depends on depression types. At the
downslope intervals, compared to other depression types, the step type depression strongly increases percolation. At the
upslope intervals, V-notch and Trough types depression have stronger effects on increasing percolation. The relative
magnitude of depression effect between these two types are consistent, and can be linearly related to the depression index
(Figure 15). With an increase of water pressure at the soil-bedrock interface downslope, the depression effect on water
partitioning decreases, similar to what is observed on slope effect. This is because depression and slope influence water
partitioning in the same way, by affecting water pressure distribution at the soil-bedrock interface (Figure 16). Thus, the
depression effect on water partitioning becomes insignificant when soil is saturated, which is observed from strongly
downslope decreasing in DI coefficient of linear functions between PI and DI for hillslopes with silt overlying depressed
bedrock (Figure 15).
Figure 3 Composite continuum model of fractured rocks
Table 1 Soil characteristics applied in simulations
Conclusions
Figure 4 Soil types circled are used in the simulations (soil
texture triangle from USDA Soil Conservation Service)
The threshold permeability of bedrock, allowing significant percolation at soil-bedrock interface, is about 1.0E-16 m^2.
Given a hillslope with a bedrock permeability above this threshold, both bedrock topography (slope and depression) and soil
characteristics affect water partitioning by affecting water pressure distribution at the soil-bedrock interface. When the soil
becomes saturated, bedrock surface topography effects become insignificant. This suggests that soil water pressure (matrix
potential) at the soil-bedrock interface is a critical measurement in field campaigns estimating water partitioning.
Acknowledgement
Table 2 Soil hydraulic functions used in simulations
SAHRA, an NSF research center, provided funding. Dr. Jirka Simunek from U.S. Salinity Laboratory, USDA, provided composite hydraulic
function for HYDRUS 2D. Dr. Jan Hendrickx at New Mexico Tech, provided assistance with the simulations.
References
Figure 5 Depression types used in the simulations and the definition
of depression index (DI)
Figure 10 The effects of various soil covers on water partitioning
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Figure 11 Vertical profiles of interflow (Darcy velocity in horizontal direction) in the
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Figure 12 Vertical profiles of pressure head in the upper 1 meter
thickness at selected locations (slope=0.2)
Figure 13 Vertical profiles of unsaturated hydraulic conductivities
of the soil layers at selected locations (slope=0.2)
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