A model of capillary water rise based on fractal theory and experimental validation
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摘要:
沿海地区的路基工程中，毛细水上升会产生路基病害，影响道路运营的安全性和耐久性，因此研究毛细水上升高度尤为重要。文章视毛细水上升为一种非饱和土的渗流现象，引入分形维数对非饱和土渗透系数进行修正，进而提出了基于分形理论的毛细水上升高度模型，得到了毛细水上升高度随时间变化的曲线；而后对南通某干线公路路基土样进行竖管法毛细水上升高度试验，改变土样的干密度及初始粒径的分形维数分布做对照组试验。研究结果表明：毛细水上升呈现初期先快速增加，然后缓慢增加，最终趋于稳定的趋势；土样颗粒粒径分布的分形维数越大，得到的毛细水上升高度越大；土样的干密度越小，即孔隙率越大，得到的毛细水上升高度越大。文章提出的毛细水上升高度模型中，毛细水上升高度与试样孔隙率、饱和渗透系数、进气值对应的毛细水上升高度、分形维数等参数相关。在模型理论值计算中认为分形维数变化仅改变进气值对应的毛细水高度，不改变饱和渗透系数，而干密度变化即孔隙率变化仅导致饱和渗透系数变化，不改变进气值对应的毛细水高度，由此得到的模型计算结果与试验结果趋势一致，验证了理论模型的正确性，可以为公路路基毛细水病害防治提供理论指导。
Abstract:As to the roadbed projects in coastal areas, capillary water rise can produce roadbed diseases and affect the safety and durability of road operation. It is important to study the capillary water rise height. The article regards capillary water rise as a kind of unsaturated soil seepage phenomenon, and introduces fractal dimension to unsaturated soil permeability coefficient modification. A capillary water rise height model based on fractal theory is proposed to obtain the capillary water rise height curve with time. Then a vertical tube method capillary water rise height test was conducted on a mainline roadbed soil sample in Nantong, with the control test of changes in the dry density of the soil sample and the fractal dimension of the initial particle size distribution. The results show that: the capillary water rise presents a rapid increase at the beginning, and then slowly increases, and finally stabilizes. The larger the fractal dimension of the particle size distribution of soil sample, the greater the capillary water rise height; the smaller the dry density of the soil sample, that is, the greater the porosity, the greater the capillary water rise height. In the capillary water rise height model, the capillary water rise height is related to the sample porosity, saturated permeability coefficient, capillary water rise height corresponding to the inlet value, fractal dimension, etc. In the theoretical model, the variation of fractal dimension only changes the capillary water height corresponding to the inlet value, not the saturated permeability coefficient; while the dry density change, i.e., the porosity change, only leads to the saturated permeability coefficient change, does not affect the intake value corresponding to the height of capillary water, the results from theoretical model are consistent with those from the test, verifying the effectiveness of the theoretical model. This study provides theoretical guidance for the prevention and control of road-base capillary water disease.
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Key words:
- capillary water /
- particle distribution /
- fractal theory /
- Darcy law /
- dry density
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表 1 试验土样基本物理指标
Table 1. Basic physical properties of soil samples
参数 液限/% 塑限/% 塑性指数 比重 取值 35.01 18.82 16.21 2.73 
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表 2 试验方案
Table 2. Experimental schemes
组号 干密度/（g·cm−3） 分形维数 1 1.30 2.7 2 1.30 2.5 3 1.30 2.3 4 1.35 2.7 5 1.40 2.7
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表 3 理论参数取值
Table 3. Theoretical parameter values
组号 孔隙率/% ks/（cm·s−1） D ha/cm 1 52.3 3.5×10−5 2.7 60 2 52.3 3.5×10−5 2.5 45 3 52.3 3.5×10−5 2.3 30 4 50.5 2.8×10−5 2.7 60 5 48.6 2.0×10−5 2.7 60
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