• Title/Summary/Keyword: 근사 공식

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Experiment on Seepage in Varied Section of Core Wall for Fill Dam Design (필댐 제체심벽(堤體心壁)의 단면변화(斷面變化)에 대한 침투류해석(浸透流解析)에 관한 실험적(實驗的) 연구(硏究))

  • Jin, Byung Ik;Kim, Jae Hong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.1
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    • pp.55-64
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    • 1985
  • This thesis, intended to establish the design criteria of core wall of a Fill Dam, has determined after a series of twenty one analytic experiments on the seepage flows in various types of core wall that the rates of rise and fall of the seepage flow changing in accordance with the variation of core wall cross section, which is to say, the transformation of slope inclination. Particularily the appropropriate design inclination was examined for the sloped core wall. Putting the resulting values into the existing approximate theoretical function has revealed the volume of theoretical seepage flows. With this result, the experiment values was compared and interestingly enough, a theoretical formula was found which is considered to be the nearest one to the resulting values of the experiment. It is also discussed in the papers that the seepage alignment and flows in the sloped core wall section that inclined to the upstream and the adoptability of the theoretical function which has been known up to present. Based on the above mentioned study it is anticipated that thesis should be available for determination of the cross section in the core wall design of a Fill Dam as large amount of references as it can be.

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A Study on Reliability Based Design Criteria for Reinforced Concrete Bridge Superstructures (철근(鐵筋)콘크리트 도로교(道路橋) 상부구조(上部構造) 신뢰성(信賴性) 설계규준(設計規準)에 관한 연구(研究))

  • Cho, Hyo Nam
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.2 no.3
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    • pp.87-99
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    • 1982
  • This study proposes a reliability based design criteria for the R.C. superstructures of highway bridges. Uncertainties associated with the resistance of T or rectangular sections are investigated, and a set of appropriate uncertainties associated with the bridge dead and traffic live loads are proposed by reflecting our level of practice. Major 2nd moment reliability analysis and design theories including both Cornell's MFOSM(Mean First Order 2nd Moment) Methods and Lind-Hasofer's AFOSM(Advanced First Order 2nd Moment) Methods are summarized and compared, and it has been found that Ellingwood's algorithm and an approximate log-normal type reliability formula are well suited for the proposed reliability study. A target reliability index (${\beta}_0=3.5$) is selected as an optimal value considering our practice based on the calibration with the current R.C. bridge design safety provisions. A set of load and resistance factors is derived by the proposed uncertainties and the methods corresponding to the target reliability. Furthermore, a set of nominal safety factors and allowable stresses are proposed for the current W.S.D. design provisions. It may be asserted that the proposed L.R.F.D. reliability based design criteria for the R.C. highway bridges may have to be incorporated into the current R.C. bridge design codes as a design provision corresponding to the U.S.D. provisions of the current R.C. design code.

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Derivation of Asymptotic Formulas for the Signal-to-Noise Ratio of Mismatched Optimal Laplacian Quantizers (불일치된 최적 라플라스 양자기의 신호대잡음비 점근식의 유도)

  • Na, Sang-Sin
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.33 no.5C
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    • pp.413-421
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    • 2008
  • The paper derives asymptotic formulas for the MSE distortion and the signal-to-noise ratio of a mismatched fixed-rate minimum MSE Laplacian quantizer. These closed-form formulas are expressed in terms of the number N of quantization points, the mean displacement $\mu$, and the ratio $\rho$ of the standard deviation of the source to that for which the quantizer is optimally designed. Numerical results show that the principal formula is accurate in that, for rate R=$log_2N{\geq}6$, it predicts signal-to-noise ratios within 1% of the true values for a wide range of $\mu$, and $\rho$. The new findings herein include the fact that, for heavy variance mismatch of ${\rho}>3/2$, the signal-to-noise ratio increases at the rate of $9/\rho$ dB/bit, which is slower than the usual 6 dB/bit, and the fact that an optimal uniform quantizer, though optimally designed, is slightly more than critically mismatched to the source. It is also found that signal-to-noise ratio loss due to $\mu$ is moderate. The derived formulas can be useful in quantization of speech or music signals, which are modeled well as Laplacian sources and have changing short-term variances.

A Numerical Solution Method of the Boundary Integral Equation -Axisymmetric Flow- (경계적분방정식의 수치해법 -축대칭 유동-)

  • Chang-Gu,Kang
    • Bulletin of the Society of Naval Architects of Korea
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    • v.27 no.3
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    • pp.38-46
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    • 1990
  • A numerical solution method of the boundary integral equation for axisymmetric potential flows is presented. Those are represented by ring source and ring vorticity distribution. Strengths of ring source and ring vorticity are approximated by linear functions of a parameter $\zeta$ on a segment. The geometry of the body is represented by a cubic B-spline. Limiting integral expressions as the field point tends to the surface having ring source and ring vorticity distribution are derived upto the order of ${\zeta}ln{\zeta}$. In numerical calculations, the principal value integrals over the adjacent segments cancel each other exactly. Thus the singular part proportional to $\(\frac{1}{\zeta}\)$ can be subtracted off in the calculation of the induced velocity by singularities. And the terms proportional to $ln{\zeta}$ and ${\zeta}ln{\zeta}$ can be integrated analytically. Thus those are subtracted off in the numerical calculations and the numerical value obtained from the analytic integrations for $ln{\zeta}$ and ${\zeta}ln{\zeta}$ are added to the induced velocity. The four point Gaussian Quadrature formula was used to evaluate the higher order terms than ${\zeta}ln{\zeta}$ in the integration over the adjacent segments to the field points and the integral over the segments off the field points. The root mean square errors, $E_2$, are examined as a function of the number of nodes to determine convergence rates. The convergence rate of this method approaches 2.

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A Review on Ultimate Lateral Capacity Prediction of Rigid Drilled Shafts Installed in Sand (사질토에 설치된 강성현장타설말뚝의 극한수평지지력 예측에 관한 재고)

  • Cho Nam Jun;Kulhawy F.H
    • Journal of the Korean Geotechnical Society
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    • v.21 no.2
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    • pp.113-120
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    • 2005
  • An understanding of soil-structure interaction is the key to rational and economical design for laterally loaded drilled shafts. It is very difficult to formulate the ultimate lateral capacity into a general equation because of the inherent soil nonlincarity, nonhomogeneity, and complexity enhanced by the three dimensional and asymmetric nature of the problem though extensive research works on the behavior of deep foundations subjected to lateral loads have been conducted for several decades. This study reviews the four most well known methods (i.e., Reese, Broms, Hansen, and Davidson) among many design methods according to the specific site conditions, the drilled shaft geometric characteristics (D/B ratios), and the loading conditions. And the hyperbolic lateral capacities (H$_h$) interpreted by the hyperbolic transformation of the load-displacement curves obtained from model tests carried out as a part of this research have been compared with the ultimate lateral capacities (Hu) predicted by the four methods. The H$_u$ / H$_h$ ratios from Reese's and Hansen's methods are 0.966 and 1.015, respectively, which shows both the two methods yield results very close to the test results. Whereas the H$_u$ predicted by Davidson's method is larger than H$_h$ by about $30\%$, the C.0.V. of the predicted lateral capacities by Davidson is the smallest among the four. Broms' method, the simplest among the few methods, gives H$_u$ / H$_h$ : 0.896, which estimates the ultimate lateral capacity smaller than the others because some other resisting sources against lateral loading are neglected in this method. But it results in one of the most reliable methods with the smallest S.D. in predicting the ultimate lateral capacity. Conclusively, none of the four can be superior to the others in a sense of the accuracy of predicting the ultimate lateral capacity. Also, regardless of how sophisticated or complicated the calculating procedures are, the reliability in the lateral capacity predictions seems to be a different issue.