Modellierung von anhydrithaltigen Tonsteinen

• Forschungsstelle: ASTRA SBT
• Projektnummer: FGU2010/007
• Projekttitel Englisch: Modelling of anhydritic swelling claystones

Schlüsselwörter (Deutsch)

Quellen, Tunnelbau, Anhydrit, gekoppelte Prozesse, Laborversuche

Schlüsselwörter (Englisch)

Swelling, tunnelling, anhydrite, coupled processes, laboratory tests

Kurzbeschreibung (Englisch)

Swelling rocks are widely distributed particularly in Switzerland and particularly anhydritic claystones have caused serious damage in a series of tunnels. Considerable knowledge gaps exist with respect to the effect of a counterpressure on heave of a tunnel, of transport processes explaining leaching or crystal growth, of seepage flow regime for inhibiting swelling and of the clay matrix for discerning the dominant mechanism during swelling. The existing models and experimental methods are insufficient for attempting to answer these questions, since they don’t consider ionic transport or chemical processes.

A hydraulic-mechanical-chemical coupled model describing the swelling of anhydritic claystones will be formulated and implemented numerically. The main processes to be considered are dissolution, crystal growth, diffusive and advective transport and water evaporation. Material-specific, constitutive equations will be formulated on the basis of thermodynamics and our own experimental investigations. The latter shall include element tests (for the characterization of the material and the determination of its constitutive behaviour) as well as physical modelling of geometrically simple systems involving coupled processes. The test results will also be used for calibrating and checking the numerical model.

The project will improve our understanding of the fundamental mechanisms governing the swelling of anhydritic rocks and provide unprecedented information for the rational design or retrofit of tunnels.

Projektbeschreibung (Deutsch)

1. Objective and goals

The proposed research will improve our knowledge of macroscopic behaviour and the mechanisms underlying the swelling of anhydritic rocks in tunnelling, thus contributing towards a clarification of a series of open questions. Although the swelling of anhydritic claystones represents a very old tunnelling problem (encountered already in 1859 during construction of the Weinsberg tunnel near Stuttgart), considerable knowledge gaps exist with respect to important aspects of swelling. These are:

(i) The role of transport processes.

Anhydrite transformation takes place through the solution phase: Anhydrite dissolves in the pore water (CaSO₄ ® Ca⁺⁺ + SO₄⁼) and, as the saturation concentration of gypsum is lower than the one of anhydrite, gypsum precipitates from the solution (Ca⁺⁺ + SO₄⁼ + 2 H₂O ® CaSO₄ ^. 2H₂O), while the calcium and sulphate ions circulate by convection (with the pore water) and, due to ionic concentration gradients, also by diffusion. Anhydrite dissolution and gypsum precipitation therefore go together with transport processes. It is not known whether and to what extent these transport processes are relevant to macroscopically observed behaviour. In addition to the reaction kinetics, the filtration rate of the pore water is also important. It is at least theoretically possible that the calcium and sulphate content is reduced by the transport processes in one rock mass region (i.e. the solution products are transported away), while in another region they are increased. In the first region leaching of the rock occurs, while in the second region gypsum formation occurs – even if this region was initially free of anhydrite. Leaching (instead of gypsum crystal growth) has been also observed in the field (Fig. 1).

(Fig. 1 siehe link unten)

 

The Schanz railway tunnel (Baden-Württemberg, Germany) was constructed 1877 - 1880. The floor of this tunnel experienced in the period 1880 - 1972 an average yearly heave of 1.6 cm, i.e. a cumulative heave of 1.50 m (Erichsen and Kurz 1996). Mineralogical investigations in 1990 revealed that the rock was completely sulphate free up to a depth of 3 m beneath the tunnel floor. The deeper rock zone contained both gypsum and anhydrite. The percentage of anhydrite increased with depth. At depths greater than about 10 m beneath the floor, the sulphate was present only as anhydrite 

Figure 1. Heave of the floor of the Schanz railway tunnel (Schächterle, 1929).

Understanding the role of transport (and particularly the conditions under which one or the other mechanism becomes dominant) is indispensable for planning and conducting meaningful laboratory tests and for evaluating their results. Since the transport conditions in the lab are as a rule different from those prevailing in the field and may have an important effect, it is uncertain to which extent the results of common swelling tests are representative for the behaviour in situ.

(ii) The role of the hydraulic boundary conditions.

The hydraulic conditions prevailing at the far field and at the tunnel boundary are, first of all, important for the transport processes mentioned above, because they determine (together with rock permeability) the velocity of the seepage flow. They also determine whether and to what extent the natural water table will be depressed and consequently the extent of the unsaturated zone as well (Anagnostou 1995a, b). The latter may be important for the swelling process since changes in the saturation degree lead to local oversaturation and therefore to crystal growth. Observations made in the Belchen tunnel, Switzerland, are interesting in this respect (Fig. 2).

(Fig. 2 siehe link unten)

 

A better understanding of the role of water circulation in the macroscale (scale of tunnel) and of the processes in the unsaturated zone is important for the conceptual design of remedial measures against swelling in existing and in future tunnels. It is currently unclear whether de-saturation triggers swelling (as suggested by Berdugo 2007, and Alonso and Olivella 2008) or rather represents an irrelevant process (as suggested by the absence of swelling above the tunnel floor level).

(iii) The role of the clay matrix.

In some cases (e.g., the Chienberg tunnel near Basle or the Engelberg tunnel near Stuttgart), the heave of the tunnel floor developed very rapidly after the rock came into contact with water (Fig. 3). As the hydration of anhydrite is a rather slow process, the highly intensive swelling phenomena points to a significant contribution from the clay matrix at least in the initial phase of the swelling process. The importance of the clay matrix relative to that of the anhydrite is unknown, as is the question of whether the dominant process changes with time.

Clarification of this question would allow a better identification and characterization of swelling rocks. Furthermore, the knowledge about the role of the clay would provide important indications about the swelling law (see point (iv) below), because the later is known in the case of clay swelling.

(Fig. 3 siehe link unten)

The swelling law.

It is well known that the swelling strain of purely argillaceous rocks (without anhydrite) decreases with the logarithm of swelling pressure (Fig. 4a). This so-called “semi-logarithmic swelling law” is taken into account (in the one or the other form) by almost all existing continuum-mechanical models of swelling rock and has a consequence which is very important from the structural point of view (Anagnostou (2007b)): the heave of the tunnel floor decreases rapidly when pressure is applied to the floor (Fig. 4b). For anhydritic claystones, however, it is not known (even qualitatively), how the final value of the swelling pressure is related to the deformation. Systematic long-term observations are available only from one test series (on samples from the Freudenstein tunnel) and one single field test, i.e. the test adit of the same tunnel. In both, the swelling process has not reached completion (around 20 years after the tests were started). The provisional results are inconsistent. The field test shows a clear reduction of floor heave with support pressure, whereas the results of the laboratory tests (Fig. 4c) seem to support the hypothesis put forward in Kirschke (1996), that the swelling strain is largely independent of pressure within the practically relevant pressure range of up to 3 - 4 MPa (Pimentel (2007b)). Such a behaviour is thoroughly conceivable if crystal growth is the dominant mechanism underlying the macrosopically observed rock expansion.

Knowledge of the relationship between swelling pressure and swelling strain (even qualitative knowledge) would be of paramount importance for a rational conceptual tunnel design.

(Fig. 4 siehe link unten)

(a) According to the so-called “semi-logarithmic swelling law”, swelling strain e depends linearly on the logarithm of the swelling pressure p. This well-known property of purely argillaceous rocks can be explained on the basis of the electrostatic interactions between the clay platelets (DLVO-theory, Madsen and Müller-Vonmoos, 1989).

(b) The strong dependency of floor heave on support pressure means that a small counter pressure suffices to limit heave considerably. On the other hand, this behaviour signifies that a considerable reduction of the pressure on the invert arch can be achieved by allowing a small heave of the tunnel floor. All design concepts for tunnel support in swelling rock are based on this feature of swelling behaviour.

( c ) Experimental results reported by Pimentel (2007b) indicate, however, that the behaviour of anhydritic claystones may be different from the one of purely argillaceous rocks, in that swelling strain is practically independent on swelling pressure within the practiclly relevant range (< 3 to 4 MPa).

Figure 4. (a) Theoretical relationship between swelling pressure and distance between the clay particles as well as macroscopically observed behaviour of claystones in the oedometer test; (b) Relation between floor heave and support pressure in tunnelling. (c) Experimental results for anhydritic claystones.

2. Methodology

The existing models and experimental methods (see “Stand der Forschung”) are obviously insufficient for attempting to answer the questions outlined in the previous section. Almost all investigations reported in the literature focus on the mechanical behaviour of the material. The swelling behaviour of anhydritic claystones has not yet been investigated with control or monitoring of the ion and water transport processes. To this purpose the proposed research project will make use both of experimental and of theoretical methods including numerical modelling. The main processes to be considered are dissolution of anhydrite, growth of gypsum crystals, transport processes (diffusion and advection) and water evaporation. A hydraulic-mechanical-chemical (HMC) numerical model will thus be developed and coupled processes will be simulated with physical models.

HMC model

Model formulation will be based on the continuum-mechanical approach of the theory of mixtures (cf., e.g., Bowen (1976), Bedford and Drumheller (1983)). In addition to general, material-independent equations (such as the equilibrium conditions, the kinematic relationships or the mass balance), the model will contain material-specific equations concerning the stress-strain behaviour, the chemically induced deformations, the kinetics and thermodynamics of the chemical reactions, the seepage flow and the ionic diffusion. In a possible, simplified formulation, elasto-plastic material behaviour will be assumed in combination with Terzaghi's principle of effective stress and with an additional term which accounts for the chemically-induced strains:

, (1)

where s_ij, d_ij, p, D_ijkl and e_kl denote the total stress tensor, the Kronecker's delta, the pore pressure, the elasticity tensor and the strain tensor, respectively; and e_kl^PL and e_kl^CH are the inelastic strains due to plasticity and chemical reactions, respectively. The latter are directly related to the anhydrite- and gypsum-production rates ?m_a/?t and ?m_g/?t:

, (2)

where r_a and r_g are the densities of anhydrite and gypsum, respectively, while a_kl and g_kl denote two material-specific tensors which shall be defined in the research project. (We assume isothermal conditions and neglect second order effects, such as the pressure-dependence of density.) The dissolution- or precipitation-rates are determined by the reaction kinetics and depend in general on the calcium- and sulphate-concentration c in the pore water, on the pore pressure p as well as on the effective stresses s_ij' in the solid phase:

. (3)

Concerning the transport processes, use will be made of the common formulation of Darcy’s law (advection) and Fick’s law (diffusion). The concentration c has to fulfil the advection - diffusion equation

, (4)

where n, D, q_k and R denote the porosity, the effective diffusion coefficient, the Darcy seepage flow velocity and the chemical sink or source term representing concentration changes due to anhydrite dissolution or gypsum growth. Seepage flow (including evaporation) will be taken into account as in Anagnostou (1995b) the only differences being that it may be necessary to introduce a porosity-dependent permeability (in order to model sealing of the rock due to gypsum growth) and, of course, that the amount of water bound during crystallisation has to be considered in the mass balance equation.

The specific form (and partially also the material constants) of the constitutive equations will be based upon (i) fundamental knowledge about the thermodynamics and kinetics of the system water - anhydrite - gypsum and other minerals; (ii) research that has already been carried out into similar topics in other areas; (iii) our own experiments which will be performed within the framework of this research project. These three points are discussed below.

With respect to point (i) and, more specifically, to the dependence of the rate of anhydrite dissolution and gypsum growth on concentration, pore pressure and applied stress (Eq. 3), we note that several authors have dealt experimentally and theoretically with the thermody-namics and reaction kinetics of anhydrite and gypsum systems (Niemann 2004, Jeschke 2002, Schierholtz 1958, Cody and Cody 1987, Prisciandaro et al. 2001) as well as those of other minerals in general (Berner 1978, Steefel and Lasaga 1994, Steefel and Cappellen 1990, Dove and Czank 1995, Lasaga 1984 & 1986, Lasaga and Rye 1993, Murphy et al. 1989) meaning that a great deal of information is available in the literature. General infor-mation on aspects of crystal growth and dissolution are also to be found elsewhere (Correns 1949, Nancollas and Purdie 1964, Steiger 2005a & b, Scherer 1999, Mullin 2001).

Concerning the above-mentioned point (ii), we note that similar approaches have also been applied successfully in other fields of civil engineering. Coupled macroscopic, 2-D, isotropic models have been developed in order to simulate processes such as leaching, sulphate attack and alkali-silica reaction (ASR) in porous materials, such as concrete and mortar (Gérard 1996, Ulm and Coussy 1995, Coussy and Ulm 1996, Gawin et al. 2006, Steffens et al. 2003, Bangert 2004, Tixier and Mobasher 2003, Bary 2008). Another application concerns the hardening and ageing of concrete (a thermo-mechanically coupled process). In most of the models, ionic transport is dominated by diffusion and is handled according to Fick’s law. Particularly interesting for our research work is the multiscale approach of Carmeliet et al. (2008) as it accounts for coupled mechanical and transport phenomena in porous media involving advection and diffusion.

Experimental investigations

As mentioned above, we will perform experimental investigations in order to find out the specific form of the constitutive equations and to quantify at least some of the material constants appearing in them. (It is uncertain at the present time whether it will be possible to quantify all individual constants directly. Maybe it will be necessary to estimate the values of some of the constants indirectly by means of back analysis of the laboratory tests.) Another goal of the experimental investigations will be to identify qualitatively the basic mechanisms (leaching, gypsum growth, clogging of the pores, fracturing, crystal growth in fractures etc.) by observations under controlled and reproducible conditions.

The experimental investigations shall be done on artificial mixtures of anhydrite, clay and inert materials such as quartz sand. (The reasons for using artificial samples are explained later in this Section.)

The main processes to be considered in the experiments have been mentioned above. It must be pointed out that reductions in the duration of the experiment are not possible in the present case: An acceleration of the experiment can be envisaged normally only if the time-development depends on one single process. So for example, chemical reactions and pore pressure dissipation can be accelerated by increasing the temperature and by employing a centrifuge, respectively. In the present case, the unilateral acceleration of one single process will lead to unrealistic results since the processes are coupled.

(Fig. 5 + 6 siehe link unten)

Depending on their goal, the planned experiments can be roughly subdivided into two groups: (a) material characterisation tests; (b) physical models for simulating complex situations.

The first group of experiments includes, besides standard tests for the direct determination of geotechnical, thermodynamical and transport parameters (such as density, grain size distribution, solubilities, kinetic constants, permeability, diffusion constants), new testing techniques which will have to be developed in order to determine the constitutive relationships of the mixtures in cases involving a non-linear or unknown material-specific behaviour. Such questions arise particularly with respect to the relationship between volumetric strain of the mixture and amount of transformed anhydrite (Eq. 2 for the isotropic case) as well as to the dependence of permeability on the chemically-induced changes of the pore space. For this purpose a special oedometer device will be developed which will allow for monitoring the development of volumetric strain over time under

constant stress and pore pressure (Fig. 5). In order to investigate the evolution of anhydrite- and gypsum-mass, a series of tests in the cell will be carried-out with identical conditions but different durations. The anhydrite- and gypsum-fraction will be determined at the end of each test by thermogravimetry and X-ray diffraction. Furthermore, at the end of each test, permeability will be measured by applying a constant hydraulic head gradient. Since only selected, isolated processes will be investigated with each test type, coupling is not included in these tests. The results of the experiments in this group can be utilised later as inputs for a database of material constants, for calibration and for improving the numerical model.

The second group of experiments concerns the coupled transport and chemical reaction process. The investigations will be carried-out on one-dimensional physical models (Fig. 6) with controlled boundary pore pressures (P₁, P₂), sulphate concentrations (C₁, C₂) and kinematic conditions (fixed displacement or constant axial stress). In this way, by selecting appropriate boundary conditions, transport processes with different dominant mechanisms can be initiated. Monitoring will focus on the evolution of the mixture (dissolution of anhydrite, formation of gypsum crystals) over time and space, as well as on time-development of the axial displacement or pressure. In order to reduce the amount of tests, the application of non-invasive measurement techniques will be advantageous.We will therefore examine the potential of spatially resolved X-ray diffraction and computer tomography by either magnetic resonance, X-rays or neutrons (Bernard (2005), Goethals et al. (2009), Poupeleer et al. (2003), Trtik et al. (2010)). The latter has been applied to porous construction materials, but not yet to anhydritic rocks. The results of the experiments in this group will be used for calibrating and improving the numerical model, as well as a database for its verification.

The numerical model developed and checked above will be the tool for systematically investigating the questions stated in the (Section 1 of the Projektbeschreibung).

As mentioned above the tests shall be performed on artificial samples. For the purposes of the present research project, the use of natural claystones is unfeasible but also unnecessary both for the experiments of the first group and for the experiments of the second group:

· Experiments of the first group.
These experiments focus on elementary processes which must be studied isolated from other processes in order to establish the constitutive relations and to measure the respective constants. This is possible only on artificial mixtures. In natural claystones, all processes occur simultaneously or concurrently without the possibility to control them (e.g., to inhibit ionic diffusion or to enforce leaching).
The mixture composition will be selected of course depending on the specific question to be answered in each individual test. So, in order to examine the role of transport and reaction kinetics or of de-saturation (see “Projektbeschreibung”, Section 1, subsections (i) and (ii)) it is sufficient to consider mixtures of anhydrite with sand. On the other hand, the addition of clay is indispensable for investigating the role of the clay minerals including their effect on the activity of the pore water and thus on the thermodynamic equilbrium of the anhydrite – gypsum – water system (see “Projektbeschreibung”, Section 1, subsection (iii)).

· Experiments of the second group.
Natural probes would be in principle suitable for these experiments, which investigate the coupled proceses in their full complexity. However, in order to gain reproducible and statistically significant results one should carry a very big number of each experiment type because the natural samples are extremely heterogeneous. A big number of experiments would be impossible on account of the very slow rate of the swelling process of claystones (several years). In addition, a long test duration does not allow for test layout improvements during the laboratory program.
Another problem with natural claystones is that their initial condition (composition, grain size, pore structure, chemistry of pore water) is unknown and cannot be established without destroying the specimen. This makes the evaluation of the results and the calibration and verification of the mathematical model hardly possible.
These problems do not exist with artificial specimens, because their initial condition is well defined and controlled. (The remarks made above concerning the mixture composition and specifically the clay fraction apply of course also to the experiments of the second group.)
On the other hand, it is hardly possible to manufacture artificial specimens with all features of natural anhydritic claystones such as diagenetic bonds, fissures or irregularly distributed anhydrite veins or nodules. These features may be relevant for selected design parameters (e.g., the diagenetic bonds reduce the free swelling strain) or for certain aspects of the swelling behaviour (e.g., the duration of the swelling process in the case of finely distributed anhydrite veins will be expectedly shorter than in the casse of large nodules), but are of secondary importance for the purposes of the experimental investigations of the present project, which is the identification of the elementary mechanisms and laws with their respective constants.

Within the present research poject we will examine the possibility of carrying out also some tests on natural samples - this however only with the purpose of observing qualitatively the developing processes and changes in the specimen structure. Such experiments might be feasible in view of EMPA’s experience with similar tests in the context of concrete durability. It must be pointed out, that we have some remaining cores from the ongoing research project FGU 2006-001. If necessary, it may be possible to gain additional samples with our portable drill equipment in the repaired areas of the Chienberg tunnel beneath the pavement deck, i.e. without traffic interruption.

The project FGU 2006-001, which investigates the swelling law of natural specimens by means of a large number of oedometric tests, might yield also some information concerning diffusion processes depending on whether the changes in the chemical composition of the water around the oedometer are measurable or not.

Relationship to research projects FGU 2008-004 and FGU 2008-005

In the field of swelling rocks, we co-operate (cf. Appendix) with the group of Prof. Huggenberger, University of Basle, which investigates whether a link does exist between the groundwater circulation systems and the spatial distribution of swelling phenomena in the Belchen tunnel and in the Chienberg tunnel (research projects FGU 2008-004 and FGU 2008-005, respectively). These investigations make use of hydrogeologic modelling of the seepage flow at different scales before and after tunnel excavation and considering surface hydrology, subsurface inflows, morphology and geological structures (Butscher and Huggenberger 2009). Our research supplements Huggenberger’s works. The later concerns the scale of the geological formation (Dm to km), while we look at the processes in the meso- to macro-scale. (Meso-scale is the scale of the specimens used for geotechnical laboratory testing, i.e. some cm to dm, while macro-scale is the scale of underground openings, i.e. some m to Dm.)

3. Distribution of the works among ETH-Z and EMPA

The present research project has an interdisciplinary character. Due to its complexity the project tasks demands the participation of specialists and young research engineers on the areas of tunnelling, modelling, material testing, chemical analysis and advanced microscopy and tomography techniques. Therefore this research project should be carried out in co-operation of the Institute for Geotechnical Engineering of the ETH Zürich and the Laboratory of Concrete of the EMPA. For the present research project the tasks can be grouped into a more theoretically-oriented work package and a more experimentally-oriented work package (see Forschungsplan). Mostly of the works will be performed by two PhD students, being supervised and supported by the specialists of both institutions. In the following the distribution of the works between the co-operation partners will be presented.

3.1 Institute for Geotechnical Engineering, ETH Zürich

Prof. Anagnostou and Dr. Pimentel will supervise and support both students (Mr. Serafeimidis and Mr. Shahab) during the course of their PhD projects. The supervision will include assistance in the formulation and implementation of the models, the modelling of selected situations, the setup of the experiments for material characterization and physical modelling. For the implementation of the models the determination of thermodynamic parameters and functions concerning the anhydrite-gypsum system as well as the chemical analysis and microscopy will be done mainly under EMPA supervision (see below). Since both work packages, i.e. the numerical modelling and the physical modelling are linked, a respective coordination is guaranteed by the supervisors.

ETH’s contribution to the project concerning facilities will include in particular:

• Design and construction of all experiment setups in the ETH workshop

• Design and installation of the data acquisition system for the experiments (without chemical analysis)

• Allocation of the experiment apparatus in an air-conditioned room

• On demand free accessibility to the laboratory facilities (soil and rock mechanics) of the Institute for Geotechnical Engineering, for determining for example geotechnical parameters, sample preparation etc.

• Workplace for both PhD students

3.2 Concrete and Construction Chemistry Laboratory, EMPA

Dr. Pietro Lura and Dr. Barbara Lothenbach will supervise and support the student (Mr. Shahab) during the course of his PhD project. The EMPA supervision will include assistance in designing and building the experimental setup at ETH Zürich and in performing the experiments. In addition, a number of experiments (chemical analysis, microscopy) will be carried out at EMPA or possibly at PSI (synchrotron X-ray tomography). Depending on the actual development of the project, also Dr. Andreas Leemann may be involved.

EMPA’s contributions to the project will include in particular:

• Thermodynamic modelling of the anhydrite-gypsum system with the GEMS-PSI modelling software. The GEMS-PSI software can precisely quantify the effect of changes in water activity, temperature and pressure on the anhydrite-gypsum system, including the changes in molar volume during the reactions;

• Determination of the kinetics of anhydrite dissolution and gypsum precipitation in model systems. The available data in the literature will be complemented by experiments performed at EMPA;

• Determination of anhydrite and gypsum content in different samples by thermogravimetry (possibly assisted by X-ray diffraction) to determine the amount of gypsum formed in the deformation and in the flow-through experiments. In addition, these data will be used as an input for thermodynamic and kinetic modelling. Dissolved concentrations will be determined by pore solution analysis by ion-chromatography and used to calculate the degree of (super)saturation.

• The infrastructure of the Concrete and Construction Chemistry Laboratory and other facilities at EMPA will be made accessible to the PhD student. Assistance of EMPA researchers or technicians will be guaranteed.

Further contributions to the project may include, depending on opportunity:

• Study of the microstructure of anhydrite/gypsum/clay system by light microscopy and scanning electron microscopy;

• Synchrotron X-ray Tomography study of the swelling of anhydrite/gypsum systems (with the possible addition of clay). A proposal for an experimental campaign at the Swiss Light Source, PSI, can be written in collaboration with EMPA and PSI researchers;

• Determination of the swelling pressure caused by gypsum precipitation in sealed systems containing anhydrite, sand and water.

Zugehörige Dokumente

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• Fig.1.pdf [PDF] 64 kB

Erwartete Erkenntnisse/ Nutzen, Nutzniesser (Englisch)

The sulphatic claystones of the late Triassic Gypsum Keuper are among the most difficult rocks to deal with from a tunnel engineering point of view. In the past, a number of older railway tunnels crossing sulphatic claystones have had to undergo extensive repair work in the north western part of Switzerland and in south Germany (e.g. the Hauenstein base, Belchen, Weinsberg, Kappelisberg, Wagenburg and Engelberg tunnel). Recent swiss projects suffering damage as a result of sulphatic swelling rock include the Chienberg motorway tunnel close to Basle and the Adler tunnel of Swiss Federal Railways. Tunnelling in Gypsum Keuper is one of the engineering tasks still associated with large inherent uncertainties, despite over one hundred years of tunnelling activity in such rock. It is characteristic of the current state of the art that the engineering community is divided over the question of suitable structural designs.

The set-backs often suffered in tunnelling through Gypsum Keuper are due to our limited knowledge about the swelling process in sulphatic rocks. The need for further research in this field is evident. The planned project will add to our knowledge about the mechanisms governing the swelling of these rocks as well as essential aspects of the macroscopic behaviour. As explained in Section 1 “Objectives and goals” of the “Projektbeschreibung”, at the end of the subsections (i) to (iv), the project focuses on fundamental aspects of the swelling problem, but there is a very strong link between these fundamental questions and issues of engineering importance: for planning, conducting and evaluating the results of laboratory swelling tests (subsections i-iii), for the identification and characterization of swelling rocks (subsection iii) and for the conceptual design of tunnels in anhydritic rock (subsections ii and iv). Consequently, the results of the present research project will be disseminated not only to the scientific community, but findings of practical importance will be also transferred in practice, i.e., depending on the nature of these results, to tunnel engineers, geotechnical engineers or engineering geologists.

Methoden (Englisch)

See “Projektbeschreibung”, Section 2, “Methodology”

Spezielle Geräte und Installationen (Englisch)

According to the „Projektbeschreibung“, Section 2, the project includes experimental research and the construction of experimental devices (a) for investigating the effect of anhydrite hydration on strain, pore space changes and permeability and, (b), for studying transport, anhydrite dissollution and gypsum growth. The estimated cost for materials and instrumentation is 50’000 CHF (about 50%-50% for the investigations (a) and (b)).

Allgemeiner Stand der Forschung (Deutsch)

1 Introduction

Swelling rocks experience a volume increase when interacting with water. Depending on the mineralogical composition of the rock, the swelling behaviour can be traced back to osmosis-driven water uptake or to gypsum growth from sulphate solutions (Ca⁺⁺+SO₄⁼ + 2 H₂O ® CaSO₄^. 2H₂O). Swelling rocks are widely distributed in Switzerland and south-west Germany and have caused serious damage, lengthy operation interruptions and very costly repaitrs in the past in a series of tunnels (Fig. 7). This is particularly true for the anhydritic rocks of the Gypsum Keuper formation. As illustrated by setbacks experienced in recently constructed tunnels (Adler tunnel of SBB, Chienberg tunnel of Sissach by-pass), claystones containing anhydrite still belong today to the most problematic rocks in tunnelling (see Erwartete Erkenntnisse / Nutzen, Nutzniesser).

 (Fig. 7 siehe link unten)

Research on the problem of swelling was triggered in the early 70's by difficulties encountered in two road tunnels, the Wagenburg tunnel in Germany and the Belchen tunnel in Switzerland. Since then a series of research projects have been carried-out which differ with respect to the questions addressed and thus also to the methods employed, the scale of the investigation and the scientific disciplines involved. At the microscale, mineralogists have carried out theoretical and experimental studies into the interactions between clay particles, anhydrite and gypsum crystals (cf. e.g. Madsen and Nüesch (1991), Madsen and Vonmoos (1989)). The scale of a geological formation (Dm to km) defines the other end of the spectrum (the megascale). Here, ongoing hydrogeological research addresses the question of possible links between regional groundwater circulation systems and the spatial distribution of swelling phenomena observed in tunnelling. More specifically, Huggenberger (2008a, b) investigates whether the observed variability of swelling intensity (which is often very large even within lithologically homogeneous geological units in one and the same tunnel) is due to different water circulation conditions.

Apart from the scientific investigations into processes at the micro- and mega-scales, considerable engineering research has been carried out into phenomena in the scale of the specimens used for geotechnical laboratory testing (‘mesoscale’, i.e. some cm to dm) and in the scale of underground openings (‘macroscale’, i.e. some m to Dm). The proposed research project addresses mainly phenomena in the mesoscale, which in several cases, however, can be upscaled to the macroscale. The following summary of the current state of research therefore focuses on theoretical modelling and experimental investigations that operate on these scales, while bearing in mind the very interesting research that has been done into microstructure and into the mineralogical changes in swelling rocks (cf., e.g., Madsen (1976), Madsen and Nüesch (1991), Ko et al. (1997)).

2. Theoretical models

Since 1972 a series of models have been proposed in order to describe the swelling behaviour of rock in tunnelling and to provide a rational basis for tunnel design. The process began with the formulation of relatively simple computational models taking account only of the mechanical response of materials (purely mechanical models) and it continued with the first attempts to simulate the interaction of mechanical behaviour, seepage flow and chemical reactions.

Simple mechanical models

Based on oedometer laboratory tests on clay rock, Grob (1972) proposed a semilogarithmic stress-swelling strain relationship. Furthermore, in his 1-D model he assumed a linearly elastic behaviour of the rock immediately after the excavation. The swelling heave in the centre of the tunnel floor is calculated from the integration of the vertical strains, which are determined based upon the results of oedometer tests and the vertical stress distribution predicted by elasticity theory. Einstein et al. (1972) extended this model into three dimensions by assuming isotropic material behaviour with a constant ratio of the principal stresses that is based also upon elasticity theory. The swelling strains in the principal stress directions are determined from the respective stresses and the semi-logarithmic relation mentioned above. Wittke and Rissler (1976) modified the isotropic model of Einstein et al. (1972) by assuming that the first invariant of volumetric swelling strain depends on the first stress invariant according to Grob’s law and that the distribution of the strains is proportional to the unloading caused by the tunnel excavation. Gysel (1977, 1987) investigated analytically the case of circular tunnels in swelling rock with the assumption of a homogeneous, non-hydrostatic initial stress state and taking account of the constitutive assumptions of Einstein et al. (1972) and Wittke and Rissler (1976). Based on laboratory swelling tests, Fröhlich (1986) emphasized that the swelling behaviour of claystones is markedly anisotropic. He proposed a two-dimensional, transversally anisotropic material model (swelling only perpendicularly to the bedding).

Models concerning behaviour under triaxial stress conditions

Bellwald and Einstein (1987) proposed an isotropic, elasto-plastic, strain-softening model in order to investigate the influence of the stress path on the mechanical behaviour of shales under drained or undrained conditions. Swelling is treated as an inverse consolidation process, i.e. it occurs when the effective stress decreases (which may also happen through the dissipation of negative excess pore pressures). This model was extended by Aristorenas (1992) by taking into account elastic anisotropy and creep behaviour together with an associated flow rule. The material constants were also determined by triaxial drained and undrained tests on shale specimens. Barla (1999) enhanced the constitutive model of Aristorenas (1992) by a swelling-specific term (Barla et al. (2003), Barla (2008)), which assumes a sigmoidal relationship between the excess pore pressure and the volumetric strain. The material constants were determined empirically by curve fitting using the results of triaxial tests and of a swelling test.

Models considering time-dependency of swelling

Kiehl (1990) proposed an elasto-viscoplastic, isotropic model with the stress - swelling strain relationship developed by Grob (1972). The verification of the model was based on the test results of Pregl et al. (1980) on remoulded clay and on leached Gypsum Keuper (Wittke (1978)). The rheological part of the model is described through a Newton viscosity. Furthermore, it is assumed that the time-development of the swelling process takes place according to an exponential decay rate law as proposed by Overbeck (1981). In order to model the in situ swelling tests of Freudenstein railway tunnel (Stuttgart, Germany), this model was enhanced by Wittke-Gattermann (1998) to include a specific watering stage. The time-water absorption relationship was calculated using Darcy’s law without a coupling to the mechanical response of the material. Wittke (2003) used diffusion theory for the water absorption of the solid, comparing the process with the one taking place in highly-compressed bentonite. Based on the saturation degree of the system, a dimensionless water content was introduced, which controls the activation of the swelling process.

Coupled models

Anagnostou (1992) developed a hydraulic-mechanical coupled model in order to investigate the effect of seepage flow on the deformation pattern around tunnels in swelling rocks. The assumed material model obeys Terzaghi's principle of effective stress, is elasto-plastic and takes into account anisotropic swelling based upon Grob's law. Seepage flow is simulated using Darcy’s law. The numerical results indicated the major importance of rock strength (the weaker the rock, the larger the floor heaves are) and of the hydraulic boundary conditions (more specifically, the absence of significant swelling deformations above the tunnel floor can be explained as a consequence of the non-uniformity of the hydraulic head field).

Alonso and Olivella (2008) proposed a chemo-mechanical micro-model for the crystal growth in a single rock fracture. The latter is considered to be embedded as a discontinuity in an elastic continuum element. It is exclusively responsible for water transport in the system, i.e. the permeability of the system depends only on the aperture of the fracture according to Poisseuille’s model. A main assumption of this model is that water in this fracture is always saturated in sulphates. Evaporation is considered to be the only activator of the swelling process, i.e. oversaturation, precipitation and subsequent crystal growth will be caused only by changes in relative humidity. The model was developed in order to prove the plausibility of the assumption that evaporation was an activator of the swelling process in the case of the Lilla tunnel (Spain). Since other processes such as dissolution of anhydrite and solute transport are not considered in this model, its applicability is limited to the specific problem studied.

3. Experimental investigations

The goal of the first laboratory tests on samples of swelling rock was to determine their characteristics (magnitude of swelling strain or pressure, relationship between swelling stress and strain) under simple experimental setups (oedometer apparatuses). Huder and Amberg (1970) used the conventional oedometer apparatus from soil mechanics for running swelling tests, while special oedometer apparatuses were later developed specifically for rock specimens (ISRM (1989, 1999)). Pimentel (1996, 2006) proposed a modified oedometer that allows the determination of the stress - strain relationship under triaxial conditions and later he improved this technique in order to be able to determine both the maximum swelling stress and the stress-strain relationship with just one test.

The effects of pore water pressure, radial stress and changes in strength and stiffness have been investigated by means of triaxial tests. Aristorenas (1992) executed such tests under drained as well as undrained conditions with pure shear stress paths in compression and extension on oriented anisotropic specimens in a specially designed apparatus. Pimentel (1996) has demonstrated through triaxial tests that swelling claystones experience a considerable loss of strength and stiffness when absorbing water, while Barla (1999) investigated the excess pore pressures developing under triaxial stress conditions.

It should be noted that most of the reported laboratory test results concern purely argillaceous rocks. Tests on sulphatic rocks have been carried out mostly within the framework of design activities for tunnelling projects and lack the quality needed for research purposes. As the duration of the swelling process is extremely long even under the optimum watering conditions prevailing in the laboratory, most of the tests have been terminated before reaching a steady state. Reliable experimental results for sulphatic rocks are therefore very scarce. Systematic long-term observations are available from only one test series which was carried out on samples from the Freudenstein railway tunnel ( Pimentel (2006) ). It is interesting to note that the swelling process has not reached completion yet, although it is now more than 20 years since the tests were started. The test results indicate that swelling strain may be largely independent of pressure - a very important finding for the conceptual design of tunnel supports. We hope to gain valuable information on this aspect from the ongoing research project FGU 2006-001.

Besides the tests mentioned above, which were performed on natural rock samples, some test results on remoulded or artificial samples are also reported in the literature. The reason for using artificial samples is to accelerate the swelling process (thus reducing test duration) and to eliminate the heterogeneity of natural samples (thus obtaining reproducible results). The scale of these investigations varies between the micro- and mesoscale. The first investigations of this kind stem from Sahores (1962). Swelling tests on artificial clay anhydrite mixtures were also performed to investigate the influence of clay content on swelling stress (Madsen and Nüesch (1991)). Furthermore, the swelling potential of mixtures of clay and calcium sulphate under oedometric conditions has been investigated by Azam and Abduljauwad (2000) and Azam et al. (2000). The soil fabric of the mixtures was evaluated using scanning electron microscope (SEM). Thuro (1993) and Rauh and Thuro (2006) performed free swelling tests on powdered pure anhydrite in order to investigate the water adsorption in relation to grain size. They also performed SEM, X-ray diffraction analysis and air permeability tests to estimate the specific surface of the particles. Berdugo (2007) performed oedometric tests both with natural and with artificial samples in order to investigate gypsum crystal growth in a discontinuity resulting from changes in sulphate concentration caused by evaporation.

4. Closing remarks

The swelling of purely argillaceous rocks, i.e. rocks not containing anhydrite, such as marls of the upper freshwater molasse or opalinus clay, is for all practical engineering purposes sufficiently well understood and, depending on the problem to be studied, it can be satisfactorily mapped by the existing mechanical or hydraulic-mechanical models. It is however questionable whether these models are applicable to anhydritic claystones as well, because systematic experimental investigations are scarce. Furthermore, with the exception of the work of Alonso and Olivella (2008), which addressed the question of crystal growth within rock fractures, none of the existing theoretical models account for the chemical and transport processes taking place in rocks containing anhydrite. As explained in the Section 1 of the Projektbeschreibung, these processes may lead to a fundamentally different behaviour of anhydritic claystones compared to purely argillaceous rocks.

The reasons for the very limited knowledge about swelling of anhydritic claystones is the duration of the swelling process (which amounts, even under laboratory conditions, to several years and makes, in combination with the large heterogeneity of natural rock, systematic experimental investigations very difficult) and the high complexity and diversity of the physico-chemical processes involved: seepage flow interacting with deformation processes and stress relief, ionic diffusion, dissolution of anhydrite and growth of gypsum crystals, evaporation, interactions of sulphate with the clay phase (in the absence of cracks and fissures the clay matrix governs water transport, while the clay minerals may affect the equilibrium of the anhydrite - gypsum - water system).

5. Proposer's own contribution to the research area

5.1 Institute for Geotechnical Engineering, ETH Zürich

The project fits in with a main line of research at our Institute, into the problems of tunnelling under difficult conditions. It also continues the long-term activity of the Institute, in general, and of the applicants, in particular, in the field of swelling rocks (Amstad and Kovari (2001), Kovari et al. (1995), Kovari et al. (1981), Anagnostou (1992, 1993, 1994, 1995b), Pimentel (1996, 2006, 2007b)).

Anagnostou (1992, 1993, 1995b) developed the first numerical, hydraulic-mechanically coupled model for argillaceous swelling rocks. His model takes into account the seepage flow processes that occur around underground openings and is able to map typical deformation patterns (tunnel floor heave without significant deformations at the tunnel walls or crown). He was a member of the Commission on Swelling Rocks of the International Society of Rock Mechanics, which issued recommendations on tunnel design and the characterization of swelling rocks. He is a member of the scientific commission for two research projects at the University of Basle (Huggenberger 2008a, b) which deal with the swelling phenomena from a hydrogeological point of view at the scale of geological formations. In addition to fundamental questions, his research interests also include conceptual design issues in relation to tunnels crossing swelling rocks (Anagnostou 2007b).

Pimentel (1996) developed a new testing device which made it possible for the first time to run long-time triaxial swelling tests and to investigate the anisotropy of the swelling behaviour of claystones as well as the effect of swelling on the strength and on the stiffness of these rocks. He proposed, furthermore, a new testing technique which produces a more reliable measure of swelling potential (Pimentel (2007a)). For more than 15 years he has supervised laboratory swelling tests on anhydritic samples from the Freudenstein tunnel in Germany. Based upon their results and microstructural considerations, he proposed a stress-strain relationship for the anhydrite swelling of Gypsum Keuper (Pimentel 2003, 2006, 2007a). He also developed a test apparatus for measuring changes in permeability that are due to the swelling of highly compacted bentonite (Pimentel 1999).

Our Institute is executing an ASTRA-research project into the long-term swelling behaviour of anhydritic claystones (FGU 2006-001). The project is co-financed by the SBB and includes the development and construction of a new robust and reliable swelling testing device specifically for long-term tests (expected duration 10 - 15 years). A series of 25 swelling tests under different axial loads are performed and will provide valuable information about the influence of pressure on the long-term swelling strain.

It should be noted that our Institute works specifically on the topic of the present research proposal since 3 years using research reserves of the professorship. The works of these 3 years included the investigation of the state of the art, the formulation of a continuum-mechanical model and the preparation of this very demanding project proposal. Approvement by the SNF was granted last winter and a second PhD student with appropriate background in material science was found this summer.

Other related research

The following research contributions do not concern the swelling problem specifically, but they do involve numerical and/or physical modelling of coupled processes and are, therefore, relevant for the planned research:

Anagnostou (1992) developed a complete finite element code (HYDMEC) for analyzing numerically hydraulic-mechanical coupled problems. Ongoing research in this field deals with the development of efficient numerical solution methods specifically for the spatial and transient problem of continuous tunnel excavation through consolidating porous media (Anagnostou (2007a)), as well as with the time-dependent behaviour of weak saturated rocks in tunnelling (Anagnostou (2009), Ramoni and Anagnostou (2010)).

Within another ASTRA research project on artificial ground freezing (FGU 2005-003), a thermo-hydraulic 3-D numerical model was developed which takes into account the strong discontinuities induced by phase changes (ice crystallization) (Sres et al. (2006, 2007)). The model is used for investigating the effect of seepage flow on the feasibility and the energy requirements of ground freezing in tunnel construction. A study was also undertaken into the problem of ice lens formation in sensitive soils and a thermo-mechanical coupled model was implemented in a commercial finite element package (FEMLAB) in order to simulate the freezing-induced heaves of the soil surface.

The Institute and the applicants in particular have a wealth of experience in developing new testing apparatuses or physical models. Vogelhuber (2007) developed a triaxial device for testing weak rocks under control of pore pressure. This technique was subsequently improved particularly for rocks with extremely low permeability (10^-13 m/s) and is currently applied to investigate the geomechanical behaviour of underconsolidated breccias within the framework of research cooperation with the national organisations that administer studies for the Gibraltar strait tunnel. In addition, for the AGF project mentioned above, a large scale laboratory model for simulating seepage flow was developed and constructed, along with an apparatus for simulating ice lens formation under specific thermal conditions (Pimentel et al. (2007)). Both models were monitored with an extensive instrumentation plan, including more than 50 temperature sensors, tensiometers and flowmeters. The experimental measurements were used as a database for the verification of the numerical models. The thermal parameters were determined completely independently from the physical model tests using TDR (time domain reflectometry) and NTSP (non steady state probe) devices, among others. All of these developments were possible thanks to the modern electronic laboratory and workshop of our Institute.

5.2 Concrete and Construction Chemistry Laboratory, EMPA

The Laboratory of Concrete and Construction Chemistry at Empa has been working for many years on the volume stability and degradation mechanisms of cementitious materials and on the interaction of cementitious materials with clay.

Dr. Pietro Lura’s (head of lab, civil engineer) main expertise is shrinkage, swelling and cracking of cementitious materials, both in the plastic and in the hardened state (Lura & Jensen (2007), Lura et al. (2007) and Lura et al. (2009)). He also applied microtomography for studying moisture transport in concrete and its relation to volume changes (Lura et al. (2006) and Trtik et al. (2010)). Recently, he extended similar measuring techniques and analysis methods to the problem of cracking in soils (Abou Najm et al. (2010)).

Dr. Barbara Lothenbach (senior scientist, environmental scientist) expertise includes the thermodynamic modelling of clay (Ochs et al. (2001) and Lothenbach et al. (1997)) and cementitious (Ochs et al. (2002), Lothenbach et al. (2008) and Winnefeld & Lothenbach (2010)) systems. Further activities include the modelling of transport related phenomena such as sulphate ingress in cementitious systems (Lothenbach et al. (2010)).

The Laboratory of Concrete and Construction Chemistry further has expertise in the field of swelling mechanisms and quantification of swelling pressures of silicate gels (Leemann et al. (2010)) (Dr. Andreas Leemann, group leader concrete Technology, geologist).

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Projektziele (Englisch)

Improvement of our knowledge of macroscopic behaviour and the mechanisms underlying the swelling of anhydritic rocks in tunneling and contributing towards a clarification of following aspects of swelling:

(i) The role of transport processes.
Understanding the transport conditions, under which anhydrite dissolution or gypsum precipitation becomes dominant, is important for performing meaningful laboratory tests and for evaluating their results.

(ii) The role of the hydraulic boundary conditions.
Understanding in which extent they can affect the transport processes in the scale of tunnels is important for the conceptual design of remedial measures, for the evaluation of laboratory testing results and for the interpretation of the observed phenomena.

(iii) The swelling law.
Knowledge (even qualitative knowledge) of the relationship between swelling pressure and swelling strain would be of paramount importance for the conceptual design of tunnels.

The role of the clay matrix.
Understanding the role of clay (e.g., whether the dominant process changes with time due to the clay matrix) is important for the identification and characterization of swelling rocks but also with respect to the swelling law mentioned above

Forschungsplan (Englisch)

Table 1 shows the tasks and milestones ("MS") of the the project.

Table 1: Working plan

(Table 1 siehe link unten)

 

The tasks can be grouped into a more theoretically-oriented work package and a more experimentally-oriented work package. The two work packages have several links, but can be executed mostly independently from another and will therefore start simultaneously.

One PhD student ("A", Table 1) will formulate the model, implement it for the 1-D case and investigate selected questions, which are less related to the physical model tests.

- Task 1 starts with an evaluation of the relevance of different aspects of the processes involved and a selection of the aspects to be considered by the model (e.g., the amount and the properties of the system constituents, hardening, softening, isotropy, thermal conditions, etc.). The constitutive relations for describing these aspects, combined with the theories and material laws mentioned above, will deliver the framework for the formulation of the equations of the continuum-mechanical model (MS 1).

- Task 2 consists of the solution of the equation system. Since no analytical solution is possible, a numerical solution in the frame of the Finite Element Method will be carried out. In order to save time the model will initially be implemented for the 1-D case. A calibration and verification of the model will be done on the basis of the laboratory experiment results (MS 2).

- Task 3 (MS 3) investigates the role of clay fraction and the effect of applied stress on swelling (Section 1 of the Projektbeschreibung).

The other PhD student ("B", Table 1) will be responsible mainly for the experimental work and the numerical investigation into questions related more strongly to transport processes (tasks 4 to 6).

- Task 4 comprises the definition of an appropriate testing material as well as the experimental work on material characterisation. It will start with the identification and determination of known material parameters, followed by the design of experiments for isolated processes (MS 4). The basic information concerning specific material equations will be obtained from task 1, while it may be possible to integrate the first results from the long-term oedometer swelling tests on natural rock samples. The results of the tests with isolated processes will allow a calibration and, where applicable, an improvement of the numerical model (MS 5).

- Task 5 consists of the physical modelling of coupled processes and includes the design of these new experiments (MS 4). The design of the test apparatuses can be done, at least partially, with the help of preliminary numerical simulations performed with the HCM-model. Furthermore, as indicated above, the experimental results will be used for establishing phenomenological relationships between the investigated processes, as well as calibration and verification of the numerical model (MS 5).

- Task 6 (MS 6) comprises a systematic, computational investigation of the effect of transport processes and hydraulic boundary conditions including evaporation (Section 1 of the Projektbeschreibung).

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Umsetzung und Anwendungen (Englisch)

The results of our research will be presented in the report series of our Institute (IGT), the relevant national and international conferences and scientific journals (Rock Mechanics and Rock Engineering, Int. J. Rock Mechanics & Mining Sciences). The results will be well disseminated in the engineering community by issuing recommendations at a later stage. Dissemination into the tunnelling practice is warranted also because ETH-Z is involved with the Swiss Federal Authorities in important tunnelling projects, particularly also several existing or planned tunnels with demanding swelling-induced problems (Belchen, Adler, Chienberg and Eggflue tunnel).

Berichtsnummer (Deutsch)

1539

Berichtsnummer (Englisch)

1539

Literatur (Englisch)

Abou Najm M., Jesiek J., Sant G., Mohtar R.H., and Lura P. (2010): Examining volume changes in unsaturated soils. A discussion of the role of the pore solution composition and clay content. Journal of Water Resources Research, in preparation.

Alonso E.E. and Olivella S. (2008): Modelling tunnel performance in expansive gypsum claystones. International Association for Computer Methods and Advances in Geomechanics (IACMAG), Goa, India, p. 891-910.

Amstad C. and Kovari K. (2001): Untertagbau in quellfähigem Fels. Schlussbericht Forschungsauftrag 52/94 des Bundesamtes für Strassen ASTRA.

Anagnostou G. (1992): Untersuchungen zur Statik des Tunnelbaus in quellfähigem Gebirge. Doctoral thesis, ETH Zürich.

Anagnostou G. (1993): A model for swelling rock in tunnelling. Rock Mech. Rock Engng, vol. 26 (4), p. 307-331.

Anagnostou G. (1994): Numerical modelling of swelling in tunnels. Computer Methods and Advances in Geomechanics, p. 2541-2546.

Anagnostou G. (1995a): The influence of tunnel excavation on the hydraulic head. INt. Journal Num. and Analyt. Meth. in Geomechanics, vol. 19, p. 725-746.

Anagnostou G. (1995b): Seepage flow around tunnels in swelling rock. International Journal for Numerical and Analytical Methods in Geomechanics, vol. 19, p. 705-724.

Anagnostou G. (2007a): Continuous tunnel excavation in a poro-elastoplastic medium. In: Pande & Pietruszczak (eds) 'Numerical Models in Geomechanics - NUMOG X'. Talylor & Francis Group, London. p. 183-188.

Anagnostou G. (2007b): Design Uncertainties in Tunnelling through Anhydritic Swelling Rocks. Felsbau, vol. p. 48-54.

Anagnostou G. (2009): The effect of advance-drainage on the short-term behaviour of squeezing rocks in tunneling. Int. Symp. On Computational Geomechanics, Juan-Ies-Pins, Cote d' Azur, France.

Aristorenas G.V. (1992): Time-dependent behaviour of tunnels excavated in shale. Doctoral thesis, Massachusetts Institute of Technology.

Azam S. and Abduljauwad S.N. (2000): Influence of gypsification on engineering behavior of expansive clay. Journal of Geotechnical an Geoenvironmental Engineering, vol. 126, p. 538-542.

Azam S., Abduljauwad S.N., Al-Shayea N.A. and Al-Amoudi O.S.B. (2000): Effects of calcium sulfate on swelling potential of expansive clay. Geotechnical Testing Journal, vol. 23, 4, p. 389-403.

Bangert F. (2004): Gekoppelte chemo-mechanische Modellierung und numerische Simulation langzeitiger Degradation von Betonstrukturen. Doctoral thesis, Universität Bochum.

Barla M. (1999): Tunnels in swelling ground. Doctoral thesis, Politecnico di Torino.

Barla M. (2008): Numerical simulation of the swelling behaviour around tunnels based on special triaxial tests. Tunnelliing and Underground Space Technology, vol. 23, p. 508-521.

Barla M., Ferrero S. and Barla G. (2003): A new approach for predicting the swelling behaviour of expansive clays in tunnelling. IC on New Developments in Soil Mechanics and Geotechnical Engineering ZM2003, Lefkosa, Turkish Republic of Northern Cyprus.

Bary B. (2008): Simplified coupled chemo-mechanical modeling of cement pastes behavior subjected to combined leaching and external sulfate attack. Int. J. Numer. Anal. Meth. Geomech., vol. 32, p. 1791-1816.

Bedford A. and Drumheller D.S. (1983): Theories of immiscible and structured mixtures Int. J. Engng Sci., vol. 21, 8, p. 863-960.

Bellwald P. and Einstein H.H. (1987): Elasto-plastic constitutive model. 6th Int Cong of the ISRM, Aachen, p. 1489-1492.

Berdugo I.R. (2007): Tunnelling in sulphate-bearing rocks - expansive phenomena. Doctoral thesis, Universitat Politècnica de Catalunya.

Bernard D. (2005): 3D quantification of pore scale geometrical changes using synchrotron computed microtomography. Oil & Gas Science and Technology - Rev. IFP, vol. 60, 5, p. 747-762.

Berner R.A. (1978): Rate control of mineral dissolution under earth surface conditions. American Journal of Science, vol. 278, p. 1235-1252.

Bowen E.M. (1976): Theory of mixtures. Academic Press.

Butscher, C. and Huggenberger, P. (2009): Swelling of clay-sulfate rocks and groundwater flow in tunnel engineering. AGU Fall Meeting 2009, San Francisco, 14-18 December 2009. Eos 90 (29), Fall Meet. Suppl., Abstract H23F-1025AGU.

Carmeliet J., Derluyn H., Mertens S. and Moonen P. (2008): Multiscale modelling of coupled processes in porous materials. International RILEM Symposium on Concrete Modelling Delft, p. 325-336.

Cody R.D. and Cody A.M. (1987): Gypsum nucleation and crystal morphology in analog saline terrestrial environments. Journal of Sedimentary Pertrology, vol. 58, 2, p. 247-255.

Correns C.W. (1949): Growth and dissolution of crystals under linear pressure. Crystal Growth, p. 267-271.

Coussy O. and Ulm F.-J. (1996): Creep and plasticity due to chemo-mechanical couplings. Applied Mechanics, vol. 66, p. 523-535.

Dove P.M. and Czank C.A. (1995): Crystal chemical controls on the dissolution kinetics of the isostructural sulfates: Celestite, anglesite and barite. Geochemica et Cosmochimica Acta, vol. 59, 10, p. 1907-1915.

Einstein H.H., Bischoff N. and Hofmann E. (1972): Verhalten von Stollensohlen in quellendem Mergel. Internationales Symposium für Untertagbau, Luzern, p. 296-319.

Erichsen C. and Kurz G. (1996): Rehabilitation of an old railway tunnel in swelling gypsum keuper. Geotechnik, vol. 19, p. 178-187.

Fröhlich B. (1986): Anisotropes Quellverhalten diagenetisch verfestigter Tonsteine. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Univerität Fridericiana in Karlsruhe, Heft 99.

Gawin D., Pesavento F. and Schrefler B.A. (2006): Hygro-thermo-chemo-mechanical modeling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena. Int. J. Numer. Meth. Engng, vol. 67, p. 299-331.

Gérard B. (1996): Contribution des couplages méchanique-chimie-transfert dans la tenue à long terme des ouvrages de stockage de déchets radioactifs. Doctoral thesis, E.N. S. Cachan.

Goethals P., Volkaert A., Jacobs P., Roels S. and Carmeliet J. (2009): Comparison of positron emission tomography and X-ray radiography for studies of physical processes in sandstone. Engineering Geology, vol. 103, p. 134-138.

Grob H. (1972): Schwelldruck im Belchentunnel. Internationales Symposium für Untertagbau, Luzern, p. 99-119.

Gysel M. (1977): A contribution to the design of a tunnel lining in swelling rock. Rock Mechanics, vol. 10, p. 55-71.

Gysel M. (1987): Design of tunnels in swelling rock. Rock Mech. Rock Engng, vol. 20, p. 219-242.

Huder J. and Amberg G. (1970): Quellung in Mergel, Opalinuston und Anhydrite. Schweizerische Bauzeitung, 88 Jahrgang Heft 43, vol. p. 975-980.

Huggenberger P. (2008a): Influence of groundwater flow on swelling in the Gipskeuper formation of the Belchentunnel. Research Project ASTRA / FGU 2008-004.

Huggenberger P. (2008b): Influence of groundwater flow on swelling in the Gipskeuper formation of the Chienbergtunnel. Research Project ASTRA / FGU 2008-005.

ISRM (1989): Suggested methods for laboratory testing of argillaceous swelling rocks. Int. J. Rock Mech. Sci. & Geomech, vol. 26, 5, p. 415-426.

ISRM (1999): Suggested methods for laboratory testing of swelling rock. Int. J. Rock. Mech. Min. Sci., vol. 36, p. 291-306.

Jeschke A.A. (2002): Lösungskinetik von Gips und Anhydrit. Doctoral thesis, Universität Bremen.

Kiehl J.R. (1990): Ein dreidimensionales Quellgesetz und seine Anwendung auf den Felshohlraum. 9. Nat. Felsmechanik Symposium Aachen 1990, p. 185-207.

Kirschke D. (1996): Neue Versuchstechniken und Erkenntnisse zum Anhydritschwellen. Taschenbuch für den Tunnelbau, p. 203-225. Verlag Glückauf GmbH, Essen.

Ko S.C., Nüesch R. and Madsen F.T. (1997): Tonmineralien und Sulfatgesteine als Ursachen für druckhaftes Verhalten von Gesteinen. Forschungsprojekt Quellverhalten der Juragesteine.

Kovari K., Amstad C. and Anagnostou G. (1995): Long term field observations of swelling phenomena in tunnel and their back analysis. Chalk and Shales" Groupement Belge de Mécanique des Roches, Brussels, p. 68-79.

Kovari K., Madsen F.T. and Amstad C. (1981): Tunnelling with yielding support in swelling rocks. International Symposium on Weak Rock, Tokyo, p. 1019-1026.

Lasaga A.C. (1984): Chemical kinetics of water-rock interactions. Journal of Geophysical Research, vol. 89, B6, p. 4009-4025.

Lasaga A.C. (1986): Metamorphic reaction rate laws and development of isograds. Mineralogical magazine, vol. 50, p. 359-373.

Lasaga A.C. and Rye D.M. (1993): Fluid flow and chemical reaction kinetics in metamorphic systems. American Journal of Science, vol. 293, p. 361-404.

Leemann A., Le Saout G., Winnefeld F., Rentsch D., Lothenbach B. (2010): Alkali-silica reaction - the influence of calcium on silica dissolution and the formation of reaction products. Journal of the American Ceramic Society, submitted.

Lothenbach B., Bary B., Le Bescop P., Schmidt T. and Leterrier N. (2010): Sulfate ingress in Portland cements. Cement and Concrete Research, 40(8), p. 1211-1225.

Lothenbach B., Furrer G. and R. Schulin (1997): Immobilization of heavy metals by polynuclear aluminium and montmorillonite compounds. Environmental Science & Technology, 31, p. 1452-1462.

Lothenbach B., Matschei T., Möschner G. and Glasser F.P. (2008): Thermodynamic modelling of the effect of temperature on the hydration and porosity of Portland cement. Cement and Concrete Research, 38(1), p. 1-18.

Lura P., Bentz D.P., Lange D.A., Kovler K., Bentur A. and van Breugel K. (2006): Measurement of water transport from saturated pumice aggregates to hardening cement paste. Materials and Structures, 39, p. 861-868.

Lura P. and Jensen O. M. (2007): Measuring techniques for autogenous strain of cement paste. Materials and Structures, 40, p. 431-440.

Lura P., Jensen O. M. and Weiss J. (2009): Cracking in cement paste induced by autogenous shrinkage. Materials and Structures, 42, 8, p. 1089-1099.

Lura P., Pease B.J., Mazzotta G., Rajabipour F. and Weiss W.J. (2007): Influence of shrinkage reducing-admixtures on the development of plastic shrinkage cracks. ACI Materials Journal, 104, 2, p. 187-194.

Madsen F.T. (1976): Quelldruckmessung an Tongesteinen und Berechnung des Quelldrucks nach der DLVO - Theorie. Mitteilungen des Institutes für Grundbau und Bodenmechanik ETH Zürich.

Madsen F.T. and Nüesch R. (1991): The swelling behaviour of clay-sulphate rocks. 7th Int. Congr. on Rock Mech, p. 263-267.

Madsen F.T. and Vonmoos M. (1989): The swelling behaviour of clays. Applied Clay Science, vol. 4, p. 143-156.

Mullin J.W. (2001): Crystallization. Forth Edition, Butterworth Heinemann.

Murphy W.M., Oelkers E.H. and Lichtner P.C. (1989): Surface reaction versus diffusion control of mineral dissolution and growth rates in geochemical processes. Chemical Geology, vol. 78, Elsevier Science Publishers, p. 357-380.

Nancollas G.H. and Purdie N. (1964): The kinetics of crystal growth. Q. Rev. Chem. Soc, vol. 18, p. 1-20.

Niemann L. (2004): Die Reaktionskinetik des Gipsabbindens: Makroskopische Reaktionsraten und Mechanismen in molekularem Massstab. Doctoral thesis, Universität Karlsruhe.

Ochs M., Lothenbach B. and E. Giffaut (2002): Uptake of oxo-anions by cements through solid-solution formation: experimental evidence and modelling. Radiochimica Acta, 90, p. 639-646.

Ochs M., Lothenbach B., Wanner H., Sato H. and Yui M. (2001): An integrated sorption-diffusion model for the calculation of consistent distribution and diffusion coefficients in compacted bentonite. J. Contaminant Hydrology, 47, p. 283-296.

Overbeck R. (1981): Verwitterung von Mergelkalken durch Trocknungs-Befeuchtungs-Wechsel Ber. 3. Nat. Tag. Ing.-Geol., Ansbach, p. 225-232.

Pimentel E. (1996): Quellverhalten von diagenetisch verfestigtem Tonstein. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Fridericiana in Karlsruhe, Heft 139.

Pimentel E. (1999): Quelldurchlässigkeitsversuche an hochverdichteten Bentoniten und Mischungen aus Bentonit und Sand. 9th International Congress on Rock Mechanics, Paris, p. 777-780.

Pimentel E. (2003): Swelling behaviour of sedimentary rocks under consideration of micromechanical aspects and its consequences on structure design. Geotechnical Measurements and Modelling, Natau, p. 367-374.

Pimentel E. (2006): Quellverhalten von Sendimentgesteinen - Neue Versuchstechniken. Proc. 3rd Colloquium ''Rock Mechanics - Theory and Practice'', Inst. f.Eng. Geol. TU, Wien, p. 165-176.

Pimentel E. (2007a): A laboratory testing technique and a model for the swelling behavior of anhydritic rock. 11th Congress of the International Society for Rock Mechanics, Lisbon, p. 143-146.

Pimentel E. (2007b): Quellverhalten von Gesteinen - Erkenntnisse aus Laboruntersuchungen. Quellprobleme in der Geotechnik, Mittelungen der Schweizerischen Gesellschaft für Boden- und Felsmechanik, Heft 154, Fribourg, p. 13-20.

Pimentel E., Sres A. and Anagnostou G. (2007): 3-D Modellierung der Frostkörperbildung beim Gefrierverfahren unter Berücksichtigung einer Grundwasserströmung. Christian Veder Kolloqium, Heft 30, TU Graz, p. 161-176.

Poupeleer A.S., Carmeliet J., Roels S. and Gemert D.V. (2003): Validation of the salt diffusion coefficient in porous material. International Journal for Restoration of Buildings, vol. 9, 6, p. 663-682.

Pregl O., Fuchs M., Müller H., Petschl G., Riedmüller G. and Schwaighofer B. (1980): Dreiaxiale Schwellversuche an Tongesteinen. Geotechnik 1, p. 1-7.

Prisciandaro M., Lancia A. and Musmarra D. (2001): Gypsum nucleation into sodium chloride solutions. AIChE Journal, vol. 47, 4, p. 929-934.

Ramoni, M., Anagnostou, G. (2010): The effect of consolidation on TBM shield loading in Water-Bearing squeezing ground. Submitted for publication in Rock Mech Rock Eng. DOI 10.1007/s00603-010-0107-4

Rauh F. and Thuro K. (2006): Why do pure anhydrites differ in their swelling capacity? 3rd Colloquium ''Rock Mechanics - Theory and Practice'', p. 191-201.

Sahores J. (1962): Contribution à l' ètude des phènomenes mèchaniques accompagnant l' hydratation de l' anhydrite. Doctoral thesis, Revue des matèriaux de construction.

Scherer G.W. (1999): Crystallization in pores. Cement and Concrete Research, vol. 29, p. 1347-1358.

Schierholtz O.J. (1958): The crystallization of calcium sulphate dihydrate. Can. J. Chem., vol. 36, p. 1057-1063.

Sres A., Pimentel E. and Anagnostou G. (2006): Numerical and physical modeling of artificial ground freezing. Proc. Numerical Modelling of Construction Processes in Geotechnical Engineering for Urban Environment, Bochum, p. 185-191.

Sres A., Pimentel E. and Anagnostou G. (2007): Simulations and measurements of ground freezing with seepage flow. 18^th European Young Geotechnical Engineers' Conference, Ascona.

Steefel C.I. and Cappellen P.V. (1990): A new kinetic approach to modeling water-rock interaction: The role of nucleation, precursors, and Ostwald ripening. Geochemica et Cosmochimica Acta, vol. 54, p. 2657-2677.

Steefel C.I. and Lasaga A.C. (1994): A coupled model for transport of multiscale chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. American Journal of Science, vol. 294, p. 529-592.

Steffens A., Kefei L. and Coussy O. (2003): Aging approach to water effect on alkali-silica reaction degradation of structures. Journal of Engineering Mechanics, vol. 129, p. 50-59.

Steiger M. (2005a): Crystal growth in porous materials - I: The crystallization pressure of large crystals. Journal of Crystal Growth, p. 455-469.

Steiger M. (2005b): Crystal growth in porous materials - II: Influence of crystal size on the crystallization pressure. Journal of Crystal Growth, p. 470-481.

Thuro K. (1993): Der Pulver-Quellversuch - ein neuer Quellhebungsversuch. Geotechnik, vol. 16, p. 101-106.

Tixier R. and Mobasher B. (2003): Modeling of Damage in Cement-Based Materials Subjected to External Sulfate Attack. I: Formulation. Journal of Materials in Civil Engineering, vol. 15, p. 305-313.

Trtik P., Muench B., Weiss W.J., Herth G., Kaestner A., Lehmann E. and Lura P.(2010): Neutron tomography investigation of water release from superabsorbent polymers in cement paste. International Conference on Material Science and 64th RILEM Annual Week September 6-10, Aachen, Germany.

Ulm F.-J. and Coussy O. (1995): Modeling of thermochemomechanical couplings of concrete at early stages. Journal of Engineering Mechanics, vol. 121, p. 785-794.

Vogelhuber M. (2007) Der Ein?uss des Porenwasserdrucks auf das mechanische Verhalten kakiritisierter Gesteine. Veröffentlichungen des Instituts für Geotechnik (IGT) der ETH Zürich, Band 230, ETH Dissertation Nr. 17079. vdf Hochschulverlag AG, ZürichWinnefeld F. and Lothenbach B. (2010): Hydration of calcium sulfoaluminate cements: experimental findings and thermodynamic modelling. Cement and Concrete Research, 40(8), p. 1239-1247.

Wittke-Gattermann P. (1998): Verfahren zur Berechnung von Tunnels in quellfähigem Gebirge und Kalibrierung an einem Versuchsbauwerk. Geotechnik in Forschung und Praxis, WBI-PRINT 1. Essen: Verlag Glückauf GmbH.

Wittke M. (2003): Begrenzung der Quelldrücke durch Selbstabdichtung beim Tunnelbau in anhydritführendem Gebirge. Geotechnik in Forschung und Praxis, WBI-PRINT 13. Essen: Verlag Glückauf GmbH.

Wittke W. (1978): Grundlagen für die Bemessung und Ausführung von Tunnels in quellendem Gebirge und ihre Anwendung beim Bau der Wendeschleife der S-Bahn Stuttgart. Veröffentlichungen des Institutes für Grundbau, Bodenmechanik, Felsmechanik und Verkehrswasserbau der RWTH Aachen, Heft 6.

Wittke W. and Rissler P. (1976): Bemessung der Auskleidung von Hohlräumen in quellendem Gebirge nach der Finite-Element-Methode. Veröffentlichungen des Institutes für Grundbau, Bodenmechanik, Felsmechanik und Verkehrswasserbau der RWTH Aachen, vol. 2, p. 7-46.