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Computations of channel flow with rough walls comprising staggered arrays of cubes having various plan area densities are presented and discussed. The cube height h is 12.5% of the channel half-depth and Reynolds numbers (uτh/ν) are typically around 700 – well into the fully rough regime. A direct numerical simulation technique, using an immersed boundary method for the obstacles, was employed with typically 35 million cells. It is shown that the surface drag is predominantly form drag, which is greatest at an area coverage around 15%. The height variation of the axial pressure force across the obstacles weakens significantly as the area coverage decreases, but is always largest near the top of the obstacles. Mean flow velocity and pressure data allow precise determination of the zero-plane displacement (defined as the height at which the axial surface drag force acts) and this leads to noticeably better fits to the log-law region than can be obtained by using the zero-plane displacement merely as a fitting parameter. There are consequent implications for the value of von Kármán's constant. As the effective roughness of the surface increases, it is also shown that there are significant changes to the structure of the turbulence field around the bottom boundary of the inertial sublayer. In distinct contrast to two-dimensional roughness (longitudinal or transverse bars), increasing the area density of this three-dimensional roughness leads to a monotonic decrease in normalized vertical stress around the top of the roughness elements. Normalized turbulence stresses in the outer part of the flows are nonetheless very similar to those in smooth-wall flows.

A split Hopkinson pressure bar (SHPB) system with a special shape striker has been suggested as the test method by the International Society for Rock Mechanics (ISRM) to determine the dynamic characteristics of rock materials. In order to further verify this testing technique and microscopically reveal the dynamic responses of specimens in SHPB tests, a numerical SHPB test system was established based on particle flow code (PFC). Numerical dynamic tests under different impact velocities were conducted. Investigation of the stresses at the ends of a specimen showed that the specimen could reach stress equilibrium after several wave reverberations, and this balance could be maintained well for a certain time period after the peak stress. In addition, analyses of the reflected waves showed that there was a clear relationship between the variation of the reflected wave and the stress equilibrium state in the specimen, and the turning point of the reflected wave corresponded well with the peak stress in the specimen. Furthermore, the reflected waves can be classified into three types according to their patterns. Under certain impact velocities, the specimen deforms at a constant strain rate during the whole loading process. Finally, the influence of the micro-strength ratio ( τ c τ c σ c σ c ) and distribution pattern on the dynamic increase factor (DIF) of the strength DIF were studied, and the lateral inertia confinement and heterogeneity were found to be two important factors causing the strain rate effect for rock materials.

Roadway instability has always been a major concern in deep underground coal mines where the surrounding rock strata and coal seams are weak and the in situ stresses are high. Under the high overburden and tectonic stresses, roadways could collapse or experience excessive deformation, which not only endangers mining personnel but could also reduce the functionality of the roadway and halt production. This paper describes a case study on the stability of roadways in an underground coal mine in Shanxi Province, China. The mine was using a longwall method to extract coal at a depth of approximately 350 m. Both the coal seam and surrounding rock strata were extremely weak and vulnerable to weathering. Large roadway deformation and severe roadway instabilities had been experienced in the past, hence, an investigation of the roadway failure mechanism and new support designs were needed. This study started with an in situ stress measurement programme to determine the stress orientation and magnitude in the mine. It was found that the major horizontal stress was more than twice the vertical stress in the East–West direction, perpendicular to the gateroads of the longwall panel. The high horizontal stresses and low strength of coal and surrounding rock strata were the main causes of roadway instabilities. Detailed numerical modeling was conducted to evaluate the roadway stability and deformation under different roof support scenarios. Based on the modeling results, a new roadway support design was proposed, which included an optimal cable/bolt arrangement, full length grouting, and high pre-tensioning of bolts and cables. It was expected the new design could reduce the roadway deformation by 50 %. A field experiment using the new support design was carried out by the mine in a 100 m long roadway section. Detailed extensometry and stress monitorings were conducted in the experimental roadway section as well as sections using the old support design. The experimental section produced a much better roadway profile than the previous roadway sections. The monitoring data indicated that the roadway deformation in the experimental section was at least 40–50 % less than the previous sections. This case study demonstrated that through careful investigation and optimal support design, roadway stability in soft rock conditions can be significantly improved.

This study used precisely digitized standard roughness profiles to determine roughness parameters such as statistical and 2D discontinuity roughness, and fractal dimensions. Our methods were based on the relationship between the joint roughness coefficient (JRC) values and roughness parameters calculated using power law equations. Statistical and 2D roughness parameters, and fractal dimensions correlated well with JRC values, and had correlation coefficients of over 0.96. However, all of these relationships have a 4th profile (JRC 6–8) that deviates by more than ±5 % from the JRC values given in the standard roughness profiles. This indicates that this profile is statistically different than the others. We suggest that fractal dimensions should be measured within the entire range of the divider, instead of merely measuring values within a suitable range. Normalized intercept values also correlated with the JRC values, similarly to the fractal dimension values discussed above. The root mean square first derivative values, roughness profile indexes, 2D roughness parameter, and fractal dimension values decreased as the sampling interval increased. However, the structure function values increased very rapidly with increasing sampling intervals. This indicates that the roughness parameters are not independent of the sampling interval, and that the different relationships between the JRC values and these roughness parameters are dependent on the sampling interval.

A new experimental model has been designed to simulate the influence of a natural fracture network on the propagation geometry of hydraulic fractures in naturally fractured formations using a tri-axial fracturing system. In this model, a parallel and symmetrical pre-fracture network was created by placing cement plates in a cubic mold and filling the mold with additional cement to create the final testing block. The surface of the plates will thus be weakly cemented and form pre-fractures. The dimension and direction of the pre-fractures can be controlled using the plates. The experiments showed that the horizontal differential stress and the angle between the maximum horizontal principal in situ stress and the pre-fracture are the dominating factors for the initiation and propagation of hydraulic fractures. For and or and , the direction of the initiation and propagation of the hydraulic fractures are consistent with or deviate from the normal direction of the pre-fracture. When the hydraulic fractures approach the pre-fractures, the direction of the hydraulic fracture propagation will be consistent with the normal direction of the pre-fracture. Otherwise, the hydraulic fracture will deflect and perpendicularly cross the parallel and symmetric pre-fracture network. For and , and or and , before the hydraulic fracture and the pre-fractures intersect, the direction of the hydraulic fracture propagation remains unchanged, and the pre-fractures open or dilate when the hydraulic fracture propagates to the intersection point, forming a complicated hydraulic fracture network with the propagation region of the overall hydraulic fracture network taking the shape of an ellipse. In this condition, the complexity level of the hydraulic fracture is controlled by the net pressure, the compressive normal stress acting on the pre-fractures, the shearing strength and the cohesion strength of the planes of weakness. The conclusions of this research are inconsistent with the formulation of the approach angle that has been widely accepted by previous studies. The principle of hydraulic fracture propagation is that it follows the least resistance, the most preferential propagation, and the shortest propagation path.

This review paper aims at giving an overview of the different applications of thermodynamic equilibrium calculations in cementitious systems. They can help us to understand on a chemical level the consequences of different factors such as cement composition, hydration, leaching, or temperature on the composition and the properties of a hydrated cementitious system. Equilibrium calculations have been used successfully to compute the stable phase assemblages based on the solution composition as well as to model the stable phase assemblage in completely hydrated cements and thus to asses the influence of the chemical composition on the hydrate assemblage. Thermodynamic calculations can also, in combination with a dissolution model, be used to follow the changes during hydration or, in combination with transport models, to calculate the interactions of cementitious systems with the environment. In all these quite different applications, thermodynamic equilibrium calculations have been a valuable addition to experimental studies deepening our understanding of the processes that govern cementitious systems and interpreting experimental observations. It should be carried in mind that precipitation and dissolution processes can be slow so that thermodynamic equilibrium may not be reached; an approach that couples thermodynamics and kinetics would be preferable. However, as many of the kinetic data are not (yet) available, it is important to verify the results of thermodynamic calculations with appropriate experiments. Thermodynamic equilibrium calculations in its different forms have been applied mainly to Portland cement systems. The approach, however, is equally valid for blended systems or for cementitious systems based on supplementary cementitious materials and is expected to further the development of new cementitious materials and blends.

Uniaxial compressive and tensile strengths are considered key properties for characterising rock material in engineering practice. They are determined, directly and indirectly, as described by the International Society for Rock Mechanics (ISRM) (1985) and the American Society for Testing Materials (ASTM) (1986).

The radial flow rate of a cement grout in a rock fracture is obtained from Bingham’s relation and the fact that the power expended by the injection mechanism is the energy dissipated by viscous effects. The energy balance reveals that the advance ratio is of fundamental importance in the grouting process and is inherently related to the rest and advance phases of a cement grout. This allows giving a precise definition of the zero flow path that divides the energy diagram into two distinct domains for advancing and non-advancing grout. The advance ratio and the zero flow path are used to explore the grouting of one or more fractures, analyze the GIN model in the context of the SL dispute, draw a terminal sequence considering the energy interval alternative, and reformulate the refusal criterion of the North American grouting method. Secondary grouting effects are also investigated.

An exact closed form solution is derived for the mechanical behaviour of a linear viscoelastic Burgers rock around an axisymmetric tunnel, supported by a linear elastic ring. Analytical formulae are provided for the displacement of the rock/lining interface and for the pressure exerted by the rock on the lining, taking into account the stiffness and its installation time. Results calculated from these formulae do validate the corresponding numerical results of a 2D finite differences code. Further, comparison to previous existing solutions for the same viscoelastic model indicates similarities and differences. A parametric study is performed to investigate the effect of the viscoelastic constants, the stiffness and installation time of the support. The derived closed form solution is used to construct the time-dependent Supported Ground Reaction Curves of the viscoelastic rock, i.e. the time contour plots on the convergence confinement diagram. The importance of the effect of the support on the restrained rock creep and the exerted pressure on the lining, during the design life of a structure, is examined.

A particle-based distinct element method and its grain-based method are used to generate and simulate a synthetic specimen calibrated to the rupture characteristics of an intact (non-jointed) low-porosity brittle rock deformed in direct shear. The simulations are compared to the laboratory-generated ruptures and used to investigate rupture at various normal stress magnitudes. The fracturing processes leading to shear rupture zone creation and the rupture mechanism are found to be normal stress dependent (progressing from tensile splitting to shear rupture) and show partial confirmation of rupture zone creation in nature and in experiments from other materials. The normal stress dependent change is found to be due to the orientation of the major principal stress and local stress concentrations internal to the synthetic specimens being deformed. The normal stress dependent rupture creation process results in a change to the rupture zone’s geometry, shear stress versus horizontal displacement response, and thus ultimate strength.