正交-等值线法在堆石料细观参数标定中的应用

王晋伟; 迟世春; 邵晓泉; 赵飞翔

doi:10.11779/CJGE202010012

正交-等值线法在堆石料细观参数标定中的应用 English Version

王晋伟^{1, 2,},
迟世春^{1, 2, ,},
邵晓泉^{1, 2},
赵飞翔^{1, 2}

1.
海岸与近海工程国家重点试验室（大连理工大学）,辽宁　大连　116024
2.
工程抗震研究所,建设工程学部水利工程学院（大连理工大学）,辽宁　大连　116024

基金项目:

国家重点研发计划项目 2016YFB0201001

详细信息

作者简介:
王晋伟(1991—),男,博士研究生,主要从事土石坝数值模拟研究。E-mail：wangjwxkl@163.com

通讯作者:
迟世春, E-mail：schchi@dlut.edu.cn

中图分类号: TU431
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出版历程
- 收稿日期: 2019-09-23
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-09-30

Application of orthogonal-contour method in calibration of microscopic parameters of rockfill materials

WANG Jin-wei^{1, 2,},
CHI Shi-chun^{1, 2, ,},
SHAO Xiao-quan^{1, 2},
ZHAO Fei-xiang^{1, 2}

1.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
2.
Institute of Earthquake Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 针对堆石料离散元模型细观参数标定过程中计算量大的现状,以堆石料室内三轴排水剪切试验为对象,采用正交试验与等值线法相结合的方法,在优化细观参数取值范围和分析宏观响应对细观参数敏感性基础上快速确定了堆石料细观参数。结果表明,多次正交试验可以较快的缩小细观参数取值范围；综合利用正交试验和等值线法的优势能快速标定堆石料离散元模型的细观参数。该方法也为其它材料离散元模型标定细观参数提供了新的手段和思路。
- 细观参数标定 /
- 正交试验 /
- 等值线 /
- 堆石料 /
- 颗粒流
Abstract: In order to solve the problem of large amount of calculation in calibration of microscopic parameters for rockfill materials in discrete element model, taking the laboratory tri-axial tests on the rockfill materials as the object, the methods of orthogonal tests and contour lines are used to determine the microscopic parameters of the rockfill materials rapidly on the basis of narrowing the scope of microscopic parameters and analyzing the sensitivity of the macroscopic behaviors of the specimens to the microscopic parameters. The results show that the multiple orthogonal tests can quickly narrow the range of microscopic parameters. The advantages of the orthogonal test and contour method can be used to calibrate the microscopic parameters in discrete element model. This method also provides reference for other materials to calibrate microscopic parameters.
- microscopic parameter calibration /
- orthogonal test /
- contour line /
- rockfill material /
- particle flow

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图 1 颗粒级配曲线

Figure 1. Grain-size distribution curves

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图 2 室内三轴试验结果^[21]

Figure 2. Results of laboratory triaxial shear tests^[21]

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图 3 制样过程示意图

Figure 3. Scheme of preparation process of specimens

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图 4 堆石料常规三轴剪切试验典型轴变-应力-体变关系^[23]

Figure 4. Stress-strain-volume relation of rockfill materials in conventional triaxial tests^[23]

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图 5 宏观指标的极差分析结果

Figure 5. Range analysis results of macroscopic indexes

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图 6 割线模量 $E_{50}$ （黑色线,100 MPa）和最大压缩量 $ε_{vmax}$ （灰色线,%）等值线图

Figure 6. Contours of secant modulus E₅₀ (black lines, 100 MPa) and maximum compression $ε_{vmax}$ (gray lines, %)

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图 7 峰值强度 $S_{P}$ （黑色线,MPa）和剪胀角ψ（灰色线,（°））等值线图

Figure 7. Contours of peak strength S_p (black lines, MPa) and dilation angle ψ (gray lines, in degree)

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图 8 室内试验与数值模拟曲线（围压800 kPa）

Figure 8. Stress-strain curves of experimental and numerical tests under confining pressure of 800 kPa

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图 9 室内试验与数值模拟曲线（围压400 kPa,1200 kPa）

Figure 9. Stress-strain curves of experimental and numerical tests under confining pressures of 400 and 1200 kPa

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表 1 初次正交试验设计表

Table 1 Design of initial orthogonal tests

因素	取值范围	因素水平
因素	取值范围	1	2	3	4
$μ_{r}$	0.3~1.0	0.3	0.5	0.7	1.0
$μ$	0.3~1.0	0.3	0.5	0.7	1.0
$E^{*}$ /100 MPa	1.0~10.0	1.0	4.0	7.0	10
$k_{r}$	1.0~2.5	1.0	1.5	2	2.5

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表 2 初次正交试验方案及宏观指标结果

Table 2 Schemes of initial orthogonal tests of micro-parameters and results of macroscopic indexes

方案	细观参数（自变量）				宏观指标（因变量）
方案		$μ_{r}$	$μ$	$E^{*}$ /100 MPa	$k_{r}$	$E_{50}$ /100 MPa	$S_{p}$ /MPa	$ε_{vmax}$ /%	$ψ$ /(°)
数值模拟	1	0.3	0.3	1.0	1.0	0.476	1.779	2.672	9.098
	2	0.3	0.5	4.0	1.5	1.391	2.897	1.164	14.142
	3	0.3	0.7	7.0	2.0	2.106	3.559	0.749	18.761
	4	0.3	1.0	10	2.5	2.691	4.219	0.540	22.030
	5	0.5	0.3	7.0	2.5	1.489	2.030	0.608	6.629
	6	0.5	0.5	10	2.0	2.589	3.562	0.553	15.871
	7	0.5	0.7	1.0	1.5	0.493	3.844	4.428	16.315
	8	0.5	1.0	4.0	1.0	1.833	5.928	1.896	21.954
	9	0.7	0.3	10	1.5	2.010	2.204	0.487	7.630
	10	0.7	0.5	7.0	1.0	2.413	4.067	0.889	16.238
	11	0.7	0.7	4.0	2.5	1.242	4.425	1.290	19.828
	12	0.7	1.0	1.0	2.0	0.422	4.488	4.629	16.151
	13	1.0	0.3	4.0	2.0	1.064	2.066	0.975	9.015
	14	1.0	0.5	1.0	2.5	0.376	2.723	3.211	12.711
	15	1.0	0.7	10	1.0	3.589	6.275	0.824	22.760
	16	1.0	1.0	7.0	1.5	2.536	7.487	1.147	28.529
室内试验	—	—	—	—	—	1.625	3.1926	0.912	2.031

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表 3 初次正交试验极差分析结果

Table 3 Range analysis results of initial orthogonal tests

宏观指标		因素
宏观指标		$μ_{r}$	$μ$	$E^{*}$ /100 MPa	$k_{r}$
$E_{50}$ /100 MPa	k₁	1.666	1.260	0.442	2.078
	k₂	1.601	1.692	1.383	1.608
	k₃	1.522	1.857	2.136	1.545
	k₄	1.891	1.870	2.720	1.449
	极差R	0.369	0.610	2.278	0.629
$S_{p}$ /MPa	k₁	3.114	2.020	3.209	4.512
	k₂	3.841	3.312	3.829	4.108
	k₃	3.796	4.526	4.286	3.349
	k₄	4.638	5.530	4.065	3.419
	极差R	1.524	3.510	1.077	1.163
$ε_{vmax}$ /%	k₁	1.281	1.186	3.735	1.412
	k₂	1.871	1.454	1.331	1.807
	k₃	1.824	1.823	0.848	1.727
	k₄	1.539	2.053	0.601	1.570
	极差R	0.590	0.867	3.134	0.395
$ψ$ /(°)	k₁	16.008	8.093	13.569	17.513
	k₂	15.192	14.741	16.235	16.654
	k₃	14.962	19.416	17.539	14.949
	k₄	18.254	22.166	17.073	15.299
	极差R	3.292	14.073	3.970	2.564

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表 4 室内试验宏观指标值及初次正交试验结果优方案

Table 4 Values of macro-indexes and optimal combination of micro-parameters

宏观指标	初次正交试验细观参数组合
E₅₀/100 MPa	$μ_{r} = 0.3$ $μ = 0.5$ E*=400 MPa $k_{r} = 1.5$
S_p/MPa	$μ_{r} = 0.3$ $μ = 0.5$ E*=100MPa $k_{r} = 2.0$
$ε_{vmax}$ /%	$μ_{r} = 0.3$ $μ = 0.3$ E*=700 MPa $k_{r} = 1.0$
$ψ$ /(°)	$μ_{r} = 0.7$ $μ = 0.3$ E*=100 MPa $k_{r} = 2.0$

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表 5 细观参数范围优化结果

Table 5 Results of micro-parameters range

细观参数	初始范围	第一次优化	第二次优化
$μ_{r}$	0.3~1.0	0.3~0.7	0.3~0.7
$μ$	0.3~1.0	0.3~0.5	0.3~0.5
$E^{*}$ /100 MPa	1.0~10.0	1.0~7.0	2.5~7.0
$k_{r}$	1.0~2.5	1.0~2.0	1.0~2.0

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表 6 第二次正交试验方案及结果

Table 6 Schemes of micro-parameters and results of macroscopic indexes in second orthogonal tests

方案	细观参数（自变量）				宏观指标（因变量）
方案	$μ_{r}$	$μ$	$E^{*}$ /100 MPa	$k_{r}$	$E_{50}$ /100 MPa	$S_{P}$ /MPa	$ε_{vmax}$ /%	$ψ$ /(°)
1	0.30	0.30	1.00	1.00	0.354	1.779	2.672	9.098
2	0.30	0.35	2.50	1.25	0.744	2.147	1.498	10.127
3	0.30	0.40	4.00	1.50	1.117	2.439	1.070	10.241
4	0.30	0.45	5.50	1.75	1.466	2.702	0.841	12.362
5	0.30	0.50	7.00	2.00	1.791	2.910	0.692	14.338
6	0.40	0.30	2.50	1.50	0.658	1.945	1.411	8.587
7	0.40	0.35	4.00	1.75	1.009	2.300	1.034	8.744
8	0.40	0.40	5.50	2.00	1.347	2.644	0.825	10.983
9	0.40	0.45	7.00	1.00	1.984	3.135	0.776	13.609
10	0.40	0.50	1.00	1.25	0.434	2.933	3.714	13.212
11	0.50	0.30	4.00	2.00	0.901	1.997	0.970	9.272
12	0.50	0.35	5.50	1.00	1.409	2.547	0.857	9.205
13	0.50	0.40	7.00	1.25	1.787	2.935	0.738	11.786
14	0.50	0.45	1.00	1.50	0.402	2.689	3.418	12.588
15	0.50	0.50	2.50	1.75	0.806	3.253	1.804	15.025
16	0.60	0.30	5.50	1.25	1.245	2.131	0.794	9.845
17	0.60	0.35	7.00	1.50	1.593	2.594	0.682	10.329
18	0.60	0.40	1.00	1.75	0.370	2.374	3.103	10.133
19	0.60	0.45	2.50	2.00	0.749	2.967	1.676	12.623
20	0.60	0.50	4.00	1.00	1.321	3.783	1.402	16.838
21	0.70	0.30	7.00	1.75	1.426	2.136	0.638	7.004
22	0.70	0.35	1.00	2.00	0.340	2.043	2.795	10.135
23	0.70	0.40	2.50	1.00	0.808	2.934	1.767	6.006
24	0.70	0.45	4.00	1.25	1.202	3.396	1.275	13.891
25	0.70	0.50	5.50	1.50	1.560	3.811	1.008	16.327

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表 7 细观参数标定结果

Table 7 The results of micro-parameters after calibration

细观参数	$E^{*}$ /MPa	$k_{r}$	$μ_{r}$	$μ$
标定值	657.7	1.376	0.6717	0.4177

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