• The Journal of Engineering Geology
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• v.19 no.2
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• pp.153-163
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• 2009

In this study, a series of triaxial tests on Jeju basalt were carried out and then rock strength parameters were estimated by the Mohr-Coulomb failure criterion and the Hoek-Brown failure criterion using the test results. The characteristics of both failure criterions were investigated through comparing the estimated rock strength parameters. As the result of the Mohr-Coulomb criterion, the cohesions and the internal friction angles are determined as 5.35 MPa and $50.25^{\circ}$ of Pyoseonri basalt, 16.99 MPa and $60.66^{\circ}$ of Trachy-basalt, and 2.33 MPa and $37.05^{\circ}$ of Scoria, respectively. The cohesions and internal friction angles were estimated by the Hoek-Brown failure criterion in the basis of the results of regression analysis. The cohesions and the internal friction angles are determined as 4.77 MPa and $52.47^{\circ}$ of Pyoseonri basalt, 14.69 MPa and $60.70^{\circ}$ of Trachy-basalt, and 2.22 MPa and $47.60^{\circ}$ of Scoria, respectively. As the result of comparison between the Mohr-Coulomb failure criterion and the failure envelope predicted by the Hoek-Brown criterion, the cohesion estimated by the Hoek-Brown criterion is usually lower than that obtained from the Mohr-Coulomb criterion, whereas the friction angle estimated by the Hoek-Brown criterion is higher than that obtained from the Mohr-Coulomb criterion.

• Journal of the Korean Geotechnical Society
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• v.32 no.3
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• pp.15-27
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• 2016

In this study, a series of triaxial compressive strength tests were conducted for basaltic intact rocks sampled in the northeastern onshore and offshore, southeastern offshore and northwestern offshore of Jeju Island. Hoek-Brown constants $m_i$ were estimated from the results of the triaxial compression tests, and the properties of the Hoek-Brown constants $m_i$ were investigated. In addition, the cohesion and internal friction angle, strength parameters of Mohr-Coulomb failure criterion, obtained from the results of the triaxial compression tests were compared and analyzed with those estimated from Hoek-Brown failure criterion, respectively. As results, it was found that the Hoek-Brown constant $m_i$ is deeply related to the internal friction angle. As the internal friction grows, the Hoek-Brown constant $m_i$ increases exponentially. The cohesions estimated from the Hoek-Brown failure criterion, on average, are approximately 24% higher than those obtained from the Mohr-Coulomb failure criterion. The internal friction angles estimated from the Hoek-Brown failure criterion are similar to those obtained from the Mohr-Coulomb failure criterion.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.8
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• pp.748-755
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• 2012

Friction causes self-excited vibration, stick-slip vibration and any other friction-induced phenomena. That kinds of vibrations cause chatter and squeal. In order to predict such vibrations accurately, employing an accurate friction model is very important because a dynamic behavior of a system with friction is dominantly governed by a friction model. A Coulomb friction model is the most widely known model. Coulomb friction model is useful model to obtain analytical solutions of the system with friction and the model gives relatively good simulation result. However, defining a friction force at a stick state in simulation is hard because of the characteristic itself and a Coulomb friction model is discontinuous function between a static and a dynamic friction coefficient. Therefore, applying the Coulomb friction model to a simulation is not appropriate. In order to resolve these problems, an approximated Coulomb friction model was developed using simple and continuous function. However, an approximated Coulomb friction model cannot realize stick. Therefore, an approximated Coulomb friction model cannot describe friction phenomena accurately. In order to analyze a friction phenomenon accurately, a friction model for a simulation was proposed in this paper. A proposed friction model realizes stick and gives reasonably good results compared to results obtained by the simulation employing an approximated Coulomb friction model. Accuracy of a proposed friction model was verified by comparing experimental results.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1481-1486
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• 2007

Frictional laws are criticized with emphasis on their application to bulk metal forming simulation in this paper. Coulomb frictional law and constant shear frictional law are investigated in detail in terms of their effect on metal forming process. A friction sensitive bulk metal forming process, a long-pipe simultaneously shrinking and expanding process, is introduced and the problems of the constant shear frictional law are revealed comparing the predictions obtained by the Coulomb frictional law and the constant shear frictional law with the experiments. It is shown that the constant shear frictional law is improper in the case that the normal stress varies very much from position to position and that the normal stress is low compared with flow stress of the adjacent material. It is also shown that the Coulomb frictional constant is more or less affected by the normal stress.

• 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.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.6
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• pp.17-24
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• 2003

The main objective of this paper is to evaluate the control performance of a coulomb friction damper(CFD) for controlling the inelastic behavior of seismically excited structures, The seismic performances of various buildings are evaluated using capacity spectrum method(CSM), and the additional dampings are calculated If the evaluated performance levels of the buildings are below the target level. Maximum friction force of the CFD to achieve additional damping is provided using the concept of equivalent viscous damping, Numerical simulations for single degree of freedom(SDOF) systems with various structural periods and post yield stiffness ratios demonstrate the effectiveness of the proposed procedure.

• Tunnel and Underground Space
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• v.23 no.3
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• pp.219-227
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• 2013

Although Mohr-Coulomb failure criterion has limitations in that it is a linear criterion and the effect of the intermediate principal stress on failure is ignored, this criterion has been widely accepted in rock mechanics design. In order to overcome these shortcomings, the Hoek-Brown failure criterion was introduced and recently a number of 3-D failure criteria incorporating the effect of the intermediate principal stress on failure have been proposed. However, in many rock mechanics designs, the possible failure of rock mass is still evaluated based on Mohr-Coulomb criterion and most of practitioners are accustomed to understanding the strength of rock mass in terms of the internal friction angle and cohesion. Therefore, if the equivalent Mohr-Coulomb strength parameters of the advanced failure criteria are calculated, it is possible to take advantage of the advanced failure criteria in the framework of the Mohr-Coulomb criterion. In this study, a method expressing the tangential Mohr-Coulomb strength parameters in terms of the stress invariant is proposed and it is applied to the generalized Hoek-Brown criterion and the HB-WW criterion. In addition, a new approach describing the geometric meaning of the ${\sigma}_2$-dependency of failure criteria in 3-D principal stress space is proposed. Implementation examples of the proposed method show that the influence of the intermediate principal stress on the tangential friction angle and cohesion of the HB-WW criterion is considerable, which is not the case for the 2-D failure criterion.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.1
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• pp.9-16
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• 2020

The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.2
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• pp.105-112
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• 2023

In this study, structural analyses were conducted to analyze the performance of a bridge to which friction pendulum systems (FPSs) were applied using different friction models. A Coulomb friction model and a rate dependent friction model were constructed using the friction coefficient of a PVDF/MgO friction material to analyze the effect of different friction analysis models. The Coulomb friction model uses a single friction coefficient regardless of friction velocity, while the rate dependent friction model can reflect the change in the friction coefficient with friction velocity. Nonlinear time history and seismic fragility analyses were conducted to confirm responses of the bridge. The seismic responses of a deck and a column were used to evaluate the performance of the base isolated bridge, and a friction model that can effectively evaluate the performance of isolated bridges was analyzed.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.893-898
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• 2003

Coulomb friction is an important factor for precise position tracking control systems. The control systems with friction causes the steady state error because of being sensitive to the change of system condition and highly nonlinear characteristics. To overcome these problems, we use an estimation scheme of Coulomb friction to experiment for it's compensating. The estimated factor for Coulomb friction is used as a feed-forward compensator to improve the tracking performance of ball-screw systems. The tracking performance was improved by compensating the estimated friction torque in the feed-forward term. And, the sliding mode control which is derived from the Lyapunov stability theorem is applied for robust stability and reducing chattering. The experimental results show that the sliding mode controller with adaptive friction compensator has a good tracking performance compared with the friction uncompensated controller.