高内压力下引水隧洞透水衬砌限裂理论分析研究

陈洁; 王艳强; 乐萍; 董启暖; 曹亚军; 王伟

doi:10.20265/j.cnki.issn.1007-2993.2024-0317

高内压力下引水隧洞透水衬砌限裂理论分析研究

doi: 10.20265/j.cnki.issn.1007-2993.2024-0317

陈洁^1,,
王艳强¹,
乐萍^{2, 3, ,},
董启暖¹,
曹亚军^{2, 3},
王伟^{2, 3}

1.
山东电力工程咨询院有限公司，山东济南　250014
2.
河海大学岩土力学与堤坝工程教育部重点实验室，江苏南京　210098
3.
河海大学岩土工程科学研究所，江苏南京　210098

基金项目: 中国博士后基金面上项目（2021M690047）

详细信息

作者简介:
陈　洁，男，1995年生，硕士，主要从事地下隧道工程研究。E-mail：chenjie@ssdepci.com

通讯作者:
乐　萍，女，2001年生，在读硕士研究生，主要从事水工隧洞衬砌设计工程研究。E-mail：1173958714@qq.com

中图分类号: TV31
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出版历程
- 收稿日期: 2024-07-11
- 修回日期: 2024-10-23
- 录用日期: 2024-10-29
- 刊出日期: 2025-08-08

Analytical study on the crack limitation theory of permeable lining of diversion tunnels under high internal pressure

Chen Jie^1
,,
Wang Yanqiang¹,
Le Ping^{2, 3
, ,},
Dong Qinuan¹,
Cao Yajun^{2, 3},
Wang Wei^{2, 3}

1.
Shandong Electric Power Engineering Consulting Institute Co., Ltd., Jinan 250014, Shandong, China
2.
Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, Jiangsu, China
3.
Institute of Geotechnical Engineering, Hohai University, Nanjing 210098, Jiangsu, China

摘要

摘要: 为了研究高内水压力下引水隧洞衬砌开裂的影响因素，进而对衬砌限裂进行优化设计，基于透水衬砌理论确定了透水衬砌的设计步骤，并给出了钢筋混凝土衬砌不同裂缝宽度的计算公式，结合实际工程，分别采用中国规范和美国规范的裂缝宽度计算公式计算得到混凝土衬砌配筋方案，并对混凝土衬砌裂缝宽度的影响因素进行了分析。结果表明：（1）中国规范计算得到的配筋面积比美国规范要更大，钢筋的应力更小；（2）影响混凝土裂缝宽度的影响因素主要有内水压力、配筋面积、渗透系数和衬砌的厚度，可以通过调整这几种影响因素来限制混凝土开裂。
- 水工隧洞 /
- 透水衬砌理论 /
- 限裂宽度 /
- 配筋方案
Abstract: Based on the theory of permeable lining, the design steps of permeable lining were determined, and the calculation formula for solving different crack widths of pressure tunnel lining concrete was given. The reinforcement scheme was obtained by combining with the actual project using the crack width calculation formula in the Chinese and U.S. codes. The results show that: (1) the reinforcing area obtained through the Chinese code is larger than the American code, and the stress of the reinforcement is smaller. (2) The major influencing factors affecting the width of concrete cracks are internal water pressure, reinforcement area, permeability coefficient and the thickness of the lining, which can be adjusted to control the cracking of the concrete by these different influencing factors.
- hydraulic tunnel /
- permeable lining theory /
- width of limiting crack /
- reinforcement design

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图 1 厚壁圆筒计算模型

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图 2 配筋面积对裂缝宽度的影响

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图 3 衬砌厚度对裂缝宽度的影响

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图 4 保护层厚对裂缝宽度的影响

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图 5 隧洞半径对裂缝宽度的影响

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图 6 渗透系数对裂缝宽度的影响

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图 7 内水压力对裂缝宽度的影响

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表 1 厚壁圆筒模型解析计算公式

计算工况	衬砌混凝土未开裂	衬砌混凝土已开裂
径向应力	$ \sigma\mathrm{_r}=\dfrac{(p_1-p_2)}{2(1-\mu)}\left(\dfrac{\mathrm{ln}\;\left(r_2/r\right)}{\mathrm{ln}\;t}+\dfrac{1-r_2^2/r^2}{t^2-1}\right) $	$ {\sigma }_{\rm{r}}=\dfrac{{(2-\mu )(p}_{1}-{p}_{2})}{3(1-\mu )}\left(\dfrac{1-{r}_{2}^{2}/{r}^{2}}{{t}^{2}-1}+\dfrac{{r}_{2}-r}{{r}_{2}-{r}_{1}}\right) $
环向应力	$ \sigma{_{{\text{θ}}}}=\dfrac{(p_1-p_2)}{2(1-\mu)}\left(\dfrac{\mathrm{ln}\;\left(r_2/r\right)+1-2\mu}{\mathrm{ln}\;t}+\dfrac{1+r_2^2/r^2}{t^2-1}\right) $	$ \sigma_{{{\text{θ}}}}=\dfrac{(2-\mu)(p_1-p_2)}{3(1-\mu)}\left(\dfrac{1+r_2^2/r^2}{t^2-1}+\dfrac{r_2}{r_2-r_1}-\dfrac{(1+\mu)r}{(r_2-r_1)(2-\mu)}\right) $
位移	$ {u}_{\rm{r}}=\dfrac{r{(p}_{1}-{p}_{2}\left)\right(1+\mu )}{2E(1-\mu )}\left(\dfrac{(1-2\mathrm{\mu })(\mathrm{l}\mathrm{n}\;\left({r}_{2}/r\right)+1-\mathrm{\mu })}{\mathrm{l}\mathrm{n}\; t}+\dfrac{1-2\mu +{r}_{2}^{2}/{r}^{2}}{{t}^{2}-1}\right) $	$ {u}_{\rm{r}}=\dfrac{r{(p}_{1}-{p}_{2}\left)\right(1+\mu \left)\right(2-\mu )}{3E(1-\mu )}\left(\dfrac{(1-2\mathrm{\mu })\left[\right(2-\mathrm{\mu }){r}_{2}-\mathrm{r}]}{({r}_{2}-{r}_{1})(2-\mu )}+\dfrac{1-2\mu +{r}_{2}^{2}/{r}^{2}}{{t}^{2}-1}\right) $

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表 2 中、美规范中混凝土最大裂缝计算公式

规范或方法	计算公式
《水工混凝土结构设计规范》（SL 191—2008）^[14]	$ w\mathrm{_{\rm{max}}}=\alpha\dfrac{\sigma_{\mathrm{sk}}}{E_{\mathrm{s}}}\left(0.03+c+0.07\dfrac{d}{\rho_{\mathrm{te}}}\right) $
《水工隧洞设计规范》（SL 279—016）^[15]	$ w_{\mathrm{max}}=2\left(\dfrac{\sigma_{\mathrm{s}}}{E_{\mathrm{s}}}\phi-0.7\times10^{-4}\right)l_{\mathrm{f}} $
Z系数法^[17]	$ w_{\mathrm{max}}=1.1\beta f_{\mathrm{s}}\sqrt[3]{d\mathrm{_c}A}\times10^{-5} $
Frosch法^[19]	$ w\mathrm{_{\rm{max}}}=2\dfrac{f\mathrm{_s}}{E_{\mathrm{s}}}\beta\sqrt[]{d_{\mathrm{c}}^2+\left(\dfrac{s}{2}\right)^2} $
Broms-Lutz法^[20]	$ w\mathrm{_{\rm{max}}}=1.45\sigma_{\mathrm{s}}\sqrt[3]{d\mathrm{_c}A}\times10^{-5} $
注：《水工混凝土结构设计规范》（SL 191—2008）中，$ \alpha $为考虑构件受力特征和荷载长期作用的综合影响系数，本文按轴心受拉计算，取$ \alpha $=2.4；$ \sigma\mathrm{_{sk}} $为纵向受拉钢筋的应力，MPa；$ E_{\mathrm{s}} $为钢筋的杨氏模量，$ \mathrm{M}\mathrm{P}\mathrm{a} $；$ c $为保护层厚度，mm；$ d $为钢筋的直径，mm；$ \rho\mathrm{_{te}} $为钢筋的配筋率。《水工隧洞设计规范》（SL279—2016）中，$ \sigma\mathrm{_s} $为纵向受拉钢筋的应力，MPa；$ E\mathrm{_s} $为钢筋的杨氏模量，MPa；$ \phi $为裂缝间纵向受拉钢筋应变不均匀系数，当$ \phi $<0.3时，取0.3；$ l\mathrm{_f} $为平均裂缝间距，m；Z系数法中，$ \beta $为钢筋到界面受拉边缘的应变梯度的影响，在本文中，近似取1.2；$ f\mathrm{_s} $为受拉钢筋应力，MPa；$ d\mathrm{_c} $从受拉区底面至最靠近该面的受拉钢筋界面形心的距离，mm；$ A $为包围一根钢筋的混凝土截面面积。Frosch法中，$ f\mathrm{_s}，\beta，d_{\mathrm{c}}，E\mathrm{_s} $均与上述相同，$ s $为钢筋的间距，mm；Broms-Lutz法中，参数含义均与上述相同。

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表 3 计算参数

计算参数	取值
内水压力/MPa	1.3
衬砌外径/m	11.8
衬砌内径/m	11
保护层厚度/mm	25
围岩弹性模量/GPa	4
围岩泊松比	0.35
围岩渗透系数/（m·s^–1）	5×10⁻⁶
单位弹抗系数/（MPa·cm^–1）	12.5
衬砌混凝土弹性模量/GPa	28
衬砌混凝土泊松比	0.167
衬砌混凝土渗透系数/（m·s^–1）	1×10⁻⁹
钢筋弹性模量/GPa	200
围岩渗透半径/m	118

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表 4 采用《水工隧洞设计规范》（SL 279—2016）限裂宽度计算公式透水衬砌配筋计算结果

钢筋的直径/m	钢筋的间距/m	钢筋的面积/mm²	脱开水头/MPa	衬砌与围岩接触面之间的水压力$ {p}_{2} $/MPa	钢筋应力/MPa	裂缝宽度/mm
0.020	0.200	1570.796	0.263	1.138	608.098	1.992
0.022	0.200	1900.664	0.267	1.134	516.325	1.520
0.025	0.200	2454.369	0.275	1.126	418.422	1.065
0.028	0.200	3078.761	0.284	1.117	350.858	0.782
0.030	0.200	3534.292	0.291	1.110	316.874	0.651
0.032	0.200	4021.239	0.299	1.103	289.206	0.549
0.036	0.200	5089.380	0.316	1.087	247.340	0.442
0.040	0.200	6283.185	0.337	1.068	217.603	0.414
0.020	0.100	3141.593	0.291	1.109	358.968	0.574
0.022	0.100	3801.327	0.303	1.097	314.452	0.450
0.025	0.100	4908.739	0.324	1.078	266.976	0.393
0.028	0.100	3141.593	0.350	1.056	234.094	0.366
0.030	0.100	3801.327	0.369	1.039	217.440	0.349
0.032	0.100	4908.738	0.390	1.022	203.771	0.333
0.036	0.100	6157.524	0.438	0.985	182.746	0.304
0.040	0.100	7068.583	0.495	0.944	167.350	0.279

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表 5 工程案例1最终配筋方案对比

规范	配筋方案	钢筋应力 /MPa	裂缝宽度 /mm
《水工混凝土结构设计规范》（SL 191—2008）	ϕ36@100	155.197	0.291
《水工隧洞设计规范》（SL 279—2016）	ϕ40@100	167.350	0.279
Z系数法	ϕ30@100	262.525	0.173
Frosch法	ϕ25@100	214.545	0.265
Broms-Lutz法	ϕ25@200	274.932	0.251

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表 6 工程案例2最终配筋方案对比

规范	配筋方案	钢筋应力 /MPa	裂缝宽度 /mm
《水工混凝土结构设计规范》（SL 191—2008）	ϕ40@100	142.002	0.284
《水工隧洞设计规范》（SL 279—2016）	ϕ40@100	181.325	0.298
Z系数法	ϕ36@200	287.680	0.239
Frosch法	ϕ28@100	237.806	0.294
Broms-Lutz法	ϕ30@100	282.616	0.205

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