Skip to main content Accessibility help

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

  • J. D. O. Williams (a1), M. R. Dobbs (a1), A. Kingdon (a1), R. M. Lark (a1), J. P. Williamson (a1), A. M. MacDonald (a2) and B. É. Ó Dochartaigh (a2)...


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.


Corresponding author

*Corresponding author


Hide All
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.
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.
Bear, J. 1972. Dynamics of fluids in porous media. New York: Dover Publications.
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.
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.
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.
British Standards Institution. 1990. BS 1377-2 Methods of test for soils for civil engineering purposes. Classification tests.
British Standards Institution. 1999. BS 5930 Code of practise for site investigations.
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.
Browne, M. A. E. & McMillan, A. A. 1989. Quaternary geology of the Clyde valley. British Geological Survey Research Report, SA/89/1.
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.
Carrier, W. D. III. 2003. Goodbye, Hazen; Hello, Kozeny-Carman. Journal of Geotechnical and Geoenvironmental Engineering 129, 10541056.
Chapuis, R. P. 2004. Predicting the saturated hydraulic conductivity of sand and gravel using effective diameter and void ratio. Canadian Geotechnical Journal 41, 787795.
Chilton, P. J. (ed.) 1999. Groundwater in the urban environment. Rotterdam: Balkema.
Cressie, N. & Hawkins, D. M. 1980. Robust estimation of the variogram. Journal of the International Association for Mathematical Geology 12, 115125.
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.
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.
Deutsch, C. V. & Journel, A. G. 1992. Geostatistical software library and user's guide. New York: Oxford University Press.
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.
Finlayson, A. 2012. Ice dynamics and sediment movement: late glacial cycle, Clyde Basin, Scotland. Journal of Glaciology 58, 487500.
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.
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.
Freeze, R. A. & Cherry, J. A. 1979. Groundwater. Englewood Cliffs, NJ: Prentice-Hall.
Gogu, R. C. & Dassargues, A. 2000. Current trends and future challenges in groundwater vulnerability assessment using overlay and index methods. Environmental Geology 39, 549559.
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.
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.
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.
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.
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.
Kolterman, C. E. & Gorelick, S. M. 1995. Fractional packing model for hydraulic conductivity derived from sediment mixtures. Water Resources Research 31, 32833297.
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.
Lark, R. M. 2002. Modelling complex soil properties as contaminated regionalized variables. Geoderma 106, 171188.
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.
Lerner, D. N. 2002. Identifying and quantifying urban recharge: a review. Hydrogeology Journal 10, 143152.
Lewis, M. A., Cheney, C. S. & Ó Dochartaigh, B. É. 2006. Guide to permeability indices. British Geological Survey Commissioned Report, CR/06/160N.
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.
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.
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.
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.
Matheron, G. 1962. Traité de géostatistique appliqué, Tome 1. Paris: Memoir du Bureau de Recherches Géologiques et Minières.
Maupin, M. A. & Barber, N. L. 2005. Estimated withdrawals from principal aquifers in the United States, 2000. U.S. Geological Survey Circular 1279.
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.
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.
Millham, N. P. & Howes, B. L. 1995. A comparison of methods to determine K in shallow coastal aquifer. Ground Water 33, 4957.
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.
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.
Nœtinger, B., Artus, V. & Zargar, G. 2005. The future of stochastic and upscaling methods in hydrogeology. Hydrogeology Journal 13, 184201.
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.
Odong, J. 2007. Evaluation of empirical formulae for determination of hydraulic conductivity based on grain-size analysis. The Journal of American Science 3, 5460.
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.
Renard, P. 2005. The future of hydraulic tests. Hydrogeology Journal 13, 259262.
Schirmer, M., Leschik, S. & Musolff, A. 2013. Current research in urban hydrogeology – a review. Advances in Water Resources 51, 280291.
Schlichter, C. S. 1899. Theoretical investigation of the motion of ground waters. U.S. Geological Survey 19th Annual Report part 2, 295384.
Seelheim, F. 1880. Methoden zur Bestimmung der Durchlässigkeit des Bodens. Zeitschrift für analytische Chemie 19, 387402.
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.
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.
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.
Vienken, T. & Dietrich, P. 2011. Field evaluation of methods for determining hydraulic conductivity from grain size data. Journal of Hydrology 400, 5871.
Vuković, M. & Soro, A. 1992. Determination of hydraulic conductivity of porous media from grain-size composition. Littleton, CO: Water Resources Publications.
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.
Woods-Ballard, B., Kellagher, R., Martin, P., Jeffries, C., Bray, R. & Shaffer, P. 2007. CIRIA C697. The SUDS manual. London: CIRIA.


Related content

Powered by UNSILO

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

  • J. D. O. Williams (a1), M. R. Dobbs (a1), A. Kingdon (a1), R. M. Lark (a1), J. P. Williamson (a1), A. M. MacDonald (a2) and B. É. Ó Dochartaigh (a2)...


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.