分数阶黏弹性饱和地基与水平受荷群桩的相互作用分析

Analysis of interaction between fractional viscoelastic saturated soils and laterally loaded pile groups

引入Abel黏壶,对经典的三元件Merchant模型进行改进,获得可以更好地描述地基黏弹性特征的分数阶Merchant模型;运用有限单元法,将群桩离散为单桩和桩单元,通过Timoshenko梁模型模拟桩单元,组装获得群桩的总刚度矩阵方程;根据地基与群桩相互作用的耦合方程和群桩承台的受力平衡与位移协调条件,推导得到水平受荷群桩各单桩桩顶剪力与承台位移的矩阵解答;结合李氏比拟法与Laplace逆变换,最终实现对分数阶黏弹性饱和地基与水平受荷群桩相互作用问题的求解;以一组蠕变试验数据为例,简要介绍在已知地基蠕变曲线的条件下,获得其对应模型黏弹性参数的具体方法;通过与已发表成果以及ABAQUS数值算例对比,验证解答的正确性,并设计算例讨论地基黏弹性参数对群桩受力与变形的影响规律,结果表明:随着地基流变的发展,角桩与中心桩的内力差距逐渐缩小,并趋于稳定。

The Abel dashpot is introduced to improve the classical three-parameter Merchant model, and a fractional Merchant model which can better describe the viscoelastic characteristics of soils is obtained. With the help of finite element method, the pile group is discretized into single piles and pile elements. The total stiffness matrix equation of the pile group can be obtained by assembling the pile elements simulated by the Timoshenko beam model. According to the interaction equation between soils and the pile group, and the equilibrium condition and the compatibility condition of the pile cap, the matrix solution of the shear force at the top of the single pile and the displacement of the pile cap is deduced. Combined with the elastic-viscoelastic correspondence principle and the Laplace inverse transformation, the problem of the interaction between fractional viscoelastic saturated soils and laterally loaded pile groups is finally solved. Taking a set of creep test data as an example, this paper briefly introduces the specific method to obtain the viscoelastic parameters of the fractional model through the creep curve. The correctness of the proposed solution is verified by comparing with the published results and ABAQUS numerical examples. Additionally, several examples are designed to discuss the effects of soil’s viscoelasticity parameters on the stress and deformation of the pile group, which shows that with the development of soil’s rheology,the internal force gap between corner piles and central piles gradually shrinks and tends to be stable.