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On the Occurrence of Anhydrite in the Sulphatic Claystones of the Gypsum Keuper

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We investigate why the sulphatic claystones of the Gypsum Keuper contain anhydrite rather than gypsum even at small depths of cover. This question is relevant due to the phenomenon of swelling of anhydritic claystones, which is attributed to the transformation of anhydrite into gypsum and has caused serious damage to a number of tunnels. In tunnelling, the Gypsum Keuper formation is crossed at rather small depths, where simplified thermodynamic considerations indicate that the calcium sulphate should be encountered in its hydrated form, i.e. as gypsum rather than as anhydrite. Understanding why anhydrite can be found at small depths is not only interesting from a fundamental point of view, but also necessary in order to formulate adequate initial conditions for the continuum-mechanical models that simulate the chemo-mechanical and transport processes in swelling anhydritic claystones. The paper quantitatively examines three reasons which, alone or in combination, might explain the occurrence of anhydrite: the small size of the pores in argillaceous rocks; locally high stresses in the vicinity of the sulphate crystals; and the thermodynamic state of the pore water. The computations of the paper take account of the results of porosimetry experiments on samples from two Swiss tunnels in Gypsum Keuper and show that the most probable reason is the thermodynamic state of the pore water, i.e. its ability to participate in chemical reactions. More specifically, the clay minerals reduce the chemical potential of the pore water, thus increasing the solubility of the gypsum and shifting the thermodynamic equilibrium in favour of anhydrite.

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b :


c eq,A :

Equilibrium concentration of anhydrite

c eq,G :

Equilibrium concentration of gypsum

c 0 :

Concentration at standard state

F p :

Area of the pores

F tot :

Total area

g :

Gravitational acceleration

H :

Depth of cover

L :

Side length

n :

Pore percentage

n cr :

Critical pore percentage

p A :

Anhydrite pressure

p G :

Gypsum pressure

p S0 :

Lithostatic pressure

p W :

Pore water pressure

p W0 :

Initial (in situ) pore water pressure

p W1 :

Pore water pressure after swelling test

p G,UL :

Upper limit of the gypsum pressure

R :

Universal gas constant

r A :

Radius of anhydrite particles

r cr :

Critical pore radius

r G :

Radius of gypsum particles

r p :

Pore radius

T :


T 0 :

Temperature at standard state

\( V_{A}^{0} \) :

Molar volume of anhydrite at standard state

\( V_{G}^{0} \) :

Molar volume of gypsum at standard state

\( V_{W}^{0} \) :

Molar volume of water at standard state

\( V_{W} \) :

Molar volume of water

a W :

Water activity

γ A :

Surface free energy of the anhydrite–water interface

γ G :

Surface free energy of the gypsum–water interface

γ ± :

Mean activity coefficient

\( \Delta_{r,GA} G^{0} \) :

Standard Gibbs energy of anhydrite hydration

\( \Delta_{r,GA} S^{0} \) :

Standard entropy of anhydrite hydration

\( \Delta_{r,A} V^{0} \) :

Standard volume of anhydrite dissolution

\( \Delta_{r,G} V^{0} \) :

Standard volume of gypsum dissolution

σ :

Total stress

σ 0 :

Initial total stress

σ s :

Maximum swelling pressure


Effective stress

σ 0 :

Initial (in situ) effective stress

ρ R :

Rock density

ρ W :

Water density

\( \phi \) :


\( \phi_{{_{cr} }} \) :

Critical porosity



Ψ0 :

Potential of pore water in situ

Ψ1 :

Potential of pore water after swelling test


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This paper evolved within the framework of the research project “Modelling of anhydritic swelling claystones”, which is being carried out at the ETH Zurich with the financing of the Swiss National Science Foundation (SNF) under Project Nr. 200021-126717/1 and the Swiss Federal Roads Office (FEDRO) under Project Nr. FGU 2010-007. The authors would like to thank Prof. Robert Flatt, ETH Zurich, for his valuable suggestions concerning the importance of pore size and liquid–crystal interfacial effects; Dr. Andreas Leemann and Dr. Mateusz Wyrzykowski from EMPA, as well as Mrs Annette Röthlisberger from our Institute’s Clay Mineralogy Lab for performing the MIP tests.

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Correspondence to G. Anagnostou.



Sections 2, 3 and 4 make frequent use of the following expressions for the equilibrium concentrations c eq,G and c eq,A of gypsum and anhydrite:

$$ RT\ln \left( {\gamma_{ \pm }^{{}} \frac{{c_{eq,G}^{{}} }}{{c_{0} }}a_{W}^{{}} } \right)^{2} = - \Delta_{r,G} G^{0} + \left( {T - T_{0} } \right)\;\Delta_{r,G} S^{0} + \left( {p_{G} + \frac{{2\gamma_{G} }}{{r_{G} }}} \right)\;V_{G}^{0} - p_{W} \;\left( {V_{G}^{0} + \Delta_{r,G} V^{0} } \right), $$
$$ RT\ln \left( {\gamma_{ \pm }^{{}} \frac{{c_{eq,A}^{{}} }}{{c_{0} }}} \right)^{2} = - \Delta_{r,A} G^{0} + \left( {T - T_{0} } \right)\;\Delta_{r,A} S^{0} + \;\left( {p_{A} + \frac{{2\gamma_{A} }}{{r_{A} }}} \right)V_{A}^{0} - p_{W} \left( {\;V_{A}^{0} + \Delta_{r,A} V^{0} } \right), $$

where T, p G , p A and p W denote the temperature, the gypsum pressure, the anhydrite pressure and the pore water pressure, respectively. The symbols γ G , r G , γ A and r A denote the surface energies and the particle radii of gypsum and anhydrite. The surface energy γ G of gypsum can be taken equal to 80 mN/m, while the effect of surface energy of the anhydrite particles (term 2γ A /r A ) can be neglected because of their relatively large size (>1 μm). The symbol γ ± denotes the mean activity coefficient of the dissolved ions and can be computed after Davies (1962). The symbols c 0 and T 0 denote the standard concentration (1 mol/l) and the standard temperature (298 K), respectively. The other symbols appearing in Eqs. (6) and (7) are the thermodynamic constants. More details, including the derivations of the equations as well as the values of the thermodynamic constants, can be found in Serafeimidis and Anagnostou (2014).

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Anagnostou, G., Serafeimidis, K. & Vrakas, A. On the Occurrence of Anhydrite in the Sulphatic Claystones of the Gypsum Keuper. Rock Mech Rock Eng 48, 1–13 (2015).

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