An Elastic Stress–Strain Relationship for Porous Rock Under Anisotropic Stress Conditions

A stress–strain relationship within porous rock under anisotropic stress conditions is required for modeling coupled hydromechanical processes associated with a number of practical applications. In this study, a three-dimensional stress–strain relationship is proposed for porous rock under elastic and anisotropic stress conditions. This relationship is a macroscopic-scale approximation that uses a natural-strain-based Hooke’s law to describe deformation within a fraction of pores and an engineering-strain-based Hooke’s law to describe deformation within the other part. This new relationship is evaluated using data from a number of uniaxial and triaxial tests published in the literature. Based on this new stress–strain relationship, we also develop constitutive relationships among stress, strain, and related stress-dependent hydraulic/mechanical properties (such as compressibility, shear modulus, and porosity). These relationships are demonstrated to be consistent with experimental observations.     

Micromechanical Modelling of the Complete Stress–Strain Relationship for Crack Weakened Rock Subjected to Compressive Loading

Summary  A micromechanics-based model, able to quantify the effect of various parameters on the complete stress–strain relationship, is described. The closed-form explicit expression for the complete stress–strain relationship of a rock material containing an echelon cracks arrangement subjected to compressive loading is obtained. The complete stress–strain relationship including the stages of linear elasticity, non-linear hardening and strain softening is established. The results show that the complete stress–strain relationship and the strength of rock with echelon cracks depend on the crack interface friction coefficient, the sliding crack spacing, the perpendicular distance between the two adjacent rows, the fracture toughness of rock material and orientation of the cracks. The present model is used to evaluate the complete stress–strain relationship and strength for crack-weakened rock at the underground cavern complex of the Ertan Hydroelectric Project. The predicted strength is in agreement with that obtained by the Hoek–Brown criterion. The numerical results obtained with the complete stress–strain relationship seem to be in good agreement with the measured values. Author’s address: Xiao-Ping Zhou, School of Civil Engineering, Chongqing University, 443002 Chongqing, P.R. China     

Solutions for Displacement and Stress in Strain-Softening Surrounding Rock Incorporating the Effects of Hydraulic–Mechanical Coupling and Rockbolts Effectiveness

This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness. It follows the generalized Hoek–Brown failure criterion. Moreover, an improved numerical approach and stepwise procedure are proposed. This approach considers the deterioration of the strength, deformation, and dilation angle and the variation of elastic strain in the plastic region considering the effect of the hydraulic–mechanical coupling and the rockbolts effectiveness. The presented solutions were validated by FLAC results. Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming. Parametric studies are also conducted to highlight the influences of hydraulic–mechanical coupling and rockbolts effectiveness on stress and displacement. Results show that stress and displacement, incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness, are between those when hydraulic–mechanical coupling or rockbolts effectiveness is considered separately. However, this theory needs more verification from practical engineering.     

A New Elasto-Viscoplastic Damage Model Combined with the Generalized Hoek–Brown Failure Criterion for Bedded Rock Salt and its Application

According to the requirement of the West–East Gas Transmission Project in China, the solution-mined cavities located in the Jintan bedded salt formation of Jiangsu province will be utilized for natural gas storage. This task is more challenging than conventional salt dome cavern construction and operation due to the heterogeneous bedding layers of the bedded salt formation. A three-dimensional creep damage constitutive model combined with the generalized Hoek–Brown model is exclusively formulated and validated with a series of strength and creep tests for the bedded rock salt. The viscoplastic model, which takes the coupled creep damage and the failure behavior under various stress states into account, enables both the three creep phases and the deformation induced by vicious damage and plastic flow to be calculated. A further geomechanical analysis of the rapid gas withdrawal for the thin-bedded salt cavern was performed by implementing the proposed model in the finite difference software FLAC^3D. The volume convergence, the damage and failure propagation of the cavern, as well as the strain rate of the salt around the cavern, were evaluated and discussed in detail. Finally, based on the simulation study, a 7-MPa minimum internal pressure is suggested to ensure the structural stability of the Jintan bedded salt cavern. The results obtained from these investigations provide the necessary input for the design and construction of the cavern project.     

Interaction of model F-bearing silicic melt with chloride fluid,uraninite, and columbite at 750°C and 1000–2000 bar and its implications for estimation of the ore-forming capability of the upper crustal magma chamber beneath the Strel’tsovka caldera,eastern Transbaikalia

The experimental study of an F-bearing silicic melt—U, Nb, Ta minerals—chloride-fluoride fluid system is focused on ascertaining the origin of uranium deposits spatially related to intraplate silicic volcanism. The first series of experiments on uranium solubility in silicic melts close in composition to ore-bearing rhyolite of the unique Strel’tsovka Mo-U ore field has been performed in order to determine more precisely the ore genesis. As starting solid phases, model homogeneous glass of the chemical composition (wt %) 72.18 SiO₂, 12.19 Al₂O₃, 1.02 FeO, 0.20 MgO, 0.33 CaO, 4.78 Na₂O, 3.82 K₂O, 1.44 Li₂O, and 2.4 F (LiF, NaF, KF, CaF₂, MgF₂); synthetic UO₂ and UO₃·0.33H₂O; and natural columbite were used. The starting solutions contained 1.0 m Cl and 10⁻² m F. The runs were conducted in a gas vessel at a pressure of 1000 bar and in a high-pressure hydrothermal vessel at 2000 bar. The O₂ (H₂) fugacity was set by Ni-NiO, Co-CoO, Fe₃O₄-Fe₂O₃, and Cu-Cu₂O buffers. The equilibrium between melt and solution for major elements is reached during the first day, whereas 5–7 days are required for ore elements (U, Nb, Ta) to come into equilibrium. The solubility of Nb and especially Ta in Cl-F solutions equilibrated with F-bearing melt is extremely low. The solubility of U is much higher (10⁻⁴−10⁻⁵ mol/kg H₂O). The energy dispersive spectroscopy of run products allowed us to establish that columbite dissolved incongruently with formation of U- and F-bearing pyrochlores. The performed experiments have shown that a silicic melt close to the rhyolitic magma of the Strel’tsovka caldera in composition is not able to generate postmagmatic ore-forming solutions containing more than 10⁻⁶−10⁻⁵ mol U/kg H₂O under the relatively low pressure necessary for the existence of the first type of fluid. The amount of uranium that could have precipitated from this fluid in the zone of ore deposition is estimated at 216–9000 t. This estimate is two orders of magnitude lower than the total uranium resources of the deposits localized in the Strel’tsovka caldera. Thus, the upper crustal silicic magma chamber hardly was a source of uranium for Mo-U deposits of the Strel’tsovka ore field.