發(fā)布時(shí)間：2018-04-26 03:09

  本文選題：任意荷載 + 分?jǐn)?shù)階導(dǎo)數(shù)��； 參考：《巖土工程學(xué)報(bào)》2017年10期

【摘要】：將分?jǐn)?shù)階導(dǎo)數(shù)理論引入Kelvin Voigt模型,來描述黏彈性飽和土體的力學(xué)行為。對(duì)飽和土體一維固結(jié)方程和分?jǐn)?shù)階導(dǎo)數(shù)Kelvin Voigt本構(gòu)方程實(shí)施Laplace變換,聯(lián)立求解得到變換域內(nèi)有效應(yīng)力和沉降的解析解。采用Crump方法實(shí)現(xiàn)Laplace數(shù)值反演,獲得了任意荷載情況下物理空間內(nèi)一維固結(jié)問題的半解析解。并將指數(shù)荷載情況下分?jǐn)?shù)階導(dǎo)數(shù)模型退化到黏彈性情形,結(jié)果與已有文獻(xiàn)解析解相同,驗(yàn)證了本研究提出任意荷載情況下分?jǐn)?shù)階導(dǎo)數(shù)黏彈性解的可靠性。最后,分析了相關(guān)參數(shù)對(duì)固結(jié)沉降的影響。研究表明,任意荷載情形下分?jǐn)?shù)階導(dǎo)數(shù)黏彈性飽和土體一維固結(jié)發(fā)展過程與黏滯系數(shù)和分?jǐn)?shù)階次有關(guān),分?jǐn)?shù)階次越大,固結(jié)沉降發(fā)展越快;黏滯系數(shù)越大,固結(jié)沉降變化越慢;荷載變化趨勢(shì)與由荷載參數(shù)變化引起的沉降變化規(guī)律是一致的,且最終沉降量一致。本研究有助于深入認(rèn)識(shí)分?jǐn)?shù)階黏彈性飽和土體的固結(jié)行為。
[Abstract]:The fractional derivative theory is introduced into the Kelvin Voigt model to describe the mechanical behavior of viscoelastic saturated soil. The one-dimensional consolidation equation of saturated soil and the fractional derivative Kelvin Voigt constitutive equation are transformed by Laplace transformation, and the analytical solutions of effective stress and settlement in the transform domain are obtained by simultaneous solution. The Crump method is used to realize the Laplace numerical inversion, and the semi-analytical solution of one-dimensional consolidation problem in physical space under arbitrary loads is obtained. The fractional derivative model under exponential load is reduced to the viscoelastic case, and the result is the same as the analytical solution in previous literatures, which verifies the reliability of the proposed fractional derivative viscoelastic solution under arbitrary loads. Finally, the influence of relevant parameters on consolidation settlement is analyzed. The results show that the development of one-dimensional consolidation of fractional derivative viscoelastic saturated soil under arbitrary loads is related to the viscosity coefficient and fractional order. The larger the fractional order, the faster the consolidation settlement develops, the larger the viscosity coefficient, the slower the consolidation settlement changes. The variation trend of load is consistent with the law of settlement caused by the change of load parameters, and the final settlement is the same. This study is helpful to understand the consolidation behavior of fractional viscoelastic saturated soil.
【作者單位】： 上海大學(xué)土木工程系;上海工程技術(shù)大學(xué)城市軌道交通學(xué)院;上海工程技術(shù)大學(xué)機(jī)械工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金項(xiàng)目(11672172)
【分類號(hào)】：TU43

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