Research papersA semi-analytical generalized Hvorslev formula for estimating riverbed hydraulic conductivity with an open-ended standpipe permeameter
Introduction
The exchange processes between surface water and groundwater are significant not only in riverbank water resource management (Chen and Chen, 2003, Winter et al., 1998) but also in water quality considerations (Calver, 2001) associated with biogeochemical interactions between streams and surrounding aquifer systems (Hiscock and Grischek, 2002). Riverbed hydraulic conductivity (K) is one of the key factors controlling the magnitude and spatial distribution of surface-groundwater exchange processes (Genereux et al., 2008, Landon et al., 2001), and it may vary over more than eight orders of magnitude, ranging from below 1.0 × 10−9 m/s to above 1.0 × 10−2 m/s (Calver, 2001), depending on the riverbed sediment materials and textures (Min et al., 2013, Taylor et al., 2013).
Although numerous approaches (e.g., grain-size distribution analysis, Darcy’s law-based in-stream tests, environmental tracer experiments, water balance techniques, integrated surface-groundwater numerical modeling, etc.) have been widely applied to investigate the hydraulic properties of riverbed sediments (Cheong et al., 2008, Kalbus et al., 2006, Wang et al., 2015), the accurate estimation of riverbed K values remains a challenge. One of the challenging aspects of estimating riverbed K is associated with its high spatial and temporal variability across measurement scales due to heterogeneity in the riverbed sediments (Chen et al., 2010), scouring and depositional processes during flooding events (Dunkerley, 2008, Hatch et al., 2010), and diurnal and seasonal changes in stream flow temperature (Constantz, 1998). Additionally, the successful application of the aforementioned methods is highly dependent on the assumptions and limitations of the applied methods, the specific equipment, and the design of the measurements (Shanafield and Cook, 2014). Therefore, to estimate riverbed K, multiple methods are recommended to reduce the method uncertainties involved in many field studies (Fleckenstein et al., 2010).
Field methods, including slug tests, in situ permeameter tests, and seepage-meter measurements, have been widely applied to determine the hydraulic properties of riverbeds. For studying riverbed vertical heterogeneity, a light-oil piezomanometer, which allows to measure very small head differences between surface water and underlying groundwater, was developed by Kennedy et al. (2007). Recently, a new type of permeameter was designed to measure two parameters, i.e., vertical flux and hydraulic gradient, simultaneously on site (Lee et al., 2015). These methods are relatively quick, inexpensive and allowing for numerous measurements to be made at many locations (Landon et al., 2001). The falling head slug tests, in which a standpipe (well or piezometer) is filled with river water and the raised water level in the standpipe is immediately allowed to fall while assuming that the general river water level remains constant (Baxter et al., 2003, Hvorslev, 1951), are considered to be a more practical in-stream approach than a permeameter for determining the riverbed K because of their ability to measure much deeper sediments (Landon et al., 2001). Another important advantage of falling head slug tests is that this type of test can evaluate the anisotropy of riverbed sediments using the L-shaped standpipe method (Chen, 2000), which provides in situ measurements of riverbed K in different directions.
Hvorslev (1951) conducted detailed interpretations of field standpipe permeameter tests using different types of piezometers and provided corresponding formulas to calculate the hydraulic conductivity. Hvorslev’s falling-head analysis generated accurate vertical hydraulic conductivities of the riverbed in homogenous sediments and layered deposits of low-K sand over high-K sand (Burnette et al., 2016). The analytical solution produced by Hvorslev (1951) highly depends on the shape factor of the installed piezometer (F), which is considered a function of the geometric constants, i.e., the length-to-diameter ratio, of the piezometer (Silvestri et al., 2012). As indicated by Klammler et al. (2011), most existing approaches used to determine F are based only on geometric or mathematical simplifications that neglect the effects of the boundaries of the flow domain. Therefore, the objectives of this study are to: (1) develop a semi-analytical expression for hydraulic resistance of an open-ended standpipe permeameter in the vicinity of a constant head boundary; (2) validate the obtained expression using numerical simulations of the falling head tests in the standpipe permeameter; (3) examine the influence of the natural vertical flow gradient in bottom sediments and medium elastic storage on the falling head test results; and (4) analyse the possibility of determining the hydraulic conductivity profiles of layered bottom sediments using falling head tests in a standpipe permeameter.
Section snippets
A semi-analytical solution for hydraulic resistance
As shown in Fig. 1, an open-ended cylindrical pipe has a diameter d and a penetration length into the riverbed sediments L. Let us assume that the initial water level in the pipe is equal to the river water level , i.e., . The water level in the pipe is instantaneously raised to above the river water level , and the subsequent raised water level in the pipe relative to the initial water level in the pipe is S(t).
A semi-infinite medium with an origin in
Model description
To validate the obtained semi-analytical expression (22), we developed the 1Well code (Lekhov, 2015), which simulates flow surrounding a pumping or injection well with different types of boundary conditions at the well surface, including falling head tests in open-ended pipes. This programme numerically solves Eq. (1) using the finite-element method in r-z coordinates. To take into account the internal resistance of the sediments inside the pipe, this programme uses Robin boundary conditions,
Summary
In this study, we developed a semi-analytical expression that accounts for flow in a bounded medium during falling head tests in a pipe penetrating the riverbed sediments. This expression considered the total hydraulic resistance of the flow through the sediments into and out of the pipe, thereby producing a generalized solution to the well-known Hvorslev (1951) formula (Eq. (25)). The developed expression was tested using the simulation results of a finite-element numerical model. Numerical
Acknowledgments
This research was supported by grants from the National Natural Science Foundation of China (No. 41301025), and the NSFC-RFBR Programme 2015–2016 (Nos. 41511130025 and 15-55-53010 ГФEH_a). The authors gratefully acknowledge the Editor, Corrado Corradini, the Associate Editor, Philip Brunner, and the anonymous reviewers for their valuable comments and suggestions that have led to substantial improvements over an earlier version of the manuscript. Special thanks to Paul Davis, the head of the
References (30)
- et al.
In-situ falling-head test for hydraulic conductivity: evaluation in layered sediments of an analysis derived for homogenous sediments
J. Hydrol.
(2016) - et al.
Stream water infiltration, bank storage, and storage zone changes due to stream-stage fluctuations
J. Hydrol.
(2003) - et al.
Spatial variability of specific yield and vertical hydraulic conductivity in a highly permeable alluvial aquifer
J. Hydrol.
(2010) - et al.
Groundwater-surface water interactions: new methods and models to improve understanding of processes and dynamics
Adv. Water Resour.
(2010) - et al.
Spatial and temporal variability of streambed hydraulic conductivity in West Bear Creek, North Carolina, USA
J. Hydrol.
(2008) - et al.
Spatial and temporal variations in streambed hydraulic conductivity quantified with time-series thermal methods
J. Hydrol.
(2010) - et al.
Attenuation of groundwater pollution by bank filtration
J. Hydrol.
(2002) - et al.
Transmission losses, infiltration and groundwater recharge through ephemeral and intermittent streambeds: a review of applied methods
J. Hydrol.
(2014) - et al.
Optimum experimental design of a monitoring network for parameter identification at riverbank well fields
J. Hydrol.
(2015) - et al.
Approximations for diffusion from a disk source
Appl. Math. Model.
(1992)
Hydraulics of Groundwater
Measuring groundwater-stream water exchange: new techniques for installing minipiezometers and estimating hydraulic conductivity
Trans. Am. Fish. Soc.
Riverbed permeabilities: information from pooled data
Ground Water
Measurement of streambed hydraulic conductivity and its anisotropy
Environ. Geol.
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