Slip-line법을 이용한 V형 암석 노치의 파괴하중 계산

이연규(Youn-Kyou Lee) 한국암반공학회 2020 터널과지하공간 Vol.30 No.4

2차원 응력조건에서 V형 암석노치의 파괴하중을 계산하는 해석적 절차를 slip-line 소성해석법 기반으로 개발하였다. 노치 주변의 암석이 소성상태에 있을 때 slip-line 중 하나인 ɑ선이 암석 노치 면과 노치 외부 수평면을 연결한다는 사실과 ɑ선을 따라서 변하지 않는 불변량이 존재한다는 이론적 사실이 해석적 절차 개발과정에서 핵심 아이디어로 활용되었다. 암석 노치 외부 수평면의 응력 경계조건을 알고 있으므로 불변량 방정식을 풀면 암석 노치 면에 작용하는 수직응력과 전단응력을 계산하는 것이 가능해진다. 노치 면에 작용하는 응력성분 값을 이용하여 쐐기에 의해 노치에 가해지는 파괴하중을 계산하였다. 개발된 해석적 절차를 적용하여 암석 노치파괴 해석을 수행하였다. 암석 노치의 파괴하중은 노치의 각도 및 노치 면의 마찰이 증가함에 따라 지수함수적 비선형성을 가지고 증가하는 특성이 있음을 해석결과는 보여주었다. 이 연구에서 개발한 해석적 절차는 쐐기형 노치 형성을 통한 암석균열 개시조건 연구, 암반 기초 지지력 계산, 암반사면 및 원형터널의 안전성 해석 등에 응용될 수 있을 것으로 기대된다. 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 ɑ-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 ɑ-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.

Slip line model for forces estimation in the radial-axial ring rolling process

Quagliato, Luca,Berti, Guido A.,Kim, Dongwook,Kim, Naksoo Elsevier 2018 International journal of mechanical sciences Vol.138 No.-

<P><B>Abstract</B></P> <P>In the research presented in this paper, a slip line-based model is proposed for the estimation of both radial and axial force in the radial-axial ring rolling (RARR) process. Based on the shape of the contact arcs between ring and tools in the two deformation gaps present in the ring rolling process, a recursive algorithm for the calculation of the two slip line fields starting from the two pairs of opposite tools is derived and implemented in a commercial spreadsheet software (MS Excel). By considering the stress boundary conditions applied to the portion of material undergoing the deformation, both for the radial and axial deformation gaps, the pressure factors those make the two slip line fields starting from the two opposite tools to intersect are calculated and utilized for the estimation of radial and axial forces, for each round of the process. The developed model has been validated by cross-comparing its results with those of laboratory experiment and numerical simulation. For the validation study case, the average deviations, in comparison to the experimental results, are calculated in 1.86% and 4.55% for the slip line force model whereas in 6.86% and 0.88% for the numerical simulation, for the radial and axial forces respectively. The proposed slip line model has been also utilized for the estimation of radial and axial forming forces of nine different study cases of flat rings having the outer diameter ranging from 800 mm to 2000 mm, observing a maximum deviation, in comparison to the relevant FEM simulation, of 4.92% (radial force) and 5.88% (axial force). The developed slip line force model allows estimating almost in real time and with a reasonable accuracy the process forces and, for this reason, it may be of interest for both industrial and academic researchers dealing with the set-up and control of the radial-axial ring rolling process.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Development of analytical slip line field construction algorithm. </LI> <LI> Slip line algorithm implementation and boundary conditions calculation procedure. </LI> <LI> Radial and axial force calculation in the ring rolling process. </LI> <LI> Model validation by comparison with experimental and numerical results. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>

Analysis of slope stability based on evaluation of force balance

Razdolsky, A.G.,Yankelevsky, D.Z.,Karinski, Y.S. Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.20 No.3

The paper presents a new approach for the analysis of slope stability that is based on the numerical solution of a differential equation, which describes the thrust force distribution within the potential sliding mass. It is based on the evaluation of the thrust force value at the endpoint of the slip line. A coupled approximation of the slip and thrust lines is applied. The model is based on subdivision of the sliding mass into slices that are normal to the slip line and the equilibrium differential equation is obtained as the slice width approaches zero. Opposed to common iterative limit equilibrium procedures the present method is straightforward and gives an estimate of slope stability at the value of the safety factor prescribed in advance by standard requirements. Considering the location of the thrust line within the soil mass above the trial slip line eliminates the possible development of a tensile thrust force in the stable and critical states of the slope. The location of the upper boundary point of the thrust line is determined by the equilibrium of the upper triangular slice. The method can be applied to any smooth shape of a slip line, i.e., to a slip line without break points. An approximation of the slip and thrust lines by quadratic parabolas is used in the numerical examples for a series of slopes.

강합성 콘크리트 복공판의 내력시험에 관한 연구

백신원,김용곤 한국안전학회 2012 한국안전학회지 Vol.26 No.6

Steel lining board usually is used as a floor on the temporary steel bridges. It also is installed in the subway construction site. However, in particular in subway construction, renovations and site of old bridges, these steel lining board structures have a problem such as noise, accidents and slip hazards. So steel composite lining board is being developed to solve this problem. Steel composite lining board consists of compressive concrete showing excellent performance in slip, durability, resistance and noise, lower tensile and shear steel showing high safety, effective and superior workability in many respects. Steel composite lining board structure gradually is used in many construction sites,because it has a high quality such as durability, little noise and slip. In this study, flexural tests of steel composite lining board in accordance with welding patterns were conducted to compare the performance of the structure

강합성 콘크리트 복공판의 내력시험에 관한 연구

백신원 ( Shin Won Paik ),김용곤 ( Yon Gon Kim ) 한국안전학회(구 한국산업안전학회) 2012 한국안전학회지 Vol.27 No.6

Steel lining board usually is used as a floor on the temporary steel bridges. It also is installed in the subway construction site. However, in particular in subway construction, renovations and site of old bridges, these steel lining board structures have a problem such as noise, accidents and slip hazards. So steel composite lining board is being developed to solve this problem. Steel. composite lining board consists of compressive concrete showing excel-lent performance in slip, durability, resistance and noise, lower tensile and shear steel showing high safety, effective and superior workability in many respects. Steel composite lining board structure gradually is used in many construction sites, because it has a high quality such as durability, little noise and slip. In this study, flexural tests of steel composite lining board in accordance with welding patterns were conducted to compare the performance of the structure.

Determination of stress state in formation zone by central slip-line field chip

Toropov Andrey,Ko Sung Lim Korean Society for Precision Engineering 2005 International Journal of Precision Engineering and Vol.6 No.3

Stress state of chip formation zone is one of the main problems in metal cutting mechanics. In two-dimensional case this process is usually considered as consistent shears of work material along one of several shear surfaces, separating chip from workpiece. These shear planes are assumed to be trajectories of maximum shear stress forming corresponding slip-line field. This paper suggests a new approach to the constriction of slip-line field, which implies uniform compression in chip formation zone. Based on the given model it has been found that imaginary shear line in orthogonal cutting is close to the trajectory of maximum normal stress and the problem about its determination has been considered as well. It has been shown that there is a second central slip-line field inside chip, which corresponds well to experimental data about stress distribution on tool rake face and tool-chip contact length. The suggested model would be useful in understanding mechanistic problems in machining.

Determination of stress state in chip formation zone by central slip-line field

Andrey Toropov,Sung Lim Ko 한국정밀공학회 2005 International Journal of Precision Engineering and Vol.6 No.3

Stress state of chip formation zone is one of the main problems in metal cutting mechanics. In two-dimensional case this process is usually considered as consistent shears of work material along one of several shear surfaces, separating chip from workpiece. These shear planes are assumed to be trajectories of maximum shear stress forming corresponding slip-line field. This paper suggests a new approach to the constriction of slip-line field, which implies uniform compression in chip formation zone. Based on the given model it has been found that imaginary shear line in orthogonal cutting is close to the trajectory of maximum normal stress and the problem about its determination has been considered as well. It has been shown that there is a second central slip-line field inside chip, which corresponds well to experimental data about stress distribution on tool rake face and tool-chip contact length. The suggested model would be useful in understanding mechanistic problems in machining.

Numerical simulation of hydro-mechanical constraints on the geometry of a critically tapered accretionary wedge

송인선,고희재 한국지질과학협의회 2020 Geosciences Journal Vol.24 No.3

A critically tapered active accretionary wedge was simulated using a numerical analysis of plastic slip-line theory to understand the mechanics of morphologic evolution. The concept of critical state soil mechanics was applied to describe the entire wedge area overlying a basal décollement fault. Presuming a condition of two-dimensional plane strain along the compressional direction, we obtained the numerical solution of conjugate plastic slip lines at a critical state of stress defined by the Coulomb yield criterion. The velocity vectors were obtained by applying the associate flow rule with the boundary conditions at the upper surface of the wedge. Finally, the detachment was determined from the effective stress condition inside the wedge and the sliding friction coefficient along the fault. Our numerical simulations demonstrate that the morphology of a critically tapered wedge is dependent on the frictional strengths of both the wedge materials and the basal fault. The critical taper angle decreases with increasing internal friction angle and decreasing basal friction coefficient. The results also revealed that the pore pressure controls the morphology of the accretionary wedge for cohesive sediments but not for non-cohesive materials. The effect of pore pressure on the morphology of a critically tapered accretionary wedge becomes more significant as the cohesion increases. Assuming that the cohesion is very low, we could infer the ranges of strengths that most observed wedge geometry data have 0.3–0.6 for the basal friction coefficient and ~35–45° for the internal friction angle of the wedge materials.

Determination of Maximum Penetration Depth of Suction Caissons in Sand

Wu Yuqi,LI Dayong,Zhang Yukun,Chen Fuquan 대한토목학회 2018 KSCE Journal of Civil Engineering Vol.22 No.8

The suction caisson is a large top-closed cylindrical steel structure in diameter, short in length and much thinner in skirt wallthickness. The total resistance of the suction caisson during installation consists of the tip resistance and the skirt wall friction. However, since the thickness of the skirt wall is very small, the skirt wall friction may produce additional vertical stress and shearstress in soil at the skirt tip level, and this additional vertical stress and shear stress will contribute to the increase in the skirt tipresistance. At the same time, seepage induced by suction also causes the tip resistance to reduce significantly. A modified slip-linefield is proposed in this study estimating the tip resistance in terms of the slip-line theory. The expression obtaining the minimumsuction to install the suction caisson is also proposed in terms of the force equilibrium. In addition, the critical suction is determinedbased on the mechanism of sand piping. Thus, the maximum penetration depth of the suction caisson can be reached when the criticalsuction equals the minimum suction. Results from calculations of the minimum suction and the maximum penetration depth havebeen proved to be in a good agreement with the measured data.

터널 소성영역에 따른 터널 천단토압 해석

박신영,한희수 한국산학기술학회 2020 한국산학기술학회논문지 Vol.21 No.11

In this study, the plastic zone and internal earth pressure of the tunnel were calculated using the following three methods: metal plasticity to analyze the deformation of metal during plastic processing, Terzaghi's earth pressure theory from the geotechnical perspective and modified Terzaghi's earth pressure theory, and slip line theory using Mohr-Coulomb yield conditions. All three methods are two-dimensional mathematical analysis models for analyzing the plane strain conditions of isotropic materials. Using the theory of metallurgical plastics, the plastic zone and the internal earth pressure of the ground were obtained by assuming that the internal pressure acts on the tunnel, so different results were derived that did not match the actual tunnel site, where only gravity was applied. An analysis of the plasticity zone and earth pressure via the slip-line method showed that a failure line is formed in a log-spiral, which was found to be similar to the real failure line by comparing the results of previous studies. The earth pressure was calculated using a theoretical method. Terzaghi's earth pressure was calculated to be larger than the earth pressure considering the dilatancy effect. 본 연구는 금속의 소성 가공 시 변형을 해석하기 위한 금속소성학의 개념, 지반공학 관점인 Terzaghi’s 토압론과 이를 수정한 수정 Terzaghi’s 토압론, Mohr-Coulomb 항복조건을 이용한 미끄러짐선장이론의 세가지 방법을 이용하여 각 방법에 따른 터널의 소성영역 및 내부 토압을 산정하였다. 세가지 방법 모두 등방성 재료의 평면변형율조건 해석의 이차원 수학적 해석 모델이다. 금속소성학의 이론을 사용할 경우, 터널에 내부압력이 작용하는 것으로 가정하여 지반의 소성영역 및 지반 내부토압을 구한 결과이므로, 중력만 작용하는 실제 터널 현장과는 맞지 않는 다른 결과가 도출되었다. 미끄러짐선장 이론을 통해 소성영역 형성범위 및 토압을 분석한 결과, 대수나선형태로 파괴면이 형성되는 것으로 나타났고 이는 선행연구와 비교를 통해 실제와 유사한 것으로 나타났다. 또한, 터널 굴착 등으로 인해 발생하는 지반의 체적 변화를 고려한 토압 산정식을 수학적으로 검토하고 이를 Terzaghi’s 토압과 비교하였다. 지반의 체적 팽창으로 인해 발생하는 다일러턴시 효과로 인한 강도 증진을 고려하였으며, Terzaghi’s 토압의 문제점을 분석하고 토피고와 내부마찰각을 변수로 이론적 방법을 통한 토압을 각각 비교·검토하였다. Terzaghi’s 토압론과 이를 수정한 수정 Terzaghi’s 토압론의 경우, 소성영역 범위를 임의로 가정하였으므로, 두 이론 모두 터널의 소성영역을 해석할 수 없다. 이론적 방법을 통한 토압 산정 결과, Terzaghi’s 토압의 경우 팽창성을 고려한 토압에 비해 토압이 과도하게 크게 산정되었으며 이는 지반의 체적변화로 인한 다일러턴시 효과를 무시하고, 이완영역을 과도하게 가정하였기 때문이다.