Determination of Equivalent Mohr-Coulomb Criterion from Generalised Hoek-Brown Criterion

A new analytical solution is presented for determining equivalent Mohr-Coulomb (MC) shear strength parameters over an arbitrary interval of minor principal stress σ3 from the generalised Hoek-Brown (HB) criterion using least squares method. Comparison with several published examples demonstrates that the proposed solution had a capacity to accurately determine equivalent MC parameters over a given interval of σ3, as well as instantaneous MC parameters by using a very small interval of σ3. EMC parameters depended heavily on the interval of σ3, which highlighted the importance of intervals of σ3. A calculation case shows that the equivalent internal friction angle and cohesion over the interval of σ3 from tension cut-off σcut−off to maximum minor principal stress σ3max were approximately 12% smaller and 10.3% larger than those over an interval from tensile strength to σ3max, respectively. The proposed solution offers great flexibility for the application of the HB criterion with existing methods based on the MC criterion for rock engineering practice.

Investigation of Percolation-Driven Fluid Transport in Rock Salt under Repository-Relevant Conditions (PeTroS)

According to the state of the art in mining and repository research, undisturbed rock salt is impermeable to fluids. Hence, rock salt formations are considered as host rock for nuclear waste repositories. Viscous, polycrystalline salt rock with low humidity contains no connected pore spaces. Two mechanisms are known for fluid transport: (a) damage due to large deviatoric and tensile stresses generates dilatancy, and hence permeability. (b) Fluid pressure exceeding the minor principal stress can open pathways (pressure-driven percolation, Minkley et al., 2013). To assess barrier integrity of rock salt barriers, the dilatancy and minimal stress criteria have been derived. Recently (Ghanbarzadeh et al., 2015; Lewis and Holness, 1996), high permeabilities in rock salt have been postulated under certain conditions. In particular, at high stresses and temperatures, including possible repository conditions, rock salt is claimed to develop a connected, thus permeable, pore space. In the PeTroS project (Minkley et al., 2020), we investigated fluid transport in the supposedly permeable region. Five points in pressure-temperature space were defined – pressures of 18 and 36 MPa, temperatures of 140, 160, and 180 ∘C. At each point, experiments with both nitrogen and saturated NaCl solution (brine) were performed. Samples were prepared from natural rock salt of German Zechstein formations, both bedded and domal salt. Sample material was generally relatively pure rock salt with minor impurities. Cylindrical samples (diameter 100 mm, length 200 mm) were loaded in a triaxial (Kármán) cell. Fluid pressure was applied to a central pressure chamber; any transmitted fluid was collected and extracted at the secondary side. The entire cell was heated to the specified temperature. Experiments generally comprised an isotropic phase (several stages of fluid pressure almost up to the confining stress) and a fluid breakthrough phase (lowering of axial stress by strain-controlled extension). After the test, a coloured tracer fluid was injected to visualise fluid discharge points. Fluid breakthroughs with fluid pressure above the minor principal stress were observed at all five pressure-temperature conditions. Some samples showed an approximately Darcian flow at fluid pressure below the minor principal stress, with permeabilities in the order of 10−22 m2, as is regularly observed due to the small size and initial damage from sample preparation (Popp et al., 2007). Tests consistently showed a gradual decrease of flow rate, i.e. reduction of the initial damage. A stable permeability over longer times, as would be expected due to the formation of a connected pore space network, was not observed in any of the experiments. Intriguingly, experiments with brine showed no initial permeability even though the wetting fluid should plausibly favour the formation of a stable connected pore network. Predictions of the static pore scale theory (Ghanbarzadeh et al., 2015) could thus not be confirmed. Regarding repositories for heat-generating waste, it can be concluded that from a geomechanical point of view, the dilatancy and minimal stress criteria are the relevant criteria for barrier integrity even at higher pressure and temperature.

Evaluation of additional confinement for three-dimensional geoinclusions under general stress state

Three-dimensional cellular geoinclusions (e.g., geocells, scrap tires) offer all-around confinement to the granular infill materials, thus improving their strength and stiffness. The accurate evaluation of extra confinement offered by these geoinclusions is essential for predicting their performance in the field. The existing models to evaluate the additional confinement are based on either a plane-strain or axisymmetric stress state. However, these geoinclusions are more likely to be subjected to the three-dimensional stresses in actual practice. This note proposes a semi-empirical model to evaluate the additional confinement provided by cellular geoinclusions under the three-dimensional stress state. The proposed model is successfully validated against the experimental data. A parametric study is conducted to investigate the influence of input parameters on additional confinement. Results reveal that the simplification of the three-dimensional stress state into axisymmetric or plane-strain condition has resulted in inaccurate and unreliable results. The extra confinement offered by the geoinclusion shows substantial variation along the intermediate and minor principal stress directions depending on the intermediate principal stress, infill soil, and geoinclusion properties. The magnitude of additional confinement increases with an increase in the geoinclusion modulus. The findings are crucial for accurate assessment of the in situ performance of three-dimensional cellular geoinclusions.

Meso-Scale Simulation of Concrete Uniaxial Behavior Based on Numerical Modeling of CT Images

It is important to study the failure mechanism of concrete by observing the crack expansion and capturing key structures at the mesoscale. This manuscript proposed a method for efficiently identifying aggregate boundary information by X-ray computed tomography technology (CT) and a discrete element modeling method (DEM) for equivalent random polygon aggregates. This method overcomes the shortcomings of the Grain Based Model (GBM) which is impossible to establish a mesoscopic model with a large difference in grain radius. Through the above two methods, the CT slice images were processed in batches, and the numbers of edges, axial length, elongation of the aggregate were identified. The feasibility of the method was verified by the comparison between experimental and simulating results. Three mesoscopic models for different porosities were established. Based on aggregate statistics, this manuscript achieved the meso-model recovery to the maximum extent. The test results show that the crack appeared at the tip of the aggregate firstly, and then the broken boundary was applied in the direction of the applied load and around the pores. Finally, the crack was selectively expanded under the axial force. During the loading process, the minor principal stress was normally distributed. As the porosity and loading time increased, the heterogeneity increased.

Numerical simulations of overflow experiments on a model dike

Dike failure due to overtopping is one of the important factors, which should be considered in the dike designing process. Although the overflow is characterized by the relatively low risk of occurrence, in many cases dikes are totally destroyed or seriously damaged. An interesting phenomenon occurring during overflow is the trapping of air in pores of the unsaturated soil material. As the infiltration progresses from all sides, the air pressure in the unsaturated region increases, which may ultimately lead to damage of the dike structure. It happens when the air is expulsed in form of bursts and forms large macropores. Such a behaviour evidenced in laboratory experiments. In this study we attempt to simulate the evolution of stress field in the model dike subjected to overtopping. The results are in qualitative agreement with observations, showing that formation of the first macropores occurs in the direction perpendicular to the minor principal stress in the soil mass along the dike slope edge.

Observations of hydraulic fracturing in soils through field testing and numerical simulations

Hydraulic fracturing is a potential cause of leakage of earth dams or loss of fluid in drilling and field permeability testing. The effect of hydraulic fracturing on soil grouting is also a major concern. Although hydraulic fracturing has been adopted for decades by the petroleum industry for oil recovery in rock formations, studies on fracturing in soils are relatively few and inconclusive. The aim of this study is to provide further insight into the mechanism of hydrofracturing in soils through a field grouting trial and numerical simulation. We observe hydraulic fracturing in soils during this field trial as predicted by generally accepted groutability requirements. The hydraulic fractures are found vertically developed up to the ground surface. Numerical simulations show the hydraulic fracturing is easier to be initiated in anisotropic stress conditions, where the minor principal stress is the key factor. Numerical simulations also demonstrate significant compressions and shears during injection, suggesting the mechanism of fracturing in soils would be a shearing type. Based on this study, we propose a punching and splitting mode for the hydrofracturing in soils. The equation associated with estimating fracturing pressure is verified, and the results are found to be in good agreement with the cases examined.