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

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Abstract

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.

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Notes

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

Abbreviations

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 :

Porosity

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

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Acknowledgments

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).

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Authors and Affiliations

  1. Jesús Granell Ingenieros Consultores, SL, Madrid, Spain

    C. M. Baena

  2. Universidad Politécnica de Madrid, Madrid, Spain

    M. Á. Toledo

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  1. C. M. Baena
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Correspondence to C. M. Baena.

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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). https://doi.org/10.1007/s12665-014-3243-4

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