• Geotechnical Engineering
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• v.14 no.2
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• pp.41-54
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• 1998

Predictions of consolidation settlement and time must be always erroneous because of heterogeneity of soil media. errors associated with the measurement of soil parameters, drawback of consolidation theories and so on. When filling is done on compressible soils, the observational procedure is a useful means in practice of evaluating the final consolidation settlement and time. However, the existing observational procedures including some disadvantages such as the difficulty of ending the linearity in the settlement curves, the unavoidable personal error, and so on. A new observational procedure($\sqrt{s}$ method) is suggested here for the consolidation analysis in field. As the results of applying the $\sqrt{s}$ method with other methods to two field data. the fecal settlements predicted by the s method as well as by the Asaoka'$\sqrt{s}$ method agreed well with the measured values. However, results obtained from the hyperbolic method(Tan, 1991) were always overestimated. and there happened many cases not to be predicted by the Hoshino's method. In the settlement curve from the $\sqrt{s}$method, the linearity between 60 and 90 eye of the average degree of consolidation is shown. and then the possibility of a personal error seems to be unusual. The final consolidation times(at $U_{95}$) predicted by the $\sqrt{s}$ method agreed well with the measured ones. but the ones by Asaoka and Tan(1996) methods were very much underestimated or overestimated. where $U_{95}$, is the average degree of consolidation of 95%. The big errors of these two methods seem to result from unconsidering the effect of stage construction.

• Current Research on Agriculture and Life Sciences
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• v.4
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• pp.77-86
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• 1986

The purpose of this study is to estimate an optimum formula of rainfall intensity on basis of the characteristics for short period of rainfall duration in Kyungpook province for the design of urban sewerage and small basin drain system. Results studied are as follows; 1. The optimum method for Taegu and Pohang, Iwai's and Gumbel-Chow's method are recommended respectively. 2. The opotimum type of rainfall intensity for these area, $I=\frac{a}{\sqrt{t}+b}$ (Japanese type), is confirmed with 2.52~4.17 and 1.86~4.54 as a standard deviation for Taegu and Pohang respectively. The optimum formula of rainfall intensity are as follows. Taegu : T : 200 year - $I=\frac{824}{\sqrt{t}+1.5414}$ T : 100 year - $I=\frac{751}{\sqrt{t}+1.4902}$ T : 50 year - $I=\frac{678}{\sqrt{t}+1.4437}$ T : 30 year - $I=\frac{623}{\sqrt{t}+1.4017}$ T : 20 year - $I=\frac{580}{\sqrt{t}+1.3721}$ T : 10 year - $I=\frac{502}{\sqrt{t}+1.3145}$ T : 5 year - $I=\frac{418}{\sqrt{t}+1.2515}$ Pohang : T : 200 year - $I=\frac{468}{\sqrt{t}+1.1468}$ T : 100 year - $I=\frac{429}{\sqrt{t}+1.1605}$ T : 50 year - $I=\frac{391}{\sqrt{t}+1.1852}$ T : 30 year - $I=\frac{362}{\sqrt{t}+1.2033}$ T : 20 year - $I=\frac{339}{\sqrt{t}+1.2229}$ T : 10 year - $I=\frac{299}{\sqrt{t}+1.2578}$ T : 5 year - $I=\frac{257}{\sqrt{t}+1.3026}$ 3. Significant I.D.F. curves derived should be applied to estimate a suitable rainfall intensity and rainfall duration.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.389-398
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• 2002

The mixed mode problem (I and II) of a peny-shaped interface cracks in remote tension loading on a bi-material cylinder is studied using finite element method. The energy release rates for the tip of the crack in the interface were calibrated for several different moduli combinations and crack ratios using the modified crack closure integral technique and J-integral method, with numerical results obtained from a commercial finite element program. Numerical results show that non-dimensional value of$\sqrt{G_{II}E^*}/\sqrt[p]{\pi a}$ increases as the crack size or moduli ratio increases. Meanwhile, non-dimensional value of$\sqrt{G_{I}E^*}/\sqrt[p]{\pi a}$ decreases as the moduli ratio increases, but above the moduli ratio of 3 its value decreases then increases again as the crack size increases. Reliability of the numerical analysis in this study was acquired with comparison to an analytical solution for the peny-shaped interface crack in an infinite medium.

• Journal of the Korean GEO-environmental Society
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• v.13 no.4
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• pp.77-91
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• 2012

Recently, construction of housing sites, complexes, roads, ports and airports is increasing for high-intensity use of the country and balanced development between regions. Presently, constructions are being conducted at soft ground. Consequently, engineering problems as long-term settlement of the ground, differential settlement, local structural damage have been reported consistently at construction site. In particular, long-term subsidence of the ground as various constructions and loads by the load will necessarily occur in the soft ground of west-south coast and inland coast. Therefore, in this study, regional proper analysis methods of the Hyperbole method, Hosino method, $\sqrt{S}$ method, Asaoka method etc as existing long-term settlement prediction methods have been examined and a study on new prediction method was conducted through deduction of a generalized equation. Correlation coefficients of soil properties and construction conditions has been analyzed and a matching coefficient of long-term settlement characteristics has been deducted. Comparison and analysis of monitoring data and numerical analysis results of 16 local area have been conducted.

• Journal of Industrial Technology
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• v.28 no.B
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• pp.91-99
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• 2008

Applicability of existing methods of predicting consolidation settlement was assessed by analyzing results of centrifuge tests modelling self-weight consolidation of soft marine clay. From extensive literature review about self-weight consolidation of soft marine clays located in southern coast in Korea, constitutive relationships of void ratio-effective stress-permeability and typical self-weight consolidation curves with time were obtained by centrifuge model experiments. For the condition of surcharge loading, exact solution of consolidation settlement curve was obtained by Terzaghi's consolidation theory and was compared with the results predicted by currently available methods such as Hyperbolic method, Asaoka's method, Hoshino's method and ${\sqrt{S}}$ method. All methods were found to have their own inherent error to predict final consolidation settlement. From results of analyzing the self-weight consolidation with time by using those methods, Asaoka's method predicted the best. Hyperbolic method predicted relatively well in error range of 2~24% for the case of showing the linearity in the relationship between T vs T/S in the stage of consolidation degree of 60~90 %. For the case of relation curve of T vs $T/S^2$ showing the lineality after the middle stage, error range from Hoshino method was close to those from Hyperbolic method. However, Hoshino method is not able to predict the final settlement in the case of relation curve of T vs $T/S^2$ being horizontal. For the given data about self-weight consolidation after the middle stage, relation curve of T vs T/S from ${\sqrt{S}}$ method shows the better linearity than that of T vs $T/{\sqrt{s}}$ from Hyperbolic method.

• Water for future
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• v.15 no.2
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• pp.33-39
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• 1982

For the determination of a reservoir capacity Rippl's mass-curve method has long been used with the past river flow data assuming the same flow records will be repeated in the future. In this study the synthetic generation methods of thomas-Fiering type and harmonic analysis were used to synthetically generate 50 years of monthly river inflows to three single-purpose reservoris(Chuncheon, Chungpyong, Hwacheon) and three multi-purpose reservoirs(Soyany, Andon, Daichung). The generated sequences of monthly flows were analyzed based on the range concept, and hence the so-determined ranges for single-prupose and multi-purpose rewervoirs were correlated with the number of monthly flow subseries, resulting an empirical equation of the Feller's type. (1) Single-purpose reservoir $$R_n=2.8357 I\sqrt{n}$$ (2) Multi-purpose reservoir $$R_n=2.5145 I\sqrt{n}$$ where, $R_n$:Range(㎥/S-M) n:periodic(12 months, ……120 months) I:Input mean(㎥/S-M) In Korea, the monthly inflow data generation will be fit to the Thomas-Fiering type, and this paper shows that the periodic range is easily calculated without the Rippl's mass-curve method as shown above formula.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.5
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• pp.15-20
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• 2023

Until now, Pollard's Rho algorithm has been known as the most efficient way for discrete algebraic problems to decrypt symmetric keys. However, the algorithm is being studied on how to further reduce the complexity of O(${\sqrt{p}}$) performance, along with the disadvantage of having to store the giant stride m=⌈${\sqrt{p}}$⌉ data. This paper proposes an array method for cycle detection in discrete logarithms. The proposed method reduces the number of updates of stack memory by at least 73%. This is done by only updating the array when (x_i<0.5x_i-1)∩(x_i<0.5(p-1)). The proposed array method undergoes the same number of modular calculation as stack method, but significantly reduces the number of updates and the execution time for array through the use of a binary search method.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1119-1133
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• 2020

In this paper, we derive an upper bound for the distance from a point in the immediate basin of a root of a complex polynomial to the root itself. We establish that if z is a point in the immediate basin of a root α of a polynomial p of degree d ≥ 12, then ${\mid}z-{\alpha}{\mid}{\leq}{\frac{3}{\sqrt{d}}\(6{\sqrt{310}}/35\)^d{\mid}N_p(z)-z{\mid}$, where N_p is the Newton map induced by p. This bound leads to a new bound of the expected total number of iterations of Newton's method required to reach all roots of every polynomial p within a given precision, where p is normalized so that its roots are in the unit disk.

• Journal of the Korean GEO-environmental Society
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• v.13 no.12
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• pp.35-42
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• 2012

There are many large-scale coastal region landfill and land development by loading to use territory efficiently, this regions are mostly soft clay ground. Constructing structures and road on the soft ground bring about engineering problems like ground shear fracture and a big amount of consolidation by bearing capacity. Improvement of soft soil is required to secure soil strength and settlement control. In improvement of soft soil, predict for the amount of settlement based on field surveyed reports are important element for estimating pre-loading banking height and the final point of consolidation. In this study, there is calculating theoretical settlement by analyzing field surveyed report and ground investigation to improvement of soft soil with pre-loading and vertical drain method. And present settlement prediction method reflect soil characteristics in Gimpo Hangang site by analysing prediction settlement and observational settlement during compaction using hyperbolic, ${\sqrt{s}}$, Asaoka method.

• Magazine of the Korean Society of Agricultural Engineers
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• v.20 no.1
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• pp.4592-4598
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• 1978

The purpose of this research is to find out mathemetically an economical intake water depth in the design of head works through the derivation of some formulas. For the performance of the purpose the following formulas were found out for the design intake water depth in each flow type of intake sluice, such as overflow type and orifice type. (1) The conditional equations of !he economical intake water depth in .case that weir body is placed on permeable soil layer ; (a) in the overflow type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }+ { 1} over {2 } { Cp}_{3 }L(0.67 SQRT { q} -0.61) { ( { d}_{0 }+ { h}_{1 }+ { h}_{0 } )}^{- { 1} over {2 } }- { { { 3Q}_{1 } { p}_{5 } { h}_{1 } }^{- { 5} over {2 } } } over { { 2m}_{1 }(1-s) SQRT { 2gs} }+[ LEFT { b+ { 4C TIMES { 0.61}^{2 } } over {3(r-1) }+z( { d}_{0 }+ { h}_{0 } ) RIGHT } { p}_{1 }L+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 }L+ { dcp}_{3 }L+ { nkp}_{5 }+( { 2z}_{0 }+m )(1-s) { L}_{d } { p}_{7 } ] =0}}}} (b) in the orifice type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }+ { 1} over {2 } C { p}_{3 }L(0.67 SQRT { q} -0.61)}}}} {{{{ { ({d }_{0 }+ { h}_{1 }+ { h}_{0 } )}^{ - { 1} over {2 } }- { { 3Q}_{1 } { p}_{ 6} { { h}_{1 } }^{- { 5} over {2 } } } over { { 2m}_{ 2}m' SQRT { 2gs} }+[ LEFT { b+ { 4C TIMES { 0.61}^{2 } } over {3(r-1) }+z( { d}_{0 }+ { h}_{0 } ) RIGHT } { p}_{1 }L }}}} {{{{+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 } L+dC { p}_{4 }L+(2 { z}_{0 }+m )(1-s) { L}_{d } { p}_{7 }]=0 }}}} where, z=outer slope of weir body (value of cotangent), h1=intake water depth (m), L=total length of weir (m), C=Bligh's creep ratio, q=flood discharge overflowing weir crest per unit length of weir (m3/sec/m), d0=average height to intake sill elevation in weir (m), h0=freeboard of weir (m), Q1=design irrigation requirements (m3/sec), m1=coefficient of head loss (0.9∼0.95) s=(h1-h2)/h1, h2=flow water depth outside intake sluice gate (m), b=width of weir crest (m), r=specific weight of weir materials, d=depth of cutting along seepage length under the weir (m), n=number of side contraction, k=coefficient of side contraction loss (0.02∼0.04), m2=coefficient of discharge (0.7∼0.9) m'=h0/h1, h0=open height of gate (m), p1 and p4=unit price of weir body and of excavation of weir site, respectively (won/㎥), p2 and p3=unit price of construction form and of revetment for protection of downstream riverbed, respectively (won/㎡), p5 and p6=average cost per unit width of intake sluice including cost of intake canal having the same one as width of the sluice in case of overflow type and orifice type respectively (won/m), zo : inner slope of section area in intake canal from its beginning point to its changing point to ordinary flow section, m: coefficient concerning the mean width of intak canal site,a : freeboard of intake canal. (2) The conditional equations of the economical intake water depth in case that weir body is built on the foundation of rock bed ; (a) in the overflow type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }- { { { 3Q}_{1 } { p}_{5 } { h}_{1 } }^{- {5 } over {2 } } } over { { 2m}_{1 }(1-s) SQRT { 2gs} }+[ LEFT { b+z( { d}_{0 }+ { h}_{0 } )RIGHT } { p}_{1 }L+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 }L+ { nkp}_{5 }}}}} {{{{+( { 2z}_{0 }+m )(1-s) { L}_{d } { p}_{7 } ]=0 }}}} (b) in the orifice type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }- { { { 3Q}_{1 } { p}_{6 } { h}_{1 } }^{- {5 } over {2 } } } over { { 2m}_{2 }m' SQRT { 2gs} }+[ LEFT { b+z( { d}_{0 }+ { h}_{0 } )RIGHT } { p}_{1 }L+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 }L}}}} {{{{+( { 2z}_{0 }+m )(1-s) { L}_{d } { p}_{7 } ]=0}}}} The construction cost of weir cut-off and revetment on outside slope of leeve, and the damages suffered from inundation in upstream area were not included in the process of deriving the above conditional equations, but it is true that magnitude of intake water depth influences somewhat on the cost and damages. Therefore, in applying the above equations the fact that should not be over looked is that the design value of intake water depth to be adopted should not be more largely determined than the value of h1 satisfying the above formulas.