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 引用本文: 艾智勇, 王禾, 慕金晶. 层状分数阶黏弹性饱和地基与梁共同作用的时效研究[J]. 力学学报, 2021, 53(5): 1402-1411.
Ai Zhiyong, Wang He, Mu Jinjing. TIME-DEPENDENT ANALYSIS OF THE INTERACTION BETWEEN MULTILAYERED FRACTIONAL VISCOELASTIC SATURATED SOILS AND BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1402-1411.
 Citation: Ai Zhiyong, Wang He, Mu Jinjing. TIME-DEPENDENT ANALYSIS OF THE INTERACTION BETWEEN MULTILAYERED FRACTIONAL VISCOELASTIC SATURATED SOILS AND BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1402-1411.

## TIME-DEPENDENT ANALYSIS OF THE INTERACTION BETWEEN MULTILAYERED FRACTIONAL VISCOELASTIC SATURATED SOILS AND BEAMS

• 摘要: 饱和地基与梁共同作用问题的研究在力学领域及工程界都具有重要意义. 采用分数阶Merchant模型研究饱和地基的流变固结, 该模型比常用整数阶黏弹性模型更能精确反映地基的时变特征. 基于层状正交各向异性黏弹性饱和地基的固结解答, 采用有限元法与边界元法耦合的方法, 研究梁与分数阶黏弹性饱和地基的共同作用问题. 依据Timoshenko梁理论将梁离散为若干单元, 进而得到梁的总刚度矩阵方程; 将黏弹性地基固结问题的精细积分解答作为边界积分的核函数, 采用边界元法建立地基柔度矩阵方程; 结合梁与地基接触面的位移协调条件以及力的平衡条件, 通过有限元法与边界元法的耦合, 最终求得层状分数阶黏弹性饱和地基与Timoshenko梁共同作用的解答. 将本文地基退化为Kelvin地基进行计算, 并与已有文献中的算例进行对比, 二者具有很好的一致性. 在此基础上, 探讨分数阶次和地基成层性对梁与黏弹性饱和地基共同作用的影响. 结果表明: 分数阶次高的黏弹性饱和地基的固结速率明显更快; 对于层状地基, 加固表层土体能有效控制地基整体沉降, 并减小差异沉降. 实际工程中, 应充分考虑饱和地基流变及土体分层性的影响, 以准确分析梁与地基的共同作用过程.

Abstract: The study of the interaction between beams and saturated soils is of great significance in both mechanics and engineering fields. In this paper, the fractional Merchant model is adopted to solve the rheological consolidation of saturated soils, which can simulate the time-depending characteristics of the soils more accurately than the common integer order viscoelastic models. Based on the solution of consolidation for multilayered cross-anisotropic viscoelastic saturated soils, the finite element method (FEM) and the boundary element method (BEM) are coupled to investigate the interaction between beams and fractional viscoelastic saturated soils. The beam is discretized into a number of elements according to the Timoshenko beam theory, and then the global stiffness matrix equation of the beam is obtained. The precise integration solution of the viscoelastic soils is considered as the kernel function of the boundary integral, and the flexibility matrix equation of soils is established by the BEM. Finally, by coupling the FEM and the BEM, the solution of the interaction between multilayered fractional viscoelastic saturated soils and the Timoshenko beam is derived by introducing the displacement coordination condition and equilibrium condition for forces between them. The soil model adopted in this study is degenerated into the Kelvin model, and the results obtained are compared with those in the existing literature, which shows a good consistency. On this basis, the effects of the fractional order and stratification of soils on the interaction between beams and viscoelastic soils are discussed. Numerical results show that: the consolidation velocity of viscoelastic saturated soils with higher fractional order is obviously faster; for layered soils, the reinforcement of topsoil can effectively control the ground settlement and reduce the differential settlement. In practical engineering, the effects of rheology of saturated soils and soil stratification should be well considered to analyze the interaction between beams and soils more accurately.

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