Lade Criterion Research Articles

Hop-to-Hug algorithm: Novel strategy to stable cutting-plane algorithm based on convexification of yield functions

Numerical challenges, incorporating non-uniqueness, non-convexity, undefined gradients, and high curvature, of the positive level sets of yield function are encountered in stress integration when utilizing the return-mapping algorithm family. These phenomena are illustrated by an assessment of four typical yield functions: modified spatially mobilized plane criterion, Lade criterion, Bigoni-Piccolroaz criterion, and micromechanics-based upscaled Drucker-Prager criterion. One remedy to these issues, named the "Hop-to-Hug" (H2H) algorithm, is proposed via a convexification enhancement upon the classical cutting-plane algorithm (CPA). The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point. Furthermore, a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform. Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence. All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation, in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented.

Strength characteristics and energy evolution of cement stone under true-triaxial loading conditions

Oil well cement is a commonly used cementing material in oil and gas extraction engineering. Due to the change of stress conditions, it is prone to microcracks or micro annular gaps, leading safety concerns. To study the strength characteristics and energy evolution of oil well cement stone under three-dimensional stress states, a series of true-triaxial compression tests were carried out. Based on the experimental results, the mechanical properties and energy evolution mechanisms during the true-triaxial compression process of cement stone under different stress states were explored. The research results indicate that there is an intermediate principal stress effect on the true-triaxial compressive strength of cement stone specimens. When the minimum principal stress remains constant, the strength of cement stone first increases and then decreases with the increase of intermediate principal stress. When the minimum principal stress is 5 MPa, the specimen exhibits brittle failure, with ε1 at peak stress approximately 0.015. As the minimum principal stress increases to 20 MPa, the specimen gradually transits to plastic failure, with ε1 at failure exceeding 0.04. The type of failure is determined by the energy ratio at the time of failure; when there is more elastic energy, it results in brittle failure, otherwise it leads to ductile failure. Due to the high porosity of cement stone samples, most of the input energy is converted into dissipated energy. At minimum principal stresses of 5 MPa, 10 MPa and 20 MPa, the ratio of peak dissipated energy to total input energy fluctuates around 0.55, 0.73 and 0.85, respectively. There is a strong linear relationship between the peak elastic energy, peak dissipated energy, and total input energy, with fitting correlation coefficients of 0.847 and 0.996, indicating that the cement stone sample also follows the linear energy storage law. A strength criterion for cement stone was established based on the modified Lade criterion, which is more suitable for describing the strength of high porosity materials compared to traditional strength criteria. Finally, based on the interaction mechanism between energy accumulation and energy dissipation, a nonlinear model of energy evolution in cement stone was established. The results of the theoretical model are in good agreement with the experimental data.

Building 1D Mechanical Earth Model for Subba Oilfield in Iraq

At the Subba oil field, wellbore stability is the main concern while drilling. The wellbore's instability causes several issues, including: (inefficient hole cleaning, tight hole, stuck pipe, mud losses, caving, bad cementing, and well kick or blowout). This increases Non-Productive Time (NPT) and well-drilling costs; hence the operator's main goal is to create a drilling program that reduces these problems and therefore reduce drilling cost. The study aims to build a 1D mechanical earth model to predict the wellbore failure and design optimum mud weight to improve the drilling efficiency for future wells. The model includes pore pressure, stress state, and rock mechanical parameters (such as UCS, angle of friction, Young-Modulus, and Poisson-Ratio). To achieve this aim, the study utilised offset well data including log data (Gama-Ray Logs (GR), Caliper Logs (CALI), Density Logs (RHOZ), and Compressional Sonic (DTCO) and Shear Sonic (DTSM)), Core tests, Mini-frac field tests, Drilling Reports, Mud Reports, and Mud Log Reports (master log) to estimate and calibrate the profiles of formation pore pressure, rock mechanical properties, and in-situ stresses. The 1D mechanical earth model was built using the Excel program for three wells data set, where all the necessary parameters to create the model was calculated, calibrated for the calculated variables with core data and pressure test points, and finally the safe mud window was detected. The results showed that the Eaton Slowness method to predict pore pressure perfectly matches the pressure test points. The most common fault regimes in the Subba oilfield are normal and strike-slip faults. The Modified Lade criteria showed a compatible match with drilling events and calliper log in predicting the failure zones, so it is the best criterion in determining minimum and maximum mud weight. Based on the results of this study and in comparison with the mud window used in drilling operations in the field, it is necessary to change the mud window used in drilling and adopt the safe MWW of this study in drilling new wells in this field and the area adjacent to the field.

Implementation of a constitutive model for anisotropic rocks based on modified Lade failure criterion

The strength anisotropy for inherent anisotropic rocks presents a challenge to simulate considering the influence of intermediate principal stress. Based on the modified Lade failure criterion, a new anisotropic modified Lade criterion combining an empirical equation is established and verified using published experimental datasets of anisotropic rocks. The incremental constitutive model for anisotropic rocks is derived by using finite difference theory. The dynamic link library (DLL) module of the model is obtained by using the VC++ program, and then the model is validated against various laboratory test results. It is concluded that the proposed criterion and derived model can describe the strength anisotropy of inherent anisotropic rocks well.

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.

Experimental study on the influence of hydrostatic stress on the Lode angle effect of porous rock

To investigate the deformation mechanisms of rock under hydrostatic stress, destructive experiments were conducted on sandstone under different levels of hydrostatic stress and stress Lode angles. The results reveal that the shape of the strength envelope on the π plane gradually changes from the shape of the Lade criterion to the shape of the Drucker-Prage criterion with an increase in hydrostatic stress. Normally, there exists a deviation between the strain and stress paths for porous rocks on the π plane, and the deviation decreases with an increase in stress Lode angle and hydrostatic stress. A rock failure hypothesis based on the rock porous structure was proposed to investigate the reasons for the abovementioned phenomena. It was found that the shear expansion in the minimum principal stress direction is the dominant factor affecting the Lode angle effect (LAE); the magnitude of the hydrostatic stress induces the variation of the porous structure and influences the shear expansion. Therefore, the hydrostatic stress state affects the LAE. The failure hypothesis proposed in this paper can clarify the hydrostatic stress effect, LAE, and the variation of the rock strength envelope shape.

Elastoplastic Analysis for Circular Tunnel Based on Modified Lade Criterion considering Strain Softening and Dilatancy

Modified Lade criterion can not only describe the strength properties of many kinds of rocks well but also has simple and practical parameters. Although the elastoplastic solution of circular tunnel has been extensively investigated, the method based on modified Lade criterion considering the effect of the intermediate principal stress, strain-softening behavior, and dilatancy has not yet been studied. In this paper, a new numerical procedure based on modified Lade criterion is proposed to calculate the elastoplastic solutions for surrounding rock of the circular tunnel. The comparisons of stress, displacement, and plastic zone radius are carried out between the presented method and published literatures under axisymmetric and nonaxisymmetric original in situ stress field. Finally, a series of parametric analyses are executed and discussed. It can be concluded that the lateral pressure coefficient, λ, influences both the size of plastic zone and the development direction. The plastic zone radius shows a negative power function change with increasing critical deviatoric plastic strain and increases slightly with increasing dilation angle, ψ.

Cracking mechanism and strength criteria evaluation of granite affected by intermediate principal stresses subjected to unloading stress state

Extensive true-triaxial unloading tests are conducted on rectangular Miluo granite specimens to investigate their crack propagation behavior and peak unloading strength properties. Experimental results demonstrate that their failure mode transforms from shear to slabbing with the increase in intermediate principal stresses σ2. Under a lower value of σ2, the dominant failure mode represented by the macro shear band is composed of several meso-extensional cracks parallel to the maximum principal stress σ1, and the fracturing process indicates intensive dislocation and slide owing to the normal force acting on extensional cracks. However, the increase in σ2 exacerbates the extensional cracks and further propagates them toward the end of the specimen along the direction of σ1, if σ3 is unloaded to 0. This is primarily due to the enhanced ability to resist mutual slide and squeeze among extensional cracks in the shear band, and the promotion of crack initiation and propagation in the unloading direction (σ3) owing to the provided free surface. The transformation of the cracking mode is revealed via three-dimensional combined finite/discrete element modeling, scanning electron microscope observations, and acoustic emission signal feature (average frequency, rise angle, Acoustic emission (AE) counts, and accumulated AE energy) analysis. The peak unloading strength exhibits an initial increase followed by a decrease as a function of σ2. Four rock-strength criteria are employed to evaluate the true-triaxial data with emphasis on predictability in practical applications and accuracy between best-fitting functions (experimental data) and theoretical (predicted) solutions. It is demonstrated that modified the Wiebols–Cook criterion and modified Lade criterion cannot accurately estimate the unloading strength throughout the true-triaxial data. Although the Mogi 1971 criterion fits the experimental data (higher correlation coefficients) well, it cannot be correlated to strength parameters (cohesion and internal frictional angle). Hence, it fails to predict the real strength values if complex true-triaxial unloading tests are not performed. The linear Mogi criterion is recommended for predicting the true-triaxial unloading strength of granite.

Modeling of Cutting Rock: From PDC Cutter to PDC Bit—Modeling of PDC Cutter

Summary The main purpose of this paper is to present our polycrystalline diamond compact (PDC) cutter model and its verification. The PDC cutter model we developed is focused on a PDC cutter cutting a rock in 3D space. The model studies the forces between a cutter and a rock and applies the theory of poroelasticity to calculate the stress state of the rock during the cutting process. Once the stress state of the rock is obtained, the model can then predict rock failure by the modified Lade criterion (Ewy 1999). This work also developed a trial-and-error procedure to predict cutting forces, and the stress state of a rock before cutting process is also considered. A complete verification of the cutter model is conducted. The model results (i.e., predicted cutting forces) are compared with measured cutting forces from cutter tests in multiple published articles. The major influencing factors on cutting forces—backrake angle, side-rake angle, depths of cut, worn depth (or wear flat area), and hydrostatic pressure—are all studied and verified. A good agreement between the model results and cutter test data is found, and the overall mean relative error is approximately 15%. The influence of inhomogeneous precut stress state of a rock is also studied. Overall, the cutter model in this paper is complete and accurate. It is ready to be integrated into a PDC bit model.

True triaxial strength and failure characteristics of cubic coal and sandstone under different loading paths

In deep underground coal mining, engineering activities are performed within anisotropic in-situ stress fields due to engineering disturbances and tectonic stress. Many such activities involve the development of excavations in soft rock and anisotropic coal. Accordingly, studying the mechanical properties of soft rocks is important for the stability of deep underground excavations. In this study, the deformation, strength, and failure characteristics of soft sandstone and raw coal under two different true triaxial loading paths were investigated using a self-developed true triaxial test apparatus. The results indicated that the inelastic strain in the pre-peak stage of sandstone and coal gradually increased with increasing intermediate principal stress. Also, the strength-drop in the post-peak stage increased. The crack initiation stress, crack damage stress, and peak strength of sandstone and coal first increased and then decreased with increasing intermediate principal stress for a given σ3. Moreover, with increasing intermediate principal stress, the failure mode of sandstone and coal changed from shear to tensile shear, and from brittle to semi-brittle. The linear Mogi criteria as found to characterize the true triaxial strength of coal well, while the modified Lade criteria was more applicable to soft sandstone. Owning to the symmetry assumption, the linear Mogi criteria predicted low strength when the intermediate principal stress coefficient exceeded to 0.5. In addition, the peak strength curve of rock on the π plane and the influence of weak structures on the failure mode of anisotropic coal was discussed. Weak structures have an important influence on the failure mode of coal, which depends on the strength difference between the structural plane and the coal rock mass. The strength envelope on the π plane had a significant stress Lode angle effect, which gradually decreased as the mean stress increased.

Study on Creep Characteristics and Constitutive Relation of Fractured Rock Mass

In order to effectively describe the whole creep process of fractured rock mass, triaxial unloading creep tests were carried out on prefractured coal samples using constant axial pressure and graded unloading confining pressure, and the axial and lateral creep laws of fractured coal samples with different dip angles were studied. Combined with the characteristics of creep curve and based on Kachanov’s creep damage theory, the damage variable is introduced into the constitutive relation and creep equation, and the evolution equation of damage variable with time in the whole creep process is derived. At the same time, a new method to calculate the initial damage is proposed. The elastoplastic body with damage variable is connected with the Burgers model in series. Meanwhile, lade criterion and switch element are introduced into the creep model to establish a new fracture damage creep model. The one-dimensional and three-dimensional damage creep equations are derived. The damage creep equation is obtained according to the superposition principle. A simple and feasible method for parameter identification of the model is given based on the characteristics of creep curve. The applicability of the model is verified by comparing the creep test curve of fractured coal sample with the theoretical curve. The results show that the two models are in good agreement. The model can not only accurately reflect the nonlinear characteristics of creep curves in the attenuation and isokinetic stages but also describe the accelerated creep characteristics of fractured rocks.

Assessing Wellbore Stability With a Modified Lade Failure Criterion

Abstract The importance of evaluating wellbore stability in analyzing and estimating the efficiency of drilling directionally into oil and gas reservoirs is well known. Geomechanical data and failure criterion can be used to model and control rock mass behavior in response to the stresses imposed upon it. Understanding and managing the risks of rock mass deformation significantly improve operational processes such as wellbore stability, sand production, and hydraulic fracturing. The modified Lade failure criterion is established as the most precise failure criterion based on previous studies. By combining it with tensions around the wellbore, a novel relationship is derived for determining the stable mud window. To investigate the accuracy of the new relationship, two geomechanical models (neural network and empirical correlations) for a one-directional wellbore are developed and their performance compared with two other failure criteria (Hoek–Brown and Mogi–Coulomb). The geomechanical parameters (Young’s modulus, Poisson ratio, uniaxial compressive strength, and internal friction coefficient) obtained from the models show that neural network configurations perform better than those built with the empirical equation. The horizontal minimum and maximum stress values across the depth interval of interest (2347–2500 m) are established for a case study reservoir. The model provides an accurate prediction of wellbore instability when applying the modified Lade criterion; the stable mud weight is derived with improved precision compared to the other failure criteria evaluated. A key advantage of the developed method is that it does not require input knowledge of the reservoir’s structural boundaries (e.g., the fault regime) or core test data.

Wellbore stability analysis and application to optimize high-angle wells design in Rumaila oil field, Iraq

Mechanical wellbore instability is one of the main issues during the drilling operations, this problem causes around 14% of drilling nonproductive time (NPT) for new wells in Rumaila oil field; these breakouts were commonly observed in the shale and weak shaly sandstones along Rumaila geological column. In this study, a quantitative wellbore failure analysis was carried out through applying modified Lade criteria on five wells in Rumaila oil field (A, B, C, E and F). The results gave a prediction of the appropriate mud density that can control the wellbore shear failure for any well type in order to eliminate or minimize wellbore instability and indicated that the preferred direction to drill deviated and horizontal wells should be parallel to maximum horizontal stress (NE–SW). The study also introduced the recommended drilling mud weight for vertical and deviated wells in Rumaila oil field for the sake of gaining wellbore stability which requires raising the drilling mud weight to more than 1.27 gm/cm3 starting from bottom of Sadi Formation to the well total depth. The results also showed that wells with low inclination (less than 30°) are less stable than highly inclination wells (more than 30°).

Selection of failure criteria for estimation of safe mud weights in a tight gas sand reservoir

In an undisturbed state, a stress field present in the earth consists of virgin stress in the rock. A change in this stress occurs due to drilling the borehole and disturbing the original stress by either introducing drilling fluids or by getting reservoir flow in the borehole. This change in stress leads to a classical problem of well bore instability. To resolve wellbore instability, evaluation of rock mechanical properties and in-situ stresses is essential. The output of this study is evaluation of safe mud weights which is critical to safe drilling. If the mud weight used for drilling is higher than those predicted by the failure criteria, the mud percolates into the formation, causing tensile failure (fracture stress) which induces fluid losses. Conversely, the lower mud weight results in shear failure (collapse stress) of rock leading to borehole breakout and collapse of wellbore. Three types of failure criteria i.e. Mohr-Coulomb, Mogi-Coulomb and Modified Lade are considered in this study. The stress around the wellbore is obtained using Kirsch equation. The input parameters required for estimating the safe mud weights from these failure criteria are rock mechanical properties, friction angle and cohesion which are estimated from well log data. The rock mechanical properties like Poisson's ratio and Uniaxial Compressive Strength are computed using sonic derived compressional and shear velocities. Internal friction angle is obtained using gamma ray log and is validated with core data before it is used in further analysis. The failure criteria have been applied to two wells located in a field in Gulf of Oman. The analyses show that the Mohr-Coulomb overestimates the mud weight while the Modified Lade criterion underestimates it. The result for a tight gas sand reservoir suggests that the Mogi-Coulomb predicts better mud weight values that are in agreement to those measured values chosen for drilling.

Quantitative comparison of fifteen rock failure criteria constrained by polyaxial test data

Failure criterion is a mathematical relationship with respect to applied stresses on rocks which shows the ultimate strength of rocks. Up until now, different investigations have been devoted for preparation of failure criteria. In this study, grid search and axis changing methods are used to compare various failure criteria for different types of rock with the experimental polyaxial test data. These criteria include; Mohr-Coulomb, Hoek-Brown, Bieniawski-Yudbir, linear, second order and power law form of Mogi 1967, linear, second order and power law form of Mogi 1971, Modified lade, Drucker-Prager, 3D Hoek-Brown, Modified Wiebols and Cook, HBMN and Modified Mohr-Coulomb. Polyaxial data were determined experimentally. The results show that, Mohr-Coulomb, Hoek-Brown and Bieniawski-Yudbir criteria in which intermediate stress is not included on rock failure, have the least accuracy and approximately have the same absolute relative error. Among all the criteria, the Modified Lade results have the best agreement with the experimental data. In particular, the Modified Lade criterion is the best choice for assessing wellbore stability in oil and gas wells drilling industry and mine tunneling.

A three invariant model of failure in true triaxial tests on Castlegate sandstone

To investigate the deformation mechanisms of rock under hydrostatic stress, destructive experiments were conducted on sandstone under different levels of hydrostatic stress and stress Lode angles. The results reveal that the shape of the strength envelope on the π plane gradually changes from the shape of the Lade criterion to the shape of the Drucker-Prage criterion with an increase in hydrostatic stress. Normally, there exists a deviation between the strain and stress paths for porous rocks on the π plane, and the deviation decreases with an increase in stress Lode angle and hydrostatic stress. A rock failure hypothesis based on the rock porous structure was proposed to investigate the reasons for the abovementioned phenomena. It was found that the shear expansion in the minimum principal stress direction is the dominant factor affecting the Lode angle effect (LAE); the magnitude of the hydrostatic stress induces the variation of the porous structure and influences the shear expansion. Therefore, the hydrostatic stress state affects the LAE. The failure hypothesis proposed in this paper can clarify the hydrostatic stress effect, LAE, and the variation of the rock strength envelope shape.

Detailed comparison of nine intact rock failure criteria using polyaxial intact coal strength data obtained through PFC3D simulations

Study of intact rock failure criteria is an important topic in rock mechanics. In this study, applicability of nine different intact rock failure criteria is investigated for intact coal strength data. PFC3D modeling was used to simulate the laboratory polyaxial tests for cubic intact coal blocks of side dimension 110 mm under different confining stress combinations. A modified grid search procedure is proposed and used to find the best-fitting parameter values and to calculate the coefficient of determination (R 2) values for each criterion. Detailed comparisons of the nine criteria are made using the following aspects: R 2 values, σ 1 − σ 2 plots for different σ 3, shapes on the deviatoric plane, linearity or nonlinearity on the meridian planes. Through the comparisons of R 2 values, σ 1 − σ 2 plots and meridian lines, the modified Wiebols–Cook and modified Lade criteria were found to fit the intact coal strength data best. The nine failure criteria are categorized into three types based on the appearances on the deviatoric plane.

A polyaxial strength model for intact sandstone based on Artificial Neural Network

A comprehensive database of the polyaxial compressive strength of eight sandstones has been compiled from the literature. An experimental study has also been conducted on local sandstone to add up to the database. A correlation-based analysis has been performed to find out the influence of each independent parameter namely uniaxial compressive strength (UCS, σci), minor principal stress (σ3), and intermediate principal stress (σ2) on the strength of sandstone, i.e., the major principal stress at failure (σ1). Additionally, a feed-forward back-propagating neural network (FFBPNN) has been proposed as a new polyaxial strength model to predict the strength of intact sandstone under polyaxial states of stresses. The database on polyaxial strength of 192 experiments on nine different sandstones has been randomly divided into a training set and a testing set. Three input parameters corresponding to the independent parameters (σci, σ3, σ2) and one output parameter corresponding to the dependent parameter (σ1) are considered. The accuracy of the proposed ANN based polyaxial strength model has been compared with five other conventional polyaxial criteria: modified Wiebols and Cook criterion (MWC), Mogi-Coulomb criterion (MC), modified Lade criterion (ML), 3D version of Hoek-Brown criterion (3DHB) and modified Mohr–Coulomb criterion (MMC). It is found that the ANN based failure model gives the best result amongst all the considered polyaxial strength criteria, for the testing dataset.

Anisotropic UH model for soils based on a simple transformed stress method

SummaryA simple method called anisotropic transformed stress (ATS) method is proposed to develop failure criteria and constitutive models for anisotropic soils. In this method, stress components in different directions are modified differently in order to reflect the effect of anisotropy. It includes two steps of mapping of stress. First, a modified stress tensor is introduced, which is a symmetric multiplication of stress tensor and fabric tensor. In the modified stress space, anisotropic soils can be treated to be isotropic. Second, a TS tensor is derived from the modified stress tensor for the convenience of developing anisotropic constitutive models to account for the effect of intermediate principal stress. By replacing the ordinary stress tensor with the TS tensor directly, the unified hardening model is extended to model the anisotropic deformation of soils. Anisotropic Lade's criterion is adopted for shear yield and shear failure in the model. The form of the original model formulations remains unchanged, and the model parameters are independent of the loading direction. Good agreement between the experimental results and predictions of the anisotropic unified hardening model is observed. Copyright © 2016 John Wiley & Sons, Ltd.

A New Improved Failure Criterion for Salt Rock Based on Energy Method

A non-linear triple shear energy yield criterion for salt rock is presented in this paper. It is the development of the triple shear energy yield criterion, of which the Mohr–Coulomb criterion can be seen as a special case. The main factors affecting the primary strength of salt rock, such as the mean stress and the Lode angle, are considered in the non-linear triple shear energy yield criterion. The non-linear new criterion provides the non-linear change trend of salt strength both in the I 1–J 2 stress space and in the deviatoric plane. Comparative study between the non-linear criterion predictions and experimental results of salt rock shows that the non-linear triple shear energy yield criterion fits quite well with both conventional triaxial test data and the true triaxial test data. For Maha Sarakham salt, the predictive capability of the non-linear triple shear energy yield criterion is clearly better than that of some other criteria used by Sriapai, such as modified Lade criterion, 3-D Hoek, and Brown criterion, Drucker–Prager criterion et al. The availability of the non-linear triple shear energy yield criterion can also be confirmed by comparative analysis between theoretical values and experimental values for non-salt rocks. So the non-linear triple shear energy yield criterion is a general failure criterion for rocks fractured by shear stress.