开采沉陷的动态过程及基于关键层理论的沉陷模型
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摘要
“三下”采煤最主要的技术难题是开采沉陷的防治技术。目前,以概率积分法为代表的开采沉陷预计方法可以预计地表充分采动或非充分采动后的各种静态指标,如下沉量、倾斜和曲率等,但不能预计地表移动的整个过程。开采沉陷对地表建(构)物的损害程度不仅取决于各种指标的最终结果(静态值),也取决于各种指标的变化过程(动态值)。因此,研究开采沉陷的动态过程对于沉陷灾害的预防和控制具有重要的理论意义和工程应用价值。本文以长壁工作面采煤引起的岩层移动和地表沉陷为主要研究对象,采用现场观测、数值模拟、理论分析、数学建模、实测验证等手段,对开采沉陷的动态过程进行了深入的研究和有益的探讨,取得了如下一些进展:
1)提出了一种长壁式工作面开采煤层形成的地表下沉盆地及其走向、倾向主断面下沉曲线的拟合函数模型。模型中参数a、b控制沉陷盆地的范围,参数wm ax、d控制沉陷盆地的深浅及走向、倾向主断面下沉曲线的形状。实测资料验证,该函数能很好地拟合沉陷盆地主断面下沉曲线,与负指数函数、双曲正切函数模型相比,具有表达形式简单、参数容易取得、拟合程度高等优点。
2)针对较大深厚比(开采深度与开采厚度之比大于25)条件下开采煤层形成矩形采空区的过程,提出了上覆岩层移动形成地表下沉盆地的形态和大小主要决定于离地表最近一层关键岩层的弯曲变形,并且地表下沉量远远小于关键岩层的厚度,关键层的变形符合弹性薄板弯曲变形的学术观点。
3)用弹性薄板理论的半逆解法分别建立了缓倾斜煤层开采和倾斜煤层开采地表下沉盆地的力学模型,推导出了倾斜煤层开采时地表最大下沉点在倾斜方向的坐标公式和形态参数d的计算公式。
4)提出了可描述地表点下沉过程的时间函数模型不仅能较好地拟合w-t曲线,而且由模型求出的v-t和a-t曲线也要符合地表点下沉的客观过程。从曲线形态、速度和加速度三个方面计算分析了knothe模型、Gompertz模型、logistic模型、Weibull模型,得出这些模型不能用于描述开采沉陷的动态过程。
5)改进了knothe时间函数模型。模型参数可采用经验方法和最小二乘法相结合的方式确定,其中参数c决定地表点下沉时间的长短,参数k决定地表点下沉在时间轴上的具体路径,但参数的决定因素和物理意义还有待进一步研究。
6)当采煤工作面以速度v0匀速向前推进时,设地表移动的启动距为l 0,工作面推进长度为l ,则可用工作面推进距离和速度代替改进的knothe时间函数模型中的时间t。
7)用FLAC~(3D)软件模拟了某矿区煤层的开采过程。在计算模型的上表面经过开采中心点的走向和倾向剖面线上布置了18个垂直位移和位移速率的检测点,得出了在走向和倾向剖面线上各检测点在开采过程中的垂直位移曲线和速度曲线,其曲线形态与改进的knothe时间函数曲线十分相似。
8)改进的knothe时间函数模型分别结合了基于关键层理论的开采沉陷模型和概率积分预计模型,建立了主断面下沉曲线、倾斜曲线和曲率曲线的动态模型。最后,主要采用南桐矿区的部分观测资料进行了验证,表明在主断面最终下沉曲线确定的情况下,动态模型可作出任意时刻的下沉曲线、倾斜曲线和曲率曲线。
The first Importance technological problem of coal mining under railway ,surface structure and water body is predicting and controlling the surface subsidence due to underground mining. The way of predicting the surface subsidence based on the theory of the probability integral is only obtained the static subsidence index such as the amount of subsidence ,incline and curvature at present. But this model is not described the whole surface subsidence course. The degree of the damage to building and structure not only is determined to the final surface subsidence due to underground mining but only the surface subsidence velocity and acceleration especially to the structure sensitive to the deformation just like railway , telecommunication line and mountain coast. So, the research of the dynamic course of the surface subsidence due to underground mining is profound theoretical and practical significance. The object of study in this paper is the rock stratum movement and surface subsidence up the long-wall mining coal face. Through the way of the field observation, numerical analysis mining, theoretical analysis, mathematical modeling and test by observation data, studied the dynamic course of the surface subsidence due to underground mining,obtain the following conclusion.
1) A function model of the subsidence, incline and curvature is set up suited to the condition of mining coal by long-wall face. The parameter a and b determine the subsidence basin range and the parameter wmax and d determine the depth of the subsidence and the shape of the subsidence curve of the section of the basin in this model. This model can fit well the observation data. It is more advanced than the negative index function and hyperbolic tangent because of the function is brief and the parameter is obtained easily.
2) The viewpoint in this paper is the suface subsidence is detemined by bend of the rock stratum near by the surface when the ratio of depth of embedment and thickness of the coal seam is very large up long-wall mining coal face. This key rock stratum is controlled the surface subsidence. The size of the surface subsidence is far below the rock thick. So the bend is fit for the theory of the flexible sheet.
3) A surface subsidence basin model due to underground mining is seted up used the theory of the key stratum and elasticity sheet and inferd the formular of the parameter d and the excursion of the maximum dot on the y axis of the steep coal seam in this paper.
4) By analyzing the dynamic course of the surface subsidence due to underground mining coal, the conclusion has been drawn that the w-t curve of the ground subsidence appears S-shaped. So the time function which can describe the subsidence course of the ground must fit not only the w-t curve but also the v-t curve and the a-t curve. Time functions which are usually used to fit the w-t curve of the foundation or roadbed settlement now such as the exponential time function, the hyperbolic time function, the Gompertz time function, the Logistic time function and the Weibull time function. Studying the w-t curve, v-t curve and a-t curve of these time functions finds that these times function is not feasible for describing the dynamic course of the ground subsidence due to underground mining.
5) By adding a constant parameter k to the Knothe time function, a new time function model has been set up. The velocity and acceleration worked out from this new time function model is in accordance with the dynamic process of the surface subsidence. In this new model the parameter c decides how long the subsidence would continue; and the parameter k decides the path of the subsidence on the axis of time.
6) The time parameter t is replance by the space parameter l of the mining face moving and the speed parameter v0 when the coal minging face is moving with a constant speed and the begin parameter l0 the surface subsidence.
7) Use the FLAC~(3D) to simulate the mining coal course because of the advantage of the FLAC~(3D) for simulating the large deformation event of rock and soil engineering mechanics. The exploit extent is the most less than the size of computational model. The conclusion is obtain that the curve of the subsidence and velocity with the iteration steps is accord with the improved knothe time function for surface subsidence due to underground mining.
8) Because of the subsidence of the point on the surface is independent on the space and time, so the model of the whole dynamic subsidence model can be set up by combining the improved knothe time function model with the section function of the surface subsidence basin or the basin model.This new subsidence dynamic model fits well the curve of the observation data of some coal mine. The dynamic model can describe the courve of the subsidence, incline and curvature when the curve of the section is certain.
1)提出了一种长壁式工作面开采煤层形成的地表下沉盆地及其走向、倾向主断面下沉曲线的拟合函数模型。模型中参数a、b控制沉陷盆地的范围,参数wm ax、d控制沉陷盆地的深浅及走向、倾向主断面下沉曲线的形状。实测资料验证,该函数能很好地拟合沉陷盆地主断面下沉曲线,与负指数函数、双曲正切函数模型相比,具有表达形式简单、参数容易取得、拟合程度高等优点。
2)针对较大深厚比(开采深度与开采厚度之比大于25)条件下开采煤层形成矩形采空区的过程,提出了上覆岩层移动形成地表下沉盆地的形态和大小主要决定于离地表最近一层关键岩层的弯曲变形,并且地表下沉量远远小于关键岩层的厚度,关键层的变形符合弹性薄板弯曲变形的学术观点。
3)用弹性薄板理论的半逆解法分别建立了缓倾斜煤层开采和倾斜煤层开采地表下沉盆地的力学模型,推导出了倾斜煤层开采时地表最大下沉点在倾斜方向的坐标公式和形态参数d的计算公式。
4)提出了可描述地表点下沉过程的时间函数模型不仅能较好地拟合w-t曲线,而且由模型求出的v-t和a-t曲线也要符合地表点下沉的客观过程。从曲线形态、速度和加速度三个方面计算分析了knothe模型、Gompertz模型、logistic模型、Weibull模型,得出这些模型不能用于描述开采沉陷的动态过程。
5)改进了knothe时间函数模型。模型参数可采用经验方法和最小二乘法相结合的方式确定,其中参数c决定地表点下沉时间的长短,参数k决定地表点下沉在时间轴上的具体路径,但参数的决定因素和物理意义还有待进一步研究。
6)当采煤工作面以速度v0匀速向前推进时,设地表移动的启动距为l 0,工作面推进长度为l ,则可用工作面推进距离和速度代替改进的knothe时间函数模型中的时间t。
7)用FLAC~(3D)软件模拟了某矿区煤层的开采过程。在计算模型的上表面经过开采中心点的走向和倾向剖面线上布置了18个垂直位移和位移速率的检测点,得出了在走向和倾向剖面线上各检测点在开采过程中的垂直位移曲线和速度曲线,其曲线形态与改进的knothe时间函数曲线十分相似。
8)改进的knothe时间函数模型分别结合了基于关键层理论的开采沉陷模型和概率积分预计模型,建立了主断面下沉曲线、倾斜曲线和曲率曲线的动态模型。最后,主要采用南桐矿区的部分观测资料进行了验证,表明在主断面最终下沉曲线确定的情况下,动态模型可作出任意时刻的下沉曲线、倾斜曲线和曲率曲线。
The first Importance technological problem of coal mining under railway ,surface structure and water body is predicting and controlling the surface subsidence due to underground mining. The way of predicting the surface subsidence based on the theory of the probability integral is only obtained the static subsidence index such as the amount of subsidence ,incline and curvature at present. But this model is not described the whole surface subsidence course. The degree of the damage to building and structure not only is determined to the final surface subsidence due to underground mining but only the surface subsidence velocity and acceleration especially to the structure sensitive to the deformation just like railway , telecommunication line and mountain coast. So, the research of the dynamic course of the surface subsidence due to underground mining is profound theoretical and practical significance. The object of study in this paper is the rock stratum movement and surface subsidence up the long-wall mining coal face. Through the way of the field observation, numerical analysis mining, theoretical analysis, mathematical modeling and test by observation data, studied the dynamic course of the surface subsidence due to underground mining,obtain the following conclusion.
1) A function model of the subsidence, incline and curvature is set up suited to the condition of mining coal by long-wall face. The parameter a and b determine the subsidence basin range and the parameter wmax and d determine the depth of the subsidence and the shape of the subsidence curve of the section of the basin in this model. This model can fit well the observation data. It is more advanced than the negative index function and hyperbolic tangent because of the function is brief and the parameter is obtained easily.
2) The viewpoint in this paper is the suface subsidence is detemined by bend of the rock stratum near by the surface when the ratio of depth of embedment and thickness of the coal seam is very large up long-wall mining coal face. This key rock stratum is controlled the surface subsidence. The size of the surface subsidence is far below the rock thick. So the bend is fit for the theory of the flexible sheet.
3) A surface subsidence basin model due to underground mining is seted up used the theory of the key stratum and elasticity sheet and inferd the formular of the parameter d and the excursion of the maximum dot on the y axis of the steep coal seam in this paper.
4) By analyzing the dynamic course of the surface subsidence due to underground mining coal, the conclusion has been drawn that the w-t curve of the ground subsidence appears S-shaped. So the time function which can describe the subsidence course of the ground must fit not only the w-t curve but also the v-t curve and the a-t curve. Time functions which are usually used to fit the w-t curve of the foundation or roadbed settlement now such as the exponential time function, the hyperbolic time function, the Gompertz time function, the Logistic time function and the Weibull time function. Studying the w-t curve, v-t curve and a-t curve of these time functions finds that these times function is not feasible for describing the dynamic course of the ground subsidence due to underground mining.
5) By adding a constant parameter k to the Knothe time function, a new time function model has been set up. The velocity and acceleration worked out from this new time function model is in accordance with the dynamic process of the surface subsidence. In this new model the parameter c decides how long the subsidence would continue; and the parameter k decides the path of the subsidence on the axis of time.
6) The time parameter t is replance by the space parameter l of the mining face moving and the speed parameter v0 when the coal minging face is moving with a constant speed and the begin parameter l0 the surface subsidence.
7) Use the FLAC~(3D) to simulate the mining coal course because of the advantage of the FLAC~(3D) for simulating the large deformation event of rock and soil engineering mechanics. The exploit extent is the most less than the size of computational model. The conclusion is obtain that the curve of the subsidence and velocity with the iteration steps is accord with the improved knothe time function for surface subsidence due to underground mining.
8) Because of the subsidence of the point on the surface is independent on the space and time, so the model of the whole dynamic subsidence model can be set up by combining the improved knothe time function model with the section function of the surface subsidence basin or the basin model.This new subsidence dynamic model fits well the curve of the observation data of some coal mine. The dynamic model can describe the courve of the subsidence, incline and curvature when the curve of the section is certain.
引文
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