基于多目标优化的同步注浆浆液性能改良研究

姚远; 刘维; 刘映晶; 陈城; 梁家馨

doi:10.20265/j.cnki.issn.1007-2993.2024-0613

基于多目标优化的同步注浆浆液性能改良研究

doi: 10.20265/j.cnki.issn.1007-2993.2024-0613

姚远^{1, 2,},
刘维^1, ,,
刘映晶³,
陈城⁴,
梁家馨⁵

1.
苏州大学轨道交通学院，江苏苏州　215131
2.
上海城建市政工程（集团）有限公司，上海　200065
3.
中天建设集团有限公司，浙江杭州　310002
4.
苏州城市学院智能制造与智慧交通学院，江苏苏州　215104
5.
太原理工大学土木工程学院，山西太原　030024

基金项目: 国家自然科学基金面上项目（51978430）；江苏省自然科学基金面上项目（BK20231318）

详细信息

作者简介:
姚　远，男，2000年生，硕士。研究方向：隧道及地下工程。E-mail：2071764988@qq.com

通讯作者:
刘　维，男，1985年生，博士，教授。研究方向：岩土工程、隧道工程。E-mail：ggoulmmeng@suda.edu.cn

中图分类号: U455.43
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- 文章访问数: 11
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- 被引次数: 0
出版历程
- 收稿日期: 2024-12-30
- 修回日期: 2025-02-10
- 录用日期: 2025-03-06
- 刊出日期: 2026-02-06

Performance improvement of shield synchronous grouting slurry based on multi-objective optimization

YAO Yuan^{1, 2
,},
LIU Wei^{1
, ,},
LIU Yingjing³,
CHEN Cheng⁴,
LIANG Jiaxin⁵

1.
School of Rail Transportation, Soochow University, Suzhou 215131, Jiangsu, China
2.
Shanghai Urban Construction Municipal Engineering (Group) Co., Ltd., Shanghai 200065, China
3.
Zhongtian Construction Group Co., Ltd., Hangzhou 310002, Zhejiang, China
4.
Institute of Intelligent Manufacturing and Smart Transportation, Suzhou City University, Suzhou 215104, Jiangsu, China
5.
College of Civil Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 针对盾构同步注浆中易发生的浆液稀释、离析等问题，通过分析实际工程案例，确定浆液配比后进行室内试验，采用SPSS及MINITAB分析试验结果，并结合MATLAB开展符合施工要求的浆液配比优化研究。分析表明：浆液水胶比集中在0.6～0.9，胶砂比集中在0.4～1.0，膨水比集中在0.1～0.3，灰粉比集中在0.2～0.6；水胶比对密度和稠度影响较大，膨水比主要影响流动度、泌水率和固结收缩率，灰粉比对凝结时间和强度影响显著；与MATLAB工具箱求解器的fmincon函数相比，改进的多目标遗传算法（NSGA-Ⅱ）优化结果精度更高，经优化得到最优配比：水胶比0.60、胶砂比0.87、膨水比0.25、灰粉比0.60。基于此，对北京12号线某盾构区间施工进行验证分析，结果表明相较于已有方案，基于多目标优化的浆液在地层变形控制上效果更优。
- 盾构同步注浆 /
- 正交试验 /
- 配比优化 /
- 多目标规划 /
- 地层沉降
Abstract: During the synchronous grouting process of shield tunneling, problems such as grout dilution and segregation are prone to occur. By analyzing actual engineering cases and determining the range of orthogonal design ratios, laboratory experiments were conducted. The experimental results were analyzed using SPSS and MINITAB, and the MATLAB multi-objective optimization tool was employed to study the optimization of grout ratios that meet the requirements of shield tunnel synchronous grouting engineering. The analysis showed that the water-cement ratio ranges from 0.6 to 0.9, the cement-sand ratio ranges from 0.4 to 1.0, the bentonite-water ratio ranges from 0.1 to 0.3, and the fly ash-cement ratio ranges from 0.2 to 0.6. The water-cement ratio significantly affects density and consistency, the bentonite-water ratio primarily influences fluidity, bleeding rate, and consolidation shrinkage rate, and the fly ash-cement ratio has a notable impact on setting time and strength. The regression formula for the grouts fits well and could be used for ratio optimization. Compared with the fmincon function of the MATLAB toolbox solver, the precision of the optimization results from the improved multi-objective genetic algorithm (Non-dominated Sorting Genetic Algorithm II) is higher. The optimal grout ratio obtained after optimization is a water-cement ratio of 0.60, a cement-sand ratio of 0.87, a bentonite-water ratio of 0.25, and a fly ash-cement ratio of 0.60. Based on this, a validation analysis was conducted on a shield section of Beijing Metro Line 12. The results indicated that, compared to the existing scheme, the grout based on multi-objective optimization of the ratios shows better performance in controlling ground deformation.
- synchronous grouting for shield tunnelling /
- orthogonal test /
- ratio optimization /
- multi-objective programming /
- ground settlement

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图 1 浆液配比分布频次

Figure 1. Distribution frequency of grout ratios

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图 2 室内试验流程图

Figure 2. Flowchart of indoor test

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图 3 浆液各性能极差分析

Figure 3. Analysis of performance deviation in grout

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图 4 浆液各性能的拟合值与测试值

Figure 4. Fitted values and test values of grout performance

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图 5 改进NSGA-II算法流程图

Figure 5. Flowchart of improved NSGA-II algorithm

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图 6 基于改进NSGA-II算法的目标函数优化曲线

Figure 6. Objective function optimization curve based on the improved NSGA-II algorithm

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图 7 盾构隧道区间工程情况

Figure 7. Shield tunnel section engineering overview

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图 8 基于修正Peck解的地表沉降对比

Figure 8. Comparison of ground surface subsidence based on the modified Peck solution

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图 9 基于Loganathan解的地表沉降对比

Figure 9. Comparison of ground surface settlement based on the Loganathan solution

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表 1 正交试验因素水平

Table 1. Orthogonal test factor levels

因子水平	A	B	C	D
1	0.6	0.4	0.1	0
2	0.7	0.6	0.15	0.2
3	0.8	0.8	0.2	0.4
4	0.9	1.0	0.25	0.6

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表 2 浆液原材料性能指标

Table 2. Performance indicators of grout raw materials

材料名称	性能指标
水泥	P∙O 42.5普通硅酸盐水泥
粉煤灰	Ⅱ级粉煤灰，含水率≤1.0%
膨润土	钠基膨润土，过200目筛量超95%
砂	细中砂，含泥量≤3.0%
水	城市自来水，pH值7～8

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表 3 浆液基本性能试验结果

Table 3. Basic performance test results of grout

浆液编号	密度/(g·cm⁻³)	流动度/cm	泌水率/%	稠度/cm	固结收缩率/%	凝结时间/h	无侧限抗压强度/MPa
浆液编号	密度/(g·cm⁻³)	流动度/cm	泌水率/%	稠度/cm	固结收缩率/%	凝结时间/h	3 d	7 d	28 d
1	1.645	23.7	1.42	12.3	5.13
2	1.730	23.6	2.59	11.8	4.79	11.5	0.50	1.21	3.14
3	1.767	21.9	1.28	10.9	4.32	10.6	1.22	2.56	6.10
4	1.796	20.1	0.61	10.3	3.98	7.9	2.34	4.58	8.52
5	1.654	24.5	2.98	12.9	5.15	11.2	1.32	2.52	5.29
6	1.678	25.4	2.54	13.1	5.49	10.5	1.60	3.53	7.23
7	1.648	/	0.03	/	4.06
8	1.756	23.1	2.08	11.5	4.54	13.3	0.51	1.07	2.28
9	1.622	24.3	3.15	12.9	4.70	11.5	1.16	2.61	5.46
10	1.671	23.4	1.84	11.8	4.49	12.1	0.71	1.55	3.74
11	1.674	*	3.83	13.2	5.97	16.7	0.22	0.68	1.50
12	1.665	24.8	1.01	12.1	5.26
13	1.583	22.5	1.47	12.0	4.34	15.6	0.25	0.59	1.28
14	1.575	/	0.01	/	4.94
15	1.647	26.8	4.68	13.1	5.65	12.0	0.78	1.67	3.90
16	1.702	*	4.89	13.0	6.50	13.4	0.44	0.93	2.62

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表 4 浆液基本性能极差分析结果

Table 4. Results of the basic performance deviation analysis of grout

性能指标	因素	因素水平				极差R	排秩
性能指标	因素	1	2	3	4	极差R	排秩
密度	A	1.73	1.68	1.66	1.63	0.11	1
	B	1.63	1.66	1.68	1.73	0.10	2
	C	1.67	1.67	1.68	1.67	0.01	4
	D	1.63	1.69	1.70	1.69	0.07	3
流动度	A	22.32	24.33	24.17	24.65	2.33	2
	B	23.75	24.13	24.35	22.67	1.68	3
	C	24.55	24.93	23.10	22.00	2.93	1
	D	24.25	23.07	23.27	24.15	1.18	4
泌水率	A	1.48	1.91	2.46	2.76	1.29	3
	B	2.26	1.74	2.46	2.15	0.71	4
	C	3.17	2.81	1.63	0.99	2.18	1
	D	0.62	2.49	2.75	2.75	2.13	2
稠度	A	10.40	12.43	11.8	12.77	2.37	1
	B	11.55	11.97	12.33	11.32	1.01	4
	C	12.45	11.75	11.4	11.13	1.32	3
	D	9.95	11.57	12.25	12.3	2.35	2
固结收缩率	A	4.55	4.81	5.11	5.36	0.80	2
	B	4.83	4.93	5.00	5.07	0.24	4
	C	5.77	5.21	4.63	4.22	1.56	1
	D	4.85	4.91	5.12	4.96	0.27	3
凝结时间	A	10.00	11.67	13.43	13.67	3.67	2
	B	12.77	11.37	13.10	11.53	1.73	4
	C	13.53	11.57	11.80	11.87	1.97	3
	D		14.28	11.82	10.47	3.80	1
3 d抗压强度	A	1.35	1.14	0.70	0.49	0.86	2
	B	0.91	0.94	0.74	1.10	0.36	3
	C	0.75	0.87	0.96	1.10	0.35	4
	D		0.37	0.92	1.47	1.10	1
7 d抗压强度	A	2.78	2.37	1.61	1.06	1.72	2
	B	1.91	2.10	1.64	2.19	0.56	3
	C	1.71	1.80	2.08	2.24	0.53	4
	D		0.89	1.89	3.10	2.21	1
28 d抗压强度	A	5.92	4.93	3.57	2.60	3.32	2
	B	4.01	4.70	3.83	4.47	0.87	3
	C	3.78	4.11	4.61	4.51	0.83	4
	D		2.05	4.44	6.28	4.23	1

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表 5 多元回归拟合结果

Table 5. Multiple regression fitting results

变量	回归公式	R²	$ R_{\mathrm{adj}}^2 $
密度	ρ=1.78−0.349A+0.166B+0.33D−0.408D²	0.979	0.972
流动度	F=20.73+10.56A−26.25C	0.888	0.863
泌水率	b=4.01−1.57A−12.28C−4.59D−11.73D²+19.93AD	0.949	0.923
稠度	s=1.99+30.47A−1.299B−11.058C+0.711D−17.54A²	0.986	0.978
固结收缩率	ε=2.167+6.171A+4.36C−19.82AC	0.981	0.976
凝结时间	t=6.42+12.77A−9.5D	0.883	0.856
3 d抗压强度	f_3d=−0.962+1.043A+10.4D−10.2AD	0.967	0.955
7 d抗压强度	f_7d=−1.362+1.48A+19.4D−18.5AD	0.987	0.982
28 d抗压强度	f_28d=1.57−2.06A+27.95D−23.18AD	0.992	0.989

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表 6 优化浆液试验结果验证

Table 6. Validation of test results of optimized grout

最优配比来源	项目	密度 /(g·cm⁻³)	流动度/cm	泌水率 /%	稠度 /cm	固结收缩率/%	凝结时间/h	无侧限抗压强度/MPa
最优配比来源	项目	密度 /(g·cm⁻³)	流动度/cm	泌水率 /%	稠度 /cm	固结收缩率/%	凝结时间/h	3 d	7 d	28 d
fmincon函数	最优配比试验值	1.806	19.9	1.2	11.5	4.43	7.9	2.10	4.31	8.15
	最优配比理论值	1.756	21.3	0.56	10.9	4.21	8.4	2.23	4.51	8.76
	误差率/%	2.77	7.04	53.33	5.22	4.97	6.33	6.19	4.64	7.48
改进NSGA-II算法	最优配比试验值	1.844	19.5	0.29	10.2	4.11	8.0	2.16	4.36	8.20
	最优配比理论值	1.766	20.5	0.2	10.5	3.99	8.4	2.23	4.51	8.76
	误差率/%	4.23	5.13	31.03	2.94	3.16	5.00	3.24	3.44	6.83

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表 7 优化算法对比

Table 7. Comparison of optimization algorithms

验证组	优化方法	A	B	C	D	其余函数求解值	目标函数求解值	更优
①	fmincon函数	0.6	0.82	0.25	0.54	ρ=1.766 g/cm³，F=20.5 cm，s=10.5 cm，t=9.0 h f_3d=1.98 MPa，f_7d=4.01 MPa，f_28d=7.92 MPa，cost=366.2元	ԑ=3.99%，b=0.52%	改进NSGA-Ⅱ
①	改进NSGA-Ⅱ	0.6	0.7	0.25	0.6	ρ=1.738 g/cm³，F=20.5 cm，s=10.7 cm，t=8.4 h f_3d=2.23 MPa，f_7d=4.51 MPa，f_28d=8.76 MPa，cost=373.6元	ԑ=3.99%，b=0.20%	改进NSGA-Ⅱ
②	fmincon函数	0.6	0.72	0.19	0.35	ρ=1.755 g/cm³，F=22.1 cm，b=1.88%, s=11.2 cm，t=10.8 h f_3d=1.16 MPa，f_7d=2.43 MPa，f_28d=5.25 MPa	ԑ=4.48%，cost=314.6元	改进NSGA-Ⅱ
②	改进NSGA-Ⅱ	0.6	0.47	0.21	0.22	ρ=1.701 g/cm³，F=21.6 cm，b=1.54%, s=11.2 cm，t=12.0 h f_3d=0.61 MPa，f_7d=1.35 MPa，f_28d=3.42 MPa	ԑ=4.29%，cost=294.6元	改进NSGA-Ⅱ
③	fmincon函数	0.6	0.75	0.19	0.43	ρ=1.761 g/cm³，F=22.1 cm，b=1.73%，s=11.2 cm，t=10.0 h f_3d=1.50 MPa，f_7d=3.10 MPa	ԑ=4.44%，f_28d=6.37 MPa， cost=335.8元	改进NSGA-Ⅱ
③	改进NSGA-Ⅱ	0.6	0.6	0.19	0.43	ρ=1.736 g/cm³，F=22.1 cm，b=1.73%，s=11.4 cm， t=10.0 h f_3d=1.50 MPa，f_7d=3.10 MPa	ԑ=4.44%，f_28d=6.37 MPa， cost=335.6元	改进NSGA-Ⅱ
④	fmincon函数	0.6	0.75	0.21	0.43	ρ=1.761 g/cm³，F=21.6 cm，s=11.0 cm，t=10.0 h f_3d=1.50 MPa，f_7d=3.10 MPa，f_28d=6.37 MPa	ԑ=4.29%，b=1.49%， cost=341元	改进NSGA-Ⅱ
④	改进NSGA-Ⅱ	0.6	0.49	0.24	0.22	ρ=1.704 g/cm³，F=21.6 cm，s=11.2 cm，t=12.0 h f_3d=0.61 MPa，f_7d=1.35 MPa，f_28d=3.42 MPa	ԑ=4.06%，b=1.17%， cost=302.9元	改进NSGA-Ⅱ

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表 8 关键计算参数取值

Table 8. Key calculation parameter values

浆液	A	B	C	D	ԑ/%	g/m	R/m	φ/(°)	Z₀/m	H/m
原配比	1.21	0.71	0.13	0.83	7.08	0.048	3.305	32	21.4	24.3
本文最优配比	0.60	0.87	0.25	0.60	3.99	0.027	3.305	32	21.4	24.3

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1 盾构隧道同步注浆材料配比案例统计

1. Case statistics of synchronous grouting material proportioning in shield tunnels

序号	项目名称	水泥/kg	粉煤灰/kg	膨润土/kg	砂/kg	水/kg	粉灰比	膨水比	水胶比	胶砂比
1	武汉长江隧道	100	312	25.5	814	288	3.12	0.09	0.70	0.51
2	武汉地铁3号线王家湾站—宗关站	120	460	50	760	350	3.83	0.14	0.60	0.76
3	西安地铁4号线15标	110	395	55	787	512	3.59	0.11	1.01	0.64
4	莞惠城际轨道交通	90	450	100	670	400	5.00	0.25	0.74	0.81
5	狮子洋隧道	150	430	50	750	344	2.87	0.15	0.59	0.77
6	哈尔滨地铁2号线一期工程	130	300	30	250	290	2.31	0.10	0.67	1.72
7	广佛地铁一期工程	9	23	3	44	214	2.56	0.13	0.65	0.73
8	郑州轨道交通4号线土建01标	195	340	106	840	475	1.74	0.22	0.89	0.64
9	太原地铁2号线学府街站—长风街站	180	350	60	750	450	1.94	0.13	0.85	0.71
10	长沙轨道交通1号线汽车北站—开福区政府站	300	245	65	750	405	0.82	0.16	0.74	0.73
11	广州地铁7号线谢村站—钟村站	120	200	200	360	400	1.67	0.50	1.25	0.89
12	常德沅江隧道	110	280	50	935	320	2.55	0.16	0.82	0.42
13	成都地铁8号线一期工程	200	450	150	800	500	2.25	0.30	0.77	0.81
14	上海地铁11号线13标	100	360	20	400	210	3.60	0.10	0.46	1.15
15	武汉地铁8号线一期工程	43	222	68	1233	401	5.16	0.17	1.51	0.21
16	深圳地铁10号线华为站—岗头站	130	300	50	630	380	2.31	0.13	0.88	0.68
17	沈阳地铁10号线理工大学站—张沙布站	170	500	60	800	420	2.94	0.14	0.63	0.84
18	广州地铁2号线越秀公园站—三元里站	80	421	56	779	463	5.26	0.12	0.92	0.64
19	沈阳地铁1号线洪湖北街站—重工街站	210	315	84	1180	580	1.50	0.14	1.10	0.44
20	深圳地铁9号线9104-3标	160	314	56	779	446	1.96	0.13	0.94	0.61
21	南京宁高城际轨道交通禄口新城南站—铜山站	120	360	120	700	500	3.00	0.24	1.04	0.69
22	长沙轨道交通2号线橘子洲站—湘江中路站	210	315	84	1180	294	1.50	0.29	0.56	0.44
23	成都地铁2号线东广场站—东洪路站	160	300	65	780	423	1.88	0.15	0.92	0.59
24	大连地铁2号线201标	140	381	55	820	460	2.72	0.12	0.88	0.64
25	天津轨道交通6号线西站站—河北大街站	200	380	55	930	460	1.90	0.12	0.79	0.62

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参考文献(19)

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