Mohr-Coulomb Failure Research Articles

Wellbore Stability Analysis in Oil and Gas Drilling by Mechanical, Chemical and Thermal Coupling (Case Study in the South of Iran)

Inadequate wellbore stability has always been the most important issue during drilling and can cause many drilling complications. The most important tools for studying this phenomenon are the use of geomechanical modeling and failure criteria. Drilling fluid temperature and chemical interactions between drilling fluid and wellbore are also significant factors in wellbore stability. Decreasing the fluid temperature changes the concentration of induced stresses around the well, influencing the wellbore's safe mud window. This study considered a vertical well drilled in a field in southwest of Iran to determine the mud window and find out the optimal path under different conditions. The upper and lower bound of the mud window were calculated separately and simultaneously with three criteria, namely Mohr–Coulomb Failure, Hoek–Brown, and modified Lade. In the modified Lade failure criterion that gives more realistic results, the lower bound under the initial conditions is 7.81–10.51 ppg; by applying the thermal effect, it is 7.68–10.48 ppg, and with a fluid chemistry effect, it is 8.47–10.69 ppg. Given these two factors simultaneously, the lower bound of the mud window changed to 8.34–10.66 ppg. The optimal path in all failure criteria is horizontal drilling of well and maximum in horizontal stress direction. Furthermore, the upper bound of the mud window under mechanical conditions was 21.36–31.13 ppg, and with the effect of temperature was reduced to 21.09–30.84 ppg. Moreover, after applying the chemical effect, it increased to 21.29–31.05 ppg and converted to 21.02–30.76 ppg simultaneously.

Ground reaction curve of a circular tunnel considering the effects of the altered zone and the self-weight of the plastic zones

Due to the excavation or reinforcement of tunnels, the properties of the rock mass close to tunnels can be significantly changed. To account this issue, a closed-form solution is presented to determine the induced stresses and deformations with consideration of the effects of the altered zone around a circular tunnel and of the self-weight of different zones. For this purpose, the Mohr–Coulomb criterion and the elastic–brittle–plastic model are assigned to both the altered zone and the initial rock mass. Due to the different properties of these zones, the plastic zone can be initiated from the altered zone, the initial rock mass, or both of them simultaneously. By gradually decreasing the internal support pressure, it can be expected that the stresses satisfy the failure criterion. Investigating possible conditions, it can be seen that six different cases can exist. These cases were analysed, and the code of which was written in the MATLAB software. After verifying the proposed procedure with the existing analytical methods, a parametric study was conducted. The results show that neither of the damaged zone nor the reinforcement zone can be neglected, and the propagation of the plastic radii must be considered.

Tensile strength of unsaturated coarse and fine-grained soils

Soils at the ground surface experience multiple cycles of drying and wetting. On drying, the soils experience shrinkage and cracks may appear. The development of cracks depends on the tensile strength of the soil. Such cracks increase the permeability of the soil and can cause slopes and earth structures to fail due to rainfall. Several tensile strength models have been proposed for unsaturated soils considering the effect of matric suction. However, the tensile strength models proposed are for either cohesionless (coarse-grained) or clayey (fine-grained) soils. The tensile strength models were shown to be different in their definition of suction stress and the presence or absence of a cohesion term. As tensile strength data of fine-grained soils with the same soil structure and soil–water characteristic curve (SWCC) data are lacking in the literature, Brazilian tensile tests and SWCC tests were conducted on compacted fine-grained soils from two residual soil formations. The test data highlighted the problem in the friction angle used in existing tensile strength models. Using a general form of the suction stress and the extended Mohr–Coulomb criterion with the Brazilian test Mohr circle, a new tensile strength model applicable to both coarse-grained and fine-grained soils was proposed. The proposed model was shown to perform better than existing models using independent data.

Improvement of DDA with a New Unified Tensile Fracture Model for Rock Fragmentation and its Application on Dynamic Seismic Landslides

Discontinuous deformation analysis (DDA) method is a discrete element method, presenting a great advantage in modelling deformation and rigid body movements, and it is also an alternative approach for problems involving the fracturing process from continuity to discontinuity if the failure mechanism in DDA is well constituted. This paper presents a new united tensile fracture model (UTFM) for the two-dimensional DDA method to simulate the fracture behaviors of various brittle materials (e.g., rock, soil, and concrete). The new fracture model unifies four classical failure modes, including the maximum normal stress criterion, Tresca criterion, Mohr–Coulomb criterion, and the von Mises criterion, for tensile fracture. By incorporating UTFM into the original DDA frame, the improved DDA (I-DDA) can predict the crack initiation and propagation paths in Brazil disc and simulate rock fracture of various brittle materials. Numerical examples of the direct tensile test and the Brazil disc split tests are investigated to verify the accuracy and validity of the I-DDA method. The simulated results agree well with those obtained from physical tests and other numerical analyses, suggesting that the I-DDA has obvious advantage in simulating the fracture behaviors of the Brazil disc split test. Further, the I-DDA is applied to analyze the failure process of a practical earthquake-induced landslide with consideration of the tensile strength of the rock mass. The results indicate that the I-DDA is more feasible to analyze the slope failure, which can consider both the tensile and shear characteristics simultaneously compared with the original DDA.

Failure criteria calibration based on the triaxial compression behavior of roller compacted concrete (RCC)

Roller compacted concrete (RCC) has been widely used in large scale constructions such as hydraulic structures and heavy-duty pavements. Understanding the failure criterion based on the compression behavior of RCC under a relatively wide range of confining pressure is essential for the better analysis and design of RCC structures subjected to potential extreme dynamic loadings. However, few experimental results of RCC under confinement are available, and, to date, no study pays close attention on the triaxial behavior of RCC under relatively high confining pressure. In this study, triaxial behavior was investigated with the aim to better understand and model the constitutive behavior of RCC material. Purposely, laboratory tests were employed on 100 × 200 mm (diameter × length) cylindrical specimens, while the mix proportion and molding method were generally consistent with field construction. Triaxial tests were conducted under seven different confining pressure levels (0, 5, 10, 15, 20, 25 and 30 MPa). Consequently, the triaxial compression behavior of RCC was obtained and the confinement effect was illustrated. Compared with conventional concrete, the effect of confinement on the failure strength and failure strain of RCC was less pronounced. The failure criteria of RCC under a relatively wide range of confining pressure were discussed. Parameters of Mohr–Coulomb and William-Warnke failure criteria were calibrated and novel empirical formulas were proposed to illustrate the compressive meridian of RCC material.

Mechanical Analysis of the Failure Characteristics of Stope Floor Induced by Mining and Confined Aquifer

Mining above confined aquifer has become an important task for water inrush prevention in China. To study the failure characteristics of stope floor along the strike, a mechanical model under combined action of mining and confined aquifer was constructed, and the distribution of vertical stress, horizontal stress, and shear stress was obtained. Based on the Mohr–Coulomb criterion, the failure range of the floor is determined and verified by the in situ test. The results indicate the following. (1) Both vertical stress and horizontal stress in the stope floor take the junction of stress increasing area and stress decreasing area as the dividing line, forming two groups of “convex arches” at the solid coal side and the goaf side, respectively. (2) The vertical stress gradient in the solid coal side is significantly higher than that in the goaf side, while the horizontal stress gradient in the solid coal side is similar to that in the goaf side. The shear stress distribution is divided into three regions by the boundary between positive and negative shear stress, which makes the stope floor in this area to show compression shear or tension shear failure. (3) According to the in situ test, the maximum floor failure depth of 41503 working face is 11.38 m, which is quite close to the theoretical calculation result of 9.68 m. (4) Applying the mechanical model to five other coal mines with different mining conditions and stress states, the maximum absolute error between the measured and theoretical values of floor failure depth is 1.1 m, the average absolute error is 0.8 m, the maximum relative error is 8.2%, and the average relative error is 6.5%. The study provides a certain mechanical basis and reference for the floor failure mechanism induced by mining and confined aquifer.

Overall Stability Analysis of Xiluodu High Arch Dam Based on Fine Three‐Dimension Numerical Modeling

The RFPA3D is used to establish a fine finite element model of 6.63 million elements, which realizes the fine simulation of the stability of the Xiluodu arch dam under layered, overall, multiworking conditions and multistress fields, and the cracking and failure process under overload. The structural design scheme of the arch dam and the corresponding foundation treatment design are evaluated. The model fully reflects the measures of dam shape structure design, angle fitting structure design, and foundation concrete replacement in the Xiluodu arch dam technical design stage. The RFPA3D adopts the mesoelement elastic damage model, which considers the Mohr–Coulomb criterion of shear fracture and the maximum tensile failure criterion, and assumes that the mechanical properties of the element satisfy Weibull distribution to consider its heterogeneity. The simulation results show that, under normal load conditions, the dam foundation surface after comprehensive reinforcement has better overall stability, the stress and deformation of the dam body have good symmetry, and the overload factor of crack initiation under overload calculation K1 = 2P0 (P0 is normal water load), the nonlinear deformation overload factor K2 = 3.5–4P0, and the limit load factor K3 = 7.5–8.0P0, dam safety can be satisfied. The RFPA3D is used to establish a superlarge fine model to study the overall stability of the high arch dam, which provides an effective method for analysis and research of other large hydraulic projects in the world.

Experimental and Numerical Study on the Shear Strength and Strain Energy of Rock Under Constant Shear Stress and Unloading Normal Stress

Excavation and earth surface processes (e.g., river incision) always induce the unloading of stress, which can cause the failure of rocks. To study the shear mechanical behavior of a rock sample under unloading normal stress conditions, a new stress path for direct shear tests was proposed to model the unloading of stress caused by excavation and other processes. The effects of the initial stresses (i.e., the normal stress and shear stress before unloading) on the shear behavior and energy conversion were investigated using laboratory tests and numerical simulations. The shear strength of a rock under constant stress or under unloading normal stress conforms to the Mohr Coulomb criterion. As the initial normal stress increases, the cohesion decreases linearly and the tangent of the internal friction angle increases linearly. Compared with the results of the tests under constant normal stress, the cohesions of the rock samples under unloading normal stress are smaller and their internal friction angles are larger. A strength envelope surface can be used to describe the relationship between the initial stresses and the failure normal stress. Shear dilatancy can decrease the total energy of the direct shear test under constant normal stress or unloading normal stress, particularly when the stress levels (the initial stresses in the test under unloading normal stress or the normal stress in the test under constant normal stress) are high. The ratio of the dissipated energy to the total energy at the moment failure occurs decreases exponentially with increasing initial stresses. The direct shear test under constant normal stress can be considered to be a special case of a direct shear test under unloading normal stress with an unloading amount of zero.

Evolution of Strength Parameters for Sandstone Specimens during Triaxial Compression Tests

Despite the lack of test data of the coefficient of pressure sensitivity α and the shearing cohesion k, the Drucker–Prager criterion is commonly applied for numerical analyses of geotechnical engineering. To bridge the gap between the wide application and insufficient knowledge of strength parameters of the Drucker–Prager criterion, this study presents experimentally calibrated strength parameters of this criterion for the first time. This paper proposes a new method to measure α and k in the Drucker–Prager criterion. The square root of the second invariant of the deviatoric stress tensor is linearly fitted with the first invariant of the stress tensor I1 in the stress space. The parameters φ and c in the Mohr–Coulomb criterion and α and k in the Drucker–Prager criterion are calibrated to the same set of triaxial compression tests of sandstones. With these testing results, five pairs of conversion formulae (which are most commonly used in the literature) are examined and the most appropriate pair of conversion formulae is identified. With parameters indicating cohesive strength (c and k) and parameters indicating frictional strength (φ and α), the evolutions of different strength components are compared with those in the cohesion‐weakening friction‐strengthening model. With an increase in plastic deformation, the cohesive strength parameters c and k firstly increase to a peak value and then decrease. The frictional strength parameters φ and α gradually increase at a decreasing rate after the initial yield point.

Estimation of Distribution Factor for Peak Penetration Resistance Prediction of Spudcan Foundations in Loose to Medium-Dense Sand Overlying Clay

A series of 3D finite element (FE) analyses were performed to estimate the peak penetration resistance of spudcan foundations in sand over clay soil profiles. Elasto-perfectly plastic models following Mohr–Coulomb and Tresca failure criteria were used for sand and clay layers, respectively. The coupled Eulerian–Lagrangian (CEL) approach was used to simulate the large deformation in soil that occurs during the spudcan penetration. The performance of the numerical model was validated against centrifuge test results. A parametric study with a broad range of strength parameters for sand and clay was performed. The numerical results were used to assess the influence of sand thickness (Hs), the diameter of spudcan (D), friction angle of sand, and undrained shear strength of clay (su). A wide range of su was utilized to predict the resistance both of the soft and stiff clays. The calculated peak resistances are compared with a published analytical model. It is demonstrated that the model highly overestimates the peak resistance for stiff clays, most likely because it was developed specifically for soft clays and, therefore, does not account for the influence of su. One of the parameters of the model is revised to account both for su. Comparisons highlight that the modified model is able to capture the simulated peak penetration resistance for both soft and stiff clays.

Research on failure characteristics of goaf floor in the inclined coal seam based on the fracture mechanics

Floor failure is the leading cause of mine water inrush after coal mining above the confined aquifer. Therefore, the prediction of floor failure depth is an important content of mine water prevention. The mining-induced failure depth and goaf floor characteristics are researched to grasp the goaf failure condition after the inclined coal seam mining with the theoretical analysis method. The inclined coal goaf floor's stress solving mechanics mode is set up based on the fracture mechanics theories. According to the Mohr–Coulomb criterion, the floor failure depth solving the equation is derived. With the theoretical analysis of the floor failure characteristics during the inclined coal seam mining, (1) the maximum failure depth of floor is nonlinear to the coal seam dip and the lateral pressure coefficient; the working face length, mining depth and floor cohesion positively correlate with the failure range; the floor cohesion is reversely proportional to the failure range. (2) There appears asymmetry in the layout of stress and plastic zones in the inclined coal goaf floor. Failure range and depth in-floor plastic zone increasingly enlarge when the coal face advances.

Three-Dimensional Combined Finite-Discrete Element Modeling of Shear Fracture Process in Direct Shearing of Rough Concrete–Rock Joints

A three-dimensional combined finite-discrete element element method (FDEM), parallelized by a general-purpose graphic-processing-unit (GPGPU), was applied to identify the fracture process of rough concrete–rock joints under direct shearing. The development process of shear resistance under the complex interaction between the rough concrete–rock joint surfaces, i.e., asperity dilatation, sliding, and degradation, was numerically simulated in terms of various asperity roughness under constant normal confinement. It was found that joint roughness significantly affects the development of overall joint shear resistance. The main mechanism for the joint shear resistance was identified as asperity sliding in the case of smoother joint roughness and asperity degradation in the case of rougher joint asperity. Moreover, it was established that the bulk internal friction angle increased with asperity angle increments in the Mohr–Coulomb criterion, and these results follow Patton’s theoretical model. Finally, the friction coefficient in FDEM appears to be an important parameter for simulating the direct shear test because the friction coefficient affects the bulk shear strength as well as the bulk internal friction angle. In addition, the friction coefficient of the rock–concrete joints contributes to the variation of the internal friction angle at the smooth joint than the rough joint.

Parametric sensitivity study of wellbore stability in transversely isotropic medium based on polyaxial strength criteria

Borehole instability in laminar formations often occurs during drilling operations without a clear explanation. Two dominant factors, rock lithology and stress concentration effects on borehole instability, are investigated in this study. The microstructure and mineral composition are evaluated to determine the possible reactions of the drilling fluid and shale interaction. A borehole stability model in a transversely isotropic medium is established using three different types of polyaxial strength criteria to study the effect of the degree of elastic anisotropy and intermediate principal stress on the lower boundary of the safe drilling window. Research has indicated that Poisson's ratio anisotropy does not markedly change the collapse pressure at low anisotropy. However, the effect of the elastic modulus anisotropy is notable, and the collapse pressure predicted by polyaxial criteria is more sensitive to elastic anisotropy. The collapse pressure calculated by the Mohr–Coulomb criterion is the upper limit; the results predicted by the Modified Lade and Modified Wiebols–Cook criterion are similar, corresponding to the wellbore orientations. This study explores the failure mechanisms of wells drilled in layered shales, which can help determine critical mud pressure and well orientation design. The outcomes of this investigation indicate the implications of fully accounting for the degree of elastic anisotropy and the influence of intermediate stress in conducting wellbore stability analysis.

Effect of 3D roughness characteristics on bonding behaviors between concrete substrate and asphalt overlay

Asphalt overlay on cement concrete pavement is a common strategy in pavement maintenance. On the other hand, an asphalt layer is generally paved on a concrete bridge deck to provide competitive performance. In this study, the bonding performance between concrete substrate and asphalt overlay was explored from a perspective of interface roughness. Concrete slabs with a strength grade of C50 were fabricated first. Asphalt concretes were paved with an air void content of 4%. The roughness parameters, including surface roughness, root mean square of roughness, and fractal dimension, were obtained from image technique and surface reconstruction. Relationships between surface roughness parameters and direct shear strength were quantitatively studied. The correlation between roughness parameters and optimal tack coat application rate was also built. Results show that the surface roughness linearly increased with the fractal dimension. Larger surface parameters, which was demonstrated as the surface roughness, root mean square of roughness and fractal dimension, contributed to a superior shear performance. Optimal tack coat application rates existed for all specimens. With the increase of surface roughness parameters, the optimal tack coat application rates increased as well. On the other hand, the cohesion strength and internal friction derived from Mohr–Coulomb theory are affected by the roughness parameters of substrates.

Hydro-mechanical properties of a low-clay shale with supercritical CO2 imbibition

The mechanical properties and permeability of shales after supercritical carbon dioxide (SC-CO2) imbibition are vital to shale gas production and CO2 sequestration in shale reservoirs. In this study, triaxial compressive strength tests, steady state permeability tests, and CT scanning tests are performed on shale samples with 30 days of SC-CO2 imbibition. The results show that minerals dissolution and precipitation occur during SC-CO2 imbibition. The porosity calculated by the digital core increases by 19.190%. The axial stresses of samples with or without SC-CO2 imbibition increase with increasing confining pressure. When the confining pressure changes between 5 and 20 MPa, the reductions range from 6 to 13% for strength and from 11.26 to 16.47% for Young’s modulus, respectively. The strength of the samples with or without imbibition agrees well with the Mohr–Coulomb criterion. The values of cohesion and internal friction angles are very close which indicates that shale samples with SC-CO2 imbibition can still refer to the failure criterion for samples without CO2 imbibition. The permeability of the sample after SC-CO2 imbibition increases exponentially with the increase in injection pressure and decreases exponentially with an increase of effective pressure. The permeability of the sample before and after imbibition is more sensitive to the change of pore pressure than confining pressure. SC-CO2 imbibition enhances the increase of permeability. The ratio of the shale permeability after imbibition to that before imbibition varies from the minimum of 42 times to the maximum of 827 times. The reduction of strength and increasing of permeability are beneficial for shale gas recovery.

Experimental Investigation on Deformation and Strength Behavior of Marble with the Complex Loading-Unloading Stress Path

The excavation of deep tunnel in rock mass undergoes complex loading and unloading stress paths, resulting in rib spalling, flaking, and even severe rockburst disasters. Based on the variation law of the stress path of the surrounding rock, laboratory tests of rock mechanics are designed, and the deformation and strength behavior of marble with different initial confining pressure and unloading rates are systematically studied. By introducing strain increment, the characteristic stress, and the dilatancy index, the rock’s dilatancy and brittleness under different unloading conditions are quantitatively analyzed. During unloading, the energy transformation mechanism of rock is described, and the law of deformation and failure is discussed based on characteristic energy. The rock failure strength fitting formula is given by applying the Mogi–Coulomb criterion and elastic strain energy criterion. The advantages of the elastic strain energy criterion are theoretically explained. This study shows that comprehensive consideration of the complex stress paths, confining pressure levels, and the loading-unloading rates of surrounding rock is an effective way to accurately study unloading rock characteristics. The results can provide theoretical basis for stability analysis of high-stress underground engineering.

Formulation of Ice Resistance in Level Ice Using Double-Plates Superposition

The estimation of ship resistance in ice is a fundamental area of research and poses a substantial challenge for the design and safe use of ships in ice-covered waters. In order to estimate the ice resistance with greater reliability, we develop in this paper an improved Lindqvist formulation for the estimation of bending resistance in level ice based on the superposition of double-plates. In the developed method, an approximate model of an ice sheet is firstly presented by idealizing ice sheeta as the combination of a semi-infinite elastic plate and an infinite one resting on an elastic foundation. The Mohr–Coulomb criterion is then introduced to determine the ice sheet’s failure. Finally, an improved Lindqvist formulation for estimation of ice resistance is proposed. The accuracy of the developed formulation is validated using full-scale test data of the ship KV Svalbard in Norway, testing the model as well as the numerical method. The effect of ice thickness, stem angle and breadth of bow on ship resistance is further investigated by means of the developed formulation.

Influence of impoundment gravity and pore pressure on reactivation of faults

For more than seven decades, the impounding of artificial water reservoirs has been known to trigger earthquakes. Accordingly, reservoir-induced seismicity (RIS) has been studied in terms of its identification and mechanisms. In this paper, we report three laboratory experiments to investigate the effects of water impoundment and pore-pressure diffusion on the reactivation of faults in high tectonic stress areas. Results showed that when the horizontal stress is larger than the vertical stress, according to the Mohr–Coulomb criterion, pore-pressure diffusion might be the main factor inducing seismicity instead of the undrained stress compression. The diffusion and oscillation of pore pressure are the controlling factors in triggering the activation of faults and releasing the elastic energy. The Mohr–Coulomb criterion is consistent in describing the critical damage pore pressure of the pre-existing faults; however, it fails to judge whether a fault is in a stable or unstable state after the pore pressure increases. The hydraulic energy from the injection pressure and volume of water is strongly related to the moment magnitude of the induced seismicity owing to pore-pressure diffusion. Moreover, the fault can be transformed from an unstable state into a stable state after continuous seismic events. The enhancement of fault permeability due to the seismic events can promote the fluid flow through fractures and influence the seepage field around the reservoir.

Comparison of Shape Characteristics of Plastic Zone Around Circular Tunnel Under Different Strength Criteria

ABSTRACTThe butterfly plastic zone theory based on Mohr Coulomb criterion has been widely used in coal mine production. In order to verify the universality of the theory, it is necessary to compare the distribution of plastic zone under different strength criteria. Based on the elastic-plastic mechanics, the principal stress distribution function around the circular tunnel is deduced in the paper, and the boundary and radius of the plastic zone under different strength criteria are calculated. The results show that the change laws of the plastic zone around the circular tunnel under different strength criteria has the following commonness: firstly, with the increase of the lateral pressure coefficient, the shape of the plastic zone presents the change laws of “circle ellipse butterfly”; Secondly, with the increase of the lateral pressure coefficient, the radius of the plastic zone is exponential distribution, while the characteristic value is different when the radius of the plastic zone is infinite. At same time, it shows that the butterfly plastic zone has a low sensitivity dependence on the strength criterion, no matter which strength criterion is adopted, and the butterfly plastic zone will inevitably appear in the surrounding rock mass of circular tunnel in the high deviator stress environment; The plastic zone with butterfly shape is highly sensitive to the stress change, and the small stress change may promote the expansion of the plastic zone. This result is significant for us to understand and prevent rock engineering disasters and accidents.

The Influence of Radial Stress on Mechanical Properties of Anchorage Structure

The research on the influence of radial stress on the mechanical properties of an anchorage structure has important theoretical and practical significance for optimizing the design of anchorage structures and saving support cost. Firstly, based on the phenomenon of concrete splitting found in the laboratory model test, the influence of radial stress on the mechanical properties of an anchorage structure is analyzed. Secondly, using the criterion of maximum tensile stress and the Mohr–Coulomb criterion, the influence of radial stress on the mechanical properties of rock around the borehole is analyzed. Finally, the influence of radial stress on the shear stress at interface and the ultimate bearing capacity of the anchorage structure is studied by numerical simulation. The results show that the existence of radial stress in the anchorage section greatly improves the bearing capacity of the anchorage structure. With the increase of confining pressure, the maximum value of interfacial shear stress increases obviously. The larger the confining pressure is, the faster the convergence speed of the finite element method (FEM) program is, which shows that the mechanical properties of the anchorage structure are improved obviously. With the increasing confining pressure, the adaptability of the anchorage structure to deformation is stronger and the anchorage structure is less likely to fail. The ultimate bearing capacity of the anchorage structure increases linearly with the increase of confining pressure, and the effect of confining pressure on the ultimate bearing capacity is very significant.