Mohr-Coulomb Criterion Research Articles

Investigation on the change of shear strength of concrete with cold joint under the action of sulfate dry–wet cycles

Large-volume concrete structures in the saline areas of Western China often have cold joint structural surfaces due to the improper handling of construction joints, dividing them into old and new layers of concrete. In this sulfate-rich environment, the shear strength of concrete with cold joint and the evolution pattern of its composition with the sulfate dry–wet cycles are particularly important in assessing the quality of the interface between old and new concrete bond surfaces. Therefore, in this paper, direct shear tests and microscopic scans were performed on concrete specimens with cold joint at different pouring age intervals and numbers of sulfate dry–wet cycles. The mechanism of the effect of both on the shear strength and failure mode of concrete was analyzed. Results show that the sulfate dry–wet cycles of erosion and the age interval have significant effects on the shear strength of the cold with cold joint and their components. As the number of sulfate dry–wet cycles increased, the shear dilation of concrete specimens with cold joints under direct shear action was reduced, the internal friction angle initially increased and then decreased for specimens with a short pouring interval (0–0.25 day), and the reduction of the internal friction angle of the specimens with a long pouring age interval (0.25–28 days) was nonlinear. The shear dilation of the specimen increased, and the internal friction angle decreased nonlinearly with the increase of the pouring interval. In addition, the failure criterion of specimens transformed from the bilinear Mohr–Coulomb criterion before erosion to the linear Mohr–Coulomb criterion under the action of sulfate dry–wet cycles.

A Three-Dimensional Elastoplastic Constitutive Model for Geomaterials

The Mohr-Coulomb (M-C) failure criterion has been a popular choice for geotechnical analysis because of its simplicity and ease of use. The fact that the M-C criterion disregards the intermediate principal stress’s impact is a significant drawback. As a result, the M-C criterion is only applied to materials under biaxial stress. This paper presents a three-dimensional version of the M-C criterion. The proposed criterion, called the Generalized Mohr-Coulomb (GMC) criterion, considers the intermediate principal stress’s effect, in addition to inheriting the original M-C criterion’s benefits. We obtained the conditions that the strength parameters must satisfy when the GMC criterion fulfills the π plane’s convexity. The GMC criterion can better describe geotechnical materials’ strengths under general stress conditions. Based on an implicit algorithm, the user material subroutine (UMAT) of the three-dimensional GMC model was developed in ABAQUS using the Fortran programming language. The established elastoplastic model’s validity and the program’s accuracy were examined using numerical simulation. Finally, a numerical simulation of a three-dimensional tunnel excavation under various working conditions was performed. The calculation results from the GMC model are precise and have some engineering-related practical significance.

Triaxial compression failure criterion and constitutive relation of concrete containing multiple solid wastes

This study analyzed the mechanical properties and failure criterion of full-solid waste concrete (SCT) made with slag, fly ash, carbide slag, soda residue, and iron tailings aggregate. SCT showed a higher strength growth rate (25.5–57.7%) compared to natural sand and gravel as aggregate (SCN) (20.7–47.5%), but lower than cement + natural sand and gravel (PCN) (32.0–86.1%), due to the latter's susceptibility to microcracks. The study proposed a parabolic pressure meridian failure criterion equation and an improved power function formulation of the Mohr-Coulomb failure criterion for SCT. The findings suggest that SCT can be used in engineering applications.

The Generalized Mohr-Coulomb Failure Criterion

With the construction of supertall buildings such as high earth dams, the linear envelope of the Mohr-Coulomb (M-C) failure criterion fitted to lower confined pressure would significantly underestimate the loading capacity of foundations, causing a huge increase in the amount of earthwork. Given that the M-C criterion has dominated in the stability analysis of geotechnical structures, it is proposed in this study that the M-C criterion remain invariant in form but the cohesion c and the frictional factor f be related to the coefficient of intermediate principal stress b, called the Generalized Mohr-Coulomb (GMC) criterion. In other words, c and f are both functions of b, written as c(b) and f(b). In the simplest way, the GMC criterion for soils, a true three-dimensional failure criterion, can be established by using a piece of conventional triaxial apparatus. The GMC has a non-smooth strength surface like its conventional version. However, we prove from true triaxial tests and the characteristic theory of stress tensors that the failure surfaces in the stress space should be non-smooth per se for b = 0 or 1. Comparisons with other prominent failure criteria indicate that the GMC fits the test data best.

A novel three-dimensional modified Griffith failure criterion for concrete

This study proposes a three-dimensional failure criterion based on the Griffith criterion, which accounts for the nonlinear influences of hydrostatic pressure and Lode angle on the failure strength of concrete. Two approaches are utilized in the proposed criterion to describe the Lode-dependence, one is to use the biaxial compressive envelopes to derive each meridian directly, and the other is to employ a scaling function between the compressive and tensile meridians. Besides, the proposed criterion can be expressed by the principal stresses in the form of f(σ1, σ2, σ3) = 0 as well as by the stress invariants in the form of J2 = f(P, θ). To comprehensively validate the proposed criterion, it collects 37 groups of tests with nearly 1000 test data conducted on concrete under biaxial and triaxial stress states. It demonstrates that predictions of the proposed criterion, including biaxial failure envelope, compressive meridian, tensile meridian, deviatoric section, and multiaxial strength, are close to the corresponding experimental observations. The proposed criterion requires four parameters, three of which have clear physical meaning, namely the tensile, compressive, and equal-biaxial compressive strength (ft, fc, and fbc), and the rest parameter n can be determined by the triaxial compressive strength. Aimed at elaborating the physical meaning of n, it interprets the proposed criterion as a combination of the original Griffith, Mohr-Coulomb, and Rankine criteria. In addition, a simple modification based on the proposed criterion is also suggested to describe the transformation from shear failure to ductile failure of concrete with the increase of pressure. Compared with the existing Ottosen and Willam-Warnke criteria, the proposed criterion is simple in determining parameters, convenient in the application, and diverse in describing the Lode-dependence.

Weakening Effect of Water on Mechanical Properties of Brittle Shale under Triaxial Compression

Abstract The mechanical properties of rock materials are remarkably affected by water. To reveal the effect of water on the mechanical properties of shale, the conventional triaxial compression tests were implemented for shale with the five kinds of water saturation coefficient. According to the test results, the influence of the saturation coefficient on strength and deformation parameters was analyzed. Based on the fitting result of the Mohr-Coulomb criterion, the relationship between the strength parameters and the water saturation coefficient was analyzed. The softening effect of water on shale is mainly due to the decrease of cohesion and internal friction coefficient with increasing of water saturation coefficient. The strength criterion considering the influence of water weakening was established according to the function relationship between the fitting parameters and the water saturation coefficient. In addition, three kinds of brittleness indexes were selected to quantitatively analyze the influence of the saturation coefficient on shale brittleness. The results indicated that the brittleness indexes all decreased with the increase of the saturation coefficient, and the brittleness of shale is weakened after water absorption. The research results can provide a reference for the evaluation of saturated shale brittleness.

Effect of gravel on rock failure in glutenite reservoirs under different confining pressures

Due to the existence of gravel, glutenite is heterogeneous and different from fine-grained rocks such as sandstone and shale in structure. To fully understand the effect of gravel on failure mode in glutenite, we performed triaxial compression tests on different glutenites. The results indicate that failure modes of glutenite are complex due to the existence of gravel. Under different confining pressures, three failure modes were observed. The first failure mode, a tensile failure under uniaxial compression, produces multiple tortuous longitudinal cracks. In this failure mode, the interaction between gravels provides the lateral tensile stress for rock splitting. The second failure mode occurs under low and medium confining pressure and produces a crack band composed of micro-cracks around gravels. This failure mode conforms to the Mohr-Coulomb criterion and is generated by shear failure. In this failure mode, shear dilatancy and shear compaction may occur under different confining pressures to produce different crack band types. In the second failure mode, gravel-induced stress concentration produces masses of initial micro-cracks for shear cracking, and gravels deflect the fracture surfaces. As a result, the fracture is characterized by crack bands that are far broader than in fine-grained rocks. The third failure mode requires high confining pressure and produces disconnected cracks around gravels without apparent crack bands. In this failure mode, the gravel rarely breaks, indicating that the formation of these fractures is related to the deformation of the matrix. The third failure mode requires lower confining pressure in glutenite with weak cement and matrix support. Generally, unlike fine-grained rocks, the failure mode of glutenite is not only controlled by confining pressure but also by the gravel. The failure of glutenite is characterized by producing cracks around gravels. These cracks are produced by different mechanisms and distributed in different manners under different confining pressures to form different fracture patterns. Therefore, understanding the rock microstructure and formation stress state is essential in guiding glutenite reservoir development.

Mechanical Characteristics of Underconsolidated Methane Hydrate-Bearing Clayed-Silty Sediments

Natural gas hydrate reserves in the South China Sea are huge, and their commercial prospects have been proved by repeated trial production. It is essential to systematically clarify the mechanical properties of hydrate-bearing sediments for the safe drilling of hydrate reservoirs. To date, most research studies focus on the undrained mechanical behavior of hydrate-bearing sandy or clayed sediments under normal consolidation conditions, but there are few reports on underconsolidated-undrained triaxial shear experiments. In this study, the present research conducts undrained triaxial shear tests on hydrate-bearing clayed-silty sediments. The results show that underconsolidated hydrate-bearing sediments appear to show a strain-hardening phenomenon, which are different from hydrate-bearing sands in Nankai Trough. The excess pore water pressure of hydrate-bearing sediments remains positive during shear. The increasing degree of consolidation will increase the failure strength and the Secant Young’s modulus E50. According to the Mohr–Coulomb criterion, the corresponding predicting formulas are established, and the cohesion increases with the increase in the degree of consolidation, while the internal friction angle is not sensitive to the degree of consolidation. In addition, the failure strength and the Secant Young’s modulus E50 increase with the increase in initial effective confining stress before shearing.

Research on the Failure Mechanisms and Strength Characteristics of Deeply Buried Mudstone under the Interaction of Water and Stress

Mudstone is a widely occurring type of rock in deep mining, and it is crucial to understand its failure mechanisms and strength characteristics under the interaction of water and high stress to ensure the stability of deeply buried engineered mudstone. In this study, the composition and the structure of mudstone were obtained, and triaxial tests were conducted on mudstone under five different water contents and four different confining pressures using a triaxial servo press. The variation rules for the peak strength and residual strength were obtained, and the applicability of the strength criteria was analyzed through fitting. The results showed that both the peak strength and the residual strength decreased linearly with increasing water content, with the peak strength decreasing more rapidly. Both the peak strength and the residual strength increased with increasing confining pressure, with the residual strength increasing more rapidly. The decrease in strength was primarily due to the decrease in cohesion, with the cohesion of the peak strength decreasing from 8.40 MPa to 0.94 MPa and the cohesion of the residual strength decreasing from 1.75 MPa to 0.82 MPa. The internal friction angle did not change much, with the internal friction angle of the peak strength decreasing from 41.57° to 37.29° and the internal friction angle of the post-peak strength increasing from 32.35° to 33.28°. For dry and low-water-content mudstone, the peak strength conformed to the Mohr–Coulomb criterion, while for mudstone with a higher water content, the peak strength conformed to the Hoek–Brown criterion. The residual strength conformed to the Hoek–Brown criterion. Under low and medium confining pressures, water played a dominant role in the damage pattern for the fractures produced by the initial damage to the mudstone. Under a high perimeter pressure, water played a guiding role for the fractures produced by the initial damage to the mudstone.

Damage Mechanism on Different Joint Types of Plain Concrete under Uniaxial Compression

Excavation of tunnels or chambers causes crack initiation, propagation and coalescence, resulting in the instability and destruction of underground projects. Understanding the damage mechanism of joint rock-like materials is important for maintaining the stability of concrete construction. Based on the Mohr–Coulomb criterion and Lemaitre strain equivalence hypothesis, the coupling-damage constitutive model of rock masses was improved for application to plain concrete. Parameters including the mesoscopic and macro-meso coupling damage variables, as well as the fractal dimension, were calculated to realize the non-linear mechanical behaviour during damage evolution. The rationality of the model was verified by comparing experimental and theoretical parameters. Results revealed that the coupled-damage constitutive model of rock masses has a good applicability to plain concrete. Furthermore, two main factors affected the damage deformation: the number of joints and the inclination angle. As the number of joints increased, the early damage accumulation increased and the inflection point of the damage rate occurred in advance. The damage deformation varied significantly when the inclination angle was changed. The cumulative damage curve of the plain-concrete specimens is shown as the evolution law of an S-type curve. Both peak strength and elastic modulus were positively correlated with the damage variable. Moreover, a smaller peak strength resulted in a larger fractal dimension and coupling-damage variable. KEYWORDS: Rock mass, Joint inclination angle, Mesoscopic, Macroscopic, Fractal dimension, Coupling-damage constitutive model.

Nonlinear Strength Reduction Method of Rock Mass in Slope Stability Evaluation.

As the strength parameters of rock mass degrade differently during slope instability, different factors should be considered in the strength reduction method. Previous nonlinear reduction methods were essentially implemented based on the Mohr-Coulomb criterion, which was reported not to reflect the nonlinear performance of rock mass. To address this deficiency, in this study, the Hoek-Brown criterion was combined with a nonlinear reduction technique for slope stability evaluation. Firstly, based on the classical definition of safety factors, the relationships that should be satisfied by each parameter of the critical slope were derived. The critical curve of the slope regarding the Hoek-Brown constant mb and the uniaxial compressive strength of rock mass σcmass was then obtained. On the assumption that the slope parameter deterioration conforms to the shortest path theory, the reduction ratio of σcmass to mb was determined. The more objective k-means algorithm was employed to automatically search the potential sliding surface, on which the slope safety factor was calculated as the ratio of sliding resistance to sliding force. Finally, the slopes in published literature were adopted for verification, and the calculated safety factors were compared with those by other methods, which showed better efficacy.

Stability analysis of artificial dam in coal mine underground water reservoir based on the hydro-mechanical damage model

A numerical hydro-mechanical damage model is proposed in this paper to investigate the stability and failure characteristics of artificial dam in coal mine underground water reservoir. The localized damage model for the coupled pore pressure and rock failure of a stressed rock is developed, and a local damage constitutive law is employed to describe its stress-strain relationship and fracture propagation. The Mohr-Coulomb criterion and maximum tension criterion are used to Judge the damage and failure of rock. Experimental data for rock samples are used to validate the proposed numerical model, and it accurately replicates the stress-strain curves and failure pattern compared with the experimental results. We then explore the influence of water pressures, cutting depth and dam strengths of artificial dam in coal mine underground water reservoir, and the simulation results show that the dam strength is the main factor affecting the strength of artificial dam. The modeling described herein is expected to assist in the management and optimization of underground water reservoirs.

Non-linear mechanical characteristics of tailings in large-scale high tailings dams

The non-linear mechanical characteristics of tailings under high pressure are the research foundation of large-scale high tailings dams. Considering the high stress caused by high tailing ponds, consolidated drained triaxial shear tests were carried out. The deterioration mechanism of non-linear mechanics was revealed by particle crushing. The test results show that sample density has a great influence on volumetric strain under low pressure. However, volumetric strain is not related to sample density under high pressure. The shear strength of the tailings is significantly non-linear. The internal friction angle under low pressure can still be obtained by the traditional linear Mohr–Coulomb criterion and the internal friction angle under high pressure by the power function of the Mohr criterion. The particle crushing of tailings occurs not only at high pressure but also at low pressure. The value of the breakage index increases with sample density. The non-linear mechanics of shear strength are affected by particle breakage. The breakage index value increases linearly with increasing shear strength, indicating that the high density of the deep part of the tailings dam is prone to particle crushing, which affects the stability of the large-scale high dam.

3D limit analysis of rock slopes based on equivalent linear failure criterion with tension cut-off

Hoek-Brown (HB) failure criterion is widely used to predict the strength of intact or heavily jointed rock mass. For stability analysis of rock slopes governed by the HB failure criterion, the equivalent linearity to Mohr-Coulomb (MC) criterion is often adopted, leading to the well-known equivalent Mohr-Coulomb method (EMCM). Existing studies on EMCM analysis mainly consider the shear strength of rock material, while consideration of the tensile strength is rare. This contradicts the fact that the underlying tensile strength of rock mass has considerable impact on the rock slope stability in real world. In this regard, this paper proposes a limit analysis-based approach that can account for tension in the three-dimensional (3D) stability analysis of HB rock slope. This approach is established on the equivalent linearity of the HB criterion with consideration of tensile strength, known as the equivalent tension cut-off MC method (ETMCM), and using a horn-like 3D mechanism of limit analysis. The safety factor solutions given by the proposed approach are validated by previous studies and numerical results. Parametric studies are conducted to investigate the effect of rock tensile strength on slope stability. Results show that the consideration of tension leads to a more conservative safety factor and a sharper curvature of the failure surface, and these impacts tend to be more obvious with the increases in slope inclination and slope width. Finally, the stability of the HB rock slope under seepage conditions is studied using the proposed approach. The results indicate that the effect of tensile strength is highly remarkable in seepage circumstances.

Failure mechanism and influencing factors of cement sheath integrity under alternating pressure

The failure of cement sheath integrity can be easily caused by alternating pressure during large-scale multistage hydraulic fracturing in shale-gas well. An elastic-plastic mechanical model of casing-cement sheath-formation (CSF) system under alternating pressure is established based on the Mohr-Coulomb criterion and thick-walled cylinder theory, and it has been solved by MATLAB programming combining global optimization algorithm with Global Search. The failure mechanism of cement sheath integrity is investigated, by which it can be seen that the formation of interface debonding is mainly related to the plastic strain accumulation, and there is a risk of interface debonding under alternating pressure, once the cement sheath enters plasticity whether in shallow or deep well sections. The matching relationship between the mechanical parameters (elastic modulus and Poisson's ratio) of cement sheath and its integrity failure under alternating pressure in whole well sections is studied, by which it has been found there is a “critical range” in the Poisson's ratio of cement sheath. When the Poisson's ratio is below the “critical range”, there is a positive correlation between the yield internal pressure of cement sheath (SYP) and its elastic modulus. However, when the Poisson's ratio is above the “critical range”, there is a negative correlation. The elastic modulus of cement sheath is closely related to its Poisson's ratio, and restricts each other. Scientific and reasonable matching between mechanical parameters of cement sheath and CSF system under different working conditions can not only reduce the cost, but also protect the cement sheath integrity.

Numerical study on cracking behavior and fracture failure mechanism of flawed rock materials under uniaxial compression

AbstractThe numerical approach is a vital means for evaluating the stability of flawed rocks. In this paper, the extended non‐ordinary state‐based peridynamics (NOSB‐PD) theory is employed to simulate the fracture process of rocks containing two pre‐existing flaws. Two stress criteria, including the maximum tensile stress criterion and the Mohr–Coulomb criterion, are implemented into the NOSB‐PD numerical method to respectively judge the tensile and shear failure of rock materials. The effects of inclination angles and ligament angles on the crack initiation and coalescence modes for flawed rocks are investigated based on the numerical results. The numerical results are in good agreement with the previous experimental results. The fracture mechanism of flawed rocks is revealed based on the evolutionary distribution characteristics of the maximum principal stress field and shear stress field obtained by the extended NOSB‐PD theory.

A failure envelope proposal based on the analysis of the requirements of nonlinear Mohr-Coulomb criteria

Nonlinear Mohr failure criterion is re-evaluated in this paper. It has been revealed that the polynomial failure criteria constructed by the normal stress σn and the shear stress τn predict the fracture angles unreasonably, and their predictions are also inconsistent with experimental observation that the two branches of failure envelope trend to be parallel to σn axis under high hydrostatic compression. In order to overcome the problems, first, the transformation of failure functions from the principal stress space (σ1, σ3) to the stress space (σn, τn) is derived. Then the failure function is expressed in terms of the principal stresses, and it is converted from the principal stress space (σ1, σ3) to the stress space (σn, τn) based on the transformation. The present failure criterion predicts more reasonable failure angles, and its envelope trends to be parallel to σn axis under high hydrostatic compression. In particular, the paper reveals that for brittle materials the fracture angle under the uniaxial tension is not 0° although the fracture surface is nearly perpendicular to the direction of the loading; under the pure shear stress the angle between the fracture surface and the direction of the loading is not 45° although it is close to 45°. The present criterion predicts this physical phenomenon reasonably.

Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming

Most of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit analysis. The conventional linear Mohr–Coulomb criterion is substituted with a nonlinear power law criterion to depict the nonlinearity of the soil strength. The non-associative feature of soil materials is considered by defining a nonlinear dilatancy coefficient. A generalized tangential technique is accordingly introduced to linearize the strength envelope for making the nonlinear criterion tractable in the analysis. A non-symmetrical translational failure mechanism that is comprised of several rigid wedges is used to characterize the failure of the foundation at the limit state. Moreover, the seismic action is considered by the classic pseudo-static method. Based upon the energy equilibrium theory of the upper-bound limit analysis, new analytical solutions are derived from the work-balanced equation with nonlinearity and dilatancy. This rigorous upper-bound solution is formulated as a multivariate optimization problem and is readily addressed by sequential quadratic programming (SQP). To verify the reliability of the new expressions, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. The comparative results show a good agreement with previous works, and the correctness and rationality of the new analytical solutions are validated. The detailed parametric study reveals that, in the non-associative flow soils, the ultimate bearing capacity is significantly decreased with a reduction in the dilatancy coefficient. Particularly in the linear condition, namely m = 1, the larger the internal friction angle is, the more obvious the influence of the non-associative feature on the bearing capacity is.

A Volume Averaging FEM-Based Fracture Model for Damage Process in Cohesive-Frictional Solids

In this study, a mesh-independent fracture model is implemented in the standard finite-element (FE) framework by leveraging a volume averaging approach. For the tension regime, a cohesive crack model is adopted for the onset and propagation of the crack, in which the direction of a new crack is defined as the eigenvector of the maximum principal stress. For the compression regime, the Coulomb criterion is considered for the onset and propagation of the crack, and the new crack direction is obtained based on the Mohr–Coulomb criterion by employing the residual friction angle. In addition, a new return mapping algorithm, i.e., the general return mapping, is developed for both compression and tension loading conditions to improve the numerical robustness, convergence, and accuracy. Finally, in order to validate the constitutive behavior, a stress-point calculation is performed, followed by boundary value problems to illustrate the robustness of the suggested return mapping algorithms and the mesh-independence effects of the volume averaging methodology.

Equivalent confining stress-based strength model for concrete under triaxial compression

In order to predict the peak strengths for different strength grades, types, or shapes of concrete under equal or unequal triaxial compression, the concept of equivalent confining stress is firstly proposed and then its calculation method for concrete specimens in the shape of a cube, an annulus, or a cylinder is illustrated. Next, a straightforward power-law type of prediction model is developed based on the aforementioned equivalent confining stress by comparing the following three common failure criteria adopted in triaxial compression: the Mohr-Coulomb failure criterion, the Willam-Warnke failure criterion, and the Power-law failure criterion. Furthermore, a rich experimental database that covers a wide parameter range is established according to the triaxial test results reported in previous literature. The model is thoroughly evaluated after calibrating the coefficients in the modified Power-law failure criterion. From the subsequent evaluation result, the proposed model can provide an accurate prediction for concrete under uniform or non-uniform triaxial compression. Besides, it also works effectively for different strength grades, types, or shapes of concrete specimens. In fact, in different conditions, the mean ratios of predicted-to-test peak triaxial strengths are all around unity, and the degrees of volatility of predicted results are all at a low level. In brief, this easily usable equivalent confining stress-based strength model can accurately predict the peak triaxial compressive strengths of concrete.