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In mathematics, a series expansion is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division). The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function. The fewer terms of the sequence are used, the simpler this approximation will be. Often, the resulting inaccuracy (i.e., the partial sum of the omitted terms) can be described by an equation involving Big O notation (see also asymptotic expansion). The series expansion on an open interval will also be an approximation for non-analytic functions.
Calculation method and system for three-dimensional steady seepage field of shield tunnel excavation face under boulder conditions
This invention belongs to the field of shield tunneling technology, specifically a method and system for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions. It includes: S1 establishing a three-dimensional geometric model of the seepage field around the tunnel excavation face as a cuboid, with the vertical direction as the z-axis, the direction perpendicular to the tunnel excavation as the x-axis, and the direction along the tunnel excavation as the y-axis; S2, combining the boundary conditions of each region of the seepage field, establishing two-dimensional hydraulic head expressions for the six face regions of the three-dimensional geometric model based on the cuboid three-dimensional geometric model; S3 using the continuity conditions between regions to construct linear partial differential equations and Fourier series expansion equations, solving for the three-dimensional hydraulic head expressions for the six regions; and S4 obtaining the analytical solution for the hydraulic head at any position in the three-dimensional seepage field in front of the excavation face based on the superposition of Fourier series. This invention can accurately calculate the water pressure borne by the excavation face, which also has significant engineering significance for ensuring the safe construction of shield tunnels.
Owner:CHINA RAILWAY 12TH BUREAU GRP CO LTD +1