Skip to main content
Log in

On the crystallisation pressure of gypsum

  • Original Article
  • Published:
Environmental Earth Sciences Aims and scope Submit manuscript

Abstract

We estimate the crystallisation pressure of gypsum quantitatively, with reference to the geological context of the Gypsum Keuper formation. The formation contains sulphatic claystones which have the property of swelling in the presence of water and have caused substantial structural damage to the linings of several tunnels in Switzerland and Germany. The swelling of these rocks is attributed to the transformation of anhydrite into gypsum, which occurs via the dissolution of anhydrite in pore water and the precipitation of gypsum from the solution. This simultaneous dissolution–precipitation process happens because the solubility of gypsum is lower than that of anhydrite under the conditions prevailing after tunnelling, and it does not cease until all of the anhydrite has been transformed. The elementary mechanism behind the development of the macroscopically observed swelling pressure is the growth of gypsum crystals inside the rock matrix: If a crystal is in contact with a supersaturated solution, but its growth is prevented by the surrounding matrix, it then exerts a so-called crystallisation pressure upon the pore walls. In the present paper, the crystallisation pressure is calculated by means of a thermodynamic model that takes coherent account of all relevant parameters, including the chemical composition of the pore water and pore size. Variations in these parameters lead to a very wide range of crystallisation pressures (from zero to several tens of megapascals). By using the results of mercury intrusion porosimetry and chemical analyses of samples from three Swiss tunnels, however, we show that the range of predicted values can be reduced significantly with the help of standard, project-specific investigations.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Abbreviations

c:

Concentration

c i :

Concentration of ion i

\( c_{{{\text{Ca}}^{{ 2 { + }}} }} \) :

Concentration of calcium ions

c eq,A :

Anhydrite equilibrium concentration

\( c_{{{\text{eq}},{\text{G}}}}^{0} \) :

Gypsum equilibrium concentration at standard state

\( c_{{{\text{SO}}_{4}^{2 - } }} \) :

Concentration of sulphate ions

K :

Ion activity product

\( K_{{{\text{eq}},{\text{A}}}}^{0} \) :

Equilibrium solubility product of anhydrite at standard state

\( K_{{{\text{eq}},{\text{G}}}}^{0} \) :

Equilibrium solubility product of gypsum at standard state

\( K_{\text{sp}} \) :

Solubility product in Flückiger’s (1994) model

\( K_{\text{sp}}^{0} \) :

Solubility product at standard state in Flückiger’s (1994) model

n :

Pore percentage

p G :

Crystallisation pressure

p G1 :

Crystallisation pressure at state 1

p G2 :

Crystallisation pressure at state 2

R :

Universal gas constant

r G :

Radius of gypsum particles

r p :

Pore radius

\( S_{\text{A}}^{0} \) :

Molar entropy of anhydrite at standard state

\( S_{\text{G}}^{0} \) :

Molar entropy of gypsum at standard state

\( S_{\text{W}}^{0} \) :

Molar entropy of water at standard state

T:

Temperature

T 0 :

Temperature at standard state

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

Molar volume of anhydrite at standard state

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

Molar volume of gypsum at standard state

α W :

Water activity

α i :

Activity of ion i

\( \gamma_{{{\text{Ca}}^{2 + } }} \) :

Activity coefficient of calcium ions

γ G :

Surface free energy of the gypsum–water interface

γ i :

Activity coefficient of ion i

\( \gamma_{{{\text{SO}}_{4}^{2 - } }} \) :

Activity coefficient of sulphate ions

ΔG r :

Free energy of the transformation of anhydrite to gypsum in Flückiger’s (1994) model

Δ r,A G 0 :

Standard Gibbs energy of anhydrite dissolution

Δ r,A S 0 :

Standard entropy of anhydrite dissolution

Δ r,A V 0 :

Standard volume of anhydrite dissolution

Δ r,GA G 0 :

Standard Gibbs energy of the transformation of anhydrite to gypsum

Δ r,GA S 0 :

Standard entropy of the transformation of anhydrite to gypsum

Δ r,GA V 0 :

Standard volume of the transformation of anhydrite to gypsum

Δ r,G G 0 :

Standard Gibbs energy of gypsum dissolution

Δ r,G S 0 :

Standard entropy of gypsum dissolution

Δr,G V 0 :

Standard volume of gypsum dissolution

References

  • Amstad C, Kovári K (2001) Untertagbau in quellfähigem Fels. Schlussbericht Forschungsauftrag 52/94 des Bundesamts für Strassen ASTRA

  • Anderson GM (1996) Thermodynamics of natural systems. University of Toronto. Wiley, New York

    Google Scholar 

  • Bachema (1995) Chemische Untersuchung von Wasserproben Adlertunnel Bahn 2000. Several reports by “Institut Bachema AG, Analytische Laboratorien”

  • Blount CW, Dickson FW (1973) Gypsum-anhydrite equilibria in systems CaSO4–H2O and CaCO3–NaCl–H2O. Am Mineral 58:323–331

    Google Scholar 

  • Correns CW, Steinborn W (1939) Experimente zur Messung und Erklärung der sogenannten Kristallisationskraft. Z Krist (A) 101:117–133

    Google Scholar 

  • Davies CW (1962) Ion association. Butterwoths, London

    Google Scholar 

  • Flatt RJ (2002) Salt damage in porous materials: how high supersaturations are generated. J Cryst Growth 242:435–454

    Article  Google Scholar 

  • Flatt RJ, Steiger M, Scherer GW (2007) A commented translation of the paper by C.W. Correns and W. Steinborn on crystallization pressure. Environ Geol 52:187–203

    Article  Google Scholar 

  • Fletcher RC, Merino E (2001) Mineral growth in rocks: kinetic-rheological models of replacement, vein formation, and syntectonic crystallization. Geochim Cosmochim Acta 65(21):3733–3748

    Article  Google Scholar 

  • Flückiger A (1994) Anhydritquellung. Rencontre Internationale des jeunes chercheurs en geologie appliquees, Lausanne, 21 Avril 1994, 103–107

  • Flückiger A, Nüesch R, Madsen F (1994) Anhydritquellung. Berichte zur Jahrestagung Regensburg der Deutschen Ton und Tonmineralgruppe e.V., 146–153

  • Freyer D, Voigt W (2003) Crystallization and phase stability of CaSO4 of and CaSO4—based salts. Monatsh Chem 134:693–719

    Article  Google Scholar 

  • Gmelin L (1961) Gmelins Handbuch der anorganischen Chemie Calcium. Gmelin-Institut, Max-Planck-Gesellschaft

    Google Scholar 

  • Huggenberger P (2014) University of Basle, Personal communication

  • Kelley KK, Southard JC, Anderson CT (1941) Thermodynamic properties of gypsum and its dehydration products. U.S G.P.O., Bureau of Mines, Washington, p 73

    Google Scholar 

  • Klepetsanis GP, Koutsoukos GP (1991) Spontaneous precipitation of calcium sulfate at conditions of sustained supersaturation. J Colloid Interface Sci 143(2):299–308

    Article  Google Scholar 

  • Leemann A, Wyrzykowski M (2012) MIP tests on gypsum Keuper samples from the Chienberg and Belchen Tunnel. Internal laboratory test report, EMPA

    Google Scholar 

  • Liu S-T, Nancollas HG (1970) The kinetics of crystal growth of calcium sulfate dihydrate. J Cryst Growth 6:281–289

    Article  Google Scholar 

  • LPM (2000-3) Wasseranalysen Chienberg Tunnel. Several reports by “Labor für Prüfung und Materialtechnologie”

  • Marsal D (1952) Der Einfluss des Druckes auf das System CaSO4–H2O. Heidelberger Beiträge zur Mineralogie and Petrographie 3:289–296

    Google Scholar 

  • Merino E, Dewers Th (1998) Implications of replacement for reaction–transport modeling. J Hydrol 209:137–146

    Article  Google Scholar 

  • Merkel JB, Planer-Friedrich B (2008) Groundwater geochemistry, 2nd edition. Springer, Berlin

    Google Scholar 

  • Noher H-P, Meyer N (2002) Belchentunnel Versuchsdrainagestollen, Beurteilung der Wasseranalysen. Report 1510720.003 by Geotechnisches Institut AG

  • Pimentel E (2007) Quellverhalten von Gesteinen – Erkenntisse aus Laboruntersuchungen. Quellprobleme in der Geotechnik, Mitteilungen der Schweizerischen Gesellschaft für Boden- und Felsmechanik, Frühjahrstagung Freiburg, No. 154:11–20

    Google Scholar 

  • Ping X, Beaudoin J (1992) Mechanism of sulphate expansion: I. Thermodynamic principle of crystallization pressure. Cem Concr Res 22:631–640

    Article  Google Scholar 

  • Röthlisberger A (2012) MIP tests on gypsum Keuper samples from the Chienberg and Belchen Tunnel. Internal laboratory test report, Institute for Geotechnical Engineering, ETH Zurich

    Google Scholar 

  • Scherer GW (1999) Crystallization in pores. Cem Concr Res 29:1347–1358

    Article  Google Scholar 

  • Serafeimidis K, Anagnostou G (2012) On the kinetics of the chemical reactions underlying the swelling of an hydritic rocks. Eurock 2012, Stockholm

  • Serafeimidis K, Anagnostou G (2014) The solubilities and thermodynamic equilibrium of anhydrite and gypsum. Rock Mech Rock Eng. doi:10.1007/s00603-014-0557-1

    Google Scholar 

  • Steiger M (2005) Crystal growth in porous materials—II: influence of crystal size on the crystallization pressure. J Cryst Growth 282:470–481

    Article  Google Scholar 

  • Steiner W, Kaiser KP, Spaun G (2010) Role of brittle fracture on swelling behaviour of weak rock tunnels: hypothesis and qualitative evidence. Geomech Tunnel 3:583–596

    Article  Google Scholar 

  • Washburn EW (1926–1933) International critical tables of numerical data, physics, chemistry and technology. New York, Published for the National Research Council by McGraw-Hill

  • White WM (2005) Geochemistry. John-Hopkins University Press, Baltimore

    Google Scholar 

  • Wichter L (1989) Quellen anhydrithaltiger Tongesteine. Bautechnik 66, Heft 1

  • Winkler EM (1973) Stone: properties durability in man’s environment. Springer, Berlin

    Google Scholar 

  • Winkler EM, Singer PC (1972) Crystallization pressure of salts in stone and concrete. Geol Soc Am Bull 83:3509–3514

    Article  Google Scholar 

Download references

Acknowledgments

The authors appreciate the support of the Swiss National Science Foundation (SNF, Project Nr. 200021-126717/1) and by the Swiss Federal Roads Office (FEDRO, Project Nr. FGU 2010-007).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Anagnostou.

Appendix: on crystallisation pressure after Flückiger et al. (1994)

Appendix: on crystallisation pressure after Flückiger et al. (1994)

From Eqs. (3)–(6), we obtain the following expression for crystallisation pressure according to Flückiger et al. (1994):

$$ p_{\text{G}} = \frac{{\Delta G_{r} (T) - \Delta G_{r} (T_{0} )}}{{V_{\text{G}}^{0} }}. $$
(12)

The nominator of the right side is equal to the change in the Gibbs energy ΔG r of the anhydrite hydration reaction due to a change in temperature from the standard temperature T 0 to another temperature T. It is well known (cf., e.g. White (2005) that

$$ \Delta G_{r} (T) - \Delta G_{r} (T_{0} ) = - (T - T_{0} )\Delta_{{r,{\text{GA}}}} S^{0} , $$
(13)

where the standard entropy Δ r,GA S 0 of the anhydrite hydration reaction can be determined from the molar entropies of the reaction products (gypsum) and reactants (anhydrite and water):

$$ \Delta_{{r,{\text{GA}}}} S^{0} = S_{\text{G}}^{0} - S_{\text{A}}^{0} - 2S_{\text{W}}^{0} , $$
(14)

Taking into account the values of the molar constants according to Table 1, Eqs. (12)–(14) lead to

$$ p_{\text{G}} = \frac{{\left( {T - T_{0} } \right)\left( {S_{\text{G}}^{0} - S_{\text{A}}^{0} - 2S_{\text{W}}^{0} } \right)}}{{V_{\text{G}}^{0} }} \cong 3.6\;{\text{MPa}}\;. $$
(15)

This value is close to Flückiger et al. (1994) result (3.7 MPa). The difference is due to rounding errors and to the fact that Flückiger (1994) used Kelley et al.’s (1941) empirical equation rather than the molar constants of Anderson (1996).

In the following, we will show that the pressure according to Eq. (15) is equal to the increase in the crystallisation pressure of the gypsum that would occur if the solution was permanently saturated with respect to anhydrite; the anhydrite was under atmospheric pressure and the temperature was reduced from the standard temperature of T = T 0 = 25 °C (hereafter referred to as “state 1”) to T = 20 °C (hereafter referred to as “state 2”). The decrease in temperature causes an increase in the crystallisation pressure of the gypsum because the solubility of anhydrite increases with decreasing temperature (cf., Freyer and Voigt 2003, for example) and, consequently, supersaturation with respect to gypsum is higher in state 2 than in state 1. At state 1, the crystallisation pressure of gypsum reads as follows:

$$ p_{G1} \; = \frac{RT}{{V_{\text{G}}^{0} }}\ln \frac{{K_{\text{eq,A}}^{0} }}{{K_{\text{eq,G}}^{0} }}, $$
(16)

where K 0eq,A and K 0eq,G denote the equilibrium solubility products of anhydrite and gypsum, respectively, at standard conditions. Eq. (16) follows directly from Eq. (2) considering that the solution is saturated with respect to anhydrite and, therefore, K = K 0eq,A . The crystallisation pressure p c2 at an arbitrary temperature T can be calculated from the following equation (cf., e.g. White 2005):

$$ RT\ln \frac{K}{{K_{\text{eq,G}}^{0} }} = V_{G}^{0} \;p_{\text{G2}} \; + \left( {T - T_{0} } \right)\,\Delta_{{r,{\text{G}}}} S^{0} , $$
(17)

where the standard entropy of gypsum dissolution Δ r,G S 0 can be determined from the molar entropies:

$$ \Delta_{{r,{\text{G}}}} S^{0} = S_{{Ca^{2 + } }}^{0} + S_{{S{\text{O}}_{4}^{2 - } }}^{0} + 2S_{\text{W}}^{0} - S_{\text{G}}^{0} $$
(18)

If the solution is always saturated with respect to anhydrite and the anhydrite is under atmospheric pressure, then the solubility product K can be obtained (analogously to Eq. 17) from the following equation:

$$ RT\ln \frac{K}{{K_{\text{eq,A}}^{0} }} = \left( {T - T_{0} } \right)\,\Delta_{{r,{\text{A}}}} S^{0} , $$
(19)

where the standard entropy of anhydrite dissolution is

$$ \Delta_{{r,{\text{A}}}} S^{0} = S_{{{\text{Ca}}^{{ 2 { + }}} }}^{0} + S_{{{\text{SO}}_{ 4}^{{ 2 { - }}} }}^{0} - S_{\text{A}}^{0} $$
(20)

Inserting K from Eq. (19) into Eq. (17) and taking account of Eqs. (14) (18) and (20) leads to the following expression for the crystallisation pressure of gypsum in state 2:

$$ p_{G2} \; = p_{G1} + \left( {T - T_{0} } \right)\frac{{S_{G}^{0} - S_{A}^{0} - 2S_{W}^{0} }}{{V_{G}^{0} }}. $$
(21)

The last term on the right side of this equation is identical with Eq. (15). This means that the value determined by Flückiger et al. (1994) is equal to the change in the crystallisation pressure (p G2p G1) that would occur if the temperature decreases from T 0  = 25 °C to T = 20 °C.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Serafeimidis, K., Anagnostou, G. On the crystallisation pressure of gypsum. Environ Earth Sci 72, 4985–4994 (2014). https://doi.org/10.1007/s12665-014-3366-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12665-014-3366-7

Keywords

Navigation