{"title":"P波和SV波作用下深部锚杆支护隧道应力和位移的解析解","authors":"Gong Chen, Haitao Yu","doi":"10.1002/nag.70021","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Rockbolt support is one of the most commonly used reinforcement measures for rock tunnels. It is important to explore the effect of rockbolts on seismic design of tunnel structures, and therefore, a design method is required for the evaluation of such effect, which was, however, still vacant in current studies. In this paper, a novel analytical solution for the seismic response of deep tunnels with rockbolts support subjected to P and SV waves is presented. The rockbolts support region is assumed to be cylindrical and anisotropic based on the equivalent material method, and the ground and liner are considered homogenous, isotropic, and linear elastic. The general solutions for the response of a cylindrical anisotropic layer subjected to arbitrary dynamic loading are derived using generalized power series. The convergence and the linear independence of the solutions are proved. Then, the solutions for displacements and stresses of the tunnel liner are obtained by utilizing these proposed general solutions. The validity of the proposed solution is demonstrated by comparing its results and those from FEM. Parametric analysis is presented with the solution where the influences of the rockbolts length and modulus of the equivalent layer reinforced by the rockbolts support on seismic responses of deep tunnels are investigated.</p>\n </div>","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"49 15","pages":"3357-3374"},"PeriodicalIF":3.6000,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical Solution for Stresses and Displacements of Deep Tunnels With Rockbolts Support Subjected to P and SV Waves\",\"authors\":\"Gong Chen, Haitao Yu\",\"doi\":\"10.1002/nag.70021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>Rockbolt support is one of the most commonly used reinforcement measures for rock tunnels. It is important to explore the effect of rockbolts on seismic design of tunnel structures, and therefore, a design method is required for the evaluation of such effect, which was, however, still vacant in current studies. In this paper, a novel analytical solution for the seismic response of deep tunnels with rockbolts support subjected to P and SV waves is presented. The rockbolts support region is assumed to be cylindrical and anisotropic based on the equivalent material method, and the ground and liner are considered homogenous, isotropic, and linear elastic. The general solutions for the response of a cylindrical anisotropic layer subjected to arbitrary dynamic loading are derived using generalized power series. The convergence and the linear independence of the solutions are proved. Then, the solutions for displacements and stresses of the tunnel liner are obtained by utilizing these proposed general solutions. The validity of the proposed solution is demonstrated by comparing its results and those from FEM. Parametric analysis is presented with the solution where the influences of the rockbolts length and modulus of the equivalent layer reinforced by the rockbolts support on seismic responses of deep tunnels are investigated.</p>\\n </div>\",\"PeriodicalId\":13786,\"journal\":{\"name\":\"International Journal for Numerical and Analytical Methods in Geomechanics\",\"volume\":\"49 15\",\"pages\":\"3357-3374\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2025-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal for Numerical and Analytical Methods in Geomechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/nag.70021\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, GEOLOGICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical and Analytical Methods in Geomechanics","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nag.70021","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, GEOLOGICAL","Score":null,"Total":0}
Analytical Solution for Stresses and Displacements of Deep Tunnels With Rockbolts Support Subjected to P and SV Waves
Rockbolt support is one of the most commonly used reinforcement measures for rock tunnels. It is important to explore the effect of rockbolts on seismic design of tunnel structures, and therefore, a design method is required for the evaluation of such effect, which was, however, still vacant in current studies. In this paper, a novel analytical solution for the seismic response of deep tunnels with rockbolts support subjected to P and SV waves is presented. The rockbolts support region is assumed to be cylindrical and anisotropic based on the equivalent material method, and the ground and liner are considered homogenous, isotropic, and linear elastic. The general solutions for the response of a cylindrical anisotropic layer subjected to arbitrary dynamic loading are derived using generalized power series. The convergence and the linear independence of the solutions are proved. Then, the solutions for displacements and stresses of the tunnel liner are obtained by utilizing these proposed general solutions. The validity of the proposed solution is demonstrated by comparing its results and those from FEM. Parametric analysis is presented with the solution where the influences of the rockbolts length and modulus of the equivalent layer reinforced by the rockbolts support on seismic responses of deep tunnels are investigated.
期刊介绍:
The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.