Bearing Capacity of Footings on Rock Masses Using Flow Laws

The influence of the non-associative flow law on the bearing capacity of shallow foundations on rock masses is, in general, a subject that is not discussed in the field of rock mechanics. The calculation methods of bearing capacity usually do not define which flow law is adopted and, in some methods, the associative flow rule is assumed without knowing how that hypothesis influences the bearing capacity of the rock mass. In this paper, the study of the influence of the dilatancy angle on the bearing capacity of shallow foundations on rock masses is presented. The variation of the bearing capacity with the associative flow law and the non-associative flow law with zero dilatancy angle is studied using the finite difference method and by considering the influence of the self-weight of rock material. The calculations confirm the great influence of the flow law on the bearing capacity and a correction coefficient is proposed, which makes it possible to estimate the variation of the bearing capacity of the rock mass in terms of the function of the flow law for the hypothesis of weightless rock masses.

Analysing the Performance of Hollow Core Slabs Strengthened with CFRP

External bonding with CFRP (Carbon Fiber Reinforced Polymers) has been investigated over the last decade, as it represents a viable technique of strengthening existing prestressed concrete structures, including hollow-core slabs (HCS) with non-circular voids. The high performance of these carbon fibers has been validated through a large volume of experimental and numerical research and yet there are a few issues which remain controversial in simulating their behaviour with the finite element modelling. Although the CFRP mechanical properties are provided by the manufacturers, they are not satisfactory for a complete understanding of the analysis and design approach of HCS strengthened with CFRP. The present research is conducted on prestressed HCS with non-circular voids. The strengthening method consisted in the application of the composite material on the slab’s end internal regions of the voids, on a 500mm length: 1 layer and 2 layers. The objective of this study is to emphasize the effect of damage in the CFRP strips and moreover the interface effectiveness on the CFRP strengthened HCS. Damage is predicted using Hashin’s initiation criteria and the cohesive behaviour in the interface is used to analyse the epoxy resin which bonds the CFRP sheets to the hollow-core units. A plastic damage model was used for modelling the concrete, after a parametric study regarding the dilatancy angle and viscosity parameter was conducted for the most appropriate choice of concrete damage plasticity parameters. The overall procedure consists of numerical FE modelling in Abaqus software. Two different modelling possibilities of CFRP-to-concrete interface were studied: a tie constraint connection was first used and secondly the contact bonding was defined with the cohesive behaviour option of the contact interaction property. The results are provided in terms of load-displacement response, equivalent plastic strain and distribution of Von Misses stresses in the CFRP strips.

Slopes Analyses - Case Study, Slope Stability of Bypass Project

The scope of this study was to compare various stability evaluation methods. Accordingly, most common LE approaches were compared with the advanced LE (M‐P) method. Similarly, the differences in FOS computed from LE and FE analyses were compared based on a simple slope considering various load cases. In addition, two real slopes in a case study were analysed for the recorded minimum‐maximum GWT, pseudo‐static and dynamic conditions. Moreover, the stability evaluations of these slopes were based on both LE (M‐P) and FE (PLAXIS) calculation approaches, which both utilized shear strength parameters from advanced triaxle tests. Similarly, Mohr‐Coulomb model was applied in both approaches. The following conclusions are hence derived based on the reported work on both idealized and real slopes. To fulfil one of the aims of the study, the LE based methods are compared based on the factor of safety (FOS) obtained for various load combinations. The comparison is mainly based on simplified slope geometry and assumed input parameters. Among the LE methods, the Bishop simplified (BS), Janbu simplified (JS) and Janbu GPS methods are compared with the Morgenstern‐Price method (M‐PM). These LE methods are well established for many years, and thus some of them are still commonly used in practice for stability analysis. Moreover, the M‐PM has been compared with results from the FE analyses. Compared with theFE (PLAXIS) analyses, the LE (M‐PM) analyses may estimate 5 – 14percent higher FOS, depending on the conditions of a dry slope and a fully saturated slope with hydrostatic pore pressure distributions. For fully saturated conditions in the slope, inaccurate computation of stresses in LE methods may have resulted in larger difference in the computed FOS. Since, the FE software is based on stress‐strain relationship, stress redistributions are surely better computed even for a complicated problem. This has been found one of the advantages in FE simulations. A parameter study shows that the application of a positive dilatancy angle in FE analysis can significantly improve the FOS (4 ‐ 10percent). On contrast, the shear surface optimization in LE (M‐PM in SLOPE/W) analysis results in lower FOS, and thus minimizing the difference in FOS compared with FE analysis

Consolidated drained (CID) behavior of fibre reinforced cemented Toyoura sand in triaxial loading conditions

The effects of fibre (0–3 %) and cement (0–3 %) additives, on Toyoura sand were examined under consolidated drained compression and extension loading conditions. All samples were prepared to a target dry density value (e.g., $${\rho }_{d}$$ ρ d = 1.489 g/cm3) of Toyoura sand using under-compaction moist tamping technique. In compression, the unreinforced specimens exhibited a behavior of medium dense sand and reached a peak deviator stress (qp) at approximately 4 % axial strain ($${\epsilon }_{a}$$ ϵ a ) for the varying mean effective stresses, pʹ (i.e. 50–400 kPa). The peak drained strength increases in fibre reinforced cemented specimens were found to be up to 132 % (lower effective stresses) and 243 % (higher effective stresses), while, the drained strength increases at critical state for the fibre reinforced cemented specimens were found to be up to 105 % (lower effective stresses) and 245 % (higher effective stresses). Overall, the fibre and cement additives increased the stiffness, peak and strength at critical state of pure Toyoura sand but were found to be least effective in extension loading. Moreover, the stress ratio, peak and critical state stress ratios increase with the addition of fibres and cement. The secant modulus shows limited increases for the fibre reinforced specimens. However, a significant improvement in the secant modulus is observed for the fibre reinforced cemented specimens. For both unreinforced and reinforced specimens there is a decrease in volumetric strain with greater effective stresses or in other words, the rate of dilation decreases with increases in effective stresses. The fibre and cement additives also increased the strength parameters (frictional angle, cohesion), dilatancy angle, slope of the critical state line, and decreased the state parameter of pure Toyoura sand.

Novel method and case study of a deep shale fracability evaluation based on the brittleness index

Deep shale has gradually become a focus point for unconventional natural gas exploration and development in China and even the world. The key to deep shale development is the fracability evaluation of a reservoir; conventional evaluation methods cannot provide accurate evaluations of deep shale fracability under high confining pressures. In this study, experimental methods are used to obtain the mechanical parameters, mineral composition, and stress–strain characteristics of shale. The fracture complexity coefficient based on the fractal dimension and fracture angle is defined by analyzing the fracture morphology of shale samples. Using the rock fracturing complexity as an index, the weight coefficients of different factors for the shale fracture morphology are obtained, thus establishing a new evaluation model for the deep shale brittleness index. The results show that the Young's modulus, dilatancy angle, and peak strain are the main factors affecting the complexity of shale fractures. The gray correlation theory is used to calculate the weights of various factors in the model. The weight coefficients of the Young's modulus, dilatancy angle, and peak strain on the rock brittleness index are 0.262, 0.353, and 0.385, respectively. Based on this, a novel method for evaluating the fracability of deep shale using the brittleness index is proposed. The fracability index of the horizontal section of the deep shale gas well in this area was calculated, and the location of the fracturing perforation cluster was optimized accordingly. This technology has been successfully applied in more than 10 deep shale gas wells in the southern Sichuan Basin, effectively reducing the fracturing pressure by 5–10 MPa, increasing the average daily production of a single well by 15.3 × 104 m3. This paper proposes a novel fracability evaluation method for deep shale based on the brittleness index, which provides a reference for optimizing deep shale fracturing design.

Numerical Study of Elasto-Plastic Hydraulic Fracture Propagation in Deep Reservoirs Using a Hybrid EDFM–XFEM Method

Rock yielding may well take place during hydraulic fracturing in deep reservoirs. The prevailing models based on the linear elastic fracture mechanics (LEFM) are incapable of describing the evolution process of hydraulic fractures accurately. In this paper, a hydro-elasto-plastic model is proposed to investigate the hydraulic fracture propagation in deep reservoirs. The Drucker–Prager plasticity model, Darcy’s law, cubic law and cohesive zone model are employed to describe the plastic deformation, matrix flow, fracture flow and evolution of hydraulic fractures, respectively. Combining the embedded discrete fracture model (EDFM), extended finite element method (XFEM) and finite volume method, a hybrid numerical scheme is presented to carry out simulations. A dual-layer iterative procedure is developed based on the fixed-stress split method, Picard iterative method and Newton–Raphson iterative method. The iterative procedure is used to deal with the coupling between nonlinear deformation with fracture extension and fluid flow. The proposed model is verified against analytical solutions and other numerical simulation results. A series of numerical cases are performed to investigate the influences of rock plasticity, internal friction angle, dilatancy angle and permeability on hydraulic fracture propagation. Finally, the proposed model is extended to simulate multiple hydraulic fracture propagation. The result shows that plastic deformation can enhance the stress-shadowing effect.

Determination and quality classification of rock mass of the Diatomite mine, Algeria

Reserch relaevance. Most ground movements are generally due to rock instability, this natural phenomenon poses a risk to humanity. The properties of the rock mass directly influence the type of movement especially in underground structures. Research aim. Our goal is to characterize and classify the rock mass of diatomite from the sig mine using geomechanical classification systems such as the RQD and RMR in order to determine the quality of the rocks in the sig mine Western Algeria from the determination of the physical and mechanical properties. Methodology. In this article, the characterization analysis of the diatomite rock mass of the sig mine was carried out. First, determinations of the physical properties and carried out the triaxial test to determine the mechanical properties (young’s modulus, the friction angle, the dilatancy angle, the cohesion, the poisson’s ratio). Secondly to classify the deposit and give a recommendation to avoid stability problems. Research results. The results from physical and mechanical analyzes, it can be said that the nature of the rock present in the diatomite (underground mine) does not have enough resistance. Conclusion. Our study definitively proves that the rock mass of sig diatomite is of very low quality and it will be very dangerous for the underground mining work of the mine especially in places where the mineralized layer is very deep. And we suggest to replace the mining technique room and pillar currently used in the diatomite mine and put another mining method which includes roof support system to ensure the safety both of the miners and the equipment.

Shear banding in a micromechanics-based brittle damage model

<p>The Earth’s brittle upper crust is commonly modeled as a non-associated Mohr-Coulomb (MC) elasto-plastic continuum. This framework enables the localization of shear strain through a process referred to as structural softening: dilatancy related to the build-up of plastic strain inside a shear band can elastically unload the surrounding material as principal stresses rotate inside the band. The strains required to weaken the material and corresponding stress drops are compatible with experimental observations, and provide useful theoretical insights into strain softening parameterizations used in numerical geodynamics. This model however does not account for time-dependent behavior documented in rock deformation experiments, such as the loading rate dependence of the peak strength, and sample failure under a fixed applied stress in brittle creep tests. It also relies on macroscopic properties (e.g., dilatancy angle) which are not straightforwardly related to micro-mechanical and micro-structural rock properties. The MC model thus inherently carries an empirical parameterization which can be an obstacle to a deeper understanding of brittle inelastic deformation.<span> </span></p><p>On the other hand, models that account for time-dependent brittle behavior typically invoke the development of tensile microcracks around shear defects, and derive macroscopic constitutive laws from the micro-mechanics of fracture growth and interaction through a damage state variable. To investigate whether this class of models can account for the time-dependence of strain localization, we perform post-bifurcation analysis on the damage rheology constructed by <em>Ashby & Sammis (1990)</em>, coupled with a stress corrosion law for crack growth kinetics. We calculate the co-evolution of stress and 2-D plane strain at a point located within an incipient damage shear band, and at a nearby point in the surrounding rock where damage cannot accumulate. We prescribe a constant shear strain rate within the band, enforce strain compatibility and stress continuity across the shear band boundary, and integrate the incremental constitutive relationships through time.</p><p>Dilatancy related to tensile crack growth in the band enables elastic unloading of the surrounding medium. In our simulations, this manifests as a sudden drop in shear stress coincident with a sharp increase in band damage. We characterize the localization phenomenon through the magnitude of both this stress drop and damage increase, and assess their sensitivity to macroscopic parameters such as shear strain rate, shear band orientation, confining pressure, as well as micro-mechanical parameters such as the orientation of shear defects, the stress exponent of the crack growth law, and the initial damage. This type of work may pave the way toward micromechanics-based parameterizations of brittle deformation in long-term tectonic models.</p>

Displacement of surrounding rock in a deep circular hole considering double moduli and strength-stiffness degradation

The problem of cavity stability widely exists in deep underground engineering and energy exploitation. First, the stress field of the surrounding rock under the uniform stress field is deduced based on a post-peak strength drop model considering the rock’s characteristics of constant modulus and double moduli. Then, the orthogonal non-associative flow rule is used to establish the displacement of the surrounding rock under constant modulus and double moduli, respectively, considering the stiffness degradation and dilatancy effects in the plastic region and assuming that the elastic strain in the plastic region satisfies the elastic constitutive relationship. Finally, the evolution of the displacement in the surrounding rock is analyzed under the effects of the double moduli characteristics, the strength drop, the stiffness degradation, and the dilatancy. The results show that the displacement solutions of the surrounding rock under constant modulus and double moduli have a unified expression. The coefficients of the expression are related to the stress field of the original rock, the elastic constant of the surrounding rock, the strength parameters, and the dilatancy angle. The strength drop, the stiffness degradation, and the dilatancy effects all have effects on the displacement. The effects can be characterized by quantitative relationships.