循环荷载作用下软土地基公路InSAR时序形变估计方法研究

郑冠峰; 邢学敏; 许文东; 王亮

doi:10.12000/JR25012

循环荷载作用下软土地基公路InSAR时序形变估计方法研究

DOI: 10.12000/JR25012 CSTR: 32380.14.JR25012

1.
长沙理工大学交通学院长沙 410014
2.
长沙理工大学航空工程学院长沙 410014

基金项目: 国家自然科学基金(42074033)，中国水利水电第八工程局有限公司科研项目(2023060)，湖南省自然资源厅科技计划项目 (20230118CH)，湖南省交通运输厅科技进步与创新计划项目(202211)，长沙市杰出创新青年培养计划项目(kq2209011)

详细信息

作者简介:
郑冠峰，博士生，主要研究方向为合成孔径雷达干涉测量在公路变形监测中的应用、不良土质路基沉降监测、水电站库岸区公路滑坡灾害监测预警、InSAR时序建模、非线性参数估计等

邢学敏，博士，教授，博士生导师，主要研究方向为雷达干涉测量学在地表变形监测中的应用、利用时间序列InSAR技术监测公路、矿区变形

许文东，硕士，主要研究方向为地基雷达地地表形变监测

王　亮，硕士生，主要研究方向为公路时序InSAR建模与形变预计

通讯作者:
邢学敏 xuemin.xing@csust.edu.cn

责任主编：朱建军 Corresponding Editor: ZHU Jianjun
中图分类号: TN95
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出版历程
- 收稿日期: 2025-01-13
- 修回日期: 2025-06-26

Estimation of InSAR Time-series Deformation for Soft-soil Highways Considering Cyclic Loading

1.
School of School of Transportation, Changsha University of Science and Technology, Changsha 410014, China
2.
School of Aeronautic Engineering, Changsha University of Science and Technology, Changsha 410014, China

Funds: The National Natural Science Foundation of China (42074033), Research Foundation of the Department of Sinohydro Engineering Bureau 8 Company (2023060), Research Foundation of the Department of Natural Resources of Hunan Province (20230118CH), Research Foundation of the Department of Traffic Transportation of Hunan Province (202211), Changsha Innovation Talent Promotion Plan Project for Distinguished Young Scholar (kq2209011)

More Information

Corresponding author: XING Xuemin, xuemin.xing@csust.edu.cn

摘要

摘要: 车辆长期循环荷载是造成公路工后沉降不可忽视的因素。目前，用于软土公路形变监测的合成孔径雷达干涉测量(InSAR)形变模型往往忽略了循环荷载的贡献，多为一种或几种纯经验函数组合而成，物理意义不够明确。该文提出一种顾及循环荷载的软土地基公路时序形变估计方法(IRTM)，这一方法针对InSAR形变建模和参数估计算法分别进行改进。在形变建模环节，以描述软土形变蠕变特性的Maxwell流变模型为基础模型，引用附加动应力模型以描述循环荷载导致的塑性变形时序演化规律，并联合热膨胀模型表征路基和桥梁受温度影响的热膨胀效应分量，以更合理地解译形变估计结果；在参数估计环节，提出一种基于遗传算法(GA)与列文伯格马尔夸特算法(LM)串行的参数估计方法，对GA获取的初值进行二次优化，提升求解效率和精度。分别开展了模拟和真实数据实验对所提方法进行验证。模拟实验发现，在施加±0.5 rad 噪声时，模型参数估计值的相对误差均低于6%。真实数据选取了北京至平谷高速公路作为研究区域，获取了其在2012年1月22日到2014年7月1日期间的时序形变。实验发现，形变累积达–140 mm，软土地基段形变贡献以流变分量为主，约占 76%；而位于道路交叉段则以循环荷载分量为主，约占 81%。分别从建模精度、有限元分析和交叉验证3方面验证本文结果的精度。建模精度利用单一Maxwell模型和传统线性模型生成结果对比，分别提高了44.4%和49.6%；利用有限元分析(FEA)方法验证真实实验获取的形变精度，得出该文方法获取的变形曲线与FEA在不同轴载下产生的变形一致，最大标准偏差仅为1.8 mm；与已有研究的交叉验证结果表明，该文所得形变速率外部精度为±1.4mm/yr，进一步证实了该文方法用于循环荷载作用下的公路工后形变估计和解译是可靠的，可为公路稳定性控制提供参考。
- 合成孔径雷达干涉测量 /
- 循环荷载 /
- 形变 /
- 软土 /
- 公路
Abstract: Long-term cyclic loading by vehicles is a non-negligible contributor to post-work settlement of highways. Current Interferometric Synthetic Aperture Radar (InSAR) deformation models used for monitoring the deformation of soft-soil highways generally neglect the contribution of cyclic loading. The InSAR time-series deformation models used for monitoring highway deformation are typically combinations of one or several purely empirical functions, which lack clarity in physical significance and overlook the impact of cyclic loading on settlement. Herein, a method for estimating the deformation of soft-ground highways that accounts for cyclic loading is proposed. The method improves InSAR deformation modeling and the parameter estimation algorithms. In the deformation modeling, the Maxwell rheological model, which describes the deformation and creep characteristics of soft soil, serves as the base model for InSAR modeling. An additional dynamic stress model was incorporated to describe the plastic deformation caused by cyclic loading, which was combined with a thermal expansion model to characterize the thermal expansion component of the road base and bridge affected by temperature. This combination provided a more reasonable interpretation of the deformation estimation data. For parameter estimation, a method based on a Genetic Algorithm (GA) and a parameter estimation algorithm was proposed. In particular, a parameter estimation method combining GA and the Levenberg-Marquardt (LM) algorithm was developed, where the initial value obtained by GA was further optimized by LM to enhance the solving efficiency and accuracy. The proposed method was validated through simulation and experiments employing real data. The simulation revealed that the relative errors of the model parameter estimates were all below 6% when ±0.5 rad noise was applied. Real data from the selected study area, i.e., the Beijing-Pinggu Expressway, were utilized, and the time-series deformations from 22 January 2012 to 1 July 2014 were obtained. The results show that the cumulative deformation reached −140 mm, where the rheological component of the soft-ground section was the dominant contributor to deformation, accounting for approximately 76%, whereas the cyclic through-load component was dominant at road intersections, accounting for 81%. Compared with single Maxwell and traditional linear models, the modeling accuracy of the developed method was improved by 44.4% and 49.6%, respectively. Finite Element Analysis (FEA) was used to verify the deformation accuracy obtained from real experiments. The deformation curves generated using the developed method were consistent with those produced by FEA under different axle loads, with a maximum standard deviation of only 1.8 mm. Cross-validation against existing studies showed that the external accuracy of the deformation rate obtained in this study was ±1.4 mm/yr, further confirming the reliability of the developed method for estimating and interpreting the post-work deformation of highways under cyclic loading. This method can provide a reference for controlling the stability of highways.
- Interferometric Synthetic Aperture Radar(InSAR) /
- Cyclic loading /
- Deformation /
- Soft soil /
- Highways

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图 1 循环荷载作用下的软土路基变形机制

Figure 1. Deformation mechanism of soft soil roadbed under cyclic loading

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图 2 顾及循环荷载的软土地基公路时序InSAR估计方法流程

Figure 2. General flow of time-series InSAR estimation for soft-soil highways considering cyclic loading

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图 3 模拟参数真实值分布

Figure 3. Simulated real values of each parameter

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图 4 时序形变真实值

Figure 4. Simulated real values of time series deformation

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图 5 参数估计值与真实值对比

Figure 5. Comparison between estimated parameter with true values

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图 6 IRTM模型的参数估计结果

Figure 6. Parameter estimation results of the IRTM model

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图 7 3座立交桥的光学影像

Figure 7. Optical images of the three overpasses

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图 8 总时间序列沉降(参考图像日期：20120122)

Figure 8. Time-series deformation over the highway (reference image date: 20120122)

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图 9 形变速率与重点形变区域放大图

Figure 9. Magnification of deformation rate and enlarged images of subsiding areas

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图 10 3种模型的残余形变RMS对比

Figure 10. Comparison of residual deformation RMS for three models

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图 11 IRTM与QPS-InSAR的交叉验证

Figure 11. Cross-validation between IRTM and QPS-InSAR

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图 12 不同载荷水平下有限元法和IRTM计算变形的比较

Figure 12. Comparison between the deformations estimated by FEA and IRTM under different levels of loadings

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图 13 特征点上的分量对比

Figure 13. Comparison of different deformation components at each feature point

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图 14 2014年7月25日特征点处光学影像

Figure 14. Feature points with Google image as background on July 25, 2014

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图 15 IRTM模型的应变-时间曲线

Figure 15. Strain-Time curves generated with IRTM

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图 16 动应力比参数敏感性分析结果(参考日期：20120122)

Figure 16. Parameter sensitivity analysis results of dynamic stress ratio at different dates (reference image date: 20120122)

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表 1 不同噪声水平下的平均相对误差 (%)

Table 1. Mean relative error at different noise levels (%)

噪声等级	z	$\eta $	$\beta $	Th
-	<0.01	0.70	2.70	<0.01
±0.1 rad	<0.01	0.74	3.07	<0.01
±0.2 rad	<0.01	0.81	3.53	<0.01
±0.3 rad	0.02	0.91	4.17	<0.01
±0.4 rad	0.03	1.02	4.81	0.01
±0.5 rad	0.04	1.15	5.77	0.02

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表 2 不同初始条件下的收敛性

Table 2. Convergence under different initial conditions

条件	与模拟值相同	模拟值的2倍	模拟值的3倍
GA迭代次数	50	50	50
平均迭代次数	8.6	10.2	16.7
最大迭代次数	12	17	26
平均SSR	21.19	25.21	46.03
最大SSR	25.80	47.32	80.92

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表 3 重要性程度判定标准

Table 3. Criteria for determining significance

参数重要性	Sobal指数取值
非常重要	$ 0.8 < {S}_{\alpha } < {S}_{\alpha }^{{\mathrm{tol}}}\le 1 $
重要	$ 0.5 < {S}_{\alpha } < {S}_{\alpha }^{{\mathrm{tol}}}\le 0.8 $
不重要	$ 0.3 < {S}_{\alpha } < {S}_{\alpha }^{{\mathrm{tol}}}\le 0.5 $
不相关	$ 0 < {S}_{\alpha } < {S}_{\alpha }^{{\mathrm{tol}}}\le 0.3 $

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表 4 GA, GARN, GALM算法性能对比

Table 4. Performance comparison of GA, GARN, and GALM algorithms

参数	GA	GARN	GALM
迭代次数(次)	300	50+250	50+250
耗时(s)	1463	651	286
残余相位STD(rad)	1.57	0.92	0.87

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