Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Modification to first-order Born approximation for improved prediction of scattered sound from weakly scattering objects

When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.

Failure probability analysis of coal crushing induced by uncertainty of influential parameters under condition of in-situ reservoir

The uncertainties of some key influence factors on coal crushing,such as rock strength,pore pressure and magnitude and orientation of three principal stresses,can lead to the uncertainty of coal crushing and make it very difficult to predict coal crushing under the condition of in-situ reservoir.To account for the uncertainty involved in coal crushing,a deterministic prediction model of coal crushing under the condition of in-situ reservoir was established based on Hoek-Brown criterion.Through this model,key influence factors on coal crushing were selected as random variables and the corresponding probability density functions were determined by combining experiment data and Latin Hypercube method.Then,to analyze the uncertainty of coal crushing,the firstorder second-moment method and the presented model were combined to address the failure probability involved in coal crushing analysis.Using the presented method,the failure probabilities of coal crushing were analyzed for WS5-5 well in Ningwu basin,China,and the relations between failure probability and the influence factors were furthermore discussed.The results show that the failure probabilities of WS5-5 CBM well vary from 0.6 to 1.0; moreover,for the coal seam section at depth of 784.3-785 m,the failure probabilities are equal to 1,which fit well with experiment results; the failure probability of coal crushing presents nonlinear growth relationships with the increase of principal stress difference and the decrease of uniaxial compressive strength.