数学代写|概率论代写Probability theory代考|POPH90148

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Mechanism of Creep Behavior for Soft Soil

The behavior of soft soil is viscous, which results in time effects and strain rate effects. The creep behavior refers to the soil deformation with time under a constant effective stress. In the early days, it is often referred to as “secondary consolidation”. Research has shown the existence of creep deformation in soft soils, and it is more obvious for the soils with lower permeability.

Creep behavior of soft soil has been considered as a challenging topic for engineers and researchers for several decades. An appropriate model is required for predicting the long-term settlement of soils. Le et al. [108] reviewed the five causes for soil creep:
(a) the breakdown of interparticle bonds [109]; (b) jumping of molecule bonds [110];
(c) sliding among particles [111]; (d) water flows in a double-pore system [112] and
(e) structural viscosity $[113,114]$.
Moreover, the mechanism of creep deformation can also be explained from the views of macro and micro deformation of soil, and this explanation is directly related to the study of settlement prediction [115]. In the macroscopic view, creep deformation is a result of soil structure rearrangement to reach a new equilibrium under the action of external force. In the microscopic view, creep deformation is considered as the deformation of microstructure caused by the drainage of adsorbed water or its structural viscosity. It is also suggested that the creep deformation will cease when there is no free water in the soil.

数学代写|概率论代写Probability theory代考|Time-Dependent Model for Creep Analysis

The time-dependent stress-strain behavior of soft soils has been investigated through the laboratory studies by the scholars [114-121]. In order to describe the viscous nature of soils, the strain rates were utilized in the models $[118,122]$. A lot of work has been done by some researchers to model the time-dependent behavior under onedimensional straining in oedometer tests $[114,118,123]$. The models for describing the time-dependent behavior under both triaxial stress states and general stress states have also been developed [124-126].

Most of the time-dependent constitutive models are based on Perzyna’s overstress theory $[128,129]$. These models can be classified into two categories: conventional overstress models and extended overstress models. The conventional overstress models assume that only elastic strains occur when the stress state is inside of the static yield surface [130-133]. The extended overstress models assume that the viscoplastic strains occur even though the stress state is located within the static yield surface [125, 127, 134,135]. The hypothesis of the conventional overstress model has been proved to be in conflict with the experimental results, and the associated viscosity parameters cannot be determined easily through the low loading-rate tests. In contrast, the parameters of soil viscosity involved in the extended overstress models can be determined straightforward based on the constant strain-rate tests or conventional oedometer tests.

At present, some elastic viscoplastic models have been developed to incorporate the anisotropy and destructuration in the description of the stress-strain-time behavior of natural soft clays. Rocchi [136] used the concepts of initial natural yield locus and intrinsic reference yield locus and the overstress theory to consider the generation of viscoplastic strain and proposed a viscoplastic model that can incorporate the strain-rate dependence and destruction process. Kimoto and Oka [135] developed a rate-dependent model to consider the destructuration and inherent anisotropy, and the stress-induced anisotropy has not been considered. Based on the isotropic creep model by Vermeer and Neher [127], Leoni et al. [137] proposed an anisotropic model. Yin et al. [138-140141, 142] have conducted extensive work to model the strain-rate-dependency behavior of natural soft soil. The final version of their models can describe the initial anisotropy, induced anisotropy, destructuration and time-dependence simultaneously [143]. Yao et al. [144] proposed a modified unified-hardening model to describe the deformation of overconsolidated clays and discussed its potential of taking into account anisotropy and structural effects.

数学代写|概率论代写Probability theory代考|Bjerrum’s Time Line Conceptual Model

Buisman [145] first modeled the effect of time on the compression of clay by introducing the term of secondary compression. Taylor and Merchant [109] later reported that one-dimensional compression of clay should be described using a family of

curves, called “time lines”, and each curve corresponds to a specific loading duration in a standard oedometer test. One implication of time lines is that the magnitude of preconsolidation pressure is different for each line. Bjerrum [114] has same observations and suggested to use the parallel lines to model the delayed compression in a $e$ – log $\sigma_{2}^{\prime}$ diagram. The parallel lines represent a series of equilibrium relationships after different durations of sustained loading.

Bjerrum’s time line model is illustrated in Fig. $1.4$ for “young” and “aged” normally consolidation ( $\mathrm{NC}$ ) clays. Young NC clays denote the deposit sediments that reach equilibrium under their own weight without experiencing the delayed compression, whereas aged NC clays have undergone substantially delayed compression at constant loading. The compression of undisturbed samples of young and aged NC clays subjected to the uniaxial consolidation is presented in two bold curves in the figure. The upper curve shows the compression behavior of the young $\mathrm{NC}$ clay, and its preconsolidation pressure $\sigma_{z, p c}^{\prime}$ is equal to $\sigma_{z, 0}^{\prime}$, that is the present vertical effective stress. Under this effective stress for 10,000 years, the young NC clay will develop the delayed compression. The compression of aged NC clay follows the lower curve, and its apparent preconsolidation pressure increases to $\sigma_{z, 1}^{\prime}$, which is caused by aging rather than by previous overloading. This implies that the reduction of void ratio caused by the delayed compression will lead to a more stable clay structure and then a larger preconsolidation pressure. It can be seen that the Bjerrum’s time line model provides a better understanding of the apparent preconsolidation pressures that resulted from aging.

数学代写|概率论代写Probability theory代考|Mechanism of Creep Behavior for Soft Soil

（a）颗粒间键的破坏 [109]；(b) 分子键的跳跃[110]；
(c) 粒子之间的滑动[111]；(d) 双孔系统中的水流 [112] 和
(e) 结构粘度[113,114].

数学代写|概率论代写Probability theory代考|Bjerrum’s Time Line Conceptual Model

Buisman [145] 首先通过引入二次压缩项来模拟时间对粘土压缩的影响。Taylor 和 Merchant [109] 后来报道说，粘土的一维压缩应该用一个族来描述

Bjerrum 的时间线模型如图 1 所示。1.4对于“年轻”和“老年”通常合并（ñC) 粘土。年轻的 NC 粘土表示沉积物沉积物在自身重量下达到平衡而没有经历延迟压缩，而老化的 NC 粘土在恒定载荷下经历了显着延迟的压缩。经受单轴固结的年轻和老化 NC 粘土的原状样品的压缩在图中以两条粗线表示。上面的曲线显示了年轻的压缩行为ñC粘土及其预固结压力σ和,pC′等于σ和,0′，即当前垂直有效应力。在这种 10000 年的有效应力下，年轻的 NC 粘土将发展延迟压缩。老化 NC 粘土的压缩遵循较低的曲线，其表观预固结压力增加到σ和,1′，这是由于老化而不是先前的超载引起的。这意味着延迟压缩引起的孔隙比降低会导致粘土结构更加稳定，从而导致预固结压力增大。可以看出，Bjerrum 的时间线模型更好地理解了老化导致的明显的预固结压力。

有限元方法代写

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MATLAB代写

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