• Geomechanics and Engineering
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• v.18 no.3
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• pp.225-234
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• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

• Nuclear Engineering and Technology
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• v.47 no.6
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• pp.700-711
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• 2015

Sodium-cooled fast breeder reactors use liquid sodium as a moderator and coolant to transfer heat from the reactor core. The main hazard associated with sodium is its rapid reaction with water. Sodium-water reaction (SWR) takes place when water or vapor leak into the sodium side through a crack on a heat-transfer tube in a steam generator. If the SWR continues for some time, the SWR will damage the surface of the defective area, causing it to enlarge. This self-enlargement of the crack is called "self-wastage phenomena." A stepwise numerical evaluation model of the self-wastage phenomena was devised using a computational code of multicomponent multiphase flow involving a sodium-water chemical reaction: sodiumwater reaction analysis physics of interdisciplinary multiphase flow (SERAPHIM). The temperature of gas mixture and the concentration of NaOH at the surface of the tube wall are obtained by a numerical calculation using SERAPHIM. Averaged thermophysical properties are used to assess the local wastage depth at the tube surface. By reflecting the wastage depth to the computational grid, the self-wastage phenomena are evaluated. A two-dimensional benchmark analysis of an SWAT (Sodium-Water reAction Test rig) experiment is carried out to evaluate the feasibility of the numerical model. Numerical results show that the geometry and scale of enlarged cracks show good agreement with the experimental result. Enlarged cracks appear to taper inward to a significantly smaller opening on the inside of the tube wall. The enlarged outer diameter of the crack is 4.72 mm, which shows good agreement with the experimental data (4.96 mm).

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.677-691
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• 2018

Reliability assessment of complex structures using simulation methods is time-consuming. Thus, surrogate models are usually employed to reduce computational cost. AK-MCS is a surrogate-based Active learning method combining Kriging and Monte-Carlo Simulation for structural reliability analysis. This paper proposes three modifications of the AK-MCS method to reduce the number of calls to the performance function. The first modification is related to the definition of an initial Design of Experiments (DoE). In the original AK-MCS method, an initial DoE is created by a random selection of samples among the Monte Carlo population. Therefore, samples in the failure region have fewer chances to be selected, because a small number of samples are usually located in the failure region compared to the safe region. The proposed method in this paper is based on a uniform selection of samples in the predefined domain, so more samples may be selected from the failure region. Another important parameter in the AK-MCS method is the size of the initial DoE. The algorithm may not predict the exact limit state surface with an insufficient number of initial samples. Thus, the second modification of the AK-MCS method is proposed to overcome this problem. The third modification is relevant to the type of regression trend in the AK-MCS method. The original AK-MCS method uses an ordinary Kriging model, so the regression part of Kriging model is an unknown constant value. In this paper, the effect of regression trend in the AK-MCS method is investigated for a benchmark problem, and it is shown that the appropriate choice of regression type could reduce the number of calls to the performance function. A stepwise approach is also presented to select a suitable trend of the Kriging model. The numerical results show the effectiveness of the proposed modifications.