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On the Time-Development of Sulphate Hydration in Anhydritic Swelling Rocks

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Abstract

Anhydritic claystones are among the most problematic rocks in tunnelling. Their swelling has caused serious damage and high repair costs in a number of tunnels, especially in Switzerland and southwest Germany. The swelling is usually attributed to the transformation of anhydrite into gypsum. It is a markedly time-dependent process which might take several decades to complete in nature. The present paper focusses on simultaneous anhydrite dissolution and gypsum precipitation in a closed system, i.e. disregarding the transport processes that may also be important for the evolution of the swelling process. The paper begins with a presentation of the governing equations and continues with parametric studies in order to investigate the role of the initial volumetric fractions of the constituents and the specific surface areas of the minerals involved. A simplified model for the hydration of anhydrite is also proposed, which identifies the governing process and the duration of the swelling process. Finally, parametric studies are performed in order to investigate the effect of the anhydrite surface being sealed by the formation of gypsum. The latter slows down the swelling process considerably.

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Abbreviations

A :

Mineral surface area in contact with water

A :

Shape factor of parellelepipedic particles

a A :

Shape factor of parellelepipedic anhydrite particles

a G :

Shape factor of parellelepipedic gypsum particles

b :

Shape factor of parellelepipedic particles

b A :

Shape factor of parellelepipedic anhydrite particles

b G :

Shape factor of parellelepipedic gypsum particles

c :

Ion concentration

\(\tilde{c}\) :

Normalized concentration

\(c_{0}\) :

Initial concentration

\(\tilde{c}_{0}\) :

Normalized initial concentration

c eq :

Equilibrium concentration

c eq,A :

Anhydrite equilibrium concentration

c eq,G :

Gypsum equilibrium concentration

\(\tilde{c}_{{{\text{eq}},{\text{G}}}}\) :

Normalized gypsum equilibrium concentration

c max :

Maximum concentration

F :

Specific surface area

F A :

Anhydrite specific surface area

F P :

Specific surface area of particles consisting of inert solid and gypsum

F S :

Inert solid specific surface area

J :

Diffusive flux

K :

Reaction rate constant

\(\tilde{k}\) :

Diffusion coefficient

k A :

Reaction rate constant for anhydrite dissolution

k G :

Reaction rate constant for gypsum precipitation

m :

Mass per unit volume of the mixture

m A :

Anhydrite mass per unit volume of the mixture

m A0 :

Initial anhydrite mass per unit volume of the mixture

m I :

Ion mass per unit volume of the mixture

m I0 :

Initial ion mass per unit volume of the mixture

m G :

Gypsum mass per unit volume of the mixture

m G0 :

Initial gypsum mass per unit volume of the mixture

m W :

Water mass per unit volume of the mixture

m W0 :

Initial water mass per unit volume of the mixture

M :

Mass

n G :

Porosity of the gypsum layer

s :

Distance of the mineral surface from its initial surface

S 0 :

Characteristic length (thickness and diameter for parellelepipedic and spherical particles, respectively)

s A :

Thickness of dissolved anhydrite

\(\bar{s}_{\text{A}}\) :

Normalized thickness of dissolved anhydrite

S A :

Characteristic length of anhydrite particles

\(\bar{S}_{\text{A}}\) :

Normalized characteristic length of anhydrite particles

S A0 :

Initial characteristic length of anhydrite particles

s G :

Gypsum layer thickness

\(\bar{s}_{\text{G}}\) :

Normalized gypsum layer thickness

S G0 :

Initial characteristic length of gypsum particles

S G,A :

Characteristic length of gypsum particles for growth on anhydrite

\(\bar{S}_{\text{G,A}}\) :

Normalized characteristic length of gypsum particles for growth on anhydrite

S G,G :

Characteristic length of gypsum particles for growth on gypsum

\(\bar{S}_{\text{G,G}}\) :

Normalized characteristic length of gypsum particles for growth on gypsum

S G,S :

Characteristic length of gypsum particles for growth on inert minerals

\(\bar{S}_{\text{G,S}}\) :

Normalized characteristic length of gypsum particles for growth on inert minerals

S S :

Inert solid particles diameter

\(\bar{S}_{\text{S}}\) :

Normalized diameter of inert solid particles

T :

Time

t d :

Time at which sealing becomes the relevant mechanism

T G :

Gypsum layer tortuosity

V :

Volume

V tot :

Total volume of the mixture

V tot,0 :

Initial total volume of the mixture

α :

Order of chemical reaction

α A :

Order of reaction for anhydrite dissolution

α G :

Order of reaction for gypsum precipitation

Λ:

Dimensionless parameter

\(\bar{\Uplambda }\) :

Dimensionless parameter

Λ* :

Dimensionless parameter

Φ :

Volume fraction

ϕ A :

Anhydrite volume fraction

ϕ A0 :

Initial anhydrite volume fraction

ϕ A0,crit :

Critical initial anhydrite volume fraction

ϕ G :

Gypsum volume fraction

ϕ G0 :

Initial gypsum volume fraction

ϕ G,A :

Volume fraction of gypsum grown on anhydrite particles

ϕ G,G :

Volume fraction of gypsum grown on gypsum particles

ϕ G,S :

Volume fraction of gypsum grown on inert solid particles

ϕ P :

Volume fraction of particles consisting of inert solid and gypsum

ϕ S :

Inert solid volume fraction

ϕ W :

Water volume fraction

ϕ W0 :

Initial water volume fraction

ρ:

Density

ρ A :

Anhydrite density

ρ G :

Gypsum density

ρ S :

Inert solid density

ρ W :

Water density

τ :

Dimensionless time

\(\bar{\tau }\) :

Dimensionless time

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Acknowledgments

This paper evolved within the framework of the research project ‘Modelling of anhydritic swelling claystones’ which is being carried out at the ETH Zurich, being financed by the Swiss National Science Foundation (SNF) and the Swiss Federal Roads Office (FEDRO).

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  1. ETH Zurich, Switzerland

    K. Serafeimidis & G. Anagnostou

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  1. K. Serafeimidis
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Correspondence to K. Serafeimidis.

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Serafeimidis, K., Anagnostou, G. On the Time-Development of Sulphate Hydration in Anhydritic Swelling Rocks. Rock Mech Rock Eng 46, 619–634 (2013). https://doi.org/10.1007/s00603-013-0376-9

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