• Geomechanics and Engineering
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• v.32 no.3
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• pp.335-346
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• 2023

For structures with underground basement walls, the soil-structure-interaction between the side soil and the walls affects the response of the system. There is interest in quantifying the relationship between the lateral earth pressure and the wall displacement using p-y curves. To date, passive p-y curves in available limited studies were assumed elastic-perfectly plastic. In reality, the relationship between earth pressure and wall displacement is complex. This paper focuses on studying the development of passive p-y curves behind rigid walls supporting granular soils. The study aims at identifying the different components of the passive p-y relationship and proposing a rigorous non-linear p-y model in place of simplified elastic-plastic models. The results of the study show that (1) the p-y relationship that models the stress-displacement response behind a rigid basement wall is highly non-linear, (2) passive p-y curves are affected by the height of the wall, relative density, and depth below the ground surface, and (3) passive p-y curves can be expressed using a truncated hyperbolic model that is defined by a limit state passive pressure that is determined using available logarithmic spiral methods and an initial slope that is expressed using a depth-dependent soil stiffness model.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.836-842
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• 2011

The lateral stability of bridge foundations against train moving load, emergency stopping load, earthquakes, and so on is very important for a railway bridge foundation. A borehole test is much more accurate than laboratory tests since it is possible to minimize the disturbance of ground conditions on the test site. The representative borehole test methods are Dilatometer, Pressuremeter and Lateral Load Tester, which usually provide force-resistance characteristics in elastic range. In order to estimate P-y curves using those methods, the non-linear characteristics of soil which is one of the most important characteristics of the soil cannot be obtained. Therefore, P-y curves are estimated usually using elastic modulus ($E_O$, $E_R$) of lateral pressure-deformation ratio obtained within the range of elastic behavior. Even though the pile foundation is designed using borehole tests in field to increase design accuracy, it is necessary to use a higher safety factor to improve the reliability of the design. A Large Displacement Borehole Testmeter(LDBT) is developed to measure nonlinear characteristics of the soil in this study. P-y curves can be directly achieved from the developed equipment. Comparisons between measured P-y curves the LDBT developed equipment, theoretical methods based on geotechnical investigations, and back-calculated P-y curves from field tests are shown in this paper. The research result shows that the measured P-y curves using LDBT can be properly matched with back-calculated P-y curves from filed tests by applying scale effects for sand and clay, respectively.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.83-96
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• 2013

Let K be a number field and fix a prime number $p$. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set $B_{K,p}$ of primes of K satisfying that any elliptic curve over K with $B_{K,p}$-reduction has no $p$-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with $B_{K,p}$-reduction and a $p$-torsion point. The action of the absolute Galois group on the $p$-torsion subgroup of E gives its associated Galois representation $\bar{\rho}_{E,p}$ modulo $p$. We also study the irreducibility and surjectivity of $\bar{\rho}_{E,p}$ for semistable elliptic curves with $B_{K,p}$-reduction.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.451-457
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• 2011

The function f(z) = $e^{p(z)}$ where p(z) is a polynomial of degree n has 2n Julia lines. Julia lines of $e^{p(z)}$ divide the complex plane into 2n equal sectors with the same vertex at the origin. In each sector, $e^{p(z)}$ has radial limits of 0 or innity. Main results of the paper are concerned with maximum curves of $e^{p(z)}$. We deal with some properties of maximum curves of $e^{p(z)}$ and we give some examples of the maximum curves of functions of the form $e^{p(z)}$.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.272-277
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• 2001

In order to evaluate variation of fatigue data of the LP steam turbine blade steel, it is important to estimate P - S - N curves to accurately define the probability distributions. In this study, new procedure is introduced to determine the expression of P - S - N curves. For this purpose, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue life were examined by the proposed analysis. Furthermore, parameter estimation for P - S - N curves was performed using various optimization to maximize the correlation coefficient. As a result of this, sequential linear programing method is used for estimation of P - S - N curves.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.821-828
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• 2011

A significantly larger lateral load and moment are applied on a high speed railway bridge foundation than other bridge foundations. Therefore most of bridge foundations on Honam high speed railway project were designed by high strength steel pipe piles to resist lateral load and moment, which caused the increase of construction costs. In order to perform optimum design, it is important to estimate accurate lateral resistance when designing this type of structure. Lateral load tests were carried out based on the field design data with the purpose of examining the lateral behavioral characteristics of a railway bridge foundation. The standard load test method(ASTM D 3966) was used for field tests by applying twice of design load. Total four load tests were performed on high speed railway bridge foundations with strain gages installed by every 1m along piles to measure load-resistance characteristics under applied lateral loads. The back-calculated P-y curves from strain gages were compared with estimated P-y curves using theoretical methods based on geotechnical investment data. Back-calculated P-y curves from field tests for sand and clay ground conditions were presented in this paper, which are different from theoretical P-y curves. By using the research results of this study, more accurate estimations of pile design under lateral loads can be available for similar geotechnical conditions.

• Geomechanics and Engineering
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• v.5 no.5
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• pp.379-399
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• 2013

In practice, analysis of laterally loaded piles is carried out using beams on non-linear Winkler springs model (often known as p-y method) due to its simplicity, low computational cost and the ability to model layered soils. In this approach, soil-pile interaction along the depth is characterized by a set of discrete non-linear springs represented by p-y curves where p is the pressure on the soil that causes a relative deformation of y. p-y curves are usually constructed based on semi-empirical correlations. In order to construct API/DNV proposed p-y curve for clay, one needs two values from the monotonic stress-strain test results i.e., undrained strength ($s_u$) and the strain at 50% yield stress (${\varepsilon}_{50}$). This approach may ignore various features for a particular soil which may lead to un-conservative or over-conservative design as not all the data points in the stress-strain relation are used. However, with the increasing ability to simulate soil-structure interaction problems using highly developed computers, the trend has shifted towards a more theoretically sound basis. In this paper, principles of Mobilized Strength Design (MSD) concept is used to construct a continuous p-y curves from experimentally obtained stress-strain relationship of the soil. In the method, the stress-strain graph is scaled by two coefficient $N_C$ (for stress) and $M_C$ (for strain) to obtain the p-y curves. $M_C$ and $N_C$ are derived based on Semi-Analytical Finite Element approach exploiting the axial symmetry where a pile is modelled as a series of embedded discs. An example is considered to show the application of the methodology.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.291-298
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• 1998

The $L^p-L^q$ mapping properties of convolution operators with measures supported on curves in $\mathbb{R}^3$ have been studied by many authors. Oberlin provided examples of nondegenerate compact space curves whose arclength measures enjoy $L^p$-improving properties. This was later extended by Pan who showed that such properties hold for all nondegenerate compact space curves. In this paper, we will prove that the operator norm of the convolution operator with the arclength measure supported on a nondegenerate compact space curve depends only on certain quantities of the underlying curve.

• Journal of IKEEE
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• v.23 no.4
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• pp.1321-1327
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• 2019

This paper describes an efficient hardware implementation of modular square root (MSQR) computation over GF(p), which is the operation needed to map plaintext messages to points on elliptic curves for elliptic curve (EC)-ElGamal public-key encryption. Our method supports five sizes of elliptic curves over GF(p) defined by the National Institute of Standards and Technology (NIST) standard. For the Koblitz curves and the pseudorandom curves with 192-bit, 256-bit, 384-bit and 521-bit, the Euler's Criterion based on the characteristic of the modulo values was applied. For the elliptic curves with 224-bit, the Tonelli-Shanks algorithm was simplified and applied to compute MSQR. The proposed method was implemented using the finite field arithmetic circuit with 32-bit datapath and memory block of elliptic curve cryptography (ECC) processor, and its hardware operation was verified by implementing it on the Virtex-5 field programmable gate array (FPGA) device. When the implemented circuit operates with a 50 MHz clock, the computation of MSQR takes about 18 ms for 224-bit pseudorandom curves and about 4 ms for 256-bit Koblitz curves.

• Journal of the Korean Geotechnical Society
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• v.36 no.2
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• pp.29-42
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• 2020

In this study, centrifuge tests were performed to investigate the effect of the lateral load-moment combination on the p-y curves for 7 m-diameter monopiles installed in sand for offshore wind turbine. For the objectives, a centrifuge testing system was developed and tests were conducted at an acceleration of 68.83 g using well-instrumented model monopiles under two different lateral load-moment combinations simulated by different loading heights: 1 and 5 times monopile diameter from the ground surface. The sand was prepared as medium loose sand. Based on the centrifuge test results, the experimental p-y curves were evaluated and compared with previous literatures including API codes. The experimental results reveal that the p-y curves were little influenced by the combination of lateral load and moment. It was also found that the embedded length affects p-y curves.