级配粗粒土机场道基累积塑性应变特征及预估模型

李冬雪; 孟晓慧; 钟杰; 李聪

doi:10.19818/j.cnki.1671-1637.2026.241

级配粗粒土机场道基累积塑性应变特征及预估模型

doi: 10.19818/j.cnki.1671-1637.2026.241

李冬雪^1, ,,
孟晓慧²,
钟杰²,
李聪³

1.
重庆交通大学交通运输学院, 重庆 400074
2.
重庆交通大学土木工程学院, 重庆 400074
3.
桂林电子科技大学建筑与交通工程学院, 广西桂林 541004

基金项目:

国家自然科学基金项目 51908095

重庆市自然科学基金项目 CSTB2023NSCQ-MSX1044

详细信息

通讯作者:
李冬雪(1983-)，女，黑龙江哈尔滨人，副教授，工学博士，博士后，E-mail: lidongxue@cqjtu.edu.cn

中图分类号: U416.1
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- 文章访问数: 33
- HTML全文浏览量: 17
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2026-01-07
- 录用日期: 2026-03-20
- 修回日期: 2026-03-13
- 刊出日期: 2026-08-28

Cumulative plastic strain characteristics and prediction models og raded coarse-grained soil airport subgrade

1.
College of Traffic & Transportation, Chongqing Jiaotong University, Chongqing 400074, China
2.
School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China
3.
School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China

Funds:

National Natural Science Foundation of China 51908095

Natural Science Foundation of Chongqing CSTB2023NSCQ-MSX1044

More Information

Corresponding author: LI Dong-xue, associate professor, PhD, E-mail: lidongxue@cqjtu.edu.cn

Article Text (Baidu Translation)

摘要

摘要: 为揭示颗粒级配、应力状态与湿度条件耦合作用下粗粒土道基累积塑性变形演化规律，解决机场道基长期循环荷载下不均匀沉降问题，采用分形维数单指标替代传统双指标表征粗粒土级配，基于Talbot分形级配方程确定粗粒土最优级配区间，并选取4组典型级配开展重复加载三轴试验，系统研究了级配、循环动荷载及干湿循环作用对压实粗粒土累积塑性应变的影响规律；通过对比典型累积变形预估模型，筛选出适用于粗粒土道基填料的基础模型，分析模型拟合参数与分形维数、循环应力比、湿度状态的统计关联，提出可同时考虑三者耦合影响的修正预估模型并验证精度。研究结果表明：循环应力比对累积塑性应变发展具有显著控制作用，将偏应力与围压的比值控制在较低水平(不大于1.23)可有效抑制累积塑性变形发展；随分形维数增大，累积塑性应变呈先减小后增大的趋势，当粗粒土达到最大干密度(分形维数为2.49)时，其累积塑性应变最小；干湿循环作用显著加剧了粗粒土的塑性变形，当循环次数大于7时，土体变形由塑性安定阶段过渡至塑性蠕变阶段；基于Monismith模型构建的修正预估模型，对不同循环应力比、分形维数及湿度条件下粗粒土道基的累积塑性应变具有良好预测效果。研究成果可为机场道基变形控制、级配优化、长期服役安全评价提供理论依据与技术支撑。
- 机场道基 /
- 预估模型 /
- 动三轴试验 /
- 累积塑性应变 /
- 分形维数
Abstract: To reveal the evolution law of cumulative plastic deformation of coarse-grained soil subgrade under the coupling effect of particle gradation, stress state, and moisture condition, and to solve the differential settlement problem of airport subgrade under long-term cyclic loading, fractal dimension was adopted as a single index to replace the traditional dual indices for characterizing the gradation of coarse-grained soil. The optimal gradation interval of coarse-grained soil was determined based on the Talbot fractal gradation equation, and four groups of typical gradations were selected to carry out repeated loading triaxial tests. The influences of gradation, cyclic dynamic loading, and dry-wet cycles on the cumulative plastic strain of compacted coarse-grained soil were systematically investigated. By comparing typical cumulative deformation prediction models, a basic model suitable for coarse-grained soil subgrade fillers was screened out, the statistical correlations between model fitting parameters and fractal dimension, cyclic stress ratio, and moisture state were analyzed, and a modified prediction model simultaneously considering the coupled effects of the three factors was proposed and its accuracy was verified. The results show that cyclic stress ratio has a significant control effect on the development of cumulative plastic strain, and controlling the ratio of deviator stress to confining pressure at a low level (less than 1.23) can effectively inhibit the development of cumulative plastic deformation. With the increase of fractal dimension, the cumulative plastic strain decreases first and then increases. When the coarse-grained soil reaches the maximum dry density (fractal dimension is 2.49), its cumulative plastic strain is the smallest. Dry-wet cycles significantly aggravate the plastic deformation of coarse-grained soil, and the soil deformation transits from the plastic shakedown stage to the plastic creep stage when the number of cycles is greater than 7. The modified prediction model established based on the Monismith model has a good prediction effect on the cumulative plastic strain of coarse-grained soil subgrade under different cyclic stress ratios, fractal dimensions, and humidity conditions. The research results can provide a theoretical basis and technical support for deformation control, gradation optimization, and long-term service safety evaluation of airport subgrade.
- airport subgrade /
- prediction model /
- dynamic triaxial test /
- cumulative plastic strain /
- fractal dimension

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图 1 击实试验结果

Figure 1. Compaction test results

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图 2 不同含水率下ρ_{d, max}与D关系曲线

Figure 2. Relationship curves between ρ_{d, max} and D

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图 3 原始土样及4组试验土样的级配曲线

Figure 3. Gradation curves of original soil sample anf our test soil samples

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图 4 动三轴试验系统

Figure 4. Dynamic triaxial test system

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图 5 不同R_c时ε_p与N关系曲线

Figure 5. ε_p-N curves at different R_c values

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图 6 不同N时ε_p与R_c关系曲线

Figure 6. ε_p-R_c curves at different N values

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图 7 不同D时ε_p与N关系曲线

Figure 7. ε_p-N curves at different D values

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图 8 不同N时ε_p与D关系曲线

Figure 8. ε_p-D curves at different N values

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图 9 不同C_w时ε_p与N关系曲线

Figure 9. ε_p-N curves at different C_w values

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图 10 不同N时ε_p与C_w关系曲线

Figure 10. ε_p-C_w curves at different N values

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图 11 ε_p实测值与不同模型预测值的对比(试样3)

Figure 11. Comparison of ε_p between measured values and predicted values of different models (sample 3)

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图 12 不同累积塑性应变预测模型的比较

Figure 12. Comparison of different cumulative plastis train prediction models

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图 13 Monismith模型拟合参数与试验变量之间的相关性分析

Figure 13. Correlation analysis between fitting parameters and test variables of Monismith model

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图 14 不同工况下ε_p实测值与预测值的对比

Figure 14. Comparison of measured and predicted ε_p under different conditions

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表 1 加载试验方案

Table 1. Loading test scheme

试样编号	分形维数	围压/kPa	循环应力比	初始含水率/%	干湿循环次数
1	2.36	28	1.23	7.00	1
2	2.43			7.60
3	2.49			7.80
4	2.55			8.20
5	2.49		0.50	7.80	1
6			0.86
7			1.23
8			1.78
9			1.23		0
10					1
11					3
12					7

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表 2 常用的累积塑性应变预测模型

Table 2. Commonly used predict models for cumulative plastic strain

编号	模型提出者	模型公式
1	Monismith等^[33]	ε_p=aN^b
2	Barksdale^[34]	ε_p=a[1+blg(N)]
3	Paute等^[35]	ε_p=a[1-(N/100)^-b]
注：a、b为拟合参数。

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表 3 预测模型参数应用范围

Table 3. Application range of prediction model parameters

模型参数	N/次	R_c	D	C_w/次
应用范围	1~1.0×10⁴	0.50~1.78	2.36~2.55	0~7

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参考文献(35)

[1]	凌道盛, 张凡, 赵云, 等. 飞机荷载作用下非均匀道基动力响应分析[J]. 土木工程学报, 2017, 50(2): 97-109. LING Dao-sheng, ZHANG Fan, ZHAO Yun, et al. Dyna-mic response analysis of inhomogeneous subgrade subjected to moving aircraft loads[J]. China Civil Engineering Journal, 2017, 50(2): 97-109.
[2]	赵云. 飞机荷载作用下高填方机场道基动力响应及累积沉降研究[D]. 杭州: 浙江大学, 2018: 85-97. ZHAO Yun. Dynamic responses and accumulative settlement of subgrade under aircraft load in high-filled airport[D]. Hangzhou: Zhejiang University, 2018: 85-97.
[3]	刘兆鹏, 徐西永, 寇璟媛, 等. 不同压实条件下富水粉土道基变形规律的数值研究[J]. 水利水电技术(中英文), 2024, 55(增1): 397-405. LIU Zhao-peng, XU Xi-yong, KOU Jing-yuan, et al. Numerical study on the deformation law of water-rich silt road base under different compaction conditions[J]. Water Resources and Hydropower Engineering, 2024, 55(S1): 397-405.
[4]	凌建明, 王增逸, 刘诗福, 等. 飞机滑跑激振和着陆冲击的动载预估模型[J]. 交通运输工程学报, 2026, 26(8): 1-19. LING Jian-ming, WANG Zeng-yi, LIU Shi-fu, et al. Dyna-mic load predictive model for aircraft taxiing excitation and landing impact[J]. Journal of Traffic and Transportation Engineering, 2026, 26(8): 1-19.
[5]	臧宏阳. 基于路基不均匀特性的沥青路面动力响应研究[D]. 哈尔滨: 哈尔滨工业大学, 2016: 69-87. ZANG Hong-yang. Dynamic response of asphalt pavement supported by uneven subgrade[D]. Harbin: Harbin Institute of Technology, 2016: 69-87.
[6]	刘彦君. 飞机荷载下川西高高原机场道基土变形特性研究[D]. 广汉: 中国民用航空飞行学院, 2025: 62-74. LIU Yan-jun. Investigation on deformation characteristics of high-plateau airport subgrade soil in western Sichuan under aircraft loading[D]. Guanghan: Civil Aviation Flight Univer-sity of China, 2025: 62-74.
[7]	高启聚, 郭忠印, 丛林, 等. 重复荷载作用下粘性路基土的永久变形预估[J]. 同济大学学报(自然科学版), 2008, 36(11): 1521-1525. GAO Qi-ju, GUO Zhong-yin, CONG Lin, et al. Evaluation of permanent deformation of clayed subgrade soils under cyclic loading[J]. Journal of Tongji University (Natural Science), 2008, 36(11): 1521-1525.
[8]	易文妮, 刘津丞, 余虔, 等. 循环荷载作用下非饱和盐化粉土动力特性[J]. 哈尔滨工业大学学报, 2023, 55(6): 125-133. YI Wen-ni, LIU Jin-cheng, YU Qian, et al. Dynamic charac-teristics of unsaturated salinized silt under cyclic loading[J]. Journal of Harbin Institute of Technology, 2023, 55(6): 125-133.
[9]	任华平, 刘希重, 宣明敏, 等. 循环荷载作用下击实粉土累积塑性变形研究[J]. 岩土力学, 2021, 42(4): 1045-1055. REN Hua-ping, LIU Xi-zhong, XUAN Ming-min, et al. Study of cumulative plastic deformation of compacted silt under cyclic loading[J]. Rock and Soil Mechanics, 2021, 42(4): 1045-1055.
[10]	黄文杰. 干湿循环及动载耦合下花岗岩残积土动力变形特性研究[D]. 长沙: 中南大学, 2024: 50-60. HUANG Wen-jie. Study on dynamic deformation charac-teristics of granite residual soil under the coupling of dry-wet cycle and dynamic load[D]. Changsha: Central South Uni-versity, 2024: 50-60.
[11]	罗其奇, 张升, 叶新宇, 等. 飞机荷载作用下湿化粉土道基变形特性研究[J]. 中南大学学报(自然科学版), 2021, 52(7): 2188-2199. LUO Qi-qi, ZHANG Sheng, YE Xin-yu, et al. Investigation on deformation characteristics of wetting silt subgrade under aircraft loading[J]. Journal of Central South University(Science and Technology), 2021, 52(7): 2188-2199.
[12]	DU Y F, CUI X Z, JIN Q, et al. Test equipment and pre-diction model for the service performance of subgrades under long-term traffic loads: A review[J]. Transportation Geote-chnics, 2026, 56: 101812. doi: 10.1016/j.trgeo.2025.101812
[13]	ZHANG C L, JIANG G L. Full-scale model testing of the dynamic response of lime-stabilized weathered red mudstone subgrade under railway excitation[J]. Soil Dynamics and Earthquake Engineering, 2020, 130: 105999. doi: 10.1016/j.soildyn.2019.105999
[14]	张莎莎, 曹俱源, 张毅, 等. 道面覆盖作用下砾质硫酸盐渍土道基水盐迁移及侵蚀特征[J]. 交通运输工程学报, 2025, 25(5): 131-144. doi: 10.19818/j.cnki.1671-1637.2025.05.010 ZHANG Sha-sha, CAO Ju-yuan, ZHANG Yi, et al. Water and salt migration and erosion characteristics of gravel sulfate salty soil subgrade under effect of pavement covering[J]. Journal of Traffic and Transportation Engineering, 2025, 25(5): 131-144. doi: 10.19818/j.cnki.1671-1637.2025.05.010
[15]	章定文, 刘文俊, 侯爵, 等. 循环湿化条件下粉土联合石灰改良弱膨胀土的动力累积变形特性[J]. 交通运输工程学报, 2025, 25(4): 71-79. doi: 10.19818/j.cnki.1671-1637.2025.04.005 ZHANG Ding-wen, LIU Wen-jun, HOU Jue, et al. Dyna-mic cumulative deformation characteristics of weak expansive soil improved by silt and lime under cyclic wetting[J]. Journal of Traffic and Transportation Engineering, 2025, 25(4): 71-79. doi: 10.19818/j.cnki.1671-1637.2025.04.005
[16]	BIAN X C, JIANG H G, CHENG C, et al. Full-scale model testing on a ballastless high-speed railway under simulated train moving loads[J]. Soil Dynamics and Earthquake Engi-neering, 2014, 66: 368-384. doi: 10.1016/j.soildyn.2014.08.003
[17]	张军辉, 张安顺, 彭俊辉, 等. 循环荷载下路基黏土永久变形特性及力学模型[J]. 中国公路学报, 2024, 37(6): 34-45. ZHANG Jun-hui, ZHANG An-shun, PENG Jun-hui, et al. Characterization and mechanics modeling of permanent defor-mation of subgrade clay under cyclic loading[J]. China Journal of Highway and Transport, 2024, 37(6): 34-45.
[18]	郑可扬, 肖源杰, 王萌, 等. 循环移动轮载下粗粒土路基填料永久变形特性及安定分析[J]. 岩石力学与工程学报, 2020, 39(9): 1930-1943. ZHENG Ke-yang, XIAO Yuan-jie, WANG Meng, et al. Per-manent deformation characteristics and shakedown analysis of coarse-grained embankment materials under moving wheel loads[J]. Chinese Journal of Rock Mechanics and Engi-neering, 2020, 39(9): 1930-1943.
[19]	孔亮, 季亮亮, 曹杰峰. 应力路径和颗粒级配对砂土变形影响的细观机制[J]. 岩石力学与工程学报, 2013, 32(11): 2334-2341. KONG Liang, JI Liang-liang, CAO Jie-feng. Deformation mesomechanism of sands with different grain gradations under different stress paths[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(11): 2334-2341.
[20]	凌华, 傅华, 韩华强. 粗粒土强度和变形的级配影响试验研究[J]. 岩土工程学报, 2017, 39(增1): 12-16. LING Hua, FU Hua, HAN Hua-qiang. Experimental study on effects of gradation on strength and deformation of coarse-grained soil[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(S1): 12-16.
[21]	肖源杰, 李文奇, 于群丁, 等. 透水性级配碎石基层填料永久变形特性及预估模型[J]. 中国公路学报, 2022, 35(12): 12-23. XIAO Yuan-jie, LI Wen-qi, YU Qun-ding, et al. Permanent deformation behavior and prediction models of unbound permeable aggregate base materials[J]. China Journal of Highway and Transport, 2022, 35(12): 12-23.
[22]	SUKKARAK R, PRAMTHAWEE P, JONGPRADIST P, et al. Deformation analysis of high CFRD considering the scaling effects[J]. Geomechanics and Engineering, 2018, 14(3): 211-224.
[23]	MAKEDON T, TREMOPOULOU E, DIMOPOULOS G. The influence of gradation on the in situ compaction of geo-materials in road construction[J]. Bulletin of Engineering Geology and the Environment, 2009, 68(1): 81-87. doi: 10.1007/s10064-008-0176-8
[24]	FULLER W B, THOMPSON S E. The laws of proportion-ing concrete[J]. Transactions of the American Society of Civil Engineers, 1907, 59(2): 67-143. doi: 10.1061/TACEAT.0001979
[25]	SWAMEE P K, OJHA C S P. Bed-load and suspended-load transport of nonuniform sediments[J]. Journal of Hydraulic Engineering, 1991, 117(6): 774-787. doi: 10.1061/(ASCE)0733-9429(1991)117:6(774)
[26]	朱俊高, 郭万里, 王元龙, 等. 连续级配土的级配方程及其适用性研究[J]. 岩土工程学报, 2015, 37(10): 1931-1936. ZHU Jun-gao, GUO Wan-li, WANG Yuan-long, et al. Equa-tion for soil gradation curve and its applicability[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(10): 1931-1936.
[27]	吴二鲁, 朱俊高, 王龙, 等. 粗粒料的单参数级配方程及其适用性研究[J]. 岩土力学, 2020, 41(3): 831-836. WU Er-lu, ZHU Jun-gao, WANG Long, et al. Single-para-meter gradation equation for coarse-grained soil and its app-licability[J]. Rock and Soil Mechanics, 2020, 41(3): 831-836.
[28]	TALBOT A N, RICHART F E. The strength of concrete: Its relation to the cement aggregates and water[J]. Bulletin, 1923, 137: 1-118.
[29]	蔡迎春, 郑元勋, 刘忠玉, 等. 飞机荷载作用下粉砂土路基动力响应研究[J]. 岩土力学, 2012, 33(9): 2863-2868. CAI Ying-chun, ZHENG Yuan-xun, LIU Zhong-yu, et al. Study of dynamic response of silty sand subgrade loaded by airplane[J]. Rock and Soil Mechanics, 2012, 33(9): 2863-2868.
[30]	GUO L, WANG J, CAI Y Q, et al. Undrained deformation behavior of saturated soft clay under long-term cyclic loading[J]. Soil Dynamics and Earthquake Engineering, 2013, 50: 28-37. doi: 10.1016/j.soildyn.2013.01.029
[31]	CAI Y Q, WU T Y, GUO L, et al. Stiffness degradation and plastic strain accumulation of clay under cyclic load with principal stress rotation and deviatoric stress variation[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2018, 144(5): 04018021. doi: 10.1061/(ASCE)GT.1943-5606.0001854
[32]	WERKMEISTER S, DAWSON A R, WELLNER F. Perma-nent deformation behavior of granular materials and the sha-kedown concept[J]. Transportation Research Record: Journal of the Transportation Research Board, 2001(1757): 75-81.
[33]	MONISMITH C L, OGAWA N, FREEME C R. Permanent deformation characteristics of subgrade soils due to repeated loading[J]. Transportation Research Record, 1975, 537: 1-17.
[34]	BARKSDALE R D. Compressive stress pulse times in flexi-ble pavements for use in dynamic testing[J]. Highway Research Record, 1971(34): 32-44.
[35]	PAUTE J L, HORNYCH P, BENABEN J P. Repeated load triaxial testing of granular materials in the French network of laboratories des ponts et chaussees flexible pavement[C]//CORREIA A G. Flexible Pavements: Proceedings of the European Symposium Euroflex. Rotterdam: Balkema, 1996: 53-64.