Cavitation in high-capacity tensiometers: effect of water reservoir surface roughness

High-capacity tensiometers (HCTs) are sensors made to measure negative pore water pressure (suction) directly. In this paper, a new approach is proposed to expand the range and duration of suction measurements for a newly designed HCT. A new technique is employed to reduce significantly the roughness of the diaphragm’s surface on the water reservoir side in order to minimise the possibility of gas nuclei development and the subsequent early cavitation at the water–diaphragm interface. The procedures employed for the design, fabrication, saturation and calibration of the new tensiometers are explained in detail. Furthermore, the performance of the developed HCTs is examined based on a series of experiments carried out on a number of unsaturated clay specimens. An improvement in maximum sustainable suction in the range of 120–150% of their nominal capacity was obtained from different surface treatment methods. Moreover, the results show an improvement of up to 177% for the long-term stability of measurements, compared to the developed ordinary HCTs with untreated diaphragms

An experimental study of the initial volumetric strain rate effect on the creep behaviour of reconstituted clays

Clayey soils tend to undergo continuous compression with time, even after excess pore pressures have substantially dissipated. The effect of time on deformation and mechanical response of these soft soils has been the subject of numerous studies. Based on these studies, the observed time-dependent behaviour of clays is mainly related to the evolution of soil volume and strength characteristics with time, which are classified as creep and/or relaxation properties of the soil. Apart from many empirical relationships that have been proposed in the literature to capture the rheological behaviour of clays, a number of viscid constitutive relationships have also been developed which have more attractive theoretical attributes. A particular feature of these viscid models is that their creep parameters often have clear physical meaning (e.g. coefficient of secondary compression, Cα). Sometimes with these models, a parameter referred to as initial/reference volumetric strain rate, v̇₀ has also been alluded as a model parameter. However, unlike Cα, the determination of v̇₀ and its variations with stress level is not properly documented in the literature. In an attempt to better understand v̇₀, this paper presents an experimental investigation of the reference volumetric strain rate in reconstituted clay specimens. A long-term triaxial creep test, at different shear stress levels and different strain rates, was performed on clay specimen whereby the volumetric strain rate was measured. The obtained results indicated the stress-level dependency and non-linear variation of v̇₀ with time

On the numerical and mesh-dependent parameters in a computationally enhanced phase-field fracture model coupled with a novel mesh refinement strategy

The phase-field method has been proven as a robust and computationally efficient approach to model the propagation of fractures in brittle solids. However, the performance of this technique in the context of finite element method can be questioned due to restrictions in the mesh structure and the element size to capture the fracture as a diffusive damaged region. This study is dedicated to developing a methodology for finding an appropriate length-scale parameter to model the fracturing process in a way that matches the physical character of failure in materials. The fracture process zone is chosen as the key feature in this study to propose relationships for estimating the length-scale parameter based on the tensile strength and cracking properties, and the robustness of the method is verified using experimental data. To employ the phase-field method in modelling large-scale domains and complex geometries, a novel mesh refinement strategy is developed to increase the computational efficiency based on predicting a corrected tensile strength limit depending on the element size to capture the crack-tip effectively. The proposed mesh refinement strategy reduces the computational effort significantly. Reliability and robustness of the developed relationships are successfully examined by simulating benchmark cases and comparisons with physically measured data

Estimation of auto-covariance of log hydraulic conductivity from Generalized Sub-Gaussian porosity and particle size random fields

We derive analytical formulations relating the spatial covariance (CY) of (log-transformed) hydraulic conductivities to auto- and cross-covariances of porosity (ϕ) and representative soil particle sizes within the framework of the classical Terzaghi model. The latter provides an empirical relationship which is widely used to obtain conductivity estimates. We frame the study within recent stochastic approaches and conceptualize appropriate transformations of ϕ and representative soil particle size as Generalized Sub-Gaussian (GSG) spatially cross-correlated random processes. Consistency of the theoretical framework against sample distributions of ϕ and particle size is assessed through the analysis of field data. A perturbation-based approach yields workable expressions of CY upon truncating the otherwise exact analytical solution at given orders of approximations. Our analytical (truncated) log-conductivity covariance is in agreement with its Monte Carlo-based counterpart. A Global Sensitivity Analysis relying on classical Sobol indices quantifies the relative importance of all parameters embedded in the formulation of CY. We show that parameters driving the GSG nature of the distribution of (transformed) porosity are key to the main features of CY. We also document the relevance of properly capturing emergences of possible cross-correlations between ϕ and representative particle size to reconstruct conductivity fields

A Bayesian assessment of an approximate model for unconfined water flow in sloping layered porous media

The prediction of water table height in unconfined layered porous media is a difficult modelling problem that typically requires numerical simulation. This paper proposes an analytical model to approximate the exact solution based on a steady-state Dupuit–Forchheimer analysis. The key contribution in relation to a similar model in the literature relies in the ability of the proposed model to consider more than two layers with different thicknesses and slopes, so that the existing model becomes a special case of the proposed model herein. In addition, a model assessment methodology based on the Bayesian inverse problem is proposed to efficiently identify the values of the physical parameters for which the proposed model is accurate when compared against a reference model given by MODFLOW-NWT, the open-source finite-difference code by the U.S. Geological Survey. Based on numerical results for a representative case study, the ratio of vertical recharge rate to hydraulic conductivity emerges as a key parameter in terms of model accuracy so that, when appropriately bounded, both the proposed model and MODFLOW-NWT provide almost identical results

Rate Dependency and Stress Relaxation of Unsaturated Clays

This paper presents the experimental program conducted for evaluation of the rate-dependent and stress-relaxation behaviour of unsaturated reconstituted London Clay. A series of drained constant rate of strain (CRS) compression-relaxation tests with single-staged (SS-CRS) and multi-staged (MS-CRS) loading modes were performed in an innovative CRS oedometer cell where soil suction evolutions were monitored using two high-capacity tensiometers (HCTs). Specimens were tested at two strain rates of 4.8×10⁻⁷ and 2.4×10⁻⁶s⁻¹ and over a suction range of 0 – 1905 kPa. The coupled and independent effects of strain-rate and soil suction on one-dimensional stress–strain and stress-relaxation responses including the effects of pre-relaxation strain, stress, and strain-rate under both saturated and unsaturated conditions were evaluated. An increase in suction and strain-rate resulted in an increase of the yield vertical net stress (σp). Furthermore, it was observed that the rate and magnitude of the relaxed stresses increase with increase in pre-relaxation strain, stress, and strain-rate, and decrease with increase in soil suction. At constant suction, an increase in the pre-relaxation strain-rate by a factor of 5 resulted in an increase of the relaxed stresses by a factor of 2.2 – 3.6. Moreover, the coefficient of relaxation (Rₐ) was found to be suction-dependent, falling within a range of 0.011 – 0.019 and 0.017 – 0.029 respectively for slow and fast strain rates during MS-CRS tests. Comparing these results with the Cₐ/Cc ratio obtained from conventional multi-stage loading (MSL) oedometer test results revealed the validity of Rₐ = Cₐ/C\u1d4b8 correlation for unsaturated reconstituted specimens

Creep and consolidation of a stiff clay under saturated and unsaturated conditions

In this paper, the one-dimensional (1D) time-dependent behaviour of natural and reconstituted London Clay samples under saturated and unsaturated conditions is studied. For this purpose, a set of 1D consolidation tests including multi-staged loading (MSL) oedometer tests and single-staged loading (SSL) long-term oedometer creep tests were carried out on saturated and unsaturated specimens. Conventional oedometer cells were used for tests on saturated specimens, whereas a newly designed unsaturated oedometer cell, equipped with two high-capacity tensiometers (HCTs) for suction measurements, was used for unsaturated tests. The tests results revealed stress dependency and suction dependency of primary and secondary consolidation responses of the soil samples. Furthermore, counter to formerly acknowledged suggestions of independency of the slope of normal consolidation line to suction changes, it was observed that an increase in suction results in a decrease of the slope of compression curve (C꜀) and the creep index (Cₐₑ) values and an increase in yield vertical net stress (σₚ). Moreover, the Cₐₑ/C꜀ ratio for London Clay was found to be stress- and suction-dependent, unlike the previously suggested hypotheses

A CRS Oedometer Cell for Unsaturated and Non-Isothermal Tests

Research into the thermo-hydromechanical (THM) behavior of unsaturated soils and the effect of strain rate on their mechanical responses requires the employment of advanced laboratory testing systems and procedures as well as protocols of correcting the measured data in order to account for errors associated with complex test conditions and apparatus calibrations. This article presents the design and calibration of an innovative constant rate of strain oedometer cell for the characterization of the THM behavior of soils under combined non-isothermal and unsaturated conditions. The advanced oedometer cell enables the simultaneous control of temperature, suction, and stress state within the soil specimens. Temperatures of 20°C to 200°C are applied through a tubular heating element placed at the base of the soil specimen. Suction is controlled using the axis-translation technique and measured using both axis translation and two high-capacity tensiometers accommodated on the periphery of the specimen. The performance of the new cell is assessed based on a set of tests performed on clay specimens, and its merits and advantages are discussed in detail

Modeling solute transport and mixing in heterogeneous porous media under turbulent flow conditions

We develop and test a modeling approach to quantify turbulence-driven solute transport and mixing in porous media. Our approach addresses two key elements: (a) the spatial variability of the effective diffusion coefficient which is typically documented in the presence of a sediment-fluid interface and (b) the need to provide a model that can yield the complete distribution of the concentration probability density function, not being limited only to the mean concentration value and thus fully addressing solute mixing. Our work is motivated by the importance of solute transport processes in the hyporheic zone, which can have strong implications in natural attenuation of pollutants. Our approach combines Lagrangian schemes to address transport and mixing in the presence of spatial variability of effective diffusion. An exemplary scenario we consider targets a setup constituted by a homogeneous (fully saturated) porous medium underlying a clear water column where turbulent flow is generated. Solute concentration histories obtained through a model based solely on diffusive transport are benchmarked against an analytical solution. These are then compared against the results obtained by modeling the combined effects of diffusion and mixing. A rigorous sensitivity analysis is performed to evaluate the influence of model parameters on solute concentrations and mixing, the latter being quantified in terms of the scalar dissipation rate