Rapid testing and prediction of soil–water characteristic curve of subgrade soils considering stress state and degree of compaction

The subgrade soil is generally in saturated or unsaturated condition. To analyze complex thermo-hydro-mechanical-chemical (THMC) behaviors of subgrade, it is essential to determine the soil–water characteristic curve (SWCC) that represents the relationship between matric suction and moisture content. In this study, a full-automatic rapid stress-dependent SWCC pressure-plate extractor was developed. Then, the influences of overburden stress and degree of compaction on the SWCC of subgrade soil such as high liquid limit silt (MH) and low liquid limit clay (CL) were analyzed. Accordingly, a new model taking into account the influences of overburden stress and degree of compaction based on the well-known Van Genuchten (VG) SWCC fitting model was presented and validated. The results show that with the increase of the degree of compaction and overburden stress, the saturated moisture content of subgrade soil decreases, while the air-entry value increases and the transition section curve becomes flat. The influences of the degree of compaction and overburden stress on the SWCC of MH is greater than that of CL. Meanwhile, there was a satisfactory agreement between the prediction and measurement, indicating a good performance of the new model for predicting the SWCC.

Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization

In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure of the distance between original high order Bézier curve and degree-reduced curve. The other part represents the second derivative of degree-reduced curve. We tackle two kinds of conditions which are position vector constraint and tangent vector constraint respectively. The explicit representations of unknown points are presented. Some examples are illustrated to show the influence of the differential terms to approximation and smoothness effect.

Degree elevation from Bzier curve to C-Bzier curve with corner cutting form

The existing results of curve degree elevation mainly focus on the degree of algebraic polynomials. The paper considers the elevation of degree of the trigonometric polynomial, from a Bezier curve on the algebraic polynomial space, to a C-Bezier curve on the algebraic and trigonometric polynomial space. The matrix of degree elevation is obtained by an operator presentation and a derivation pyramid. It possesses not a recursive presentation but a direct expression. The degree elevation process can also be represented as a corner cutting form.

A quadratic programming method for optimal degree reduction of Bézier curves with G^1-continuity

This paper presents a quadratic programming method for optimal multi-degree reduction of B6zier curves with G^1-continuity. The L2 and I2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applications of degree reduction of Bezier curves with their parameterizations close to arc-length parameterizations are also discussed.

APPROXIMATE COMMON DIVISORS OF POLYNOMIALS AND DEGREE REDUCTION FOR RATIONAL CURVES

Abstract This paper deals with how to perturb a given set of polynomials so as to include a common linear factor. An algorithm is derived for determining such a set of perturbation polynomials which are subject to certain constrains at the endpoints of a prescribed parametric interval and minimized in a certain sense. This result can be combined with subdivision technique to obtain a continuous piecewise approximation to a rational curve.

“Algorithms for Degree-Raising of Splines”中的问题及其解决办法

研究表明，Ｃｏｈｅｎ，Ｌｙｃｈｅ和Ｓｃｈｕｍａｋｅｒ于１９８５年在ＡＣＭＴｒａｎｓａｃｔｉｏｎｓｏｎＧｒａｐｈｉｃｓ杂志上所发表的论文“ＡｌｇｏｒｉｔｈｍｓｆｏｒＤｅｇｒｅｅ－ＲａｉｓｉｎｇｏｆＳｐｌｉｎｅｓ”中存在着严重问题．文中给出了解决Ｂ样条曲线升阶的经典理论中的这些问题的三个算法，同时也给出了计算实例．

Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable

The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.

Determination of site-specific soil-water characteristic curve from a limited number of test data-A Bayesian perspective

Determining soilewater characteristic curve(SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ and/or laboratory tests. Such direct measurements are, however, costly and timeconsuming due to high standards for equipment and procedural control and limits in testing apparatus. As a result, only a limited number of data points(e.g., volumetric water content vs. matric suction)on SWCC at some values of matric suction are obtained in practice. How to use a limited number of data points to estimate the site-specific SWCC and to quantify the uncertainty(or degrees-of-belief) in the estimated SWCC remains a challenging task. This paper proposes a Bayesian approach to determine a site-specific SWCC based on a limited number of test data and prior knowledge(e.g., engineering experience and judgment). The proposed Bayesian approach quantifies the degrees-of-belief on the estimated SWCC according to site-specific test data and prior knowledge, and simultaneously selects a suitable SWCC model from a number of candidates based on the probability logic. To address computational issues involved in Bayesian analyses, Markov Chain Monte Carlo Simulation(MCMCS), specifically Metropolis-Hastings(M-H) algorithm, is used to solve the posterior distribution of SWCC model parameters, and Gaussian copula is applied to evaluating model evidence based on MCMCS samples for selecting the most probable SWCC model from a pool of candidates. This removes one key limitation of the M-H algorithm, making it feasible in Bayesian model selection problems. The proposed approach is illustrated using real data in Unsaturated Soil Database(UNSODA) developed by U.S. Department of Agriculture. It is shown that the proposed approach properly estimates the SWCC based on a limited number of site-specific test data and prior knowledge, and reflects the degrees-of-belief on the estimated SWCC in a rational and quantitative manner.

Unifying representation of Bézier curve and two kinds of generalized ball curves

This paper presents a new basis, the WSB basis, which unifies the Bemstein basis, Wang-Ball basis and Said-Ball basis, and therefore the Bézier curve, Wang-Ball curve and Said-Ball curve are the special cases of the WSB curve based on the WSB basis In addition, the relative degree elevation formula, recursive algorithm and conversion formula between the WSB basis and the Bern- stein basis are given.

Constrained multi-degree reduction of triangular Bézier surfaces

This paper proposes and applies a method to sort two-dimensional control points of triangular Bezier surfaces in a row vector. Using the property of bivariate Jacobi basis functions, it further presents two algorithms for multi-degree reduction of triangular Bezier surfaces with constraints, providing explicit degree-reduced surfaces. The first algorithm can obtain the explicit representation of the optimal degree-reduced surfaces and the approximating error in both boundary curve constraints and corner constraints. But it has to solve the inversion of a matrix whose degree is related with the original surface. The second algorithm entails no matrix inversion to bring about computational instability, gives stable degree-reduced surfaces quickly, and presents the error bound. In the end, the paper proves the efficiency of the two algorithms through examples and error analysis.

Preliminary study on characteristics of earthquake precursor of earth resistivity anisotropy degree in East China

Introduction The degree of earth-resistivity anisotropy was described (MAO, et al, 1995, 1998) as follows: S=|1\nn∑I=1(ρSN\ρEW)I|-1|×103 n=6(1) whereρNS and ρEW are monthly mean values of earth resistivity in the direction of NS and EW, respectively, S is the half-year value. Equation (1) shows that if ρNS=ρEW, then S =0 and the electrical property of medium is isotropic; if ρNS≠ρEW, then S≠0 and the electrical property of medium is anisotropic. When S increases, the anisotropy of electrical property of medium is enhanced. Because the rightside of equation (1) is absolute value and the possibility ofρNS＞ρEW and ρNS＜ρEW can be different at different stations, the increase or decrease of S cannot reflect the relative changes between ρNS and ρEW. FENG, et al (2000) defined S as follows:……

UNIFYING REPRESENTATION OF BZIER CURVE AND GENERALIZED BALL CURVES

This paper presents two new families of the generalized Ball curves which include the Be ′zier curve, the generalized Ball curves defined by Wang and Said independently and some intermediate curves. The relative degree elevation and reduction schemes, recursive algorithms and the Bernstein\|Be ′zier representation are also given.

Establishment and Analysis of Growth Curve of Muchuan Black Chicken

To find out the growth and development regularity,the growth curves of Muchuan black chicken at the age of 0-21 weeks were established by Logistic,Bertalanffy and Gompertz models in this study.The results showed that all the three models can well fit the growth curve of Muchuan black chicken with a degree above 0.988,while the Gompertz model and the Bertalanffy model was the best for hens and cocks,respectively.Finally,the weight of hens and cocks were analyzed according to their corresponding high fitting models.Results showed that the inflexion age of Muchuan black chicken was 6.8-6.9 weeks old with an inflexion weight of 692.98 g in hens and 805.57 g in cocks.In conclusion,it was feasible to establish the growth curve of Muchuan black chicken with Logistic,Bertalanffy and Gompertz model.

On Two Problems About Isogenies of Elliptic Curves Over Finite Fields

Isogenies occur throughout the theory of elliptic curves.Recently,the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic protocols.Given two elliptic curves E1,E2 defined over a finite field k with the same trace,there is a nonconstant isogeny b from E2 to E1 defined over k.This study gives out the index of Homk(E1,E2)b as a nonzero left ideal in Endk(E2)and figures out the correspondence between isogenies and kernel ideals.In addition,some results about the non-trivial minimal degree of isogenies between two elliptic curves are also provided.

稳定分析中滑动面构造方法分析

滑动面的构造方法是边坡稳定分析的关键课题之一。任意滑动面的构造比较复杂,基于Logistic函数积分等基函数构造的曲线可以代替传统的折线形滑动面,改善滑动面的光滑性,也有利于减少其自由度。对基于基函数的滑动面构造方法进行梳理,将其划分为基于连续函数叠加的构造方法和基于积分运算的构造方法。重点对Logistic函数及其积分的性质进行分析,得到了不同参数对曲线形态的影响规律,从而缩小了相关参数的取值范围,为减小滑动面自由度提供了依据。在此基础上也给出了一种确定给定滑动面参数初值的方法。针对两个边坡算例的计算表明,所提出的方法能够满足边坡稳定分析的要求。

潮湿细粒煤复合式干法分选特性研究

为研究潮湿细粒煤复合式干法分选效率,对潮湿细粒煤进行了振动强度和气速的单因素试验,结合RSM-BBD预测模型获得了最优参数;并探索了不同水分的原煤在不同分选时间内的分选效果,同时分析了气流对潮湿细粒煤分选过程的影响,并评价了分选效果。结果表明:随着分选时长的增加,分选效果明显提高,最大灰分离析度可达12.05。试验煤样在气速为0.78 m/s,振动频率为25 Hz,振幅为3 mm时达到最佳分选效果,此时可能偏差E=0.135 g/cm^(3),且在此条件下分选产品有很好的脱水效果,复合式干法分选可实现潮湿煤炭的提质。该研究可以对细粒煤炭的干法分选工艺提供理论和技术支持。

基于改进剩余强度模型的复合材料疲劳寿命预测

复合材料强度退化规律对研究结构疲劳寿命具有重要意义,然而现有剩余强度模型均需利用剩余强度试验数据确认模型参数,模型构建成本较高。通过探究复合材料疲劳寿命和剩余强度的关系,以疲劳寿命累积分布函数为出发点,构建具有明确物理意义的损伤度,进而提出改进剩余强度模型。改进剩余强度模型不需要剩余强度试验数据,仅需初始静强度和疲劳寿命数据。在改进剩余强度模型基础上,构建S-N-φ疲劳寿命预测模型,该模型可以考虑初始静强度对疲劳寿命的影响。算例结果表明,改进剩余强度模型的预测精度是满意的,S-N-φ模型相比经典S-N曲线模型具有更好的预测精度。

肺癌化疗患者血清TBNK淋巴细胞亚群水平变化与预后的相关性研究

目的:探究肺癌化疗患者血清TBNK淋巴细胞亚群水平变化,并分析其与预后的相关性。方法:分析2020年1月至2023年6月就诊于北京京煤集团总医院的92例肺癌化疗患者,行标准方案化疗,检测首次化疗前、化疗1、3个周期后TBNK淋巴细胞亚群水平,化疗结束后3个月评价预后,分为缓解组(63例)、未缓解组(29例),分析TBNK淋巴细胞亚群水平与预后的相关性。结果:Ⅲ期组化疗1、3个周期后CD3^(+)、CD3^(+)CD4^(+)、CD3^(-)CD19^(+)低于Ⅳ期组,CD3^(+)CD8^(+)、CD3^(-)CD16^(+)CD56^(+)高于Ⅳ期组(P<0.05);缓解组化疗1、3个周期后CD3^(+)、CD3^(+)CD4^(+)、CD3^(-)CD19^(+)低于未缓解组,CD3^(+)CD8^(+)、CD3^(-)CD16^(+)CD56^(+)高于未缓解组(P<0.05);肺癌化疗患者分期、预后与CD3^(+)、CD3^(+)CD4^(+)、CD3^(-)CD19^(+)呈正相关,与CD3^(+)CD8^(+)、CD3^(-)CD16^(+)CD56^(+)呈负相关(P<0.05);化疗3个周期后TBNK淋巴细胞亚群联合预测肺癌化疗患者预后的AUC最大,为0.907(P<0.05)。结论:肺癌化疗患者外周血TBNK淋巴细胞亚群变化与免疫功能状态及预后有关,监测相关指标水平可预测肺癌化疗患者预后。

2060 MPa级高强钢丝高温力学性能及破断模式

采用非接触式光学应变测试系统,跟踪测试了2060 MPa级高强钢丝试件在20~900℃下的全过程应力-应变曲线,建立了高温钢丝各力学性能指标的高温函数模型,得到其高温破断参数.结果表明:高温下高强钢丝试件的各力学性能指标均有不同程度折损.当温度低于200℃时,试件的力学性能指标折损率不超过10%,破断模式为脆性破坏;当温度超过200℃后,试件的各力学性能指标折损率显著增大,破断模式逐渐由脆性破坏转变为塑性破坏.

基于相对结构度的水泥固化压实土力学与变形特性研究

由于胶结作用和孔隙结构的影响,结构性土的力学与变形特性显著区别于重塑土.为了解结构性土的特性,采用人工制备水泥固化压实土,并通过固结试验和固结排水剪切试验对其相对结构度及其衰变规律展开研究.详细分析了胶结作用和初始孔隙比对水泥固化压实土压缩特性与剪切特性的影响,并根据压缩试验结果建立了适用于水泥固化压实土的相对结构度发展式,最后采用所提出的相对结构度发展式对水泥固化压实土的剪切特性进行分析.研究结果表明,相对结构度的衰变速率随着水泥掺量的增大而减小,但初始孔隙比并不影响水泥固化压实土变形过程中相对结构度随塑性体应变的衰变速率;水泥固化压实土的峰值应力与相对结构度有关,并随着相对结构度的降低而减小.