A Falling-Head Method for Measuring Intertidal Sediment Hydraulic Conductivity

Transcription

1 Methods Note/ A Falling-Head Method for Measuring Intertidal Sediment Hydraulic Conductivity by Hailong Li 1,2, Pingping Sun 1,3, Shi Chen 1,4, Yuqiang Xia 1, and Shuang Liu 1,5 Abstract This paper presents an in situ falling-head method for measuring hydraulic conductivity of beach sediments in a tidal environment. A polyvinyl chloride (PVC) standpipe was vertically pushed into the submerged beach sediments so that its lower part was filled by a sediment column. During the experiment, the sediments were submerged by sea water and the standpipe top was higher than the sea level. The pipe was fully filled with sea water at the beginning of the experiment. Then the water level time series inside and outside the standpipe were recorded. Analytical solutions were derived to describe the relation among the sediment s hydraulic conductivity and the water levels inside and outside the standpipe and used to analyze the experiment data obtained from the intertidal zone of Puqian Bay, Haikou, Hainan Province, China. The water levels predicted by the analytical solution agreed very well with all the experiment data. Experiments for horizontal hydraulic conductivity estimation were also conducted using an L-shaped standpipe,which bends from vertical to horizontal in the beach sediments. The averaged hydraulic conductivity anisotropy ratio at the study area is about 2.9. After each in situ experiment, the sediments in the standpipe were stored in a plastic box and transported to a university laboratory to measure the hydraulic conductivity using falling-head method. It is found that the in situ hydraulic conductivity averages one order of magnitude greater than the laboratory one, indicating that the original beach surface sediments were loose due to tidal and wave actions and that the samples were significantly compacted during the transportation to laboratory. Introduction Submarine groundwater discharge (SGD) and the interactions among sea water and groundwater in coastal 1 Corresponding author: School of Environmental Studies & (MOE) Biogeology and Environmental Geology Lab, China University of Geosciences-Wuhan, Wuhan , China; ; fax: ; hailong@graduate.hku.hk 2 China University of Geosciences-Beijing, Beijing , China 3 Department of Hydrology & Environmental Geology, Xi an Center of Geological Survey, China Geological Survey, Xi an , China 4 Institute of Hydrogeology, Xi an Branch, China Coal Research Institute, Xi an , China 5 Department of Mathematics, Anshan Normal University, Anshan , China Received June 2009, accepted August Copyright 2009 The Author(s) Journal compilation 2009 National Ground Water Association. doi: /j x aquifers are important issues in coastal ecology, environment and hydrogeology. The hydraulic conductivity K of the beach sediments is a key parameter affecting the SGD and interactions among many factors in the intertidal zone (Li et al. 1999, 2008; Michael et al. 2005; Prieto and Destouni 2005; Robinson et al. 2006). It is of great significance for hydrogeologists to estimate this parameter accurately and economically. There are many methods for evaluating the sediments K values (Landon et al. 2001). In the laboratory, one can use the well-known constant-head or fallinghead tests, or grain-size analysis method (Alyamani and Sen 1993; Liu and Evett 2001). In the field, one can implement the slug test (Hvorslev 1951; Jiao and Leung 2003), double-ring infiltrometer (Lai and Ren 2007), and constant-head test using Guelph permeameter or pumping tests to estimate K values. Owing to disturbance of the sediment samples, spatial variations in K, and many other factors, there are substantial differences between NGWA.org GROUND WATER 1

2 laboratory and field measurements of the hydraulic conductivity (Landon et al and references therein). It is of great importance to try to analyze and understand these differences. Compared with the other methods of estimating the hydraulic conductivity, pumping tests have advantages such as large-scale and reliable accuracy. In the intertidal zone, however, due to the periodic tidal submersions of the beach surface, pumping tests are difficult to apply and analyze, and therefore are seldom used. In the case that the sediments are covered with water, the common in situ methods such as double-ring infiltrometer do not apply. Chen (2000) introduced a simple falling-head method for measuring the in situ hydraulic conductivities of stream beds when the stream level is constant. Here, we generalized Chen s (2000) method so that the falling-head method can be used to measure the in situ hydraulic conductivities of beach sediments in the submerged intertidal zone where the tidal level varies with time. Eight in situ falling-head experiments were conducted in an intertidal zone at Puqian Bay, Haikou, China. Analytical solutions were derived to describe the relationship among the water levels inside and outside the standpipe, the sediments hydraulic conductivity, and the length of the sediments column in the standpipe. Estimations of the hydraulic conductivity of the beach sediment columns for the eight experiments were obtained based on the least-squares fittings between the observed data and the analytical solution. Beach sediments in the standpipe were also sampled for laboratory falling-head tests. The differences of the hydraulic conductivity values between in situ and laboratory methods were analyzed. The possible reasons for the differences were discussed. Experiment Description The apparatus for the in situ falling-head test comprises a PVC pipe 2.0 m long with an inside diameter of m. The test procedure is similar to that by Chen (2000) and is as follows: The PVC standpipe was vertically pushed into the beach sediments so that its lower part was filled with a sediment column of length.during the experiment, the beach sediments were submerged by sea water and the top of the standpipe was higher than the sea level. Four radial channels were dug in the beach sediments around the pipe so that the hydraulic head at the bottom of the standpipe equals approximately the sea water head outside the pipe, that is, the tidal level H tide (Figure 1a). Then the pipe was fully filled very slowly along its inner wall with clean sea water to avoid disturbing the sediments inside the pipe. The water level H pipe in the pipe would drop since the water head in the pipe was higher than that outside the pipe and water in the pipe would discharge through the sediment column. The water level time series inside and outside the standpipe were recorded. Using an L-shaped pipe with its horizontal part shoved into the wall of a trench dug in advance, the same experimental procedure described above can also be used to measure the hydraulic conductivity of the beach sediments in horizontal direction (Figure 1b). Owing to the small thickness of the pipe wall (2.8 mm) and the looseness and softness of the sediments, the disturbance of the sediments by the pipe was slight and neglected. Eight in situ falling-head experiments were conducted at different locations in the middle intertidal zone at Puqian Bay of Haikou, Hainan Province, China on December 22 and 23, 2007 (Figure S1, Supporting Information). Three of them measured the vertical hydraulic conductivity and five, the horizontal one. The geographical coordinates of the field site are N, E. Tides in this area are mixture of diurnal and semidiurnal components. The tidal range is about 1.86 m during spring tides and 0.6 m during neap tides (NMDIS 2008). Our experiments were conducted during spring tides. There was no rainfall during experiment period. Beach sediments of the study area are mainly fine sand, and the beach slope is about 14%. Details of the eight experiments are listed in Table 1. After each in situ experiment, the sediments in the standpipe were collected in a plastic box and transported to university laboratory to measure the hydraulic conductivity using a falling-head permeameter (TST-55 Permeameter, sample diameter 61.8 mm, sample height 40 mm, Nanjing Soil Instrument Factory Co., Ltd.), details of which were included in Supporting Information. The eight experiments were conducted during rising or falling tides, with their durations ranging from 0.83 to 4.66 h. The tidal level can be generally expressed as: H tide (t) = H 0 + n A i cos(ω i t + ϕ i ) (1) where H 0 is the mean sea level [L], A denotes the tidal amplitude [L], ω = 2π/T is the tidal frequency [T 1 ] with T being the tidal period [T], ϕ is the initial phase [radian], the subscript i indicates the ith harmonic component, and n is the total number of harmonic components such as M 2,S 2,N 2,K 1,andO 1 etc. (Melchior 1978; Li and Jiao 2003). During each experiment, the observed tidal level changed approximately linearly with time (Figures 2a and 2b); thus the tidal level Equation 1 was fitted approximately by: H tide (t) = at + b (2) where a is the rising or falling rate [LT 1 ] of the tidal level and b is the initial tidal level [L]. The values of parameters a and b were obtained using least-squares fitting to the observed tidal level time series (Table S1, Supporting Information). The linear approximations based on Equation 2 are shown in Figures 2a and 2b. Data Analysis Analytical Solutions In order to derive the analytical solution for describing the water level variations inside and outside the 2 H. Li et al. GROUND WATER NGWA.org

3 (a) Channel H pipe H tide Seawater Sediments Vertical cross section Bird's eye view Perimeter of stand-pipe (b) Perimeter of horizental pipe Channel H pipe H tide Seawater Sediments Vertical cross section Bird's eye view Figure 1. Schematic representation of the apparatus for measuring (a) vertical and (b) horizontal hydraulic conductivity using in situ falling-head method. To avoid the collapse of the channel wall, each channel has a trapezoidal cross section as deep as the pipe in the sediments [bottom width 2 cm, top width 6 10 cm in panel (a); and bottom width >10 cm, top width >20 cm in panel (b)]. Table 1 Results of the Eight In Situ and Laboratory Experiments 1 Experiment No. (cm) Duration (s) Direction N m K (cm/s) K lab (cm/s) S (K )(cm 2 ) K /K lab Test Horizontal Test Horizontal Test Vertical Test Vertical Test Vertical Test Horizontal Test Horizontal Test Horizontal Average (H ) Average (V ) Average Data include the length ( ) of sediment column in the pipe, the experiment duration, the direction of the hydraulic conductivity to be measured, and the number of measurement (N m ) of the water level time series in each experiment. Notation K denotes the hydraulic conductivity estimated by the in situ standpipe method, and K lab, by the falling-head method in laboratory. The notation S (K ) denotes the sum of squares of the residues in the least-squares method (defined by Equation (8)). Average (H ) means the average of the Horizontal tests (Tests 1, 2, 6, 7, and 8). Average (V ) means the average of the Vertical tests (Tests 3, 4, and 5). Average in the last row is the average of all the tests (Tests 1 8). NGWA.org H. Li et al. GROUND WATER 3

4 H tide (cm) H tide (cm) H pipe (cm) (a) Test 1 Test 2 Test t (h) (b) Test 4 Test 5 Test 6 Test 7 Test t (h) (c) t (h) Figure 2. (a) Changes of the observed tidal level (empty symbols) and water levels inside the standpipe (solid symbols) with time for the three in situ falling-head tests conducted during rising tides. Changes of the observed (b) tidal level and (c) water levels inside the standpipe with time for the five in situ falling-head tests conducted during falling tides. The linear approximation of the tidal level by Equation 2 and the theoretical prediction of the water level in the pipe by Equation 7 are also shown as solid lines. standpipe and the sediment hydraulic conductivity, it is assumed that (A) the disturbance in the samples when pushing the PVC pipe into the beach sediments is negligible, and that (B) the hydraulic head at the bottom of the standpipe equals the tidal level H tide. Let the beach surface be the datum of the water head, then H pipe (t) and H tide (t) can be regarded as the hydraulic head inside and outside the standpipe at time t, respectively. The hydraulic head H pipe falls with time during the test. During the time interval [t,t + t], the loss of the volume of sea water in the pipe is: H pipe (cm) where K and are the hydraulic conductivity [LT 1 ]and the length [L] of the sediment column in the pipe, respectively. Since V loss = V leaking, from Equations 3 and 4 one has tk(h pipe H tide ) = [H pipe (t) H pipe (t + t)]. Let t tend to zero, yielding: K H pipe H tide = dh pipe dt Equation 5 is an ordinary differential equation for describing the unknown water level H pipe (t) inside the pipe. Given the expression of the tidal level H tide (t) and the initial condition for H pipe (t), one can solve Equation 5 for the unknown H pipe (t). For the general tidal level variation, the solution of Equations 1 and 5 is given by: H pipe (t) = H 0 n A i [K cos(ω i t + ϕ +K i ) + ω i sin(ω i t + ϕ i )] K 2 + L 2 v ω2 i +(h 0 H p0 ) e Kt/ (5) (6a) where h 0 is the initial water level in the standpipe, H p0 is the initial tidal level defined as: H p0 = H 0 + K n A i (K cos ϕ i + ω i sin ϕ i ) K 2 + L 2 v ω2 i (6b) Equation 6 describes the water level variation with time in the pipe for any general tidal level. It is useful for measuring the hydraulic conductivities of low-porous sediments such as mud and silt in the intertidal zone using the falling-head method. In this case, the dropping speed of the water level in the standpipe will be very slow and the duration of the experiment will be long (e.g., at least one tidal cycle). Owing to the inconvenience caused by the large tidal range of spring tides, such experiments are recommended to be conducted during neap tides (much smaller tidal range). In the study area, there are also many intertidal zones covered with mud and silt. The spring tides during our field study, however, prevented us from conducting long-duration in situ falling-head experiments for the mud and silt cover in these intertidal zones. Nevertheless, Equation 6 is presented here for the completeness of the falling-head methods in various intertidal zones. In the case that the tidal level variation can be approximated by the linear Equation 2, the solution of Equations 2 and 5 is given by: V loss = S[H pipe (t) H pipe (t + t)] (3) where S is area [L 2 ] of the cross section of the standpipe. On the other hand, according to Darcy s law, the sea water volume leaking through the sediment column in the standpipe during [t,t + t] is: V leaking = KS t H pipe H tide (4) H pipe (t) = at a K + b + ( alv K b + h 0 ) ( exp K ) t Least-Squares Estimation of In Situ K-Values Owing to the nonlinear dependence of the water level H pipe (t) on K, it is difficult to obtain the explicit expression of K from Equation 7 or 6. To estimate the hydraulic conductivity K from the in situ falling-head 4 H. Li et al. GROUND WATER NGWA.org (7)

5 experiment data, we define the following least-squares objective function: N m S(K) = [H pipe (t i ; K) Hi ]2 (8) where H pipe (t i ; K) is the water level inside the pipe at time t i predicted by Equation 7, Hi is the observed water level in the pipe at time t i,andn m is the number of water level measurements for the considered experiment (Table 1). Then the function S(K) is minimized with respect to K and the value of K corresponding to the global minimum of S(K) is regarded as the estimated hydraulic conductivity. A Fortran code was developed to minimize S(K) using quasi-newton iteration method. Different initial parameter guess values were used for K, and the converged values of K are the same for the global minimum. Results and Discussion The estimated values of K and the objective function S(K) are listed in Table 1. The averaged hydraulic conductivity is cm/s in the horizontal direction and cm/s in the vertical direction. The ratio of the horizontal to vertical hydraulic conductivity is about 2.9, which is within the typical literature range from 1.0 to (Freeze and Cherry 1979; Butler 1998). We compared the observed water level with the theoretical prediction of Equation 7 using estimated K values (Figures 2a and 2c). The theoretical predictions are very close to the observations for the eight experiments. Table 1 lists the results and the hydraulic conductivity ratio of the in situ falling-head method to the laboratory falling-head method for each experiment. One can see that the ratio is greater than 3.0 for seven of the eight experiments with only one exception of Test 3. The in situ measurements of the hydraulic conductivity average 26, 20.6, and 24 times of the laboratory ones for horizontal, vertical and all tests, respectively. The difference may result from the following processes. The in situ beach surface sediments in the intertidal zone are generally loose due to the periodic tidal and wave actions and the samples might be compacted during the transportation and laboratory experiments. Conclusions This paper introduces an in situ falling-head method for measuring hydraulic conductivity of beach surface sediments in submerged intertidal zones. The method is a generalization of that by Chen (2000), which is for measuring the in situ hydraulic conductivities of streambed when the stream level is constant. Eight experiments were conducted in the middle intertidal zone at Puqian Bay, Haikou, Hainan Province, China. Three experiments were for measuring hydraulic conductivities in the vertical direction, and five in the horizontal direction. Analytical solutions were derived to describe the relationship among the water levels inside and outside the pipe during the experiments. The hydraulic conductivities of the beach sediments for the eight experiments were estimated using the least-squares fittings between the observed data and the analytical solution. The water levels predicted by the analytical solution agreed very well with the experiment data. The average hydraulic conductivity anisotropy ratio at the study area is about 2.9. After each in situ fallinghead experiment, the sediments in the standpipe were sampled for laboratory analysis also using the fallinghead method. The in situ estimation of the beach sediment hydraulic conductivity averages one order of magnitude greater than the laboratory one. This implies that the original beach surface sediments were loose due to tidal and wave actions and that the samples were significantly compacted during the transportation and laboratory experiments. Hydraulic conductivity is strongly dependent on the packing conditions. The packing conditions of beach surface sediments in the intertidal zone are usually seriously influenced by the tide and wave actions, which is difficult to consider in the laboratory. The in situ fallinghead method is considered the most robust method for measuring hydraulic conductivity of the upper 0.25 m of the streambed sediments (Landon et al. 2001). Our results indicated that the conclusion of Landon et al. (2001) is also applicable for shallow beach sediments in the intertidal zones. In situ falling-head experiment also has the advantages such as economy, reliability, and simplicity. Acknowledgments This research was supported by the National Natural Science Foundation of China (No ) and Academic Exploration and Innovation Foundation for Graduate Students in China University of Geosciences in the years of The work was also partially supported by the 111 Project (B08030). We thank Yuchen Zhang, Chao Liu, Fangxuan He, Guohui Li, Li Wang, Qiaona Guo, Ye Tian, Ying Yang, and Xiaolong Geng for their field work. The authors are grateful to Matthew Landon and two other anonymous reviewers for their helpful review comments. Supporting Information Supporting Information may be found in the online version of this article: Figure S1. Location map of the study area. Table S1. The values of parameters a and b obtained using least-squares fitting to the observed tidal level time series for the eight experiments. Detailed information of the laboratory falling-head permeameter test. Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting materials NGWA.org H. Li et al. GROUND WATER 5

6 supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article. References Alyamani, M.S., and Z. Sen Determination of hydraulic conductivity from complete grain-size distribution curves. Ground Water 31, no. 4: Butler, J.J The Design, Performance, and Analysis of Slug Tests, New York: Lewis Publishers. Chen, X.H Measurement of streambed hydraulic conductivity and its anisotropy. Environmental Geology 39, no. 12: Freeze, R.A., and J.A. Cherry Groundwater. Englewood Cliffs, New Jersey: Prentice Hall. Hvorslev, M.J Time lag and soil permeability in groundwater observations. Waterways Experiment Station, U.S. Army Bulletin 36. Vicksburg, Mississippi: Corps of Engineers. Jiao, J.J., and C.M. Leung Spreadsheets for the analysis of aquifer-test and slug-test data (review article). Ground Water 41, no. 1: Lai, J., and L. Ren Assessing the size dependency of measured hydraulic conductivity using double-ring infiltrometers and numerical simulation. Soil Science Society of America Journal 71, no. 6: Landon, M.K., D.L. Rus, and F.E. Harvey Comparison of instream methods for measuring hydraulic conductivity in sandy streambeds. Ground Water 39, no. 6: Li, H.L., M.C. Boufadel, and J.W. Weaver Tideinduced seawater-groundwater circulation in shallow beach aquifers. Journal of Hydrology 352, no. 1 2: Li, H.L., and J.J. Jiao Tide-induced seawatergroundwater circulation in a multi-layered coastal leaky aquifer system. Journal of Hydrology 274, no. 1 4: Li, L., D.A. Barry, F. Stagnitti, and J.-Y. Parlange Submarine groundwater discharge and associated chemical input to a coastal sea. Water Resources Research 35, no. 11: Liu, C., and J.B. Evett Soil and Foundation. Upper Saddle River, New Jersey: Prentice Hall. Melchior, P.J The Tides of the Planet Earth. NewYork: Pergamon Press. Michael, H.A., A.E. Mulligan, and C.F. Harvey Seasonal oscillations in water exchange between aquifers and the coastal ocean. Nature 436, no. 7054: doi /nature NMDIS Tide table. National Marine Data & Information Service, China. Accessed September 2, Prieto, C., and G. Destouni Quantifying hydrological and tidal influences on groundwater discharge to coastal waters. Water Resources Research 41, no. 12: W doi /2004wr Robinson, C., B. Gibbes, and L. Li Driving mechanisms for groundwater flow and salt transport in a subterranean estuary. Geophysical Research Letters 33, no. 3: L doi /2005gl H. Li et al. GROUND WATER NGWA.org