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In this work, a novel elastoplastic damage model is proposed to capture the mechanical and deformation behaviors of hard rocks subjected to true triaxial compression (TTC). A yield function based on the Mogi–Coulomb strength criterion is constructed in the stress space. Generalized plastic shear strain as a function of a continuous and smooth hardening or softening variable is adopted in the yield function; this guarantees that the yield function at the peak stress level has the same form as the strength criterion. Moreover, a proper damage criterion is derived, considering the development of microcrack-induced damage. The novelty of the proposed model consists in the ability to derive its analytical solutions under a novel TTC loading with a constant load angle; this is helpful for calibrating the model parameters. For application, an efficient and convergent semi-implicit return mapping (SIRM) algorithm involving a plasticity-damage decoupling correction procedure is then developed for the numerical implementation of the proposed model under general loading cases. The robustness of the SIRM algorithm is examined through comparisons between numerical results and the derived analytical solutions. An interesting observation is that, for the SIRM algorithm, plasticity and damage evolution are insensitive to the size of the load step. The verification of the model is finally shown through applications to Westerly and Linghai granite under a typical TTC loading path. [ABSTRACT FROM AUTHOR]

Borehole breakout initiation, progression, and stabilization are modeled using a semi-analytical method based on Melentiev's graphical conformal mapping procedure, and Kolosov–Muskhelishvili complex stress potentials. The only input data required are the elastic moduli of the rock, the Coulomb strength parameters (cohesion and angle of internal friction), and the far-field stresses. The stresses around the borehole wall are computed, the region in which the rock has failed is then "removed", creating a new borehole shape. This process is iterated until a shape is obtained for which the breakout will progress no further, and a stable state has been reached. This modeling shows that stresses around the flank of the breakout evolve so as to reduce the propensity for shear failure, which helps to explain why the breakout width remains relatively constant throughout the process, even as the breakout region deepens radially. The failed area around the borehole becomes smaller and more localized, as the breakout tip sharpens and deepens. Using the Mogi–Coulomb failure criterion, a good match is obtained between the modeled breakout geometry and the geometry observed by Herrick and Haimson in laboratory experiments on an Alabama limestone. The new method leads to a correlation between breakout geometry, rock strength properties, and in situ stress. The paper ends with a critical discussion of the possibility of inferring the in situ stress state from observed breakout geometries. Highlights: A semi-analytical method is presented for modeling borehole breakouts around an initially circular borehole in a stressed rock mass. The stresses around the borehole wall are computed using complex stress potentials and conformal mapping. The region of "failed" rock is "removed", creating a new borehole shape; this process is iterated until a stable borehole shape is obtained. Using the Mogi-Coulomb failure criterion, a good match is obtained with the geometry observed by Herrick and Haimson in experiments on limestone. A critical discussion is given of the possibility of inferring the in situ stress state from observed breakout geometries. [ABSTRACT FROM AUTHOR]

Describing rock strength under true triaxial conditions with the limit condition of Mogi‐Coulomb It is known that investigations of rock strength under true triaxial conditions can show the influence of the mean principal stress on failure. For numerical calculations of tunnels and boreholes, where the mean and minimum principal stresses are not identical, limit conditions that take into account the influence of the mean principal stress would be advantageous. With the limit condition according to Mogi‐Coulomb, unlike with the well‐known limit condition according to Mohr‐Coulomb, the influence of the mean principal stress can be taken into account. At the same time, however, these two limit conditions are identical for triaxial extension and compression. In order to be able to map limit states even more appropriate, the modified limit condition according to Mogi‐Coulomb is presented in this article. In this modified form, the limit conditions according to Drucker‐Prager and von Mises are included as a special case. In order to understand the Mogi‐Coulomb criterion and to show possible applications, the present article shows its form, the influence of the parameters, the convexity and parameter acquisition of laboratory tests are examined. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a unified approach through which the influence of the elastic and strength anisotropy on wellbore instability can be thoroughly examined. The stresses at the wellbore wall are first calculated using the Lekhnitskii-Amadei solution, which accounts for elastic anisotropy. Then, shear failure is treated by combining the Mogi-Coulomb criterion for intact rock, with the Jaeger plane of weakness concept. The developed model accounts for all three principal stresses in predicting the onset of shear failure. The results of the specific case investigated show that rock elastic anisotropy induce higher stress concentrations. The difference, compared with the stresses found using the isotropic elastic model, could reach as high as 25% for the highest degree of anisotropy that might be expected for rocks of practical interest. The strengthening effect of the intermediate stress, as reflected in the Mogi-Coulomb criterion, reduces the required mud weight density by approximately 1.0 pounds-per-gallon (ppg). Furthermore, it is demonstrated that the risk posed by bedding slippage, for a wellbore with an inclination between 15° and 50° from the vertical, is masked when an isotropic elastic stress model is used. In contrast, the fully anisotropic model shows that an extra mud weight of approximately 4.5 ppg would be required, in order to avoid bedding plane slippage for the case under investigation. Although these results apply for a particular choice of strength properties and elastic properties, they give an indication of the implications of fully accounting for anisotropy and the effect of the intermediate stress when doing borehole stability analysis. [ABSTRACT FROM AUTHOR]

A major component of the Mohr-Coulomb (M-C) criterion is that the failure of the material is independent of the intermediate principal stress σ 2 along the potential planes of sliding. To account for the effect of σ 2, a linear relationship between the octahedral shear stress τ oct and the mean stress σ m,2 on the plane of failure (called the Mogi-Coulomb criterion) is widely used to represent rock failure in polyaxial compression (PXC) in practice. In this research, a linear relationship between the equivalent stress σ e (or τ oct ) and major principal stress σ 1 (or minor principal stress σ 3 ) is proposed, which has a similar expression as the Mogi-Coulomb criterion. The relationship between the proposed failure criteria and M-C criterion is like the relationship between the Tresca and Von-Mises criteria. The material parameters can be related to the M-C strength parameters, and can be easily obtained from conventional triaxial tests. The proposed criteria are numerically calibrated against triaxial compression (TXC) and PXC data sets using three different methods. Sensitivity of the range of TXC stress data employed for fitting on the prediction results in PXC are further discussed. Comparisons of two proposed criteria with the Mogi-Coulomb criterion for rocks in PXC demonstrate that one new criterion with convex failure envelope gives the best performance for seven rock types and provides an acceptable modelling for the rest of rock types. Another new criterion and the Mogi-Coulomb criterion result in large prediction error for three (or two) rock types though they can give best performance for some rock types. [ABSTRACT FROM AUTHOR]

The failure criterion is a very important aspect of the wellbore stability analysis. But the Mohr–Coulomb criterion, a most commonly used failure criterion, is usually too conservative, due to the influence of the intermediate principal stress is not taken into account. Furthermore, the safe mud weight (MW) predicted by the conventional method is usually too high, due to the safe MW is predicted to yield no shear failure around the borehole. To solve the above problems, a semi-analytic model of wellbore stability analysis was proposed based on the stress distribution model, failure criteria and the breakout width model. The Mogi–Coulomb criterion, a new true-triaxial failure criterion, is involved in this semi-analytic model to determine the shear failure. The computational models of the lowest and highest safe MW are derived for different failure mode. The numerical method and flowchart of this semi-analytic model is provided, and a computer program is also developed in Matlab software. The impacts of the failure criteria, stress regimes and breakout width had been systematically analyzed. The optimal well path had been optimized for different stress regimes. The results showed that the lowest safe MW predicted by Mogi-Coulomb criterion is always lower than the Mohr-Coulomb criterion. The most stable drilling direction is along the minimum horizontal stress for the NF and NF–SS stress regimes, while it’s along the maximum horizontal stress in the SS, SS–RF and RF stress regimes. If the breakout width model is used, the lowest safe MW is always lower than the traditional method. The optimal well path and the wellbore stability are different between traditional and new methods. The most stable path is always the horizontal and deviated well for the traditional method, instead, it’s always the vertical well for this new method, it’s more consistent with the actual situation. These results also illustrated that an acceptable breakout is usually allowed to occur in the actual borehole, and the borehole still has enough arc to support the wellbore wall and to prevent collapse accident. Finally, both of the traditional and new methods are applied in the field case studies. The results showed that the lowest safe MW predicted by the integration of the breakout width model and Mogi–Coulomb criterion is closest to the real MW, instead, the lowest safe MW predicted by the traditional methods has exceeded the actual MW. It also illustrated the traditional method is too conservative in predicting wellbore stability, while this new method is more accurate for the integration of the breakout width model and MG–C criterion. This research can provide support to optimize the well path and MW in the drilling practices. [ABSTRACT FROM AUTHOR]