Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

The characterization of the time-dependent nonlinear viscoelastic of an LDPE melt using a simple thixotropy model

A new simple thixotropy model was proposed in the present paper to characterize the thixotropy-loop experiments and the start-up experiment of an LDPE （PE-FSB23D0221Q200） melt. The thixotropy model is a combination of a viscoelastic-component and a postulated kinetics process of structure change, which is constituted in terms of the indirect microstructural approach usually adopted in the characterization of thixotropy. The descriptions of the thixotropy model on both the thixotropy-loop tests and the startup test show good agreement with the experimental values, indicating the good capability of the model in characterizing the time-dependent nonlinear viscoelastic. The stress overshoot phenomenon and the stress relaxation after cessation of the thixotropy loop test can be described well by the model, whereas both of the typical viscoelastic phenomena could not be described in our previous work with a variant Huang model.

Development of a time-dependent energy model to calculate the mining-induced stress over gates and pillars

Generally, longwall mining-induced stress results from the stress relaxation due to destressed zone that occurs above the mined panel. Knowledge of induced stress is very important for accurate design of adjacent gateroads and intervening pillars which helps to raise the safety and productivity of longwall mining operations. This study presents a novel time-dependent analytical model for determination of the longwall mining-induced stress and investigates the coefficient of stress concentration over adjacent gates and pillars. The model is developed based on the strain energy balance in longwall mining incorporated to a rheological constitutive model of caved materials with time-varying parameters. The study site is the Tabas coal mine of Iran. In the proposed model, height of destressed zone above the mined panel, total longwall mining-induced stress, abutment angle, induced vertical stress, and coefficient of stress concentration over neighboring gates and intervening pillars are calculated. To evaluate the effect of proposed model parameters on the coefficient of stress concentration due to longwall mining, sensitivity analysis is performed based on the field data and experimental constants. Also, the results of the proposed model are compared with those of existing models. The comparative results confirm a good agreement between the proposed model and the in situ measurements. According to the obtained results, it is concluded that the proposed model can be successfully used to calculate the longwall mining-induced stress. Therefore, the optimum design of gate supports and pillar dimensions would be attainable which helps to increase the mining efficiency.

Time-dependent behavior comparison of long-span concrete arch bridge between prototype and model

Beipanjiang Bridge is a long-span concrete arch bridges with stiffened skeleton(CABSS)in China.It has a fixed end arch with the span of 445 m and the rise of 100 m.To evaluate the rationality of the construction sequence and the time-dependent behavior of CABSS,an experimental study of a model bridge was explored.But the measured displacement and stress ratios of arch rib between prototype and model bridge did not subject to linear similarity relation when the time-dependent behavior was considered.So,the three-dimensional finite element models were established,and verified by the measured data.Then,the displacements and stresses of the prototype and model were compared with each other,when the elastic analysis or coupling of temperature and shrinkage,creep effect was considered.Furthermore,a parametric study was studied.The results showed that when the temperature,shrinkage and creep effect of concrete are considered,the finite element analysis results of prototype and model agree well with the measured results.The displacement and stress ratios of prototype and model bridge in construction and bridge completed stage do not present the geometric similarity ratio 7.5 and 1.0,respectively.They are also much influenced by concrete predicting model and variation of temperature.

Marginal Distribution Plots for Proportional Hazards Models with Time-Dependent Covariates or Time-Varying Regression Coefficients

Given a sample of regression data from (Y, Z), a new diagnostic plotting method is proposed for checking the hypothesis H0: the data are from a given Cox model with the time-dependent covariates Z. It compares two estimates of the marginal distribution FY of Y. One is an estimate of the modified expression of FY under H0, based on a consistent estimate of the parameter under H0, and based on the baseline distribution of the data. The other is the Kaplan-Meier-estimator of FY, together with its confidence band. The new plot, called the marginal distribution plot, can be viewed as a test for testing H0. The main advantage of the test over the existing residual tests is in the case that the data do not satisfy any Cox model or the Cox model is mis-specified. Then the new test is still valid, but not the residual tests and the residual tests often make type II error with a very large probability.

Numerical modeling of time-dependent closure of coal seam artificial fractures

In order to improve efficiency of coal seam gas drainage, many fracturing techniques, such as waterjet fracturing, hydraulic fracturing and explosive fracturing, etc, have been developed and widely used in China coal mining industry. How- ever, during the engineering applications, it is observed that the efficiency of gas drainage initially improves, but reduces there- after. Thus, it is speculated that the contrasts in coalbed methane drainage efficiency may reflect variation of the closure be- havior of the artificial fracture created. Based on comprehensive gas drainage monitoring data in underground coal mines, the work presented herein uses numerical simulation to show the behavior of the time-dependent closure of coal seam fractures as- sociated with various levels of waterjet fracturing parameters and geomechanical conditions.

Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow

A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau （TDGL） equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.

糖尿病肾脏疾病预后影响因素的COX比例风险回归模型分析

目的基于COX比例风险回归模型分析糖尿病肾脏疾病(diabetic kidney disease,DKD)预后的影响因素,为临床早期评估和防治DKD提供科学的依据。方法收集多中心(河南中医药大学第一附属医院、河南中医药大学第三附属医院、河南省中医院及郑州市人民医院)2010—2021年就诊治疗的DKD患者资料,包括一般资料、实验室指标、中医辨证分型及中医药治疗,以肾小球滤过率(eGFR)下降≥50%、血肌酐(Scr)翻倍、DKD 5期、死亡为结局指标,随访其发生时间及情况,利用COX比例风险回归模型分析筛选DKD预后影响因素。结果本研究最终纳入1947例患者,随访时间为4.65(4.557~4.746)年,发生复合终点事件305例(15.67%)。单因素COX回归分析结果表明,不同年龄、DKD病程≥4年、饮酒史、吸烟史、高血压、冠心病、脑血管病、糖尿病足、糖尿病眼病、糖化血红蛋白(HbA1c)、血尿酸(SUA)、Scr、24 h尿蛋白定量(24 h-UTP)、eGFR、湿热血瘀证、脾肾气虚兼湿聚血瘀证、脾肾阳虚兼血瘀证、中药熏洗、服用中药患者DKD预后情况比较,差异有统计学意义(P<0.05)。多因素COX回归分析结果表明,年龄[HR(95%CI)=2.52(1.92,3.30)]、DKD病程[HR(95%CI)=1.62(1.09,2.42)]、吸烟史[HR(95%CI)=1.61(1.13,2.29)]、饮酒史[HR(95%CI)=1.41(1.01,1.95)]、脑血管病[HR(95%CI)=1.33(1.01,1.75)]、糖尿病眼病[HR(95%CI)=1.43(1.13,1.82)]、SUA[HR(95%CI)=1.72(1.26,2.33)]、24 h-UTP[HR(95%CI)=1.48(1.14,1.91)]、脾肾气虚兼湿聚血瘀证[HR(95%CI)=2.22(1.44,3.43)]与DKD发生终点事件的风险关系密切(P<0.05),服用中药[HR(95%CI)=2.57(2.00,3.31)]能够减少终点事件的发生(P<0.05)。结论年龄、DKD病程、吸烟史、饮酒史、脑血管病、糖尿病眼病、SUA、24 h-UTP、脾肾气虚兼湿聚血瘀证是影响DKD患者预后的危险因素,而服用中药治疗为其保护因素。

Cox模型中基于Model-X Knockoffs的高维控制变量选择方法

在生物医学、临床试验和流行病学等领域的研究中,由于获得生存数据的试验设计、观测时间的局限,以及观测对象在进入或退出试验时的个体差异等方面的原因,与所关注事件的发生时间相关的数据经常存在右删失。基于右删失生存数据解析协变量和生存时间的关系时,应用最为广泛的统计模型是Cox模型。随着科学技术的进步,数据收集变得越来越容易,导致数据库规模越来越大、复杂性越来越高,数据的维度通常可以达到成百上千维,甚至更高。文章提出一种Cox模型中基于Model-X Knockoffs的高维控制变量选择方法。首先基于Knockoffs框架建立一个Knockoffs变量,并基于原始协变量和其相应的Knockoffs变量构造一个正则化的目标函数,然后通过求解目标函数的最优解构造一个统计量和基于数据的阈值,最后进行变量选择。模拟分析和实证研究结果表明:所提方法可以在变量选择的同时提供可靠的FDR控制,优于传统的LASSO方法。

基于Cox健康行为互动模式的护理措施在宫颈癌患者护理中的应用

目的探讨基于Cox健康行为互动模式的护理措施在宫颈癌患者护理中的应用效果。方法选择2022年3月至2023年3月新乡医学院第一附属医院收治的96例宫颈癌术后患者作为研究对象,按随机数表法将患者分为对照组和观察组各48例。对照组患者术后采用常规护理,观察组患者在对照组护理的基础上给予基于Cox健康行为互动模式的护理措施,两组患者均接受护理至出院,出院后均随访3周。护理结束后出院时,比较两组患者的术后恢复情况(手术切口愈合时间、留置导尿管时间、住院时间)以及护理前、护理后T淋巴细胞亚群中CD3^(+)、CD4^(+)、CD4^(+)/CD8^(+)水平;随访3周回院复查时,比较两组患者的生活质量量表(SF-36)评分;护理结束后出院时,比较两组患者对护理工作的满意度。结果观察组患者的手术切口愈合时间、住院时间、留置导尿管时间分别为(7.60±1.39)d、(1.50±0.24)周、(17.78±2.11)d,明显短于对照组的(10.55±1.51)d、(2.54±0.30)周、(20.10±2.32)d,差异均有统计学意义(P<0.05);观察组患者护理后的CD3^(+)、CD4^(+)及CD4^(+)/CD8^(+)水平分别为(70.64±11.67)%、(39.91±5.23)%、1.50±0.27,明显高于对照组的(66.25±11.32)%、(35.21±5.08)%、1.24±0.18,差异均有统计学意义(P<0.05);随访3周回院复查时,观察组患者的家庭生活、精神活力、社交能力、心理承受评分分别为(36.14±1.58)分、(36.02±1.57)分、(37.10±2.55)分、(36.26±2.31)分,明显高于对照组的(32.31±1.62)分、(30.15±1.63)分、(32.19±2.40)分、(33.11±2.14)分,差异均有统计学意义(P<0.05);观察组患者对护理工作的满意度为95.83%,明显高于对照组的83.33%,差异有统计学意义(P<0.05)。结论基于Cox健康行为互动模式的护理措施在宫颈癌患者术后护理中的应用效果良好,能促进患者术后恢复,提高免疫功能和生活质量。

Numerical investigation into pillar failure induced by time-dependent skin degradation

This paper focuses on the instability mechanism of an isolated pillar, caused by time-dependent skin degradation and strength heterogeneity. The time-dependent skin degradation is simulated with a non-linear rheological model capable of simulating tertiary creep, whereby two different pillar failure cases are investigated. The first case is of an isolated pillar in a deep hard rock underground mine and subjected to high stresses. The results show that pillar degradation is limited to the regions near the surface or the skin until two months after ore extraction. Afterwards degradation starts to extend deeper into the pillar, eventually leaving a highly-stressed pillar core due to stress transfer from the failed skin.Rockburst potential indices show that the risk increases exponentially at the core as time goes by. It is then demonstrated that the progressive skin degradation cannot be simulated with conventional strain-softening model assuming brittle failure. The parametric study with respect to the degree of heterogeneity reveals that heterogeneity is key to the occurrence of progressive skin degradation. The second case investigated in this study is pillar failure taking place in a very long period. Such failure becomes significantly important when assessing the risk for ground subsidence caused by pillar collapse in an abandoned mine. The analysis results demonstrate that the employed non-linear rheological model can simulate gradual skin degradation taking place over several hundred years. The percentage of damage zone volume within the pillar is merely 1% after a lapse of one days and increases to 50% after one hundred years, indicating a high risk for pillar collapse in the long term. The vertical displacements within the pillar also indicate the risk of subsidence. The proposed method is suitable for evaluating the risk of ground surface subsidence above an abandoned mine.

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

Comparison of Cox proportional hazards model,Cox proportional hazards with time-varying coefficients model,and lognormal accelerated failure time model:Application in time to event analysis of melioidosis patients

Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

Time-dependent viscoelastic behavior of an LDPE melt

Two differential constitutive equations, i.e. Giesekus model and Johnson-Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. JohnsonSegalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the melt at high shear rate.

Time-dependent behaviour of the Callovo-Oxfordian claystone-concrete interface

In the context of the Cigeo project,the French National Radioactive Waste Management Agency(Andra)is studying the behaviour of a deep geological facility for radioactive waste deposit in the CallovoOxfordian(COx)claystone.The assessment of durability of this project requires the prediction of irreversible strain over a large time scale.The mechanical interaction of the host rock and the concrete support of tunnels must be investigated to ensure the long-term sustainability of the structure.The instantaneous and time-dependent behaviour of the claystone-concrete interface is experimentally investigated with direct shear tests and long-duration shear tests of a few months.The mechanical and structural state of the claystone which is affected after interaction with concrete reflects to the response of the claystone-concrete interface,and thus different types of COx claystone-concrete interfaces are tested.The delayed deformation of the interface is found to be linked to the level of the normal loading and the loading history while a different response of the interface was observed from the short-and long-duration tests,indicating a possible progressive modification of interface under long-duration loadings.

Clinical Study on the Impact of Long-term Survival Quality in 204 Postoperative Patients with Breast Cancer by Cox Proportional Hazard Models

The aim of study was to evaluate clinical characteristics, social support and the association with the prognosis of breast cancer patients. A total of 204 participants were followed from 2003 until the end of 2008. Information about patients with breast cancer was submitted by investigators. Data were analyzed by Cox’s proportional hazard model. The clinical staging of breast cancer we used was the TNM classification. A 'T' score is based upon the size and/or extent of invasion. The 'N' score indicates the extent of lymph node involvement. Age at diagnose was associated with protective factors (HR=0.972;95%CI (0.834-1.130)), T staging (HR=2.075;95%CI (1.424-3.022)), N staging (HR=1.513;95%CI (1.066-2.148)), were associated with risk factor. Two survival graphs of nodes with negative effects by histology and nodes with positive effects by histology was analyzed by log-rank test, there was statistically significant relationship between two survival graphs (χ2 =136.8467, p <.0001). Age at diagnoses, Clinical stage tumor and node could contribute to the development of breast cancer and disease free survival in Chinese women.

A Cox Proportional Hazard Model Approach to Age at First Sexual Intercourse in Nigeria

Early age at first sexual intercourse comes with many negative sexual outcomes namely: having unprotected sex on first sexual intercourse, condom misuse, high rate of sexually transmitted infections (STIs), teenage pregnancy, increased number of sexual partners, etc. In this paper, we considered some socio-demographic and cultural factors and their relationship with age at first sexual intercourse so as to reduce the numerous negative sexual outcomes of early age at first sexual intercourse using the 2018 Nigerian Demographic and Health Survey data. The analysis was made using the Cox proportional hazard model and the Kaplan-Meier plot. The result shows that some respondents started having their first sexual intercourse at the age of 8 years and about 54.4% of the respondents had their first sexual intercourse before age 17 years. The median age of first sexual intercourse is 16 years which implies that about 50% of the respondents had their first sexual intercourse on or before their 16th birthday. Education, religion, region and residence significantly affects the age of first sexual intercourse while circumcision has no significant effect.

The Cox Proportional Hazard Regression Model Vis-à-Vis ITN-Factor Impact on Mortality Due to Malaria

This study has provided a starting point for defining and working with Cox models in respect of multivariate modeling. In medical researches, there may be situations, where several risk factors potentially affect patient prognosis, howbeit, only one or two might predict patient’s predicament. In seeking to find out which of the risk factors contribute the most to the survival times of patients, there was the need for researchers to adjust the covariates to realize their impact on survival times of patients. Aside the multivariate nature of the covariates, some covariates might be categorical while others might be quantitative. Again, there might be cases where researchers need a model that has the capability of extending survival analysis methods to assessing simultaneously the effect of several risk factors on survival times. This study unveiled the Cox model as a robust technique which could accomplish the aforementioned cases. An investigation meant to evaluate the ITN-factor vis-à-vis its contribution towards death due to Malaria was exemplified with the Cox model. Data were taken from hospitals in Ghana. In doing so, we assessed hospital in-patients who reported cases of malaria (origin state) to time until death or censoring (destination stage) as a result of predictive factors (exposure to the malaria parasites) and some socioeconomic variables. We purposefully used Cox models to quantify the effect of the ITN-factor in the presence of other risk factors to obtain some measures of effect that could describe the relationship between the exposure variable and time until death adjusting for other variables. PH assumption holds for all three covariates. Sex of patient was insignificant to deaths due to malaria. Age of patient and user status were both significant. The magnitude of the coefficient (0.384) of ITN user status depicts its high contribution to the variation in the dependent variable.

The Cox-Aalen Models as Framework for Construction of Bivariate Probability Distributions, Universal Representation

Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.

SURVIVAL ANALYSIS OF GASTRIC CANCER PATIENTS BY COX REGRESSION MODEL

Mortality rate of gastric cancer is about 20.93/100000 which is the highest malignancy in China. The scientist of our country are at present interested in studying the postoperative survival model by multivariate analysis method just as stepwise regression model. The proportional hazard model initiated by Cox (1972) is more advanced than other regression method which is unneccessary to suppose the distribution of survival time and easy to analyse censoring data (the latter is difficult). This paper presented the first time application of Cox model in survival analysis of gastric cancer in China. The survival analysis system (SAS-Ⅰ) software complied by the author includes multivariate anlysis by Cox model, PV analysis and estimation of survival function which could provide useful information to surgeon for treatment of cancer patients.