The characteristics of deformation and failure of coal seam floor due to mining in Xinmi coal field in China

Abstract

Deformation and failure of a “three-weak” (weak roof, thick weak coal, and weak floor) coal seam floor subject to mining are studied in this paper. Firstly, by using a group of strain sensors buried at different floor depths, we measured the relationships of the axial strain to the distance from the advancing face field. The floor depths and stratum positions, and as well as the peak width, which is the distance of the first maximum strain increment to the working face, were drawn. The axial stress and its zone of influence, which is the distance from the face to the borehole along the roadway, and at which there is obvious strain increment difference, were also drawn. Secondly, we established an analytical mechanical model and found the analytical solution of the floor’s supporting pressure distribution ahead of the face. And thirdly, we set up a numerical simulation engineering geological model and simulated stress distribution and deformation characteristics of the floor with complex multi-stratum (11 strata) structure. The results from the three approaches showed that: (1) the failure depth (<10.0 m) and zone of influence (up to 36.0 m) induced by mining ahead of the three-weak seam face were much smaller than those common seam faces; (2) the axial strain fluctuated greater than the radial one, with its max peak keeping at about 8.0 m ahead of the advancing face, and its zone of influence spreading to 36.0 m; (3) the peak width of axial strain and its zone of influence in the haulage roadway were stronger than those in the ventilation roadway; and (4) the three weak coal seam played a strong buffering action against deformation and failure due to mining. This research may be of interest to assist with improving strata control and health and safety in operating coal mines.

Appendix: The equations

$$ \begin{aligned} d\sigma_{z} & = - \frac{2qd\xi }{\pi }\frac{{z^{3} }}{{[(x - \xi )^{2} + z^{2} ]^{2} }} \\ d\sigma_{x} & = - \frac{2qd\xi }{\pi }\frac{{z(x - \xi )^{2} }}{{[(x - \xi )^{2} + z^{2} ]^{2} }} \\ \end{aligned} $$

(3)

$$ \begin{aligned} \sigma_{z} & = - \frac{2}{\pi }\int\limits_{ - a}^{b} {\frac{{qz^{3} d\xi }}{{\left[ {(x - \xi )^{2} + z^{2} } \right]^{2} }}} \\ \sigma_{x} & = - \frac{2}{\pi }\int\limits_{ - a}^{b} {\frac{{qz(x - \xi )^{2} d\xi }}{{\left[ {(x - \xi )^{2} + z^{2} } \right]^{2} }}} \\ \end{aligned} $$

(4)

$$ \left. {\begin{array}{*{20}l} {P_{Z}^{(1)} = \frac{{k_{0} \gamma H}}{{x_{0} }}x} \hfill & {(0 \le x \le x_{0} )} \hfill \\ {P_{Z}^{(2)} = - \frac{{(k_{0} - 1)\gamma H}}{{L_{0} - x_{0} }}x + \frac{{\gamma H(k_{0} L_{0} - x_{0} )}}{{L_{0} - x_{0} }}} \hfill & {(x_{0} \le x \le L_{0} )} \hfill \\ \end{array} } \right\} $$

(5)

$$ \sigma_{z} = \sigma_{z}^{(1)} + \sigma_{z}^{(2)} $$

(6)

$$ \sigma_{x} = \sigma_{x}^{(1)} + \sigma_{x}^{(2)} $$

(7)

$$ \sigma _{z} = \frac{{k_{0} \gamma H}}{\pi }\left. {\left\{ {(n - 1)\left( {\tan ^{{ - 1}} \frac{{nx_{0} }}{z} + \tan ^{{ - 1}} \frac{{(1 - n)x_{0} }}{z}} \right) - \frac{{nzx_{0} }}{{z^{2} + (nx_{0} )^{2} }}} \right.} \right\} - \frac{{\gamma (k_{0} - 1)H}}{{\pi (L_{0} - x_{0} )}}\left\{ {(1 - n)x_{0} \times \left( {tg^{{ - 1}} \frac{{x_{0} - nx_{0} - L_{0} }}{z} + tg^{{ - 1}} \frac{{nx_{0} }}{z}} \right) + \frac{{z[(x_{0} - nx_{0} )(x_{0} - nx_{0} - L_{0} ) + z^{2} )]}}{{z^{2} + (x_{0} - nx_{0} - L_{0} )^{2} }} - \frac{{z[n(n - 1)x_{0}^{2} + z^{2} )]}}{{z^{2} + (nx_{0} )^{2} }}} \right\} + \frac{{\gamma (k_{0} L_{0} - x_{0} )H}}{{\pi (L_{0} - x_{0} )}}\left. {\left\{ {\left( {\tan ^{{ - 1}} \frac{{x_{0} - nx_{0} - L_{0} }}{z} - \tan ^{{ - 1}} \frac{{nx_{0} }}{z}} \right) + \frac{{z(x_{0} - nx_{0} - L_{0} )}}{{z^{2} + (x_{0} - nx_{0} - L_{0} )^{2} }} - \frac{{znx_{0} }}{{z^{2} + (nx_{0} )^{2} }}} \right.} \right\} $$

(8)

$$ \begin{aligned} \sigma_{x} & = \frac{{k_{0} \gamma {\text{H}}}}{{\pi .x_{0} }}\left. {\left\{ {x_{0} (n - 1) \left( \tan^{ - 1} \frac{{nx_{0} }}{z} + \tan^{ - 1} \frac{{(1 - n)x_{0} }}{z}\right) + \frac{{znx_{0}^{2} }}{{z^{2} + (nx_{0} )^{2} }}} \right. - z\ln \frac{{(nx_{0} )^{2} + z^{2} }}{{(x_{0} - nx_{0} )^{2} + z^{2} }}} \right\} \\ & \quad + \frac{{\gamma (k_{0} - 1)H}}{{\pi (L_{0} - x_{0} )}}\left\{ {(n - 1)x_{0} \left( {\tan^{ - 1} \frac{{x_{0} - nx_{0} - L_{0} }}{z} + \tan^{ - 1} \frac{{nx_{0} }}{z}} \right) + \frac{{z[(x_{0} - nx_{0} )(x_{0} - nx_{0} - L_{0} ) + z^{2} )]}}{{z^{2} + (x_{0} - nx_{0} - L_{0} )^{2} }}} \right. \\ & \quad - \left. {\frac{{z[n(n - 1)x_{0}^{2} + z^{2} )]}}{{z^{2} + (nx_{0} )^{2} }} + z\ln \frac{{z^{2} + (x_{0} - nx_{0} - L_{0} )^{2} }}{{z^{2} + (nx_{0} )^{2} }}} \right\} \\ & \quad + \frac{{\gamma (k_{0} L_{0} - x_{0} )H}}{{\pi (L_{0} - x_{0} )}}\left\{ {\left( {\tan^{ - 1} \frac{{x_{0} - nx_{0} - L_{0} }}{z} + \tan^{ - 1} \frac{{nx_{0}}}{z}- \frac{{z(x_{0} - nx_{0} - L_{0} )}}{{z^{2} + (x_{0} - nx_{0} - L_{0} )^{2} }} - \frac{{znx_{0} }}{{z^{2} + (nx_{0} )^{2} }}} \right)} \right\} \\ \end{aligned} $$

(9)