• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.127-134
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• 1998

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

• Proceedings of the Korean Geotechical Society Conference
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• 1999.03a
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• pp.3-46
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• 1999

A new method called SRICOS is proposed to predict the scour depth z versus time t around a cylindrical bridge pier of diameter D founded in clay. The steps involved are ; 1. taking samples at the bridge pier site, 2. testing them in an Erosion Function Apparatus called the EFA to obtain the scour rate z versus the hydraulic shear stress applied $\tau$, 3. predicting the maximum shear stress r max which will be induced around the pier by the water flowing at ν Ο before the scour hole starts to develop, 4. using the measured z versus r curve to obtain the initial scour rate zi corresponding to r max , 5. predicting the maximum depth of scour zmax for the pier, 6. using zi and zmarx to develop the hyperbolic function describing the scour depth z versus time t curve, and 7. reading the z vs. t curve at a time corresponding to the duration of the flood to find the scour depth which will develop around the pier. A new apparatus is developed to measure the z vs t curve of step 2, a series of advanced numerical simulations are performed to develop an equation for the $\tau$ max value of step 3, and a series of flume tests are performed to develop an equation for the zmax value of step 5. The method is evaluated by comparing predictions and measurements in 42 flume experiments.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.10a
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• pp.409-429
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• 2006

In designing rock-socketed drilled shaft, bearing capacity evaluation is very important because the maximum values of base and side resistance are not generally mobilized at the same value of displacement, FHWA and AASHTO code suggest different ultimate bearing capacity formular according to rock type and shaft settlement. In domestic code suggest base resistance and side resistance can be added on condition that after confirming the result of field load test with axial load transfer test. This paper shows that static load test and hi-directional load test result analysis of deep rock-socketed drilled shaft in three different sites. Load-settlement curve, t-z, and q-w curve in rock-socketed part were calculated and compared. t-z curve in weathered and soft rock showed no deflection softening behavior in pretty large strain (about 2-3% of diameter). Ultimate resistance could be the summation of side resistance and base resistance in rock-socketed drilled shaft in domestic sites.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.367-379
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• 1996

Let $V = {(z, y) : f(z, y) = z^n + Ay^\alpha z^p + y^\beta z^q + y^k = 0}$ and $W = {(z, y) : g(z, y) = z^n + By^\gamma z^s + y^\delta z^t + y^k = 0}$ be germs of analytic irreducible subvarieties of a polydisc near the origin in $C^2$ with n < k and (n, k) = 1 where A and B are complex numbers. Assume that V and W are topologically equivalent near the origin.

• Journal of the Korean Geotechnical Society
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• v.33 no.1
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• pp.31-38
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• 2017

Skin friction of prebored and precast pile may be one of the most critical factors affecting the bearing capacity and settlement. Special attention was given to the interface behavior of pile-cement milk-surrounding soil when the load is acting on the prebored and precast pile. The cases of single pile were analyzed through a three-dimensional finite element approach and pile loading tests. A series of numerical analyses of the interface of pile-cement milk-soil was conducted with the proposed t-z curve and field measurements. It is shown that the use of cement milk around the pile increases the skin friction and reduces the pile settlement. It is also known that the suggested t-z curve between the cement milk and the soil, enhances the accuracy of the numerical analysis results.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.899-900
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• 2009

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.401-419
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• 2024

Let K, H, K_II and H_II be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface T_γ(α) with the radius γ along a timelike curve α(s) in Minkowski 3-space E³₁. We prove that T_γ(α) must be a (K, H)-Weingarten surface and a (K, H)-linear Weingarten surface. We also show that T_γ(α) is (X, Y)-Weingarten type if and only if its central curve is a circle or a helix, where (X, Y) ∈ {(K, K_II), (K, H_II), (H, K_II), (H, H_II), (K_II , H_II)}. Furthermore, we prove that there exist no timelike tubular surfaces of (X, Y)-linear Weingarten type, (X, Y, Z)-linear Weingarten type and (K, H, K_II, H_II)-linear Weingarten type along a timelike curve in E³₁, where (X, Y, Z) ∈ {(K, H, K_II), (K, H, H_II), (K, K_II, H_II), (H, K_II, H_II)}.

• Journal of the Korean Geotechnical Society
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• v.34 no.12
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• pp.43-58
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• 2018

In this study, the load-transfer behavior along the shaft of the prebored and precast piles was investigated by pile loading tests. Special attention was given to quantifying the skin frictions developed between the pile-soil interfaces of the 14 instrumented test piles. Based on this detailed field tests, the load - settlement curves and axial load distributions of piles were obtained and the load-transfer curves (t-z curves) for the test piles were proposed. As such, it is found that the test results show two different load transfer behaviors; ductile and brittle behavior curves. The corresponding t-z curves are proposed based on the hyperbolic- and sawtooth-shape, respectively. By validating the accuracy of the proposed curves, it is also found that the prediction results based on the proposed load-transfer curve are in good agreement with the general trends observed by the field loading tests.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.379-383
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• 2007

We show that the modular equation ${\phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${\Gamma}_0$(n) gives an affine model of the modular curve $X_0$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $T_n(z)\;and\;T_n$(mz).

• Proceedings of the Korean Geotechical Society Conference
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• 2010.09a
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• pp.357-367
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• 2010

In this study, several design and construction cases of the pile bent system for bridges were introduced. The lateral displacement of the pile bent system is larger than the displacement of pile cap system, due to the smaller bending stiffness and the longer unsupported length. So, the analysis of the lateral pile displacement is main factor for the design of pile bent system and superstructure. For the accurate estimation of the pile displacement, an iterative analysis method was developed. The superstructure was analyzed regarding the pile foundation as $6{\times}6$ spring and the substructure was analysed using non-linear load transfer curves (p-y, t-z, q-z curve). And, to verify this analysis method, the estimated displacements are compared with the results of lateral load test. This analysis method is expected to be a viable alternative approach for the design of bridge foundation hereafter.