CN113049326B - Sample preparation method with quantitatively controllable structural surface shape and spectrum components - Google Patents
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Abstract
Description
技术领域Technical field
本发明涉及岩土工程技术领域，具体涉及一种结构面形貌频谱成分定量可控的制样方法。The invention relates to the technical field of geotechnical engineering, and specifically relates to a sample preparation method with quantitatively controllable structural surface morphology spectrum components.
背景技术Background technique
边坡岩体中所赋存的结构面受地球内外地质营力共同作用，其力学性质远低于岩块，降低了岩体的完整性和整体强度，使得边坡岩体易沿控制性结构面发生滑动失稳。考虑到天然结构面三维形貌具有一定的频谱特征，由不同频率特征的起伏成分组成，剪切过程中不同起伏成分的磨损演化特征对结构面的剪切机制与剪切强度影响存在较大差异。因此，有必要制作高频起伏与低频起伏成分含量比例可定量控制的结构面试样，为定量研究不同频率成分在剪切过程中的磨损演化规律奠定基础。The structural planes existing in the slope rock mass are affected by the geological forces inside and outside the earth. Their mechanical properties are much lower than those of the rock mass, which reduces the integrity and overall strength of the rock mass, making it easy for the slope rock mass to follow the control structure. Sliding instability occurs on the surface. Considering that the three-dimensional morphology of natural structural surfaces has certain spectral characteristics and is composed of undulating components with different frequency characteristics, the wear evolution characteristics of different undulating components during the shearing process have greatly different effects on the shearing mechanism and shear strength of structural surfaces. . Therefore, it is necessary to produce structural test specimens whose content ratios of high-frequency undulation and low-frequency undulation components can be quantitatively controlled to lay the foundation for quantitative research on the wear evolution rules of different frequency components during the shear process.
杜时贵等将岩体结构面表面形态划分为宏观几何轮廓、表面起伏形态以及微观粗糙度三级要素，且研究表明不同频率成分或起伏形态要素在剪切过程中对结构面抗剪强度的贡献存在明显差异。结构面的宏观几何轮廓是结构面表面最大一级的几何轮廓，反映结构面表面宏观总体的起伏形状，它由较小级别的形态要素(即表面起伏形态)峰谷包路线(面)表征；表面起伏形态是结构面表面常见的波状起伏形态，构成结构面表面可见规模的峰谷起伏轮廓；微观粗糙度是岩体结构面表面最小一级的粗糙起伏形态，反映表面起伏形态峰谷坡面的微小几何起伏，体现矿物颗粒或细小晶体在结构面表面的分布和排列特征。针对结构面表面形态三级要素中的表面起伏形态和微观粗糙度，学者们采用了诸如“一阶起伏和二阶起伏”、“大尺度波纹分量和小尺度不规则分量”、“波纹度分量和随机不规则度分量”等名称或方式对其起伏特点进行描述和划分。实际上，起伏频率小但起伏高度较高的表面起伏形态(“一阶起伏”或“大尺度波纹分量”或“波纹度分量”)属于低频起伏成分，而起伏频率大但起伏高度较低的微观粗糙度(“二阶起伏”或“小尺度不规则分量”或“随机不规则分量”)属于高频起伏成分。在上述所描述的结构面形貌三级要素中，结构面的表面起伏形态往往是影响结构面力学性质和剪切行为的决定性因素。尽管结构面的宏观几何轮廓可由表面起伏形态的峰谷包络线直接得到，但结构面表面起伏形态和微观粗糙度之间的不存在明显界限，直观上难以定量划分。Du Shigui et al. divided the surface morphology of the rock mass structural surface into three-level elements: macro geometric contour, surface undulation morphology and micro-roughness, and research showed that different frequency components or undulation morphology elements contribute to the shear strength of the structural surface during the shearing process. Significant differences. The macroscopic geometric profile of the structural surface is the largest geometric profile of the structural surface, which reflects the macroscopic overall undulating shape of the structural surface. It is characterized by the peak and valley envelope routes (surfaces) of smaller-level morphological elements (i.e., surface undulating shapes); The surface relief form is the common undulating form on the surface of the structural surface, which constitutes the visible-scale peak and valley contours on the surface of the structural surface; the micro-roughness is the smallest level of rough relief form on the surface of the structural surface of the rock mass, reflecting the peak and valley slopes of the surface relief form. The tiny geometric undulations reflect the distribution and arrangement characteristics of mineral particles or fine crystals on the surface of the structural plane. For the surface relief morphology and micro-roughness among the third-level elements of structural surface surface morphology, scholars have used methods such as "first-order relief and second-order relief", "large-scale ripple component and small-scale irregular component", "waviness component" Names or methods such as "and random irregularity component" are used to describe and divide its fluctuation characteristics. In fact, surface undulations with small undulation frequency but high undulation height ("first-order undulation" or "large-scale ripple component" or "waviness component") belong to low-frequency undulation components, while those with large undulation frequency but low undulation height Microscopic roughness ("second-order undulation" or "small-scale irregular component" or "random irregular component") belongs to high-frequency undulation components. Among the three-level elements of structural surface morphology described above, the surface relief morphology of the structural surface is often the decisive factor affecting the mechanical properties and shear behavior of the structural surface. Although the macro-geometric profile of the structural surface can be directly obtained from the peak and valley envelope of the surface undulation, there is no obvious boundary between the surface undulation and micro-roughness of the structural surface, making it difficult to quantitatively divide intuitively.
现有学者通常采用傅立叶级数、高斯滤波、小波变换、不同采样精度等方法人为控制或分离结构面形貌中的不同起伏成分。例如，夏才初等通过移动的数据窗和最小二乘平滑提取了波纹分量和不规则分量；Yang et al.、唐志成和刘泉声采用剖面线的不同傅立叶级数代表一阶和二阶起伏成分；蒋喆等采用2.5mm的高斯滤波器截止波长对剪切前后结构面形貌进行滤波，对结构面的一阶起伏和二阶起伏进行了提取；Li et al.采用小波分析所近似表征的结构面二维剖面线的第四层对一阶起伏进行了提取；Liu et al.将大采样间距绘制的标准剖面线作为一阶起伏成分，剩余成分作为二阶起伏成分；朱小明等和Liu etal.则采用两种起伏高度的三角突起体代表结构面的一阶和二阶起伏体；孙盛玥等、黄曼等依据不同网格尺寸的形貌面积变化速率对一阶和二阶起伏进行划分。然而构成结构面的不同起伏成分在宏观尺寸上一般连续变化，不同学者基于宏观尺寸差异采用高斯滤波或小波分析等方法所分解得到的起伏成分往往不一致。Existing scholars usually use methods such as Fourier series, Gaussian filtering, wavelet transform, and different sampling precisions to artificially control or separate different fluctuation components in the structural surface topography. For example, Xia Caichu et al. extracted ripple components and irregular components through moving data windows and least square smoothing; Yang et al., Tang Zhicheng and Liu Quansheng used different Fourier series of profile lines to represent the first-order and second-order fluctuation components; Jiang et al. Zhe et al. used a Gaussian filter cutoff wavelength of 2.5mm to filter the structural surface morphology before and after shearing, and extracted the first-order undulations and second-order fluctuations of the structural surface; Li et al. used wavelet analysis to approximately characterize the structural surface The fourth layer of the two-dimensional profile line extracted the first-order relief; Liu et al. used the standard profile drawn with a large sampling interval as the first-order relief component, and the remaining components as the second-order relief component; Zhu Xiaoming et al. and Liu et al. Triangular protrusions with two undulation heights were used to represent the first-order and second-order undulations of the structural surface; Sun Shengyue et al., Huang Man et al. divided the first-order and second-order undulations based on the change rate of the morphological area of different grid sizes. However, the different undulation components that constitute the structural surface generally change continuously in macroscopic size. The undulation components decomposed by different scholars using methods such as Gaussian filtering or wavelet analysis based on differences in macroscopic size are often inconsistent.
二维功率谱密度函数可以有效分析结构面形貌的频谱特征，描述结构面形貌不同起伏成分的起伏高度在不同频率范围内的分布情况，可有效解决宏观尺寸上结构面不同起伏成分之间频率界限无法定量识别的问题，进而可完成结构面三维形貌中高频起伏与低频起伏成分的定量分解。基于所定量分解得到的起伏成分，依据所指定的高频起伏与低频起伏成分的含量比例，采用傅立叶逆变换即可完成高频起伏与低频起伏成分含量比例不同且可定量控制的结构面形貌模型。The two-dimensional power spectral density function can effectively analyze the spectral characteristics of the structural surface topography, describe the distribution of the undulation heights of different undulation components of the structural surface morphology in different frequency ranges, and can effectively solve the problem of differences between different undulation components of the structural surface on a macro scale. The frequency limit cannot be quantitatively identified, and the quantitative decomposition of high-frequency fluctuations and low-frequency fluctuations components in the three-dimensional morphology of the structural surface can be completed. Based on the undulation components obtained by quantitative decomposition, and according to the specified content ratio of high-frequency undulation and low-frequency undulation components, the inverse Fourier transform can be used to complete a structural surface morphology with different content ratios of high-frequency undulation and low-frequency undulation components that can be quantitatively controlled Model.
发明内容Contents of the invention
为了克服现有岩体结构面形貌中高频起伏成分与低频起伏成分界限无法定量确定，难以定量控高频起伏与低频起伏成分含量比例的问题，本发明提供了一种结构面形貌频谱成分定量可控的制样方法。In order to overcome the problem that the boundaries between high-frequency undulation components and low-frequency undulation components in the existing rock mass structural surface morphology cannot be determined quantitatively, and it is difficult to quantitatively control the content ratio of high-frequency undulation components and low-frequency undulation components, the present invention provides a structural surface morphology spectrum component. Quantitative and controllable sample preparation method.
本发明解决其技术问题所采用的技术方案是：The technical solutions adopted by the present invention to solve the technical problems are:
一种结构面形貌频谱成分定量可控的制样方法，所述方法包括以下步骤：A sample preparation method with quantitatively controllable structural surface morphology spectrum components, the method includes the following steps:
S1、获取与岩体结构面实际剪切状态一致的结构面三维形貌模型；S1. Obtain a three-dimensional morphology model of the structural surface that is consistent with the actual shear state of the rock mass structural surface;
S2、基于二维功率谱密度确定岩体结构面三维形貌起伏高度均方值在频率范围内的分布函数，计算公式如下述公式(1)：S2. Determine the distribution function of the mean square value of the three-dimensional morphology fluctuation height of the rock mass structural surface in the frequency range based on the two-dimensional power spectral density. The calculation formula is as follows (1):
其中，P3D为高度均方值，PSD(fx,fy)为结构面形貌的二维功率谱密度，fx和fy分别为结构面形貌频率成分在x轴和y轴方向的空间频率，ft为频率阀值，fmax为最大频率值；Among them, P 3D is the height mean square value, PSD (f x , f y ) is the two-dimensional power spectral density of the structural surface topography, f x and f y are the frequency components of the structural surface topography in the x-axis and y-axis directions respectively. The spatial frequency of , f t is the frequency threshold, and f max is the maximum frequency value;
S3、绘制岩体结构面三维形貌起伏高度均方值在频率范围内的分布函数图像，以函数图的转折点所对应的频率作为结构面形貌高频成分和低频成分的界限频率ftc；S3. Draw the distribution function image of the mean square value of the three-dimensional morphology fluctuation height of the rock mass structural surface within the frequency range, and use the frequency corresponding to the turning point of the function graph as the limiting frequency f tc of the high-frequency component and low-frequency component of the structural surface morphology;
S4、保持岩体结构面中低频起伏成分含量不变，通过调整高频起伏成分的含量定量控制岩体结构面高频起伏与低频起伏成分的含量比例γ0，则与含量比例γ0所对应的高频起伏成分的频率上限fu的计算公式为：S4. Keep the content of low-frequency undulation components in the rock mass structural surface unchanged, and quantitatively control the content ratio γ 0 of high-frequency undulation components and low-frequency undulation components in the rock mass structural surface by adjusting the content of high-frequency undulation components, which corresponds to the content ratio γ 0 The calculation formula for the upper frequency limit fu of the high-frequency fluctuation component is:
S5、依据所确定的界限频率ftc或高频起伏成分的频率上限fu，提取岩体结构面三维形貌不同频率的起伏成分，建立高频起伏和低频起伏成分不同含量比例的结构面三维形貌模型；S5. Based on the determined limit frequency f tc or the upper frequency limit f u of the high-frequency undulation component, extract the undulation components of the three-dimensional morphology of the rock mass structural surface at different frequencies, and establish a three-dimensional structural surface with different proportions of high-frequency undulation and low-frequency undulation components. Morphological model;
S6、依据所定量建立的高频起伏和低频起伏成分含量比例不同的结构面三维形貌模型，采用岩石雕刻机雕刻制作高频起伏和低频起伏成分定量可控的岩体结构面试样。S6. Based on the quantitatively established three-dimensional morphology model of the structural plane with different proportions of high-frequency undulation and low-frequency undulation components, use a rock engraving machine to carve and produce rock mass structure sample with quantitatively controllable high-frequency undulation and low-frequency undulation components.
进一步，所述步骤S1包括：Further, the step S1 includes:
S11、沿剪切方向采集岩体结构面三维形貌离散坐标数据，以坐标数据最小二乘拟合平面与坐标平面的夹角作为结构面三维形貌的趋势向，沿趋势向反向旋转结构面形貌数据，确保旋转后的结构面三维形貌趋势向呈水平状态；S11. Collect the discrete coordinate data of the three-dimensional morphology of the rock mass structural surface along the shear direction, use the angle between the least squares fitting plane of the coordinate data and the coordinate plane as the trend direction of the three-dimensional morphology of the structural surface, and reversely rotate the structure along the trend direction. Surface topography data ensures that the three-dimensional topography trend of the rotated structural surface is horizontal;
S12、平移旋转后的结构面三维形貌数据，使得其起伏高度平均平面与坐标平面重合，建立结构面三维形貌模型。S12. Translate and rotate the three-dimensional topography data of the structural surface so that the average plane of its undulation height coincides with the coordinate plane, and establish a three-dimensional topography model of the structural surface.
优选的，所述步骤S2中，岩体结构面形貌二维功率谱密度PSD(fx，fy)的计算公式为：Preferably, in step S2, the calculation formula of the two-dimensional power spectral density PSD (f x , f y ) of the rock mass structural surface topography is:
其中，Lx和Ly为别为岩体结构面三维形貌在x轴和y轴方向的长度，Z(fx,fy)为结构面三维形貌z(x,y)在空间频域内的二维傅里叶变换，j2＝-1。Among them, L x and L y are the lengths of the three-dimensional morphology of the rock mass structural surface in the x-axis and y-axis directions respectively, and Z ( f Two-dimensional Fourier transform in the domain, j 2 =-1.
优选的，所述步骤S5的过程如下：Preferably, the process of step S5 is as follows:
若建立仅含高频起伏成分，低频起伏成分含量为零的结构面三维形貌模型，可基于结构面三维形貌在频域空间的二维傅里叶变换，将小于界限频率ftc的频率成分设为零值，然后通过傅里叶逆变换得到仅含高频起伏成分的结构面三维形貌模型，计算公式如下述公式(4)：If a three-dimensional topography model of the structural surface is established that contains only high-frequency fluctuation components and zero low-frequency fluctuation components, the frequency that is smaller than the limit frequency f tc can be calculated based on the two-dimensional Fourier transform of the three-dimensional topography of the structural surface in the frequency domain space. The component is set to zero, and then the three-dimensional topography model of the structural surface containing only high-frequency undulation components is obtained through inverse Fourier transform. The calculation formula is as follows (4):
若保持低频起伏成分含量不变，建立高频起伏和低频起伏成分不同含量比例的结构面三维形貌模型，可基于结构面三维形貌在频域空间的二维傅里叶变换，将大于高频起伏成分的频率上限fu的频率成分设为零值，然后通过傅里叶逆变换得到高频起伏和低频起伏成分含量比例为γ0的三维形貌模型，计算公式如下述公式(5)：If the content of the low-frequency undulation component is kept unchanged and a three-dimensional morphology model of the structural surface with different content ratios of high-frequency undulation and low-frequency undulation components is established, the two-dimensional Fourier transform of the three-dimensional morphology of the structural surface in the frequency domain space will be larger than the high-frequency undulation component. The frequency upper limit of the frequency fluctuation component f u is set to zero, and then the three-dimensional topography model with a content ratio of high-frequency fluctuation and low-frequency fluctuation component is γ 0 is obtained through the inverse Fourier transform. The calculation formula is as follows: formula (5) :
本发明的有益效果主要表现在：以结构面三维形貌中高频起伏成分的起伏高度显著低于低频起伏成分的特征为切入点，基于结构面三维形貌起伏高度均方值在频率范围内的分布函数，深入研究结构面三维形貌起伏高度均方值随频率值逐渐增大的变化特征，找准结构面三维形貌低频成分与高频成分起伏高度的转折点，定量划分高频起伏成分与低频起伏成分之间的频率界限，确定岩体结构面高频起伏与低频起伏成分的含量比例所对应的高频起伏成分的频率上限，解决了宏观尺寸上结构面不同起伏成分之间频率界限无法定量识别的问题，进而完成含不同高频起伏与低频起伏成分的结构面形貌定量生成，制作高频起伏与低频起伏成分定量可控的结构面试样。The beneficial effects of the present invention are mainly manifested in: taking the characteristic that the undulation height of the high-frequency undulation component in the three-dimensional topography of the structural surface is significantly lower than that of the low-frequency undulation component as the starting point, based on the mean square value of the undulation height of the three-dimensional topography of the structural surface within the frequency range. Distribution function, in-depth study of the changing characteristics of the mean square value of the three-dimensional morphology fluctuation height of the structural surface as the frequency value gradually increases, pinpoint the turning point of the fluctuation height of the low-frequency component and the high-frequency component of the three-dimensional morphology of the structural surface, and quantitatively divide the high-frequency fluctuation components and The frequency limit between low-frequency undulation components determines the upper frequency limit of the high-frequency undulation component corresponding to the content ratio of high-frequency undulation and low-frequency undulation components on the structural surface of the rock mass, solving the problem of the inability to determine the frequency limit between different undulation components on the structural surface at the macro scale. To quantitatively identify the problem, and then complete the quantitative generation of structural surface morphology containing different high-frequency undulation and low-frequency undulation components, and produce structural test samples with quantitatively controllable high-frequency undulation and low-frequency undulation components.
附图说明Description of the drawings
图1是实例天然砂岩结构面的三维形貌模型；Figure 1 is a three-dimensional morphology model of the structural surface of an example natural sandstone;
图2是实例天然砂岩结构面形貌起伏高度均方值在频率范围内的分布函数图像；Figure 2 is a distribution function image of the mean square value of the undulation height of the natural sandstone structural surface in the frequency range of an example;
图3是仅含高频起伏成分形貌模型；Figure 3 is a morphology model containing only high-frequency fluctuation components;
图4是高频起伏与低频起伏成分含量比例γ0＝0的形貌模型；Figure 4 is a morphology model with a content ratio of high-frequency fluctuations and low-frequency fluctuations γ 0 =0;
图5是高频起伏与低频起伏成分含量比例γ0＝1的形貌模型。Figure 5 is a morphology model with a content ratio of high-frequency fluctuations and low-frequency fluctuations γ 0 =1.
具体实施方式Detailed ways
下面结合附图对本发明作进一步描述。The present invention will be further described below in conjunction with the accompanying drawings.
参照图1～图5，一种结构面形貌频谱成分定量可控的制样方法，所述方法包括以下步骤：Referring to Figures 1 to 5, a sample preparation method with quantitatively controllable structural surface morphology spectrum components includes the following steps:
S1、获取与岩体结构面实际剪切状态一致的结构面三维形貌模型；S1. Obtain a three-dimensional morphology model of the structural surface that is consistent with the actual shear state of the rock mass structural surface;
S2、基于二维功率谱密度确定岩体结构面三维形貌起伏高度均方值在频率范围内的分布函数，计算公式如下述公式(1)：S2. Determine the distribution function of the mean square value of the three-dimensional morphology fluctuation height of the rock mass structural surface in the frequency range based on the two-dimensional power spectral density. The calculation formula is as follows (1):
其中，P3D为高度均方值，PSD(fx,fy)为结构面形貌的二维功率谱密度，fx和fy分别为结构面形貌频率成分在x轴和y轴方向的空间频率，ft为频率阀值，fmax为最大频率值；Among them, P 3D is the height mean square value, PSD (f x , f y ) is the two-dimensional power spectral density of the structural surface topography, f x and f y are the frequency components of the structural surface topography in the x-axis and y-axis directions respectively. The spatial frequency of , f t is the frequency threshold, and f max is the maximum frequency value;
具体的，由式(1)可知，随着阀值频率ft的增大，结构面的起伏高度均方根值P3D逐渐增大，当ft增大至最大频率值时可得到结构面三维形貌整体的起伏高度均方值；Specifically, it can be seen from equation (1) that as the threshold frequency f t increases, the root mean square value P3 D of the fluctuation height of the structural surface gradually increases. When f t increases to the maximum frequency value, the structural surface can be obtained The mean square value of the overall undulation height of the three-dimensional topography;
S3、绘制岩体结构面三维形貌起伏高度均方值在频率范围内的分布函数图像，以函数图的转折点所对应的频率作为结构面三维形貌高频成分和低频成分的界限频率ftc；S3. Draw the distribution function image of the mean square value of the three-dimensional morphology fluctuation height of the rock mass structural surface within the frequency range, and use the frequency corresponding to the turning point of the function graph as the limiting frequency f tc of the high-frequency component and low-frequency component of the three-dimensional morphology of the structural surface. ;
具体的，结构面三维形貌中高频起伏成分的起伏高度显著低于低频起伏成分，当ft取值小于界限频率ftc时，随着阀值频率的增大结构面三维形貌起伏高度均方值增长速率较快，此时阀值频率仍处于低频成分区域；当ft取值大于界限频率ftc时，随着阀值频率的增大结构面三维形貌起伏高度均方值增长速率将变缓，因此，可依据式(1)函数图像的转折点定量确定结构面三维形貌高频成分和低频成分界限频率ftc的取值；Specifically, the undulation height of the high-frequency undulation component in the three-dimensional morphology of the structural surface is significantly lower than that of the low-frequency undulation component. When f t is less than the limit frequency f tc , as the threshold frequency increases, the undulation height of the three-dimensional morphology of the structural surface becomes uniform. The growth rate of the square value is fast, and the threshold frequency is still in the low-frequency component region at this time; when the value of f t is greater than the limit frequency f tc , as the threshold frequency increases, the growth rate of the mean square value of the three-dimensional morphology fluctuation height of the structural surface increases with the increase of the threshold frequency. will slow down, therefore, the values of the high-frequency component and low-frequency component limit frequency f tc of the three-dimensional topography of the structural surface can be quantitatively determined based on the turning point of the function image of Equation (1);
S4、保持岩体结构面中低频起伏成分含量不变，通过减少高频起伏成分的含量定量控制岩体结构面高频起伏与低频起伏成分的含量比例γ0，则与含量比例γ0所对应的高频起伏成分的频率上限fu的计算公式为：S4. Keep the content of low-frequency undulation components in the rock mass structural surface unchanged, and quantitatively control the content ratio γ 0 of high-frequency undulation and low-frequency undulation components in the rock mass structural surface by reducing the content of high-frequency undulation components, which corresponds to the content ratio γ 0 The calculation formula for the upper frequency limit fu of the high-frequency fluctuation component is:
具体的，结构面形貌高频起伏和低频起伏成分含量的比例可通过高频起伏与低频起伏频率范围的比值确定；Specifically, the ratio of the content of high-frequency fluctuations and low-frequency fluctuations in the structural surface morphology can be determined by the ratio of the frequency range of high-frequency fluctuations and low-frequency fluctuations;
S5、依据所确定的界限频率ftc或高频起伏成分的频率上限fu，提取岩体结构面三维形貌不同频率的起伏成分，建立高频起伏和低频起伏成分不同含量比例的结构面三维形貌模型；S5. Based on the determined limit frequency f tc or the upper frequency limit f u of the high-frequency undulation component, extract the undulation components of the three-dimensional morphology of the rock mass structural surface at different frequencies, and establish a three-dimensional structural surface with different proportions of high-frequency undulation and low-frequency undulation components. Morphological model;
S6、依据所定量建立的高频起伏和低频起伏成分含量比例不同的结构面三维形貌模型，采用岩石雕刻机雕刻制作高频起伏和低频起伏成分定量可控的岩体结构面试验。S6. Based on the quantitatively established three-dimensional morphology model of the structural surface with different proportions of high-frequency undulation and low-frequency undulation components, use a rock engraving machine to carve and produce a rock mass structural surface test with quantitatively controllable high-frequency undulation and low-frequency undulation components.
所述步骤S1包括：The step S1 includes:
S11、沿剪切方向采集岩体结构面三维形貌离散坐标数据，以坐标数据最小二乘拟合直线与坐标轴的夹角作为结构面三维形貌的趋势向，沿趋势向反向旋转结构面形貌数据，确保旋转后的结构面三维形貌趋势向呈水平状态；S11. Collect the discrete coordinate data of the three-dimensional morphology of the rock mass structural surface along the shear direction, use the angle between the coordinate data's least square fitting straight line and the coordinate axis as the trend direction of the three-dimensional morphology of the structural surface, and reversely rotate the structure along the trend direction. Surface topography data ensures that the three-dimensional topography trend of the rotated structural surface is horizontal;
S12、平移旋转后的结构面三维形貌数据，使得其起伏高度平均直线与坐标横轴重合，建立结构面三维形貌模型。S12. Translate and rotate the three-dimensional topography data of the structural surface so that the average straight line of its undulation height coincides with the horizontal axis of the coordinates, and establish a three-dimensional topography model of the structural surface.
具体的，在室内试验或现场试验测试岩体结构面的剪切强度时，应当使结构面剪切面保持与所施加的法向应力垂直，排除结构面整体趋势向向上所增加的抗剪强度或整体趋势向向下所减弱的抗剪强度。因此，在对结构面形貌的起伏特征进行描述或粗糙度进行计算时，应当排除结构面整体趋势向的影响。此外，通过将去除趋势向影响的结构面坐标数据进行平移，使其起伏高度平均直线与坐标轴重合可去除结构面形貌直流分量的影响，使后续步骤所计算得到的结构面三维形貌起伏高度均方值在频率范围内的分布函更为清晰的反映结构面在不同频率范围内的起伏特征。Specifically, when testing the shear strength of the rock mass structural surface in indoor tests or field tests, the shear surface of the structural surface should be kept perpendicular to the applied normal stress, and the increase in shear strength caused by the overall upward trend of the structural surface should be excluded. Or the shear strength is weakened by the overall downward trend. Therefore, when describing the undulation characteristics of the structural surface topography or calculating the roughness, the influence of the overall trend of the structural surface should be eliminated. In addition, the influence of the DC component of the structural surface topography can be removed by shifting the detrend to the affected structural surface coordinate data so that the average straight line of the undulation height coincides with the coordinate axis, so that the three-dimensional morphology fluctuations of the structural surface calculated in subsequent steps can be removed. The distribution function of the height mean square value in the frequency range more clearly reflects the fluctuation characteristics of the structural surface in different frequency ranges.
所述步骤S2中，岩体结构面三维形貌单边功率谱密度PSD*的计算公式为：In the step S2, the calculation formula of the one-sided power spectral density PSD * of the three-dimensional topography of the rock mass structural surface is:
其中，Lx和Ly为别为岩体结构面三维形貌在x轴和y轴方向的长度，Z(fx,fy)为结构面三维形貌z(x,y)在空间频域内的二维傅里叶变换，j2＝-1。Among them, L x and L y are the lengths of the three-dimensional morphology of the rock mass structural surface in the x-axis and y-axis directions respectively, and Z ( f Two-dimensional Fourier transform in the domain, j 2 =-1.
所述步骤S5的过程如下：The process of step S5 is as follows:
若建立仅含高频起伏成分，低频起伏成分含量为零的结构面三维形貌模型，可基于结构面三维形貌在频域空间的二维傅里叶变换，将小于界限频率ftc的频率成分设为零值，然后通过傅里叶逆变换得到仅含高频起伏成分的结构面三维形貌模型，计算公式如下述公式(4)：If a three-dimensional topography model of the structural surface is established that contains only high-frequency fluctuation components and zero low-frequency fluctuation components, the frequency that is smaller than the limit frequency f tc can be calculated based on the two-dimensional Fourier transform of the three-dimensional topography of the structural surface in the frequency domain space. The component is set to zero, and then the three-dimensional topography model of the structural surface containing only high-frequency undulation components is obtained through inverse Fourier transform. The calculation formula is as follows (4):
若保持低频起伏成分含量不变，建立高频起伏和低频起伏成分不同含量比例的结构面三维形貌模型，可基于结构面三维形貌在频域空间的二维傅里叶变换，将大于高频起伏成分的频率上限fu的频率成分设为零值，然后通过傅里叶逆变换得到高频起伏和低频起伏成分含量比例为γ0的三维形貌模型，计算公式如下述公式(5)：If the content of the low-frequency undulation component is kept unchanged and a three-dimensional morphology model of the structural surface with different content ratios of high-frequency undulation and low-frequency undulation components is established, the two-dimensional Fourier transform of the three-dimensional morphology of the structural surface in the frequency domain space will be larger than the high-frequency undulation component. The frequency upper limit of the frequency fluctuation component f u is set to zero, and then the three-dimensional topography model with a content ratio of high-frequency fluctuation and low-frequency fluctuation component is γ 0 is obtained through the inverse Fourier transform. The calculation formula is as follows: formula (5) :
实例：一种高频起伏与低频起伏成分含量比例定量可控的岩体结构面制样方法，包括如下步骤：Example: A rock mass structural surface sample preparation method with quantitatively controllable proportions of high-frequency undulation and low-frequency undulation components, including the following steps:
首先，选定位于湖北省宜昌市秭归县归州镇马家沟滑坡区域的砂岩结构面为研究对象，采用0.4mm的采样间距沿剪切方向采集天然砂岩结构面的形貌离散坐标数据，以坐标数据最小二乘拟合平面与坐标轴的夹角作为结构面三维形貌的趋势向，沿趋势向反向旋转结构面形貌数据，确保旋转后的结构面三维形貌趋势向呈水平状态，平移旋转后的三维形貌数据，使得其起伏高度平均平面与坐标平面重合，建立其三维形貌模型，如图1所示；First, the sandstone structural surface located in the Majiagou landslide area, Guizhou Town, Zigui County, Yichang City, Hubei Province was selected as the research object. The morphological discrete coordinate data of the natural sandstone structural surface was collected along the shear direction using a sampling spacing of 0.4mm. The angle between the least squares fitting plane of the coordinate data and the coordinate axis is used as the trend direction of the three-dimensional morphology of the structural surface. The structural surface morphology data is reversely rotated along the trend direction to ensure that the trend direction of the three-dimensional morphology of the structural surface after rotation is horizontal. , translate and rotate the three-dimensional topography data so that the average plane of its undulation height coincides with the coordinate plane, and establish its three-dimensional topography model, as shown in Figure 1;
然后，依据式(1)和(3)计算结构面三维形貌起伏高度均方值在频率范围内的分布函数，绘制结构面形貌起伏高度均方值在频率范围内的分布函数图像，如图2所示，以函数图的转折点所对应的频率作为结构面三维形貌高频成分和低频成分的界限频率ftc，即ftc＝0.1/mm；Then, according to formulas (1) and (3), calculate the distribution function of the mean square value of the three-dimensional morphology fluctuation height of the structural surface within the frequency range, and draw the distribution function image of the mean square value of the undulation height of the structural surface topography within the frequency range, such as As shown in Figure 2, the frequency corresponding to the turning point of the function graph is used as the limiting frequency f tc of the high-frequency component and low-frequency component of the three-dimensional topography of the structural surface, that is, f tc =0.1/mm;
进而，依据式(4)建立仅含高频起伏成分的结构面三维形貌模型，如图3所示；依据式(5)建立高频起伏和低频起伏成分含量比例γ0分别为0和1的三维形貌模型，分别如图4和图5所示。Furthermore, based on equation (4), a three-dimensional morphology model of the structural surface containing only high-frequency undulation components is established, as shown in Figure 3; based on equation (5), the content ratio γ 0 of high-frequency undulation and low-frequency undulation components is established, which is 0 and 1 respectively. The three-dimensional morphology model is shown in Figure 4 and Figure 5 respectively.
最后，依据所建立的高频起伏和低频起伏成分含量比例不同的结构面三维形貌模型图3～5，采用岩石雕刻机对岩石试块进行雕刻即可得到所需高频起伏与低频起伏比例γ0的岩体结构面试样。Finally, based on the established three-dimensional morphology model of the structural surface with different proportions of high-frequency undulations and low-frequency undulations components, as shown in Figures 3 to 5, the required ratio of high-frequency undulations and low-frequency undulations can be obtained by using a rock engraving machine to carve the rock test block. Sample of rock mass structure with γ 0 .
本说明书的实施例所述的内容仅仅是对发明构思的实现形式的列举，仅作说明用途。本发明的保护范围不应当被视为仅限于本实施例所陈述的具体形式，本发明的保护范围也及于本领域的普通技术人员根据本发明构思所能想到的等同技术手段。The content described in the embodiments of this specification is only an enumeration of implementation forms of the inventive concept, and is for illustrative purposes only. The protection scope of the present invention should not be considered to be limited to the specific forms stated in this embodiment. The protection scope of the present invention also extends to equivalent technical means that a person of ordinary skill in the art can think of based on the concept of the present invention.
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