考虑颗粒破碎的砂土UH模型及其参数反演

熊海斌; 余虔; 张升; 童晨曦; 兰鹏; 刘光庆

doi:10.11779/CJGE20211299

考虑颗粒破碎的砂土UH模型及其参数反演 English Version

熊海斌^1,,
余虔²,
张升¹,
童晨曦^1, ,,
兰鹏¹,
刘光庆^{1, 3}

1.
中南大学土木工程学院, 湖南长沙 410075
2.
民航机场规划设计研究总院有限公司, 北京 101312
3.
福建兆翔机场建设有限公司, 福建厦门 361000

基金项目:

国家自然科学基金项目 52008402

湖南省自然科学基金项目 2021JJ40758

湖湘高层次人才聚集工程项目 2019RS1008

详细信息

作者简介:
熊海斌(1998—)，男，硕士研究生，主要从事智能岩土工程的研究。E-mail: xiong_haibin@csu.edu.cn

通讯作者:
童晨曦, E-mail: cxtong@csu.edu.cn

中图分类号: TU441
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出版历程
- 收稿日期: 2021-12-06
- 网络出版日期: 2023-02-03
- 发布日期: 2021-12-06
- 刊出日期: 2022-12-31

UH model and parameter inversion for crushable sands

1.
School of Civil Engineering, Central South University, Changsha 410075, China
2.
China Airport Construction Group Corporation, Beijing 101312, China
3.
Fujian Panport Airport Construction Co., Ltd., Xiamen 361000, China

摘要

摘要: 颗粒破碎对粒状土临界状态的影响十分显著，研究认为在e-lnp空间内，粒状土的临界状态线会随着破碎的进行向下漂移，而捕捉颗粒破碎量与临界状态线漂移量之间的一一映射关系是一项巨大的挑战。通过引入颗粒破碎参数e_B对砂土UH模型进行了修正，并将其嵌入实数编码免疫遗传算法（RIGA）中，构建了RIGA-MUH模型，提出了可获取不同破碎程度下临界状态线的新方法。为得到更加准确的临界状态参数，模型通过调整粒状土临界状态下在误差函数中的权重比进行优化改进，并通过Toyoura砂和Cambria砂的常规排水三轴压缩试验结果，验证模型的稳定性、合理性和准确性。结果表明，该模型可以得到某一颗粒破碎量下精度较高的临界状态线，为提出考虑颗粒破碎的本构方程提供一种新方法。
- 颗粒破碎 /
- 临界状态 /
- UH模型 /
- 实数编码 /
- 免疫遗传算法 /
- 参数反演
Abstract: The effect of particle breakage on the critical state of granular soils is of great significance. The existing studies have shown that the critical state line (CSL) of granular soils in the e-lnp space shifts downward as a result of particle breakage. However, it remains a big challenge for capturing the degree of particle breakage and the movement of CSL. In this study, the UH model for sands is modified by introducing the particle breakage parameter e_B and embedded in the real number encoding immune genetic algorithm (RIGA) to establish the RIGA-MUH model, which proposes a new method that can obtain the CSLs for the sands with varying particle-size distributions. The model is optimized and improved to obtain more accurate critical state parameters by adjusting the weight ratio in the error function under the critical state of granular soils. The stability, rationality and accuracy of the model are verified through the results of conventional drainage triaxial compression tests on the Toyoura sand and Cambria sand. The results show that the proposed model can be used to obtain the CSLs with high accuracy under a certain amount of particle breakage, which provides new insight into the constitutive modeling of crushable sands.
- particle breakage /
- critical state /
- UH model /
- real number encoding /
- immune genetic algorithm /
- parameter inversion

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图 1 CSL随PSD漂移及颗粒破碎参数示意图

Figure 1. Schematic diagram of shifting CSL with varying PSDs and particle breakage parameter

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图 2 GA流程图

Figure 2. Flow chart of GA

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图 3 RIGA-MUH模型流程图

Figure 3. Flow chart of RIGA-MUH model

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图 4 Toyoura砂的三轴试验结果和预测结果对比

Figure 4. Comparison between triaxial test results and predicted results for Toyoura sand

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图 5 不同初始孔隙比下χ-w_c曲线

Figure 5. χ-w_c curves under different initial void ratios

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图 6 第一阶段稳定解与最终解预测结果对比

Figure 6. Comparison of predicted results between first-stage stable solution and final solution

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图 7 RGA-MUH模型和RIGA-MUH模型稳定性分析对比

Figure 7. Comparison of stability analysis between RGA-MUH model and RIGA-MUH model

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图 8 Toyoura砂试验结果与模型预测结果

Figure 8. Test results and model predictions of Toyoura sand

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图 9 B_r定义

Figure 9. Definition of B_r

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图 10 Cambria砂中高围压组试验结果与模型预测结果对比

Figure 10. Comparison between test results and model predictions for Cambria sand subjected to medium and high confining pressures

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图 11 Cambria砂高围压组试验结果与模型预测结果对比

Figure 11. Comparison between test results and model predictions for Cambria sand subjected to high confining pressure

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图 12 Cambria砂不同B_r下的CSL

Figure 12. CSLs of Cambria sands with different B_r

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图 13 Cambria砂不同颗粒破碎指标B_r下的CSL截距

Figure 13. Intercepts of CSL of Cambria sands with different particle breakage index B_r

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表 1 Toyoura砂UH模型参数

Table 1 UH model parameters of Toyoura sand

M	$\chi$	$\nu$	Z	m	$\lambda$	$\kappa$	N
1.25	0.55	0.3	0.943	1.8	0.135	0.04	1.973

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表 2 RGA-MUH模型超参数

Table 2 Hyperparameters of RGA-MUH model

参数名称	RGA参数取值
种群规模N	50
变异概率 ${p_{\text{m}}}$	0.7
选择操作后个体数M	25
最大迭代次数G	100
变异系数 ${\delta _{\text{m}}}$	0.5

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表 3 RIGA-MUH模型免疫超参数分析试验方案及结果

Table 3 Experimental protocols and results of immune hyperparameter analysis of RIGA-MUH model

试验号	激励度系数 $\alpha$	克隆次数N_c	相似度阈值 ${\delta _{\text{s}}}$	试验结果
1	1(0.3)	1(3)	1(0.1)	0.621
2	1	2(6)	2(0.2)	0.603
3	1	3(9)	3(0.3)	0.610
4	2(0.6)	1	2	0.623
5	2	2	3	0.594
6	2	3	1	0.622
7	3(0.9)	1	3	0.597
8	3	2	1	0.596
9	3	3	2	0.597

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表 4 各参数方差分析

Table 4 Analysis of variance for each parameter

方差来源	平方和	自由度	均方差	F值
激励度系数 $\alpha$	0.000494	2	0.000247	5.501
克隆次数N_c	0.000457	2	0.000229	5.100
相似度阈值δ_s	0.000284	2	0.000142	3.163
空列误差	0.0000897	2	0.0000449
总和	0.00132	8

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表 5 RIGA-MUH模型参数

Table 5 Parameters of RIGA-MUH model

M	$\nu$	Z	m	λ	κ	N
1.45	0.1	0.61	3	0.112	0.0102	1.5578

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表 6 不同围压下颗粒破碎指标B_r

Table 6 Values of B_r under different confining pressures

围压/kPa	5800	8000	11500	15000	17200
B_r	0.151	0.247	0.280	0.341	0.340

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表 7 RIGA-MUH模型和RGA-MUH模型预测结果

Table 7 Predicted results of RIGA-MUH and RGA-MUH models

参数名称		围压/MPa
参数名称		5.8	8.0	11.5	15.0	17.2
RIGA	χ	0.886	0.899	0.883	0.866	0.843
RIGA	${e_{\text{B}}}$	0.072	0.090	0.114	0.215	0.237
RGA	χ	0.827	0.883	0.926	0.883	0.816
RGA	${e_{\text{B}}}$	0.115	0.151	0.088	0.228	0.266

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