黄河冲积平原细粒土小应变剪切模量试验研究

王津津; 王志才; 高涛; 宋润钊

doi:10.11899/zzfy20240404

黄河冲积平原细粒土小应变剪切模量试验研究

doi: 10.11899/zzfy20240404

山东省地震局, 济南 250014

基金项目: 国家自然科学基金项目（YB2308、41974105、YW2304）

详细信息

作者简介:
王津津，女，生于1983年。工程师，硕士。主要从事土动力学及年代学方面的研究工作。E-mail：byewjj@163.com

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出版历程
- 收稿日期: 2023-10-30
- 刊出日期: 2024-12-31

Experimental Study on Small Strain Shear Modulus of Fine Grained Soil in the Yellow River Alluvial Plain

Earthquake Administration of Shandong Province, Ji'nan 250014, China

摘要

摘要: 本文通过采用原位波速法、弯曲元试验法和共振柱试验法，深入探讨了室内测试与原位波速法在小应变剪切模量试验中的差异。选取山东省境内黄河冲积平原典型场地细粒土钻孔资料，统计原位波速法和室内测试2种测试手段测得的剪切波速，并对测试结果进行对比分析。研究结果表明，在保持土的有效应力状态和减少土样扰动的基础上，原位波速法、弯曲元试验法和共振柱试验法测得的小应变剪切模量总体趋势一致，原位波速法的结果普遍小于室内测试的结果，但相对误差大多不超过10%。其中弯曲元试验法测试细粒土得到的小应变剪切模量与原位波速法的结果更为接近。建议工程实践中采用弯曲元试验法快速测得细粒土小应变剪切模量。将Rampello的经验公式描述的小应变剪切模量与实测结果进行对比，给出相关土层经验参数。研究结果可为该地区地下工程计算分析中小应变剪切模量的估算提供参考。
- 细粒土 /
- 小应变剪切模量 /
- 原位波速法 /
- 弯曲元 /
- 共振柱
Abstract: This study investigates the differences in small strain shear modulus (G_max) measured using laboratory tests and the in-situ wave velocity method. The research utilizes data from a typical fine-grained soil site in the Yellow River alluvial plain, Shandong Province, China. The shear wave velocities measured by both in-situ wave velocity and laboratory methods (including bending element and resonant column tests) were compared. The results demonstrate a consistent trend in G_max values across all methods, assuming the effective stress state of the soil is maintained and sample disturbance is minimized. While G_max values from the in-situ wave velocity method tend to be lower than those from laboratory tests, the relative errors are generally less than 10%. The bending element test yields G_max values that are closer to those obtained from the in-situ wave velocity method. It is suggested that, for engineering applications, the bending element test offers a quick and accurate means of determining the small strain shear modulus of fine-grained soils. Additionally, Rampello's empirical formula for G_max is compared to the measured results, and the relevant empirical parameters for different soil layers are provided. These findings offer valuable insights for estimating the shear modulus at small and medium strains in underground engineering design and analysis in this region.
- Fine grained soil /
- Small strain shear modulus /
- In-situ wave velocity method /
- Bending element /
- Resonant column

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图 1 RCA型共振柱试验系统结构布置图

Figure 1. Layout of RCA type resonance column test system structure layout

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图 2 安装弯曲元的共振柱压力室剖面结构图

Figure 2. Resonance column pressure chamber profile structure for installing bending element

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图 3 内置于共振柱的弯曲元结构示意图

Figure 3. Schematic diagram of the curved element structure built into the resonant column

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图 4 PS声波测井示意图

Figure 4. PS sonic logging diagram

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图 5 现场测试及取土点地理空间分布图

Figure 5. Field test and geospatial distribution of sampling sites

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图 6 K23号钻孔土层剪切波速列图

Figure 6. Shear wave velocity diagram of borehole K23

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图 7 剪切波速的原位波速法与室内试验结果对比

Figure 7. Comparison of test results of shear wave velocity in situ to in laboratory

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图 8 剪切模量的实测平均值与预测值的对比

Figure 8. Comparison between the measured mean value and the predicted value of shear modulus

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表 1 试样参数

Table 1. Specimen parameters

取土地点	土样编号	取样深度/m	天然含水率/%	天然重度/(g·cm⁻³)	固结压力/kPa	土类	颜色状态
陵城区	K23-1	2.8	24.3	2.0	50	粉土	褐黄色，中密
	K23-2	3.8	37.3	1.9	50	粉质黏土	黄褐色，可塑
	K23-3	8.8	30.4	2.0	100	粉质黏土	黄褐色，可塑
	K23-4	16.0	35.1	2.0	160	淤泥质土	黑灰色，可塑～软塑
	K23-6	30.8	24.5	2.1	300	粉质黏土	褐黄色，可塑
	K23-7	36.8	22.9	2.1	370	粉土	褐黄色，中密
	K23-9	44.8	27.9	2.0	450	粉质黏土	褐黄色，可塑
	K23-10	49.8	20.0	2.1	500	粉砂	褐黄色，密实
	K23-14	60.8	22.5	2.1	600	黏质粉土	褐黄色，可塑～硬塑
	K23-16	64.8	20.4	2.1	650	粉质黏土	黄褐色，硬塑
	K23-17	67.8	19.5	1.9	680	粉砂	褐黄色，密实
庆云县	K19-2	7.8	21.7	2.0	100	粉质黏土	黄褐色，可塑
	K19-3	13.8	24.3	2.1	140	粉质黏土	褐黄色，可塑
	K19-4	16.8	20.8	2.1	170	粉质黏土	褐黄色，可塑
	K19-5	21.0	22.0	2.1	200	黏土	黄褐色，可塑～硬塑
	K19-7	32.0	27.7	2.0	300	粉质黏土	褐色，可塑～硬塑
	K19-8	35.8	20.1	2.1	350	粉土	黄色，中密
	K19-9	42.8	27.3	2.0	450	粉质黏土	褐黄色，可塑～硬塑
	K19-11	48.8	25.1	2.0	500	粉质黏土	黄褐色，硬塑
	K19-12	55.8	37.5	2.0	550	黏土	褐色，硬塑
注：原位波速法钻孔为取样钻孔。

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表 2 3种方法剪切波速测试结果对比

Table 2. Comparison of shear wave velocity test results from three methods

取土点	测试深度/m	土层性质	现场测试结果/ (m·s⁻¹)	弯曲元测试结果/ (m·s⁻¹)	共振柱测试结果/ (m·s⁻¹)	相对误差/%
取土点	测试深度/m	土层性质	现场测试结果/ (m·s⁻¹)	弯曲元测试结果/ (m·s⁻¹)	共振柱测试结果/ (m·s⁻¹)	现场与弯曲元	现场与共振柱	弯曲元与共振柱
陵城区	2.8	粉土	164.0	170.9	201.9	4.2	23.1	18.1
	3.8	粉质黏土	164.0	161.1	169.17	1.7	3.2	5.0
	8.8	粉质黏土	179.0	191.0	231.2	6.7	29.2	21.1
	16.0	淤泥质土	229.0	234.0	254.6	2.2	11.2	8.8
	30.8	黏质粉土	307.0	310.0	282.8	1.0	7.9	8.8
	36.8	粉土	337.0	355.0	323.0	5.3	4.2	9.0
	44.8	粉质黏土	355.0	360.0	345.9	1.4	2.6	3.9
	49.8	粉砂	348.0	335.0	324.7	3.7	6.7	3.1
	60.8	黏质粉土	377.0	402.0	412.0	6.6	9.3	2.5
	64.8	粉质黏土	434.0	431.0	453.0	0.7	4.4	5.1
	67.8	粉砂	408.0	425.3	446.9	4.2	9.5	5.1
庆云县	7.8	黏质粉土	168.0	187.5	207.3	11.6	23.4	10.6
	13.8	粉质黏土	182.0	238.7	242.4	31.2	33.2	1.6
	16.8	粉质黏土	211.0	230.8	250.6	9.4	18.8	8.6
	21.0	黏土	231.0	214.8	243.7	−7.0	5.5	13.4
	32.0	粉质黏土	298.0	276.3	315.0	−7.3	5.7	14.0
	35.8	粉土	311.0	281.9	277.8	−9.4	−10.7	−1.4
	42.8	粉质黏土	335.0	347.7	344.6	3.8	2.9	−0.9
	48.8	粉质黏土	357.0	342.3	365.2	−4.1	2.3	6.7
	55.8	黏土	365.0	370.8	395.1	1.6	8.3	6.6

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表 3 3种测试手段得到的土体小应变剪切模量G_max值

Table 3. The small strain shear modulus of soil mass obtained with three testing methods

取样点	测试深度/m	土层性质	弯曲元G_max/MPa	共振柱G_max/MPa	现场测试G_max/MPa
陵城区	3.8	粉质黏土	51.4	49.6	54.7
	8.8	粉质黏土	64.7	73.7	108.0
	16.0	淤泥质土	102.8	107.3	127.0
	30.8	黏质粉土	198.9	202.8	168.7
	36.8	粉土	240.8	267.2	221.2
	44.8	粉质黏土	254.6	261.8	241.7
	49.8	粉砂	253.1	234.6	220.4
	60.8	黏质粉土	298.5	339.4	356.5
	64.8	粉质黏土	391.8	386.4	426.8
	67.8	粉砂	322.9	350.9	387.5
	7.8	黏质粉土	56.2	70.0	85.5
庆云县	13.8	粉质黏土	69.9	120.2	124.0
	16.8	粉质黏土	94.8	113.4	133.7
	21.0	黏土	113.7	98.3	126.5
	32.0	粉质黏土	173.2	148.9	193.5
	35.8	粉土	200.2	164.5	159.7
	42.8	粉质黏土	226.7	244.2	239.9
	48.8	粉质黏土	256.2	235.4	268.1
	55.8	黏土	261.1	269.4	306.0

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表 4 土体经验参数S、n取值

Table 4. Values of soil empirical parameters S and n

数据类别	试验方法	e	f（e）	S	n	参考文献
经验值	三轴试验、共振柱试验	0.5～6.2	$ {\left(1+e\right)}^{-2.4} $	15000～50000	0.5	Vardanega等（2013）
本次测试	单孔波速测试	0.7～1.13	$ {\left(1+e\right)}^{-2.4} $	30000～45000	0.5	本文结果

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