数学代写|概率论代写Probability theory代考|STAT4028

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  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
数学代写|概率论代写Probability theory代考|STAT4028

数学代写|概率论代写Probability theory代考|Influencing Factors on $S W C C$

Several experimental techniques or apparatuses have been developed to measure the SWCC, for example, filter paper method [64], different types of pressure plate apparatuses [54, 65-68] and modified direct shear apparatus [69]. These methods or apparatuses have their own features, and they may be applicable to different cases, for example, measurable range of suction, drying or wetting path.

Based on a large number of experimental results, researchers have found that a number of factors have significant influence on SWCC, such as the type of soil and mineralogy, grain-size distribution, initial void ratio, plastic limit, liquid limit, compaction energy, stress state and stress history, initial water content, clay fraction and temperature. Marinho and Chandler [70] indicated that there was a distinct relationship between the slope of SWCC and the liquid limit. Vanapalli et al. [71] studied the effect of soil structure and stress history on the SWCC based on the tests and found that the beginning of the SWCC was affected greatly. Kawai et al. [72] investigated the dependency of SWCC on initial void ratio. Uchaipichat and Khalili [73] conducted experimental work on the thermo-hydro mechanical behavior of an unsaturated silt. Iyer et al. [74] demonstrated that the initial water content only influenced the initial stage of the $S W C C$, and the specimen thickness had no significant influence on the shape of SWCC. Wang et al. [33] studied the effects of sample dimensions and shapes on the testing duration of SWCC. Elkady et al. [75] found that the SWCC of sand-natural expansive clay mixtures was mainly dependent on the clay content and compaction state.

Among these influencing factors, the effect of void ratio or soil compaction degree is the most significant in geotechnical engineering. Due to the limitations in measuring SWCC, for example, long-term cycle, high cost and discrete data points, the calculation model, which can simulate the effect of void ratio on SWCC, should be established to avoid the tedious experimental work. Considering that the shape and location of SWCC in the space depend on the parameters in SWCC model, some researchers have attempted to construct the relations of model parameters with the void ratio $[76,77]$. There are some researchers trying to introduce the void ratio based on the existing empirical SWCC models [78-80].

数学代写|概率论代写Probability theory代考|Empirical Equations

Numerous empirical equations have been proposed to fit the laboratory data, and they contain two or three fitting parameters. Table $1.1$ lists several commonly used equations for $S W C C$. Leong and Rahardjo [81] reviewed and evaluated five popular SWCC equations and found that the Fredlund and Xing [82] equation possesses the best fitting ability. These models can provide the good fitting results with the measured data using the least-squares regression method [82]. They can deduce the whole SWCC using the limited test data, and the estimated results are suitable to be used in the computer model. Zhang and Chen [83] later extended the Fredlund and Xing [63] model and the van Genuchten [84] model to describe bimodal and multimodal SWCCs.

From the view of these empirical equations, some researchers have also investigated the relationships between the associated fitting parameters and the soil basis properties and established the estimation equations. Zapata [86] analyzed the three fitting parameters $(a, k, m)$ in Fredlund and Xing [63] equation using the grain size diameter $D_{60}$ and the product of the percent passing and the plasticity index for different soil types, that is, granular nonplastic materials and plastic materials, respectively. Chin et al. [87] based on regression analysis and one-point SWCC measurement proposed a simplified technique to estimate the $\mathrm{SWCC}$, and the relationships of four fitting parameters $\left(a, k, m, \varphi_{r}\right)$ in Fredlund and Xing equation [63] with basic soil properties were formulated for both coarse- and fine-grained soils, respectively. Torres [88] also obtained the correlation of the fitting parameter $a$ with the grain-size diameter $D_{I O}$ for granular materials, and the other two fitting parameters $k$ and $m$ were found to be related to $a$ and the relevant relation equations were also built.

数学代写|概率论代写Probability theory代考|Pedotransfer Functions

The physico-empirical models are built to estimate the water content based on the particle-size distribution and the characteristic of soil-pore structure. Based on the observation of similarity between the shape of water retention curve and particlesize distribution, Arya and Paris [96] first proposed a physico-empirical model to estimate the SWCC using the particle-size distribution and unit weight. The model adopted three assumptions of soil particles and pore structure to deduce the estimated equation of the water content, and an important empirical parameter $\alpha$ was introduced in the model. In order to improve this model, Arya et al. [97] proposed the method of back analysis to determine $\alpha$. Zhuang et al. [98] derived an analytical model using nonsimilar media method to estimate SWCC based on the measured soil physical properties, for example, particle-size distribution, unit weight and bulk density.
This model does not require measuring $S W C C$ in advance; it can make use of most of the available data. However, the physico-empirical models cannot obtain the close predictions for soils where aggregation, cracking and root effects may be pronounced. Otherwise, the model works reasonably well [96].

The fractal theory was first introduced to estimate the SWCC by Tyler and Wheatcraft [99], and then they derived the other fractal model of SWCC based on the Sierpinski carpet [100]. This fractal model considered only the fractal characteristics of the pore space but not the mass. At present, many models have been proposed for the fractal characteristic of SWCC [101-103]. They have been used to describe the water retention behavior and the variation of hydraulic conductivity in soils with different textural structures [104-107].

The disadvantage of the fractal models is that the fractal scaling considers only the effects of tortuosity of pore lengths, but not the effects of other factors on the water retention property, such as organic matter content, packing density, the chemical characteristic of particle surface and fluid property.

数学代写|概率论代写Probability theory代考|STAT4028


数学代写|概率论代写Probability theory代考|Influencing Factors on 小号在CC

已经开发了几种实验技术或装置来测量 SWCC,例如滤纸法 [64]、不同类型的压板装置 [54、65-68] 和改进的直剪装置 [69]。这些方法或装置各有特点,它们可以适用于不同的情况,例如可测量的吸力、干燥或湿润路径的范围。

研究人员根据大量实验结果发现,土壤类型和矿物学、粒度分布、初始孔隙比、塑限、液限、压实能、应力状态和应力历史、初始含水量、粘土分数和温度。Marinho 和 Chandler [70] 指出 SWCC 的斜率与液限之间存在明显的关系。瓦纳帕利等人。[71] 根据试验研究了土壤结构和应力历史对 SWCC 的影响,发现 SWCC 的开始受到很大影响。川井等人。[72] 研究了 SWCC 对初始空隙率的依赖性。Uchaipichat 和 Khalili [73] 对非饱和淤泥的热水力学行为进行了实验工作。艾耶等人。小号在CC, 试样厚度对 SWCC 的形状没有显着影响。王等人。[33] 研究了样品尺寸和形状对 SWCC 测试持续时间的影响。埃尔卡迪等人。[75] 发现砂-天然膨胀粘土混合物的 SWCC 主要取决于粘土含量和压实状态。

在这些影响因素中,孔隙比或土壤压实度在岩土工程中的影响最为显着。由于测量 SWCC 的局限性,如周期长、成本高、数据点离散,应建立模拟空隙率对 SWCC 影响的计算模型,避免繁琐的实验工作。考虑到 SWCC 在空间中的形状和位置取决于 SWCC 模型中的参数,一些研究人员试图构建模型参数与空隙率的关系。[76,77]. 有一些研究人员试图在现有的经验 SWCC 模型的基础上引入空隙率[78-80]。

数学代写|概率论代写Probability theory代考|Empirical Equations

已经提出了许多经验方程来拟合实验室数据,它们包含两个或三个拟合参数。桌子1.1列出了几个常用的方程小号在CC. Leong 和 Rahardjo [81] 回顾和评估了五个流行的 SWCC 方程,发现 Fredlund 和 Xing [82] 方程具有最佳拟合能力。这些模型可以使用最小二乘回归方法[82]提供与测量数据的良好拟合结果。他们可以利用有限的测试数据推导出整个SWCC,估计结果适合用于计算机模型。Zhang 和 Chen [83] 后来扩展了 Fredlund 和 Xing [63] 模型和 van Genuchten [84] 模型来描述双峰和多峰 SWCC。

从这些经验方程来看,一些研究人员还研究了相关拟合参数与土壤基础性质之间的关系,并建立了估计方程。Zapata [86] 分析了三个拟合参数(一个,ķ,米)在 Fredlund 和 Xing [63] 方程中使用粒度直径D60以及不同土壤类型即粒状非塑性材料和塑性材料的通过率与塑性指数的乘积。钦等人。[87] 基于回归分析和单点 SWCC 测量提出了一种简化技术来估计小号在CC, 以及四个拟合参数的关系(一个,ķ,米,披r)在 Fredlund 和 Xing 方程 [63] 中,分别针对粗粒和细粒土壤制定了具有基本土壤性质的公式。Torres [88] 也得到了拟合参数的相关性一个与粒度直径D我○对于粒状材料,以及其他两个拟合参数ķ和米被发现与一个并建立了相关的关系方程。

数学代写|概率论代写Probability theory代考|Pedotransfer Functions

建立物理经验模型,根据粒径分布和土壤孔隙结构特征估计含水量。基于对保水曲线形状和粒度分布相似性的观察,Arya 和 Paris [96] 首次提出了一种物理经验模型,利用粒度分布和单位重量来估计 SWCC。该模型采用土壤颗粒和孔隙结构三个假设推导出含水量的估计方程,以及一个重要的经验参数一个在模型中引入。为了改进这个模型,Arya 等人。[97] 提出了反分析法确定一个. 庄等人。[98] 使用非相似介质方法推导出分析模型,根据测量的土壤物理特性(例如,粒度分布、单位重量和容重)估计 SWCC。
该模型不需要测量小号在CC提前; 它可以利用大部分可用数据。然而,物理经验模型无法获得对聚集、开裂和根系效应可能很明显的土壤的准确预测。否则,该模型工作得相当好[96]。

Tyler 和 Wheatcraft [99] 首次引入分形理论来估计 SWCC,然后他们基于 Sierpinski 地毯 [100] 推导出了另一个 SWCC 分形模型。该分形模型只考虑了孔隙空间的分形特征,而没有考虑质量。目前,针对 SWCC 的分形特征提出了多种模型[101-103]。它们已被用于描述具有不同质地结构的土壤中的保水行为和水力传导率的变化 [104-107]。


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