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在软土地基三向固结理论研究中R·A·Barron给出了二类边界条件下三维拋物型方程混合问题的解(见[1],[2],[3]),但这个解是不准确的。本文一方面指出B·A·Barron解的问题所在,另一方面用一、二类Bessel函数求出了该问题的精确解,指明了解的适定性,给出了高级超越方程J_o(x)Y_1(kx)-J_1(kx)Y_o(x)=0当k<1时的零点求法;最后利用所得结果求出软土路基的平均固结度。
In the study of the three-dimensional consolidation theory of soft soils, R.A. Barron gives solutions to the mixed problem of three-dimensional parabolic equations under the boundary conditions of two types (see [1], [2], [3]), but the solution It is inaccurate. On the one hand, this paper points out the problem of B.A. Barron’s solution. On the other hand, it uses the first and second Bessel functions to find the exact solution to the problem, specifies the well-posedness of understanding, and gives the advanced transcendental equation J_o(x)Y_1. (kx)-J_1 (kx) Y_o (x) = 0 When zero <1, the zero point method is used. Finally, the average degree of consolidation of the soft soil roadbed is obtained by using the obtained results.