一个描述封闭系统非饱和黏土冻结变形的数学模型 English Version
A mathematical model describing the frozen deformation of unsaturated clayey soils in a closed system
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摘要: 冻结作用下黏性土体的变形规律与饱和度密切相关，呈现为低饱和度时冻缩、高饱和度时冻胀的变形特征，针对该现象已有一些试验报道，但理论模型方面的研究相对匮乏。基于土体冻结变形试验规律及物理机制分析，建立了在封闭系统中统一描述非饱和黏土体冻缩-冻胀变形的数学模型。主要开展以下工作：（1）提出有效系数η和有效饱和度Sre，量化土体孔隙比和饱和度对冻结变形的影响，推导了冻结体应变与孔隙比、饱和度之间的数学关系。（2）综合考虑冻吸力的收缩作用和冰水相变的膨胀作用，将冻结变形过程划分为“冷缩”、“冻缩”和“冰胀”三阶段，定义临界冻缩温度Ti，求解气相在土体冻结过程中产生的变形值，实现冻缩-冻胀现象的统一解释。本模型简单有效，参数少；可较好地反映冻结变形规律，能准确预测临界饱和度。应用该模型对已报道的粉质黏土冻结试验规律进行预测，验证了模型的有效性。
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关键词:
- 非饱和黏土 /
- 冻胀/缩；饱和度；孔隙比；数学模型
Abstract: The deformation pattern of frozen soil is closely related to its saturation, exhibiting shrinkage at low saturation and expansion at high saturation. While there have been experimental reports on this phenomenon, research on theoretical models remains relatively scarce. Based on the analysis of the laws governing soil freezing deformation and its physical mechanisms, a mathematical model has been established to uniformly describe the shrinkage-swelling deformation of unsaturated soil in a closed system. This work includes the following key aspects: (1) The proposal of effective coefficient η and effective saturation Sre to quantify the influence of pore size and saturation on freezing deformation, along with deriving the mathematical relationship between freezing volumetric strain and void ratio as well as degree of saturation. (2) Based on the freeze shrinkage mechanism induced by cryogenic suction and ice phase expansion, the freezing deformation process can be described into three stages: cold shrinkage, frost shrinkage, and ice expansion. Additionally, the critical frost shrinkage temperature Ti is defined to estimate the deformation generated by gas phase during soil freezing, thereby achieving a unified explanation for the swelling-shrinkage deformation under freezing. This model is characterized by its simplicity, effectiveness, and minimal parameters; it can effectively reflect patterns in freezing deformation and accurately predict its critical degree of saturations. Application of this model to predict results from some reported freezing tests conducted on fine-grained clay has validated its rationality and effectiveness.-
Keywords:
- Unsaturated clayey soils /
- Frost expansion/shrinkage
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