![]() The other is to consider the extension of LHS when the original LHS was subsequently determined to be too small and a new LHS of a larger size without original sampling points might be time consuming. ![]() One is sequential sampling for sequential analysis, adaptive metamodeling, and so on. There are at least two situations that need the extension of sampling, especially for time consuming simulation systems. The extension of LHS is to obtain a LHS of a larger size that reserves the preexisting LHS (or the original LHS). Compared with other random or stratified sampling algorithms, LHS has a better space filling effect, better robustness, and better convergence character. Latin Hypercube Sampling (LHS) is one of the most popular sampling approaches, which is widely used in the fields of simulation experiment design, uncertainty analysis, adaptive metamodeling, reliability analysis, and probabilistic load flow analysis. These algorithms are illustrated by an example and applied to evaluating the sample means to demonstrate the effectiveness. ![]() Therefore, a general extension algorithm based on greedy algorithm is proposed to reduce the extension time, which cannot guarantee to contain the most original points. The basic general extension algorithm is proposed to reserve the most original points, but it costs too much time. The relationship of original sampling points in the new LHS structure is shown by a simple undirected acyclic graph. In order to get a strict LHS of larger size, some original points might be deleted. The extension algorithms start with an original LHS of size and construct a new LHS of size that contains the original points as many as possible. These findings may provide a useful reference for the reliability-based seismic design of tunnels.For reserving original sampling points to reduce the simulation runs, two general extension algorithms of Latin Hypercube Sampling (LHS) are proposed. The results also show that the soil parameter uncertainty can be properly considered by introducing a factor of safety. The distribution type effect increases sharply for the cases with high variation degrees, and the lognormal distribution generally predicts a lower mean, standard deviation, and probability of exceedance. The influence of shear strength parameters is insignificant, despite a slightly larger standard deviation appears for the positive correlation. Increased motion intensity leads to an increased standard deviation, especially for flexible tunnels. The results indicate that the parameter uncertainty can have a significant impact on tunnel seismic deformations. Analyses are performed for a wide range of soil shear wave velocities, ground motion intensities, lining Young’s moduli, correlation structures, distribution types, and coefficients of variation. Two-dimensional nonlinear finite difference models combined with the Monte Carlo simulation are employed to assess the influence of parameter uncertainty. Opposite to traditionally performed deterministic analysis, this paper introduces stochastic dynamic time-history analysis to quantify the variability of seismic-induced tunnel deformations in a probabilistic framework. ![]() Tunnel damages are increasing worldwide in major earthquakes, some of which may result from the underestimated seismic actions and uncertainties associated with the design parameters. ![]()
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