基于分形理论的坝基裂隙岩体注灰量与导水率关系研究

Research on the relationship between cement take and transmissivity of fractured rocks under dam foundation based on fractal theory

由于天然岩体裂隙分布的隐蔽性和不确定性,很难准确评价天然裂隙岩体的渗透性和可灌性。离散裂隙网络作为描述天然裂隙网络的有力工具,能在一定程度上反应裂隙岩体的某些特征,但都是基于统计意义上的概率分布,无法反应裂隙网络参数的内部联系以及微观特征。Mandelbrot提出的分形几何是描述不规则物体的重要工具,研究发现裂隙网络中的裂隙迹长分布服从分形特征,很多学者利用这一理论对裂隙网络的渗透性进行了研究,推导了裂隙网络渗透系数的表达式。然而缺乏裂隙网络的可灌性和灌浆量的研究。本文首先利用裂隙网络的分形特征和裂隙迹长与隙宽的关系,建立了裂隙岩体导水率的分形模型,推导了裂隙岩体导水率与分形维数的关系表达式,并与已有研究结果进行了对比,证实了该关系式的可靠性。其次,分析了裂隙岩体灌浆注灰量与分形维数的关系,进而推导了注灰量与导水率的关系式,根据注灰量与导水率的关系曲线对灌浆区域的划分,定义了3个不同的灌浆区域:正常区域、微小裂隙区域和扩展区域,分别对应于正常灌浆、微小裂隙较多和裂隙扩展变形这3种不同的灌浆状态。最后,通过与工程实测数据的对比,证实了本文注灰量与导水率关系式的可靠性和适用性,也说明了3个灌浆区域的划分是合理并且重要的。因此,该关系式和灌浆区域的划分可以用来预测和评价实际工程灌浆施工的合理性和可灌性。

Due to the imperceptibility and uncertainty of the fractures and cracks under the dam foundation, it is difficult to accurately evaluate the permeability and groutability of the fractured rocks. As a useful tool to describe the natural fracture networks, discrete fracture network can represent the statistical properties of the natural fracture networks, but it cannot reveal the microscopic characteristics and internal relations of the fractures in the fractured rocks. The fractal geometry, proposed by Mandelbrot, is an important tool to describe the characteristics of the fraetal objects. The fractures distributed in fracture networks have been found to exhibit fractal characteristics, many researchers have studied the permeability of fracture networks by using this theory. However, the groutability and grout take of the fractured rocks have been rarely re- searched. In this paper, firstly, the fraetal model of permeability and groutability for the fractured rocks are established, the equation of relationship between transmissivity and fractal dimension is derived. By com- paring with the existing research results, the equation is proved to be reliable. Secondly, the fractal model of cement take for the fractured rocks grouting is analyzed, based on which the equation of relationship be- tween cement take and transmissivity is derived. According to the delimitation by the curve of cement take vs transmissivity, the graph is divided into three grouting zones, which are defined as normal zone,tiny fracture zone and dilation zone, respectively. Finally, for verification purposes, the measured data from a cement grouting project in China are compared with the calculation values, the results show that the rela- tionship between cement take and transmissivity derived in the paper is reliable, and defined grouting zones is reasonable and important. Therefore, the relationship and the grouting zones can used to predict and evaluate the reasonability and groutability of grouting.