两向不等压圆形孔口压缩与扩张问题的塑性区半径统一解  

Unified solution of plastic zone radius for compression and expansion of circular hole under two-dimensional unequal pressure stress field

作　　者：于旭光 郑宏[2] YU Xuguang;ZHENG Hong(Tangshan Polytechnic College,Tangshan 063299,Hebei,China;School of Civil Engineering,Chang′an University,Xi′an 710061,Shaanxi,China)

机构地区：[1]唐山工业职业技术学院,河北唐山063299 [2]长安大学建筑工程学院,陕西西安710061

出　　处：《水利水电技术（中英文）》2023年第7期193-204,共12页Water Resources and Hydropower Engineering

基　　金：国家自然科学基金项目(50678025)。

摘　　要：【目的】在地下工程中,隧道或水平定向钻井过程中的最大泥浆压力分析等所处真实应力场常为远处两向不等压应力场。为了求解两向不等压应力场下圆形孔口压缩和扩张问题的统一解析解,【方法】基于统一强度理论和弹脆塑性模型,借鉴鲁宾涅特解的求解方法,推导了两向不等压圆形孔口压缩和扩张问题的塑性区半径统一解,并与复变函数解、摄动解进行了对比,最后分析了各因素对塑性区半径的影响以及在实际工程中的应用。【结果】结果显示:当两向为不等压应力场时,弹塑性交界线均呈现类椭圆形状,对于压缩问题,类椭圆长轴方向与两向不等压应力场较小值处一致,并且弹塑性交界线在极角0°~90°范围内分成两段,在极角0°~30°范围内,弹塑性交界线随两向不等压应力场的应力比增加水平向左移动,在30°~90°范围内,弹塑性交界线随两向不等压应力场的应力比增加竖直向上移动,而对于扩张问题则相反;对于压缩问题,支护力、中间主应力、残余黏聚力和残余内摩擦角对塑性区半径影响显著,而对于扩张问题,扩孔压力、中间主应力、残余内摩擦角对塑性区半径影响显著,残余黏聚力对塑性区半径几乎无影响。【结论】在实际工程分析中,应充分考虑两向不等压应力场、中间主应力和弹脆塑性模型的影响,并且采用弹脆塑性模型比理想弹塑性模型计算的塑性区半径大,更适合岩土类材料弹塑性分析。[Objective]In underground engineering,the real stress field of tunnel or maximum mud pressure analysis in horizontal directional drilling was usually the distant two-dimensional unequal pressure stress field.In order to solve the unified analytical solution for compression and expansion of a circular hole under two-dimensional unequal pressure stress field,[Methods]the unified solution for plastic zone radius of the compression and expansion of a circular hole under two-dimensional unequal pressure was derived by referring to the solution method of Rubin′s solution based on the unified strength theory and elastic-brittle-plastic model,and compared with the complex function solution and perturbation solution.Finally,the influence of various factors on the plastic zone radius and its application in practical engineering were analyzed.[Results]The result show that the elastoplastic boundary line is ellipse-like when the two directions are unequal compressive stress fields.For the compression problem,the ellipse-like long axis direction is consistent with the smaller value of the two directions unequal compressive stress field,and the elastoplastic boundary line is divided into two sections in the polar angle range of 0°~90°.In the polar angle range of 0°~30°,the elastoplastic boundary line moves horizontally to the left with the increase of the stress ratio of the two directions unequal compressive stress field,and in the range of 30°~90°,the elastoplastic boundary line moves vertically upward with the increase of the stress ratio of the two directions unequal compressive stress field,but for the expansion problem,it is opposite;For compression problems,support force,intermediate principal stress,residual cohesion and residual internal friction angle have significant effects on the radius of plastic zone,while for expansion problems,reaming pressure,intermediate principal stress and residual internal friction angle have significant effects on the radius of plastic zone,while residual cohesion has almost no e

关 键 词：两向不等压应力场 统一强度理论 弹脆塑性模型 鲁宾涅特解 中间主应力 

分 类 号：TU452[建筑科学—岩土工程]