基于立体几何学的岩体结构面产状取值方法研究

A METHOD OF DETERMINING THE VALUE OF ROCK OCCURRENCE BASED ON SOLID GEOMETRY

现场测量岩质高边坡岩层产状存在一定困难,常采用倾斜摄影来辅助测量。以往大多数研究选用解析几何中的向量关系和最小二乘法拟合平面的方法来求解结构面产状的三点问题,而本文基于传统的三点法原理,利用立体几何学的基本逻辑法来推导倾角、倾向的计算公式求解上述问题。首先,基于选取点的经纬度建立两点之间距离和方位角的表达式。然后推导出以三点之间平距和高差为变量的倾角代数表达式和三点之间平距、高差及三点连线的方位角为变量的倾向代数表达式。用Python编程语言对计算方法程序化并建立简单的用户窗口界面。最后通过工程实例验证计算方法对的准确性,结果表明该方法准确率较高。

It is difficult to measure the occurrence of rock formations on high rock slopes on-site, and oblique photography is often used to assist the measurement. Most of the previous studies have used the vector relationship in analytic geometry and the method of least squares to fit the plane to solve the three-point problem of the occurrence of structural planes. Based on the traditional three-point method principle, this paper uses the basic logic method of solid geometry to derive the calculation formula of the inclination angle and inclination to solve the above problems. First, based on the longitude and latitude of the selected point, an expression for the distance and azimuth angle between two points is established. Then, the algebraic expression of inclination with the horizontal distance and height difference between the three points as variables and the algebraic expression of the tilt angle with the horizontal distance, height difference between three points and the azimuth angle of the three-point line as variables are derived. Use the Python programming language to program the calculation method and establish a simple user window interface. Finally, an engineering example is used to verify the accuracy of the calculation method, and the result shows that the method has a high accuracy rate.