Research on function model of lime-improved high liquid limit soil strength characteristics
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摘要:
针对广西荔玉高速路基沿线产生的大量高液限土弃方问题，采用生石灰对高液限土进行改良处理。选取弃土场的高液限土，分别配制不同初始含水率、不同石灰掺量的试样进行侧限压缩试验和快剪试验，采用基本初等数学函数模型拟合不同饱和状态、不同初始含水率下石灰掺量对试件压缩特性和抗剪强度影响。结果表明：(1)高液限土的压缩系数随石灰掺量增加呈指数形式减小；(2)不同饱和状态试件的黏聚力和内摩擦角随石灰掺量增加呈二次函数形式变化；(3)高液限土具有水敏性，饱和素土试件最大抗剪强度对应的含水率较击实试验最大干密度对应的含水率高3%～6%；(4)当初始含水率不高于26.73%时，建议石灰掺量不低于6%，否则改良高液限土的石灰掺量不低于8%，可在满足经济性的前提下达到较好的改良效果。
Abstract:In view of the large number of high liquid limit soil abandonment problems along the roadbed of the Liyu Expressway in Guangxi, quick lime was used to improve the high-liquid limit soil. the high-liquid limit soil samples with different initial water content and different lime content from the spoil field were used to conduct lateral compression test and fast shear test, and the basic elementary mathematical function model was used to fit different saturation states and different initial water content. The effect of lower lime content on the compression characteristics and shear strength of the specimen is tested. The results show that: (1) The compression coefficient of high liquid limit soil decreases exponentially with the increase of lime content; (2) the cohesion and internal friction angle of the specimens in different saturated states change with the increase of lime content in the form of quadratic function; (3) High liquid limit soil has water sensitivity. The moisture content corresponding to the shear strength is 3%～6% higher than the moisture content corresponding to the maximum dry density of the compaction test; (4) When the initial moisture content is lower than 26.73%, it is recommended that the lime content is not less than 6%, otherwise the lime content of the modified high liquid limit soil is not less than 8%, which can be achieved under the premise of meeting economics and better improvement effect.
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表 1 弃方段高液限土参数指标
Table 1. Parameters of high liquid limit soil of spoil
样品状态 取样深度/m 天然含水率/% 液限/% 塑限/% 土粒比重 原状土 2.1～2.3 31.30 53.30 28.50 2.76 原状土 6.5～6.7 36.30 52.10 33.70 2.74 扰动土 1.3～1.5 33.43 51.93 22.46 2.79 
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表 2 试件压缩系数与石灰掺量的指数模型拟合结果
Table 2. Fitting results of exponential model between compression coefficient and lime content
数学模型 
初始含水率 20.84% 23.68% 26.73% 29.71% 33.75% 34.93% A 0.04±0.00 0.05±0.00 0.05±0.00 0.05±0.00 0.08±0.00 0.07±0.00 B 0.10±0.00 0.13±0.00 0.16±0.00 0.20±0.00 0.25±0.00 0.29±0.00 C 2.26±0.07 2.59±0.11 2.67±0.20 2.88±0.14 2.46±0.07 3.24±0.05 R2 0.9998 0.9996 0.9989 0.9996 0.9998 1.0000 Adj.R2 0.9996 0.9992 0.9977 0.9991 0.9997 0.9999 注：R2 为相关系数平方；Adj.R2为调整后相关系数平方。
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表 3 不同状态试件黏聚力幂函数模型拟合结果
Table 3. Fitting results of power function model for cohesion of specimens in different states
试件状态 数学模型 
初始含水率 20.84% 23.68% 26.73% 29.71% 33.75% 34.93% 未饱和 
139.62±4.55 126.32±6.07 98.34±3.01 54.77±1.94 28.24±1.05 22.19±2.48 A 24.06±2.69 21.46±3.59 22.70±1.78 19.02±1.15 18.65±0.62 17.65±1.74 B −1.19±0.32 −0.92±0.43 −1.04±0.21 −0.89±0.14 −0.87±0.07 −0.76±0.18 R2 0.9947 0.9899 0.9976 0.9986 0.9996 0.9975 Adj.R2 0.9894 0.9798 0.9952 0.9971 0.9991 0.9949 饱和 
12.89±2.05 22.30±2.76 15.94±1.47 10.58±1.32 4.14±1.17 3.08±0.71 A 11.56±1.21 15.26±1.63 13.36±0.87 8.20±0.78 5.57±0.69 4.57±0.42 B −0.62±0.15 −0.99±0.20 −0.77±0.10 −0.44±0.09 −0.29±0.08 −0.21±0.05 R2 0.9948 0.9929 0.9978 0.9958 0.9932 0.9968 Adj.R2 0.9896 0.9857 0.9956 0.9916 0.9863 0.9936
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表 4 未经饱和试件内摩擦角的幂函数模型拟合结果
Table 4. Fitting results of power function model for internal friction angle of unsaturated specimen
函数模型 
初始含水率 20.84% 23.68% 26.73% 29.71% 33.75% 34.93% 
30.79±0.32 29.17±0.45 26.75±0.43 24.83±0.49 24.39±0.28 24.21±0.35 A 1.49±0.19 1.43±0.27 1.69±0.26 1.77±0.26 1.43±0.17 1.40±0.21 B −0.09±0.02 −0.06±0.03 −0.07±0.03 −0.07±0.03 −0.04±0.02 −0.04±0.02 R2 0.9913 0.9872 0.9915 0.9910 0.9966 0.9943 Adj.R2 0.9827 0.9745 0.9830 0.9821 0.9932 0.9887
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表 5 试验设计方案
Table 5. Experimental design scheme
初始含水率/% 石灰掺量/% 黏聚力 内摩擦角 R Adj. R2 29.71 10 51.85 31.10 1.000 0.999 12 47.45 31.78 0.998 0.996 33.75 10 32.20 29.87 0.998 0.996 12 33.5 29.89 0.998 0.995 34.93 10 26.5 29.56 0.999 0.997 12 30.25 30.29 0.994 0.989
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表 6 饱和试件内摩擦角拟合结果
Table 6. Fitting results of internal friction angle of saturated specimen
函数模型 方程 
初始含水率 20.84% 23.68% 26.73% 29.71% 33.75% 34.93% 幂函数 
23.14±0.14 24.12±0.72 24.36±0.95 23.92±0.76 23.79±0.23 23.58±0.12 A 2.00±0.08 2.51±0.43 2.74±0.56 2.53±0.45 1.98±0.14 1.97±0.07 B −0.15±0.01 −0.21±0.05 −0.23±0.07 −0.21±0.05 −0.16±0.02 −0.16±0.01 R2 0.9984 0.9702 0.9539 0.9672 0.9954 0.9988 Adj.R2 0.9968 0.9404 0.9078 0.9345 0.9908 0.9975
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