Empirical formula for permeability coefficient of coarse grained soil based on gradation equation and its verification
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摘要: 粗粒土广泛应用于土石坝工程和道路工程,其渗流特性关系到工程的稳定性和安全性,渗透系数是衡量其渗流特性的基本参数,其中级配是影响渗流的关键影响因素。为研究级配对粗粒土渗透系数的影响,基于已有研究的渗透试验成果,采用连续级配方程对级配连粗粒土试验级配进行定量描述,研究级配与渗透系数的关系,建立了考虑级配曲线面积的渗透系数经验公式,并用现有其它文献的渗透试验成果验证所建立公式的适用性。结果表明,采用连续级配方程可以较好地定量描述级配连续粗粒土的级配曲线；基于级配面积建立的渗透系数经验公式适用于不同最大粒径及不同级配的粗粒土。Abstract: The coarse-grained soil is widely used in earth-rock dams and road projects. Its seepage characteristics are related to the stability and safety of the projects. The permeability coefficient is the basic parameter of seepage characteristics, and the gradation is the key factor affecting seepage. In order to study the effect of gradation on the permeability coefficient of the coarse-grained soil, based on the results of permeability tests in the existing literatures, a continuous gradation equation is used to describe the gradation of quantitatively graded coarse-grained soil, the relationship between the gradation and the permeability coefficient is studied, and an empirical formula for the permeability coefficient considering the area of gradation curve is established, and other literatures are used to study the relationship between the gradation and the permeability coefficient. The results show that the gradation curve of graded continuous coarse-grained soil can be quantitatively described by the continuous gradation equation, and the empirical formula for the permeability coefficient based on gradation area can be applied to the coarse-grained soil with different maximum particle sizes and gradations.
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图 1 不同P5含量试验级配曲线及拟合级配曲线
Figure 1. Fitting and test gradation curves with different P5 contents
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图 3 文献[2]渗透系数的实测值和预测值与级配面积间关系
Figure 3. Measured and predicted values of permeability coefficient with area of gradation curve in Literature 2
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图 4 文献[3]渗透系数的实测值和预测值与级配面积间关系
Figure 4. Measured and predicted values of permeability coefficient with area of gradation curve in Literature 3
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图 5 文献[5]渗透系数的实测值和预测值与级配面积间关系
Figure 5. Measured and predicted values of permeability coefficient with area of gradation curve in Literature 5
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图 6 文献[9]渗透系数的实测值和预测值与级配面积间关系
Figure 6. Measured and predicted values of permeability coefficient with area of gradation curve in Literature 9
表 1 土石混合体天然状态的基本物理指标
Table 1 Basic physical parameters of soil-rock mixture
天然密度/(g·cm-3) 天然含水率/% 相对密度Gs 孔隙比e 最大干密度/(g·cm-3) 最优含水率/% 1.64 28 2.778 1.17 1.733 18 
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表 2 级配参数及试验实测渗透系数
Table 2 Gradation parameters and test permeability coefficients
砾石含量/% 级配参数 渗透系数k/(cm·s-1) m b 10 1.296 0.958 0.0014 20 1.136 0.915 0.0032 30 1.020 0.850 0.0081 40 0.880 0.715 0.0194 50 0.828 0.546 0.0494 60 0.841 0.403 0.1114 70 0.780 0.001 0.2844 80 1.370 0.520 0.6966 90 3.152 0.895 1.6028 100 7.225 0.993 3.5377
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表 3 不同砾石含量级配曲线面积与渗透系数拟合值
Table 3 Areas of gradation curve with different gravel contents and fitting values of permeability coefficients
砾石含量/% 级配曲线面积S 渗透系数拟合值/(cm·s-1) 10 1.074 0.0116 20 0.990 0.0175 30 0.906 0.056 40 0.815 0.0427 50 0.705 0.0788 60 0.608 0.1411 70 0.501 0.2944 80 0.415 0.6113 90 0.333 1.6398 100 0.294 3.5321
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表 4 文献[3,5,9]级配参数及级配曲线面积与渗透系数实测值和拟合值及误差分析
Table 4 Gradation parameters and areas gradation curve of Literature 3, 5 and 9 and test and fitting values of permeability coefficients with error analysis
文献 试验编号 dmax/mm 级配参数 面积S 渗透系数k/(cm·s-1) 误差/% m b 实测值 拟合值 [3] 3-1# 20 1.280 0.860 0.740 0.5122 0.5123 0.02 3-2#-1 0.880 0.760 0.875 0.0804 0.0792 1.49 3-3#-1 0.730 0.740 1.021 0.0055 0.0106 92.73 3-4# 0.690 0.790 1.178 0.0046 0.0012 73.91 [5] 1 40 0.173 -10.283 0.419 0.331 0.347 4.83 2 0.890 0.57 0.518 0.56 0.247 75.3 3 1.677 0.9072 0.651 0.192 0.156 11.91 8 1.234 0.834 0.791 0.047 0.097 106.4 [9] TYU1 60 0.387 -1.06 0.658 0.067 0.067 0 TYU2 0.476 -0.33 0.697 0.045 0.042 6.67 TYU3 0.582 0.18 0.747 0.028 0.031 10.71 TYU4 0.668 0.451 0.798 0.024 0.025 4.17 TYU5 0.858 0.735 0.862 0.023 0.022 4.35 TYU7 1.175 0.928 1.010 0.019 0.019 0 注： 误差=|预测值-试验值|/试验值×100%。
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