• Geomechanics and Engineering
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• v.16 no.6
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• pp.655-667
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• 2018

To evaluate the stability of a rock slope with one pre-exiting vertical crack, this paper performs corresponding probabilistic stability analysis. The existence of cracks is generally ignored in traditional deterministic stability analysis. However, they are widely found in either cohesive soil or rock slopes. The influence of one pre-exiting vertical crack on a rock slope is considered in this study. The safety factor, which is usually adopted to quantity the stability of slopes, is derived through the deterministic computation based on the strength reduction technique. The generalized Hoek-Brown (HB) failure criterion is adopted to characterize the failure of rock masses. Considering high nonlinearity of the limit state function as using nonlinear HB criterion, the multivariate adaptive regression splines (MARS) is used to accurately approximate the implicit limit state function of a rock slope. Then the MARS is integrated with Monte Carlo simulation to implement reliability analysis, and the influences of distribution types, level of uncertainty, and constants on the probability density functions and failure probability are discussed. It is found that distribution types of random variables have little influence on reliability results. The reliability results are affected by a combination of the uncertainty level and the constants. Finally, a reliability-based design figure is provided to evaluate the safety factor of a slope required for a target failure probability.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.1
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• pp.9-16
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• 1990

The safety of concrete nuclear containment structures should be secured against all kinds of loading due to various natural disasters or extraordinary accidental loads. The current design criteria of concrete containment structures are not based on the reliabillty-based design concept but rely on the conventional design concept. In this paper, a probabillty-based reliability analysis were proposed based on a FEM-based random vibration analysis and serviceability limit state of structures. The limit state model defined for the study is a serviceability limit state in terms of the more realistic crack failure that might cause the emission of radioactive materials, and the results are compared with those of the strength limit state. More accurate reliability analyses under various dynamic loads such as earthquake loads were made possible by incorporation the FEM and random vibration theory, which is different from the conventional reliability analysis method. The uncertainties in loads and resistance available in Korea and the refernces were adapted to the situation of Korea, and especially in the case of earthquake, the design earthquake was assessed based on the available re ports on probabilistic description of earthquake ground acceleration in the Korea peninsula.

• Geomechanics and Engineering
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• v.28 no.4
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• pp.405-419
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• 2022

Cavity expansion and contraction solutions for cylindrical and spherical cavities in unsaturated residual soils are presented in this paper. Varying soil state in the plastic zone is accounted by a numerical approach, wherein an element-by-element discretization of the plastic zone of both expanding and contracting cavities is carried out. Unlike existing methods utilizing self-similarity technique, the solution procedure enables the prediction of entire soil-state at any stage of expansion and subsequent contraction. It is also applicable for both cavity creation and expansion problems. The approach adopts constant contribution of suction to effective stress (constant X^s drainage condition) for analysis. The analysis procedure is validated by interpreting the previously reported pressuremeter test results in lateritic residual soil. The typical cavity expansion and contraction characteristics of unsaturated Indian lateritic soil were then examined using this solution procedure. The effect of initial soil-state on cavity limit pressure, plastic radius, reverse yield pressure, and reverse plastic radius are also presented.

• Computers and Concrete
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• v.4 no.4
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• pp.259-272
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• 2007

A method based on the lower-bound theorem of limit analysis is presented for the capacity assessment of nodal zones in strut-and-tie models. The idealized geometry of the nodal zones is formed by the intersection of effective widths of the framing struts and ties. The stress distribution is estimated by dividing the nodal zones into constant stress triangles separated by lines of stress discontinuity. The strength adequacy is verified by comparing the biaxial stress field in each triangle with the corresponding failure criteria. The approach has been implemented in a computer-based strut-and-tie tool called CAST (Computer-Aided Strut-and-Tie). An application example is also presented to illustrate the approach.

• Journal of Korean Tunnelling and Underground Space Association
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• v.20 no.6
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• pp.1125-1146
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• 2018

Segment lining applied to the TBM tunnel is mainly made of concrete, and it requires sufficient structural capacity to resist loads received during the construction and also after the completion. When segment lining is design to the Limit State Design, both Ultimate Limit State (ULS) and Service Limit State (SLS) should be met for the possible load cases that covers both permanent and temporary load cases - such as load applied by TBM. When design segment lining, it is important to check structural capacity at the joints as both temporary and permanent loads are always transferred through the segment joints, and sometimes the load applied to the joint is high enough to damage the segment - so called bursting failure. According to the various design guides from UK (PAS 8810, 2016), compression stress at the joint surface can generate bursting failure of the segment. This is normally from the TBM's jacking force applied at the circumferential joint, and the lining's hoop thrust generated from the permanent loads applied at the radial joint. Therefore, precast concrete segment lining's joints shall be designed to have sufficient structural capacity to resist bursting stresses generated by the TBM's jacking force and by the hoop thrust. In this study, bursting stress at the segment joints are calculated, and the joint's structural capacity was assessed using Leonhardt (1964) and FEM analysis for three different design cases. For those three analysis cases, hoop thrust at the radial joint was calculated with the application of the most widely used limit state design codes Eurocode and AASHTO LRFD (2017). For the circumferential joints bursting design, an assumed TBM jack force was used with considering of the construction tolerance of the segments and the eccentricity of the jack's position. The analysis results show reinforcement is needed as joint bursting stresses exceeds the allowable tensile strength of concrete. This highlights that joint bursting check shall be considered as a mandatory design item in the limit state design of the segment lining.

• Journal of the Korea Institute of Military Science and Technology
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• v.11 no.5
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• pp.5-11
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• 2008

Recently developed radars use the solid-state power amplifier to amplify the RF signal. The stability of RF signal directly depends on that of the electric power. So the stable and reliable electric power should be needed. When the electric power switch is tuned on for the first time in order to operate the radar system, the in-rush current is generated because of the capacitive characteristic. The excess in-rush current breaks the element. Therefore, the analysis about the in-rush current to design the electric power system is necessary. In this paper, modeling and simulation on the whole power system is carried out and the necessity of limiting the in-rush current is verified. After the analysis, the circuit to limit the in-rush current is designed and examined to verify the analysis. The circuit is good enough to limit the in-rush current.

• Journal of the Korean Society of Safety
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• v.31 no.6
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• pp.58-66
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• 2016

This study aims to estimate the failure probability of concrete gravity dams for their risk analysis under flood situation. To the end, failure modes of concrete gravity dams and their limit state functions are proposed based on numerous review of domestic and international literatures on the dam failure cases and design standards. Three failure modes are proposed: overturning, sliding, and overstress. Based on the failure modes the limit state functions, the failure probability is assessed for a weir section and a non-weir section of a dam in Korea. As water level is rising from operational condition to extreme flood condition, the failure probability is found to be raised up to the warning condition, especially for overturning mode at the non-weir section. The result can be used to reduce the risk of the dam by random environmental variables under possible flood situation.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.293-303
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• 2010

The purpose of this study is to classify a three-fold role of the history of mathematics through epistemological analysis. Based on the history of infinity and limit, the "potential infinity" and "actual infinity" discourses are described using four different historical epistemologies. The interdependence between the mathematical concepts is also addressed. By using these analyses, three different uses of the history of mathematical concepts, infinity and limit, are discussed: past, present, and future use.

• Earthquakes and Structures
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• v.18 no.3
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• pp.285-296
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• 2020

Dams are important structures for management of water supply for irrigation or drinking, flood control, and electricity generation. In seismic regions, the structural safety of concrete gravity dams is important due to the high potential of life and economic loss if they fail. Therefore, the seismic analysis of existing dams in seismically active regions is crucial for predicting responses of dams to ground motions. In this paper, earthquake response of concrete gravity dams is investigated using the finite element (FE) method. The FE model accounts for dam-water-foundation rock interaction by considering compressible water, flexible foundation effects, and absorptive reservoir bottom materials. Several uncertainties regarding structural attributes of the dam and external actions are considered to obtain the fragility curves of the dam-water-foundation rock system. The structural uncertainties are sampled using the Latin Hypercube Sampling method. The Pine Flat Dam in the Central Valley of Fresno County, California, is selected to demonstrate the methodology for several limit states. The fragility curves for base sliding, and excessive deformation limit states are obtained by performing non-linear time history analyses. Tensile cracking including the complex state of stress that occurs in dams was also considered. Normal, Log-Normal and Weibull distribution types are considered as possible fits for fragility curves. It was found that the effect of the minimum principal stress on tensile strength is insignificant. It is also found that the probability of failure of tensile cracking is higher than that for base sliding of the dam. Furthermore, the loss of reservoir control is unlikely for a moderate earthquake.

• Journal of Korea Water Resources Association
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• v.43 no.11
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• pp.967-976
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• 2010

AFDA (Approximate Full Distribution Approach) model of FORM (First-Order Reliability Model) which can quantitatively calculate the probability that storm sewer reach to performance limit state was developed in this study. It was defined as a failure if amount of inflow exceed the capacity of storm sewer. Manning's equation and rational equation were used to determine the capacity and inflow of reliability function. Furthermore, statistical characteristics and distribution for the random variables were analyzed as a reliability analysis. It was found that the statistical distribution for annual maximum rainfall intensity of 10 cities in Korea is matched well with Gumbel distribution. Reliability model developed in this study was applied to Y shaped storm sewer system to calculate the probability that storm sewer may exceed the performance limit state. Probability of failure according to diameter was calculated using Manning's equation. Especially, probability of failure of storm sewer in Mungyeong and Daejeon was calculated using rainfall intensity of 50-year return period. It was found that probability of failure can be significantly increased if diameter is decreased below the original diameter. Therefore, cleaning the debris in sewer pipes to maintain the original pipe diameter should be one of the best ways to reduce the probability of failure of storm sewer. In sewer system, two sewer pipes can flow into one sewer pipe. For this case, probability of system failure was calculated using multiple failure mode. Reliability model developed in this study can be applied to design, maintenance, management, and control of storm sewer system.