基于分形理论的砂层注浆加固体性能预测

    Mechanical performance prediction of sand layer grouting-reinforced mass based on fractal theory

    • 摘要: 在地质环境日趋复杂和恶劣的工程背景下,注浆加固的质量要求越来越高,建立科学合理的注浆效果预测-评价方法,具有重要的理论意义和研究价值。利用分形理论描述砂土复杂的空间结构形态与变化特征,定义迂曲度为实际流动长度Le与理论流动长度L比值的平方,推导了砂土多孔介质面孔隙率和体孔隙率的关系,然后分别以面孔隙率和体孔隙率为变量,建立了基于分形理论和Mori-Tanaka的砂土注浆加固体强度和刚度理论预测方法,并应用于实际项目预测。结果表明:注浆加固体的强度取决于拉伸和剪切破坏两种模式下的最小强度,刚度则与基体弹性常数、夹杂体积占比及Eshelby张量等因素相关;工程现场实测值与所建方法预测的强度和刚度值之间最大误差仅为18.6%和16.6%。

       

      Abstract: Under the increasingly complex and harsh geological environment of engineering, the quality requirements for grouting reinforcement are becoming more stringent.Establishing a scientific and reasonable grouting effect prediction and evaluation method has important theoretical significances and research values.By applying fractal theory to describe the intricate spatial structure and variation characteristics of sandy soil, tortuosity was defined as the square of the ratio of the actual flow length (Le) to the theoretical flow length (L), by which the relationship between the surface porosity and bulk porosity of sandy soil's porous media was induced.Subsequently, using surface porosity and bulk porosity as variables, a theoretical prediction method for calculating the strength and stiffness of grouting-reinforced masses was established based on fractal theory and the Mori-Tanaka method.This method was then applied to an actual engineering project for validation.The results demonstrate that the strength of the grouting-reinforced mass is governed by the minimum strength under both tensile and shear failure modes, while stiffness depends on factors such as the matrix's elastic constant, the proportion of inclusions, and the Eshelby tensor.The errors between on-site measured values and the predicted values were only 18.6% (strength) and 16.6% (stiffness), respectively.This confirms that the proposed model accurately analyzes the mechanical response of tunnel structures and possesses high practical value for engineering applications.

       

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