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Stochastic modelling of hydraulic conductivity derived from geotechnical data; an example applied to central Glasgow

Published online by Cambridge University Press:  13 November 2018

J. D. O. Williams*
British Geological Survey, Environmental Science Centre, Keyworth, Nottingham NG12 5GG, UK. Email:
M. R. Dobbs
British Geological Survey, Environmental Science Centre, Keyworth, Nottingham NG12 5GG, UK. Email:
A. Kingdon
British Geological Survey, Environmental Science Centre, Keyworth, Nottingham NG12 5GG, UK. Email:
R. M. Lark
British Geological Survey, Environmental Science Centre, Keyworth, Nottingham NG12 5GG, UK. Email:
J. P. Williamson
British Geological Survey, Environmental Science Centre, Keyworth, Nottingham NG12 5GG, UK. Email:
A. M. MacDonald
British Geological Survey, The Lyell Centre, Research Avenue South, Edinburgh EH14 4AP, UK.
B. É. Ó Dochartaigh
British Geological Survey, The Lyell Centre, Research Avenue South, Edinburgh EH14 4AP, UK.
*Corresponding author


Characterising the three-dimensional (3D) distribution of hydraulic conductivity and its variability in the shallow subsurface is fundamental to understanding groundwater behaviour and to developing conceptual and numerical groundwater models to manage the subsurface. However, directly measuring in situ hydraulic conductivity can be difficult and expensive and is rarely carried out with sufficient density in urban environments. In this study we model hydraulic conductivity for 603 sites in the unconsolidated Quaternary deposits underlying Glasgow using particle size distribution and density description widely available from geotechnical investigations. Six different models were applied and the MacDonald formula was found to be most applicable in this heterogeneous environment, comparing well with the few available in situ hydraulic conductivity data. The range of the calculated hydraulic conductivity values between the 5th and 95th percentile was 1.56×10–2–4.38mday–1 with a median of 2.26×10–1 mday–1. These modelled hydraulic conductivity data were used to develop a suite of stochastic 3D simulations conditioned to existing 3D representations of lithology. Ten per cent of the input data were excluded from the modelling process for use in a split-sample validation test, which demonstrated the effectiveness of this approach compared with non-spatial or lithologically unconstrained models. Our spatial model reduces the mean squared error between the estimated and observed values at the excluded data locations over those predicted using a simple homogeneous model by 73 %. The resulting 3D hydraulic conductivity model is of a much higher resolution than would have been possible from using only direct measurements, and will improve understanding of groundwater flow in Glasgow and reduce the spatial uncertainty of hydraulic parameters in groundwater process models. The methodology employed could be replicated in other regions where significant volumes of suitable geotechnical and site investigation data are available to predict ground conditions in areas with complex superficial deposits.

Copyright © British Geological Survey UKRI 2018 

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6. References

Angulo-Jaramillo, R., Vandervaere, J. P., Roulier, S., Thony, J. L., Gadet, J. P. & Vauclin, M. 2000. Field measurements of soil surface hydraulic properties by disc and ring infiltrometers. A review and recent developments. Soil & Tillage Research 55, 1029.CrossRefGoogle Scholar
Barahona-Palomo, M., Riva, M., Sanchez-Vila, X., Vasquez-Sune, E. & Guadagnini, A. 2011. Quantitative comparison of impeller-flowmeter and particle-size-distribution techniques for the characterization of hydraulic conductivity variability. Hydrogeology Journal 19, 603612.CrossRefGoogle Scholar
Bear, J. 1972. Dynamics of fluids in porous media. New York: Dover Publications.Google Scholar
Bianchi, M., Kearsey, T. & Kingdon, A. 2015. Integrating deterministic lithostratigraphic models in stochastic realizations of subsurface heterogeneity. Impact on predictions of lithology, hydraulic heads and groundwater fluxes. Journal of Hydrology 531, 557573.CrossRefGoogle Scholar
Bonsor, H. C., Bricker, S. H., Ó Dochartaigh, B. É. & Lawrie, K. I. G. 2010. Project progress report 2010–11: groundwater monitoring in urban areas – a pilot study in Glasgow, UK. British Geological Survey Open Report, IR/10/087.Google Scholar
Bricker, S. H. & Bloomfield, J. P. 2014. Controls on the basin-scale distribution of hydraulic conductivity of superficial deposits: a case study from the Thames Basin, UK. Quarterly Journal of Engineering and Hydrogeology 47, 223236.CrossRefGoogle Scholar
British Standards Institution. 1990. BS 1377-2 Methods of test for soils for civil engineering purposes. Classification tests.Google Scholar
British Standards Institution. 1999. BS 5930 Code of practise for site investigations.Google Scholar
Brown, E. J., Rose, J., Coope, R. G. & Lowe, J. J. 2007. An MIS 3 age organic deposit from Balglass Burn, central Scotland: palaeoenvironmental significance and implications for the timing of the onset of the LGM ice sheet in the vicinity of the British Isles. Journal of Quaternary Science 22, 295308.CrossRefGoogle Scholar
Browne, M. A. E. & McMillan, A. A. 1989. Quaternary geology of the Clyde valley. British Geological Survey Research Report, SA/89/1.Google Scholar
Campbell, S. D. G., Merritt, J. E., Ó Dochartaigh, B. E., Mansour, M., Hughes, A. G., Fordyce, F. M., Entwistle, D. C., Monaghan, A. A. & Loughlin, S. C. 2010. 3D geological models and their hydrogeological applications: supporting urban development: a case study in Glasgow–Clyde, UK. Zeitschrift der Deutschen Gesellschaft fur Geowissenschaften 161, 251262.CrossRefGoogle Scholar
Carrier, W. D. III. 2003. Goodbye, Hazen; Hello, Kozeny-Carman. Journal of Geotechnical and Geoenvironmental Engineering 129, 10541056.CrossRefGoogle Scholar
Chapuis, R. P. 2004. Predicting the saturated hydraulic conductivity of sand and gravel using effective diameter and void ratio. Canadian Geotechnical Journal 41, 787795.CrossRefGoogle Scholar
Chilton, P. J. (ed.) 1999. Groundwater in the urban environment. Rotterdam: Balkema.Google Scholar
Cressie, N. & Hawkins, D. M. 1980. Robust estimation of the variogram. Journal of the International Association for Mathematical Geology 12, 115125.CrossRefGoogle Scholar
Culshaw, M. G. 2005. From concept towards reality: developing the attributed 3D geological model of the shallow subsurface. Quarterly Journal of Engineering Geology and Hydrogeology 38, 231284.CrossRefGoogle Scholar
Cuthbert, M. O., Mackay, R., Tellam, J. H. & Barker, R. D. 2009. The use of electrical resistivity tomography in deriving local scale models of recharge through superficial deposits. Quarterly Journal of Engineering Geology and Hydrogeology 42, 199209.CrossRefGoogle Scholar
Deutsch, C. V. & Journel, A. G. 1992. Geostatistical software library and user's guide. New York: Oxford University Press.Google Scholar
Elrick, D. E., Reynolds, W. D. & Tan, K. A. 1989. Hydraulic conductivity measurements in the unsaturated zone using improved well analyses. Groundwater Monitoring & Remediation 9, 184193.CrossRefGoogle Scholar
Finlayson, A. 2012. Ice dynamics and sediment movement: late glacial cycle, Clyde Basin, Scotland. Journal of Glaciology 58, 487500.CrossRefGoogle Scholar
Finlayson, A., Merritt, J., Browne, M., Merritt, J., McMillan, A. & Whitbread, K. 2010. Ice sheet advance, dynamics, and decay configurations: evidence from west central Scotland. Quaternary Science Reviews 29, 969988.CrossRefGoogle Scholar
Fordyce, F. M., Ó Dochartaigh, B. É., Bonsor, H. C., Ander, E. L., Graham, M. T., McCuaig, R. & Lovatt, M. J. 2018. Assessing threats to shallow groundwater quality from soil pollutants in Glasgow, UK: development of a new screening tool. Earth and Environmental Science Transactions of the Royal Society of Edinburgh. DOI: 10.1017/S1755691018000336.Google Scholar
Freeze, R. A. & Cherry, J. A. 1979. Groundwater. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Gogu, R. C. & Dassargues, A. 2000. Current trends and future challenges in groundwater vulnerability assessment using overlay and index methods. Environmental Geology 39, 549559.CrossRefGoogle Scholar
Graham, M., Ball, D., Ó Dochartaigh, B. É. & MacDonald, A. 2009. Using transmissivity, specific capacity and borehole yield data to assess the productivity of Scottish aquifers. Quarterly Journal of Engineering Geology and Hydrogeology 42, 227235.CrossRefGoogle Scholar
Hazen, A. 1892. Some physical properties of sands and gravels, with special reference to their use in filtration. 24th Annual Report, Massachusetts State Board of Health Document 34, 539556.Google Scholar
Jacobi, R. M., Rose, J., MacLeod, A. & Higham, T. F. G. 2009. Revised radiocarbon ages on woolly rhinoceros (Coelodonta antiquitatis) from western central Scotland: significance for timing the extinction of woolly rhinoceros in Britain and the onset of the LGM in central Scotland. Quaternary Science Reviews 28, 25512556.CrossRefGoogle Scholar
Jones, L. 1993. A comparison of pumping and slug tests for estimating the hydraulic conductivity of unweathered Wisconsin age till in Iowa. Ground Water 31, 896904.CrossRefGoogle Scholar
Kearsey, T., Williams, J., Finlayson, A., Williamson, P., Dobbs, M., Marchant, B., Kingdon, A. & Campbell, D. 2015. Testing the application and limitation of stochastic simulations to predict the lithology of glacial and fluvial deposits in Central Glasgow, UK. Engineering Geology 187, 98112.CrossRefGoogle Scholar
Kolterman, C. E. & Gorelick, S. M. 1995. Fractional packing model for hydraulic conductivity derived from sediment mixtures. Water Resources Research 31, 32833297.CrossRefGoogle Scholar
Labolle, E. M. & Fogg, G. E. 2001. Role of molecular diffusion in contaminant migration and recovery in an alluvial aquifer system. Transport in Porous Media 42, 155179.CrossRefGoogle Scholar
Lark, R. M. 2002. Modelling complex soil properties as contaminated regionalized variables. Geoderma 106, 171188.CrossRefGoogle Scholar
Lee, J. R., Busschers, F. S. & Sejrup, H. P. 2012. Pre-Weichselian Quaternary glaciations of the British Isles, The Netherlands, Norway and adjacent marine areas south of 68°N: implications for long-term ice sheet development in Northern Europe. Quaternary Science Reviews 44, 213228.CrossRefGoogle Scholar
Lerner, D. N. 2002. Identifying and quantifying urban recharge: a review. Hydrogeology Journal 10, 143152.CrossRefGoogle Scholar
Lewis, M. A., Cheney, C. S. & Ó Dochartaigh, B. É. 2006. Guide to permeability indices. British Geological Survey Commissioned Report, CR/06/160N.Google Scholar
MacCormack, K. E., Maclachlan, J. C. & Eyles, C. H. 2005. Viewing the subsurface in three-dimensions: initial results of modelling the Quaternary sedimentary infill of the Dundas Valley, Hamilton, Ontario. Geosphere 1, 2331.CrossRefGoogle Scholar
MacDonald, A. M., Maurice, L., Dobbs, M. R., Reeves, H. J. & Auton, C. A. 2012. Relating in situ hydraulic conductivity, particle size and relative density of superficial deposits in a heterogeneous catchment. Journal of Hydrology 434–435, 130141.CrossRefGoogle Scholar
MacDonald, A. M., Lapworth, D. J., Hughes, A. G., Auton, C. A., Maurice, L., Finlayson, A. & Gooddy, D. C. 2014. Groundwater, flooding and hydrological functioning in the Findhorn floodplain, Scotland. Hydrology Research 45, 755773.CrossRefGoogle Scholar
Marchant, A. P., Banks, V. J., Royse, K. R. & Quigley, S. P. 2013. The development of a GIS methodology to assess the potential for water resource contamination due to new development in the 2012 Olympic Park site, London. Computer and Geosciences 51, 206215.CrossRefGoogle Scholar
Matheron, G. 1962. Traité de géostatistique appliqué, Tome 1. Paris: Memoir du Bureau de Recherches Géologiques et Minières.Google Scholar
Maupin, M. A. & Barber, N. L. 2005. Estimated withdrawals from principal aquifers in the United States, 2000. U.S. Geological Survey Circular 1279.Google Scholar
McKay, L. D., Cherry, J. A. & Gillham, R. W. 1993. Field experiments in a fractured clay till: 1. Hydraulic conductivity and fracture aperture. Water Resources Research 29, 11491162.CrossRefGoogle Scholar
Merritt, J. E., Monaghan, A. A., Entwisle, D. C., Hughes, A. G., Campbell, S. D. G. & Brown, M. A. E. 2007. 3D attributed models for addressing environmental and engineering geoscience problems in areas of urban regeneration: a case study in Glasgow, UK. First Break 25, 7984.Google Scholar
Millham, N. P. & Howes, B. L. 1995. A comparison of methods to determine K in shallow coastal aquifer. Ground Water 33, 4957.CrossRefGoogle Scholar
Misstear, B. D. R., Brown, L. & Johnston, P. 2009. Estimation of groundwater recharge in a major sand and gravel aquifer in Ireland using multiple approaches. Hydrogeology Journal 17, 693706.CrossRefGoogle Scholar
Mondol, N. H., Bjorlykke, K., Jahren, J. & Hoeg, K. 2007. Experimental mechanical compaction of clay mineral aggregates – changes in physical properties of mudstones during burial. Marine and Petroleum Geology 24, 289311.CrossRefGoogle Scholar
Nœtinger, B., Artus, V. & Zargar, G. 2005. The future of stochastic and upscaling methods in hydrogeology. Hydrogeology Journal 13, 184201.CrossRefGoogle Scholar
Ó Dochartaigh, B. É., Bonsor, H. & Bricker, S. 2018. Improving understanding of shallow urban groundwater: the Quaternary groundwater system in Glasgow, UK. Earth and Environmental Science Transactions of the Royal Society of Edinburgh. DOI: 10.1017/S1755691018000385.Google Scholar
Odong, J. 2007. Evaluation of empirical formulae for determination of hydraulic conductivity based on grain-size analysis. The Journal of American Science 3, 5460.Google Scholar
Peacock, J. D. 2003. Late Quaternary sea level change and raised marine deposits of the Western Highland Boundary: a) the deglaciation of the lower Clyde valley: a brief review. In Evans, D. J. A. (ed.) The Quaternary of the Western Highland Boundary: field guide, 3041. London: Quaternary Research Association.Google Scholar
Renard, P. 2005. The future of hydraulic tests. Hydrogeology Journal 13, 259262.CrossRefGoogle Scholar
Schirmer, M., Leschik, S. & Musolff, A. 2013. Current research in urban hydrogeology – a review. Advances in Water Resources 51, 280291.CrossRefGoogle Scholar
Schlichter, C. S. 1899. Theoretical investigation of the motion of ground waters. U.S. Geological Survey 19th Annual Report part 2, 295384.Google Scholar
Seelheim, F. 1880. Methoden zur Bestimmung der Durchlässigkeit des Bodens. Zeitschrift für analytische Chemie 19, 387402.CrossRefGoogle Scholar
Self, S., Entwistle, D. & Northmore, K. 2012. The structure and operation of the BGS National Geotechnical Properties Database. Version 2. British Geological Survey Internal Report, IR/12/056, 68 pp.Google Scholar
Song, J. X., Chen, X. H., Cheng, C., Wang, D. M., Lackey, S. & Xu, Z. X. 2009. Feasibility of grain-size analysis methods for determination of vertical hydraulic conductivity of streambeds. Journal of Hydrology 375, 428437.CrossRefGoogle Scholar
Turner, R. J., Mansour, M. M., Dearden, R., Ó Dochartaigh, B. É. & Hughes, A. C. 2015. Improved understanding of groundwater flow in complex superficial deposits using three-dimensional geological-framework and groundwater models: an example from Glasgow, Scotland (UK). Hydrogeology Journal 23, 493506.CrossRefGoogle Scholar
Vienken, T. & Dietrich, P. 2011. Field evaluation of methods for determining hydraulic conductivity from grain size data. Journal of Hydrology 400, 5871.CrossRefGoogle Scholar
Vuković, M. & Soro, A. 1992. Determination of hydraulic conductivity of porous media from grain-size composition. Littleton, CO: Water Resources Publications.Google Scholar
Watson, C., Richardson, J., Wood, B., Jackson, C. & Hughes, A. 2015. Improving geological and process model integration through TIN to 3D grid conversion. Computers & Geosciences 82, 4554.CrossRefGoogle Scholar
Woods-Ballard, B., Kellagher, R., Martin, P., Jeffries, C., Bray, R. & Shaffer, P. 2007. CIRIA C697. The SUDS manual. London: CIRIA.Google Scholar