• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.7
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• pp.529-535
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• 2016

In this theoretical study, the strength parameters of the Drucker-Prager yield criterion and Mohr-Coulomb yield criterion were set to equal values, in order to analyze the correlation among the parameters. The Drucker-Prager strength parameters ${\alpha}$ and k were represented by the Mohr-Coulomb strength parameters c and ${\phi}$. Specifically it can be seen that k is function of c, ${\phi}$ and ${\alpha}$ is function of ${\phi}$ alone. Drucker-Prager strength parameter ${\alpha}$ increases as the internal friction angle of soil increases. ${\alpha}_{av}$ which is the average of ${\alpha}_c$ and ${\alpha}_i$ was proportional to internal friction angle in which ${\alpha}_c$ and ${\alpha}_i$ are ${\alpha}$ values corresponding to the circles of the Drucker-Prager yield cirteria circumscribes and inscribes the Mohr-Coulomb yield criterion respectively. The values of the ${\alpha}_{av}$ was 0.07 and 0.29 which correspond to the internal friction angle of $10^{\circ}$ and $45^{\circ}$ respectively. In addition, value of ${\alpha}_c/{\alpha}_i$ was proportional to internal friction angle of soil and the values of ${\alpha}_c/{\alpha}_i$ 1.12 and 1.62 which corresponds to internal friction angle of $10^{\circ}$ and $45^{\circ}$ respectively.The influence of the Mohr-Coulomb strength parameters on the Drucker-Prager strength parameter k was investigated and it was found that k was mainly influenced by the cohesion of the soil, except in the case of the minimum assumed value of c of 10kPa. The deviator stresses, $S_{c0}$ and $S_{t0}$, which correspond to the cases of the Mohr-Coulomb yield criterion under uniaxial compression and uniaxial tension, respectively, and $S_{0(ave)}$, which is the average value of $S_{c0}$ and $S_{t0}$, decrease as the internal friction angle increases. Furthermore, the hexagon, which represents the Mohr-Coulomb yield locus, becomes more irregular, and the deviations of $S_{c0}$ and $S_{t0}$ from $S_{0(ave)}$ also increase, as the internal friction angle increases.

• Fibers and Polymers
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• v.7 no.3
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• pp.276-285
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• 2006

Development and numerical implementation for an elastoplastic constitutive model for anisotropic and asymmetric materials are presented in this paper. The Coulomb-Mohr yield criterion was modified to consider both the anisotropic and asymmetric properties. The modified yield criterion is an isotropic function of the principal values of a symmetric matrix which is linearly transformed from the Cauchy stress space. In addition to the constitutive equation, the numerical treatment for the singularity in the vertex region of yield surface and stress integration algorithm based on elastoplasticity were presented. In order to assess the accuracy of numerical algorithm, isoerror maps were considered. Also, extension of a strip with a circular hole was simulated and results compared with those obtained using the (smooth) Mises yield criterion to validate stress output for a complex stress state.

• Geomechanics and Engineering
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• v.32 no.1
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• pp.49-68
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• 2023

The three-dimensional failure criterion is essential for maintaining wellbore stability and sand production problem. The convenient factor for a stable wellbore is mud weight and borehole orientation, i.e., mud window design and selection of borehole trajectory. This study proposes a new three-dimensional failure criterion with linear relation of three in-situ principal stresses. The number of failure criteria executed to understand the phenomenon of rock failure under in-situ stresses is the Mohr-Coulomb criterion, Hoek-Brown criterion, Mogi-Coulomb criterion, and many more. A new failure criterion is the extended Mohr-Coulomb failure criterion with the influence of intermediate principal stress (σ₂). The influence of intermediate principal stress is considered as a weighting of (σ₂) on the mean effective stress. The triaxial compression test data for eleven rock types are taken from the literature for calibration of material constant and validation of failure prediction. The predictions on rock samples using new criteria are the best fit with the triaxial compression test data points. Here, Drucker-Prager and the Mogi-Coulomb criterion are also implemented to predict the failure for eleven different rock types. It has been observed that the Drucker-Prager criterion gave over prediction of rock failure. On the contrary, the Mogi-Coulomb criterion gave an equally good prediction of rock failure as our proposed new 3D failure criterion. Based on the yield surface of a new 3D linear criterion it gave the safest prediction for the failure of the rock. A new linear failure criterion is recommended for the unique solution as a linear relation of the principal stresses rather than the dual solution by the Mogi-Coulomb criterion.

• Tunnel and Underground Space
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• v.15 no.3 s.56
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• pp.228-235
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• 2005

Friction angle and cohesion of rock masses can be estimated from Hoek and Brown failure criterion and then plastic corrections can be applied using Mohr-Coulomb yield function. This study finds that this estimation procedure would not be appropriate for weak rock masses and for cases where low confining stress is expected to develop. A procedure is outlined in this paper for estimating plastic corrections directly from Hoek and Brown material model. Comparative study shows that direct procedure would simulate non-linear failure surface better than indirect procedure especially in the low confining stress regime.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.04a
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• pp.17-20
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• 2000

Polymeric foams are excellent energy absorber and have found a wide range of applications especially in the automotive industry. The purpose of the present study is to develop experimental and theoretical methodology to characterize the pressure dependent yield behavior of polymeric foams. For the compression test in a triaxial stress sate a specially designed device was placed in a press machine to produce and control oil pressure. From the experiment results it was observed that the size of Mother circles is changed with mean normal stress in contrast to general metal. Then the Coulomb-Mohr criterion was applied to the data.

• Geomechanics and Engineering
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• v.36 no.4
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• pp.355-366
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• 2024

The original elastoplastic Hardening Soil model is formulated actually partly under hexagonal pyramidal Mohr-Coulomb failure criterion, and can be only used in specific stress paths. It must be completely generalized under Mohr-Coulomb criterion before its usage in engineering practice. A set of generalized constitutive equations under this criterion, including shear and volumetric yield surfaces and hardening laws, is proposed for Hardening Soil model in principal stress space. On the other hand, a Mohr-Coulumb type yield surface in principal stress space comprises six corners and an apex that make singularity for the normal integration approach of constitutive equations. With respect to the isotropic nature of the material, a technique for processing these singularities by means of Koiter's rule, along with a transforming approach between both stress spaces for both stress tensor and consistent stiffness matrix based on spectral decomposition method, is introduced to provide such an approach for developing generalized Hardening Soil model in finite element analysis code ABAQUS. The implemented model is verified in comparison with the results after the original simulations of oedometer and triaxial tests by means of this model, for volumetric and shear hardenings respectively. Results from the simulation of oedometer test show similar shape of primary loading curve to the original one, while maximum vertical strain is a little overestimated for about 0.5% probably due to the selection of relationships for cap parameters. In simulation of triaxial test, the stress-strain and dilation curves are both in very good agreement with the original curves as well as test data.

• Geomechanics and Engineering
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• v.8 no.6
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• pp.829-844
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• 2015

In the current paper the results of a numerical simulation that were verified by a well instrumented experimental procedure for studying the arching effect over a trapdoor in sand is presented. To simulate this phenomenon with continuum mechanics, the experimental procedure is modeled in ABAQUS code using stress dependent hardening in elastic state and plastic strain dependent frictional hardening-softening with Mohr Coulomb failure criterion applying user sub-routine. The apparatus comprises rectangular trapdoors with different width that can yield downward while stresses and deformations are recorded simultaneously. As the trapdoor starts to yield, the whole soil mass deforms elastically. However, after an immediate specified displacement, depending on the width of the trapdoor, the soil mass behaves plastically. This behavior of sand occurs due to the flow phenomenon and continues until the stress on trapdoor is minimized. Then the failure process develops in sand and the measured stress on the trapdoor shows an ascending trend. This indicates gradual separation of the yielding mass from the whole soil body. Finally, the flow process leads to establish a stable vault of sand called arching mechanism or progressive collapse of the soil body.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.03a
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• pp.434-443
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• 2009

Slope stability analysis is an essential part of rock slope design. For highly fractured rock, the limit equilibrium method (LEM) based slope stability analysis with a circular failure surface is often carried out assuming the rock mass behaves more or less as a continuum. This paper examines first, the applicability of the finite-element method (FEM) based shear strength reduction (SSR) technique for highly fractured rock slope, and second the use of Mohr-Coulomb (MC) failure criterion in conjunction with generalized Hoek-Brown (HB) failure criterion. The numerical results on a number of cases are compared in terms of the factor of safety (FS). The results indicated that the FEM-based SSR technique yields almost the same FSs from LEM, and that the MC and HB failure criteria yield almost identical FSs when the strength parameters for MC failure criterion are obtained based on the modified HB failure criterion if and only if value of the Hoek-Brown constant $m_i$ is smaller than 10 and slope angle is smaller than 1:1, otherwise MC failure criteria over-estimate the factor of safety.

• Computers and Concrete
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• v.31 no.4
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• pp.307-314
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• 2023

In this paper we back-analyze a failure event of a 9 m high concrete cantilever wall subjected to earth loading. Granular soil was deposited into the space between the wall and a nearby rock slope. The wall segments were not designed to carry lateral earth loading and collapsed due to excessive bending. As many geotechnical programs rely on the Mohr-Coulomb (MC) criterion for elastoplastic analysis, it is useful to apply this failure criterion to the concrete material. Accordingly, the back-analysis is aimed to search for the suitable MC parameters of the concrete. For this study, we propose a methodology for accelerating the back-analysis task by automating the numerical modeling procedure and applying a machine-learning (ML) analysis on FE model results. Through this analysis it is found that the residual cohesion and friction angle have a highly significant impact on model results. Compared to traditional back-analysis studies where good agreement between model and reality are deemed successful based on a limited number of models, the current ML analysis demonstrate that a range of possible combinations of parameters can yield similar results. The proposed methodology can be modified for similar calibration and back-analysis tasks.

• Transactions of Materials Processing
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• v.11 no.1
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• pp.69-74
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• 2002

In addition to lightweight and moldable characteristics, polymeric foams possess an excellent energy absorbing capability that can be utilize for a wide range of commercial applications, especially in the crashworthiness of the automobiles. The purpose of the present study is to develop experimental methodology to characterize the pressure dependent yield behavior of the energy absorbing polymeric foams. For the compression test in a triaxial stress sate, a specially designed device was placed in a hydraulic press to produce and control oil pressure. For the test material, the polyurethane foams of two different densities were used. The displacement of the specimen, the load subjected to the specimen, and oil pressure applied to the specimen were measured and controlled. Stress strain curves and yield stresses for the four different oil pressure were obtained. It was found from the present experiments that the polyurethane foams exhibited significant increases in yield stress with applied pressure or mean normal stress. Based on this observation, a yield criteria which included the effect of the stress invariant were established for the polymeric foams. The obtained experimental constants which constituted the pressure-dependent yield criterion were verified.