Academic literature on the topic 'Mohr–Coulomb yield function'
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Journal articles on the topic "Mohr–Coulomb yield function"
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Giraldo-Londoño, Oliver, and Glaucio H. Paulino. "A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler– Pister and Willam–Warnke." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2238 (2020): 20190861. http://dx.doi.org/10.1098/rspa.2019.0861.
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An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr–Coulomb criteria—an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.
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Zhang, Tan, Song-Tao Lin, Hong Zheng, and Yan-Jiang Chen. "Elastoplastic Integration Method of Mohr-Coulomb Criterion." Geotechnics 2, no. 3 (2022): 599–614. http://dx.doi.org/10.3390/geotechnics2030029.
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A new method for implicit integration of the Mohr-Coulomb non-smooth multisurface plasticity models is presented, and Koiter’s requirements are incorporated exactly within the proposed algorithm. Algorithmic and numerical complexities are identified and introduced by the nonsmooth intersections of the Mohr-Coulomb surfaces; then, a projection contraction algorithm is applied to solve the classical Kuhn–Tucker complementary equations which provide the only characterization of possible active yield surfaces as a special class of variational inequalities, and the actual active yield surface is further determined by iteration. The basic idea is to calculate derivatives of the yield and potential functions with the expressions in the principal stresses and perform the return manipulations in the general stress space. Based on the principal stress characteristic equation, partial derivatives of principal stresses are calculated. The proposed algorithm eliminates the error caused by smoothing the corner of Mohr-Coulomb surfaces, avoids the numerical singularity at the intersections in the general stress space, and does not require the stress transformation needed in the principal stress space method. Lastly, several numerical examples are given to verify the validity of the proposed method.
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Seta, E., T. Kamegawa, and Y. Nakajima. "Prediction of Snow/Tire Interaction Using Explicit FEM and FVM." Tire Science and Technology 31, no. 3 (2003): 173–88. http://dx.doi.org/10.2346/1.2135267.
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Abstract A three-dimensional prediction model has been developed in which the interaction between snow and a rolling tire with tread pattern is considered. An explicit finite element method (FEM) and a finite volume method (FVM) are used to model tire and snow respectively. Snow deformation is calculated by the Eulerian formulation to solve the complex interaction between snow and tire tread pattern. Coupling between a tire and snow is automatically computed by the coupling element. Numerical modeling of snow is essential to the tire performance prediction on snow. In this study, snow is assumed to be homogeneous and considered to be an elasto-plastic material. The Mohr-Coulomb yield model, in which the yield stress is a single function of pressure, is adopted. This function is investigated by tire traction tests under a wide range of tire contact pressures using several tires with different inflation pressures and patterns. The predicted results using the Mohr-Coulomb yield model are compared with those using the Capped Drucker-Pragger and the Cam-Clay yield models. Snow traction of a tire featuring different tread patterns is simulated by this technology. Results are shown to be in good qualitative agreement with experimental data.
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Sloan, S. W., and J. R. Booker. "Removal of singularities in tresca and mohr-coulomb yield functions." Communications in Applied Numerical Methods 2, no. 2 (1986): 173–79. http://dx.doi.org/10.1002/cnm.1630020208.
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Linnik, E. Yu. "EVALUATING CONTACT STRESSES IN AN IMPACTOR PENETRATING A HARD SOIL." Problems of strenght and plasticity 82, no. 1 (2020): 52–63. http://dx.doi.org/10.32326/1814-9146-2020-82-1-52-63.
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Finite formulas have been derived for evaluating contact stresses in a rigid impactor penetrating a soil, taking into account the friction in the framework of the local interaction model. In analyzing dynamic deformation of the soil, its volumetric compressibility, shear resistance and initial strength are accounted for. The obtained evaluations of resistance to penetration of an impactor into the soil are based on a quadratic relation between the stress normal to the impactor surface and impact velocity. The authors have pioneered in deriving finite expressions for coefficients of a trinomial approximation as a function of experimentally determined physical-mechanical parameters of the soil - a dynamic compressibility diagram (a shock adiabat) and a yield strength - pressure diagram. Impact compressibility of soils is described based on Hugoniot's adiabat - a linear relation between shock wave velocity and mass velocity of the medium particles behind the shockwave front. Plastic deformation obeys the Mohr - Coulomb yield criterion with a constraint on the limiting value of maximal tangential stresses according to Tresca's criterion - the Mohr - Coulomb - Tresca plasticity condition. An earlier obtained analytical solution of a one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a half-space occupied by a plastic soil medium is used. A formula for determining critical pressure (a minimal pressure required for the formation of a cavity, accounting for internal pressure in the framework of Mohr - Coulomb's yield criterion) is also used, which generalizes a known solution for an elastic ideally plastic medium with Tresca's criterion. The derived formulas have been verified by comparing their results with the available data from experiments on the penetration of a steel conical impactor into a frozen sandy soil. It is shown that the disagreement between the numerical and experimental results is within 10%.
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Zhan, Tao, Tengfei Jiang, Shengbiao Shan, Fu Zheng, Annan Jiang, and Xinping Guo. "Research on Constitutive Model and Algorithm of High-Temperature-Load Coupling Damage Based on the Zienkiewicz–Pande Yield Criterion." Applied Sciences 13, no. 17 (2023): 9786. http://dx.doi.org/10.3390/app13179786.
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The mechanical properties of rock can be weakened under the influence of high temperatures. To describe the mechanical behavior of rock under the action of high temperature more accurately, based on the Zienkiewicz–Pande yield criterion, the damage variable Dc which accounts for the coupling between high temperature and load is introduced. According to plastic potential theory and plastic flow law, the iterative incremental method for a high-temperature and load-coupled damage constitutive model in Flac3D is deduced in detail and compiled into the corresponding dynamic link library file (.dll file). By modifying the shape function to degenerate into the Mohr–Coulomb constitutive model, an elastic–plastic analysis of an ideal circular tunnel is performed, and a comparison is made between calculation results obtained from the built-in Mohr–Coulomb constitutive model in Flac3D, proving the correctness of the secondary development program. Finally, numerical simulations are conducted to study the effects of high-temperature damage using rock uniaxial compression tests, and the model’s validity is established by comparing it with previous experimental results.
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Chakraborty, Manash, and Jyant Kumar. "Lower Bound Axisymmetric Limit Analysis Using Drucker–Prager Yield Cone and Simulation with Mohr–Coulomb Pyramid." International Journal of Computational Methods 12, no. 05 (2015): 1550023. http://dx.doi.org/10.1142/s0219876215500231.
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This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker–Prager (D–P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D–P yield cone with the Mohr–Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors Nc, Nq and Nγ have been computed, as a function of ϕ, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.
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Zhao, Jun-hai, Yue Zhai, Lin Ji, and Xue-ying Wei. "Unified Solutions to the Limit Load of Thick-Walled Vessels." Journal of Pressure Vessel Technology 129, no. 4 (2006): 670–75. http://dx.doi.org/10.1115/1.2767356.
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Unified solutions to the elastoplastic limit load of thick-walled cylindrical and spherical vessels under internal pressure are obtained in terms of the unified strength theory (UST) and the unified slip-line field theory (USLFT). The UST and the USLFT include or approximate an existing strength criterion or slip-line field theory by adopting a parameter b, which varies from 0 to 1. The theories can be used on pressure-sensitive materials, which have the strength difference (SD) effect. The solutions, based on the Tresca criterion, the von Mises criterion, the Mohr–Coulomb criterion, and the twin shear strength criterion, are special cases of the present unified solutions. The results based on the Mohr–Coulomb criterion (b=0) give the lower bound of the plastic limit load, while those according to the twin shear strength criterion (b=1) are the upper bound. The solution of the von Mises criterion is approximated by the linear function of the UST with a specific parameter (b≈0.5). Plastic limit solutions with respect to different yield criteria are illustrated and compared. The influences of the yield criterion as well as the ratio of the tensile strength to the compressive strength on the plastic limit loads are discussed.
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Ruggiero, Andrew, Gianluca Iannitti, Stefano Masaggia, and Federico Vettore. "ADI 1050-6 Mechanical Behavior at Different Strain Rates and Temperatures." Materials Science Forum 925 (June 2018): 196–202. http://dx.doi.org/10.4028/www.scientific.net/msf.925.196.
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An experimental characterization of the austempered ductile iron ISO 17804/JS/1050-6/S was performed carrying out tensile tests under different strain rates, temperatures and stress triaxiality levels. Then, composing a yield function surface, a hardening relation, and a damage criterion, a constitutive model was developed to describe the salient features of the observed macroscopic response. In particular, the Mohr-Coulomb yield function was selected to account for the pressure effect observed on the yield surface. A new hardening relation was proposed in order to account for both strain rate and temperature effects. The Bonora’s damage model, developed in the framework of the continuum damage mechanics, was adopted to capture the failure condition under different stress triaxiality levels. The damage model was appropriately modified to account for the effect of strain rate and temperature on the failure strain.
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Liu, Yuhang, Ruiqiang Bai, and Dongqing Li. "Study on the Strength and Yield Behaviors of Modified Silty Clay." Geofluids 2022 (July 16, 2022): 1–17. http://dx.doi.org/10.1155/2022/6337345.
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To study the strength and yield behaviors of the modified soil, a series of triaxial compression tests were carried out for modified silty clay with different contents of red Pisha sandstone and carbide slag, respectively. The test results showed that the strength variation of the modified soils are obviously nonlinear with the hydrostatic pressure increasing, and the nonlinear strength can be described by a modified critical state function. Then, the friction angle and the cohesive force of the modified soils were obtained according to the nonlinear Mohr-Coulomb equation, and the relationships between the friction angle, the cohesive force, and the hydrostatic pressure were studied. Finally, the yield behavior of the modified soil was investigated based on a generally criterion, and the yield surface of the modified soils locates between the SMP criterion and the Lade-Duncan criterion. This study will help to understand the strength and yield characteristics of modified soils.
Book chapters on the topic "Mohr–Coulomb yield function"
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Yu, Jian-qiang, Qi Li, Yong-lu Wang, and Shuai Tao. "Numerical Simulation of Rockburst Characteristics of Tunnel Surrounding Rock Under Dilatancy Effect." In Advances in Frontier Research on Engineering Structures. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-8657-4_15.
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AbstractRockburst is one of the most intense reactions in various instability phenomena of underground cavern surrounding rock, which seriously threatens the safety of underground engineering construction personnel and equipment. Based on Mohr–Coulomb strain softening model, the non-associated flow rule is adopted for plastic flow after material yield. By implanting Gu Ming-cheng and Tao Zhen-yu rockburst criterion in the software, the effects of different dilatancy angles on rockburst grade and circumferential stress distribution of surrounding rock of circular tunnel are simulated. The calculation results show that the larger the dilatancy angle is, the more difficult the rock burst pit is to form. The elements of serious rockburst are mainly concentrated in the wall of the tunnel, and the shear bands formed in the high value area of shear strain increment are short. When the dilatancy angle is small, the circumferential stress reaches the maximum at the interface of elastic-plastic zone. With the increase of dilatancy angle, the number of elements entering the plastic state and occurring medium and severe rockburst increases first and then decreases, while the number of elements occurring slight rockburst decreases monotonously. Different dilatancy angles have significant effects on the number of elements occurring rockburst at all levels.
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Tiwari, Binod, and Beena Ajmera. "Advancements in Shear Strength Interpretation, Testing, and Use for Landslide Analysis." In Progress in Landslide Research and Technology. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-44296-4_1.
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AbstractLandslides are devastating natural disasters that result in loss of life, property damage, and community disruption. They have global impacts, causing fatalities and economic losses, particularly in mountainous regions near densely populated areas. Landslides can be caused by natural factors, including water saturation from heavy rainfall, snowmelt, and changes in groundwater levels, as well as seismic activity such as earthquakes and volcanic eruptions. Human activities, such as altering drainage patterns, destabilizing slopes, and removing vegetation, also contribute to landslides. Construction and development on slopes, over-steepening, and improper land management practices can further increase the risk of landslides. A key component in understanding the stability of slopes will be knowledge of the shear strength of the soils involved. However, to do so, it will be necessary to understand the various measuring methods of shear strength, loading conditions, and other parameters. Different methods and tests are employed to determine the shear strength of soil, depending on the specific conditions and objectives. Direct shear tests are often utilized to measure peak and fully softened shear strengths. Triaxial tests, on the other hand, are suitable for assessing both peak and fully softened shear strengths under drained or undrained conditions. Generally, the ring shear device is preferred for measurements of the residual shear strengths. However, multiple reversal direct shear tests and specifically modified direct shear tests as well as triaxial tests have also been utilized for this purpose. The cyclic simple shear test is recommended as an effective technique for replicating in-situ conditions to investigate the cyclic resistance and post-cyclic shear strengths of soils. Several correlations have been developed in the literature to estimate various shear strengths, including the fully softened and residual shear strengths of soil, as summarized in this paper. These correlations utilize parameters such as the liquid limit, plasticity index, mineralogy, clay fraction, and effective normal stress. The undrained shear strength of over-consolidated soils can be captured with the use of the Stress History and Normalized Soil Engineering Properties (SHANSEP) method. Extending this approach with the use of the normalized undrained strength ratio can result in two correlations that can capture the undrained shear strength. The paper also presents correlations for the true and base friction angles to estimate the shear strength using Hvorslev’s theory. This allows for a departure from the use of the cohesion intercept and friction angle in the Mohr-Coulomb failure envelope, both of which are dependent on the over-consolidation ratio. The power function effectively represents the cyclic strength curves in soils with the curve fitting parameters a and b defining their shape and position. A correlation between the normalized undrained strength ratio and post-cyclic effective stress ratio to assess the undrained shear strength after cyclic loading was also introduced. This correlation was shown to also capture the effects of excess pore pressure dissipation and reductions in shear strength induced by a second cyclic load.
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Okajima K., Tanaka T., Zhusupbekov A., Baitassov T., Bazarbayev D., and Popov V. "Elasto-plastic FEM model for researching of problematic soil ground of St. Petersburg city." In Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering. IOS Press, 2009. https://doi.org/10.3233/978-1-60750-031-5-773.
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A test pit work was carried out in 2007 in the area of the Extension of Mariinsky Theatre. It was applied to the work to use sheet pile cofferdam. In the work large displacement of sheet pile was measured. We analyzed this work by our elasto-plastic FEM in total stress condision. In this study Mohr-Coulomb type yield function and Drucker-Plager type plastic potential were applied to constitutive equation. We decided the cohesion of each soil layer from the geological colum and the Young's modulus of the strut and sheet pile not to be able to get the detailed soil parameter and the sheet pile and strut data. For this analysis, it was obvious that the ineffective strut progressed the measured large displacement of the sheet pile.
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Murianni A., Federico A., and di Prisco C. "Progressive failure and the strain localization problem." In Proceedings of the 15th European Conference on Soil Mechanics and Geotechnical Engineering. IOS Press, 2011. https://doi.org/10.3233/978-1-60750-801-4-1275.
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In this paper progressive failure and activation of landslides in soils characterized by strain-softening mechanical behavior is numerically analyzed. As it is well known, the analysis of this phenomenon, from a computational point of view, presents many difficulties because the numerical procedures are often affected by lack of convergence, and because the solution may depend strongly on the mesh adopted. In order to overcome these numerical drawbacks, in the present study, finite numerical analyses of the stability of an ideal slope are performed by employing a non-local elasto-viscoplastic constitutive model. A yield function of the Mohr-Coulomb type is adopted, and the strain-softening behaviour of the soil is simulated by reducing the strength parameters at increasing deviatoric plastic strain. Four different versions of the same model are implemented, and the relative numerical results are critically compared.
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Anand, Lallit, Ken Kamrin, and Sanjay Govindjee. "Limits to elastic response." In Introduction to Mechanics of Solid Materials. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192866073.003.0010.
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Abstract This chapter presents conditions for determining the limits to elastic behaviour for isotropic materials. Common limiting theories are discussed, including models for brittle tensile failure and ductile yield. Rankine’s failure criterion for brittle materials in tension is discussed. For ductile yield of polycrystalline metallic materials, the pressure-independent Mises and Tresca yield conditions are discussed, and for yield of granular materials the pressure-dependent Coulomb–Mohr and Drucker–Prager yield conditions are presented.
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Anand, Lallit, and Sanjay Govindjee. "Limits to elastic response. Yielding and failure." In Continuum Mechanics of Solids. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198864721.003.0019.
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This chapter presents conditions for determining the limits of elastic behaviour for isotropic materials. The stress invariants of equivalent pressure, equivalent shear stress, and equivalent tensile stress are defined. These are then used to define common yield conditions, viz. the pressure-independent Mises and Tresca yield conditions, as well as the pressure-dependent Coulomb-Mohr and the Drucker-Prager yield conditions. Rankine’s failure criterion for brittle materials in tension, that is failure in a brittle material will initiate when the maximum principal stress at a point in the body reaches a critical value, is also discussed.
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Coombs W.M. and Crouch R.S. "Reuleaux plasticity: improving Mohr-Coulomb and Drucker-Prager." In Geotechnical Engineering: New Horizons. IOS Press, 2011. https://doi.org/10.3233/978-1-60750-808-3-241.
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The yielding of soil exhibits both a Lode angle dependency and a dependency on the intermediate principal stress. Ignoring these leads to a loss of realism in geotechnical analysis, yet neither of the widely used Mohr-Coulomb (M-C) or Drucker-Prager (D-P) models include both. This paper presents a simple pressure-dependent plasticity model based on a modified Reuleaux (mR) triangle which overcomes these limitations and yet (like the M-C and D-P formulations) allows for an analytical backward-Euler stress integration solution scheme. This latter feature is not found in more sophisticated (and computationally expensive) models. The mR deviatoric function is shown to provide a significantly improved fit to experimental data when compared with the M-C and D-P functions. Finite deformation finite-element analysis of the expansion of a cylindrical cavity is presented, verifying the use of the mR constitutive model for practical analyses.
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Mamaghani, Iraj H. P. "Application of Discrete Finite Element Method for Analysis of Unreinforced Masonry Structures." In Computational Modeling of Masonry Structures Using the Discrete Element Method. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-5225-0231-9.ch017.
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In this chapter, through some illustrative examples, the applicability of the Discrete Finite Element Method (DFEM) to analysis of unreinforced masonry structures such as rock pillars, open rock slopes, underground openings, tunnels, fault propagations, and fault-structure interactions is examined and discussed. In the numerical study, the behavior of contacts and blocks is assumed to be elasto-plastic or elastic. The Mohr-Coulomb yield criterion, representing material behavior of contacts, is implemented in the developed codes for DFEM used in the analysis. The secant stiffness method with the updated Lagrangian scheme is employed to deal with non-linear behavior. The constant strain triangular element with two degrees of freedoms at each node, formed by properly joining the corners and contact nodes of an individual block, is adopted for finite element meshing of the blocks. The DFEM provides an efficient and promising tool for designing, analyzing, and studying the behavior of unreinforced masonry structures.
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Putera Agung M A., Pramusandi S., Ardianto A., and Sunaryo B. "Assessment Analysis of Lateral Movement of Gate Shaft Structure on Fractured Rock Mass, Jatigede Dam Area, West Java, Indonesia." In Advances in Soil Mechanics and Geotechnical Engineering. IOS Press, 2014. https://doi.org/10.3233/978-1-61499-464-0-329.
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Gate shaft is one of parts the power waterway system of dam structure and as an intake vertical tunnel or well function for hydroelectric power plants in Jatigede area, Sumedang, West Java. Paper concerns some consideration in determining a constitutive model of soil and rock material. Comparison of existing lateral movement and the analysis results identified that Hoek – Brown failure criterion were more suitable than Mohr – Coulomb. Study analysis was carried out using without and with reinforcement system, the risk assessment to a rock shaft during excavation is greater than that to a soil shaft, even though the two averages designed safety factors are the same. For the analysis, it should be considered to use the failure criteria of intermediate material.
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Younian, Lü, and Cai Xiaohong. "APPLYING MOHR-COULOMB YIELD CRITERION TO CALCULATE ELASTOPLASTIC STRESS IN ADHESIVE SHOTCRETE AND ROCKBOLT LINING OF HYDRAULIC PRESSURE TUNNEL AND ITS SURROUNDING ROCK." In Proceedings of the International Symposium on Engineering in Complex Rock Formations. Elsevier, 1988. http://dx.doi.org/10.1016/b978-0-08-035894-9.50080-9.
Full textConference papers on the topic "Mohr–Coulomb yield function"
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Ma, Jeff, Joshua David Summers, and Paul F. Joseph. "Application of Meshless Integral Method in Soil Mechanics." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47046.
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An elastic-perfect plastic model associated with the Mohr-Coulomb yield criterion is applied to describe the behavior of soil material in the framework of Meshless Integral Method (MIM) [1][2]. In MIM, we obtained the governing integral equation from the weak form of elastoplasticity over a local sub-domain and the meshless function approximation is realized by using moving least-squares approximation. The advantages of this method are efficient removing of singularity by subtraction method, more accurate handling of the weak singularity, and the exact imposition of essential boundary conditions. Two flow rules of Mohr-Coulomb yield criterion are considered: associative and non-associative. Solution algorithm for elastoplastic analysis is given in detail. The results obtained through these two flow rules are compared and the meshless results are also compared to the FEM results. The numerical results show the accuracy and robustness of the meshless integral method in soil mechanics.
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Kumar, J. S., R. K. Kandasami, A. Chaudhuri, and E. Detournay. "Investigating the Deformation Characteristics of Dry Mohr-Coulomb Material During Radial Fluid Injection." In 58th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2024. http://dx.doi.org/10.56952/arma-2024-1201.
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ABSTRACT: Understanding of the deformation behaviour of porous geomaterials during fluid injection has direct relevance in several field applications. Studies exploring the resulting deformation field and instability growth within porous media during fluid injection remains limited. Prior research has focused on utilising steady-state/asymptotic cavity expansion models to study the deformation characteristics, with only a few transient models predicting the time-dependent cavity growth. Increased fluid pressure relative to porous material stiffness enhances fluid-solid coupling, inducing plastic deformations beyond linear poroelasticity. Hence, in this study, a transient cavity expansion model proposed by Kumar et al. (2024a) for dry porous media is used to investigate the poroelastic-plastic deformation characteristics during fluid injection. By introducing a new time dependent parameter known as the permeation coefficient, the model adeptly captures the fluid-induced transient behavior of dry porous media. It employs Mohr-Coulomb theory to represent the constitutive behavior under assumptions of small deformation and zero-far field stress. Further, the sensitivity of solid parameters such as porosity and yield strength are investigated for better understanding. During small deformation conditions, crucial dimensionless model parameters such as n and Y exerted significant control over interface growth. It's noteworthy that the expansion of the cavity radius and the elastic-plastic boundary were governed by the dimensionless constant Y. 1 INTRODUCTION The flow of fluid through porous media is critical in many geomechanics related applications such as grouting (Kandasami and Kumar, 2022; Christodoulou et al., 2021; Kumar and Kandasami, 2024; Kumar et al., 2024b), hydraulic fracturing (Peirce and Detournay, 2022; Konstantinou et al., 2023; de Borst, 2017; Kumar and Kandasami, 2021; Atefi Monfared and Rothenburg, 2016), energy extraction (Wang et al., 2018; Mujeebu et al., 2009; Kandasami et al., 2023), and tunneling (Lukose and Thiyyakkandi, 2022). The complexity of these problems lies in precisely coupling and modeling the fluid-solid interactions using appropriate constitutive models and boundary conditions. Further, the material and geometric non-linearity also influences the kinematic response of porous medium under both steady state and transient conditions. When fluid is injected into the medium, the pressure gradient across the boundaries results in permeation which induces an effective stress causing both elastic and plastic deformations. In addition to the permeation front, there exists an elastic-plastic deformation boundary which are a function of time (Huynen and Detournay, 2017). At larger time scales, the plastic deformation accumulates leading to the formation of instabilities (Konstantinou et al., 2021; Huang et al., 2012; MacMinn et al., 2015). Previous poroelastic-plastic models focused only on understanding the steady-state deformation characteristics of the saturated porous medium. However, the emphasis on the coupled time-dependent response of dry porous medium during fluid injection is not properly investigated. The existing time-dependent models (MacMinn et al., 2015, 2016; Auton and MacMinn, 2018) which are capable of predicting the fluid-induced poroelastic deformation, generally consider the fluid as a means of applying pressure (without considering the flux) on the saturated medium, while the coupled elastic-plastic responses are ignored. Recently, Kumar et al. (2024a) proposed a time-dependent poroelastic plastic model on a Mohr-Coulomb porous dry medium with a point source of injection. In this research, a parametric study on this model is carried out to understand the formation and evolution of permeation zone, plastic zone and the deformation characteristics along with the sensitivity analysis of the fluid and solid parameters on the interface growth.
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Chen, Haohua, Hehua Zhu, and Lianyang Zhang. "An Analytical Solution for Deep Circular Tunnels in Rock Based on GZZ Criterion." In 58th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2024. http://dx.doi.org/10.56952/arma-2024-0668.
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ABSTRACT: Tunnels in rock are often used for transportation, mining, and storage. It is important to perform accurate analysis and design so as to ensure the safety of tunnels during construction and operation. Currently, most of the analysis and design methods of tunnels in rock are based on the Hoek-Brown criterion, which ignores the effect of the intermediate principal stress (i.e., the three-dimensional (3D) strength) and might underestimate the rock strength. In this regard, this paper presents a new analytical solution for deep circular tunnels in rock with consideration of disturbed zone and 3D strength. The rock is assumed to be elastic–brittle– plastic and governed by a 3D Hoek–Brown yield criterion, the newly modified generalized Zhang-Zhu (GZZ) criterion. Based on the equilibrium equation, constitutive law, and large-strain theory, the governing equations for the stresses and radial displacement around the tunnel were derived and solved by using the programming language MATLAB. The proposed solution was validated by using it to analyze a tunnel and comparing the results with those from numerical analysis using commercial software FLAC3D. Finally, extensive parametric studies were performed on tunnels in both poor-quality and good-quality rock masses with a special focus on stresses and radial displacement of the rock mass. The proposed analytical solution can be used for the preliminary analysis and design of tunnels in different rock masses with the consideration of 3D strength. 1. INTRODUCTION Tunnels in rock are often used for transportation, mining, and storage. It is important to perform accurate analysis and design so as to ensure the safety of tunnels during construction and operation. Cavity contraction theory has been used to analyze tunnels by regarding the tunnel as a cylindrical cavity (Mair and Taylor 1993, Wang 1996, Carranza-Torres and Fairhurst 1999, Yu 1999). Early studies on cavity contraction were developed mostly using the linear Mohr-Coulomb criterion (Florence and Scher 1978; Kennedy and Lindberg 1978). To consider the non-linearity of rock, stresses and displacements around a tunnel were analyzed based on the original Hoek-Brown criterion with some simplifying assumptions (Brown et al. 1983; Wang 1996). Later, Carranza-Torres and Fairhurst (1999) presented an analytical solution to the cavity contraction problem in the original Hoek-Brown criterion-based rock mass without additional assumptions, but the elastic-perfectly-plastic behavior of rock mass was considered. Park and Kim (2006) provided a solution to tunnel in an elastic-brittle-plastic rock mass, but the Mohr-Coulomb criterion rather than the Hoek-Brown criterion was adopted as the potential function in their solution. Since both the Mohr-Coulomb and Hoek-Brown criteria are two-dimensional (2D) strength criteria with respect to the major and minor principal stresses, the intermediate principal stress was ignored in the abovementioned solutions. Wang et al. (2012) proposed a more general solution to the cavity contraction problem using the Mohr-Coulomb criterion by considering the out-of-plane stress, and the plastic strain in the out-of-plane direction was simply assumed to be zero. More recently, to consider the large strain around a tunnel, solutions based on the Mohr-Coulomb criterion were presented to analyze excavated tunnels (Park 2014; Zhang et al. 2019).
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Shen, Meng, Lei Qiao, and Ali Dogru. "Plasticity Modeling for Coupled Geomechanics and Reservoir Simulation for Large-Scale Reservoirs." In SPE Reservoir Simulation Conference. SPE, 2025. https://doi.org/10.2118/223903-ms.
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Abstract The objective of this work is to introduce the workflow for modeling plasticity in an in-house geomechanics simulator. The simulator is coupled with an in-house reservoir simulator through one-way and two-way coupling to perform large-scale reservoir geomechanics simulations. Plasticity is modelled using an implicit cutting plane algorithm in the finite element context, which is of second order convergence rate. The continuum tangent matrix is used to avoid second order derivative evaluation. For Mohr Coulomb plasticity, it has multi yield surfaces and the yield surfaces form corners (intersections). At these corners, the Koiter theorem is numerically implemented, which makes the stress return to the exact corner point. The isotropic strain hardening is included. These features make the in-house simulator suitable for modeling plasticity in large-scale models. This method can be used for a transversely isotropic medium. The workflow of the in-house simulator for plasticity modeling is verified with commercial software. Two types of plasticity yield functions for rocks are tested, Drucker Prager and Mohr Coulomb. Both the initialization stage and transient stages are compared. For both types of plasticity, the results match with commercial software. Moreover, the computational performance is also compared and shows an improvement over commercially available software. The simulation of plasticity modeling for a billion-cell reservoir has been performed to demonstrate the capability of the in-house simulator for studying gigantic field models. This work demonstrates the capability of modeling plasticity for billion cell reservoirs using an in-house geomechanics simulator. Use of the second order convergence rate plasticity algorithm and tangent matrix method offers a significant improvement in performance and efficiency when compared to a constant matrix (visco-plastic) approach typically used in commercial software.
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Gonzalez, Hector, Salem Algarni, and Ahmed Alqroos. "Improving Plugs Selection for Single-Stage Triaxial Tests with Micro-Rebound Hardness." In 58th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2024. http://dx.doi.org/10.56952/arma-2024-0712.
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ABSTRACT: The primary objective of this study is to characterize the full description mechanical properties of rocks. The study aims to achieve this characterization using single stage triaxial (SST) tests instead of multistage triaxial (MST) test by grouping non-consecutives plugs from the same rock mechanical type. A novel approach to address the challenge of obtaining enough samples from the same depth or target layer involves grouping samples based on their hardness using the Micro-rebound technique. This method offers a potential solution to the issue of limited samples and could help improve the reliability of failure envelope parameters, especially for cohesion and friction angle in the case of the Mohr-Coulomb failure envelope. The SST test results on the selected plugs using the hardness criteria shows very good calibration of the Mohr-Coulomb failure envelope and the possibility to study the post-failure behavior of the rock as function of the confining pressure. 1. INTRODUCTION A comprehensive laboratory rock mechanics characterization applicable to the majority of geomechanics applications on the oil & gas industry should include the determination of the static & dynamic elastic properties at different confining effective pressures, at least, up to the mean effective in-situ stress and the full description of the stress-strain behavior including the post-failure description or the residual strength. The primary objective of this study is to characterize the mechanical properties of rocks, specifically focusing on static elastic properties in relation to effective confining pressure, and key strength parameters such as unconfined compressive strength (UCS), residual strength, cohesion, and friction angle. The study aims to achieve this characterization using single stage triaxial (SST) tests instead of multistage triaxial (MST) test by grouping plugs from the same rock mechanical type. The study employs two variations of triaxial tests, namely the MST and SST tests and micro-rebound measurements. The key difference between these methods is that MST requires only one sample, while SST necessitates at least three samples for a comprehensive mechanical characterization. The MST test is favored when there are limited homogeneous samples within the target formation or layer. The SST test is considered a more reliable procedure for a comprehensive mechanical characterization of rock behavior. The micro-rebound test was used to measure the hardness of 12 plugs as a classification mechanical parameter for grouping purpose. MTS tests have high probability getting the rock failure before reaching the last stage or high probability of having premature stopping point when the test is manual of fully controlled by an operator. Also, the cumulative damage on each stage may influence the elastic properties, like having Poisson ratio equal or higher than 0.4 after the first stage could drive the evaluation of non-representative properties. Additionally, estimating the failure envelope from the yield envelope introduces uncertainty due to the wide range of mechanical behaviors exhibited by different rock types, and it is not possible to study the residual stress as a function of effective confining pressure. By grouping samples using the Hardness criteria and performing SST tests results indicate that the Mohr circles from each SST test are matching very well a Mohr-Coulomb failure envelope model and the full stress-strain curve is available to study the residual strength, however, some degree of variability was observed on the static elastic Young's modulus. One novel approach to address the challenge of obtaining enough samples from the same depth or target layer involves grouping samples based on their hardness using the micro-rebound technique. This technique assigns a mechanical parameter for grouping sets of three or four samples for the SST test at different confining pressures. This method offers a potential solution to the issue of limited samples and could help improve the reliability of failure envelope parameters, especially for cohesion and friction angle in the case of the Mohr-Coulomb failure envelope.
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Sysala, Stanislav. "Estimation of EDZ zones in great depths by elastic-plastic models." In Programs and Algorithms of Numerical Mathematics 21. Institute of Mathematics, Czech Academy of Sciences, 2023. http://dx.doi.org/10.21136/panm.2022.21.
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This contribution is devoted to modeling damage zones caused by the excavation of tunnels and boreholes (EDZ zones) in connection with the issue of deep storage of spent nuclear fuel in crystalline rocks. In particular, elastic-plastic models with Mohr-Coulomb or Hoek-Brown yield criteria are considered. Selected details of the numerical solution to the corresponding problems are mentioned. Possibilities of elastic and elastic-plastic approaches are illustrated by a numerical example.
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Yang, Zhenning, Carlton L. Ho, Richard Joy, and Nandan C. Dabhade. "Influence of Water Content on the Behavior of Partially Saturated Fouled Ballast." In 2016 Joint Rail Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/jrc2016-5724.
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The water content of fouled ballast is important when considering the shear strength and deformability of the ballast, and therefore critical in evaluating whether the track is at risk of excessive deformations warranting a speed restriction order. Fouled ballast from northeastern United States was tested in the laboratory to assess changes in shear strength and deformability as a function of water content. X-ray fluorescence analysis determined that the fouling material was 95% by weight basalt in origin. No more than 5% of the fouling material could be attributed to the abraded concrete ties. The field capacity of the fouled ballast was measured to be at a water content of 10%. Freezing and thawing tests indicated that approximately 4% of mass loss could be expected as a result of 25 freeze/thaw cycles. 6-inch triaxial tests, TX-CIDC, were conducted on the ballast at water contents between dry and field capacity (10%). As the ballast was partially saturated, volume change was measured using circumferential string potentiometers. The water content had an influence on the shear strength and the modulus of elasticity of the fouled ballast. The Mohr-Coulomb friction angle decreased from 47.3° for the dry ballast to 42.5° for the field capacity ballast. The Mohr-Coulomb cohesion decreased from 3.38 psi to nearly zero with initial addition of water, but increased to 6.18 psi as the water content reached field capacity. This is likely attributable to changes in capillary tension of the partially saturated fouling material. The average shear strength, Mohr-Coulomb friction angle, Mohr-Coulomb cohesion, modulus of elasticity and Poisson’s Ratio all showed weakening and strengthening effect by addition of water.
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Sable, Peter, and John P. Borg. "Mechanical Behavior of Thermosetting Polymers Undergoing High Strain-Rate Impact." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10459.
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Abstract A series of uniaxial and oblique flyer-plate impact experiments were conducted on fully dense, high durometer, polyurethane and epoxy formulations to investigate the high strain-rate dynamic material response. Samples were impacted at velocities ranging from 50 to 1,200 m/s at strain-rates of 105 – 106 s−1. The Hugoniot constants, yield strengths, and friction coefficients were inferred from velocity measurements taken from the back surface of the targets. Polymer Hugoniots were found to closely approximate those previously found in literature, with nonlinear curvature at low impact speeds due to viscoelastic effects. Strength behavior demonstrated pressure dependence which fit into a Mohr-Coulomb or Drucker-Prager yield surface criterion. Coefficients of friction between both epoxy and polyurethane, alongside a 7075-T6 aluminum tribological partner were quantified and results were used in conjunction with yield observations to hypothesize on the role of adhesion in high strain-rate shear of polymer-metal interfaces.
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Wang, X., S. L. Chen, Y. H. Han, and Y. Abousleiman. "A Graph-Based Drained Wellbore Stability Analysis in Mohr-Coulomb Rock Formation Under Hydrostatic in Situ Stress Field." In 58th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2024. http://dx.doi.org/10.56952/arma-2024-0097.
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ABSTRACT: This paper focuses on the development of a rigorous analytical solution for the drained wellbore drilling problem in a non-associated Mohr-Coulomb rock formation subjected to hydrostatic in-situ stress field, for a specific case that the axial/vertical stress is strictly the intermediate principal stress in the drilling process. The proposed solution is extended from the graphical analysis-based method recently proposed by Chen in 2024 for the cylindrical cavity expansion problem. The wellbore support pressure versus the contracted borehole radius, i.e., the well-known wellbore drilling curves, are numerically calculated through the radial equilibrium equation in the Lagrangian form. The graphical solution effectively avoids the common yet unnecessary intermediacy assumption for the axial/vertical stress in most existing wellbore drilling analyses. Selective numerical results are presented for the desired wellbore drilling curves and the impacts of some rock mechanical parameters on the calculated curves are also investigated. 1. INTRODUCTION Wellbore drilling in the petroleum industry is a process whereby natural resources, such as natural gas and oil, can be extracted from the rock formation. Wellbore stability must be maintained during both wellbore drilling and the well construction phase to support the structural integrity an oil and gas well. In the wellbore drilling, the rock mass inside the circular borehole is relaxed progressively and removed eventually, which results in the wellbore contraction. The stress field around the wellbore will also be redistributed, which is therefore necessary to be determined during the drilling process (Risnes et al., 1982). In the past few decades, the stress field around the wellbore undergoing drilling is primarily obtained based on the linear elasticity or poroelasticity theory (Al-Ajmi & Zimmerman, 2006; Bradley, 1979; Carter & Booker, 1982; Cui et al., 1997; Detournay & Cheng, 1988; Kanfar et al.; 2015; Mehrabian & Abousleiman, 2013). However, the rock mass around the wellbore will develop plastic deformation, which is inevitable in many scenarios (Charlez, 1997; Papanastasiou & Zervos, 2004; Potts & Zdravkovic, 1999). It follows that plastic deformation of rock occurs due to high stresses concentrated near and around the wellbore during active drilling operations (Ito, et al., 1998; Zoback, et al., 2003). The stress distribution determined based on the elastic analysis will be invalid after the rock mass runs into plasticity (Chen, et al., 2011; Huang, et al. 2018). Note that the plastic yielding state of a rock mass depends upon the stress state, the strength properties of the rock mass around the wellbore, and the plastic yield criterion for the rock mass. It should be emphasized that the end of the pure elastic deformation does not indicate the failure of the rock mass around the wellbore. Furthermore, an allowable tolerance plastic yielding around the wellbore induced by the drilling will not affect the wellbore stability but can reduce the collapsed mud weight subsequently the cost of the drilling job. It is, therefore, necessary to evaluate the elastoplastic behavior of the rock mass around the wellbore under the drilling process.
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Liu, Jun, and Yuxia Hu. "Numerical Simulation of the Installation and Extraction Process of Spudcan Foundations in Clay." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79222.
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This paper presents results from large displacement finite element analysis for spudcan foundation penetrating into and extracting from normally consolidated (NC) clay. The soil was idealized as an elastic-perfectly plastic material obeying a Mohr-Coulomb yield criterion and the large displacement analysis was carried out using Remeshing and Interpolating Technique with Small Strain (RITSS) model to simulate the full installation and extraction process. The numerical results were compared with centrifuge model test data and existing analytical solutions. A full parametric study was undertaken to quantify the influence on spudcan extraction process from soil strength profile, foundation interface roughness and penetration depth. The extraction results showed that the normalized uplift resistance after spudcan installation was much lower than that from small strain analysis, and it was also lower than that of pre-embedded case. Thus it is necessary to apply RITSS method in spudcan extraction simulation after installation.