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Analytical Solution of the Two-Dimensional Steady-State Seepage Field of a Seepage Anisotropy Pit Considering the Free Surface

Author

Listed:
  • Jun Yu

    (School of Civil Engineering, Central South University, Changsha 410075, China)

  • Yang Zhang

    (School of Civil Engineering, Central South University, Changsha 410075, China)

  • Dongkai Li

    (School of Civil Engineering, Central South University, Changsha 410075, China)

  • Jingfan Zheng

    (School of Civil Engineering, Central South University, Changsha 410075, China)

Abstract

An anisotropic foundation pit steady-state seepage field under a suspended waterproof curtain support considering the position of the free surface is studied analytically, and an analytical solution for the free surface position is given. The head distribution in the three zones is expressed as a series solution using the separation of variables method, and the explicit solution for the extent of the seepage field in each zone is obtained by combining the continuity condition between zones and the series orthogonality condition. The free surface position is determined according to the condition that the total head of the free surface is equal to the position head. A comparison of the calculation results of the analytical method and the indoor test and finite element analysis results verifies the correctness of the analytical solution, and the analytical method has more calculation efficiency than the finite element numerical method. Employing the aforementioned methods to analyze the influence parameters of the free surface position, the results show that drawdown increases as the ratio of the vertical permeability coefficient to the horizontal permeability coefficient increases; the greater the ratio of pit width to depth, the more significant the drawdown, but when the ratio continues to exceed 1.5, the drawdown is negligible.

Suggested Citation

  • Jun Yu & Yang Zhang & Dongkai Li & Jingfan Zheng, 2024. "Analytical Solution of the Two-Dimensional Steady-State Seepage Field of a Seepage Anisotropy Pit Considering the Free Surface," Mathematics, MDPI, vol. 12(13), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2098-:d:1428540
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