Mohr-Coulomb Failure Research Articles

Shear strength equation of soils in a wide suction range under various initial void ratios

AbstractShear strength equation is a basic theory for solving many geotechnical engineering problems. Although the shear strength equation has received widespread attention, shear strength of clay under wide suction range and different initial void ratio conditions cannot be well predicted. This study aims to establish a new strength equation applicable to soils within a wide suction range. Considering the capillary and adsorptive parts of soil–water interactions, a cohesion expression related to the degree of adsorbed water saturation Sra and the effective stress related to the degree of capillary water saturation Src are proposed. After that, based on the Mohr–Coulomb theory, a shear strength equation of unsaturated soils in a wide range of suction under various is proposed. Five parameters are included in the equation. It is easy to calibrate them through shear tests on saturated and the fully dried soils. It is verified that not only the sandy clay till and clayed silt but also the expansive soil's shear strength in wide ranges of suction under various can be well predicted.

Three-pressure prediction method of jointing well-seismic data in JT1 well area of Sichuan Basin in China

With the high yield of many wells represented by Well JT1 in the Maokou Formation, has catalyzed a surge in exploration activities along the platform margin facies of the Maokou Formation in central Sichuan and further showed the significant exploration potential of the Maokou Formation in the northern slope. However, the fracture cave body of the Maokou Formation exhibits a high degree of development, strong longitudinal and horizontal heterogeneity, large formation pressure differences, and drilling events such as gas kicks and lost circulation occur frequently, which seriously affects the efficient implementation of drilling. Understanding the spatial distribution of the three-pressure in the formation can help better deal with and solve the above problems. Therefore, in order to help the safe, high-quality and rapid drilling of the Maokou Formation in the study area, and enhance the efficiency of oil and gas development, this paper explores the research on the prediction method of the three-pressure of jointing well-seismic data based on the geomechanical experimental data and the actual drilling data. In the process of prediction of pore pressure, this study found that the pore pressure and formation velocity in the study area have an exponential relationship. In order to enhance the applicability of the Filippone’s method in the study area and improve the prediction accuracy of pore pressure, the linear relationship between pore pressure and formation velocity in the Filippone’s method is modified to an exponential relationship, and a pore pressure prediction model suitable for the work area was established. Based on the Mohr–Coulomb criterion and Huang's model, the prediction models of collapse pressure and fracture pressure applicable to the study area were established, respectively. Then, the elastic parameters were obtained through pre-stack inversion, and the three-pressure bodies were calculated based on the elastic parameter bodies. The results indicate that: (1) The three-pressure prediction method of the jointing well-seismic data in this paper can predict the formation's longitudinal and transverse pressure anomaly zones in advance. (2) The Maokou Formation in the study area is characterized by abnormally high pressure, to balance the pressure of the high-ground formation, high-density drilling fluid is necessary. (3) The prediction results of three-pressure in this paper are highly consistent with the actual drilling engineering events, which verifies the reliability of the three-pressure prediction results presented in this study. The results of the study can provide a basis for decision-making in drilling geological design, such as the determination of drilling fluid density, the evaluation of borehole stability and other engineering problems that require support from three-pressure data.

Analytical solutions for cavity contraction in strain-softening materials with linear or exponential strength decay

This paper presents an analytical investigation into the contraction of spherical and cylindrical cavities excavated in strain-softening rock masses obeying the Mohr–Coulomb or Tresca yield criterion, with linear or exponential uniaxial compressive strength decay. The derivation of the ground response curves is based on the simplifying assumption that the strains inside the plastic zone are completely plastic. This significantly simplifies the mathematical formulation, enabling the derivation of closed-form solutions. An alternative simplifying approach which partially neglects the elastic strains inside the plastic zone and which is commonly adopted in the literature, is also examined. The accuracy of the simplified solutions is evaluated by comparing their predictions with rigorous solutions obtained by numerical finite-difference analyses. The investigation demonstrates that the proposed closed-form solutions represent a significant improvement on those based on the commonly-made simplifying assumption involving partial neglect of elastic strains.

Stress Field Dynamics and Fault Slip Potential in the Paradox Basin

AbstractThe Paradox Basin, straddling Utah, Colorado, Arizona, and New Mexico is characterized by an intricate amalgamation of evaporites and clastic layers and is dominated by prominent salt walls and related subsurface structures. Our research offers a new examination of the stress distribution across the basin, deriving from continuous and discrete stress measurements conducted in boreholes in the region and focal mechanism analysis, emphasizing variations over salt structures. Integrating Coulomb failure criteria with probabilistic methods, we assess potential fault movements resulting from fluid pressure alterations. Our approach provides a comprehensive understanding of the Paradox Basin's state of stress, showing a continuous change of the maximum horizontal stress orientation from N‐S at the Wasatch Fault Zone to WNW‐ESE in the northern part of the Paradox Basin and to WSW‐ENE in the southern part of the basin. Further East, into the Colorado Plateau and the Uncompahgre Uplift, the SHmax orientation becomes E‐W. Decoding stress orientation dynamics has enabled critical insights into fault slip potential, especially in the basin's northern region. The salt wall faults are less likely to slip, and the Paradox Formation's evaporite and clastic rock sequence can serve as a potential low seismic risk target for carbon storage and hydrocarbon extraction.

Stability of highly inclined non-circular wellbores in isotropic formations

The shear and tensile stabilities of highly inclined non-circular wellbores are investigated in this study. Using the equivalent-ellipse hypothesis, the non-circular geometry was approximated as an ellipse, and the corresponding stress concentration equations are presented. With the new set of stress concentration equations, a comprehensive study of the tensile and shear stabilities of an elliptical borehole was conducted, including the impact of well inclination and azimuthal angles, horizontal stress difference, degree of ellipticity, and orientation of the maximum horizontal stress to the major axis of the ellipse. Using five commonly used shear failure criteria, we observed that both Mohr–Coulomb and Drucker Prager (inscribed) failure criteria predicted higher collapse pressures, relative to the others including Drucker Prager (inscribed), Mogi-Coulomb, and Modified Lade. While Drucker Prager's (circumscribed) failure criterion underestimates the collapse pressure. Both the linear elastic and poroelastic models were used in investigating the fracture initiation orientation and pressure of highly inclined elliptical boreholes. The prediction from the poroelastic model is always less than the linear elastic model. In some instances, they predict different fracture initiation orientations. From this study, we observed that generally, a near-circular wellbore is more stable than elliptical borehole in both shear and tension. Nevertheless, there are some well inclination and azimuthal angles than can make an elliptical borehole have more shear and tensile stabilities than a near-circular wellbore.

Finite–Discrete Element Method Simulation Study on Development of Water-Conducting Fractures in Fault-Bearing Roof under Repeated Mining of Extra-Thick Coal Seams

The formation of water-conducting fractures in overlying strata caused by underground coal mining not only leads to roof water inrush disasters, but also water-conducting fractures penetrate the aquifer, resulting in the occurrence of a mine-water-inrush disaster and the loss of water resources. It destroys the sustainability of surface water and underground aquifers. This phenomenon is particularly significant in extra-thick coal seams and fault-bearing areas. Numerical simulation is an effective method to predict the failure range of mining overburden rock with low cost and high efficiency. The key to its accuracy lies in a reasonable constitutive model and simulation program. In this study, considering that the three parts of penetrating cracks, non-penetrating cracks, and intact rock blocks are often formed after rock failure, the contact state criterion and shear friction relationship of discrete rock blocks and the mixed fracture displacement–damage–load relationship are established, respectively. Combined with the Mohr–Coulomb criterion, the constitutive model of mining rock mass deformation–discrete block motion and interaction is formed. On this basis, according to the engineering geological conditions of Yushupo Coal Mine, a numerical model for the development of water-conducting cracks in the roof with faults under repeated mining of extra-thick coal seams is established. The results show the following: The constitutive relation of the continuous deformation–discrete block interaction of overlying strata and the corresponding finite element–discrete element FDEM numerical program and VUSDFLD multi-coal seam continuous mining subroutine can numerically realize the formation process of faults and water flowing fractures in overlying strata under continuous mining of extra-thick multi-coal seams. The toughness of sand mudstone is low, and the fracture will be further developed under the repeated disturbance of multi-thick coal seam mining. Finally, it is stabilized at 216–226 m, and the ratio of fracture height to mining thickness is 14.1. When the working face advances to the fault, the stress concentration occurs in the fault and its overlying rock, which leads to the local fracture of the roof rock mass and the formation of cracks. The fault group makes this phenomenon more obvious. The results have been preliminarily applied and tested in Ningwu mining area, which provides theoretical support for further development of roof water disaster control under the condition of an extra-thick coal seam and avoids the loss of water resources in surface water and underground aquifers.

Temperature Dependency of Modified Mohr–Coulomb Criterion Parameters for Advanced High Strength Dual-Phase Steel DP780

The Modified Mohr–Coulomb criterion has been demonstrated to exhibit high accuracy in the prediction of fracture in high-strength steels. Taking DP780 as the research object, the undetermined parameters of the Modified Mohr–Coulomb criterion at different temperatures were calibrated by tensile and shear tests combined with simulation. The relationships between the parameters and temperature were investigated. Finally, the relationship between criterion parameters and temperature was verified using the stretch-bending tests of U-shape parts. The fracture of automotive parts can be accurately predicted by simulation during warm stamping, thereby guiding actual production.

Constitutive Characteristics of Rock Damage under Freeze–Thaw Cycles

Freeze–thaw effect is one of the most important environmental conditions that rocks may be subjected to. Through laboratory model tests, the damage characteristics of rocks under the FTC were studied. Based on assuming that the strength of rocks subject to the FTC follows the Weibull distribution, the cumulative damage variable of the number of FTCs was introduced. A cumulative damage constitutive model of shear strength attenuation of rock that meets the Mohr–Coulomb criterion is established. The rationality and applicability of the proposed damage constitutive model are verified by comparing the results of rock shear strength parameters under cyclic freeze–thaw loads.

Phase-field model for 2D cohesive-frictional shear fracture: An energetic formulation

This paper presents a phase-field model for cohesive-frictional shear fracture. The model is derived based on two energetic principles: the energy conservation law and a variational inequality of virtual work that serves as a stability condition. We show that all the governing equations for frictional fracture can be obtained from the above two principles, including the equilibrium condition, the phase-field evolution law and, most importantly, the yield function and flow rule for the plasticity-like frictional slip. The information of crack direction is naturally included in the flow rule. Theoretical and numerical results show that the proposed model is faithfully consistent with the Mohr–Coulomb theory of frictional failure in terms of the crack nucleation stress and direction. In addition, the presented phase-field model has an explicit frictional cohesive law.

Fracture prediction on hydrogen-charge notched samples using a stress-state-dependent phenomenological model

There is a consensus for transitioning to clean energy sources to meet the world’s energy demands. Hydrogen is a candidate to supply green energy. However, hydrogen embrittlement (HE) in materials is an issue that needs to be assessed. Based on the damage concept, a straightforward and robust computational framework is presented to predict the harmful effects on material resistance caused by the HE phenomenon. The adopted model framework builds upon dealing with the coupled mechanical diffusion problem in a simplified approach by considering the local equilibrium between hydrogen concentration at interstitial sites and Cauchy stresses. A modified version of the Mohr–Coulomb criterion dependent on the stress triaxiality and Lode angle introduces a damage indicator parameter. The proposed model is applied to study the brittle intergranular fracture of a high-strength AISI 4135 steel. A detailed description of the stress state and hydrogen-driven failure parameters are presented for two specimens with different notch radii. The proposed model is implemented in a VUMAT subroutine and made available for download to the technical community for research and educational use. After calibrating the model parameters, the numerical results yield good agreements of the predicted fracture strength of notched hydrogen-charged samples compared to the experimental ones. Maximum differences of around 10% among experimental and numerical tests are observed.

Mechanisms for Microseismicity Occurrence Due to CO2 Injection at Decatur, Illinois: A Coupled Multiphase Flow and Geomechanics Perspective

ABSTRACT We numerically investigate the mechanisms that resulted in induced seismicity occurrence associated with CO2 injection at the Illinois Basin–Decatur Project (IBDP). We build a geologically consistent model that honors key stratigraphic horizons and 3D fault surfaces interpreted using surface seismic data and microseismicity locations. We populate our model with reservoir and geomechanical properties estimated using well-log and core data. We then performed coupled multiphase flow and geomechanics modeling to investigate the impact of CO2 injection on fault stability using the Coulomb failure criteria. We calibrate our flow model using measured reservoir pressure during the CO2 injection phase. Our model results show that pore-pressure diffusion along faults connecting the injection interval to the basement is essential to explain the destabilization of the regions where microseismicity occurred, and that poroelastic stresses alone would result in stabilization of those regions. Slip tendency analysis indicates that, due to their orientations with respect to the maximum horizontal stress direction, the faults where the microseismicity occurred were very close to failure prior to injection. These model results highlight the importance of accurate subsurface fault characterization for CO2 sequestration operations.

Simulation of controlled modulus column installation using a large deformation finite element analysis

Controlled modulus columns (CMC) are widely used in ground improvement techniques where grout columns are constructed by penetrating an auger into the ground using the displacement approach. Numerical simulation of this problem is challenging owing to the large soil deformations associated with installation. Small strain-based finite element analysis procedures available in commercial finite element modeling software are unsuitable for simulating this problem because they cannot simulate large soil deformations around the auger during column installation. Hence, this study presents a numerical approach based on the finite element method to simulate the installation of CMCs. The numerical modeling technique adopted in this study considers large soil deformations around columns during penetration, and the proposed approach is based on remeshing and interpolation techniques. This method was developed using the Python development environment (PDE) within the ABAQUS/standard finite element program. It can penetrate columns below the ground surface without causing large mesh distortions. In this study, silty sand-type soil was considered; hence, the constitutive behavior was simulated using the Mohr–Coulomb criteria. The load-carrying capacity of a controlled modulus column was predicted and compared with an empirical equation based on the cone penetration resistance. The influence zone and failure mechanism of the soil during installation were determined by considering the stress distribution and soil flow pattern around the column.

Experimental study on the triaxial mechanical properties of hybrid steel fiber–reinforced self-compacting concrete

In this study, the triaxial mechanical properties of hybrid steel fiber–reinforced self-compacting concrete (HSFRSCC) were investigated. Based on previous research, a mixture of HSFRSCC that satisfies the requirements of compression and workability performance was determined. Conventional triaxial compression tests were performed at confining pressures of 0, 4, 8, 12, and 16 MPa. The results showed that all the specimens had excellent deformation ability, and both the steel fibers and confining pressure improved the ductility of HSFRSCC. With an increase in the confining pressure, the triaxial peak stress and strain of concrete were increased. The differences in the damage characteristics of HSFRSCC and plain concrete were compared based on scanning electron microscopy test results. Finally, the applicability of the Mohr–Coulomb criterion with that of the Willam–Warnke (W–W) criteria to HSFRSCC was compared. the results showed that the nonlinear W–W criterion had a better fitting effect. Hence, the relationship between triaxial peak stress, peak strain, and confining pressure was established, and the triaxial compression meridian formula for HSFRSCC was obtained.

Modified rock stress factor for the Mathews stability graph method and its application

It is difficult to accurately predict and assess the instability of the stope. This article uses the improved Mathews stability graph method to scientifically analyse and evaluate the quality and stability of the surrounding rock. It utilizes the failure factor (FF) to express the degree of rock failure under different stress states based on the Mohr–Coulomb criterion and to determine the new rock stress factor. This new method is successfully applied in a case study at a lead–zinc mine in Hongling and makes a comparative analysis with the actual situation of the site.

Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules

The stability analysis of homogeneous rock slope following the Hoek–Brown failure criterion under the hypothesis of different flow rules is performed based on limit equilibrium and finite element methods. The applied failure criterion is the generalized Hoek–Brown that can be introduced as a shear/normal function in analysis applying different flow rules. The results are compared with those obtained by the application of equivalent shear strength parameters of the Mohr–Coulomb criterion, considering that this is still the most widely used criterion in rock slope stability analysis and is still the base for the shear strength reduction method applied in finite element modelling. Different proposals for estimating the equivalent strength parameters based on confining stress level are evaluated. The limitation of stress-dependent linear Mohr–Coulomb parameters is emphasized by analysing the vertical cut problem, for which, depending on the chosen stress level, different critical heights are obtained for the same material. Sensitivity analysis of geotechnical parameters used as input for failure criterion is performed to determine their influence on slope stability. Probabilistic analysis is conducted to determine the probability of failure when different flow rules are applied. If slope stability analysis is performed with an assumption of associative flow rule, the probability of failure is within the acceptable limits for the considered case study, while employing non-associative flow rule, the probability of failure is rather high. The chart is presented that could be readily used to estimate the combination of σci, GSI, and mi values that produce failure for the analysed case study.

Modified Mohr–Coulomb criterion for nonlinear strength characteristics of rocks

AbstractThe classical Mohr–Coulomb criterion has an extremely wide range of applications in the field of engineering geology, while it cannot accurately characterize rock failure under high confining stresses. Therefore, a nonlinear modification is implemented based on the Mohr–Coulomb criterion for achieving wider usage in all stress environments. The cohesion and internal friction angle are firstly calculated by regression based on the triaxial experiments of diorite and other typical rocks in different confining stress ranges, and the variation modes of cohesion and internal friction angle are then formalized and integrated into the classical Mohr–Coulomb criterion. Using the experimental results of 435 triaxial compression tests in existing publications, the predictions of the modified criterion are compared with those of the previous nonlinear criteria, which show that the predicted values of the modified criterion are in good agreement with the measured strength. Compared with the previous nonlinear criteria, the modified criterion has a wider application range and always maintains a higher accuracy.

A New Shear Strength Model with Structural Damage for Red Clay in the Qinghai-Tibetan Plateau

Under the background of climate warming in the Qinghai-Tibetan Plateau (QTP), frequent freeze–thaw cycling (FTC) brings about great geological disasters such as subgrade failure, landslides, and mudslides, which is closely related to the strength reduction caused by the structural damage of soils. In this study, to explore the association between macro shear strength and microstructure evolution of soils subjected to FTC, the red clay distributed widely in the QTP was chosen and used to conduct a series of triaxial shear and nuclear magnetic resonance (NMR) tests in the range of 1 to 7 FTCs. Triaxial shear test results reveal that the shear strength reduction of specimens mainly occurs within five FTCs, and the trend of peak deviator stress with increasing FTCs can be described in three stages: rapid descent (FTCs less than three), slow descent (FTCs between three and five), and stabilization (FTCs greater than five). NMR tests show that the T2 spectrum curves exhibit a distinct bimodal distribution characteristic, corresponding to macropores and micropores. Part of the micropores gradually develop into macropores with increasing FTCs, especially within five FTCs. The increase in macropores proportion leads to a loose soil structure, which is consistent with the deterioration of the shear strength of specimens. Finally, based on the experimental results and classical Mohr–Coulomb theory, a new shear strength model with structural damage for red clay has been proposed by introducing a damage factor expressed by T2 spectral area.

Multiphysics simulations of uniaxial compression applied to various rock samples subject to microwave pretreatment

PurposeAmong the various applications involving the use of microwave energy, its growing utility within the mining industry is particularly noteworthy. Conventional grinding processes are often overburdened by energy inefficiencies that are directly related to machine wear, pollution and rising project costs. In this work, we numerically investigate the effects of microwave pretreatment through a series of compression tests as a means to help mitigate these energy inefficiencies.Design/methodology/approachWe investigate the effects of microwave pretreatment on various rock samples, as quantified by uniaxial compression tests. In particular, we assign sample heterogeneity based on a Gaussian statistical distribution and invoke a damage model for elemental tensile and compressive stresses based on the maximum tensile stress and the Mohr–Coulomb theories, respectively. We further couple the electromagnetic, thermal and solid displacement relations using finite element modeling.Findings(1) Increased power intensity during microwave pretreatment results in decreased axial compressive stress. (2) Leveraging statistics to induce variable compressive and tensile strength can greatly facilitate sample heterogeneity and prove necessary for damage modeling. (3) There exists a nonlinear trend to the reduction in smax with increasing power levels, implying an optimum energy output efficiency to create the maximum degradation-power cost relationship.Originality/valuePrevious research in this area has been largely limited to two-dimensional thermo-electric models. The onset of high-performance computing has allowed for the development of high-fidelity, three-dimensional models with coupled equations for electromagnetics, heat transfer and solid mechanics.

Verification of a novel stress path method by true-triaxial test

To verify the novel method of achieving a true-triaxial stress path with the pseudo-triaxial apparatus, a series of drained and undrained tests were carried out for the identical scheme with pseudo-triaxial apparatus and true-triaxial apparatus respectively. The differences between the two types of tests were quantified. The results show that the novel method effectively achieved the true-triaxial stress path by controlling the loading ratio of the pseudo-triaxial apparatus. The relationships of q − ε1 and η − εs measured by the two apparatuses had a higher similarity which decreases slightly with the b increase. When 0 ≤ b < 0.5, the slope of the critical state line measured by both apparatuses was almost identical. When 0.5 ≤ b ≤ 1, the slope of the critical state line measured by the novel method was slightly lower, but the biggest change was within 10% compared with the two Mohr–Coulomb criteria, the peak strength measured by the two apparatuses was distributed near the criteria, indicating the feasibility and rationality of the novel method. The tests show that the novel method greatly enriches the test range of pseudo-triaxial apparatus, which not only simplifies the process of soil 3D testing but also reduces the test cost.

On the Unloading‐Induced Fault Reactivation: The Effect of Stress Path on Failure Criterion and Rupture Dynamics

AbstractFault reactivations induced by deep excavation can pose significant challenges to underground construction or resource extraction. Laboratory experiments on rock faults demonstrate that unloading‐induced fault reactivations obey the Coulomb failure criterion derived from loading‐induced events. However, the effect of stress path during unloading on the failure criterion and rupture dynamics of fault reactivations remains poorly understood. Here, we present findings from a series of laboratory experiments aimed at elucidating the effect of the unloading path on the failure criterion and rupture dynamics of fault reactivations. We conducted experiments under various stress conditions, examining two cases of unloading paths. In Case I, we unloaded the minimum principal stress, while in Case II, the maximum principal stress was unloaded. Strain gauges and high‐speed photography were employed to capture the transient dynamic rupture process. Our investigations have yielded new insights into the effect of unloading path on the rupture dynamics when the fault is reactivated. In Case I, we observed fault reactivations resembling those loading‐induced events characterized by forward sliding. Conversely, in Case II, fault reactivations associated with stress reversal produce mild reversed sliding with lower stress drop and rupture velocity. Furthermore, we find that there is a remarkable reduction in static friction for reversed sliding, indicating that the failure criterion for fault reactivation is influenced by the stress path. We demonstrate that enhanced stress heterogeneity, caused by stress reversal, serves as a mechanism for reduced static friction. These findings contribute to our understanding of the mechanisms underlying fault reactivations, particularly those involving reversed sliding.