Hydraulic conductivity of a dense prehydrated GCL: impact of free swell and swelling pressure

Exposure to liquids with high electrolyte concentrations or high cation valence present in landfill leachates can cause significant increases in hydraulic conductivity of clays due to a reduction in the thickness of the double layer. Methods to prevent compression of the interlayer are: prehydration of the bentonite, compression with increasing the solids content and addition of polymers. The aim of this study is to evaluate the performance of a dense prehydrated GCL (DPH GCL) compressed during manufacturing and pre-hydrated with a polymeric solution. A series of hydraulic conductivity tests with deionised water, sea water and a 0.01 M CaCl 2 solution were performed on single sheet and overlapped DPH GCL samples. Free swell and swelling pressure tests have also been performed with this solutions and with a series of KCI and CaCl 2 solutions with a concentration varying from 0.001 M to 1 M. The overlapped samples were analysed in large scale laboratory permeameters at different effective stresses. In addition, swelling pressure tests on single sheet samples were conducted to analyse the swelling behaviour of the factory prehydrated GCL. The concomitant effect of prehydration, addition of polymeric compounds and densification increased the hydraulic performance of GCLs under aggressive conditions. The use of bentonite paste to seal the overlap in presence of seawater was shown to be crucial. The swelling pressure test may be proposed as an alternative to the swell index test to characterize the swelling behaviour of polymer prehydrated GCLs

A space-time discontinuous Galerkin method for coupled poroelasticity-elasticity problems

This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The mathematical model consists of the low-frequency Biot's equations in the poroelastic medium and the elastodynamics equation for the elastic one. To realize the coupling, suitable transmission conditions on the interface between the two domains are (weakly) embedded in the formulation. The proposed PolydG discretization in space is then coupled with a dG time integration scheme, resulting in a full space-time dG discretization. We present the stability analysis for both the continuous and the semidiscrete formulations, and we derive error estimates for the semidiscrete formulation in a suitable energy norm. The method is applied to a wide set of numerical test cases to verify the theoretical bounds. Examples of physical interest are also presented to investigate the capability of the proposed method in relevant geophysical scenarios

Numerical modelling of wave propagation phenomena in thermo-poroelastic media via discontinuous Galerkin methods

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and $hp$-version error estimates in suitable energy norms are derived for the semi-discrete problem. The fully-discrete scheme is then obtained based on employing an implicit Newmark-$\beta$ time integration scheme. A wide set of numerical simulations is reported, both for the verification of the theoretical estimates and for examples of physical interest. A comparison with the results of the poroelastic model is provided too, highlighting the differences between the predictive capabilities of the two models

Critical issues in the determination of the bentonite cation exchange capacity

The swelling pressure and transport properties of bentonites are controlled by the electric charge density of solid particles, which is commonly estimated from the laboratory measurement of the cation exchange capacity (CEC). However, the standard ammonium displacement method for CEC determination does not take into account the fabric changes that occur in bentonites under exposure to high salt concentration solutions. A series of laboratory tests was conducted to assess the relevance of such a critical issue, by varying the concentration of the extracting KCl solution with respect to that of the standard test. The obtained results show that the release of the adsorbed ammonium cations depends on the bentonite fabric, which is controlled by the KCl concentration. As a consequence, the ammonium displacement method may provide an unrepresentative estimate of the CEC of bentonites. The methylene blue titration method, despite its apparently more limited accuracy, instead seems to provide a more reliable estimation of the CEC, as the bentonite fabric is maintained dispersed during the test

A high-order discontinuous Galerkin method for the poro-elasto-acoustic problem on polygonal and polyhedral grids

The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by the acoustics equations in the acoustic domain and the low-frequency Biot's equations in the poroelastic one. The coupling is introduced by considering (physically consistent) interface conditions, imposed on the interface between the domains, modeling both open and sealed pores. Existence and uniqueness is proven for the strong formulation based on employing the semigroup theory. For the space discretization we introduce and analyze a high-order discontinuous Galerkin method on polygonal and polyhedral meshes, which is then coupled with Newmark-$\beta$ time integration schemes. A stability analysis both for the continuous problem and the semi-discrete one is presented and error estimates for the energy norm are derived for the semidiscrete problem. A wide set of numerical results obtained on test cases with manufactured solutions are presented in order to validate the error analysis. Examples of physical interest are also presented to test the capability of the proposed methods in practical cases.Comment: The proof of the well-posedness contains an error. This has an impact on the whole paper. We need time to fix the issu

High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes

We propose and analyze a high-order Discontinuous Galerkin Finite Element Method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal and polyhedral elements. We analyze the well posedness of the resulting formulation, prove hp-version error a-priori estimates, and present a dispersion analysis, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion properties. The theoretical estimates are confirmed through various two-dimensional numerical verifications

A hybrid finite volume -- spectral element method for aeroacoustic problems

We propose a hybrid Finite Volume (FV) - Spectral Element Method (SEM) for modelling aeroacoustic phenomena based on the Lighthill's acoustic analogy. First the fluid solution is computed employing a FV method. Then, the sound source term is projected onto the acoustic grid and the inhomogeneous Lighthill's wave equation is solved employing the SEM. The novel projection method computes offline the intersections between the acoustic and the fluid grids in order to preserve the accuracy. The proposed intersection algorithm is shown to be robust, scalable and able to efficiently compute the geometric intersection of arbitrary polyhedral elements. We then analyse the properties of the projection error, showing that if the fluid grid is fine enough we are able to exploit the accuracy of the acoustic solver and we numerically assess the obtained theoretical estimates. Finally, we address two relevant aeroacoustic benchmarks, namely the corotating vortex pair and the noise induced by a laminar flow around a squared cylinder, to demonstrate in practice the effectiveness of the projection method when dealing with high order solvers. The flow computations are performed with OpenFOAM [46], an open-source finite volume library, while the inhomogeneous Lighthill's wave equation is solved with SPEED [31], an opensource spectral element library