• Title/Summary/Keyword: Hyperbolic equation

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Development of an Empirical Equation for Estimating Lond Transfer Curve for Micropile in Weathered Soils (풍화지반에 근입된 마이크로파일의 하중전이곡선 추정을 위한 경험식 개발)

  • Park, Seong-Wan;Cho, Kook-Hwan;Roh, Kang-Koo
    • Journal of the Korean Geotechnical Society
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    • v.23 no.1
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    • pp.5-11
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    • 2007
  • Micropiles have been used for underpinning or rehabilitation of existing foundations, and direct structural support system as well. However, relatively few studies have been done on the load-transfer mechanism of micropile systems in Korea. In addition to that, only the limited information is available for estimating the side friction values on micropiles installed in weathered soils. In this study, a full-scale test on an instrumented micropile is performed in order to establish the load-transfer curves based on a hyperbolic function. Then, an empirically derived equation that correlates the load-transfer curve of micropiles with the N values from field standard penetration tests is proposed. The results from all procedures are presented in this paper. Finally, back analysis using a finite difference method and the published field data are adopted for examination of a developed skin friction equation of micropile in weathered soils respectively.

Estimation of hourly daytime air temperature on slope in complex terrain corrected by hourly solar radiation (복잡지형 경사면의 일사 영향을 반영한 매시 낮 기온 추정 방법)

  • Yun, Eun-jeong;Kim, Soo-ock
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.20 no.4
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    • pp.376-385
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    • 2018
  • To estimate the hourly temperature distribution due to solar radiation during the day, on slope in complex terrain, an empirical formula was developed including the hourly deviation in the observed temperature following solar radiation deviation, at weather stations on the east-facing and west-facing slopes. The solar radiation effect was simulated using the empirical formula to estimate hourly temperature at 11 weather observation sites in mountainous agricultural areas, and the result was verified for the period from January 2015 to December 2017. When the estimated temperature was compared with the control, only considering temperature lapse rate, it was found that the tendency to underestimate the temperature from 9 am to 3 pm was reduced with the use of an empirical formula in the form of linear expression; consequently, the estimation error was reduced as well. However, for the time from 5 pm to 6 pm, the estimation error was smaller when a hyperbolic equation drawn from the deviation in solar radiation on the slope, which was calculated based on geometric conditions, was used instead of observed values. The reliability of estimating the daytime temperature at 3 pm was compared with existing estimation model proposed in other studies; the estimation error could be mitigated up to an ME (mean error) of $-0.28^{\circ}C$ and RMSE (root mean square error) of $1.29^{\circ}C$ compared to the estimation error in previous models (ME $-1.20^{\circ}C$, RMSE $2.01^{\circ}C$).

Dynamic Analysis of Specimen Under Ultrasonic Fatigue Using Finite Element Method (초음파 피로시험시 시험편의 유한요소 동적 해석)

  • Myeong, No-Jun;Choi, Nak-Sam;Kwon, Hena
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.7
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    • pp.711-717
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    • 2014
  • An accelerated ultrasonic fatigue test (UFT) was used for analyzing very high cycle fatigue (VHCF, $N_f$ > $10^7$) behaviors of a specimen with a test resonance of 20 kHz. Using the finite element method (FEM), the dynamic behaviors of the specimen was studied by calculating the stresses along its gauge portion, with displacement. The shape of gauge portion profile was assumed to be a hyperbolic according to the stress equation of the UFT. However, as the specimen used in the test had a circular arc profile, the FEM was used for studying the local stresses for two cases of the gauge profile. The results were compared with those obtain from the stress equation of the UFT. The dynamic behavior of the gauge portion could be understood for further comparison with the actual results.

Development of a Simplified Treatment Technique of Partial Wave Reflection and Transmission for Mild-Slope Wave Model (완경사 방정식에서의 간편화된 파의 부분 반사 및 투과 처리기법)

  • Chun Je-Ho;Ahn Kyung-Mo
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.18 no.1
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    • pp.84-96
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    • 2006
  • This paper presents a simplified numerical method that can be used to incorporate the partial reflection and transmission of water waves in the hyperbolic mild-slope equation. For given reflection and transmission coefficients, wave fields around a porous breakwater including reflection, transmission, and diffraction can be simulated accurately. For the verification of the proposed method, numerical experiments have been carried out and compared with analytic solutions given by Yu(1995) and McIver(1999). The proposed method is easy to implement and is computationally efficient. It is demonstrated that the method performs well with a sloping bottom bathymetry and varying incident wave angles.

Hybrid Element Model for Wave Transformation Analysis (파랑 변형 해석을 위한 복합 요소 모형)

  • 정태화;박우선;서경덕
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.15 no.3
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    • pp.159-166
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    • 2003
  • In this study, we develop a finite element model to directly solve the Laplace equation while keeping the same computational efficiency as the models based on the extended mild-slope equation which has been widely used for calculation of wave transformation in shallow water. For this, the computational domain is discretized into finite elements with a single layer in the vertical direction. The velocity potential in the element is then expressed in terms of the potentials at the nodes located at water surface, and the Galerkin method is used to construct the numerical model. A common shape function is adopted in horizontal direction, and the cosine hyperbolic function in vertical direction, which describes the vertical behavior of progressive waves. The model was developed for vertical two-dimensional problems. In order to verify the developed model, it is applied to vertical two-dimensional problems of wave reflection and transmission. It is shown that the present finite element model is comparable to the models based on extended mild-slope equations in both computational efficiency and accuracy.

Taylor Series-Based Long-Term Creep-Life Prediction of Alloy 617 (Taylor 급수를 이용한 617 합금의 장시간 크리프 수명 예측)

  • Yin, Song-Nan;Kim, Woo-Gon;Park, Jae-Young;Kim, Soen-Jin;Kim, Yong-Wan
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.4
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    • pp.457-465
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    • 2010
  • In this study, a Taylor series (T-S) model based on the Arrhenius, McVetty, and Monkman-Grant equations was developed using a mathematical analysis. In order to reduce fitting errors, the McVetty equation was transformed by considering the first three terms of the Taylor series equation. The model parameters were accurately determined by a statistical technique of maximum likelihood estimation, and this model was applied to the creep data of alloy 617. The T-S model results showed better agreement with the experimental data than other models such as the Eno, exponential, and L-M models. In particular, the T-S model was converted into an isothermal Taylor series (IT-S) model that can predict the creep strength at a given temperature. It was identified that the estimations obtained using the converted ITS model was better than that obtained using the T-S model for predicting the long-term creep life of alloy 617.

An Evaluation of Shear Strength Parameters$(c,\varphi)$ for Weathering Decomposed Granite Soil (화강풍화토의 전단정수$(c,\varphi)$ 평가)

  • 이문수;이광찬
    • Journal of the Korean Geotechnical Society
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    • v.15 no.2
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    • pp.181-194
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    • 1999
  • Both the chemical components and the physical and mechanical properties of the compacted and undisturbed weathered granite soils were estimated to investigate the influences of the degree of weathering and saturation on the shear strength. The weathered granite soils used in this study were taken from six different sites in Korea. The results showed that the shear strength of weathered granite soil decreased with increasing the degree of weathering and saturation. Under the normal stresses less that 40kPa, the shape of Mohr-Coulomb failure envelope followed curved or hyperbolic relationship and a half of cohesion value obtained by the common shear test was observed. Using the Sueoka's method, the values of CWI were ranged from 21.5 to 31.26 which can be characterized as a completely weathered granite soil. Large decrease in shear strength and remarkable variation in dilatancy were observed in saturated granite soil compared to unsaturated soil. It was also found that the shear strength of undisturbed weathered granite soil of Pungam site can be expressed approximately by the equation of ${(\tau)_{sat}= 1.0(\tau)_{unsat}-12.48}$ and this equation can be extended to the other sites considered in this study.

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Unsteady Flow Analysis in the Youngsan River Using Explicit and Implicit Finite Difference Methods (양해법과 음해법을 이용한 영산강에서의 부정류해석)

  • Choi, Sung-Uk;Yeo, Woon-Kwang;Choo, Cheol;Kim, Chang-Wan;O, Yu-Chang
    • Water for future
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    • v.24 no.4
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    • pp.49-58
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    • 1991
  • Flood routing in the Youngsan River was performed for the flood event of July, 1989 by two finite difference methods. The Saint Venant eq., a kind of hyperbolic partial differential equation is employed as governing equation and the explicit scheme (Leap Frog) and implicit scheme (Preissmann) are used to discretize the GE. As for the external boundary conditions, discharge and tidal elevation are upstream and downstream BC, respectively and estuary dam is included in internal BC. Lateral inflows and upstream discharges are the hourly results from storage function method, At Naju station, a Relatively upstream points in this river, the outputs are interpreted as good ones by comparing two numerical results of FDMs with the observed data and the calibrated results by storage function method. and two computational results are compared at the other sites, from middle stream and downstream points, and thus are considered reliable. Therefore, we can conclude from this research that these numerical models are adaptable in simulating and forecasting the flood in natural channels in Korea as well as existing hydrologic models. And the study about optimal gate control at the flood time is expected as further study using these models.

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Comprehensive evaluation of structural geometrical nonlinear solution techniques Part I: Formulation and characteristics of the methods

  • Rezaiee-Pajand, M.;Ghalishooyan, M.;Salehi-Ahmadabad, M.
    • Structural Engineering and Mechanics
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    • v.48 no.6
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    • pp.849-878
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    • 2013
  • This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.

Modeling and Simulation for PIG with Bypass Flow Control in Natural Gas Pipeline

  • Nguyen, Tan-Tien;Kim, Sang-Bong;Yoo, Hui-Ryong;Park, Yong-Woo
    • Journal of Mechanical Science and Technology
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    • v.15 no.9
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    • pp.1302-1310
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    • 2001
  • This paper introduces modeling and simulation results for pipeline inspection gauge (PIG) with bypass flow control in natural gas pipeline. The dynamic behaviour of the PIG depends on the different pressure across its body and the bypass flow through it. The system dynamics includes: dynamics of driving gas flow behind the PIG, dynamics of expelled gas in front of the PIG, dynamics of bypass flow, and dynamics of the PIG. The bypass flow across the PIG is treated as incompressible flow with the assumption of its Mach number smaller than 0.45. The governing nonlinear hyperbolic partial differential equations for unsteady gas flows are solved by method of characteristics (MOC) with the regular rectangular grid under appropriate initial and boundary conditions. The Runge-Kuta method is used for solving the steady flow equations to get initial flow values and the dynamic equation of the PIG. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. The simulation is performed with a pipeline segment in the Korea Gas Corporation (KOGAS) low pressure system, Ueijungboo-Sangye line. Simulation results show us that the derived mathematical model and the proposed computational scheme are effective for estimating the position and velocity of the PIG with bypass flow under given operational conditions of pipeline.

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