• Title/Summary/Keyword: Mohr-Coulomb

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Calculation of Failure Load of V-shaped Rock Notch Using Slip-line Method (Slip-line법을 이용한 V형 암석 노치의 파괴하중 계산)

  • Lee, Youn-Kyou
    • Tunnel and Underground Space
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    • v.30 no.4
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    • pp.404-416
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    • 2020
  • An analytical procedure for calculating the failure load of a V-shaped rock notch under two-dimensional stress conditions was developed based on the slip-line plastic analysis method. The key idea utilized in the development is the fact that the α-line, one of the slip-lines, extends from the rock notch surface to the horizontal surface outside the notch when the rock around the notch is in the plastic state, and that there exists an invariant which is constant along the α-line. Since the stress boundary condition of the horizontal surface outside the rock notch is known, it is possible to calculate the normal and shear stresses acting on the rock notch surface by solving the invariant equation. The notch failure load exerted by the wedge was calculated using the calculated stress components for the notch surface. Rock notch failure analysis was performed by applying the developed analytical procedure. The analysis results show that the failure load of the rock notch increases with exponential nonlinearity as the angle of the notch and the friction of the notch surface increase. The analytical procedure developed in this study is expected to have applications to the study of fracture initiation in rocks through wedge-shaped notch formation, calculation of bearing capacity of the rock foundation, and stability analysis of rock slopes and circular tunnels.

Prediction of Brittle Failure within Mesozoic Granite of the Daejeon Region (대전지역 중생대 화강암 암반 내 취성파괴 예측연구)

  • Jang, Hyun-Sic;Choe, Mi-Mi;Bae, Dae-Seok;Kim, Geon-Young;Jang, Bo-An
    • The Journal of Engineering Geology
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    • v.25 no.3
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    • pp.357-368
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    • 2015
  • Brittle failure of Mesozoic granite in the Daejeon region is predicted using empirical analysis and numerical modeling techniques. The input parameters selected for these techniques were based on the results of laboratory tests, including damage-controlled tests. Rock masses that were considered to be strong during laboratory testing were assigned to "group A" and those considered to be extremely strong were assigned to "group B". The properties of each group were then used in the analyses. In-situ stress measurements, or the ratio of horizontal to vertical stress (k), were also necessary for the analyses, but no such measurements have been made in the study area. Therefore, k values of 1, 2, and 3 were assumed. In the case of k=1, empirical analysis and numerical modeling show no indication of brittle failure from the surface to1000 m depth. When k=2, brittle failure of the rock mass occurs at depths below 800 m. For k=3, brittle failure occurs at depths below 600 m. Although both the Cohesion Weakening Friction Strengthening (CWFS) and Mohr-Coulomb models were used to predict brittle failure, only the CWFS model performed well in simulating the range and depth of the brittle failure zone.

Comparison of Shear Strength of Coarse Materials Measured in Large Direct Shear and Large Triaxial Shear Tests (대형 직접전단시험과 대형 삼축압축시험에 의한 조립재료의 전단강도 비교)

  • Seo, Minwoo;Kim, Bumjoo;Ha, Iksoo
    • Journal of the Korean GEO-environmental Society
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    • v.10 no.1
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    • pp.25-34
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    • 2009
  • Since the particle sizes of the coarse materials used in dam or harbor constructions are much larger than those of typical soils, it is desirable that large shear testing apparatuses are used when performing shear tests on the coarse materials to obtain as accurate results as possible. Two large-scale shear testing apparatuses, large direct shear testing apparatus and large triaxial shear testing apparatus, are commonly used. Currently in Korea, however, there have not been many cases in which shear tests were done using the large apparatus due to mainly difficulties in manufacturing, diffusing, and operating them. In present study, both large direct shear tests and large triaxial shear tests were performed on the coarse materials, which are used as dam fill materials, for 6 test cases in which particle sizes, specimen sizes, vertical pressure (confining pressure) conditions were little different, and then, the shear strength characteristics of the materials were compared with the two different shear tests. The test results showed that, by the Mohr-Coulomb failure criterion, overall the shear strength obtained by the large direct shear tests was larger than that by the large triaxial shear tests. Moreover, the shear strength under the normal stress of 1,000 kPa was about 10 to 70% larger for the large direct shear tests than for the large triaxial shear tests, revealing the larger differences in the coarse materials, compared to typical soils.

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Numerical Studies on Combined VH Loading and Inclination Factor of Circular Footings on Sand (모래지반에서 원형기초의 수직-수평 조합하중 지지력과 경사계수에 대한 수치해석 연구)

  • Kim, Dong-Joon;Youn, Jun-Ung;Jee, Sung-Hyun;Choi, Jaehyung;Lee, Jin-Sun;Choo, Yun Wook
    • Journal of the Korean Geotechnical Society
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    • v.30 no.3
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    • pp.29-46
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    • 2014
  • For circular rigid footings with a rough base on sand, combined vertical - horizontal loading capacity was studied by three-dimensional numerical modelling. A numerical model was implemented to simulate the swipe loading and the probe loading methods and an interpretation procedure was devised in order to eliminate the numerical error from the restricted mesh density. Using the Mohr-Coulomb plasticity model, the effect of friction angle was studied under the associated flow-rule condition. The swipe loading method, which is efficient in that the interaction diagram can be drawn with smaller number of analyses, was confirmed to give similar results with the probe loading method, which follows closely the load-paths applied to real structures. For circular footings with a rough base, the interaction diagram for combined vertical (V) - horizontal (H) loading and the inclination factor were barely affected by the friction angle. It was found that the inclination factors for strip and rectangular footings are applicable to circular footings. For high H/V ratios, the results by numerical modelling of this study were smaller than the results of previous studies. Discussions are made on the factors affecting the numerical results and the areas for further researches.

Numerical Studies on Combined VM Loading and Eccentricity Factor of Circular Footings on Sand (모래지반에서 원형기초의 수직-모멘트 조합하중 지지력과 편심계수에 대한 수치해석 연구)

  • Kim, Dong-Joon;Youn, Jun-Ung;Jee, Sung-Hyun;Choo, Yun Wook
    • Journal of the Korean Geotechnical Society
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    • v.30 no.3
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    • pp.59-72
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    • 2014
  • For circular rigid footings with a rough base on sand, combined vertical - moment loading capacity was studied by three-dimensional numerical modelling. Mohr-Coulomb plasticity model with the associated flow-rule was used for the soil. After comparing the results of the swipe loading method, which can construct the interaction diagram with smaller number of analyses, and those of the probe loading method, which can simulate the load-paths in the conventional load tests, it was found that both loading methods give similar results. Conventional methods based on the effective width or area concept and the results by eccentricity factor ($e_{\gamma}$) were reviewed. The results by numerical modelling of this study were compared with those of previous studies. The combined loading capacity for vertical (V) - moment (M) loading was barely affected by the internal friction angle. It was found that the effective width concept expressed in the form of eccentricity factor can be applied to circular footings. The numerical results of this study were smaller than the previous experimental results and the differences between them increased with the eccentricity and moment load. Discussions are made on the reason of the disparities between the numerical and experimental results, and the areas for further researches are mentioned.

Fracture Simulation of UHPFRC Girder with the Interface Type Model (경계형 모델을 사용한 초고강도 섬유보강 콘크리트거더의 파괴역학적 해석)

  • Guo, Yi-Hong;Han, Sang-Mook
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.23 no.1
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    • pp.81-94
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    • 2010
  • This paper deals with the fracture simulation of UHPFRC girder with the interface type model. Based on the existing numerical simulation of quasi-brittle fracture in normal strength concrete, constitutive modeling for UHPFRC I-girder has been improved by including a tensile hardening at the failure surface. The finite element formulation is based on a triangular unit, constructed from constant strain triangles, with nodes along its sides and neither at the vertex nor the center of the unit. Fracture is simulated through a hardening/softening fracture constitutive law in tension, a softening fracture constitutive law in shear as well as in compression at the boundary nodes, with the material within the triangular unit remaining linear elastic. LCP is used to formulate the path-dependent hardening-softening behavior in non-holonomic rate form and a mathematical programming algorithm is employed to solve the LCP. The piece-wise linear inelastic yielding-failure/failure surface is modeled with two compressive caps, two Mohr-Coulomb failure surfaces, a tensile yielding surface and a tensile failure surface. The comparison between test results and numerical results indicates this method effectively simulates the deformation and failure of specimen.

Evaluation of Weathering Intensity and Strength Parameter for Weathered Granite Masses (I) (화강 풍화암의 풍화도 및 강도정수의 평가 (I))

  • 이종규;장서만
    • Journal of the Korean Geotechnical Society
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    • v.19 no.2
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    • pp.227-236
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    • 2003
  • The evaluation of the reliable strength and deformation characteristics of weathered granite masses is very important for the design of geotechnical structure under working stress conditions. Various types of laboratory test such as triaxial compression test can be performed to determine the strength parameters. However, it is very difficult to obtain the representative undisturbed samples on the site and also the rock specimen cannot represent rock mass including discontinuities, fracture zone, etc. This study aims to investigate the strength and deformation characteristics of granite masses corresponding to its weathering and develop a practical strength parameter evaluation method using the results of PMT. To predict weathering intensity and strength parameters of the weathered granite masess in the field, various laboratory tests and in-situ tests including field triaxial test and PMT are carried out. Based on the results of weathering index tests, the classification method is proposed to identify the weathering degree in three groups for the weathered granite masses. Using the analytical method based on the Mohr-Coulomb failure criteria and the cavity expansion theory, the strength parameters of rock masses were evaluated from the results of PMT. It shows that weathering intensity increases with decreasing the strength parameters exponentially. The strength parameters evaluated with the results of PM almost coincide with the results of field triaxial test.

Parametric Study of Dynamic Soil-pile-structure Interaction in Dry Sand by 3D Numerical Model (3차원 수치 모델을 이용한 건조사질토 지반-말뚝-구조물 동적 상호작용의 매개변수 연구)

  • Kwon, Sun-Yong;Yoo, Min-Taek
    • Journal of the Korean Geotechnical Society
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    • v.32 no.9
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    • pp.51-62
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    • 2016
  • Parametric studies for various site conditions by using 3d numerical model were carried out in order to estimate dynamic behavior of soil-pile-structure system in dry soil deposits. Proposed model was analyzed in time domain using FLAC3D which is commercial finite difference code to properly simulate nonlinear response of soil under strong earthquake. Mohr-Coulomb criterion was adopted as soil constitutive model. Soil nonlinearity was considered by adopting the hysteretic damping model, and an interface model which can simulate separation and slip between soil and pile was adopted. Simplified continuum modeling was used as boundary condition to reduce analysis time. Also, initial shear modulus and yield depth were appropriately determined for accurate simulation of system's nonlinear behavior. Parametric study was performed by varying weight of superstructure, pile length, pile head fixity, soil relative density with proposed numerical model. From the results of parametric study, it is identified that inertial force induced by superstructure is dominant on dynamic behavior of soil-pile-structure system and effect of kinematic force induced by soil movement was relatively small. Difference in dynamic behavior according to the pile length and pile head fixity was also numerically investigated.

Development of Numerical Method for Large Deformation of Soil Using Particle Method (입자법을 이용한 토사의 대변형 해석법 개발)

  • Park, Sung-Sik;Lee, Do-Hyun;Kwon, Min-Ho
    • Journal of the Korean Geotechnical Society
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    • v.29 no.12
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    • pp.35-44
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    • 2013
  • In this study, a particle method without using grid was applied for analysing large deformation problems in soil flows instead of using ordinary finite element or finite difference methods. In the particle method, a continuum equation was discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. Soil behavior changes from solid to liquid state with increasing water content or external load. The Mohr-Coulomb failure criterion was incorporated into the particle method to analyze such three-dimensional soil behavior. The yielding and hardening behavior of soil before failure was analyzed by treating soil as a viscous liquid. First of all, a sand column test without confining pressure and strength was carried out and then a self-standing clay column test with cohesion was carried out. Large deformation from such column tests due to soil yielding or failure was used for verifying the developed particle method. The developed particle method was able to simulate the three-dimensional plastic deformation of soils due to yielding before failure and calculate the variation of normal and shear stresses both in sand and clay columns.

A Case Study on Earthquake-induced Deformation of Quay Wall and Backfill in Pohang by 2D-Effective Stress Analysis (2차원 유효응력 해석에 의한 지진시 포항 안벽구조물의 변형 사례 분석)

  • Kim, Seungjong;Hwang, Woong-Ki;Kim, Tae-Hyung;Kang, Gi-Chun
    • Journal of the Korean Geotechnical Society
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    • v.35 no.7
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    • pp.15-27
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    • 2019
  • The purpose of this study is to investigate the mechanism about damages occurring at quay wall and backfill in Youngilman Port during Pohang earthquake (M5.4) on November 15, 2017. In the field investigation, the horizontal displacement of the caisson occurred between 5 cm and 15 cm, and the settlement at backfill occurred higher than 10 cm. 2D-effective Stress Analysis was performed to clarify the mechanism for the damage. The input earthquake motion used acceleration ($3.25m/s^2$) measured at bedrock of Pohang habor. Based on a numerical analysis, it was found that the effective stress decreased due to the increase of excess pore pressure in the backfill ground and the horizontal displacement of the caisson occurred by about 14 cm, and the settlement occurred by about 3 cm. In backfill, the settlements occurred between 6 cm and 9 cm. This is similar to field investigation results. Also, it was found that the backfill soil was close to the Mohr-Coulomb failure line due to the cyclic loading from the effective stress path and the stress-strain behavior. It may be related to decreasing of bearing capacity induced by the reduction of effective stress caused by the increase of the excess pore water pressure.