基于双分形级配模型参数的粗粒土渗透系数计算公式

曲诗章; 刘晓明; 黎莉; 陈仁朋

doi:10.11779/CJGE20210543

基于双分形级配模型参数的粗粒土渗透系数计算公式 English Version

曲诗章^1,,
刘晓明¹,
黎莉^{1, 2, ,},
陈仁朋^{1, 2}

1.
湖南大学土木工程学院, 湖南长沙 410082
2.
湖南大学建筑安全与节能教育部重点实验室, 湖南长沙 410082

基金项目:

国家重点研发计划项目 2019YFC1904705

详细信息

作者简介:
曲诗章(1992—)，男，博士研究生，主要从事地基基础和岩土基本性质等方面的研究工作。E-mail: qsz.cxdl@hnu.edu.cn

通讯作者:
黎莉, E-mail: lilicivil@hnu.edu.cn

中图分类号: TU441
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出版历程
- 收稿日期: 2021-05-13
- 网络出版日期: 2023-02-03
- 发布日期: 2021-05-13
- 刊出日期: 2022-12-31

Formula for permeability coefficient of coarse-grained soil based on parameters of two-dimensional fractal gradation model

QU Shizhang^1,,
LIU Xiaoming¹,
LI Li^{1, 2, ,},
CHEN Renpeng^{1, 2}

1.
College of Civil Engineering, Hunan University, Changsha 410082, China
2.
Key Laboratory of Building Safety and Energy Efficiency of Ministry of Education, Hunan University, Changsha 410082, China

摘要

摘要: 粗粒土在自然界中分布广泛且在工程中应用普遍。渗透性是粗粒土的重要性质，对于同种粗粒土，因颗粒级配与孔隙特征几乎决定其渗透性，原则上其渗透系数应该可基于颗粒级配和孔隙特征参量计算得到。采用基于分形理论建立的双分形级配模型对粗粒土的连续级配、间断级配进行定量描述，以确定该级配模型的适用性并获得级配模型参数。在此基础上，基于双分形级配模型参数和Kozeny-Carman公式构造出包含级配参量及孔隙率的渗透系数计算公式。在论述了计算公式中各项物理意义后，基于现有文献的实测数据验证该计算公式的有效性。结果表明，双分形级配模型能准确唯一地定量描述粗粒土的颗粒级配；建立的含颗粒级配参量和孔隙率的粗粒土渗透系数计算公式是合理的，该公式适用于计算连续和间断级配粗粒土的渗透系数。
- 粗粒土 /
- 渗透系数 /
- 分形模型 /
- 颗粒级配 /
- 孔隙率
Abstract: The coarse-grained soil is widely distributed in nature and used in engineering. The permeability is one of its key properties, and for the same type of coarse-grained soil, its permeability is almost determined by the grain-size distribution and the pore characteristics. In principle, its permeability coefficient can be calculated based on the grain-size distribution and the pore characteristic parameters. The two-dimensional fractal gradation model based on the fractal theory is used to quantitatively describe the continuous gradation and gap gradation of the coarse-grained soil so as to determine the applicability of the gradation model and obtain its parameters. Then, based on the parameters of the two-dimensional fractal gradation model and the Kozeny-Carman formula, a formula for calculating the permeability coefficient including grain-size distribution parameters and the porosity is established. After discussing the physical meaning of each item in the formula, the validation of the formula is verified by using the measured data in the existing researches. The results show that the two-dimensional gradation model can accurately and uniquely describe the grain size distribution of the coarse-grained soil. The established formula for calculating the permeability coefficient of the coarse-grained soil including grain-size distribution parameters and the porosity is reasonable, and it is suitable for calculating the permeability coefficient of continuously graded and gap-graded coarse-grained soil.
- coarse-grained soil /
- permeability coefficient /
- fractal model /
- grain-size distribution /
- porosity

HTML全文

图 1 花岗岩级配碎石试验级配曲线及双分形模型拟合曲线

Figure 1. Fitting curves of granite-graded macadam by tests and two-dimensional fractal model

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图 2 渭河粗粒土试验级配曲线及双分形模型拟合曲线

Figure 2. Fitting curves of coarse-grained soil from Weihe River by tests and two-dimensional fractal model

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图 3 砂岩粗粒料试验级配曲线及双分形模型拟合曲线

Figure 3. Fitting curves of sandstone coarse-grained materials by tests and two-dimensional fractal model

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图 4 花岗岩级配碎石渗透系数实测值及计算值

Figure 4. Measured and calculated values of permeability coefficient of granite-graded macadam

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表 1 粗粒土双分形级配模型参数

Table 1 Parameters of two-dimensional fractal gradation model for coarse-grained soil

文献来源	级配编号	级配类型	D₁	D₂	R_T1/mm	R_T2/mm	M_T1	M_T2	R²
文献[4]	JP1	连续	2.592	1.912	45	3.0623	64.00	36.00	0.9971
	JP2	连续	2.588	2.528	45	9.1935	55.00	45.00	0.9972
	JP3	连续	2.564	2.580	45	10.3868	49.95	50.05	0.9980
	JP4	连续	2.500	2.000	45	3.9093	69.00	31.00	0.9983
	JP5	连续	2.512	2.472	45	8.1350	67.25	32.75	0.9966
	JP6	连续	2.616	2.204	45	7.1977	83.15	16.85	0.9969
	JP7	连续	2.400	2.024	45	4.9916	75.00	25.00	0.9996
	JP8	连续	2.400	2.224	45	4.4177	75.00	25.00	0.9991
	JP9	连续	2.396	2.416	45	3.9097	74.35	25.65	0.9981
文献[5]	TYU1	连续	1.904	2.328	20	1.4164	77.00	23.00	0.9962
	TYU2	连续	2.292	0.104	20	0.3199	90.00	10.00	0.9979
	TYU3	连续	2.404	1.284	20	0.6747	92.05	7.95	0.9969
	TYU4	连续	2.308	2.380	20	3.6713	71.15	28.85	0.9960
	TYU5	连续	2.300	2.380	20	6.2355	47.10	52.90	0.9964
	TYU6	连续	2.324	2.296	20	5.0453	41.85	58.15	0.9970
	TYU7	连续	2.404	1.924	20	2.6729	39.95	60.05	0.9981
	TYU8	连续	1.840	1.980	20	2.4032	20.00	80.00	0.9984
	TYU9	连续	2.544	0.848	20	1.1443	28.35	71.65	0.9979
	TYU10	连续	2.692	0.400	20	1.0331	17.00	83.00	0.9974
文献[7]	1-3#	间断	2.600	1.584	60	24.5036	58.00	42.00	0.9927
	1-4#	间断	2.376	2.172	60	24.5033	43.50	56.50	0.9959
	1-7#	间断	2.616	1.704	60	18.9698	66.05	33.95	0.9915
	2-1#	间断	2.620	2.004	60	21.5590	65.00	35.00	0.9928
	2-2#	间断	1.500	2.608	60	27.8484	16.05	83.95	0.9824
	2-3#	间断	2.604	1.204	60	0.5987	76.00	24.00	0.9807

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表 2 渭河粗粒土试样渗透系数实测值及计算值

Table 2 Measured and calculated values of permeability coefficient of coarse-grained soil samples from Weihe River

级配编号	渗透系数k/ (10^-2cm·s^-1)			$\frac{{M{\text{(}}r < {d_{\text{c}}}{\text{)}}}}{{{M_{\text{T}}}}}/$ %	相对误差δ/%
级配编号	试验值	计算值^[5]	式（10）计算值		δ^[5]	δ_式（10）
TYU1	6.70	9.50	6.64	31.54	41.79	0.90
TYU2	4.50	7.90	4.71	31.74	75.56	4.67
TYU3	2.80	—	2.66	35.79	—	5.00
TYU4	2.40	5.20	2.48	41.54	116.67	3.33
TYU5	2.30	4.10	2.31	42.97	78.26	0.43
TYU6	2.10	3.00	1.86	48.13	42.86	11.43
TYU7	1.90	2.20	1.74	72.13	15.79	8.42
TYU8	1.00	1.50	1.35	81.95	50.00	35.00
TYU9	0.96	—	1.07	83.01	—	11.46
TYU10	0.88	—	0.77	92.16	—	12.50
注：相对误差δ=\|k_计算值-k_实测值\|/k_实测值×100%。

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表 3 砂岩粗粒料的渗透系数实测值与计算值

Table 3 Measured and calculated values of permeability coefficient of sandstone coarse-grained materials

级配编号	实测值		$\frac{{M(r < {d_{\text{c}}})}}{{{M_{\text{T}}}}}/$ %	渗透系数计算值/(10^-2 cm·s^-1)					相对误差/%
级配编号	ρ_d/ (g·cm^-3)	k/ (10^-2 cm·s^-1)	$\frac{{M(r < {d_{\text{c}}})}}{{{M_{\text{T}}}}}/$ %	k_式（11）	k_T	k_C	k_水科院	k_杨志浩	δ_式（11）	δ_T	δ_C	δ_水科院	δ_杨志浩
1-3#	1.89	84.10	32.27	84.14	4.15	37.12	149.84	8.78	0.05	95.07	55.86	78.17	89.56
1-4#	1.91	60.71	32.10	60.39	20.45	143.42	138.75	15.62	0.53	66.32	136.24	128.55	74.27
1-7#	1.89	6.17	38.95	5.32	2.51	25.65	31.71	6.09	13.78	59.32	315.72	413.94	1.30
2-1#^①	1.91	7.14	40.80	8.56	1.67	18.21	22.20	4.90	19.89	76.61	155.04	210.92	31.37
2-1#^②	1.82	8.76	40.80	9.22	2.54	27.93	30.93	6.73	5.25	71.00	218.84	253.08	23.17
2-1#^③	1.74	10.64	40.80	10.04	3.50	39.91	40.39	8.79	5.64	67.11	275.09	279.61	17.39
2-2#^①	1.91	0.79	50.08	0.75	0.90	8.80	0.89	2.32	5.06	13.92	1013.92	12.66	193.67
2-2#^②	2.00	0.39	50.08	0.29	0.54	5.53	0.61	1.65	25.64	38.46	1317.95	56.41	323.08
2-2#^③	1.79	1.17	50.08	1.69	1.55	15.47	1.37	3.53	44.44	32.48	1222.22	17.09	201.71
2-3#^①	1.91	0.59	56.83	0.58	0.67	5.17	0.50	1.32	1.69	13.56	776.27	15.25	123.73
2-3#^②	2.00	0.11	56.83	0.11	0.40	3.25	0.34	0.94	0	263.64	2854.55	209.09	754.55
2-3#^③	1.81	0.90	56.83	1.33	1.06	8.30	0.72	1.87	47.78	17.78	822.22	20.00	107.78

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