工程地质学报  2018, Vol. 26 Issue (5): 1384-1389   (#KB#)
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LI Yalan, SONG Fei, ZHAO Fasuo. 2018. Prediction of ground surface movement and deformation of inclined tunnel excavation based on stochastic medium theory[J]. Journal of Engineering Geology, 26(5): 1384-1389. doi: 10.13544/j.cnki.jeg.2018141.

PREDICTION OF GROUND SURFACE MOVEMENT AND DEFORMATION OF INCLINED TUNNEL EXCAVATION BASED ON STOCHASTIC MEDIUM THEORY
LI Yalan, SONG Fei, ZHAO Fasuo
School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054
Abstract: Aiming at different surface movement and deformation can be produced by the inclined tunnel excavation. The formulas of ground surface movement and deformation due to semicircle-tunnel excavation have been derived by using stochastic medium theory. By calculating the ground surface movement and deformation at different sections of inclined tunnel, the surface of maximum subsidence, horizontal displacement, the maximum value of tilt and maximum curvature are obtained. The influence of surface movement and deformation is analyzed at different positions of inclined tunnel. Result may provide reference for the planning of the electric power plant.
Key words: Stochastic medium theory    Inclined tunnel    Ground surface movement and deformation

0 引言

1 斜巷道概况

 图 1 巷道平面分布图 Fig. 1 Plan of mine tunnel

2 随机介质理论
2.1 单元开挖引起的地表移动与变形

 $W\left(X \right) = \iint\limits_{\mathit{\Omega } - \omega } {\frac{{\tan \beta }}{\eta }\exp [ - \frac{{{\rm{ \mathsf{ π}}}{{\tan }^2}\beta }}{{{\eta ^2}}}{{\left({X - \xi } \right)}^2}]{\text{d}}\xi {\text{d}}\eta }$ (1)

 $U\left(X \right) = \iint\limits_{\mathit{\Omega } - \omega } {\frac{{\left({X - \xi } \right)\tan \beta }}{{{\eta ^2}}}\exp [ - \frac{{{\rm{ \mathsf{ π}}}{{\tan }^2}\beta }}{{{\eta ^2}}}{{\left({X - \xi } \right)}^2}]{\text{d}}\xi {\text{d}}\eta }$ (2)

 $w\left({X, \xi, \eta } \right) = \frac{{\tan \beta }}{\eta }\exp [ - \frac{{{\rm{ \mathsf{ π}}}{{\tan }^2}\beta }}{{{\eta ^2}}}{\left({X - \xi } \right)^2}]$ (3)

 $u\left({X, \xi, \eta } \right) = \frac{{\left({X - \xi } \right)\tan \beta }}{{{\eta ^2}}}\exp [ - \frac{{{\rm{ \mathsf{ π}}}{{\tan }^2}\beta }}{{{\eta ^2}}}{\left({X - \xi } \right)^2}]$ (4)

 $W\left(X \right) = \iint\limits_{\mathit{\Omega } - \omega } {w\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta }$ (5)

 $U\left(X \right) = \iint\limits_{\mathit{\Omega } - \omega } {u\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta }$ (6)

2.2 半圆拱形断面开挖引起的地表移动与变形

 图 2 半圆拱形断面巷道 Fig. 2 Cross section of semicircle-tunnel

 $\begin{gathered} W\left(X \right) = \smallint _a^b\smallint _c^dw\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta + \smallint _e^f\smallint _g^hw\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta - {\text{ }} \hfill \\ \;\;\smallint _i^j\smallint _k^lw\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta + \smallint _m^n\smallint _o^pw\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta \hfill \\ \end{gathered}$ (7)

 $\begin{gathered} U\left(X \right) = \smallint _a^b\smallint _c^du\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta + \smallint _e^f\smallint _g^hu\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta - \hfill \\ \;\;\;\;{\text{ }}\smallint _i^j\smallint _k^lu\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta + \smallint _m^n\smallint _o^pu\left({X, \xi, \eta } \right){\text{d}}\xi {\text{d}}\eta \hfill \\ \end{gathered}$ (8)

 $\begin{array}{l} a = H;b = H + A;c = - \sqrt {{A^2} - {{\left({H + A - \eta } \right)}^2}} ; \hfill \\ d = \sqrt {{A^2} - {{\left({H + A - \eta } \right)}^2}} ;e = H + A; \hfill \\ f = H + A + B;g = - A;h = A;i = H + \Delta A; \hfill \\ j = H + A;k = - \sqrt {{{\left({A - \Delta A} \right)}^2} + {{\left({H + A - \eta } \right)}^2}} ; \hfill \\ l = \sqrt {{{\left({A - \Delta A} \right)}^2} + {{\left({H + A - \eta } \right)}^2}} ;m = H + A; \hfill \\ n = H + A + B - \Delta A;o = - \left({A - \Delta A} \right);p = A - \Delta A。\\ \end{array}$

3 计算结果及分析

 图 3 地层主要影响角 Fig. 3 Main influencing angle of stratum

《建筑物、水体、铁路及主要井巷煤柱留设与压煤开采规程》对建筑物地表允许变形值规定如下：倾斜≤3.0 mm·m-1，曲率≤0.2×10-3m-1，水平变形≤2.0 mm·m-1。由上表可以看出，6-6剖面最大曲率值超出了建筑物地表允许变形值，7-7剖面、8-8剖面的最大倾斜、最大曲率及最大水平变形都超出了建筑物地表允许变形值。为分析巷道可能的主要影响范围，再对该3条剖面逐渐减少β，计算相应的地表移动及变形。计算结果详见表 2~表 4

6-6剖面(β=38°)、7-7剖面(β=29°)、8-8剖面(β=28°)相应的地表移动及变形曲线见图 4~图 6

 图 4 6-6剖面地表移动及变形(β=38°) Fig. 4 Surface movement and deformation of 6-6 section a.地表下沉；b.地表倾斜；c.地表曲率；d.地表水平变形

 图 5 7-7剖面地表移动及变形(β=29°) Fig. 5 Surface movement and deformation of 7-7 section a.地表下沉；b.地表倾斜；c.地表曲率；d.地表水平变形

 图 6 8-8剖面地表移动及变形(β=28°) Fig. 6 Surface movement and deformation of 8-8 section a.地表下沉；b.地表倾斜；c.地表曲率；d.地表水平变形

4 结论

(1) 基于随机介质理论，推导出了半圆拱形断面巷道开挖引起地表变形的计算公式，确定了积分上下限及相关参数。

(2) 通过对斜巷道在不同剖面位置的计算，得出：斜巷道开挖对6-6剖面以西的地表区域影响较小，可在地表布置辅助建筑物；对6-6剖面以东的地表区域影响较大，在影响范围内禁止布置建筑物。

(3) 通过计算确定斜巷道对地表的主要影响区域为：在6-6剖面位置地表影响范围为±36 m，在7-7剖面位置地表影响范围为±29 m，在8-8剖面位置地表影响范围为±21 m。

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