基于动态图像技术的南海钙质土颗粒形态特征研究

刘鑫; 李飒; 尹福顺; 姚婷

doi:10.11779/CJGE20220010

基于动态图像技术的南海钙质土颗粒形态特征研究 English Version

刘鑫^{1, 2,},
李飒^{1, 2, ,},
尹福顺^{1, 2},
姚婷³

1.
天津大学建筑工程学院，天津 300350
2.
天津大学水利工程仿真与安全国家重点实验室，天津 300350
3.
中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室，湖北武汉 430071

基金项目:

国家自然科学基金面上项目 42072294

国家自然科学基金重大项目 51890911

天津市研究生科研创新项目 2021YJSB183

详细信息

作者简介:
刘鑫(1995—)，男，博士研究生，主要从事钙质土力学特性方面的研究。E-mail: 1085568118@qq.com

通讯作者:
李飒, E-mail: lisa@tju.edu.cn

中图分类号: TU411
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出版历程
- 收稿日期: 2022-01-02
- 网络出版日期: 2023-03-15
- 刊出日期: 2023-02-28

Morphological characteristics of carbonate soil in South China Sea based on dynamic image technology

LIU Xin^{1, 2,},
LI Sa^{1, 2, ,},
YIN Fushun^{1, 2},
YAO Ting³

1.
School of Civil Engineering, Tianjin University, Tianjin 300350, China
2.
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300350, China
3.
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China

摘要

摘要: 颗粒形态是一项重要的细观指标，影响着粒状土的物理力学性质。钙质土因为其特殊的生物成因，有着复杂的颗粒形态。为了研究其颗粒形态特征，采用PartAn 3D颗粒动态图像分析仪对粒径0.5~20 mm的南海钙质土颗粒开展形状测试，采用延伸率、扁平度、球形度、圆度、棱角度和凸度指标定量描述颗粒形态特征。结果显示：南海钙质土颗粒的延伸率、扁平度、球形度和圆度符合正态分布，而棱角度和凸度符合幂律分布；颗粒形状以块状居多，随着粒径的减小，钙质土颗粒变得更扁平，形状更规则；通过研究样本数量对颗粒形状量化结果的影响，建议采用形状指标的算术平均值量化单一粒组钙质土颗粒形状特征时，颗粒数目不少于600。最后，运用统计学中的主成分分析方法，得到一个综合考虑钙质土颗粒形状信息的新指标，建立了该指标与钙质土最大、最小孔隙比的关系。
- 钙质土 /
- 动态图像技术 /
- 颗粒形状 /
- 最大孔隙比 /
- 最小孔隙比
Abstract: The particle morphology is an important microscopic characteristic that affects the physical and mechanical properties of granular soils. Carbonate soil particles have complex morphology due to special biogenesis. In order to study the morphological characteristics of the soil particles, the PartAn 3D particle dynamic image analyzer was used to test the particle shape of the carbonate soil with grain sizes of 0.5 ~ 20 mm from the South China Sea. The elongation, flatness, sphericity, roundness, angularity and convexity were used to quantitatively describe the morphological characteristics of the particles. The results show that the frequency distribution of the elongation, flatness, sphericity and roundness of carbonate soil particles in the South China Sea complies with the normal one, while the frequency distribution of the angularity and convexity complies with that of the power law. The particle shape of the carbonate soil is mostly blocky, and with the decrease of grain size, the soil particles become flatter and more regular in shape. Through investigating the effects of sample size on the results of particle shape quantification, it is suggested that the number of particles should be not less than 600 when using the arithmetic mean of shape descriptors to quantify the morphological characteristics of the uniformly graded carbonate soil. Finally, a comprehensive shape index which can fully describe the morphological characteristics of the carbonate soil particles is obtained with the aid of the principal component analysis method in statistics, and the relationship between this shape index and the maximum to minimum void ratio of the carbonate soil is established.
- carbonate soil /
- dynamic image technology /
- particle shape /
- maximum void ratio /
- minimum void ratio

HTML全文

图 1 PartAn 3D颗粒动态图像分析仪^[11]

Figure 1. PartAn 3D particle dynamic image analyzer^[11]

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图 2 下落过程中颗粒翻滚的一系列图像

Figure 2. A series of images of particles tumbling as they fall

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图 3 颗粒形状、棱角和纹理示意图

Figure 3. Schematic diagram of particle shape, angularity and texture

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图 4 不同粒组钙质土颗粒各尺寸参数的累积分布曲线

Figure 4. Cumulative distribution curves of particle size indices of carbonate soil with different grain fractions

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图 5 不同粒组钙质土颗粒形状指标的频率分布

Figure 5. Frequency distribution of particle shape indices of carbonate soil with different grain fractions

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图 6 不同粒组钙质土颗粒形状指标的累积分布曲线

Figure 6. Cumulative distribution curves of particle shape indices of carbonate soil with different grain fractions

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图 7 各粒组形状指标统计量与10~20 mm粒组的差异

Figure 7. Statistical differences of shape indices for each grain fraction and 10~20 mm-grain fraction

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图 8 1~2 mm颗粒的形状指标特征值的相对误差平均值随样本数量的变化

Figure 8. Variation of average relative error of characteristic value of shape indices of 1~2 mm particles with the number of samples

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图 9 主成分分析流程图

Figure 9. Flow chart of principal component analysis

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图 10 主成分与极限孔隙比的关系

Figure 10. Relationship between principal component and limit void ratio

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表 1 本文选用的表征颗粒形状特征的指标

Table 1 Indices chosen to characterize particle shape in this paper

指标	定义	取值范围	描述特征
延伸率	${{{F_{{\text{W}}}}} \mathord{\left/ {\vphantom {{{F_{{\text{W}}}}} {F_{{\text{L}}}^{}}}} \right. } {F_{{\text{L}}}^{}}}$	0~1	宏观形状。颗粒越狭长，其值越小
扁平度	${{{F_{{\text{T}}}}} \mathord{\left/ {\vphantom {{{F_{{\text{T}}}}} {{F_{{\text{W}}}}}}} \right. } {{F_{{\text{W}}}}}}$	0~1	宏观形状。颗粒越扁平，其值越小
球形度	${({D_{{\text{a}}}}/{D_{{\text{p}}}})^2}$	0~1	宏观形状、中观棱角。颗粒越接近球形，其值越大
圆度	$4A/({{\text{π }}}F_{{\text{L}}}^{{\text{2}}})$	0~1	宏观形状、中观棱角。颗粒越接近圆形，其值越大
棱角度	$A/{A_{{\text{C}}}}$	0~1	中观棱角。颗粒棱角越多，越突出，其值越小
凸度	${P_{{\text{C}}}}/P$	0~1	细观纹理。颗粒表面越光滑，其值越大
注： ${D_{{\text{a}}}}$ 为与颗粒投影图像等面积圆的直径； ${D_{{\text{p}}}}$ 为与颗粒投影图像等周长圆的直径； ${F_{{\text{L}}}}$ ， ${F_{{\text{W}}}}$ 和 ${F_{{\text{T}}}}$ 分别为Feret长度、宽度和厚度；A为颗粒投影图像面积； $P$ 为颗粒投影图像周长； ${A_{{\text{C}}}}$ 为颗粒投影图像外接最小凸边形面积； ${P_{{\text{C}}}}$ 为颗粒投影图像外接最小凸边形周长。在本次试验中， ${D_{{\text{a}}}}$ ， ${D_{{\text{p}}}}$ ，A， $P$ ， ${A_{{\text{C}}}}$ 和 ${P_{{\text{C}}}}$ 取一系列图像的平均值； ${F_{{\text{L}}}}$ 取一系列图像中的最大长度， ${F_{{\text{W}}}}$ 取一系列图像中的最大宽度， ${F_{{\text{T}}}}$ 取一系列图像中的最小宽度。

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表 2 不同粒组钙质土颗粒形状指标统计表

Table 2 Statistical list of particle shape indices of carbonate soil with different grain fractions

粒组	统计量	延伸率	扁平度	球形度	圆度	棱角度	凸度
10~20 mm	平均值	0.667	0.689	0.794	0.471	0.954	0.979
	中位数	0.681	0.703	0.806	0.475	0.961	0.984
	最小值	0.219	0.162	0.389	0.144	0.730	0.814
	最大值	0.947	0.990	0.961	0.854	0.998	0.998
	标准差	0.125	0.159	0.081	0.112	0.031	0.017
5~10 mm	平均值	0.670	0.668	0.808	0.471	0.961	0.985
	中位数	0.683	0.673	0.818	0.473	0.966	0.988
	最小值	0.233	0.162	0.254	0.070	0.543	0.802
	最大值	0.945	0.988	0.978	0.857	0.997	0.999
	标准差	0.123	0.149	0.071	0.104	0.026	0.012
2~5 mm	平均值	0.685	0.629	0.806	0.460	0.960	0.990
	中位数	0.699	0.649	0.818	0.461	0.967	0.993
	最小值	0.096	0.105	0.153	0.047	0.599	0.874
	最大值	0.963	0.967	0.979	0.826	0.999	1.000
	标准差	0.120	0.175	0.081	0.111	0.030	0.009
1~2 mm	平均值	0.686	0.635	0.834	0.461	0.972	0.995
	中位数	0.698	0.649	0.848	0.465	0.980	0.997
	最小值	0.109	0.235	0.300	0.051	0.667	0.893
	最大值	0.963	0.956	0.980	0.827	1.000	1.000
	标准差	0.114	0.147	0.075	0.113	0.026	0.006
0.5~1 mm	平均值	0.684	0.605	0.850	0.424	0.987	0.998
	中位数	0.692	0.607	0.859	0.432	0.992	0.999
	最小值	0.153	0.202	0.283	0.055	0.693	0.945
	最大值	0.934	1.000	1.000	0.744	1.000	1.000
	标准差	0.115	0.118	0.059	0.098	0.018	0.003

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表 3 量化钙质土颗粒形状特征所需的最小样本数量

Table 3 Minimum number of samples required to quantify shape characteristics of carbonate soil particles

粒组	延伸率	扁平度	球形度	圆度	棱角度	凸度
10~20 mm	345	446	238	344	14	10
5~10 mm	326	583	135	292	12	10
2~5 mm	270	439	121	224	32	10
1~2 mm	111	473	68	136	17	10
0.5~1 mm	318	241	77	242	10	10

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表 4 不同粒组钙质土的极限孔隙比

Table 4 Limit void ratios of carbonate soil with different fractions

孔隙比	10~20 mm	5~10 mm	2~5 mm	1~2 mm	0.5~1 mm
${e_{\max }}$	2.225	1.821	1.703	1.576	1.456
${e_{\min }}$	1.586	1.241	1.143	1.138	1.112
注： ${e_{\max }}$ 为最大孔隙比； ${e_{\min }}$ 为最小孔隙比。

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表 5 现有预测极限孔隙比的经验公式

Table 5 Existing empirical equations for predicting limit void ratio

文献	经验公式
Santamarina等^[3]	${e_{\max }} = 0.554 + 0.154{R^{ - 1}}$ ， ${e_{\min }} = 0.359 + 0.082{R^{ - 1}}$
Cho等^[5]	${e_{\max }} = 1.5 - 0.41\left( {R + S} \right)$ ， ${e_{\min }} = 0.9 - 0.22\left( {R + S} \right)$
Patra等^[22]	${e_{\max }} = 0.6042{D_{50}}^{ - 0.304}$ ， ${e_{\min }} = 0.3346{D_{50}}^{ - 0.491}$
Zheng等^[23]	${e_{\max }} = {R^{ - 0.20}}{S^{ - 0.25}}{C_{{\text{u}}}}^{ - 0.10}e_{\max }^ \circ$ ， ${e_{\min }} = {R^{ - 0.15}}{S^{ - 0.25}}{C_{{\text{u}}}}^{ - 0.50}e_{\min }^ \circ$
Hryciw等^[24]	${e_{\max }} = 0.50{R^{ - 0.2}} + 0.41{S^{ - 0.6}} + 0.34{C_{{\text{u}}}}^{ - 0.2} - 0.51$ ， ${e_{\min }} = 0.37{R^{ - 0.2}} + 0.28{S^{ - 0.6}} + 0.31{C_{{\text{u}}}}^{ - 0.3} - 0.48$
Chang等^[25]	${e_{\max }} = 0.619{R^{ - 0.372}}{({D_{50}}/{D_{{{\text{ref}}}}})^{ - 0.048}}$ ， ${e_{\min }} = 0.413{R^{ - 0.291}}{({D_{50}}/{D_{{{\text{ref}}}}})^{ - 0.043}}$
注： $e_{\max }^ \circ$ 为参考最大孔隙比，等于0.75； $e_{\max }^ \circ$ 为参考最小孔隙比，等于0.50； ${D_{{{\text{ref}}}}}$ 为参考粒径，等于1 mm。

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表 6 方差贡献率表

Table 6 Variance contribution rates

成分	特征值	方差贡献率/%	累积方差贡献率/%
1	3.698	92.455	92.455
2	0.238	5.942	98.397
3	0.060	1.488	99.886
4	0.005	0.114	100.000

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