Geomembrane strains from wrinkle deformations

Methods to compute geomembrane strains caused by the deformation of a geomembrane wrinkle when subject to vertical overburden stress are examined. Thin shell theory, small strain-displacement, and large strain-displacement methods are developed to compute geomembrane strains from wrinkle deformations. The implementation of each method is validated for three hypothetical trial cases against results obtained with finite element analysis. It was found that it is necessary to employ large strain-displacement theory and explicitly consider both vertical and horizontal components of wrinkle displacement to compute strain. Results are then presented from six physical experiments where the vertical and horizontal components of wrinkle displacement were measured under simulated landfill base liner conditions. For the particular conditions tested, it was found that without a thick sand protection layer on top of the geomembrane, the largest calculated tensile strain due to wrinkle deformations of 8% was much less than the tensile strain caused by overlying gravel particles, and thus local strains from gravel contacts would govern in the assessment of maximum geomembrane strain; whereas, with a thick sand protection, the maximum tensile strain was from wrinkle deformations, but the measured values were below a proposed long-term allowable strain of 3%.     

Geotechnical analysis of two Nigerian soils for use as clay liners

The cretaceous Auchi shale and the Tertiary Imo shale in SW Nigeria were investigated for their suitability for use as a clay seal in waste disposal landfills. Geotechnical analyses indicated they are highly plastic inorganic clays. Although their geotechnical and chemical properties were within the range suggested by various authors for use as mineral seals, care would need to be taken with the Okada shales as they contain smectite and would be difficult to work and liable to cracking.      

Geomembrane strains from coarse gravel and wrinkles in a GM/GCL composite liner

The physical response of a 1.5-mm-thick, high-density polyethylene geomembrane (GM) is reported when placed on top of a needle-punched geosynthetic clay liner (GCL), buried beneath 50-mm coarse gravel and subjected to vertical pressure in laboratory experiments. Local strains in the geomembrane caused by indentations from the overlying gravel and deflections of a wrinkle in the geomembrane are quantified. A peak strain of 20% was calculated when a flat geomembrane was tested without a protection layer at an applied vertical pressure of 250 kPa. Strains were smaller with a nonwoven needle-punched geotextile protection layer between the gravel and geomembrane. Increasing the mass per unit area of the geotextile up to 2200 g/m² reduced the geomembrane strain. However, none of the geotextiles tested were sufficient to reduce the geomembrane strain below an allowable limit of 3%, for the particular 50-mm gravel tested and when subjected to a vertical pressure of 250 kPa. Increasing the initial GCL water content and reducing the stiffness of the foundation layer beneath the GCL were found to increase the geomembrane strains. These local strains were greater when a wrinkle was present in the geomembrane. The wrinkle in the geomembrane experienced a decrease in height and width. The wrinkle deformations lead to larger pressures beside the wrinkle and hence producing larger local strains. A 150-mm-thick sand protection layer was effective in limiting the peak strain to less than 0.3% even with a wrinkle in the geomembrane, at a vertical pressure of 250 kPa.     

Calculating local geomembrane strains from a single gravel particle with thin plate theory

A new method is presented to calculate geomembrane strains induced by a single gravel particle (or grain) under vertical load from the deformed shape of the geomembrane for axisymmetric conditions. Past equations consider only vertical displacements of the geomembrane and neglect the contribution of radial displacements on strain and, consequently, underestimate the maximum strain. Axisymmetric large-strain-displacement relationships are used to relate radial strain to vertical and radial displacements. Vertical displacements are obtained from measurements of the deformed geomembrane from a physical experiment. Radial displacements do not need to be measured, but are related to tangential strain in the strain-displacement formulation. A linear elastic constitutive relationship is invoked and radial strains at the midsurface of the geomembrane from membrane elongation are solved for using Airy's stress function. Bending strains are obtained from the curvature of the deformed shape. Extreme fibre strains are the sum of the membrane and bending strains. Results from the new method match the maximum strain and pattern of strain when compared to large-displacement finite-element analysis. The new method is used to show that neglecting radial displacements underestimates the maximum strain by 25%, while neglecting radial displacements and bending strains underestimates the maximum strain by 60% (for a 2.5-mm-deep, Gaussian-shape indentation) and hence could affect selection of an appropriate geomembrane protection layer.     

The role of undrained clay soil subgrade properties in controlling deformations in geomembranes

Strains were evaluated in a 1.5 mm HDPE geomembrane from overlying coarse uniform drainage gravel when placed above six different compacted clayey soils while keeping pressure, protection, loading rate equal. In each case, a protection layer consisting of 400 g/m² nonwoven geotextile was placed over the geomembrane. Vertical load of 300 kPa was applied in a relatively short duration. A photogrammetry procedure was used to develop a digital elevation model for each deformed geomembrane surface and the distribution of resulting strain in the geomembrane was evaluated on a percent area basis. The proportion of the overall geomembrane area in which the localised strain exceeded 3% was related to the compacted water content, index soil properties, and undrained shear strength of the six different clayey soils. It was found that an increase in moulding moisture content resulted in increased geomembrane strain in all cases, but the magnitude of the increase in strain varied considerably, depending on the plasticity and silt content of the soil used.     

Geomembrane tensions and strains resulting from differential settlement around rigid circular structures

A simplified model is presented that analyzes tensions and strains in a geomembrane. The membrane analysis is applied to circular structures subjected to differential settlement. It was found that wrinkles are induced in the geomembrane around the circular structure and the associated mechanism was investigated. An improved predictive model was developed based on the wrinkled membrane theory. The model introduced the concept of a “variable Poisson's ratio”, and allowed tensions and strains associated with wrinkles in the geomembrane to be considered. Parametric studies and a comparison between the simplified model and the improved model were performed. Limitations associated with the two models are discussed and some practical recommendations are made with regard to the control of geomembrane tensions and strains around circular structures.     

Development of geomembrane strains in waste containment facility liners with waste settlement

The development of tensile strains in geomembrane liners due to loading and waste settlement in waste containment facilities is examined using a numerical model. Two different constitutive models are used to simulate the waste: (a) a modified Cam-Clay model and (b) a Mohr-Coulomb model. The numerical analyses indicate the role of the slope inclination on the maximum geomembrane liner strains for both short-term loading (immediately post closure) and long-term waste settlement. A geosynthetic reinforcement layer over the geomembrane liner is shown to reduce the maximum geomembrane liner strains, but the strain level of the geosynthetic reinforcement itself may become an engineering concern on steeper slopes (i.e., greater than 3H:1V) for cases and conditions examined in this paper. The paper considers some factors (e.g., slope inclination, use of a high stiffness geosynthetic over the geomembrane liner) and notes others (e.g., the designer selection of interface characteristics below and above the geomembrane, use of a slip layer above the geomembrane) that warrant consideration and further investigation to ensure good long-term performance of geomembrane liners in waste containment facilities.     

Homogenization in clay barriers and seals: Two case studies

The paper presents two case studies that provide information on the process of homogenization of initially heterogeneous clay barriers and seals. The first case is the canister retrieval test performed in the Aspö Hard Rock Laboratory (Sweden). The heterogeneity arises from the use of a combination of blocks and pellets to construct the engineered barrier. The degree of homogenization achieved by the end of the tests is evaluated from data obtained during the dismantling of the test. To assist in the interpretation of the test, a fully coupled thermo-hydro-mechanical (THM) analysis has been carried out. The second case involves the shaft sealing test performed in the HADES underground research laboratory (URL) in Mol (Belgium). Here the seal is made up of a heterogeneous mixture of bentonite pellets and bentonite powders. In addition to the full scale test, the process of homogenization of the mixture has also been observed in the laboratory using X-ray tomography. Both field test and laboratory tests are successfully modelled by a coupled hydro-mechanical (HM) analysis using a double structure constitutive law. The paper concludes with some considerations on the capability of highly expansive materials to provide a significant degree of homogenization upon hydration.     

Relationship between the shrinkage crack characteristics and the water content gradient of compacted clay liner in a landfill final cover

Shrinkage cracking is the primary reason for the anti-seepage failure of compacted clay liner (CCL) in a landfill final cover. With a focus on the surface crack characteristics and the water content distribution of three CCLs with different liquid limits and their mineral compositions, experiments were conducted to investigate the cracking mechanism of a CCL during the drying process. The results showed that the total crack ratio (TCR), the sum of the surface shrinkage crack ratio (SCR) and the surface boundary shrinkage ratio (BSR), is a function of the surface water content of a CCL. The change in the TCR with surface water content is consistent with the soil shrinkage characteristic curve (SSCC). The surface SCR is a function of the surface water content gradient of a CCL. The variations in the SCR with the water content gradient can be divided into the following three stages: the crack open stage, the crack linear expansion stage and the crack linear close stage. The effect of sample size, surface boundary shrinkage and shrinkage cracking are the main deformations of CCL specimens with low and high liquid limits, respectively, during the drying process. An increase in the amount of clay minerals in CCLs enhances the soil shrinkage capacity, leading to an increase in the SCR under the same water content gradient. A unified linear relationship exists between $\mathit{SCR}/K_{\text{j}}$ (where K_j is the slope of the SSCC) and the water content gradient in the crack linear expansion stage and the crack linear close stage for different CCL types.     

Coupled HM effects in a crystalline rock mass due to glaciation: indicative results from groundwater flow regimes and stresses from an FEM study

This paper highlights certain aspects of glacial impact on groundwater flow and rock mechanics, of particular interest in future scenarios for the geological disposal of nuclear waste. The investigation took the form of a generic exercise based on conditions at the underground research facility in Whiteshell, Canada. The site scale model domain boundaries were set up based on a number of major deformation zones. The surface boundary conditions comprised a transient ice sheet load and related hydraulic heads, generated by meltwater. It has thus been possible to compare glacial impact in relation to present-day climatological conditions. The main issues in the investigation were to evaluate the groundwater flow regime and the pre-requisites for underground jacking as well as shearing according to the prescribed geoscientific properties of a benchmark protocol. Special attention has been devoted to a solution to the hydromechanical (HM) problem (1) with or without process coupling, (2) with or without a transient approach, and (3) considering a two- or three-dimensional mode. The study underlines the need for transient analyses in 3D of these coupled phenomena.