Abstract
To determine depth dependence of permeability in various geologic deposits, exponential models have often been proposed. However, spatial variability in hydraulic conductivity, K, rarely fits this trend in coarse alluvial aquifers, where complex stratigraphic sequences follow unique trends due to depositional and post-depositional processes. This paper analyzes K of alluvial-fan gravel deposits in several boreholes, and finds exponential decay in K with depth. Relatively undisturbed gravel cores obtained in the Toyohira River alluvial fan, Sapporo, Japan, are categorized by four levels of fine-sediment packing between gravel grains. Grain size is also analyzed in cores from two boreholes in the mid-fan and one in the fan-toe. Profiles of estimated conductivity, \( \overline{K} \), are constructed from profiles of core properties through a well-defined relation between slug-test results and core properties. Errors in \( \overline{K} \) are eliminated by a moving-average method, and regression analysis provides the decay exponents of \( \overline{K} \) with depth. Moving-average results show a similar decreasing trend in only the mid-fan above ∼30-m depth, and the decay exponent is estimated as ≈0.11 m−1, which is 10- to 1,000-fold that in consolidated rocks. A longitudinal cross section is also generated by using the profiles to establish hydrogeologic boundaries in the fan.
Résumé
Pour déterminer la dépendance de la perméabilité à la profondeur dans divers dépôts géologiques, des modèles exponentiels ont souvent été proposés. Toutefois, la variabilité spatiale de la conductivité hydraulique, K, reflète rarement cette tendance dans les aquifères alluviaux grossiers, où les séquences stratigraphiques complexes représentent des tendances spécifiques dues aux processus antérieurs et postérieurs aux dépôts. Cet article analyse le K des dépôts du cône de déjection dans plusieurs trous de forage, et en montre la décroissance exponentielle avec la profondeur. Les carottes de gravier relativement non perturbées obtenues dans le cône alluvionnaire de la rivière Toyohira, Sapporo, Japon, sont caractérisées par quatre niveaux de sédiments fins emballant des graviers. La granulométrie est aussi analysée dans les carottes de deux forages dans le cône moyen et d’un forage dans l’apex du cône de déjection. Des profils de la conductivité estimée \( \overline{K} \) sont construits à partir de profils des propriétés des carottes à l’aide d’une relation bien établie entre les résultats de tests d’infiltration et les propriétés des carottes. Les erreurs sur \( \overline{K} \) sont éliminées par la méthode de la moyenne mobile, et une analyse de régression fournit l’exposant de la décroissance de \( \overline{K} \) en fonction de la profondeur. Les résultats de la moyenne mobile montrent une tendance similaire à la décroissance seulement dans le mi cône au dessus de ∼30-m de profondeur, et l’exposant de décroissance est estimé ≈0.11 m−1, ce qui est 10- à 1000 fois celui des roches consolidées. Une coupe longitudinale a aussi été générée en utilisant les profils pour établir les limites hydrogéologiques du cône.
Resumen
Para determinar la dependencia de la profundidad con la permeabilidad en varios depósitos geológicos, se han propuesto a menudo modelos exponenciales, Sin embargo, la variabilidad espacial en la conductividad hidráulica, K, raramente se ajusta a esta tendencia en acuífero aluviales gruesos, donde las secuencias estratigráficas complejas siguen tendencias únicas debido a los procesos deposicionales y post-deposicionales. Este trabajo analiza la K de los depósitos de gravas de abanicos aluviales en varias perforaciones y encuentra una disminución exponencial en K con la profundidad. Testigos de gravas relativamente no disturbados obtenidos en el abanico aluvial del Río Toyohira, Sapporo, Japón, son categorizados por cuatros niveles de empaquetamientos de sedimentos finos entre granos de grava. El tamaño de grano es también analizado en testigos a partir de dos perforaciones en el sector medio del abanico y una en el pie del abanico. Los perfiles de la conductividad estimada, \( \overline{K} \), se construyeron a partir de perfiles de las propiedades de los testigos a través de una bien definida relación entre los resultados de los slug tests y las propiedades de los testigos. Los errores en \( \overline{K} \) son eliminados por un método de media móvil, y los análisis de regresión que proporcionan los exponentes de decrecimiento de \( \overline{K} \) con la profundidad. Los resultados de la media móvil muestran una tendencia decreciente similar en solo el abanico medio por encima de ∼30-m de profundidad y el exponente de decrecimiento es estimado como ≈0.11 m−1, lo cual es 10- a 1000- veces el de las rocas consolidadas. Se genera también una sección longitudinal usando los perfiles para establecer los límites hidrogeológicos en el abanico.
Resumo
Têm sido frequentemente propostos modelos exponenciais para determinar a dependência da permeabilidade em função da profundidade em vários depósitos geológicos. No entanto, a variabilidade espacial da condutividade hidráulica, K, raramente se enquadra nesta tendência em aquíferos aluviais formados por sedimentos grosseiros, onde complexas sequências estratigráficas seguem tendências únicas, relacionadas com os processos de deposição e pós-deposição. Este artigo analisa a condutividade hidráulica, K, de cones aluviais de depósitos de cascalheiras em vários furos, e encontra um decaimento exponencial de K com a profundidade. Amostras relativamente intactas de cascalheiras, obtidas no cone aluvial do Rio Toyohira, Sapporo, Japão, são caraterizadas por uma matriz de quatro níveis de sedimentos finos entre os elementos das cascalheiras. O tamanho dos grãos também é analisado em amostras de dois furos localizados na zona média do cone aluvial, e num furo localizado na base do cone aluvial. Perfis de condutividade estimada, \( \overline{K} \), são construídos a partir de perfis de propriedades das amostras, através de uma relação bem definida entre resultados dos ensaios slug e as propriedades das amostras. Os erros em \( \overline{K} \) são eliminados através de um método de média móvel, e a análise de regressão fornece os expoentes de decaimento de \( \overline{K} \) com a profundidade. Resultados da média móvel mostram uma tendência decrescente semelhante apenas para a zona média do cone aluvial, acima da profundidade aproximada de 30 m, e o expoente de decaimento é estimado em ≈0.11 m−1, 10 a 1000 vezes menor do que em rochas consolidadas. Também é gerada uma seção transversal longitudinal, usando os perfis, para definir as fronteiras hidrogeológicas no cone aluvial.
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Acknowledgements
The authors acknowledge the Hokkaido Regional Development Bureau, the administrator of the Toyohira River, for providing core samples, slug test data and technical reports. Special thanks are given to Prof. Satoshi Okamura of the Hokkaido University of Education and Dr. Tsumoru Sagayama of the Geological Survey of Hokkaido, who performed volcanic ash analysis and diatom analysis on the BW7 core, respectively. Helpful comments about the geology in the fan from Mr. Daisuke Nagaoka of Raax Co., Ltd. and Dr. Kenji Kizaki were also received with gratitude. Comments from the reviewer John Ong, the Associate Editor Bayani M Cardenas, and the Editor Maria-Theresia Schafmeister have helped us make substantial improvements in the manuscript.
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Sakata, Y., Ikeda, R. Depth dependence and exponential models of permeability in alluvial-fan gravel deposits. Hydrogeol J 21, 773–786 (2013). https://doi.org/10.1007/s10040-013-0961-8
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DOI: https://doi.org/10.1007/s10040-013-0961-8