Elastoplastic stress analysis of multi-refrigerant combined heterogeneous artificial frozen wall

Authors

WANG Bin, School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China; Postdoctoral Research Station , China Coal Mine Construction Group Co., Ltd., Hefei 230091, China; Henan Key Laboratory of Underground Engineering and Disaster Control, Henan Polytechnic University, Jiaozuo 454000, ChinaFollow
LIANG Xiuling, School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China
ZHANG Zihao, School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China
CAI Haibing, School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China
RONG Chuanxin, School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China

Abstract

Objective Affected by the temperature difference of the refrigerant and the distance difference between the frozen formation and the freezing pipes, the heterogeneity of the multi-refrigerant combined double-row-pipe frozen wall is more significant. In order to evaluate the safety of such frozen wall reasonably, the elastic plastic stress analysis should be carried out for the artificial frozen wall with multi-refrigerant considering the heterogeneity. Methods The frozen wall at 1/4 pipe distance was selected as the characteristic section. Then, the temperature distribution curve on this section was equivalently converted to three linear functions, and the frozen wall was regarded as a heterogeneous material that changes linearly with temperature. On this basis, the analytical expression of plastic-elastic stress of multi-refrigerant combined double-row-pipe heterogeneous frozen wall was derived according to four kinds of frozen soil yield criteria. Based on the analytical expression, the mechanical characteristics of the multi-refrigerant frozen wall were calculated, and the calculated results were compared with those of the homogeneous frozen wall. Results and Conclusions The study indicates that: (1) The radial stress increases with the increase of the relative radius r, and the circumferential stress shows different trends in different frozen intervals (Ⅰ, Ⅱ, Ⅲ) in the brine-CO₂ combined double-row-pipe frozen wall. (2) Based on the calculation theory of the homogeneous frozen wall, the maximum circumferential stress appears on the inner side of the frozen wall in the elastic limit state, at the elastic-plastic interface of the frozen wall in the elastic-plastic state, and at the outermost side of the frozen wall in the plastic limit state . However, based on the calculation theory of heterogeneous frozen wall, the maximum circumferential stress always occurs at the partition boundary of frozen wall (r=2). (3) With consideration to the heterogeneity, the elastic ultimate bearing capacity of the frozen wall decreases by 1.8%, while the plastic ultimate bearing capacity increases by 8.1%. In the plastic-elastic state, the heterogeneous frozen wall has higher bearing capacity compared with that in the same relative radius of plastic zone, and this phenomenon becomes more obvious with the increase of the relative radius of the plastic zone. The research results have important reference value for the design of multi-refrigerant combined freezing curtain in water-rich strata.

Keywords

artificial ground freezing method, double-row-pipe frozen wall, multi-refrigerant combined freezing curtain, heterogeneity, yield criteria, elastic-plastic analysis

DOI

10.12363/issn.1001-1986.24.05.0337

Recommended Citation

WANG Bin, LIANG Xiuling, ZHANG Zihao, et al. (2024) "Elastoplastic stress analysis of multi-refrigerant combined heterogeneous artificial frozen wall," Coal Geology & Exploration: Vol. 52: Iss. 9, Article 11.
DOI: 10.12363/issn.1001-1986.24.05.0337
Available at: https://cge.researchcommons.org/journal/vol52/iss9/11

Reference

[1] 荣传新，王彬，程桦，等. 大流速渗透地层人工冻结壁形成机制室内模型试验研究[J]. 岩石力学与工程学报，2022，41(3)：596−613.

RONG Chuanxin，WANG Bin，CHENG Hua，et al. Laboratory model test study on formation mechanisms of artificial frozen walls in permeable strata with high seepage velocity[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(3)：596−613.

[2] WANG Bin，RONG Chuanxin，CHENG Hua，et al. Experimental investigation on heat transfer law of multiple freezing pipes in permeable stratum with high seepage velocity[J]. International Journal of Heat and Mass Transfer，2022，182：121868.

[3] 王彬，荣传新，陆鹏举. 大流速渗透地层人工冻结壁形成机理及其力学特性研究[M]. 中国矿业大学出版社，2023.

[4] 荣传新，王彬. 立井冻结法凿井技术[M]. 中国矿业大学出版社，2023.

[5] 杨哲，蔡海兵，王彬，等. 高流速富水砂层地铁隧道液氮冻结温度场演化规律研究[J/OL]. 铁道科学与工程学报，https://doi.org/10.19713/j.cnki.43-1423/u.T20240484.

YANG Zhe，CAI Haibing，WANG Bin，et al. Study on the evolution of liquid nitrogen freezing temperature field in high velocity water-rich sand layer metro tunnel[J/OL]. Journal of Railway Science and Engineering，https://doi.org/10.19713/j.cnki.43-1423/u.T20240484.

[6] 段寅，荣传新，蔡海兵，等. 管幕冻结隧道“顶管-冻土” 复合结构力学特性试验研究[J]. 煤田地质与勘探，2022，50(12)：159−169.

DUAN Yin，RONG Chuanxin，CAI Haibing，et al. Experimental research on mechanical properties of“jacked pipe-frozen soil” composite structure in freeze-sealing pipe roof tunnel[J]. Coal Geology & Exploration，2022，50(12)：159−169.

[7] 黄诗清，荣传新，龙伟，等. 祁南矿东风井冻结温度场时空演化规律分析[J]. 煤田地质与勘探，2022，50(8)：125−133.

HUANG Shiqing，RONG Chuanxin，LONG Wei，et al. Analysis on spatio-temporal evolution law of freezing temperature field in eastern shaft of Qinan Coal Mine[J]. Coal Geology & Exploration，2022，50(8)：125−133.

[8] 胡向东，舒畅，佘思源. 均布荷载下抛物线形FGM冻结壁弹塑性解[J]. 煤炭学报，2012，37(3)：379−384.

HU Xiangdong，SHU Chang，SHE Siyuan. Elastic-plastic analytical solution for functionally graded material frozen soil wall with parabolic property under uniform load[J]. Journal of China Coal Society，2012，37(3)：379−384.

[9] 胡向东，舒畅. 考虑FGM特性的双排管竖井冻结壁应力场分析[J]. 工程力学，2014，31(1)：145−153.

HU Xiangdong，SHU Chang. Stress field analysis of functionally graded material frozen soil wall in double-row-pipe shaft freezing[J]. Engineering Mechanics，2014，31(1)：145−153.

[10] 荣传新，王彬，彭世龙，等. 基于DP准则的功能梯度材料冻结壁受力分析[J]. 广西大学学报(自然科学版)，2015，40(6)：1339−1344.

RONG Chuanxin，WANG Bin，PENG Shilong，et al. Study on mechanical characteristics of functionally graded material frozen soil wall basing on Druker-Prager strength criterion[J]. Journal of Guangxi University (Natural Science Edition)，2015，40(6)：1339−1344.

[11] 王彬，荣传新，程桦，等. 基于DP准则双排管冻结壁力学特性理论分析[J]. 科学技术与工程，2016，16(25)：44−50.

WANG Bin，RONG Chuanxin，CHENG Hua，et al. Theoretical analysis of the Double-row-pipe frozen soil wall basing on Druker-Prager strength criterion[J]. Science Technology and Engineering，2016，16(25)：44−50.

[12] 王彬，荣传新，程桦. 三排管非均质冻结壁弹塑性分析[J]. 长江科学院院报，2019，36(8)：104−111.

WANG Bin，RONG Chuanxin，CHENG Hua. Elastic and plastic analysis of heterogeneous frozen soil wall of triple-row piped freezing[J]. Journal of Yangtze River Scientific Research Institute，2019，36(8)：104−111.

[13] 曹雪叶. 人工冻土粘弹塑性蠕变本构理论及冻结壁力学特性研究[D]. 西安：长安大学，2017.

CAO Xueye. Study on viscoelastic-plastic creep constitutive theory of artificial frozen soil and mechanical properties of frozen wall[D]. Xi’an：Changan University，2017.

[14] 曹雪叶，赵均海，张常光. 基于三剪统一强度准则的厚壁圆筒自增强分析[J]. 中国机械工程，2017，28(1)：75−81.

CAO Xueye，ZHAO Junhai，ZHANG Changguang. Autofrettage analysis of thick-walled cylinder based on triple-shear unified strength criterion[J]. China Mechanical Engineering，2017，28(1)：75−81.

[15] 曹雪叶，赵均海，张常光. 基于统一强度理论的冻结壁弹塑性应力分析[J]. 岩土力学，2017，38(3)：769−774.

CAO Xueye，ZHAO Junhai，ZHANG Changguang. Elastoplastic stress analysis of frozen soil wall based on unified strength theory[J]. Rock and Soil Mechanics，2017，38(3)：769−774.

[16] 杨维好，杨志江，韩涛，等. 基于与围岩相互作用的冻结壁弹性设计理论[J]. 岩土工程学报，2012，34(3)：156−159.

YANG Weihao，YANG Zhijiang，HAN Tao，et al. Elastic design theory of frozen soil wall based on interaction between frozen soil wall and surrounding rock[J]. Chinese Journal of Geotechnical Engineering，2012，34(3)：156−159.

[17] 杨维好，杜子博，杨志江，等. 基于与围岩相互作用的冻结壁塑性设计理论[J]. 岩土工程学报，2013，35(10)：1857−1862.

YANG Weihao，DU Zibo，YANG Zhijiang，et al. Plastic design theory of frozen soil wall based on interaction between frozen soil wall and surrounding rock[J]. Chinese Journal of Geotechnical Engineering，2013，35(10)：1857−1862.

[18] 杨维好，杨志江，柏东良. 基于与围岩相互作用的冻结壁弹塑性设计理论[J]. 岩土工程学报，2013，35(1)：175−180.

YANG Weihao，YANG Zhijiang，BAI Dongliang. Elastic-plastic design theory of frozen soil wall based on interaction between frozen wall and surrounding rock[J]. Chinese Journal of Geotechnical Engineering，2013，35(1)：175−180.

[19] 王彬，荣传新，程桦. 考虑与周围土体相互作用的非均质冻结壁力学特性分析[J]. 煤炭学报，2017，42(增刊2)：354−361.

WANG Bin，RONG Chuanxin，CHENG Hua. Stress analysis of heterogeneous frozen wall considering interaction with surrounding soil[J]. Journal of China Coal Society，2017，42(Sup.2)：354−361.

[20] 王彬，荣传新，程桦. 定向渗流诱导的非对称冻结帷幕稳态温度场解析解[J]. 工程科学与技术，2022，54(4)：76−87.

WANG Bin，RONG Chuanxin，CHENG Hua. Analytical solution of steady-state temperature field of asymmetric frozen wall induced by directional seepage[J]. Advanced Engineering Sciences，2022，54(4)：76−87.

[21] 王彬，荣传新，程桦，等. 定向渗流诱导的非均质冻结壁力学特性分析[J]. 冰川冻土，2022，44(3)：1011−1020.

WANG Bin，RONG Chuanxin，CHENG Hua，et al. Analysis of mechanical properties of heterogeneous frozen wall induced by directional seepage[J]. Journal of Glaciology and Geocryology，2022，44(3)：1011−1020.

[22] 袁杰. 双排孔液氮盐水联合冻结方案优化研究[D]. 徐州：中国矿业大学，2023.

YUAN Jie. Study on optimization of combined freezing scheme of liquid nitrogen and brine with double rows of holes[D]. Xuzhou：China University of Mining and Technology，2023.

[23] 叶庆. 斜井液氮盐水联合冻结温度场研究[D]. 徐州：中国矿业大学，2015.

YE Qing. Study on combined freezing temperature field of liquid nitrogen and salt water in inclined shaft[D]. Xuzhou：China University of Mining and Technology，2015.

[24] 权晓甜. 液氮盐水联合冻结叠加温度场的发展规律研究[D]. 徐州：中国矿业大学，2021.

QUAN Xiaotian. Study on the development law of combined freezing and superposition temperature field of liquid nitrogen and brine[D]. Xuzhou：China University of Mining and Technology，2021.

[25] 董涛，廖先斌. 多冷媒联合冻结技术在盾构抢险中的应用[J]. 隧道建设(中英文)，2024，1–6.

DONG Tao，LIAO Xianbin. Application of multi-refrigerant combined freezing technology in shield tunnel rescue[J]. Tunnel Construction (English and Chinese)，2024，1–6.

[26] LI Yuanlu，XIN Gongming，YUAN Baoqiang，et al. Experimental investigation on natural circulation heat transfer of supercritical CO₂ in a closed loop[J]. International Journal of Heat and Mass Transfer，2023，200：123503.

[27] DENG Bili，CHEN Lin，ZHANG Xinrong，et al. The flow transition characteristics of supercritical CO₂ based closed natural circulation loop (NCL) system[J]. Annals of Nuclear Energy，2019，132：134−148.

[28] HU Xiangdong，SHE Siyuan，YU Ruizhi. Average temperature calculation for straight single-row-piped frozen soil wall[J]. Sciences in Cold and Arid Regions，2011，3(2)：124−131.

[29] 胡向东，刘阳辉，洪泽群，等. 直线形单排管冻土帷幕平均温度计算[J]. 煤炭学报，2019，44(4)：1092−1097.

HU Xiangdong，LIU Yanghui，HONG Zequn，et al. Calculation of average temperature of frozen soil wall by single row-piped freezing[J]. Journal of China Coal Society，2019，44(4)：1092−1097.

[30] 胡向东，赵飞，佘思源，等. 直线双排管冻结壁平均温度的等效抛物弓形模型[J]. 煤炭学报，2012，37(1)：28−32.

HU Xiangdong，ZHAO Fei，SHE Siyuan，et al. Equivalent parabolic arch method of average temperature calculation for straight double-row-pipe frozen soil wall[J]. Journal of China Coal Society，2012，37(1)：28−32.

[31] 胡向东，任辉. 3排管冻结梯形–抛物弓叠合等效温度场模型和平均温度[J]. 煤炭学报，2014，39(1)：78−83.

HU Xiangdong，REN Hui. A trapezoidal-parabolic arch superimposed equivalent temperature field model and its average temperature formula for triple-row-pipe freezing[J]. Journal of China Coal Society，2014，39(1)：78−83.

[32] 梁沈伟，王彬，荣传新，等. 卸载状态下非均质圆形寒区隧道围岩弹塑性统一解[J]. 冰川冻土，2024，46(2)：650−661.

LIANG Shenwei，WANG Bin，RONG Chuanxin，et al. Elastoplastic unified solutions of the non-homogeneous surrounding rock of circular tunnels in cold regions under unloading state[J]. Journal of Glaciology and Geocryology，2024，46(2)：650−661.

[33] 徐芝纶. 弹性力学[M]. 北京：人民教育出版社，2004.

[34] 郑颖人，孔亮. 岩土塑性力学[M]. 2版. 北京：中国建筑工业出版社，2019.

[35] 汪仁和，李栋伟，王秀喜. 摩尔–库仑强度准则计算冻结壁应力场和位移场[J]. 工业建筑，2005，35(10)：40−42.

WANG Renhe，LI Dongwei，WANG Xiuxi. Calculating frozen wall stress and displacement fields by Mohr-coulomb strength criterion[J]. Industrial Construction，2005，35(10)：40−42.