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Equivalent Friction Angle and Cohesion of the Generalized Hoek-Brown Failure Criterion in terms of Stress Invariants (응력불변량으로 표현한 일반화된 Hoek-Brown 파괴조건식의 등가 마찰각 및 점착력)

  • Lee, Youn-Kyou;Choi, Byung-Hee
    • Tunnel and Underground Space
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    • v.22 no.6
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    • pp.462-470
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    • 2012
  • Implementing the generalized Hoek-Brown failure criterion in the framework of the Mohr-Coulomb criterion requires the calculation of the equivalent friction angle and cohesion. In the conventional method based on the Balmer (1952)'s theory, the tangential instantaneous friction angle and cohesion are expressed in terms of the minimum principal stress ${\sigma}_3$, which does not provide the information about the dependency of the equivalent parameters on the hydrostatic pressure and the stress path. In this study, this defect of the conventional method has been overcome by representing the equivalent parameters in terms of stress invariants. Through the example implementation of the new method, the influence of the magnitude of the hydrostatic pressure and the Lode angle on the tangential instantaneous friction angle and cohesion is investigated. It turns out that the tangential instantaneous friction angle is maximum when the stress condition is triaxial extension, while the tangential cohesion is maximum when the stress condition is triaxial compression. The dependency of the equivalent Mohr-Coulomb strength parameters on the hydrostatic pressure and the Lode angle tends to be more substantial for the favorable rockmass of larger GSI value.

Dependency of Tangential Friction Angle and Cohesion of Non-linear Failure Criteria on the Intermediate Principal Stress (비선형 암석 파괴조건식의 접선 마찰각과 점착력의 중간주응력 의존성)

  • Lee, Youn-Kyou;Choi, Byung-Hee
    • 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.

A Laboratory Study on Erosional Properties of Fine Cohesive Sediments from Saemankeum Artificial Lake (새만금 인공호 점착성 퇴적물의 침식특성에 대한 실험적 연구)

  • Hwang, Kyu-Nam;Kim, Hyun-Min;Ahn, Ik-Jang
    • Journal of Korea Water Resources Association
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    • v.41 no.5
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    • pp.473-482
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    • 2008
  • The purpose of this study is to quantitatively estimate the erosional properties for cohesive sediment from Saemankeum artificial lake. A series of erosion tests were conducted with Chonbuk annular flume, which is the first one constructed in this country and verified with validities. Each erosion tests were conducted under a uniform bed condition but a different bed density respectively, and its critical shear stress for erosion(${\tau}_{ce}$) as well as the erosion rate coefficient (${\varepsilon}_M$) were determined quantitatively. Since the erosional properties of the cohesive sediments vary largely depending in the physico-chemical properties, such properties of Saemankeum sediments were also estimated and their effects on the erosional properties were analyzed. For Saemankeum sediments, it can be seen that ${\tau}_{ce}$ increases from $0.26N/m^2$ to $0.52N/m^2$ and ${\varepsilon}_M$ decreases exponentially from $14.28mg/cm^2\;hr$ to $6.02mg/cm^2\;hr$, as the bed density varies from $1.17g/cm^3$ to $1.34g/cm^3$. The erosional parameters of Saemankeum sediments are found to be remarkably different in quantity as compared with those for cohesive sediments from other sites. Particularly, ${\tau}_{ce}$ for Saemankeum sediments is known to be larger than that of Kunsan sediments but similar with that of Shihwa sediments, while ${\varepsilon}_M$ for Saemankeum sediments is shown to be smaller than that for Kunsan sediments.

Analytical Formula for the Equivalent Mohr-Coulomb Strength Parameters Best-fitting the Generalized Hoek-Brown Criterion in an Arbitrary Range of Minor Principal Stress (임의 최소주응력 구간에서 일반화된 Hoek-Brown 파괴기준식을 최적 근사하는 등가 Mohr-Coulomb 강도정수 계산식)

  • Lee, Youn-Kyou
    • Tunnel and Underground Space
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    • v.29 no.3
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    • pp.172-183
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    • 2019
  • The generalized Hoek-Brown (GHB) failure criterion developed by Hoek et al. (2002) is a nonlinear function which defines a stress condition at failure of rock mass. The relevant strength parameter values are systematically determined using the GSI value. Since GSI index is a value quantifying the condition of in-situ rock mass, the GHB criterion is a practical failure condition which can take into the consideration of in-situ rock mass quality. Considering that most rock mechanics engineers are familiar with the linear Mohr-Coulomb criterion and that many rock engineering softwares incorporate Mohr-Coulomb criterion, the equations for the equivalent friction angle and cohesion were also proposed along with the release of the GHB criterion. The proposed equations, however, fix the lower limit of the minor principal stress range, where the linear best-fitting is performed, with the tensile strength of the rock mass. Therefore, if the tensile stress is not expected in the domain of analysis, the calculated equivalent friction angle and cohesion based on the equations in Hoek et al. (2002) could be less accurate. In order to overcome this disadvantage of the existing equations for equivalent friction angle and cohesion, this study proposes the analytical formula which can calculate optimal equivalent friction angle and cohesion in any minor principal stress interval, and verified the accuracy of the derived formula.

A Study on the estimation of the flow characteristics and the bottom shear stress in an annular flume (환형수조의 내부 흐름특성 및 바닥전단응력 산정에 대한 연구)

  • Yang, Su-Hyun;Im, Ik-Tae;Hwang, Kyu-Nam
    • Proceedings of the Korea Water Resources Association Conference
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    • 2011.05a
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    • pp.176-176
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    • 2011
  • 환형수조는 점착성 퇴적물의 이송특성 연구를 위해 가장 선호되는 실험 장치로 알려져 있다. 과거 많은 연구자들은 퇴적물의 이송특성, 특히 침식/퇴적 특성 조사를 위해 주로 수로를 이용한 실험적 연구를 수행하였는데, 최초의 실험적 연구들은 주로 직선수조에서 수행되었다. 그러나 입자간의 응집이 중요한 역할을 하는 점착성 퇴적물의 경우에, 직선수조 끝단에서의 자유낙하 및 재순환 펌프의 날개에 의해 응집된 토사가 쉽게 분리될 수 있어 그 타당성이 의문시 되어 왔으며, 이러한 단점을 보완하기 위해 환형수조가 고안되었다. 환형수조는 수면과 접하여 회전하는 상부링의 마찰력에 의해 흐름이 생성되기 때문에 시간의 제약 없이 흐름조건을 동일하게 만들 수 있다는 큰 장점을 갖는다. 그러나 환형수조는 원주유속의 속도차이 및 원심력으로 인한 2차 순환류를 형성시켜 반경 방향(radial direction)에서의 바닥전단응력을 불균일하게 하는 단점을 갖는다. 이러한 2차 순환류와 바닥전단응력의 불균일을 저감시키기 위하여 환형수조의 몸체를 상부링의 회전 방향과 역방향으로 직접 회전시키는 방법이 채택되어져 왔다. 한편, 환형수조의 상부링과 몸체를 서로 역방향으로 동시에 회전시키는 양방향 회전(counter-rotation)의 적용을 위해서는 2차 순환류가 최소가 되며 바닥전단응력이 균일해지는 최적 회전속도비에 대한 분석은 필수적 사항이다. 이를 위하여, 상부링과 몸체의 회전속도에 따라 변화하는 수조내부의 흐름특성 및 평균바닥전단응력에 대한 연구가 선행되어야만 한다. 이에 본 연구에서는 전산유체역학을 이용하여 전북대에 설치된 환형수조의 상부링과 몸체의 회전속도에 따라 변화하는 수조내부에서의 흐름특성 및 바닥전단응력에 대한 분석이 수행되었다. 또한, 이를 기초로, 환형수조의 최적 회전속도비 산출을 위한 연구가 수행 중에 있다. 이러한 결과들은 추후 환형수조를 이용한 점착성 퇴적물의 침식/퇴적 등과 같은 이송특성 연구시, 퇴적물에 작용하는 흐름조건의 정밀산정을 위한 기초자료로 활용될 수 있을 것이다.

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Erosional Properties of the Newly Deposited Muddy Beds (갓 퇴적된 점토 저면의 침식특성)

  • Hwang, Kyu-Nam;Lee, Seung-Jong;Kim, Hyun-Min
    • Proceedings of the Korea Water Resources Association Conference
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    • 2008.05a
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    • pp.909-914
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    • 2008
  • 미세-점착성 퇴적물로 구성되는 퇴적저면의 침식특성을 해석하기 위해, 고령토 퇴적저면에 대한 침식실험이 환형수조를 이용하여 수행되었다. 현재, 퇴적저면의 침식특성 연구에 대한 국내사례는 전무한 실정으로, 본 연구는 퇴적저면에 대한 침식실험 방법 및 결과의 타당성 검증을 목적으로 한다. 이를 위하여, 본 연구에서는 압밀시간 조건에 따라 4가지의 서로 다른 퇴적저면이 조성되었고, 각 저면별로 저면깊이에 따른 저면밀도의 변화가 우선적으로 정밀 측정되었다. 각 퇴적저면별 침식실험으로부터는, 바닥전단응력(${\tau}_b$)의 변화에 따른 저면 침식깊이(즉, 수층 부유사 농도)의 변화 측정을 통하여, 저면깊이에 따른 저면전단강도(즉, 침식한계전단응력, ${\tau}_S$)의 변화 값들이 정량적으로 분석되었으며, 최종적으로 잉여전단응력(${\tau}_b-{\tau}_S$)과 침식률 간의 관계식이 산정되었다. 퇴적저면 침식특성에 관한 과거 해외 연구 결과와의 비교 검토를 통하여, 본 연구에서 사용 혹은 적용된 실험장치, 실험 방법 및 실험결과가 타당성이 있음이 확인되었다.

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Stress-strain Behavior of Sand Reinforced with Geocell (지오셀로 보강된 모래의 응력-변형 거동)

  • Yoon, Yeo-Won;Kim, Jae-Youn;Kim, Bang-Sik
    • Journal of the Korean GEO-environmental Society
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    • v.4 no.2
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    • pp.27-37
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    • 2003
  • In this research stress-strain behavior of composite geocell-soil systems under triaxial condition and the influence of strength due to the presence of geocell were studied. For the research a series of triaxial tests were carried out on sand specimens confined by flexible-walled single rubber cell. The diameter of all rubber cells placed at the center of the soil sample were 50 mm. Three rubber sizes, i.e. 35, 50 and 70 mm height, were applied to the soil specimen and the size of soil specimen was 50 mm in diameter and 100 mm in height. Three different densities of soil were used for the tests. In general, it was observed that the sand specimen develops an apparent cohesion due to the confinement by the geocell. The magnitude of this cohesion seemed to be dependent to the properties of the geocell material. The test results have shown that the geocell material for this research not only develops the apparent cohesion but also increases the angle of friction whereas geosynthetic material in the references showed only the increase of apparent cohesion. From the application of geocell-soil composites to the hyperbolic model, it was recognized that the determination of the peak strength influences the behavior of the geocell-soil composites.

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An analysis of erosional properties in Shihwa Lake : Local and spatial variation (시화호 점착성 퇴적물의 침식특성 해석 : 지엽적.공간적 변화)

  • Ryu, Hong-Ryul;Hwang, Kyu-Nam
    • Proceedings of the Korea Water Resources Association Conference
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    • 2007.05a
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    • pp.581-585
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    • 2007
  • 본 연구는 시화호 표층에 분포하는 점착성 퇴적물의 침식특성을 정량적으로 산정하고 산정된 침식특성의 지엽적 변화 및 타 지역 침식특성 결과와의 비교/분석을 통한 공간적 변화 해석을 목적으로 환형수조를 이용한 침식 실험을 수행하였다. 또한 퇴적물 자체의 물리 화학적 특성 및 해수 특성이 침식특성에 미치는 영향을 파악하기 위하여 시화호 점착성 퇴적물에 대한 물리 화학적 특성 및 해수 특성에 대한 분석이 수행되었다. 침식실험은 균일저면 조건에서 3개 지점에 대해 지점별로 $5{\sim}7$회씩 총 17회의 실험이 수행되었으며, 본 연구를 통하여 도출되어지는 시화호 점착성 퇴적물의 침식특성 매개변수들은 시화호 해역에서의 수층 탁도 분포 및 세굴/퇴적량 산정 등을 위한 수치모형실험 시에 기초 입력 자료로 크게 활용될 수 있을 것이다.

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An Experimental Study for Estimation of Erosion Rate of Fine Cohesive Sediments (미세-점착성 퇴적물의 침식률 산정을 위한 실험적 연구)

  • Hwang Kyu-Nam;So Sang-Don;Kim Tae-Min
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.17 no.2
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    • pp.119-128
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    • 2005
  • An annular flume has been constructed in order to estimate the erosion rate of fine cohesive sediments. Under an uniform bed condition, some erosion tests for Kaolinite sediments have been conducted to examine the performance of the flume and to check the validity of experimental method and results. In this study, the critical shear stress for erosion and the erosion rate coefficient are estimated and compared with the existing measurements. It is concluded that the performance of the annular flume is good enough to conduct erosion tests and the experimental method and results are valid.

An Experimental Study on Depositional Parameters of Cohesive Sediments in Semi-closed Bay (준 폐만 점착성 퇴적물의 퇴적매개변수 산정에 관한 실험적 연구)

  • Jung, Eui-Taek;Kim, Yong-Muk;Kim, Dong-Ho;Hwang, Kyu-Nam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.24 no.3
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    • pp.159-165
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    • 2012
  • In this study, a series of deposition tests have been performed using an annular flume and depositional parameters of natural cohesive sediments have been estimated domestically for the first time. The natural cohesive sediments for deposition tests have been collected from Kwangyang Bay and total 18 deposition tests have been carried out on different bed shear stress respectively but with the same initial concentration. Test results for natural cohesive sediments of Kwangyang bay show that minimum bed shear stress ${\tau}_{bmin}$, standard deviation ${\sigma}_1$, and time scale parameter $({\tau}_b^*-1)_{50}$ are $0.11N/m^2$, 0.68 and 0.85, respectively. Through the comparison with results of previous studies for other sediments, the results of this study are shown to be good enough to verify.