循环荷载下双曲线模型修正土体一维固结解

Solution for one-dimensional consolidation based on hyperbola model under cyclic loading

假定土体的应力-应变关系满足双曲线模型、渗透系数的降低与压缩系数的减小成正比以及初始有效应力沿深度均匀分布,推导出任意荷载下单层地基的非线性一维固结方程。结合具体的定解条件采用分离变量法求出土体有效应力的通解,并进一步求出超静孔隙水压力、按沉降定义的平均固结度Us以及按孔隙水压力定义的平均固结度Up的通解。根据通解求出梯形低频循环荷载作用下的解,并找出循环荷载作用下土体固结性状的影响因素。基于循环荷载作用下的解,采用FORTRAN语言编制了计算程序,计算并分析考虑土体本构关系非线性时的固结性状,以及反映土体本构特征的参数E和n对固结性状的影响。计算结果表明:①Us稍大于Up;②距排水平面越近,附加有效应力受加载方式的影响越明显,距排水平面越远则相反;③E和n对Us的影响很小,可以忽略不计;④E和n对Up和附加有效应力的影响较大且不容忽略。

Suppose the constitutive relation of soil to satisfy the hyperbola model. By assuming that the decrease of the hydraulic conductivity is proportional to the decrease of the compression conductivity and the distribution of initial effective pressure doesn＇t vary with depth, the one-dimensional nonlinear partial differential consolidation equation which is under random time-depending loading is deduced. According to the idiographic initial conditions and the boundary conditions, the equation is solved using the variable separation method. The general solution of the effective stress is achieved; and then the general solution of the excess pore pressure, the general solution of the average consolidation degree defined according to the settlement and the general solution of the average consolidation degree defined according to the excess pore pressure are achieved. Finally, the solutions under trapezium low-fi＇equency cyclic loading are achieved using the general solutions; and the factors which influence the consolidation characters are found. Based on the solutions under low-frequency cyclic loading, the relevant computer program is developed using FORTRAN language. Using this program, the consolidation characters and the influences of the parameters E and n which reflect the constitutive relation on the consolidation characters are analyzed. The computing results show that the average consolidation degree defined according to the settlement is a little bigger than the average consolidation degree defined according to the excess pore pressure; the closer to the drainage plane, the more obviously the mode of the loading influence the additional effective stress; the influences of E and n on the average consolidation degree defined according to the settlement are so small that can be ignored; however, the influences of E and n on the average consolidation degree defined according to the excess pore pressure and the additional effective stress are bigger, so that they can not be ignored.