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Analytical solution and parameter inversion of transient seepage model
of groundwater near ditch during drainage period

REN Honglei，TAO Yuezan，LIN Fei，WEI Ting
（School of Civil Engineering，Hefei University of Technology，Hefei 230009，China）

Abstract：In this paper，the vertical replenishment and drainage effects of phreatic water such as evapora⁃
tion are discretized into daily step functions， and the ditch is generalized as the first kind of boundary
with stable water level，and the phreatic unsteady seepage model near the drainage ditches with step func⁃
tion source and sink term is established. According to the first-linearization method of Boussinesq equation，
the analytical solution of the model is given by using the "integral property" of Laplace transform and the
Laplace transformation property of step function. The reliability of the analytical solution has been verified
by numerical method， and the specific solution and its mathematical significance are discussed. According
to the mathematical law that the fluctuation rate of groundwater level varying with time，the methods of in⁃
flection points and matching line are established to calculate the model parameters by using the method of
solving the inverse problem of model. An actual calculated example shows that the inversion algorithm is
more direct and concise than the current forward trial method.
Keywords： the drainage ditches； transient seepage of phreatic water； ladder function； Boussinesq equa⁃
tion；the inverse problem

（责任编辑：耿庆斋）

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