隧道围岩收敛变形预测模型动态选择与变形量概率预测

曾鹏; 张志强; 李天斌; 唐浩; 严祖龙; 孟陆波

doi:10.19509/j.cnki.dzkq.tb20240187

隧道围岩收敛变形预测模型动态选择与变形量概率预测

doi: 10.19509/j.cnki.dzkq.tb20240187

1.
成都理工大学环境与土木工程学院, 成都 610059
2.
四川宁西高速公路建设开发有限公司, 四川西昌 615000
3.
四川高速公路建设开发集团有限公司, 成都 610047

基金项目:

国家自然科学基金重点项目 42130719

详细信息

作者简介:
曾鹏, E-mail: zengpeng15@cdut.edu.cn

通讯作者:
张志强, E-mail: 1299502491@qq.com

中图分类号: TU457
计量
- 文章访问数: 87
- PDF下载量: 26
- 被引次数: 0
出版历程
- 收稿日期: 2024-04-25
- 录用日期: 2024-07-01
- 修回日期: 2024-06-06

Dynamic selection of optimal tunnel convergence prediction model for a probabilistic deformation prediction

1.
College of Environment and Civil Engineering, Chengdu University of Technology, Chengdu 610059, China
2.
Sichuan Ningxi Expressway Construction & Development Co., Ltd., Xichang Sichuan 615000, China
3.
Sichuan Expressway Construction & Development Group Co., Ltd., Chengdu 610047, China

More Information

Author Bio:
ZENG Peng, E-mail: zengpeng15@cdut.edu.cn

Corresponding author: ZHANG Zhiqiang, E-mail: 1299502491@qq.com

摘要

摘要:
高地应力或复杂地质条件下隧道围岩极易变形侵限。在隧道施工期对围岩的变形趋势与收敛变形值进行超前判识, 对保障施工人员安全、提高隧道施工效率具有重要意义。传统单一预测模型难以适应隧道收敛变形的动态变化, 预测效果有限。建立了一个基于连续贝叶斯反分析方法和最优模型选择的围岩收敛变形动态预测模型, 利用隧道收敛变形监测信息作为观察值, 对用于围岩收敛变形曲线预测的3种经验模型参数进行了连续更新校准, 选择最优模型预测围岩最终收敛变形值并量化其不确定性。将该模型应用于白马隧道9个断面16组测点的围岩收敛变形预测, 预测与监测的最终收敛变形量平均相对误差仅3.22%。动态预测模型仅需开挖后10 d的观测数据即可有效预测40 d的最终变形收敛结果, 为全断面开挖法隧道围岩变形侵限和大变形灾害防治提供了重要技术支撑。
- 隧道 /
- 收敛变形 /
- 动态预测 /
- 模型选择 /
- 贝叶斯理论
Abstract: Objective
In high geostress or complex geological conditions, tunnel convergence frequently exceeds the threshold, resulting in damage to support structures and, in extreme cases, tunnel collapse. Accurately predicting the deformation trend and convergence of surrounding rock during tunnel construction is crucial to ensuring the safety of workers and improving construction efficiency. Traditional single prediction models struggle to adapt to the dynamic nature of tunnel convergence, limiting their predictive accuracy.
Methods
To address this, this study introduces a dynamic prediction model for tunnel convergence based on continuous Bayesian updating and an optimal model selection strategy. Utilizing real-time monitoring data of tunnel convergence deformation, the parameters in three empirical models are continuously updated and refined. The optimal model is then selected to predict the final convergence deformation of the surrounding rock and quantify its associated uncertainty.
Results
The model was tested on 16 measurement points across 9 sections of the Baima Tunnel, achieving a mean relative error of only 3.22% between the predicted and monitored final convergence rates.
Conclusion
Additionally, with just 10 days of observed data, the model can forecast the final convergence deformation for up to 40 days post-excavation, offering valuable technical support for preventing squeezing disasters in the full-section tunnel excavation.
- tunnel /
- convergence /
- dynamic forecasting /
- model selection /
- Bayesian theory
注释:

所有作者声明不存在利益冲突。

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图 1 8类围岩收敛变形特征曲线(b~i)及占比(a)

Figure 1. Convergence deformation characteristic curves and proportions for eight types of surrounding rock

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图 2 经验模型2的随机变量先验信息(d_x^*, Y, d_t^*, Q含义见公式(2))

Figure 2. Prior information of random variables for empirical model 2

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图 3 经验模型3的随机变量先验信息

Figure 3. Prior information of random variables for empirical model 3

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图 4 K39+405断面拱顶沉降预测结果

a.每次预测的最终拱顶沉降均值与标准差; b.拱顶沉降连续更新的预测值与实际测量值(经验模型2)

Figure 4. Prediction results of K39+405 vault settlement

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图 5 K39+695断面周边收敛预测结果

a.周边收敛连续更新的预测值与实际测量值(经验模型3);b.每次预测的最终周边收敛均值与标准差

Figure 5. Prediction results for the convergence around K39+695

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表 1 经验模型1的随机变量先验信息

Table 1. Prior information of random variables for empirical model 1

随机变量	X/m	T/d	C_∞x/mm	m
均值	20.00	2.20	24.80	3.89
标准差	2.00	0.22	2.48	0.39
变异系数	0.10	0.10	0.10	0.10
分布类型	正态	正态	正态	正态
注：X，T，C_∞x, m含义见公式(1)

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表 2 随机变量的后验统计信息

Table 2. Posterior statistical information of random variables

经验模型1			经验模型2			经验模型3
随机变量	均值	标准差	随机变量	均值	标准差	随机变量	均值	标准差
X/m	21.28	2.36	d_x^*/mm	21.31	10.24	a	21.39	3.79
T/d	2.37	0.26	Y/m	17.88	4.54	σ_ε	2.16	1.26
C_∞x/mm	26.95	2.66	d_t^*/mm	51.19	10.70	—	—	—
m	4.20	0.44	Q/d	12.07	1.74	—	—	—
σ_ε	2.13	1.35	σ_ε	2.02	1.35	—	—	—
模型证据权重	0.327 8		模型证据权重	0.362 3		模型证据权重	0.309 9
注：σ_ε.模型偏差系数标准差, 其余随机变量的含义见公式(1)~(3)，下同

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表 3 K39+405断面拱顶沉降第2~10次模型选择的模型证据权重

Table 3. Model evidence weights for the 2nd to 10th model selection of K39+405 vault settlement

模型类别	第2次选择	第3次选择	第4次选择	第5次选择	第6次选择	第7次选择	第8次选择	第9次选择	第10次选择
经验模型1	0.345 0	0.129 7	0.052 0	0.009 7	0.002 2	0.000 3	0.000 1	0.000 1	0.000 1
经验模型2	0.440 3	0.762 9	0.854 6	0.952 0	0.974 4	0.990 2	0.994 0	0.999 2	0.999 6
经验模型3	0.214 7	0.107 4	0.093 4	0.038 3	0.023 3	0.009 5	0.005 9	0.000 7	0.000 3

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表 4 K39+405断面拱顶沉降最优模型随机变量的后验信息统计(经验模型2)

Table 4. Posterior statistical information of random variables for the optimal model of K39+405 vault settlement

第2次更新			第3次更新			第4次更新
随机变量	均值	标准差	随机变量	均值	标准差	随机变量	均值	标准差
d_x^*/mm	17.02	8.50	d_x^*/mm	13.65	5.58	d_x^*/mm	13.38	4.42
Y/m	16.40	4.80	Y/m	14.78	4.02	Y/m	14.01	4.13
d_t^*/mm	49.45	10.57	d_t^*/mm	48.55	9.52	d_t^*/mm	46.36	9.08
Q/d	11.49	1.87	Q/d	10.80	1.64	Q/d	11.00	1.47
σ_ε	0.83	1.02	σ_ε	0.21	0.35	σ_ε	0.15	0.16

第5次更新			第6次更新			第7次更新
随机变量	均值	标准差	随机变量	均值	标准差	随机变量	均值	标准差
d_x^*/mm	13.86	3.58	d_x^*/mm	13.53	3.60	d_x^*/mm	13.57	3.80
Y/m	13.00	3.61	Y/m	12.33	3.13	Y/m	12.17	2.89
d_t^*/mm	43.87	8.36	d_t^*/mm	44.43	8.03	d_t^*/mm	41.69	7.18
Q/d	11.46	1.42	Q/d	11.67	1.43	Q/d	11.01	1.78
σ_ε	0.10	0.08	σ_ε	0.08	0.05	σ_ε	0.07	0.03

第8次更新			第9次更新			第10次更新
随机变量	均值	标准差	随机变量	均值	标准差	随机变量	均值	标准差
d_x^*/mm	14.49	2.54	d_x^*/mm	12.71	1.67	d_x^*/mm	14.31	1.78
Y/m	13.46	2.23	Y/m	10.49	1.88	Y/m	12.03	1.56
d_t^*/mm	43.50	5.50	d_t^*/mm	44.24	3.62	d_t^*/mm	45.19	3.98
Q/d	11.77	1.87	Q/d	11.60	1.14	Q/d	12.86	1.87
σ_ε	0.07	0.03	σ_ε	0.05	0.02	σ_ε	0.04	0.02

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表 5 K39+695断面周边收敛的模型证据权重

Table 5. Model evidence weights for the convergence around K39+695

模型类别	第1次选择	第2次选择	第3次选择	第4次选择	第5次选择	第6次选择	第7次选择	第8次选择	第9次选择	第10次选择	第11次选择
经验模型1	0.169 2	0.067 9	0.011 6	0.002 2	0.000 4	0.000 1	0.000 1	0.000 1	0.000 1	0.000 1	0.000 1
经验模型2	0.238 3	0.152 2	0.068 8	0.033 9	0.019 5	0.004 8	0.003 0	0.014 9	0.261 8	0.017 8	0.005 4
经验模型3	0.592 5	0.779 9	0.919 6	0.963 9	0.980 1	0.995 1	0.996 9	0.985 1	0.738 0	0.982 1	0.994 5

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表 6 16组测点动态预测模型的计算结果

Table 6. Computational results of dynamic prediction models for 16 groups of measuring points

测点编号	桩号、围岩级别及测点位置	预测次数	最优模型选择	模型预测结果			实际测量值 U_obs/mm	相对误差 $\Delta U=\frac{\left\|U_{\mathrm{m}}-U_{\mathrm{obs}}\right\|}{U_{\mathrm{obs}}} / \%$
测点编号	桩号、围岩级别及测点位置	预测次数	最优模型选择	均值U_m/mm	标准差σ/mm	变异系数	实际测量值 U_obs/mm
1	K39+405(Ⅴ)拱顶沉降	10	经验模型2	57.34	4.29	0.07	60.36	5.00
2	K39+405(Ⅴ)周边收敛	10	经验模型2	53.95	5.74	0.11	58.47	7.73
3	K39+655(Ⅴ)拱顶沉降	8	经验模型3	73.89	1.83	0.02	75.13	1.65
4	K39+655(Ⅴ)周边收敛	11	经验模型3	55.66	5.67	0.10	54.56	2.02
5	K39+695(Ⅴ)拱顶沉降	9	经验模型3	76.85	7.04	0.09	76.57	0.37
6	K39+695(Ⅴ)周边收敛	11	经验模型3	69.92	6.46	0.09	68.90	1.48
7	K39+790(Ⅴ)拱顶沉降	11	经验模型3，2	65.72	7.70	0.12	71.47	8.05
8	K39+790(Ⅴ)周边收敛	10	经验模型3	84.28	10.59	0.13	86.46	2.52
9	K39+820(Ⅴ)拱顶沉降	11	经验模型1	172.91	22.67	0.13	163.58	5.70
10	K39+830(Ⅴ)周边收敛	13	经验模型1	131.20	16.07	0.12	131.06	0.11
11	K40+090(Ⅴ)拱顶沉降	13	经验模型3，1	152.15	14.42	0.09	153.86	1.11
12	K40+090(Ⅴ)周边收敛	13	经验模型1	186.11	19.69	0.11	180.00	3.39
13	K40+160(Ⅴ)拱顶沉降	10	经验模型1	132.77	15.52	0.12	131.03	1.33
14	K40+160(Ⅴ)周边收敛	15	经验模型3，2	203.01	30.03	0.15	208.96	2.85
15	K40+180(Ⅴ)拱顶沉降	8	经验模型2	52.04	5.90	0.11	56.55	7.98
16	K40+180(Ⅴ)周边收敛	11	经验模型2	55.32	3.57	0.06	55.45	0.23
相对误差(ΔU)均值/%								3.22
注：K39+790拱顶沉降模型选择结果第1~5次预测选择经验模型3，第6~11次预测选择经验模型2；K40+090拱顶沉降模型选择结果第1~4次预测选择经验模型3，第5~13次选择经验模型1；K40+160周边收敛模型选择结果第1~3次预测选择经验模型3，第4~15次预测选择经验模型2

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