膨润土膨胀变形的分形模型

Fractal model for swelling of bentonite

膨润土的膨胀变形计算一直是核废料处置库垫层设计的关键难题之一,膨润土的膨胀变形过程就是膨润土吸水过程,膨润土吸附水体积与膨润土的表面特征有关,膨润土的表面特性可以采用分形模型描述,由此可以建立膨润土吸附水体积与上覆压力的关系.根据膨润土表面和膨润土膨胀后的团粒(aggregate)的分形模型,建立了膨润土膨胀变形、膨胀压力、侵蚀(自由膨胀)和饱和膨润土压缩变形的计算理论,导出由溶质吸力产生的有效应力表达式,建立了有效应力表示的盐溶液中膨润土膨胀变形方程,并得到膨胀变形试验数据的验证.结果表明,膨润土吸水体积是上覆压力的幂函数,指数为Ds-3;侵蚀临界剪切应力是膨润土团粒的有效密度、直径的幂函数,膨润土侵蚀质量是水流量的幂函数,指数是团粒分维的函数.

To develop engineered barriers using bentonite and its mixtures with sand, it is very necessary to quantitatively evaluate the swelling characteristics of bentonite and its mixtures. Swelling properties of bentonite occur simultaneously with water absorption, and the adsorption water volume of bentonite is related to its surface characteristics, which can be described by fractals, so the relationship between adsorption water volume and vertical stress can be established. Calculation theories of swelling deformation, erosion threshold, erosion mass and compression of saturated bentonite are constructed based on the surface fractal model of bentonite and the fractal model for bentonite aggregates. Effective stress induced by osmotic suction is presented using the fractal surface of bentonite to express the swelling properties of bentonite in saline solution. Calculation theories of swelling deformation, erosion threshold, erosion mass and compression of saturated bentonite are verified by the experimental data. The results show that adsorption water volume is a power function of the vertical stress, and the exponent of power function equals to Ds - 3. Erosion threshold is a power function of the diameter and effective density of bentonite aggregates, and the erosion mass of bentonite is a power function of water volume, the exponents of power function are related to the fractal dimension of bentonite aggregates.