CN106872579A - The method that normal distribution fitting rock mass velocity divides rock-mass quality classification - Google Patents
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Abstract
本发明提供一种正态分布拟合岩体波速划分岩体质量分级的方法,包括如下步骤:步骤一、将实测的岩体波速数据按从小到大排序,并统计各波速数据的个数,将波速数据概率归一化;步骤二、利用最小二乘法下正态分布概率密度函数拟合概率归一化后的波速数据,得到岩体波速数据模型函数;步骤三、利用正态分布概率密度函数f(x,μ,σ)曲线在x=μ±σ处为拐点的特性,在岩体波速数据模型函数F(x)中以x=μi±σi作为岩体分级标准值,利用岩体波速数据模型函数F(x)中期望值、标准差进行岩体分级。本发明只根据工区岩体波速值,再利用统计学中正态分布概率密度函数来进行划分岩体质量分级划分,其可减少工地现场试验工作量,显著提高工效。
The present invention provides a method for grading rock mass quality by fitting rock mass wave velocities with normal distribution, comprising the following steps: step 1, sorting the measured rock mass wave velocities data from small to large, and counting the number of each wave velocity data, Normalize the wave velocity data probability; Step 2, use the normal distribution probability density function under the least squares method to fit the probability normalized wave velocity data, and obtain the rock mass wave velocity data model function; Step 3, use the normal distribution probability density The function f(x, μ, σ) curve is the inflection point at x=μ±σ. In the rock mass wave velocity data model function F(x), x=μ i ±σ i is used as the rock mass classification standard value, using The expected value and standard deviation in the rock mass wave velocity data model function F(x) are used to classify the rock mass. The invention only uses the normal distribution probability density function in statistics to classify the quality of the rock mass according to the wave velocity value of the rock mass in the work area, which can reduce the workload of field tests on the construction site and significantly improve the work efficiency.
Description
技术领域technical field
本发明涉及工程勘察设计工程勘察设计技术领域,具体是一种正态分布拟合岩体波速划分岩体质量分级的方法。The invention relates to the technical field of engineering survey and design engineering survey and design, in particular to a method for dividing rock mass quality and grading by fitting rock mass wave velocity with normal distribution.
背景技术Background technique
目前在划分岩体质量分级方面,现有水利、电力、公路、铁路等各行业勘察领域均无具体明确的算法,目前各行业规程、规范均采用岩体坚硬程度(坚硬岩、较硬岩、较软岩、软岩、极软岩)与岩体完整程度(完整、较完整、较破碎、破碎、极破碎)列表对应方式来划分岩体质量分级。实际工作中,岩体质量分级划分一般根据实验室岩块测试结果(抗压强度,波速)、现场波速测试等数据再结合经验值来划分。存在的突出问题是计算方法不明确、掺杂个人经验、分级标准值不准确、工区实际情况针对性不强等缺陷。At present, in terms of classification of rock mass quality, there are no specific and clear algorithms in the existing water conservancy, electric power, highway, railway and other industry survey fields. Soft rock, soft rock, extremely soft rock) and rock mass integrity (complete, relatively complete, relatively broken, broken, extremely broken) are listed to classify rock mass quality. In actual work, the classification of rock mass quality is generally based on laboratory rock block test results (compressive strength, wave velocity), on-site wave velocity test data and other data combined with empirical values. The outstanding problems are that the calculation method is not clear, personal experience is mixed, the grading standard value is not accurate, and the actual situation of the work area is not targeted.
发明内容Contents of the invention
本发明的目的是提供一种更适用于工程勘察设计的较准确、更具针对性的岩体质量分级计算方法,即只根据工区岩体波速值,再利用统计学中正态分布概率密度函数来进行划分岩体质量分级划分。The purpose of the present invention is to provide a more accurate and more targeted rock mass quality classification calculation method that is more suitable for engineering survey and design, that is, only according to the wave velocity value of the rock mass in the work area, and then use the normal distribution probability density function in statistics To carry out the division of rock mass quality classification.
本发明的技术方案是这样实现的:Technical scheme of the present invention is realized like this:
一种正态分布拟合岩体波速划分岩体质量分级的方法,包括如下步骤:A method for dividing rock mass quality by fitting rock mass wave velocity with normal distribution, comprising the following steps:
步骤一、将实测的岩体波速数据按从小到大排序,并统计各波速数据的个数,将波速数据概率归一化:Step 1. Sort the measured rock mass wave velocity data from small to large, and count the number of each wave velocity data, and normalize the wave velocity data probability:
上式中:n代表排序统计后不同岩体波速值的数量;In the above formula: n represents the number of different rock mass wave velocity values after sorting statistics;
Vpi代表第i个岩体波速值;V pi represents the wave velocity value of the i-th rock mass;
Ni代表第i个岩体波速值的个数;N i represents the number of wave velocity values of the i-th rock mass;
S代表波速数据曲线与坐标横轴间面积;S represents the area between the wave velocity data curve and the horizontal axis of the coordinate;
Di代表概率归一化后波速数据的概率密度;D i represents the probability density of wave velocity data after probability normalization;
步骤二、利用最小二乘法下正态分布概率密度函数(根据实际情确定正态分布概率密度函数个数,同一工区,同一岩性的情况下用1至2个正态分布概率密度函数,复杂情况下可用3个以上正态分布概率密度函数)Step 2. Use the least squares method to determine the normal distribution probability density function (determine the number of normal distribution probability density functions according to the actual situation, use 1 to 2 normal distribution probability density functions in the same work area and the same lithology, which is complicated In some cases, more than 3 normal distribution probability density functions can be used)
拟合概率归一化后的波速数据,得到岩体波速数据模型函数:Fit the wave velocity data after probability normalization to obtain the rock mass wave velocity data model function:
上式中:n代表正态分布概率密度函数数量;In the above formula: n represents the number of normal distribution probability density functions;
λi代表第i个正态分布概率密度函数权重,λi≥0且∑λi=1;λ i represents the i-th normal distribution probability density function weight, λ i ≥ 0 and Σλ i = 1;
μi代表第i个正态分布概率密度函数中期望值;μ i represents the expected value in the i-th normal distribution probability density function;
σi代表第i个正态分布概率密度函数中标准差;σ i represents the standard deviation in the i-th normal distribution probability density function;
步骤三、利用正态分布概率密度函数f(x,μ,σ)曲线在x=μ±σ处为拐点的特性,在岩体波速数据模型函数F(x)中以x=μi±σi作为岩体分级标准值,利用岩体波速数据模型函数F(x)中期望值、标准差进行岩体分级。分级基本原则为,当波速适合单条正态分布概率密度函数曲线拟合时,以波速大于μ+σ值划分为第一级;以波速大于μ-σ且小于μ+σ值划分为第二级;以波速小于μ-σ值划分为第三级。当波速适合两条正态分布概率密度函数曲线拟合时,在两条曲线相邻拐点处取平均值作为分界值,其他不变。Step 3, using the characteristic of the normal distribution probability density function f(x, μ, σ) curve at x=μ±σ as the inflection point, in the rock mass wave velocity data model function F(x) with x=μ i ±σ i is used as the rock mass classification standard value, and the rock mass classification is carried out by using the expected value and standard deviation in the rock mass wave velocity data model function F(x). The basic principle of grading is that when the wave velocity is suitable for a single normal distribution probability density function curve fitting, the wave velocity greater than the value of μ+σ is divided into the first level; the wave velocity is greater than the value of μ-σ and less than the value of μ+σ into the second level ; It is divided into the third level by the wave velocity less than the μ-σ value. When the wave velocity fits two normal distribution probability density function curves, take the average value at the adjacent inflection points of the two curves as the cut-off value, and keep the others unchanged.
进一步的,步骤三中分级基本原则为:当波速适合单条正态分布概率密度函数曲线拟合时,以波速大于μ+σ值划分为第一级;以波速大于μ-σ且小于μ+σ值划分为第二级;以波速小于μ-σ值划分为第三级。Further, the basic principle of classification in step three is: when the wave speed is suitable for a single normal distribution probability density function curve fitting, the wave speed is greater than the value of μ+σ to be divided into the first level; the wave speed is greater than μ-σ and less than μ+σ The value is divided into the second level; the wave velocity is less than the μ-σ value is divided into the third level.
进一步的,步骤二之前还包括对波速数据应进行预处理步骤,剔除明显的孤立异常值后,再进行正态分布概率密度函数拟合。Further, before the second step, a preprocessing step should be performed on the wave velocity data, and after the obvious isolated outliers are eliminated, the normal distribution probability density function is then fitted.
进一步的,步骤二中进行拟合的正态分布概率密度函数数量视岩体波速统计曲线形态中波峰数确定。Further, the number of normal distribution probability density functions to be fitted in step 2 is determined depending on the number of peaks in the shape of the rock mass wave velocity statistics curve.
本发明的优点是:The advantages of the present invention are:
1.只需要岩体的波速值即可划分岩体分级,不需要其他岩体测试参数,从而减少工地现场试验工作量,可显著提高工效。1. Only the wave velocity value of the rock mass is needed to classify the rock mass, and no other rock mass test parameters are required, thereby reducing the workload of on-site testing and significantly improving work efficiency.
2.本方法建立在数理统计基础上,参与计算的岩体波速值越多,结果越能真实放映工区岩体实际情况。本发明可随着参与计算的岩体波速值的增多,及时修正。2. This method is based on mathematical statistics. The more rock mass wave velocity values involved in the calculation, the more realistic the results can reflect the actual situation of the rock mass in the work area. The present invention can be corrected in time with the increase of rock mass wave velocity values participating in the calculation.
3.引入权重λi可以降低模型函数中各正态分布概率密度函数中的期望值μi和标准差σi互相影响,如当波速测试数据大部分集中低波速区或高波速区时,所拟合的模型F(x)函数会主要体现在在权重λi的变化,而期望值μi和标准差σi则变化很小,保持拟合结果的准确性。3. Introducing the weight λ i can reduce the interaction between the expected value μ i and the standard deviation σ i in each normal distribution probability density function in the model function, such as when most of the wave velocity test data are concentrated in the low wave velocity area or high wave velocity area, the proposed The fitted model F(x) function will be mainly reflected in the change of weight λ i , while the expected value μ i and standard deviation σ i will change very little, maintaining the accuracy of the fitting result.
4.实用简便,计算迅速,易于推广普及。经过多个工区进行的实际应用,结果证明本发明在技术上是可行的,与传统分级方法相对比,其计算差异不大于5%,且更能体现出工区岩体的实际情况。4. Practical and simple, quick calculation, easy to popularize. After practical application in many work areas, the result proves that the present invention is technically feasible. Compared with the traditional grading method, the calculation difference is not more than 5%, and it can better reflect the actual situation of the rock mass in the work area.
附图说明Description of drawings
图1是本发明实施例中实测的岩体波速值统计图;Fig. 1 is the statistical diagram of the rock mass wave velocity value measured in the embodiment of the present invention;
图2是本发明实施例中正态分布概率密度曲线拟合岩体波速概率密度曲线图;Fig. 2 is a normal distribution probability density curve fitting rock mass wave velocity probability density curve figure in the embodiment of the present invention;
图3是本发明实施例中正态分布拟合岩体质量分级示意图;Fig. 3 is a schematic diagram of normal distribution fitting rock mass quality classification in the embodiment of the present invention;
图4是本发明正态分布拟合岩体分级与常规岩体分级对比图,其中图4(a)为常规岩体分级,图4(b)为正态分布拟合岩体分级。Fig. 4 is a comparison chart of normal distribution fitting rock mass classification and conventional rock mass classification of the present invention, wherein Fig. 4 (a) is conventional rock mass classification, and Fig. 4 (b) is normal distribution fitting rock mass classification.
具体实施方式detailed description
下面将结合本发明中的附图,对本发明中的技术方案进行清楚、完整地描述。The technical solutions in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention.
本发明提供一种正态分布拟合岩体波速划分岩体质量分级的方法,包括如下步骤:The present invention provides a method for classifying rock mass quality by fitting rock mass wave velocity with normal distribution, comprising the following steps:
步骤一、将实测的岩体波速数据按从小到大排序,并统计各波速数据的个数,如表1所示,并绘制岩体波速值统计图,见图1。Step 1. Sort the measured rock mass wave velocity data from small to large, and count the number of each wave velocity data, as shown in Table 1, and draw a statistical map of rock mass wave velocity values, as shown in Figure 1.
表1岩体波速值统计表Table 1 Statistical table of wave velocity values of rock mass
将波速数据概率归一化:即利用归一化公式,将岩体波速值与坐标横轴间面积归为1,绘制岩体波速值概率密度曲线(岩体波速值概率密度曲线与岩体波速值统计曲线形态相似,为倍数关系)。Normalize the wave velocity data probability: that is, use the normalization formula to classify the area between the rock mass wave velocity value and the coordinate horizontal axis as 1, and draw the rock mass wave velocity value probability density curve (rock mass wave velocity value probability density curve and rock mass wave velocity The shape of the value statistics curve is similar, which is a multiple relationship).
上式中:n代表排序统计后不同岩体波速值的数量;In the above formula: n represents the number of different rock mass wave velocity values after sorting statistics;
Vpi代表第i个岩体波速值;Vpi represents the wave velocity value of the i-th rock mass;
Ni代表第i个岩体波速值的个数;N i represents the number of wave velocity values of the i-th rock mass;
S代表波速数据曲线与坐标横轴间面积;S represents the area between the wave velocity data curve and the horizontal axis of the coordinate;
Di代表概率归一化后波速数据的概率密度;D i represents the probability density of wave velocity data after probability normalization;
步骤二、利用最小二乘法下正态分布概率密度函数(根据实际情况确定正态分布概率密度函数个数,同一工区,同一岩性的情况下用1至2个正态分布概率密度函数,复杂情况下可用3个以上正态分布概率密度函数)Step 2. Use the least squares method to determine the normal distribution probability density function (determine the number of normal distribution probability density functions according to the actual situation, use 1 to 2 normal distribution probability density functions in the same work area and the same lithology, which is complicated In some cases, more than 3 normal distribution probability density functions can be used)
拟合概率归一化后的波速数据,得到岩体波速数据模型函数F(x)及各项参数(λi、μi、σi):Fit the wave velocity data after probability normalization to obtain the rock mass wave velocity data model function F(x) and various parameters (λ i , μ i , σ i ):
上式中:n代表正态分布概率密度函数数量;In the above formula: n represents the number of normal distribution probability density functions;
λi代表第i个正态分布概率密度函数权重,λi≥0且∑λi=1;λ i represents the i-th normal distribution probability density function weight, λ i ≥ 0 and Σλ i = 1;
μi代表第i个正态分布概率密度函数中期望值;μ i represents the expected value in the i-th normal distribution probability density function;
σi代表第i个正态分布概率密度函数中标准差;σ i represents the standard deviation in the i-th normal distribution probability density function;
在执行步骤二之前还可对波速数据应进行预处理步骤,剔除明显的孤立异常值后,再进行正态分布概率密度函数拟合。Before step 2, the wave velocity data should be preprocessed, and after removing obvious isolated outliers, the normal distribution probability density function can be fitted.
利用正态分布概率密度函数基于最小二乘法拟合岩体波速值概率密度曲线如图2所示,其中一个实施例中,岩体波速数据模型函数为:Utilize the normal distribution probability density function to fit the rock mass wave velocity value probability density curve based on the least squares method as shown in Figure 2, in one of the embodiments, the rock mass wave velocity data model function is:
F(x)=0.46·f(x,3920,390)+(1-0.46)·f(x,4820,290)F(x)=0.46 f(x,3920,390)+(1-0.46)f(x,4820,290)
步骤三、利用正态分布概率密度函数f(x,μ,σ)曲线在x=μ±σ处为拐点的特性,在岩体波速数据模型函数F(x)中以x=μi±σi作为岩体分级标准值,利用岩体波速数据模型函数F(x)中期望值、标准差进行岩体分级。分级基本原则为,当波速适合单条正态分布概率密度函数曲线拟合时,以波速大于μ+σ值划分为第一级;以波速大于μ-σ且小于μ+σ值划分为第二级;以波速小于μ-σ值划分为第三级,如图3所示。当波速适合两条正态分布概率密度函数曲线拟合时,在两条曲线相邻拐点处取平均值作为分界值,其他不变。Step 3, using the characteristic of the normal distribution probability density function f(x, μ, σ) curve at x=μ±σ as the inflection point, in the rock mass wave velocity data model function F(x) with x=μ i ±σ i is used as the rock mass classification standard value, and the rock mass classification is carried out by using the expected value and standard deviation in the rock mass wave velocity data model function F(x). The basic principle of grading is that when the wave velocity is suitable for a single normal distribution probability density function curve fitting, the wave velocity greater than the value of μ+σ is divided into the first level; the wave velocity is greater than the value of μ-σ and less than the value of μ+σ into the second level ; It is divided into the third level by the wave velocity less than the μ-σ value, as shown in Figure 3. When the wave velocity fits two normal distribution probability density function curves, take the average value at the adjacent inflection points of the two curves as the cut-off value, and keep the others unchanged.
本方法分级与常规方法分级对比见图4及表2。See Figure 4 and Table 2 for the comparison between the grading of this method and the grading of the conventional method.
表2岩体分级标准对比表Table 2 Comparison table of rock mass classification standards
以上所述,仅为本发明的具体实施方式,但本发明的保护范围并不局限于此,任何属于本技术领域的技术人员在本发明揭露的技术范围内,可轻易想到的变化或替换,都应涵盖在本发明的保护范围之内。因此,本发明的保护范围应该以权利要求的保护范围为准。The above is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto, any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention, All should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.
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CN113657515A (en) * | 2021-08-20 | 2021-11-16 | 盾构及掘进技术国家重点实验室 | Classification method for judging and improving tunnel surrounding rock grade of FMC model based on rock sensitivity parameters |
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