一维冻结土体冻胀曲线的分形优化

分形几何理论作为研究自然界具有自相似性质的非线性问题的主要手段，被广泛应用于岩土工程中。土体的冻结涉及到土体本身的性质、温度场、水分场和应力场的共同作用，采用数值解法又必须对其进行大量的简化，使其所求得的数值解或拟解析解与实际值存在较大差距。采用神经网络方法研究表明，在冻胀初期系统难以稳定，同时对于低含水量的土体误差也较大。近年来，通过国内外学者的大量研究，发现土体冻结过程中同样存在分形现象。通过分析土体冻胀特征，提出采用分形插值方法研究一维冻结土体的冻胀问题。采用Douglas-Peuker算法和随机中点移位法相结合的方法对一维冻结土体的冻胀曲线进行了优化。研究结果表明，采用该方法对冻胀曲线进行优化，既可保留其原有的宏观结构特征也可以反映微观结构动态；经过插值处理后，曲线的特征点和特征形状并无变化；但细节部分随着分形维数的增加，逐步得到细化。由此真实地反映了冻胀过程，为研究土体的冻胀过程提供了一种新的方法。

Fractal optimization of frost heave curve on one-dimensional freezing soil body

Fractal geometry theory is the main measure to research on the self-similar and nonlinear problems, and it has been widely used in geotechnical engineering. Soil freezing relates to common action such as the properties of soil body itself, temperature field, moisture field and stress field. The enormous simplifications are carried on in the adoption of the numerical solution, therefore the obtained numerical solution or similar analysis solution causes considerable drifts to practical value. The research of neural network method make known that the system is unsteady in the beginning of freezing, and the error is considerably large to low moisture soil. In the past few years, the scholars in home and abroad discovered that fractal appearance lied in the process of soil freezing. By analyzing the property of frost heave on freezing soil, this paper proposes using fractal interpolation method to study the problem of frost heave on one-dimensional freezing soil body. Frost heave curve of one-dimensional freezing soil is optimized using the method of Douglas-Peuker algorithm and random midpoint displacement. The research make known that this method not only maintains original macrostructure property, but also shows microstructure developments when using it optimizes frost heave. After the interpolation, the feature point and feature shape of curve does not be changed, but the particulars section gradually divides with the increase of fractal dimension wake of branch, therefore it more truly make known the frost heave process. This supplies a new method to study the process of frost heave on soil body.