基于分数阶导数的冻土–结构接触面剪切蠕变模型研究

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摘要在拱北隧道施工中首次采用的管幕冻结法暴露了设计阶段未能预见的施工期长期稳定性问题，涉及管幕冻土复合结构中冻土与结构接触面的剪切蠕变特性。目前尚缺乏针对冻土与结构接触面的蠕变模型来准确描述接触面的剪切蠕变特性。基于分数阶导数推导建立能够同时描述冻土与结构接触面在衰减蠕变、稳态蠕变和加速蠕变3个阶段力学行为的理论模型，该模型将Maxwell模型中的黏弹性部分替换为Abel黏壶元件，并融合一个由剪应力控制的蠕变加速元件；通过自主改装仪器，得到冻土与钢材接触面剪切蠕变试验结果；基于Python语言开发含分数阶的多参数同步最小二乘拟合程序，拟合对比各因素条件下冻土与结构接触面剪切蠕变试验曲线；最后，分析模型中应力控制加速元件参数敏感性，揭示加速指数N和分数阶阶数对加速蠕变阶段的影响规律。研究结果表明：(1) 分数阶Maxwell加速模型中分数阶导数明显改善蠕变曲线的非线性渐进过程，而剪应力控制加速元件准确地模拟加速蠕变阶段；(2) 与传统模型相比，在不同试验条件下分数阶Maxwell加速模型均展现了更高的适用性和精准性；(3) 蠕变模型中加速指数N越大，其加速效果越明显，速率也越快；随着分数阶阶数的增加，加速蠕变阶段所占的时间比例也随之增大。研究成果为描述管幕冻结工程、冻土区桩土相互作用等领域的蠕变力学行为数值模拟计算提供了理论基础。

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	邓声君1
	2
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	张金海1
	陈浩林1
	蒋刚1
	龚晓南2
	3

关键词 ：土力学, 管幕冻结法, 接触面, 剪切蠕变, 分数阶导数, Maxwell模型

Abstract：The freezing-sealing pipe roof method was firstly applied in the construction of the Gongbei Tunnel. However，the long-term stability issues during the construction period were not foreseen in the design phase. These issues involve the shear creep characteristics at the interface between the frozen soil and the structure within the pipe-roof frozen soil composite structure. Currently，there is a lack of creep models that accurately describe the shear creep characteristics at this interface between the frozen soil and the structure. A theoretical model based on fractional derivatives that can simultaneously describe the mechanical behavior at the interface between frozen soil and the structure during the attenuated，steady-state，and accelerated creep stages is derived. The model replaces the viscoelastic component of the Maxwell model with the Abel dashpot element and incorporates a creep acceleration element controlled by shear stress，then the shear creep test results of the interface between frozen soil and steel are obtained through tests. A least square fitting program incorporating fractional derivative is developed using Python，which adopted multi-parameter simultaneously. This program is used to fit the shear creep curves of the interface between frozen soil and the structure under various conditions. Finally，this paper analyzes the sensitivity of the parameters affected by the stress-controlled acceleration element within the model，revealing the influence of the acceleration index N and the fractional order on the accelerated creep stage. The research findings are demonstrated as follow：(1) The fractional derivative in the fractional-order Maxwell acceleration model significantly improves the nonlinear progression of the creep curve，and the shear stress-controlled acceleration element accurately simulates the accelerated creep stage. (2) The fractional-order Maxwell acceleration model shows higher applicability and precision compared to traditional models Under different experimental conditions. (3) Sensitivity analysis indicates that a larger acceleration index N results in more noticeable acceleration effects and a faster rate. As the fractional order increases，the proportion of time in the accelerated creep stage also grows. This study provides a theoretical foundation for numerical simulations of creep mechanical behavior in analogous freezing engineering such as pipe-roof freezing projects and pile-soil interactions.

Key words： soil mechanics freeze-sealing pipe roof method interface shear creep fractional derivative Maxwell creep model

引用本文:

邓声君1，2，3，张金海1，陈浩林1，蒋刚1，龚晓南2，3. 基于分数阶导数的冻土–结构接触面剪切蠕变模型研究[J]. 岩石力学与工程学报, 2024, 43(12): 3070-3080.
DENG Shengjun1，2，3，ZHANG Jinhai1，CHEN Haolin1，JIANG Gang1，GONG Xiaonan2，3. A shear creep model of the interface between frozen soil and structure based on fractional derivative. , 2024, 43(12): 3070-3080.

链接本文:

https://rockmech.whrsm.ac.cn/CN/Y2024/V43/I12/3070

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