A model test on an open-cut tunnel structure under the effect of a stick-slip normal fault

Purpose–Large displacement misalignment under the action of active faults can cause complex threedimensional deformation in subway tunnels,resulting in severe damage,distortion and misalignment.There is no developed system of fortification and related codes to follow.There are scientific problems and technical challenges in this field that have never been encountered in past research and practices.Design/methodology/approach–This paper adopted a self-designed large-scale active fault dislocation simulation loading system to conduct a similar model test of the tunnel under active fault dislocation based on the open-cut tunnel project of the Urumqi Rail Transit Line 2,which passes through the Jiujiawan normal fault.The test simulated the subway tunnel passing through the normal fault,which is inclined at 608.This research compared and analyzed the differences in mechanical behavior between two types of lining section:the opencut double-line box tunnel and the modified double-line box arch tunnel.The structural response and failure characteristics of the open-cut segmented lining of the tunnel under the stick-slip part of the normal fault were studied.Findings–The results indicated that the double-line box arch tunnel improved the shear and longitudinal bending performance.Longitudinal cracks were mainly distributed in the baseplate,wall foot and arch foot,and the crack position was basically consistent with the longitudinal distribution of surrounding rock pressure.This indicated that the longitudinal cracks were due to the large local load of the cross-section of the structure,leading to an excessive local bending moment of the structure,which resulted in large eccentric failure of the lining and formation of longitudinal cracks.Compared with the ordinary box section tunnel,the improved double-line box arch tunnel significantly reduced the destroyed and damage areas of the hanging wall and footwall.The damage area and crack length were reduced by 39 and 59.3%,respectively.This indicates that the improved double-line box arch tunnel had good anti-sliding performance.Originality/value–This paper adopted a self-designed large-scale active fault dislocation simulation loading system to conduct a similar model test of the tunnel under active fault dislocation.This system increased the similarity ratio of the test model,improved the dislocation loading rate and optimized the simulation scheme of the segmented flexible lining and other key factors affecting the test.It is of great scientific significance and engineering value to investigate the structure of subway tunnels under active fault misalignment,to study its force characteristics and damage modes,and to provide a technical reserve for the design and construction of subway tunnels through active faults.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

Applications of Normality Test in Statistical Analysis

In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.

Analysis of College Students’ Test Scores Based on Two-Component Mixed Generalized Normal Distribution

In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.

Testing for Normality from the Parametric Seven-Number Summary

The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.

On Rotational Robustness of Shapiro-Wilk Type Tests for Multivariate Normality

The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.

Wigner-Matrix-Based Normality Test and Application to Weak Signal Detection in SISO/SIMO Systems

Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.

Test of Normality of Waist Measurement Data of Young Male and Female Adults based on the Quantile - Quantile Plot

This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q plot is used to determine the normality or otherwise of the data set. In this regards, the probabilities of the quantiles were computed, modified and plotted. Thereafter the correlation coefficients for the quantile - quantile plots were obtained. Results indicate that at 0.1 level of significance, the data for young adult males of the sample were not normally distributed, and had a mean value that is within the range of low risk, healthwise, whereas the distribution of the data for young female adults showed reasonable normality, but also with a mean value that is within the range of low risk in terms of health condition.

Study on Key Biological Indicators of Diabetes Based on Statistical Tests

Normality testing is a fundamental hypothesis test in the statistical analysis of key biological indicators of diabetes.If this assumption is violated,it may cause the test results to deviate from the true value,leading to incorrect inferences and conclusions,and ultimately affecting the validity and accuracy of statistical inferences.Considering this,the study designs a unified analysis scheme for different data types based on parametric statistical test methods and non-parametric test methods.The data were grouped according to sample type and divided into discrete data and continuous data.To account for differences among subgroups,the conventional chi-squared test was used for discrete data.The normal distribution is the basis of many statistical methods;if the data does not follow a normal distribution,many statistical methods will fail or produce incorrect results.Therefore,before data analysis and modeling,the data were divided into normal and non-normal groups through normality testing.For normally distributed data,parametric statistical methods were used to judge the differences between groups.For non-normal data,non-parametric tests were employed to improve the accuracy of the analysis.Statistically significant indicators were retained according to the significance index P-value of the statistical test or corresponding statistics.These indicators were then combined with relevant medical background to further explore the etiology leading to the occurrence or transformation of diabetes status.

关于用SPSS中单样本K-S检验法进行正态分布等的一致性检验时适用条件的研究

根据柯尔莫哥洛夫单样本分布一致性检验的基本原理,通过实际的计算比较分析发现,SPSS中的K-S检验法实质上是Lilliefors修正。原假设成立的概率是基于nDn的极限分布计算得出的,所以它适用于样本含量超过100以上的连续型计量资料的分布一致性检验。

基于自正则的K-S方法的均值变点检验——对我国上证综指的实证分析

将基于自正则的K-S方法应用于检测我国上证综指收盘价序列的均值变点.与传统的Kolmogorov-Smirnov检验以及"滑窗"检验相比,基于自正则的K-S检验方法避免了长程方差的相合估计和带宽参数的选取.最终构造的检验统计量的渐近分布不受冗余参数的影响,而且其功效也是单调的.

基于最优k值k-means聚类分析的湖相沉积土层岩土参数分布研究

对岩土参数进行传统的k-means聚类分析时,因无法确定k值,而导致无法有效剔除误差数据。为得到岩土参数可靠取值范围,基于最优k值的k-means算法进行研究,通过量化样本内距离和聚类紧密性来确定聚类数目k值,避免了传统k值的随机选取。对粉土的三个基本物理力学指标:黏聚力c、内摩擦角φ、压缩模量E_(s)进行空间聚类分析。通过比较不同k值时的E_(E)值,确定最优k值为5。聚类完成后,原样本被划分为5类子样本。样本数量最多的一类为最优子样本,这类子样本与原样本分布一致,且数量偏离程度及变异性较小。对除最优类外的其他四类子样本进行分布检验,可知A-D检验法适用于小样本,而K-S检验法适用于大样本。根据偏度系数c值,调整合适的区间长度,进一步优化参数取值范围,并与工程实际采用值对比,检验方法的可行性。该分析方法实现由小样本代替大样本进行参数统计分析求取可靠的取值区间,简化计算,提高工作效率。

Seismic response of tunnel under normal fault slips by shaking table test technique

Mountain tunnel crossing a normal fault in seismically active zone is easily affected by normal fault slip and earthquake. It is necessary to study tunnel dynamic response under action of normal fault slip and earthquake. In this paper, a three-dimensional normal fault sliding device was designed, and a shaking table test was carried out to study tunnel seismic performance under normal fault slip. The results show that peak acceleration of lining is dominated by an existence of fault and direction of seismic excitation, not normal fault slip. And the incremental strains of lining in critical zone with 1.7 times fault thickness and centered in faults induced by normal fault slip and seismic excitation are larger than ones only by seismic excitation. And the incremental strains in critical zone increase with the increase of normal fault slip magnitude ranging from 0 to 2 mm. And normal fault slip results in a significant reduction of overall tunnel stiffness subjected to an earthquake. These experimental results provide a scientific reference for prevention and control measurement of tunnel damage under earthquake and normal fault slip.

基于K-S检验法和ALTA的IGBT模块可靠性寿命分布研究

为了获得绝缘栅双极晶体管(insulated gate bipolar transistor,IGBT)的寿命信息及确定其寿命分布,提出了一种利用Kolmogorov-Smirnov检验法和加速寿命测试数据分析软件(accelerated life testing dataanalysissoftware,ALTA)对其加速寿命试验数据进行研究的新方法。该方法首先对IGBT模块寿命做对数正态分布假设,然后利用K-S检验法对一组IGBT加速寿命数据进行Weibull、对数正态等分布检验对比分析,进而利用ALTA对另一组IGBT加速寿命数据进行仿真分析,结果表明在阿伦尼斯(Arrhenius)加速模型下,IGBT模块寿命服从对数正态分布。该方法使得快速估算IGBT模块寿命成为可能。

Frictional behavior of quartz gouge during slide-hold-slide considering normal stress oscillation

Slide-hold-slide(SHS)test is an essential experimental approach for studying the frictional stability of faults.The origin SHS framework was established based on a consistent constant normal stress,which cannot truly reflect the stress disturbance around fault zones.In this paper,we conducted a series of'dynamic SHS tests',which includes normal stress oscillations in the relaxation stage with different oscillation amplitudes and frequencies on synthetic quartz gouge using a double direct shear assembly.The experimental results reveal that the amplitude of the normal load oscillation has a remarkable effect on the frictional relaxation and healing patterns.However,the frequency of the normal load oscillation has a minor effect.Additionally,the shear loading rate is proportional to the normal loading rate during the relaxation stage,and the normal stiffness of the quartz layer remains nearly constant under various loading conditions.The creep rate during the hold phase is not obviously affected by the normal load oscillation,while the precursory slip is also sensitive to the oscillation amplitude.This study provides insights into the evolution of frictional stability in discontinuities and is beneficial for controlling relative disasters in fault zones.

Constant-Step Stress Accelerated Life Test of VFD under Logarithmic Normal Distribution Case

In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.

A note on self-normalized Dickey-Fuller test for unit root in autoregressive time series with GARCH errors

In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.

The Normal Color Vision Evaluated With FM 100-hue Test

One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant difference in the total error score (TES) between the malesand females or between the right and left eyes,but there existed some rela-tionships between the TES and age.The total error score (TES) was thelowest in the 20-29 age group and increased gradually with aging.Theanalysis of the partial...

Normalized fatigue properties of asphalt mixture at various temperatures

This study normalized the mixture's fatigue behavior at various temperatures,and the strength and fatigue tests of the mixture were conducted.The stress state of the asphalt mixture includes direct tensile,uniaxial compression,and indirect tensile.The Desai yield surface and fatigue path were proposed.And a normalized fatigue characteristics model of the mixture was established.The following conclusions were obtained.With the increases in the loading rate,the strength of the asphalt mixture increased.As the temperature increases,the strength of the mixture is reduced.At various temperatures and rates,the strength forms a closed curved surface.The Desai strength yield surface was established,which forms a closed curved surface.When the loading rate and temperature are below a certain critical line,the asphalt mixture will not undergo strength damage.At a fixed stress state,the fatigue damage path of the mixture was determined.The stress ratio was determined considering the influence of the loading rate.In this way,a normalized model can be described to express the asphalt mixture fatigue properties at various temperatures and stress levels.For the asphalt mixture in an indirect tensile state,the normalized fatigue equation parameter is 4.09.This model is more suitable for reflecting the viscous-elastic behavior of the mixtures than the fatigue equation determined by the notional stress ratio.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.