Rock Strength Criteria Research Articles

The influence of temperature, seepage and stress on the area and category of wellbore instability

This study investigates the challenge of borehole instability in shale gas development, focusing on the interactions among temperature, fluid flow, and stress. Using a thermal-hydro-mechanical coupling model of borehole elastic stress combined with a true triaxial rock strength criterion and tensile failure criterion, the research systematically examines the effects of different models on borehole stability in shale formations. The findings reveal that while temperature has a relatively minor impact on the stress distribution and failure zones around boreholes, bottom hole pressure plays a critical role in influencing both the extent of unstable regions and the modes of rock failure. Under varying inclination angles, the unstable zones and failure patterns generally remain consistent, with higher stability observed when drilling aligns with the direction of minimum horizontal stress. Moreover, the study highlights the significance of appropriate drilling fluid density in maintaining borehole stability. Specifically, when the bottom hole pressure ranges from 50.66 to 70.66 MPa, the tensile and shear instability areas are minimized within seven days of contact with the drilling fluid. The research underscores the importance of optimizing drilling fluid density, carefully managing bottom hole pressure, and selecting proper borehole trajectories to enhance stability during shale gas drilling. These findings provide both theoretical insights and practical guidance, contributing to the optimization of shale gas drilling engineering practices.

A novel triaxial strength criterion for rocks based on the ultimate strength and its application

Strength criteria are the basis for rock engineering stability assessment and structural optimization design. To predict the triaxial strength of various lithologies, a novel strength criterion is established based on the ultimate strength. A database consisting of over 1,642 triaxial tests conducted on rocks is established to calibrate and validate the criterion. According to the measured and predicted results, the fitting accuracy of the criterion is analyzed and compared with several classical criteria, and the sensitivity of the criterion parameters is further discussed. Results indicate that the criterion exhibits high accuracy in fitting and performs better in sandstone but worse in gneiss. In most samples, the criterion underestimates the triaxial strength, which is beneficial for establishing safety redundancy in engineering. Compared to other classical strength criteria, this particular criterion demonstrates superior fitting accuracy and displays lower sensitivity to parameters that lack physical significance. In addition, a simplified criterion is proposed to predict the strength without triaxial test data. Although its fitting accuracy falls slightly below that of the original criterion, its predictive performance is acceptable. Consistent with the original criterion, the simplified criterion performed significantly better in sandstone than in gneiss, and the simplified criterion also underestimated the strength in most lithologies. Finally, the simplified criterion is applied in the Jinping II hydropower station, and the prediction results confirm its applicability of the simplified criterion on the strength prediction of rocks.

A comparative study of three types of strength criteria for rocks

Currently, the unified strength criterion (USC), the three-dimensional Hoek-Brown (3D H-B) criterion and the generalized unified strength theory (GUST) are the three types of typical rock strength criteria. In this paper, a comparative study of the three types of strength criteria is performed for rocks. Based on the nonlinear characteristics of rock strength on meridian and deviatoric planes, the USC can predict rock strength under triaxial stress state. The USC is composed of two failure functions on meridian and deviatoric planes. The failure surface of the USC in principal stress space satisfies smoothness and convexity. The predicted strength for five types of rock under the true triaxial tests were compared among the USC, the GUST, and the 3D H-B criterion. The results indicate that the USC can effectively reflect the influence of the intermediate principal stress on rock strength and accurately predict rock strength under both triaxial tension (σ1=σ2>σ3) and triaxial compression (σ1>σ2=σ3). Additionally, the conventional triaxial tests were conducted on other eight types of rock to measure the strength on meridian plane. The predicted strengths for the eight types of rock on meridian plane were compared between the USC and the original H-B, which suggests that the USC is suitable for various types of rock and provides higher accuracy.

A Novel Mohr–Coulomb–Matsuoka–Nakai Strength Criterion for Rocks Considering Brittle–Ductile Domain

A Novel Mohr–Coulomb–Matsuoka–Nakai Strength Criterion for Rocks Considering Brittle–Ductile Domain

An improved three-dimensional extension of Hoek–Brown criterion for rocks

The Hoek–Brown (H–B) criterion has found widespread application in numerous rock engineering projects. However, its efficacy is compromised by an underestimation of rock strength due to its neglect of the influence of the intermediate principal stress (σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma_{2}$$\\end{document}). Experimental evidence underscores the significant impact of σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma_{2}$$\\end{document}. Consequently, there exists an imperative to formulate a three-dimensional (3D) criterion. In this study, a new deviatoric function with two additional parameters (k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document} and A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A$$\\end{document}) is developed firstly, which ensure compliance with the prerequisites of smoothness and convexity. In addition, the parameters k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document} and A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A$$\\end{document} are bonded with the weakening effect of the Lode angle (θσ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta_{\\sigma }$$\\end{document}) and the strengthening effect of the mean stress (σm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma_{m}$$\\end{document}), respectively. Then a new 3D strength criterion for rocks is proposed by combining this new deviatoric function and the triaxial compression meridian function of the original H–B criterion. Four distinct sets of test data encompassing various rock types are employed to validate the proposed criterion. The results demonstrate that the proposed criterion adeptly captures the strength characteristics of the four rock types, providing a good depiction of failure surfaces within the 3D principal stress space. Comparative analyses involve the utilization of several existing 3D H–B criteria for strength predictions. The proposed criterion exhibits superior fitting performance for all the selected rocks.

Integrated approach of predicting rock stability in high mountain valley underground caverns

High mountain valleys are characterized by the development of intricate ground stress fields due to geological processes such as tectonic stress, river erosion, and rock weathering. These processes introduce considerable stability concerns in the surrounding rock formations for underground engineering projects in these regions, highlighting the imperative need for rigorous stability assessments during the design phase to ensure construction safety. This paper introduces an innovative approach for the pre-evaluation of the stability of surrounding rocks in underground caverns situated within high mountain valleys. The methodology comprises several pivotal steps. Initially, we conduct inverse calculations of the ground stress field in complex geological terrains, combining field monitoring and numerical simulations. Subsequently, we ascertain stress-strength ratios of the surrounding rocks using various rock strength criteria. To assess the stability characteristics of the surrounding rocks in the 1# spillway cave within our project area, we employ numerical simulations to compute stress-strength ratios based on different rock strength criteria. Furthermore, we undertake a comparative analysis, utilizing data from the 5# Underground Laboratory (Lab 5) of Jinping II Hydropower Station, aligning the chosen rock strength criterion with the damage characteristics of Lab 5′s surrounding rocks. This analysis serves as the cornerstone for evaluating other mechanical responses of the surrounding rocks, thereby validating the pre-evaluation methodology. Our pre-evaluation method takes into account the intricate geological evolution processes specific to high mountain valleys. It also considers the influence of the initial geostress field within the geological range of underground caverns. This comprehensive approach provides a robust foundation for the analysis and assessment of the stability of surrounding rocks, especially in high mountain valley areas, during the design phase of underground engineering projects. The insights derived from this analysis hold substantial practical significance for the effective guidance of such projects.

Deep/ultra-deep shale strength criterion: A case study of southern Sichuan Basin shale

Deep/ultra-deep shale gas reservoirs are a vital area for future shale gas development, which mainly relies on the stimulation of network fracturing. In such a reservoir, engineering technologies such as wellbore stability evaluation and network fracturing design are all closely related to the shale mechanical characteristics. Currently, most studies focus on the elastic-plastic, brittle-ductile properties of shale, which are characterized based on shale strength. However, there is still a lack of in-depth research on their failure strength and strength criteria specifically for deep/ultra-deep shale. To accurately characterize shale failure strength, numerous scholars have researched shale strength criteria. Nevertheless, due to the high geo-stress of deep/ultra-deep reservoirs, shale properties tend to transition from brittle to ductile, resulting in poor fitting of classical rock strength criteria to test data under high confining stresses. This study focused on the outcrops of the Longmaxi Formation shale, and high-confining-stress triaxial compression tests were conducted to investigate the strength variation characteristics of shale. Based on the Mohr-Coulomb criterion, a power-form MC criterion was proposed by introducing a power function of confining stress as a correction term, and its reliability, sensitivity, and applicability were evaluated. The results indicate that the non-linear characteristics of the power-form MC criterion curve better match the actual situation, allowing for a more accurate prediction of shale strength under high confining stress. Furthermore, the power-form MC criterion has low sensitivity to changes in confining stresses, indicating that the required amount of test data for fitting can be appropriately reduced during application. Additionally, the power-form MC criterion is applicable to some extent to other types of high-strength rocks buried at greater depths. The results of this study contribute to understanding the strength characteristics of deep/ultra-deep shale under high confining stress, providing important references and theoretical basis for drilling, completion, and stimulation practices in deep shale gas reservoirs.

Study of Rock Damage Constitutive Model Considering Temperature Effect Based on Weibull Distribution

The deformation and damage process of rocks is accompanied by crack extension and penetration. The rock strength criterion, as a macroscopic characterization of the rock strength microelement, is the basis for establishing the damage constitutive modeling of rock. Aiming at the problem of the Hoek–Brown (H–B) strength criterion having a large strength prediction value under high confining pressure, the H–B strength criterion is corrected by considering the influence of the initial cracks on the development of the rock strength, and its applicability is verified. Based on the damage theory, assuming that the rock strength microelement obeys the Weibull distribution and considering the influence of residual strength, the damage correction coefficient is introduced, and a thermal damage statistical constitutive model that can reflect the whole process of the development of initial cracks inside the rock is established. The degree of penetration up to the damage is established, and the method of determining the parameters of the model is given. The theoretical curves of the established model are compared and analyzed with the curves of a conventional triaxial compression test of rock samples, and the study shows that the statistical constitutive model of the thermal damage of rock, established based on the modified H–B strength criterion, can better simulate the stress–strain relationship of rock under a conventional triaxial test. It also verifies the reasonableness and applicability of the model, which is expected to provide a basis for the exploitation of deep resources and the safety assessment of underground engineering.

A Three-Dimensional Nonlinear Strength Criterion for Rocks Considering Both Brittle and Ductile Domains

A Three-Dimensional Nonlinear Strength Criterion for Rocks Considering Both Brittle and Ductile Domains

A new three-dimensional rock strength criterion based on shape function in deviatoric plane

Rock strength criteria are the theoretical grounding of geotechnical design and stability estimation, the Mohr–Coulomb (MC) and Hoek–Brown (HB) criteria are the widely accepted criteria at present, due to their reasonability and unambiguous concept, however they overlook the effect of intermediate principal stress, and contain six singular corners in π plane. Aimed at overcoming those limitations, the MC and normal parabolic criterion (NPC) were improved to their 3D versions that lead to smooth and convex for a wide range of strength parameters. The extended 3D strength criteria coincide with corresponding original forms in the triaxial compression and triaxial extension states, which not only take intermediate principal stress into account, but also provide great convenient in numerical calculation. Multigroup of poly-axial strength datasets gathered from the references are used to check the prediction accuracy of the proposed 3D criteria by the least absolute deviation method. Research proved that the 3D NPC criterion has a relatively larger deviation on poly-axial strength data prediction, but the proposed 3D MC criterion can describe peak strength with low misfit for soft or hard rocks. Peak strength σ1 increases first and then decreases with the increase of σ2, whether increasing or decreasing σ2, both will result in rock failure. Moreover, the 3D MC can fit the poly-axial strength data well for lower or higher values of σ3, which strongly suggests the proposed 3D MC criterion is adequate. Applicability of the proposed strength criterion will be discussed in further research.

A new Hoek-Brown-Matsuoka-Nakai failure criterion for rocks

In the current paper, we propose a new three-dimensional strength criterion for rocks expressed in terms of the first principal stress invariant, I1, and the second and third invariants of the deviatoric stress tensor, J2 and J3.The design of this constitutive model conjugates the characteristics of two of the most well-known and widely used criteria in geotechnical engineering: Hoek-Brown and Matsuoka-Nakai. Its material parameters can be calibrated based on conventional axisymmetric compression and extension tests.Experimental polyaxial test data from a dozen different rock types were used to validate the current criterion.

A true triaxial strength criterion for rocks by gene expression programming

A true triaxial strength criterion for rocks by gene expression programming

The modification of Mohr-Coulomb criteria based on shape function and determination method of undetermined parameters

Rock strength criteria is a key step to estimate the stability of rock engineering, especially, the effect of intermediate principal stress on rock failure should be considered in formation at great depth. However, the mostly used Mohr-Coulomb criterion don't consider the effect of intermediate principal stress, besides, most rock mechanics laboratories do not have the ability to do true triaxial strength, the strength parameters in poly-axial strength criteria are difficult to be determined. In order to solve these problems, based on the least absolute deviation method, the square of the correlation coefficient, absolute difference and mean difference are adopted to verify the fitting effect of 10 strength criteria on 32 groups of true triaxial strength data. On this basis, the elliptical Lode angle shape function, hyperbolic Lode angle shape function, and the Lode angle shape function based on spatial slip plane are used to establish the modified MC strength criteria, which not only meets the requirements of smoothness and convexness, but also can be used widely in many geomaterials. Besides, strength parameters of the established criteria can be decided by conventional triaxial strength experiment, and the prediction accuracy of the modified MC strength criteria for the 32 groups of true triaxial strength data is better than or close to the lowest fitting error of the existing poly-axial strength criteria.

Measures of slope stability in bonded soils governed by linear failure criterion with tensile strength cut-off

The linear failure criterion with a tensile strength cut-off is increasingly applied to geotechnical stability problems in response to the uncertainty originating from the predicted tensile strength in soil. However, several attempts at slope stability analysis have employed classical failure mechanisms with geometrical and computational constraints. In the context of limit analysis, an advanced failure mechanism was utilized in this study for more accurate and comprehensive solutions of practical stability measures, including stability factors and factors of safety. This mechanism delivers lower stability factors and enables the estimation of the traditionally defined factor of safety, particularly in the tensile regime associated with the nonlinear part of the envelope. A technique that transforms the Hoek–Brown rock strength criterion into the equivalent linear failure criterion with a tensile strength cut-off is presented. The factors of safety based on the equivalent Mohr–Coulomb envelope subjected to the tension cut-off showed exceptional agreement with those based on the original Hoek–Brown equation, owing to the truncation of the overestimated strength in the low-stress regime.

Investigation of collapse pressure in layered formations based on a continuous anisotropic rock strength criterion

Wellbore instability severely constrains the exploration and development of shale gas. In order to evaluate the impacts of anisotropy and water on wellbore instability, three different types of criteria are fitted to strength data of LMX shales with different moisture contents. A new model of transversely isotropic borehole stability considering compliance incremental tensor induced by natural fractures is proposed, then a more preferred drilling direction is performed by the new model. Results indicated that, Pariseau’s model is more attractive in predicting shale strength, including the difference of strength between vertical bedding and parallel bedding. Based on Pariseau’s model, the prediction accuracy of shale strength is improved by 33.04%. The Pariseau’ model gives a disparate collapse pressure from Jæger’s weak plane criterion, the most unstable drilling area shifts from northeast and southwest to the central area corresponding to relatively lower inclination. The collapse pressure only decreased by 0.55 MPa with considering the anisotropy of elastic parameters, but the strength criteria have a distinct influence. Compared with the results predicted by Jæger’s plane of weakness, the collapse pressure increased by 8.55 MPa using Pariseau’ model. Besides, invasion of water in bedding plane will aggravate borehole instability, especially in late drilling period, collapse pressure for the vertical wellbore increased by 6.35 MPa. Shale strength depends not only on the hydrostatic pressure and orientation angle, but also on the water content, which should be considered in mud weight design and well trajectory optimum.

Analytical Model of Wellbore Stability Analysis of Inclined Well Based on the Advantageous Synergy among the Five Strength Criteria

The proper drilling mud density is vital for wellbore stability maintenance, which relies on both stress distribution on the borehole wall and rock strength. Thus, the selection of rock strength criterion is vital for wellbore stability analysis (WSA), and several strength criteria have been developed and employed to perform WSA, but the real collapse pressure does not comply with any single strength criterion. Therefore, to accurately predict the critical mud weight against wellbore collapse, an analytical model of WSA was proposed for inclined wells based on the advantageous synergy among the five types of strength criteria, such as the Mohr-Coulomb criterion, Mogi-Coulomb criterion, Drucker-Prager criterion, modified Wiebols-Cook criterion, and modified Lade criterion. The predicted results among these analytical and five conventional models were compared under three kinds of typical stress regimes, such as normal, strike-slip, and reverse faults. Finally, five kinds of typical oil and gas field data were collected to further verify the accuracy of this new model. The results indicated that different models predicted different collapse pressure, owing to the Mohr-Coulomb criterion ignoring the intermediate principal stress ( σ 2 ), so as to always give the greatest collapse pressure, followed by the present analytical model and the Mogi-Coulomb criterion, while the other three types of strength criteria gave different results, because of the difference in the influence of σ 2 , while the present analytical model integrated the advantageous synergy among the five strength criteria. The prediction error of the conventional analytical model ranges from 9.4 to 34.2% with an average of 22.1%, while the prediction error of this new model ranges from 2.3 to 12.5% with an average of 7.1%, so that the present analytical model has much higher accuracy than that of any single strength criterion. In addition, this new analytical model can be simplified as the conventional analytical model by adjusting the weight coefficients.

Elastic-plastic analysis of circular tunnel based on unified strength theory and considering multiple plastic zones

Considering that the internal friction angle of the surrounding rock is not a constant but a function of the mean normal stress, and the unified strength theory (UST) is used as the plastic condition of the tunnel surrounding rock, the plastic zone of the circular tunnel surrounding rock is divided into multiple annular regions. For different plastic zones, there are different yield conditions represented by different stress functions, the elastic-plastic analysis of circular tunnels is performed by using the piecewise linearization of nonlinear yield function, stress and displacement in the elastic-plastic zone and the radius of the plastic zone are obtained by combining the equilibrium equations. It is shown that the radius of the plastic zone increases, the radial stresses in the elastic-plastic zone and the circumferential stresses in the plastic zone become smaller and the circumferential stresses in the elastic zone becomes larger compared with that of only one plastic zone. By using single factor analysis method, the calculated values of the tunnel displacements and plastic radii by UST were compared with those obtained by the Mohr-Coulomb (M-C) criterion, Drucker-Prager (D-P) criterion, and Zienkiewicz-Pande (Z-P) criterion. The analysis shows that under the same conditions, the solution of UST is smaller than M-C criterion and D-P criterion, therefore, the selection of rock strength criterion has great influence on the calculation of rock mechanics and engineering, the proper application of UST will guarantee the safety of engineering practice and have more practical value.

Study on Rock Mechanical Properties and Wellbore Stability of Fractured Carbonate Formation Based on Fractal Geometry.

To mitigate borehole wall instability in fractured carbonate formations in an oilfield, the main factors affecting borehole wall instability were determined by combining the characteristics of underground cores, logging data, and a series of laboratory mechanics experiments. The geometric morphology characteristics of a carbonate rock fracture surface were studied together with an artificial rock fracture surface formed by triaxial mechanics experiments. A relationship between the geometric morphology characteristics of a fracture surface and rock mechanical properties was established based on fractal geometry. Using the Mohr-Coulomb failure and weak plane failure criteria, a rock strength criterion based on the fractal characteristics of a rock fracture surface was established. Finally, the mechanical rock properties characterized by fractal geometry were imported into the established borehole stability evaluation model. The results show that a collapse formation is mainly limestone with relatively developed microfractures, and some fractures are filled with expansive clay. The anisotropy of mechanical properties of bedrocks and microfractured rocks is obvious, whereas drilling-fluid immersion has little effect on the mechanical properties of a rock. 3D scanning experiments of artificial fracture surfaces formed after a triaxial mechanical test of a bedrock and fracture surfaces of a rock with microfractures show that the geometric characteristics of fracture surfaces after bedrock failure were more complex than those of fractured rocks. The geometric characteristics of rock fracture surfaces were numerically expressed through astatistical analysis and fractal geometry. Function relationships among cohesion, an internal friction angle, and fractal dimensions of bedrocks and microfracture rocks were fitted. A numerical simulation of borehole stability based on the fractal model of a carbonate fracture surface shows that different fracture inclinations and borehole trajectories significantly influence the collapse pressure equivalent density of a borehole wall. On drilling a horizontal well along the inclination of a fracture, the collapse pressure equivalent density of the borehole wall is relatively low when the fracture inclination is along the direction of the minimum horizontal principal stress. Unlike that from a conventional borehole stability model, the collapse pressure equivalent density calculated from the fractal model will increase by 0.1-0.2 g/cm3. The study results provide a theoretical basis for safe and efficient drilling in fractured carbonate formations.

Modeling of true triaxial strength of rocks based on optimized genetic programming

The strength of a rock is the main factor affecting the stability of an engineered rock mass. As laboratory testing requires sophisticated equipment and considerable time to determine rock strength, prediction models are needed for establishing rock strength criteria. Genetic programming (GP) is a soft computing technology often used to address rock mechanics and engineering challenges. However, GP also has limitations, such as a long running time, complex individual growth without a corresponding fitness improvement, and difficulty in finding the optimal solution. Therefore, we conducted this study by applying a dynamic restriction on individual size, local search of the neighborhood of the optimal individual, and multithreaded evaluation to optimize GP and guarantee the accuracy of the results and to build a prediction model for the true triaxial strength involving different rock types. The results showed that the restriction dynamically changes to restrict the redundant bloat of strength individuals without a corresponding fitness improvement; using local search rules can effectively find individuals with high fitness, so the strength predicted by the system was in good agreement with the measured strength. We also found the predicted strength was suitable for fitting the rock strength criteria. Using this multithreaded evaluation sped up the operation of the algorithm and produced accurate predictions; and for complex problems, increasing the threads had a more pronounced effect on the runtime and fitness improvements. Based on the Sobol global sensitivity analysis, we analyzed the influence of each prediction parameter on the true triaxial strength of rocks. Combined with the statistical assessment indices involving sum of the absolute error, mean, a10-index, and regression determination coefficient, the predictions of the optimized GP model that we established in this study were more accurate than those of multiple regression analysis.

An insight into modeling wellbore stability using the extended Mogi-Coulomb criterion and poly-axial test data

The cost of drilling oil and gas wells is likely to be charged by billions of dollars each year due to wellbore stability problems. In engineering practice, a linear poroelasticity stress model in combination with a rock strength criterion is commonly used to determine a minimum mud weight for stable well drilling. In this paper, new models for predicting the stability of vertical wellbores using the nonlinear form of Mogi criterion and poly-axial test results were perfumed. Afterward, by applying analytical models to the real field data, the applicability of the models has been verified. From comparing the results of this nonlinear and the liner Mogi-Coulomb criterions, the impact of the nonlinearity on the wellbore stability prediction has been identified. Thus, the results of nonlinear form of Mogi failure criterion were very close to the field mud weight used to successfully drill the borehole.