Modified Mohr-Coulomb Failure Criterion Research Articles

Numerical study on the shear strength of granular materials under the low confining pressure

The relationship between stress and strength in granular soil differs under low confining pressure as compared to high confining pressure, which is of great importance for the geotechnical engineering. Numerical simulations using discrete element method (DEM) are conducted to model consolidated-drained triaxial compression tests, with the confining pressure σc ranging from 1 to1000 kPa. From the analysis of the shear strength of granular soils under various confining pressures and void ratios, it is found that the peak stress ratio ηp under a low σc is significantly lower than that under the high σc, particularly for samples with the same initial void ratio. As the confining pressure increases, ηp for samples with the same initial void ratio increases up to 29 % under the low σc while stabilizing under the high σc. Conversely, ηp for samples with the same void ratio after the consolidation can increase up to 13.5 % under the low σc while declining under the high σc. In addition, the critical confining pressure distinguishing the low and high confining pressures is about 200 kPa for dense samples with initial void ratio of 0.605 used in the study, and it increases as the sample void ratio increases. From the microscopic analysis, the variation of ηp under the low σc can be attributed to the enhanced anisotropy of normal contact force and contact normal under the low confining pressure. Finally, a modified Mohr-Coulomb failure criterion is proposed, which can determine the strength of granular soils under the low confining pressure with different void ratios.

Calibration of the Modified Mohr–Coulomb Failure Criterion and Its Application in the Study of Collision Response of Ship Hull Plate Frame Structures

Calibration of the Modified Mohr–Coulomb Failure Criterion and Its Application in the Study of Collision Response of Ship Hull Plate Frame Structures

Roof stability analysis of cylindrical tunnels in hard soil/soft rock with reduced tension strength

Three-dimensional roof stability analyses of cylindrical tunnel segments limited along the tunnel direction were performed based on the modified Mohr–Coulomb failure criterion with reduced tensile strength. A wedge-shaped region of the classical Mohr–Coulomb envelope, where unrealistic tensile and shear strengths are predicted, is truncated by a Mohr circle associated with the true tensile strength. This revised failure criterion with partial nonlinearity allows geomaterials deep into the roof to deform with large velocity gradients under the normality plastic flow rule, observed in field investigations. Using the kinematic approach of limit analysis, rigorous bounds for three quantitative stability measures–stability number, factor of safety, and supporting pressure–were calculated. The roof failure mechanism adopted is relatively elaborate, involving three-dimensional geometry intersecting with a cylindrical tunnel segment; thus, an efficient approach was presented for tunnels with long length constraints. With respect to extremely short tunnel lengths, a modified roof failure mechanism with distinct ridges was proposed. The factor of safety with accommodation of the nonlinear pressure dependency was estimated by a consistent procedure associated with a reduced elliptic failure criterion. The results show that roof stability distinctly depends on the magnitude of the true tensile strength, internal friction angle, and length constraint.

Multiaxial Strength and Deformations of Concrete, Failure Modes and a New Failure Criterion

The multiaxial strength of concrete, the associated stress-strain relationships, the failure modes and the failure criteria are again and again in the interest of researchers. After a historical review the most important bi- and triaxial experiments loading through brushes are analyzed. Based on the principal strengths and the loading path-concept a new, transparent type of presentation of the ultimate strength surface (USS) is introduced. For concrete classes ≤ C100 simplified relative strength-increase values are proposed. The difficulties of deformation measurements are reviewed. The outlines of future bi- and triaxial tests are discussed. Two failure modes are appointed. Stress failure criterion of biaxial state of stress are presented. Instead of the Modified Mohr-Coulomb failure criterion Extended Rankine-type failure criteria are proposed. Further systematic tests are necessary to detect the rate of participation of the loading equipment.

Edge punching shear of waffle slabs subjected to moment parallel to the slab's free edge

The test results of five one-tenth scale micro-concrete waffle slabs subjected to edge punching shear in the presence of moment transfer parallel to the slab's free edge are presented. Although the observed punching failure mechanism of the waffle slabs was found to be very similar to that of a flat slab, the shear capacity was reduced because some of the potential failure surface is lost when it extends into the waffle section. Since the current codes of practice do not specifically consider the punching shear mechanism of waffle slabs, comparisons with test results revealed that the application of various codes overestimated the punching capacities of waffle slabs. An upper-bound plasticity theory model was developed to predict the punching shear failure load. The proposed model assumes concrete to be a perfectly rigid plastic material with the modified Mohr–Coulomb failure criterion. The model showed good agreement with the test results.

A state parameter-dependent constitutive model for sands based on the Mohr-Coulomb failure criterion

Experimental data have demonstrated that a strong relationship exists between the state parameter and the peak strength and dilatancy characteristics of sands. This paper proposes a way of reproducing this behaviour using a modified Mohr-Coulomb failure criterion, which retains its simplicity while improving substantially its modelling capabilities. The formulated constitutive model is calibrated for Nevada sand following a well-defined procedure and used in the prediction of four centrifuge tests investigating the behaviour of axially loaded footings. It is shown that the proposed model reproduces well both the element tests and the more complex footing problems, demonstrating its usefulness for engineering practice. Moreover, a simplified version which does not require the definition of the Critical State Line is proposed for situations when this aspect of soil behaviour cannot be determined with confidence. It is shown that such simplification results in only slightly less accurate predictions than the full version of the model, while simulating aspects of soil response that cannot be reproduced using constant values for strength and dilatancy parameters.

Extended Rankine failure criteria for concrete

As possible failure criteria MC2010 refers to those of Rankine, Drucker-Prager and Mohr-Coulomb, respectively, and to modifications or combinations of them. After a brief overview of these failure criteria the characteristics of Mohr-circle are described. Next chapter discusses why the Modified Mohr–Coulomb failure criterion fails in case of concrete. Displaying the Mohr-circles of different bi- and triaxial test series reveal that neither the straight nor the parabolic failure criteria fit. The failure patterns of uniaxial compressive and tensile test specimens prove that concrete fails due to principal tensile stresses/strains in separation and concrete is not a frictional material. The proposed Extended Rankine failure criteria are based directly on the principal stresses. The criteria limit the greatest- and the actual smallest principal stress, respectively. This latter is function of the two other principal stresses. It is shown that the Ultimate Strength Surface cannot be properly described as stated by CEB Bulletin Nr. 156.

Upper-Bound Limit Analysis for Slope Stability Based on Modified Mohr–Coulomb Failure Criterion with Tensile Cutoff

Abstract Using the classical (linear) Mohr–Coulomb (M–C) failure criterion, the failure mechanism of slopes is commonly treated as a completely shear failure. However, the tension failure mechanism...

A constitutive model for modified cable bolts exhibiting cone shaped failure mode

This study presents a novel constitutive model to characterise the mechanical behaviour of cable bolts under axial loading and subjected to different boundary conditions including constant confining pressure and constant normal stiffness. Such a model is developed based on the modified Mohr-Coulomb failure criterion as well as a newly proposed non-linear dilation formulae for the development of governing equations. The cone shaped failure mode of grout due to the axial movement of cable bolt is considered as a widely observable failure mode at the cable bolt to the grout interface. The load carrying capacity of the cable bolt under axial loading is significantly affected by both the progressive reduction in the volume of failed cone zone of grout annulus and the continuous degradation of dilation angle at the cable bolt to the grout interface. Hence, the full load-displacement performance of different cable bolts under axial loading subjected to both constant confining pressure and constant normal stiffness are simulated. Finally, an acceptable agreement between the model simulations and the experimental data confirms the credibility of proposed constitutive model for predicting the mechanical behaviour of different cable bolts under axial loading.

Effect of landfill leachate on the hydromechanical behavior of bentonite-geomaterials mixture

The paper presents an experimental study on the compressibility, conductivity hydraulic (ksat) shear strength, unconfined compressive strength, and unconfined tensile strength and chemical characteristics of compacted bentonite- geomaterials mixtures for use as landfill bottom liners. To complete each experiment, MSW landfill leachate was used to determine the stress of strength under the effect of pollution on the mineralogy of the optimal mixture (the least permeable mixture). All three materials used in this study, including bentonite and two types of geomaterials (tuff and calcareous sand (crushed sand)) were obtained in the Laghouat, South Algeria, region. First, a study of the geotechnical properties of all selected materials and mixtures (under the effect of leachate) was carried out. A mineralogical survey was also conducted on these three materials to better understand the experimental results obtained. Measurements of the pH and EC of leachate-contaminated mixtures indicated a decrease in pH values and an increase in EC values. Interaction results of these mixtures with the MSW landfill leachate indicated that it reduces the compressibility behaviour, decrease the saturated hydraulic conductivity and increase the compressive strength and tensile strength. As for shear strength, an increase was observed in shear strength with an increase in calcareous sand content. The shear strength of the previously contaminated optimal mixture is shown an increase in the cohesion and a decrease in the friction angle. This observation was demonstrated by the Fang and Hirst (1973) method (Modified Mohr-Coulomb failure criterion). Finally, a consolidated drained study of the optimal mixture was carried out using a triaxial test. Results showed that the optimal mixture behavior is normally consolidated, and the internal friction angle value has attained 35°. It can be summarized that the 10% bentonite – 20% calcareous sand – 70% tuff mixture (named: B10CS20T70) meets the design requirements for landfill bottom liners.

Stability of plane strain tunnel headings in soils with tensile strength cut-off

This paper focuses on stability analysis of plane strain tunnel headings in soils governed by the modified Mohr-Coulomb failure criterion. In terms of a very small or even zero tensile strength of soils, the tensile strength cut-off is introduced to modify the classical Mohr-Coulomb failure criterion which allows a nonlinear strength envelope of soils in tensile regime. An improved rotational failure mechanism of tunnel face is constructed to search the portion that is subjected to tensile stress along the whole failure block. It is discovered that the face pressure is the most critical when the tensile stress only appears at the top of the failure block. The numerical results obtained by the proposed approach are compared with those without tensile strength cut-off to highlight its influence on tunnel face stability. The finite difference method of FLAC3D is employed to further validate the proposed approach. The variations of cohesion, internal friction angle and unit weight of soils as well as the dimensionless coefficient ξ are investigated using the proposed approach to gain some insight into the improved failure mechanism. The elementary energy analysis is performed by dividing the failure block into numerous infinitesimal elements with respect to the rotation angle to give some extended discussions. It is shown that the top portion of the failure block that plays a role of anti-sliding is cut away due to the tensile strength cut-off, which eventually yields the critical face pressure. Conclusively, the proposed approach is an improved method for the stability analysis of plane strain tunnel headings in soils with tensile strength cut-off.

A discrete numerical method for brittle rocks using mathematical programming

A computational formulation of discrete simulations of damage and failure in brittle rocks using mathematical programming methods is proposed. The variational formulations are developed in two and three dimensions. These formulations naturally lead to second-order cone programs and can conveniently be solved using off-the-shelf mathematical programming solvers. Pure static formulations are derived so that no artificial damping parameters are required. The rock is represented by rigid blocks, with interfaces between blocks modelled by zero-thickness springs based on the rigid-body–spring network method. A modified Mohr–Coulomb failure criterion is proposed to model the failure of the interfaces. When the interface’ strength limits are reached, a microscopic crack forms and its strength is irreversibly lost. The microscopic elastic properties of the springs are related to the observed elastic behaviour of rocks with the developed empirical equations. The program is first validated with three simple tests. Then, numerical uniaxial and biaxial compression tests and the Brazilian tests are conducted. Furthermore, the proposed approach is employed to study the rock crack propagation and coalescence using cracked Brazilian disc test. The results are in good agreements with reported experimental data, which shows its potential in modelling mechanical behaviour of brittle rocks.

Granular contact dynamics with elastic bond model

This paper proposes an elastic bond model in the framework of contact dynamics based on mathematic programming. The bond model developed in this paper can be used to model cemented materials. The formulation can be reduced to model pure static problems without introducing any artificial damping. In addition, omitting the elastic terms in the objective function turns the formulation into rigid bond model, which can be used for the modeling of rigid or stiffly bonded materials. The developed bond model has the advantage over the explicit DEM that large time step or displacement increment can be used. The tensile and shear strength criteria of the bond model are formulated based on the modified Mohr–Coulomb failure criterion. The torque transmission of bonds is introduced based on rolling resistance model. The loss of shear or tensile strength, or torque transmission will lead to the breakage of bonds, and turn the bond into purely frictional contact. Three simple examples are first used to validate the bond model. Numerical examples of uniaxial and biaxial compression tests are used to show its potential in modeling cemented geomaterials. Numerical results show that elastic bonds are indeed necessary for the modeling of cemented granular material under static conditions.

The effect of soil type on matric suction and stability of unsaturated slope under uniform rainfall

It is well understood that rainfall infiltration decreases the unsaturated shear strength of soil slope due to reduction in matric suction as the wetting front moves through it. However, how much the matric suction is reduced that may affect slope stability results is still unknown. The paper presents the numerical results of wetting front depth, matric suction and stability results in term of reliability index for a single rainfall intensity. The analyses are for five soils using the modified Mohr-Coulomb failure criterion in conjunction with a finite element saturated-unsaturated seepage model. The numerical results show that the matric suction results are differently affected for soils with rainfall infiltration. The change in reliability index result is insignificant as long the soil remains unsaturated as the wetting front moves. The reliability index results are however become noticeable if the infiltrated rainfall produces saturation and positive pore-water pressure. The difference in results may be attributed to the wetting front depth and its saturation that depends on saturated-unsaturated hydraulic conductivity and matric suction head.

Research on borehole stability of shale based on seepage-stress-damage coupling model

In oil drilling, one of the most complicated problems is borehole stability of shale. Based on the theory of continuum damage mechanics, a modified Mohr-Coulomb failure criterion according to plastic damage evolution and the seepage-stress coupling is established. Meanwhile, the damage evolution equation which is based on equivalent plastic strain and the permeability evolution equation of shale are proposed in this paper. The physical model of borehole rock for a well in China western oilfield is set up to analyze the distribution of damage, permeability, stress, plastic strain and displacement. In the calculation process, the influence of rock damage to elastic modulus, cohesion and permeability is involved by writing a subroutine for ABAQUS. The results show that the rock damage evolution has a significant effect to the plastic strain and stress in plastic zone. Different drilling fluid density will produce different damage in its value, range and type. This study improves the theory of mechanical mechanism of borehole collapse and fracture, and provides a reference for the further research of seepage-stress-chemical-damage coupling of wall rock.

Effect on Tailing Dam Stability of Rainfall Infiltration

Flow-deformation coupled unsaturated soil model is built based on rainfall infiltration condition and modified Mohr-Coulomb failure criterion according to modeling a tailing dam with ABAQUS software. A few conclusions are obtained by adopting proper hydraulic curve soil water characteristic curve and compared with actually measures data. Studies yields provide foundations for simulation analysis on tailing dam on the condition of rainfall infiltration.

Soil water balance model for precipitation-induced shallow landslides

Precipitation infiltration is one of the most significant triggering factors for slope failure occurrence in many places around the world. Knowledge of the mechanisms leading to precipitation-induced slope failures is of great importance to the management of landslide hazard. In this study, a soil water balance model is developed to estimate soil water flux during the process of infiltration from rainfall data, with consideration of storm periods and non-storm periods. Two important assumptions in this study are given: (1) instantaneous uniform distribution of the degree of saturation and (2) a linear relationship between evapotranspiration and the related degree of saturation. For storm periods, the Brooks and Corey model estimates both the soil water retention curve and soil water parameters. The infiltration partition is employed by an infinite-series solution of Philip in conjunction with the time compression approximation. For none-storm periods, evapotranspiration can be derived for the moisture depletion of soil water. This study presents a procedure for calculating the safety factor for an unsaturated slope suffering from precipitation infiltration. The process of infiltration into a slope due to rainfall and its effect on soil slope behavior are examined using modified Mohr–Coulomb failure criterion in conjunction with a soil water balance model. The results indicate that the matric suction, which is closely related to slope stability, is affected by the degree of saturation controlled by rainfall events.

Why permafrost rocks become unstable: a rock–ice‐mechanical model in time and space

ABSTRACTIn this paper, we develop a mechanical model that relates the destabilization of thawing permafrost rock slopes to temperature‐related effects on both, rock‐ and ice‐mechanics; and laboratory testing of key assumptions is performed. Degrading permafrost is considered to be an important factor for rock–slope failures in alpine and arctic environments, but the mechanics are poorly understood. The destabilization is commonly attributed to changes in ice‐mechanical properties while bedrock friction and fracture propagation have not been considered yet. However, fracture toughness, compressive and tensile strength decrease by up to 50% and more when intact water‐saturated rock thaws. Based on literature and experiments, we develop a modified Mohr–Coulomb failure criterion for ice‐filled rock fractures that incorporates fracturing of rock bridges, friction of rough fracture surfaces, ductile creep of ice and detachment mechanisms along rock–ice interfaces. Novel laboratory setups were developed to assess the temperature dependency of the friction of ice‐free rock–rock interfaces and the shear detachment of rock–ice interfaces. In degrading permafrost, rock‐mechanical properties may control early stages of destabilization and become more important for higher normal stress, i.e. higher magnitudes of rock–slope failure. Ice‐mechanical properties outbalance the importance of rock‐mechanical components after the deformation accelerates and are more relevant for smaller magnitudes. The model explains why all magnitudes of rock–slope failures can be prepared and triggered by permafrost degradation and is capable of conditioning long para‐glacial response times. Here, we present a synoptic rock‐ and ice‐mechanical model that explains the mechanical destabilization processes operating in warming permafrost rocks. Copyright © 2013 John Wiley & Sons, Ltd.

비등방 균질 댐의 정상상태에서의 침투면과 신뢰성지수

균질한 재료로 설계된 댐에서 수직 수평 투수계수가 서로 다를 경우에 이 비등방성 비율이 침투수의 침투면과 신뢰성지수에 어떤 영향을 주는지를 분석하였다. 정상상태에 있는 포화-불포화 침투수 현상을 유한요소법을 사용하여 분석하였다. 수평방향 투수계수를 고정한 상태에서 수직방향 투수계수만을 줄여주는 방법으로 여러가지 다른 비등방성 비율을 해석하였다. 댐제체의 전단강도는 수정된 모어-쿨롱 파괴기준을 사용하여 결정하였다. 해석 결과에 따르면 비등방성 비율이 증가함에 따라 침투면의 거리와 신뢰성지수는 증가하는 것으로 나타났으나 댐 상하류의 전체 수두차에 따라 차이를 보였다. 이러한 침투면과 신뢰성지수의 차이는 비등방성 비율이 변동함에 따라 등가수두선도 변화하는 현상에 의한 것으로 판단된다. This paper evaluates the effect of anisotropic conductivity on the seepage face and reliability index of an homogeneous dam with and without toe drain. The analysis are conducted under steady state saturated-unsaturated seepage condition using finite element method. Various anisotropic conductivity ratios were interpreted under such conditions as the vertical conductivity is reduced while the horizon conductivity is fixed. The shear strength of soil is defined by the modified Mohr-Coulomb failure criterion. The analysis results demonstrate that the length of seepage face and reliability index at the downstream and upstream of the dam increase with an increasing anisotropic ratio. These results of the seepage face and reliability index, however, depend on the total head difference between the upstream slope and downstream toe. The difference in seepage face and reliability index is attributed to the different equipotential head with different anisotropic ratios of the dam material.

Study on hydromechanical damage coupled model of Boom clay during tunnel excavation and construction

Based on the theory of continuum damage mechanics, a modified Mohr–Coulomb failure criterion according to plastic damage evolution and the hydromechanical coupling is applied to analyse the excavation damage of Boom clay influenced by the evolution of pore pressure and plastic strain. Considering the actual case of construction of the connecting gallery of radioactive waste disposal in the deep Boom clay formation in Belgium, a nonlinear finite element damage model for simulating shield tunnelling is proposed to study the evolution of damage, pore pressure and permeability of the surrounding rock. The variations of damage and permeability around the tunnel with time are analysed in detail. The proposed model is able to effectively depict the main features of hydromechanical behaviours of Boom clay. Therefore, the present model can provide references for the distribution, degree and evolution of damage and fractures self‐sealing process analysis of surrounding rock.