基于应变梯度理论的砂土中扩孔闭合解  

Closed-form solution for cavity expansion in sand based on strain gradient plasticity

作　　者：周航[1,2] 吴晗 曾少华 ZHOU Hang;WU Han;ZENG Shao-hua(Key Laboratory of New Technology for Construction of Cities in Mountain Area,Chongqing University,Chongqing 400045,China;College of Civil Engineering,Chongqing University,Chongqing 400045,China)

机构地区：[1]重庆大学山地城镇建设与新技术教育部重点实验室,重庆400045 [2]重庆大学土木工程学院,重庆400045

出　　处：《岩土力学》2023年第3期757-770,共14页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.51978105,No.52027812)。

摘　　要：扩孔理论作为一种简单适用的理论工具,目前已经被广泛用于隧道、土工原位测试、桩基和锚定板承载力设计等岩土工程问题的研究中。现有扩孔理论无法考虑土体小半径扩孔的尺寸效应问题,以砂土中的圆柱孔和球孔扩张为研究对象,基于应变梯度塑性理论,引入能够考虑土体尺寸效应的力学参数——土体特征长度l并给出解释,同时考虑土体大变形特性,推导出能够考虑土体微观结构尺寸效应的扩孔问题闭合解。通过将土体归一化特征长度l/a_(0)(a_(0)为初始圆孔半径)退化为0(即不考虑尺寸效应),将该解退化为经典不考虑尺寸效应的扩孔解答,验证了本文理论解答的正确性。同时开展参数分析,详细探讨了土体归一化特征长度l/a_(0)、摩擦系数μ、剪胀系数β、形状系数k对压力扩张关系、孔周应力分布、孔周应变梯度、极限扩孔应力的影响规律。最后将提出的理论解答应用到微型圆锥贯入试验(micro cone penetration test,简称MCPT)等实际问题中,提出了MCPT贯入阻力的计算公式,通过跟既有试验结果对比,验证了本文理论的适用性。As a simple and applicable theoretical tool,cavity expansion theory has been widely used in the research of geotechnical engineering problems such as tunnel,geotechnical in-situ test,bearing capacity design of pile foundation and anchor plate.The existing expansion theory cannot consider the size effect of soil with small radius expansion.This paper takes the expansion of cylindrical and spherical cavity in sand as the research object to investigate this issue.Based on the strain gradient plasticity theory,this paper introduces and explains the mechanical parameter that can consider the size effect of soil,i.e.,soil characteristic length l;meanwhile,considering the large deformation characteristics of soil,a closed solution of cavity expansion that can take the size effect of soil microstructure into account is derived.The correctness of the theoretical solution in this paper is verified by reducing the normalized characteristic length of soil l/α_(0)(α_(0)is the initial radius of circular hole)to 0(i.e.,without considering the size effect),and thus the solution is reduced to the classical expansion solution without considering the size effect.Then,the effects of normalized characteristic length,friction coefficient,dilatancy coefficient and shape coefficient of soil on pressure expansion relationship,stress distribution around hole,strain gradient around hole and ultimate expansion stress are discussed in detail.Finally,the theoretical solution proposed in this paper is applied to the practical problems such as micro cone penetration test(MCPT),and the formula for calculating the penetration resistance of MCPT is proposed.By comparing with the existing test results,the applicability of this solution is verified.

关 键 词：应变梯度理论 小孔扩张 尺寸效应 MCPT试验 

分 类 号：TU441[建筑科学—岩土工程]