基于瑞利-里兹法的岩土三棱柱堆积体的基底应力分布的研究

Study of stress distribution on base of geotechnical triangular prism by Rayleigh-Ritz method

对岩土三棱柱堆积体的基底应力分布进行了研究,在基底应力的理论解难以求得的情形下,基于瑞利-里兹法求解出基底应力分布的近似解,并具体计算且对比了不同坡比、泊松比、基底边界条件下基底应力分布的变化,得出如下结论:基底法向应力存在应力凹陷现象,坡度越陡,应力凹陷程度越大,底边有约束时应力凹陷程度更明显;泊松比对基底法向应力的分布几乎无影响,泊松比主要影响基底切向应力分布的形态,且泊松比越大,基底切向应力值越大;坡比改变基底切向应力的最大值及其所处位置,坡比越大,基底切向应力值越大,且基底切向应力最大值距离基底中心越远。

The basal stress of geotechnical triangular prism is studied. While it is impossible to get the analytical solution of basal stress distribution of geotechnical triangular prism, the approximate solution of basal stress distribution of geotechnical triangular prism is got with the Rayleigh-Ritz method. By comparison with different solutions of different slope ratios, different Poisson’s ratios, and different boundary conditions at the base, the results are drawn as follows. There is depression of basal normal stress on the base of geotechnical triangular prism. The steeper the slope is, the more depression of basal normal stress is. Much more depression occurs with the boundary condition of constraints on the base. Meanwhile, the value of Poisson’s ratio has little impact on the distribution of basal normal stress. The Poisson’s ratio mainly impacts the distribution of basal shear stress. The larger the value of Poisson’s ratio is, the larger the basal shear stress is. The slope ratio has large influence on the position and value of the maximum basal shear stress. The larger the slope ratio is, the larger the basal shear stress is, and the larger distance between the maximum basal shear stress and center of base is.