• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.701-716
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• 2014

The limiting distribution for the linear placement statistics under the null hypotheses has been provided by Orban and Wolfe [9] and Kim [5] when one of the sample sizes goes to infinity, and by Kim, Lee and Wang [6] when the sample sizes of each group go to infinity simultaneously. In this paper we establish the generalized Kruskal-Wallis one-way analysis of variance for the linear placement statistics.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.365-372
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• 2017

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

• Geomechanics and Engineering
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• v.13 no.4
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• pp.701-714
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• 2017

The effect of nearby cohesionless sloping ground on the uplift capacity of horizontal strip plate anchor embedded in sand deposit with horizontal ground surface has been studied numerically. The numerical analysis has been carried out by using the lower bound theorem of limit analysis with finite elements and linear optimization. The results have been presented in the form of non-dimensional uplift capacity factor of anchor plate by changing its distance from the slope crest for different slope angles, embedment ratios and angles of soil internal friction. It has been found that the decrease in horizontal distance between the edge of the anchor plate and the slope crest causes a continuous decrease in uplift capacity of anchor plate. The optimum distance is that distance between slope crest and anchor plate below which uplift capacity of an anchor plate has been found to decrease with a decrease in normalized crest distance from the anchor plate in presence of nearby sloping ground. The normalized optimum distance between the slope crest and the anchor plate has been found to increase with an increase in slope angle, embedment ratio and soil internal friction angle.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.7-19
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• 1992

An efficient approach to limit analysis is presented whereby a continuous perfectly plastic structure is replaced by a discrete mathematical model. It is formulated as a mathematical programming problem using the static theorem of plasticity. The discretization is accomplished by writing the governing equilibrium equations in finite difference form, and is combined with piecewise linearization of the nonlinear yield curve, thus converting the formulation into a linear programming exercise. Examples of reported cases involving plates and shells are solved to illustrate the ease of application of the present method, its flexibility and accuracy - features which it make attractive to practising engineers.

• Geomechanics and Engineering
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• v.32 no.6
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• pp.639-652
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• 2023

Stepped earth slopes incorporated with anti-slide piles are widely utilized in landslide disaster preventions. Explicit consideration of the three-dimensional (3D) effect in the slope design warrants producing more realistic solutions. A 3D limit analysis of the stability of pile stabilized stepped slopes is performed in light of the kinematic limit analysis theorem. The influences of seismic excitation and surcharge load are both considered from a kinematic perspective. The upper bound solution to the factor of safety is optimized and compared with published solutions, demonstrating the capability and applicability of the proposed method. Comparative studies are performed with respect to the roles of 3D effect, pile location, pile spacing, seismic and surcharge loads in the safety assessments of stepped slopes. The results demonstrate that the stability of pile reinforced stepped slopes differ with that of single stage slopes dramatically. The optimum pile location lies in the upper portion of the slope around L_x/L = 0.9, but may also lies in the shoulder of the bench. The pile reinforcement reaches 10% universally for a looser pile spacing D_c/d_p = 5.0, and approaches 70% when the pile spacing reaches D_c/d_p = 2.0.

• International Journal of Highway Engineering
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• v.18 no.6
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• pp.69-76
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• 2016

OBJECTIVES : The objective of this study is to propose a capacity analysis methodology for riverside bike-exclusive roads. METHODS : Three steps were performed to develop a methodology to estimate bikeway capacity. First, we reviewed previous studies on the vehicle-road capacity analysis and proposed their applicability to bikeways. Second, two assumptions were made based on the traffic flow characteristics of bikeways: (1) the capacitated state in bikeways occur within a bicycle platoon, and (2) a bicycle platoon consists of more than three bicycles running in close proximity. In addition, it is assumed that the mean time headway of a bicycle platoon represents the characteristics of the platoon. The normality of the mean-time headway of a bicycle platoon calculated using the central limit theorem leads to the development of a method that estimates the riverside bikeway capacity using data collected from two different riverside bike-exclusive roads (Han-river and Anyangcheon). We used a location-fixed video camera to record videos of running bicycles and wrote a special-purpose software program to code the time-headway data from the videos. RESULTS : Time headways from 189 bicycle platoons were analyzed. The estimated mean-time headway of the capacitated bicycle flow is 1.01 s, from which the capacity of the bikeway is found to be 3578 vehicles/h. CONCLUSIONS : The proposed method that estimates bikeway capacity could be applicable to the analysis of short-range congested area rather than planning the number of lanes. In other words, it determines the sections that are temporarily highly congested and proposes appropriate strategies to mitigate the congestion.

• Geomechanics and Engineering
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• v.8 no.5
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• pp.741-756
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• 2015

The prediction of impending collapse of deep tunnel is one of the most difficult problems. Collapse mechanism of deep tunnel in layered soils is derived using a new curved failure mechanism within the framework of upper bound theorem, and effects of seepage forces are considered. Nonlinear failure criterion is adopted in the present analysis, and the possible collapse shape of deep tunnel in the layered soils is discussed in this paper. In the layered soils, the internal energy dissipations along velocity discontinuity are calculated, and the external work rates are produced by weight, seepage forces and supporting pressure. With upper bound theorem of limit analysis, two different curve functions are proposed for the two different soil stratums. The specific shape of collapse surface is discussed, using the proposed curve functions. Effects of nonlinear coefficient, initial cohesion, pore water pressure and unit weight on potential collapse are analyzed. According to the numerical results, with the nonlinear coefficient increase, the shape of collapse block will increase. With initial cohesion of the upper soil increase, the shape of failure block will be flat, and with the lower soil improving, the size of collapsing will be large. Furthermore, the shape of collapsing will decrease with the unit weight decrease.

• Coupled systems mechanics
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• v.2 no.1
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• pp.23-51
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• 2013

An analytical algorithm for the estimation of the resistance forces exerted on the dipper of a cable shovel and the specific energy consumed in the cutting-loading process is presented. Forces due to payload and to cutting of geomaterials under given initial conditions, cutting trajectory of the bucket, bucket's design, and geomaterial properties are analytically computed. The excavation process has been modeled by means of a kinematical shovel model, as well as of dynamic payload and cutting resistance models. For the calculation of the cutting forces, a logsandwich passive failure mechanism of the geomaterial is considered, as has been found by considering that a slip surface propagates like a mixed mode crack. Subsequently, the Upper-Bound theorem of Limit Analysis Theory is applied for the approximate calculation of the maximum reacting forces exerted on the dipper of the cable shovel. This algorithm has been implemented into an Excel$^{TM}$ spreadsheet to facilitate user-friendly, "transparent" calculations and built-in data analysis techniques. Its use is demonstrated with a realistic application of a medium-sized shovel. It was found, among others, that the specific energy of cutting exhibits a size effect, such that it decreases as the (-1)-power of the cutting depth for the considered example application.

• Geomechanics and Engineering
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• v.23 no.1
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• pp.1-13
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• 2020

To give a solution for seismic stability of tunnel faces subjected to earthquake ground shakings, the pseudo-dynamic approach is originally introduced to analyze tunnel face stability in this study. In the light of the upper-bound theorem of limit analysis, an advanced three-dimensional mechanism combined with pseudo-dynamic approach is proposed. Based on this mechanism, the required support pressure on tunnel face can be obtained by equaling external work rates to the internal energy dissipation and implementing an optimization searching procedure related to time. Both time and space feature of seismic waves are properly accounted for in the proposed mechanism. For this reason, the proposed mechanism can better represent the actual influence of seismic motion and has a remarkable advantage in evaluating the effects of vertical seismic acceleration, soil amplification factor, seismic wave period and initial phase difference on tunnel face stability. Furthermore, the pseudo-dynamic approach is compared with the pseudo-static approach. The difference between them is illustrated from a new but understandable perspective. The comparison demonstrates that the pseudo-static approach is a conservative method but still could provide precise enough results as the pseudo-dynamic approach if the value of seismic wavelengths is large or the height of soil structures is small.

• Geomechanics and Engineering
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• v.10 no.5
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• pp.617-633
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• 2016

A numerical study has been conducted to examine the improvement achieved in the ultimate pullout capacity of horizontal circular anchor plates embedded in undrained clay, by constructing granular columns of varying diameter over the anchor plates. The analysis has been carried out by using lower bound theorem of limit analysis and finite elements in combination with linear programming. The improvement in uplifting capacity of anchor plate is expressed in terms of an efficiency factor (${\xi}$). The efficiency factor (${\xi}$) has been defined as the ratio of ultimate vertical pullout capacity of anchor plate having diameter D embedded in soft clay reinforced by granular column to the vertical pullout capacity of the anchor plate with same diameter D embedded in soft clay only. The variation of efficiency factor (${\xi}$) for different embedment ratios and different diameter of granular column has been studied considering a wide range of softness of clay and different value of soil internal friction angle (${\phi}$) of the granular material. It is observed that ${\xi}$ increases with an increase in diameter of the granular column ($D_t$) and increase in friction angle of granular material. Also, the effectiveness of the usage of granular column increases with decrease in cohesion of the clay.