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在竖向荷载和切向荷载共同作用下,求解了具有下卧基岩的横观各向同性土的Biot固结问题。首先,基于Biot固结理论得到控制方程,同时引入3个状态变量;然后,对时间t进行Laplace变换和对半径r进行Hankel变换。利用Laplace-Hankel联合积分变换求解状态方程,得到交通荷载作用下横观各向同性土骨架位移、孔隙水压力等的一般积分形式解。结合算例验证了该方法的正确性,并分析了切向荷载和竖向荷载共同作用下对横观各向同性土层沉降和孔压的影响,可以发现切向荷载和竖向荷载共同作用所产生的前期沉降明显小于竖向荷载单独作用的情况。为了更好地模拟实际情况,竖向荷载还采用正弦循环荷载。在循环荷载作用下,沉降变化周期滞后于荷载周期。
Under the joint action of vertical load and tangential load, the Biot consolidation problem of transversely isotropic soils with underlying bedrock is solved. First, the governing equations are obtained based on Biot’s consolidation theory, and three state variables are introduced. Then, Laplace transform is performed on time t and Hankel transform is performed on radius r. The Laplace-Hankel joint integral transform is used to solve the equation of state, and the general integral form solution to the displacement of skeletally isotropic soil and pore water pressure under traffic load is obtained. The correctness of this method is verified by an example and the influence of tangential and vertical loads on the settlement and pore pressure of transversely isotropic soils is analyzed. It can be found that the tangential and vertical loads act together The resulting pre-settlement is significantly less than the vertical load acting alone. In order to better simulate the actual situation, the vertical load is also used sinusoidal cyclic load. Under cyclic loading, the period of sedimentation change lags behind the load cycle.