A semi-analytical generalized Hvorslev formula for estimating riverbed hydraulic conductivity with an open-ended standpipe permeameter

Abstract

a b s t r a c tThe well-known Hvorslev (1951) formula was developed to estimate soil permeability using single-well slug tests and has been widely applied to determine riverbed hydraulic conductivity using in situ standpipe permeameter tests. Here, we further develop a general solution of the Hvorslev (1951) formula that accounts for flow in a bounded medium and assumes that the bottom of the river is a prescribed head boundary. The superposition of real and imaginary disk sources is used to obtain a semi-analytical expression of the total hydraulic resistance of the flow in and out of the pipe. As a result, we obtained a simple semi-analytical expression for the resistance, which represents a generalization of the Hvorslev (1951). The obtained expression is benchmarked against a finite-element numerical model of 2-D flow (in r-z coordinates) in an anisotropic medium. The results exhibit good agreement between the simulated and estimated riverbed hydraulic conductivity values. Furthermore, a set of simulations for layered, stochastically heterogeneous riverbed sediments was conducted and processed using the proposed expression to demonstrate the potential associated with measuring vertical heterogeneity in bottom sediments using a series of standpipe permeameter tests with different lengths of pipe inserted into the riverbed sediments.

Spatial and depth variability of streambed vertical hydraulic conductivity under the regional flow regimes

“…Again, a permeameter test at 0‐ to 60‐cm depth was conducted. After the tests, the streambed K v can be calculated using the following formula (Hvorslev, ), which has been developed by Pozdniakov, Wang, and Lekhov (). where L v is the length of the sediment column in the pipe; D is the interior diameter of the pipe (5.4 cm); h 1 and h 2 are the hydraulic heads inside the pipe measured at times t 1 and t 2 , respectively; and .…”

“…Again, a permeameter test at 0-to 60-cm depth was conducted. After the tests, the streambed K v can be calculated using the following formula (Hvorslev, 1951), which has been developed by Pozdniakov, Wang, and Lekhov (2016).…”

Numerical modelling of stream–aquifer interaction: Quantifying the impact of transient streambed permeability and aquifer heterogeneity

“…Many field studies have demonstrated the existence of spatial and temporal variations of streambed permeability (Min, Yu, Liu, Zhu, & Wang, ; Wang et al, ; Wu et al, ). Many approaches are available to estimate streambed permeability, such as by direct measurements (e.g., pumping, slug, and permeameter tests) and indirect estimation (e.g., grain size analysis and seepage meter; Cheong et al, ; Kalbus, Reinstorf, & Schirmer, ; Pozdniakov, Wang, & Lekhov, ). Numerous field studies have demonstrated the importance of variable streambed permeability on surface water–groundwater interaction (Newcomer et al, ; Pozdniakov et al, ; Simpson & Meixner, ).…”

“…Many approaches are available to estimate streambed permeability, such as by direct measurements (e.g., pumping, slug, and permeameter tests) and indirect estimation (e.g., grain size analysis and seepage meter; Cheong et al, ; Kalbus, Reinstorf, & Schirmer, ; Pozdniakov, Wang, & Lekhov, ). Numerous field studies have demonstrated the importance of variable streambed permeability on surface water–groundwater interaction (Newcomer et al, ; Pozdniakov et al, ; Simpson & Meixner, ). In most numerical investigations of surface water–groundwater interaction, streambed permeability was assumed to be temporally constant due to difficulties in detecting and measuring transient variations in permeability (e.g., Engelhardt, Prommer, Schulz, et al, ; Sun et al, ; Tian et al, ).…”

西北干旱区间歇性河流与含水层水量交换研究进展与展望

“…; 靳孟贵等, 2017)。对具有淤塞层的河流脱节 过程研究发现， 当河水与地下水发生脱节之后， 在 淤塞层下方能够形成悬挂饱水带， 其最大厚度约等 于河水深 。Xie 等(2014)研究发 现， 在一定条件下， 未淤塞河流脱节之后同样可在 河床下方发育有悬挂饱水带。围绕 "河流-悬挂饱 水带-非饱和带-地下水" 系统的饱和与非饱和水流 形成与转化研究， 将有助于精准刻画间歇性河流与 含水层之间的水分迁移过程。 作为河流与含水层相互作用的重要物理界面 (Constantz, 2016)， 河床直接影响河水与地下水交换 强度以及潜流带生物地球化学过程 (Brunner et al, 2017; 杜尧等, 2017)。河床渗透系数(K)是反映河床 沉积物导水能力的重要参数， 其大小不仅取决于河 床沉积物的性质， 如粒度、 成分、 颗粒排列、 充填状 况、 沉积结构等， 同时与河水的物理性质， 如容重、 粘滞性具有密切的关系 (薛禹群, 1997;Cuthbert et al, 2010)。受多种因素的影响， 河床沉积物 K 值有 一个较大的变化范围， 从小于 1×10 -9 m/s 到大于 1× 10 -2 m/s 不等 (Calver, 2001)。不仅如此， 河床渗透性 能具有强烈的空间非均质性， 并在时间上也呈现出 一定的变异性 (Chen, 2004;Tang et al, 2017)。河床 沉积物所具有的这种时空变异特征， 一方面， 影响 河流与含水层之间的转化关系； 另一方面， 造成难 以准确定量河水与地下水交换量。当前， 对河床渗 透性能时空变异性及其影响因素的识别不仅是研 究河水与地下水水量交换的关键与难点 (束龙仓 等, 2008;Rosenberry et al, 2009;Pozdniakov et al, 2016)， 也 是 河 流 与 含 水 层 相 互 作 用 研 究 的 热 点 (Constantz, 2016;Brunner et al, 2017)。 1.2 河流与地下水交换研究方法 河水与地下水交换的研究方法主要包括室内 物理模拟实验、 野外测定、 数值模拟等 (Yager, 1993;Landon et al, 2001; Kalbus et al, 2006;Rosenberry et al, 2008;Fleckenstein et al, 2010)。野外测定的方法 很多， 比如， 河道流量测定法、 抽水试验法、 微水试 验 法 、 渗 水 试 验 法 、 离 子 示 踪 法 等 (Scanlon et al, 2002;Cook, 2015)。近年来， 基于达西定律的各种 形式原位渗流实验方法得到不断改进与完善， 并在 此基础上发展出原位测定河床渗透性能的一些新 方法。如 Chen(2000)所提出的原位竖管法已在河 床沉积物渗透系数的野外测定上得到了较为广泛 的应用 (束龙仓等, 2002; 何志斌等, 2007; 宋进喜 等, 2009)。圆盘渗流仪(seepage meter)也被广泛用 于研究干旱区河流与含水层水量交换速率 (Landon et al, 2001;Rosenberry, 2008)。 当前， 随着温度示踪逐渐成为国际上研究河水 与地下水交换的一种有效手段， 利用温度变化信息 定量研究河水与地下水交换， 以及河水温度变化对 河床沉积物 K 值的影响正逐渐成为一种新趋势 (Ronan et al, 1998;Anderson, 2005;Hatch et al, 2006;Selker et al, 2006;Constantz, 2008;吴志伟等, 2011;Halloran et al, 2016;Caissie et al, 2017)。通过 记录河床的温度剖面， 可观测到河水温度瞬变信号 在河床内的...…”