An experimentally verified model of the seepage progress due to dissolution of soluble particles in foundations subject to intergranular flow


The foundations of dams containing soluble material, typically gypsum and limestone, undergo a dissolving process as a consequence of reservoir seepage. In due course, such dissolution of soluble material increases the volume of holes through which water may flow, in turn involving an increase in flow rate through the dam foundation. To adapt dam design to the particular conditions of these foundations, especially in foundations containing gypsum, with the main aims of delaying the dissolution process and avoiding damage or loss of functionality during dam lifespan, a procedure that models the dissolution process coupled with seepage phenomena is necessary. The objective of this paper is to provide this procedure and test it under experimental conditions. This entails coupling a conventional code for calculation of seepage networks, by means of the finite-element method, with a code developed by the authors to calculate the solution front advance (the zone where the dissolution is taking place). The procedure is verified by performing permeameter testing using sand and soluble material mixtures, with the tests being numerically modelled.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. 1.

    FastSEEP program: graphical pre and post-processor of the program Seep2D, developed by Boss International. Seep2D was written by Fred Tracy of the US Army Engineer Waterways Experiment Station.

  2. 2.

    Dissolution2D program: developed by Luis Medina Martinez and Carmen María Baena Berrendero (2007) For the entire code, see Baena (2011).


A :

Area exposed to dissolution (L2)

A f :

Acceleration factor

C :

Concentration (M/L3)

C s :

Concentration of saturation (M/L3)

d :

Representative pore size (L)

D 50 :

Sieve aperture that allows 50 % of the material to pass (L)

g :

Gravity (L/T2)

h 0 :

Constant head (in test) (L)

i :

Hydraulic gradient

i 0 :

Initial hydraulic gradient (in test)

K :

Permeability coefficient (L/T)

K d :

Dissolution rate constant (L/T). Usually K in bibliography

K 0 :

Initial permeability coefficient (L/T)

K td :

Permeability coefficient after dissolution (L/T)

K i :

Intrinsic permeability (L2)

M :

Mass of soluble solid (M)

M ms :

Mass of soluble material (in test) (M)

n :


n 0 :

Initial porosity

Q :

Volumetric flow rate (L3/T)

Q 0 :

Initial flow rate (L3/T)

Q td :

Flow rate after dissolution (L3/T)

Re :

Reynolds number

S :

Surface of grain (L2)

t :

Time (T)

t ab :

Arriving time downstream (T)

t u-cte :

Time for constant u (T)

u :

Solution front velocity (L/T)

u 0 :

Initial solution front velocity (L/T)

v :

Seepage velocity (L/T)

v 0 :

Initial seepage velocity (L/T)

V :

Dissolution volume (L3)

V g :

Volume of grain (L3)

V t :

Soil volume (L3)

V h :

Fraction for interconnected pore holes (L3)

V s :

Fraction for soluble particles (L3)

V in :

Fraction for insoluble particles (L3)

ρ :

Density (M/L3)

θ :

Order of the dissolution kinetic

ν :

Viscosity (M/L/T)

σ 0 :

Mass per unit volume of soluble particle (M/L3)

ϕ :

Percentage in volume of soluble material


  1. Araoz Sánchez-Albornoz A (1992) Cimentación de presas en terrenos terciarios con disolución de evaporitas y erosión interna en la Cuenca del Ebro. Rev Obras Públicas 139(3309):265–290

    Google Scholar 

  2. Baena CM (2011) Análisis de la filtración en presas con cimientos yesíferos. Tesis doctoral, UPM, Madrid

  3. Calvino F, Costantino F, Mirri F (1981) Design criteria for a dam, reservoir and irrigation system on a Middle East evaporite formation. Bull Int Assoc Eng Geol 24:53–54

    Article  Google Scholar 

  4. Carman PC (1956) Flow of gases through porous media. Butterworths Scientific Publications, London

    Google Scholar 

  5. Dreybrodt W, Romanov D, Gabrovsek F (2001) Dam sites in soluble rocks: a model of increasing leakage by dissolutional widening of fractures beneath a dam. Eng Geol 70:17–35

    Google Scholar 

  6. Dreybrodt W, Romanov D, Gabrovsek F (2002) Karstification below dam sites: a mode of increasing leakage from reservoirs. Environ Geol 45:518–524

    Google Scholar 

  7. Farid AM, Habibagahi G (2007) Dissolution-seepage coupled analysis through formations containing soluble materials. J Eng Mech 133(6):713–722

    Article  Google Scholar 

  8. Flores CE, Rodríguez P (1967) Problemas de disolución de yesos en algunos sitios de presas. Boletín de la Sociedad Venezolana de Mecánica de Suelo e Ingeniería de Fundaciones: 3–14

  9. Ghobadi MH, Khanlari GR, Djalaly H (2005) Seepage problems in the right abutment of the Shahid Abbaspour dam, southern Iran. Eng Geol 82:119–126

    Article  Google Scholar 

  10. Gumusoglu MC, Ulker R (1982) The investigation of the effect of gypsum on foundation design. Bull Int Assoc Eng Geol 25:99–105

    Article  Google Scholar 

  11. Guzina BJ, Saric M, Petrovic N (1991) Seepage and dissolution at foundations of a dam during the first impounding of the reservoir. In: XVII congress of ICOLD (Vienna) Q.66 R.78, pp 1459–1475

  12. James AN (1977) Calcium sulphate in the foundations of major embankment dams. Q J Eng Geol 11:332–333 (summaries of papers read at the engineering regional meeting–Cardiff)

  13. James AN (1982) Engineering properties of evaporitic rock. Bull Int Assoc Eng Geol 25:125–126

    Article  Google Scholar 

  14. James AN (1992) Soluble materials in civil engineering. Ellis Horwood, New York

    Google Scholar 

  15. James AN, Edworthy KJ (1985) The effects of water interactions on engineering structures. Hydrol Sci J 30(3):395–406

    Article  Google Scholar 

  16. James AN, Kirkpatrick IM (1980) Design of foundations of dams containing soluble rocks and soils. Q J Eng Geol Hydrogeol 13(3):189–198

    Article  Google Scholar 

  17. James AN, Lupton ARR (1978) Gypsum and anhydrite in foundations of hydraulic structures. Geótechnique 28(3):249–272

    Article  Google Scholar 

  18. James AN, Lupton ARR (1985) Further studies of the dissolution of soluble rocks. Geótechnique 35(2):205–210

    Article  Google Scholar 

  19. James AN, Cooper AH, Holliday DW (1981) Solution of the gypsum cliff (Permian, Middle Marl) by the River Ure at Ripon Parks, North Yorkshire. In: Proceedings of Yorkshire Geological Society, vol 43, 4 (24), pp 433–450

  20. Johnson KS (2008) Gypsum-karst problems in constructing dams in the USA. Environ Geol 53:945–950

    Article  Google Scholar 

  21. Kolditz O, Bauer S, Bilke L, Böttcher N, Delfs JO, Fischer T, Görke UJ, Kalbacher T, Kosakowski G, McDermott CI, Park CH, Radu F, Rink K, Shao H, Shao HB, Sun F, Sun YY, Singh AK, Taron J, Walther M, Wang W, Watanabe N, Wu N, Xie M, Xu W, Zehner B (2012) OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. Environ Earth Sci 67(2):589–599. doi:10.1007/s12665-012-1546-x

    Article  Google Scholar 

  22. Kolditz O, Görke UJ, Shao HB, Wang W, Shao H, Hudson JA, Feng XT (2013) Thermo-hydro-mechanical-chemical processes in fractured rock. In: 3rd ISRM symposium on rock characterisation, modelling an engineering design methods, SINOROCK 2013, Shanghai, 18–20 June 2013 (code 97711)

  23. Kozeny J (1927) Ueber Kapillare Leitung des Wassers im Boden. Sitz Akad Wiss Wien 136(2):271–306

    Google Scholar 

  24. Liu S, Nancollas GH (1970) The kinetics of dissolution of calcium sulfate dihydrate. J Inorg Nucl Chem 23:2311–2316

    Google Scholar 

  25. Macau F, Riba O (1962) Situación, características y extensión de los terrenos yesíferos en España. In: I Coloquio Internacional sobre las Obras Públicas en terrenos yesíferos, vol V, C 0–1, pp 157–184

  26. Milanović PT (2000) Geological engineering in karst. Zebra, Belgrade

    Google Scholar 

  27. Milanović PT (2004) Water resources engineering in karst. CRC, Boca Raton

    Google Scholar 

  28. Nedriga VP, Dem’yanova ÉA (1986) Construction of dams on soils containing soluble salts. Hydrotech Constr 20(2):116–121

    Article  Google Scholar 

  29. Nernst WZ (1904) Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen. Phys Chem 47:52–55

    Google Scholar 

  30. Samper J, Ayora C (1993) Acoplamiento de modelos de transporte de soluto y de modelos de reacciones químicas. Estud Geol 49:233–251

    Article  Google Scholar 

  31. Steefel CI, Lasaga AC (1990) Evolution of dissolution patterns. Permeability change due to coupled flow and reaction. In: Chemical modelling of aqueous systems II, Chap 16, pp 212–223. American Chemical Society, Washington

  32. Szymczak P, Ladd AJC (2012) Reactive-infiltration instabilities in rocks. Fracture dissolution. J Fluid Mech 702:239–264

    Article  Google Scholar 

  33. Verhoef PNW (2009) Dam and canal design on soluble rock (West Gode Irrigation Project, Ethiopia). Geointernational 44–50

  34. Yagüe J, Alonso M (1999) Control de filtraciones en cimientos erosionables de presas de materiales sueltos. VI Jorn Esp Presas (Málaga) 53:75–83

    Google Scholar 

  35. Yilmaz I (2001) Gypsum/anhydrite: some engineering problems. Bull Eng Geol Environ 59:227–230

    Article  Google Scholar 

Download references


We wish to show our appreciation to Raúl González Guijarro for his valuable help in the methodology and interpretation of the tests and Luis Medina Martínez for his assistance in writing Dissolution2D, as well as to the Geotechnical Laboratory at ETSICCP (UPM) and the Geotechnical Laboratory at CEDEX (Madrid).

Author information



Corresponding author

Correspondence to C. M. Baena.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Baena, C.M., Toledo, M.Á. An experimentally verified model of the seepage progress due to dissolution of soluble particles in foundations subject to intergranular flow. Environ Earth Sci 72, 3369–3382 (2014).

Download citation


  • Dissolution
  • Seepage
  • Dam
  • Gypsum
  • Foundation
  • Permeability