One-Dimensional Rheological Consolidation Analysis Of Saturated Clays Based On Fractional Order Derivate Models

To predict the settlement of the saturated clayey foundation more accurately,the fractional order derivate models is introduced into the analysis of one dimensional rheological consolidation of saturated clay.The equation of rheological consolidation based on the fractional order derivate models is derived,and its numerical solution is obtained by the Laplace transform and Laplace numerical inversion transform.Given that there exists non-Darcy phenomenon for seepage of pore water in clay,the Hansbo seepage model is introduced into the equation of one dimensional rheological consolidation and its numerical solution is obtained by FEM.One trust region method which can deal with the bounds of the variables is introduced to determine the parameters of the rheological consolidation models.Programming and computing are conducted with the MTALAB software.According to calculation and analysis,some conclusions can be made as follows:(1)The fitting results of the test data show that both on describing the settlement of the clayey samples and on explaining the dissipation of pore water pressure,the fractional order models have advantages over the integer order models.And the fractional order models are composed of fewer elements,which means that their parameters are less than the integer order models.(2)The fractional order ? is a parameter corresponding to rheology overall.With the increase of fractional order ?,the settlement of ground becomes slower in the early phase of the rheological consolidation process.However,the situation goes opposite in the later phase.In the whole process of the rheological consolidation,the settlement of ground becomes slower with the increase of the viscosity coefficient.(3)The predictions of the dissipation of pore water pressure,based on fractional order models with small value of the ratio of modulus,are possibly greater than those based on Terzaghi's theory in the early phase of the rheological consolidation process.And the dissipation of pore water pressure shows faster with the increase of the fractional order ? and the viscosity coefficient.However,in the later phase,the influence of fractional order ? on the dissipation of pore water pressure goes opposite.(4)The development of the settlement could be always lagging behind the dissipation of pore water pressure in the clay layer,and it turns out to be more significant with the decrease of the fractional order ? and the increase of the viscosity coefficient.(5)The calculation result based on Hansbo seepage model shows that,the dissipation of pore water pressure and the development of the settlement becomes significantly slower with the increase of the initial hydraulic gradient of line segment and the exponential of curve segment.Hansbo seepage would significantly delays the rheological consolidation process.