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

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我们提供的概率论Probability theory及其相关学科的代写,服务范围广, 其中包括但不限于:

  • 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|POPH90148

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|POPH90148


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


几十年来,软土的蠕变行为一直被认为是工程师和研究人员面临的一个具有挑战性的课题。需要一个合适的模型来预测土壤的长期沉降。乐等人。[108] 回顾了土壤蠕变的五个原因:
(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|Time-Dependent Model for Creep Analysis

学者们通过实验室研究研究了软土的时变应力-应变行为[114-121]。为了描述土壤的粘性,模型中使用了应变率[118,122]. 一些研究人员已经做了大量工作来模拟在 oedometer 测试中的一维应变下的时间相关行为[114,118,123]. 还开发了用于描述三轴应力状态和一般应力状态下随时间变化的行为的模型 [124-126]。

大多数时间相关的本构模型都是基于 Perzyna 的过应力理论[128,129]. 这些模型可以分为两类:常规过应力模型和扩展过应力模型。传统的过应力模型假设只有弹性应变发生在应力状态位于静态屈服面内时 [130-133]。扩展过应力模型假设即使应力状态位于静态屈服面内,也会发生粘塑性应变 [125, 127, 134,135]。传统过应力模型的假设已被证明与实验结果相矛盾,相关的粘度参数无法通过低加载率试验轻易确定。相比之下,扩展过应力模型中涉及的土壤粘度参数可以根据恒定应变率测试或传统的测得仪测试直接确定。

目前,已经开发了一些弹性粘塑性模型,将各向异性和破坏结合到描述天然软粘土的应力-应变-时间行为中。Rocchi [136] 使用初始自然屈服轨迹和内在参考屈服轨迹的概念和过应力理论来考虑粘塑性应变的产生,并提出了一种可以结合应变率依赖性和破坏过程的粘塑性模型。Kimoto 和 Oka [135] 开发了一个速率依赖模型来考虑破坏和固有的各向异性,并且没有考虑应力引起的各向异性。基于 Vermeer 和 Neher [127] 的各向同性蠕变模型,Leoni 等人。[137]提出了一个各向异性模型。尹等人。[138-140141, 142]已经进行了大量工作来模拟天然软土的应变率依赖性行为。他们模型的最终版本可以同时描述初始各向异性、诱导各向异性、破坏和时间依赖性[143]。姚等人。[144] 提出了一种改进的统一硬化模型来描述超固结粘土的变形,并讨论了其考虑各向异性和结构效应的潜力。

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

曲线,称为“时间线”,每条曲线对应于标准里程计测试中的特定加载持续时间。时间线的一个含义是每条线的预固结压力大小不同。Bjerrum [114] 有相同的观察结果,并建议使用平行线来模拟延迟压缩和- 日志σ2′图表。平行线代表不同持续加载持续时间后的一系列平衡关系。

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。

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