• Geomechanics and Engineering
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• v.12 no.2
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• pp.313-326
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• 2017

Based on the reliability theory and limit analysis method, the roof stability of a shallow tunnel is investigated under the condition of surface settlement. Nonlinear Hoek-Brown failure criterion is adopted in the present analysis. With the consideration of surface settlement, the internal energy and external work are calculated. Equating the rate of energy dissipation to the external rate of work, the expression of support pressure is derived. With the help of variational approach, a performance function is proposed to reliability analysis. Improved response surface method is used to calculate the Hasofer-Lind reliability index and the failure probability. In order to assess the validity of the present results, Monte-Carlo simulation is performed to examine the correctness. Sensitivity analysis is used to estimate the influence of different variables on reliability index. Among random variables, the unit weight significantly affects the reliability index. It is found that the greater coefficient of variation of variables lead to the higher failure probability. On the basis of the discussions, the reliability-based design is achieved to calculate the required tunnel support pressure under different situations when the target reliability index is obtained.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.2 no.3
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• pp.87-99
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• 1982

This study proposes a reliability based design criteria for the R.C. superstructures of highway bridges. Uncertainties associated with the resistance of T or rectangular sections are investigated, and a set of appropriate uncertainties associated with the bridge dead and traffic live loads are proposed by reflecting our level of practice. Major 2nd moment reliability analysis and design theories including both Cornell's MFOSM(Mean First Order 2nd Moment) Methods and Lind-Hasofer's AFOSM(Advanced First Order 2nd Moment) Methods are summarized and compared, and it has been found that Ellingwood's algorithm and an approximate log-normal type reliability formula are well suited for the proposed reliability study. A target reliability index (${\beta}_0=3.5$) is selected as an optimal value considering our practice based on the calibration with the current R.C. bridge design safety provisions. A set of load and resistance factors is derived by the proposed uncertainties and the methods corresponding to the target reliability. Furthermore, a set of nominal safety factors and allowable stresses are proposed for the current W.S.D. design provisions. It may be asserted that the proposed L.R.F.D. reliability based design criteria for the R.C. highway bridges may have to be incorporated into the current R.C. bridge design codes as a design provision corresponding to the U.S.D. provisions of the current R.C. design code.

• Computers and Concrete
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• v.26 no.5
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• pp.385-395
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• 2020

The influence of combination of nano silica and silica fume, as partial cement replacement materials, on the properties of concrete has been studied through the measurement of compressive strength. The compressive strength of concrete in terms of mean, standard deviation and with-in-test coefficient of variation related to the variation in the nominated parameters have also been developed. The compressive strength data developed experimentally has been analyzed using normal-probability distribution and partial safety factors of composite concretes have been evaluated by using first order second moment approach with Hasofer Lind's method. The use of Nano silica and silica fume in concrete decreases the partial safety factor of concrete i.e., increase the reliability of concrete. The experimental results show that the properties of concrete having nano silica and silica fume in combination were better than that of a plain concrete. The SEM test results showing the level of Ca(OH)₂ in plain concrete and consumption level Ca(OH)₂ of concrete containing nano silica & silica fume have also been presented.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.1 no.1
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• pp.21-32
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• 1981

Recent trends in design standards development in some European countries and U.S.A. have encouraged the use of probabilistic limit sate design concepts. Reliability based design criteria such as LSD, LRFD, PBLSD, adopted in those advanced countries have the potentials that they afford for symplifying the design process and placing it on a consistent reliability bases for various construction materials. A reliability based design criteria for RC flexural members are proposed in this study. Lind-Hasofer's invariant second-moment reliability theory is used in the derivation of an algorithmic reliability analysis method as well as an iterative determination of load and resistance factors. In addition, Cornell's Mean First-Order Second Moment Method is employed as a practical tool for the approximate reliability analysis and the derivation of design criteria. Uncertainty measures for flexural resistance and load effects are based on the Ellingwood's approach for the evaluation of uncertainties of loads and resistances. The implied relative safety levels of RC flexural members designed by the strength design provisions of the current standard code were evaluated using the second moment reliability analysis method proposed in this study. And then, resistance and load factors corresponding to the target reliability index(${\beta}=4$) which is considered to be appropriate level of reliability considering our practices are calculated by using the proposed methods. These reliability based factors were compared to those specified by our current ultimate strength design provisions. It was found that the reliability levels of flexural members designed by current code are not appropriate, and the code specified resistance and load factors were considerably different from the reliability based resistance and load factors proposed in this study.

• International Journal of Highway Engineering
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• v.16 no.6
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• pp.105-113
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• 2014

PURPOSES: The objective of this paper is to select the confidential intervals by utilizing the second moment reliability index(Hasofer and Lind; 1974) related to the number of load applications to failure which explains the fatigue failure and rut depth that it indicates the permanent deformation. By using Finite Element Method (FEM) Program, we can easily confirm the rut depth and number of load repetitions without Pavement Design Procedures for generally designing pavement depths. METHODS : In this study, the predictive models for the rut depth and the number of load repetitions to fatigue failure were used for determining the second moment reliability index (${\beta}$). From the case study results using KICTPAVE, the results of the rut depth and the number of load repetitions to fatigue failure were deducted by calculating the empirical predictive equations. Also, the confidential intervals for rut depth and number of load repetitions were selected from the results of the predictive models. To determine the second moment reliability index, the spreadsheet method using Excel's Solver was used. RESULTS : From the case studies about pavement conditions, the results of stress, displacement and strain were different with depth conditions of layers and layer properties. In the clay soil conditions, the values of strain and stresses in the directly loaded sections are relatively greater than other conditions. It indicates that the second moment reliability index is small and confidential intervals for rut depth and the number of load applications are narrow when we apply the clay soil conditions comparing to the applications of other soil conditions. CONCLUSIONS : According to the results of the second moment reliability index and the confidential intervals, the minimum and maximum values of reliability index indicate approximately 1.79 at Case 9 and 2.19 at Case 22. The broadest widths of confidential intervals for rut depth and the number of load repetitions are respectively occurred in Case 9 and Case 7.