Multiscale hydro-chemo-mechanical modelling of the weathering of calcareous rocks: an experimental, theoretical and numerical study

In this thesis the study of hydro-chemo-mechanical effects of weathering on calcarenite, a soft porous rock very common in the Mediterranean regions and in many other coastal areas around the world has been discussed. The comprehension of these processes and their simulation can be, in fact, very useful for (i) conceiving ad hoc experimental tests, (ii) assessing the risk associated with slope and natural cave collapses and (iii) designing new mitigation measures. In particular, the work focused on incorporating hydro-chemical effects, induced by saturation and long term dissolution of a porous rock, into the theory of strain hardening elasto-plasticity. Its main peculiarity is to frame the changes in microstructure in the context of a multi-scale scenario of an array of coupled phenomena. In this way, by means of up-scaling and downscaling procedures, it was possible to reproduce the macro-effects of weathering on the strength and stiffness of calcarenite. In order to reproduce correctly the ad hoc designed weathering tests, the numerical implementation into a finite element based context was necessary. Accordingly, the reactive transport of dissolved ions in a porous rock was also considered and modelled. This allowed to incorporate the dissolution reactions that characterize weathering in a boundary value problem. The obtained results are here below detailed in three (experimental, theoretical and numerical) sections: • Experimental study: a) In this part the identification of hydro-chemo microstructural mechanisms occurring during the process of wetting in the short term, and during the long term dissolution of calcite that composes the calcarenite structure is approached. This was possible thanks to an accurate and critical microstructural experimental investigation using sophisticated techniques such as dispersive X-ray spectroscopy (EDS), X-ray Micro-Computer-Tomography (MCT), Scanning Electron Microscope (SEM) analyses and Mercury Intrusion Porosimetry (MIP). b) Mechanical characterisation of the intact and weathered rock by means of standard geomechanical laboratory experimental tests (such as uniaxial, oedometric or triaxial compression tests to name a few) and the transition rock-soil induced by chemical degradation with an ad hoc designed apparatus (such as the Weathering Test Device under oedometric conditions and the acid controlled creep test). It has been observed that a variation of the stress-strain state occurs without any change in either external load or imposed displacement. The initial rock material, progressively loses its mechanical strength due to the dissolving mass, progressively assuming the typical behaviour of a non-cohesive soil. • Theoretical study: a) Formulation of a multiscale constitutive model to describe the rate of dissolution of calcite in a stressed configuration. The developing irreversible micro-cracks induce an increase in the specific surface area. As the reaction rate per volume of fluid is proportional to the surface area at the fluid/solid interface, it follows that the rate evolves with the mechanical damage. In order to develop a numerical model for such a mechanism it is necessary to refer to the scale the mechanism is taking place. To reach predictions at a macro or even regional scale, a multi-scale model was developed. The formulation for dissolution and increase in the specific surface area is developed at the micro-scale, whereas the phenomena of damage described above are formulated at a meso-scale (the size of a macro-pore). Finally, quantities from these two scales are transferred to the macro-scale level where the continuum mechanics constitutive models are formulated. b) A macro scale constitutive model, conceived to describe the material state (stress and strain) variation induced by hydro-chemo processes like weathering. It has been shown as hydro-chemo-mechanical processes can be dealt with in the framework of a suitably formulated elastoplastic strain-hardening theory. The simulations confirm that weathering can be treated as a non-mechanical debonding process. It is also worth noting that the model formulation is general and can be extended to describe other engineering interesting situations in which the variation in the mechanical properties is a consequence of external processes, acting at a constitutive material level (for instance temperature and diagenesis). • Numerical study: a) The description and modelling of advective diffusive reactive transport of chemical species governing the rate of dissolution of calcite in the finite element method context was fundamental. In fact, the reactive transport of chemical agents induces inevitably inhomogeneity and the time and space evolution of chemically active species is mandatory. b) Realization of a useful tool for numerical analyses (FEM code) to apply the constitutive model previously defined to boundary value problems. As is shown in the numerical analyses, it has been possible to deal with non-mechanical processes, like acid accelerated dissolution of calcarenite in numerical analyses of small scale boundary value problems. Despite the fact that the case considered is a preliminary study and has deliberately only academic flavour, it shows that the main goal of the work has been reached, since a real problem can be tackled. The model was implemented into a finite element code (GeHoMadrid). The model has been integrated with an implicit algorithm suitable for getting in the linearization procedure the consistent operator in a closed form. As is shown in Chapter 10, both quadratic convergence in the global iteration and high accuracy have been obtained even when non-conventional external loads (as weathering) are imposed. A further innovation of this tool is the possibility of analysing on one side larger scale boundary value problems where weathering was cause of failure and, on the other hand, as a predicting tool since physical time is now a driving variable of the constitutive model.

Il lavoro di tesi è stato rivolto allo studio sperimentale, teorico e numerico del comportamento meccanico di materiali debolmente cementati di formazione carbonatica molto comuni nel territorio italiano e in tutta la zona del Mediterraneo. La tesi riguarda un campo della geomeccanica molto interessante e altrettanto complicato e poco esplorato quale il degrado chimico di rocce tenere come la calcarenite. Alterazioni minerali dovute da fenomeni chimici (dissoluzione, precipitazione, cristallizzazione di sali) avvengono alla microscala e pertanto una modellazione adeguata di tali processi richiede una modellazione basata su diverse scale. Uno dei risultati raggiunti è la formulazione di un modello capace di valutare nel tempo la variazione delle caratteristiche meccaniche della calcarenite sottoposte ad un ambiente marino aggressivo. Considerando le reazioni chimiche, il tempo fisico è una variabile intrinseca del modello rendendolo, essendo stato implementato in un codice numerico, un ottimo strumento con il quale è possibile compiere analisi di stabilità di fenomeni evolutivi. Il lavoro è stato sviluppato in tre parti: 1. Studio sperimentale al fine di identificare i meccanismi micromeccanici dovuti da processi idro-chimici durante (i) la saturazione del materiale (Comportamento a breve termine) e (ii) la dissoluzione a lungo termine della matrice calcarea che compone il materiale stesso. Per fare ciò sono state svolte, presso il laboratorio del Dipartimento di Geologia dell’Università degli Studi Milano Bicocca, delle indagini spreimentali alla microscala utilizzando tecniche sofisticate quali la X-ray spectroscopy (EDS), X-ray Micro-Computer-Tomography (MCT), Scanning electron microscope (SEM) e la porosimetria al mercurio (MIP). Inoltre prove monoassili, edometriche, sono state effettuate presso il laboratorio di geotecnica del Politecnico, mentre quelle triassiali e isotrope presso il laboratorio del Dipartimento di Geologia dell’Università degli Studi Milano Bicocca. 2. Modellazione costitutiva allo scopo di riprodurre il comportamento chemo-meccanico osservato nei differenti percorsi di carico con un unico modello costitutivo. E’ stato sviluppato un modello elasto-plastico incrudente, caratterizzato da leggi di incrudimento estese, in grado di cogliere la risposta meccanica della calcarenite anche sotto l’effetto di danneggiamento chimico. Il processo di dissoluzione risulta essere accoppiato al comportamento meccanico per via del fatto che la velocità di dissoluzione è direttamente proporzionale alla superficie reagente del materiale. Tale area aumenta durante la formazione di micro fessure causate da azioni meccaniche. Allo stesso tempo la dissoluzione diminuisce la resistenza del materiale e dunque i due meccanismi risultano accoppiati in entrambe le direzioni. Per incormporare l’accoppiamonto chemo-meccanico è stata adoperata una modellazione a più scale: la chimica viene infatti descritta alla microscala, l’accoppiamento viene considerato alla meso-scala ed infine la massa discilta viene utilizzata alla mcaroscala per regolare le leggi di incrudimento macro. 3. Il modello è stato implementato all’interno di un codice ad elementi finiti e si sono eseguiti delle analisi numeriche allo scopo di mettere in luce l’importanza del trasporto di agenti chimici in un mezzo poroso sulla risposta meccanica del materiale e di descrivere la propagazione del danno all’interno di un provino di calcarenite attaccato da un fronte di acido dal basso verso l’alto in condizioni edometriche.