橡胶-砂-聚氨酯复合材料冻融循环后强度特性及本构模型

尹平保; 余伟; 杨朝晖; 罗佩婷

doi:10.13801/j.cnki.fhclxb.20210804.003

橡胶-砂-聚氨酯复合材料冻融循环后强度特性及本构模型

doi: 10.13801/j.cnki.fhclxb.20210804.003

尹平保^{1, 3, ,},
余伟^{1, 3},
杨朝晖^{1, 2},
罗佩婷^{1, 3}

1.
长沙理工大学　土木工程学院，长沙 410114
2.
阿拉斯加大学　阿拉斯加安克雷奇 99508，美国
3.
长沙理工大学　南方地区桥梁长期性能提升技术国家地方工程实验室，长沙 410114

基金项目: 国家自然科学基金 (51878069；52078055)；湖南省自然科学基金(2019JJ50647)；长沙理工大学南方地区桥梁长期性能提升技术国家地方工程实验室开放基金 (18KE01)

详细信息

通讯作者:
尹平保，副教授，研究生导师，博士后，研究方向为桩基础及支挡结构工程等　 E-mail：pingbaby921@163.com

中图分类号: TB35
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出版历程
- 收稿日期: 2021-06-11
- 修回日期: 2021-07-19
- 录用日期: 2021-07-28
- 网络出版日期: 2021-08-05
- 刊出日期: 2022-07-30

Strength characteristics and constitutive model of rubber-sand-polyurethane composites after freeze-thaw cycles

YIN Pingbao^{1, 3
, ,},
YU Wei^{1, 3},
YANG Zhaohui^{1, 2},
LUO Peiting^{1, 3}

1.
School of Civil Engineering, Changsha University of Science and Technology, Changsha 410114, China
2.
University of Alaska Anchorage, Anchorage 99508, Alaska, USA
3.
National-Local Joint Laboratory of Engineering Technology for Long-Term Performance Enhancement of Bridges in Southern District, Changsha University of Science & Technology, Changsha 410114, China

摘要

摘要: 研究废旧轮胎颗粒材料改良方法及强度特性是将其用于寒区桩基抗冻性能改善的基础。首先，按橡胶∶砂∶聚氨酯=3∶2∶1的质量比制作了若干复合材料试样；其次，通过静三轴试验，获得了不同温度、冻融循环次数及围压下试样的应力-应变曲线。试验结果表明：橡胶-砂-聚氨酯复合材料的应力-应变曲线无明显峰值点，具有显著的应变强硬化特征；试样破坏强度随温度降低而增加；冻结状态下，试验温度每降低5.0℃，其破坏强度约增加15.0%；试样破坏强度随冻融循环次数增加而降低，但平均降幅不足5.0%；围压对20.0℃常温试样破坏强度的影响幅度达15.0%，而对冻结试样破坏强度的影响幅度不足5.0%。敏感性分析显示：温度对试样破坏强度的影响最大，围压及冻融循环次数的影响相对较小，说明橡胶-砂-聚氨酯复合材料具有强度适中、结构稳定和抗冻融等特性。在此基础上，建立了考虑温度、围压和冻融循环的橡胶-砂-聚氨酯复合材料应力-应变本构模型，验证了模型参数拟合公式的合理性。
- 橡胶 /
- 聚氨酯 /
- 冻融循环 /
- 强度特性 /
- 本构模型
Abstract: The improvement methods and strength properties of scrap tire granular materials are the research basis on the frost resistance performance improvement of piles in cold regions. Several composite samples were made according to the mass ratio of rubber∶sand∶polyurethane = 3∶2∶1. The stress-strain curves of samples under different temperatures, confining pressures and number of freeze-thaw cycles were obtained by triaxial tests. The test results show that the stress-strain curve of rubber-sand-polyurethane composite has no obvious peak point, and has obvious strain hardening characteristic. The failure strength of the sample increases with the decrease of temperature, and increases by 15.0% when the test temperature decreases by 5.0℃ for frozen samples. The failure strength values of samples decrease with the increase of freeze-thaw cycles, but the average decrease is less than 5.0%. The effect of confining pressures on the failure strength of the 20.0℃ sample is about 15.0%, while that of the frozen samples is less than 5.0%. The sensitivity analysis shows that the temperature has the greatest impact on the failure strength of rubber-sand-polyurethane composites, while the confining pressure and the number of freeze-thaw cycles have little effect. The rubber-sand-polyurethane composites have the characteristics of moderate strength, stable structure and freeze-thaw resistance. The stress-strain constitutive model of rubber-sand-polyurethane composite after consideration of the temperature, confining pressure and freeze-thaw cycle was established, and the rationality of the model parameters fitting formula was verified.
- rubber /
- polyurethane /
- freeze-thaw cycle /
- strength property /
- constitutive model

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图 1 试验材料

Figure 1. Testing materials

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图 2 试验材料级配曲线

Figure 2. Gradation curves of tested materials

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图 3 试验材料及橡胶-砂-聚氨酯复合材料试样制备

Figure 3. Test materials and preparation of rubber-sand-polyurethane composite samples

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图 4 橡胶-砂-聚氨酯复合材料试样中心温度T-时间关系曲线

Figure 4. Center temperature T-time curves of rubber-sand-polyurethane composite samples

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图 5 橡胶-砂-聚氨酯复合材料试样冻融循环曲线

Figure 5. Freeze-thaw cycle curves of rubber-sand-polyurethane composite samples

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图 6 GDS液压式三轴仪

Figure 6. GDS hydraulic triaxial apparatus

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图 7 温度T对橡胶-砂-聚氨酯复合材料大小主应力差(σ₁–σ₃)-应变ε₁曲线的影响

Figure 7. Influence of temperature T on stress (σ₁–σ₃)-strain ε₁curves of rubber-sand-polyurethane composites

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图 8 围压σ₃对橡胶-砂-聚氨酯复合材料大小主应力差(σ₁–σ₃)-应变ε₁曲线的影响

Figure 8. Effect of confining pressure σ₃ on stress (σ₁–σ₃)-strain ε₁ curves of rubber-sand-polyurethane composites

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图 9 冻融循环对橡胶-砂-聚氨酯复合材料大小主应力差(σ₁–σ₃)-应变ε₁曲线的影响

Figure 9. Effect of freeze-thaw cycles on stress (σ₁–σ₃)-strain ε₁ curves of rubber-sand-polyurethane composites

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图 10 T=−15.0℃、N=50及σ₃=50 kPa下试验加载前后橡胶-砂-聚氨酯复合材料试样：(a) 加载前；(b) 加载后

Figure 10. Rubber-sand-polyurethane composite samples before and after loading (T=−15.0℃, N=50, σ₃=50 kPa): (a) Unloaded; (b) Loaded

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图 11 橡胶-砂-聚氨酯复合材料试验与计算结果对比

Figure 11. Comparison of test and calculation results of rubber-sand-polyurethane composites

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表 1 试验材料的物理参数

Table 1. Physical parameters of testing materials

Material	d₅₀/mm	C_u	C_c	Bulk density /(g·cm⁻³)	Apparent density /(g·cm⁻³)
Sands	2.79	1.40	0.89	1.87	2.68
Rubber particles	2.81	2.68	1.35	0.68	1.25
Notes: d₅₀—Average size; C_u—Coefficient of uniformity; C_c—Coefficient of curvature.

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表 2 试验方案

Table 2. Testing programs

Serial number	T/℃	N/times	σ₃/kPa
A	20.0	0、25、50	25、50、100
B	−5.0	0、25、50	25、50、100
C	−10.0	0、25、50	25、50、100
D	−15.0	0、25、50	25、50、100
Notes: T—Temperature; N—Number of freeze-thaw cycles; σ₃—Confining pressure.

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表 3 冻融循环对不同类别土体强度的影响

Table 3. Influences of freeze-thaw cycles on strength of different types of soils

Soil type	N/times	σ_f/kPa	Strength decrement/%
Silty sand^[30]	0	566	51.4
Silty sand^[30]	10	275	51.4
Silty clay^[31]	0	288	24.1
Silty clay^[31]	9	219	24.1
Rubber-sand-polyurethane composite	0	853	2.5
Rubber-sand-polyurethane composite	25	832	2.5
Notes: Compactness of the soil in the table is 90%, dry density of silty sand is 1.85 g/cm³, and dry density of silty clay is 1.65 g/cm³.

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表 4 橡胶-砂-聚氨酯复合材料试样破坏强度(单位：kPa)

Table 4. Failure strength of rubber-sand-polyurethane composite samples (Unit: kPa)

N/times	σ₃/kPa	T/℃
N/times	σ₃/kPa	20.0	−5.0	−10.0	−15.0
0	25	620	846	967	1113
	50	630	853	1010	1190
	100	755	897	1075	1280
25	25	618	825	960	1102
	50	618	832	982	1157
	100	748	892	1058	1228
50	25	612	845	964	1124
	50	610	850	973	1147
	100	705	883	1042	1251

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表 5 影响因素(A, B)的频数列联表

Table 5. Frequency contingency of influencing factors (A, B)

	B₁	B₂	···	B_c	Total
A₁	n₁₁	n₁₂	···	n₁_c	n₁₊
A₂	n₂₁	n₂₂	···	n₂_c	n₂₊
···	···	···	···	···	···
A_r	n_r₁	n_r₂	···	n_rc	n_r₊
Total	n₊₁	n₊₂	···	n₊_c	n

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表 6 卡方检验统计量汇总表

Table 6. Summary table of chi-square statistics

Variable factor		Fixed factor	DOF	$\chi _{0.05}^2 $(DOF)	$\chi _{n}^2 $
A	B	Fixed factor	DOF	$\chi _{0.05}^2 $(DOF)	$\chi _{n}^2 $
T	σ₃	N=0	6	12.592	6.15
		N=25			5.22
		N=50			2.96
N	T	σ₃=25 kPa	6	12.592	0.32
		σ₃=50 kPa			0.46
		σ₃=100 kPa			1.64
σ₃	N	T=20.0℃	4	9.488	0.73
		T=−5.0℃			0.32
		T=−10.0℃			0.35
		T=−15.0℃			0.83
Note: DOF—Degree of freedom.

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表 7 橡胶-砂-聚氨酯复合材料破坏强度极差分析(单位：kPa)

Table 7. Range analysis of failure strength of rubber-sand-polyurethane composites (Unit: kPa)

Impact factor	T/℃	σ₃/kPa	N/times
K₁	5916	10596	11236
K₂	7723	10852	11020
K₃	9031	11814	11006
K₄	10592	—	—
k₁	657	883	936
k₂	858	904	918
k₃	1003	985	917
k₄	1177	—	—
R_j	520	102	19
Notes: K_i is the sum of the corresponding calculation results when the influencing factor is i; k_i=K/s, s is the number of occurrences of each level in any column; R_j=max{k₁, k₂, k₃}-min{k₁, k₂, k₃}.

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表 8 橡胶-砂-聚氨酯复合材料本构模型的拟合参数α和β

Table 8. Fitting parameters α and β of the constitutive model of rubber-sand-polyurethane composites

N/times	σ₃/kPa	T/℃	α	β	R²
0	50	20.0	2136.79	0.76	0.9992
		−5.0	2798.09	0.73	0.9971
		−10.0	3615.17	0.78	0.9979
		−15.0	4214.97	0.78	0.9994
	100	20.0	2427.85	0.72	0.9983
		−5.0	3031.68	0.75	0.9983
		−10.0	3959.97	0.80	0.9991
		−15.0	4545.01	0.78	0.9953
25	25	20.0	1951.92	0.72	0.9991
		−5.0	2617.91	0.71	0.9992
		−10.0	2917.70	0.69	0.9990
		−15.0	3788.79	0.77	0.9985
	100	20.0	2699.34	0.79	0.9972
		−5.0	3025.88	0.76	0.9988
		−10.0	3919.82	0.81	0.9994
		−15.0	4490.65	0.80	0.9966
50	25	20.0	2707.83	0.92	0.9994
		−5.0	2879.89	0.75	0.9990
		−10.0	3434.36	0.78	0.9973
		−15.0	3885.88	0.77	0.9992
	50	20.0	2136.79	0.76	0.9992
		−5.0	2729.17	0.72	0.9983
		−10.0	3255.56	0.75	0.9977
		−15.0	4134.18	0.79	0.9994

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表 9 橡胶-砂-聚氨酯复合材料试验与计算结果对比

Table 9. Comparison of test and calculation results of rubber-sand-polyurethane composites

N/times	σ₃/kPa	T/℃	Failure strength/kPa		Error/%
N/times	σ₃/kPa	T/℃	Test value	Calculated value	Error/%
0	25	20.0	620	575	−7.3
		−5.0	846	915	8.2
		−10.0	967	983	1.7
		−15.0	1113	1051	−5.6
25	50	20.0	618	629	1.8
		−5.0	832	914	9.9
		−10.0	982	1047	6.7
		−15.0	1157	1116	−3.6
50	100	20.0	705	757	7.4
		−5.0	883	962	8.9
		−10.0	1042	1165	11.8
		−15.0	1251	1234	−1.4

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