Article(id=1273953249859244105, tenantId=1146029695717560320, journalId=1272209045839646724, issueId=1273953231114887613, articleNumber=null, orderNo=null, doi=10.20174/j.JUSE.2026.02.04, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1738771200000, receivedDateStr=2025-02-06, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1781663723673, onlineDateStr=2026-06-17, pubDate=1776614400000, pubDateStr=2026-04-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1781663723673, onlineIssueDateStr=2026-06-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1781663723673, creator=13701087609, updateTime=1781663723673, updator=13701087609, issue=Issue{id=1273953231114887613, tenantId=1146029695717560320, journalId=1272209045839646724, year='2026', volume='22', issue='2', pageStart='377', pageEnd='752', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1781663719203, creator=13701087609, updateTime=1781663760928, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1273953406235467954, tenantId=1146029695717560320, journalId=1272209045839646724, issueId=1273953231114887613, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1273953406235467955, tenantId=1146029695717560320, journalId=1272209045839646724, issueId=1273953231114887613, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=412, endPage=426, ext={EN=ArticleExt(id=1273953250140262475, articleId=1273953249859244105, tenantId=1146029695717560320, journalId=1272209045839646724, language=EN, title=Analytical Solution for Determining Plastic Zones around Shallow Twin-Circular Tunnels Based on the Schwarz Alternation Method, columnId=null, journalTitle=Chinese Journal of Underground Space and Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to investigate the plastic yielding mode of surrounding rock caused by the excavation of shallow twin tunnels, the displacement and additional surface force joint controlling the Schwarz alternation method and complex function method are adopted to solve the elastic stress function of surrounding rock of shallow twin circular tunnels through iterative cycles as an example. The expression of plastic stress components of surrounding rock is obtained based on Mohr-Coulomb failure criterion. The elastoplastic solution of the radius of the plastic zone is determined preferentially by using the stress continuity condition at the interface of the elastic-plastic zones around the shallow twin circular tunnels. The analytical solution for the distribution range of the plastic zones around the shallow twin circular tunnels is established, according to the interconversion relationship between polar coordinates and right-angle coordinates. The rationality and applicability of the analytical solution are verified by numerical simulation results and field measurement results of engineering application. The influence of the center spacing of the twin tunnels on the plastic zones around shallow twin circular tunnels are also analyzed. The results show that the analytical solution in this study can be used to solve the problem of predicting the distribution range of the plastic zones around shallow twin tunnels in actual engineering, and meets the requirement of 20% engineering accuracy, fits well with the numerical simulation results, and has a high calculation accuracy. The distribution range of the plastic zones around shallow twin circular tunnels are positively correlated with the center spacing s of the twin tunnels. Based on the distribution pattern of the plastic zone around shallow twin circular tunnels under the influence of this factor, when the plastic zone reaches the critical state of penetration, the reasonableness of the calculation results of the distribution range of the plastic zones is preliminarily judged. It provides theoretical guidance for similar tunnel engineering design calculation and deformation control of surrounding rock.

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为探究浅埋双线隧道开挖引起围岩塑性屈服模式，以浅埋双线圆形隧道为例，采用位移和附加面力联合控制Schwarz交替法和复变函数法，通过迭代循环求解浅埋双线圆形隧道围岩弹性应力函数，并基于Mohr-Coulomb屈服准则获得围岩塑性应力分量表达式，利用浅埋双线圆形隧道周围弹塑性区交界面上的应力连续性条件优先确定塑性区半径的弹塑性解，并根据极坐标与直角坐标相互转化关系建立浅埋双线圆形隧道周围塑性区分布范围的解析计算方法，通过数值模拟结果和现场实测结果分别验证本文解析计算方法的合理性和工程适用性，并分析双线隧道中心间距对浅埋双圆隧道周围塑性区的影响规律。结果表明：本文解析计算方法可用于解决实际工程中浅埋双线隧道周围塑性区分布范围的预测问题，且满足20%的工程精度要求，与数值模拟结果拟合良好，具有较高的计算精度；浅埋双线圆形隧道周围塑性区分布范围与双线隧道中心间距s呈正相关，可根据该因素影响下致使浅埋双线圆形隧道周围塑性区达到贯通的临界状态时的分布规律，初步判断塑性区分布范围计算结果的合理性。研究成果可为类似隧道工程设计和围岩变形控制提供理论指导。

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王超（1994—），男，河南郑州人，博士生，主要从事岩土与地下工程稳定性分析方法与加固关键技术的研究。E-mail: wangchao214801069@yeah.net

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王超（1994—），男，河南郑州人，博士生，主要从事岩土与地下工程稳定性分析方法与加固关键技术的研究。E-mail: wangchao214801069@yeah.net

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