CN106872579A - The method that normal distribution fitting rock mass velocity divides rock-mass quality classification - Google Patents

Abstract

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

Method for Classifying Rock Mass Quality by Fitting Rock Mass Wave Velocity with Normal Distribution

technical field

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.

Background technique

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.

Contents of the invention

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.

Technical scheme of the present invention is realized like this:

A method for dividing rock mass quality by fitting rock mass wave velocity with normal distribution, comprising the following steps:

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:

In the above formula: n represents the number of different rock mass wave velocity values after sorting statistics;

V _pi represents the wave velocity value of the i-th rock mass;

N _i represents the number of wave velocity values of the i-th rock mass;

S represents the area between the wave velocity data curve and the horizontal axis of the coordinate;

D _i represents the probability density of wave velocity data after probability normalization;

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)

Fit the wave velocity data after probability normalization to obtain the rock mass wave velocity data model function:

In the above formula: n represents the number of normal distribution probability density functions;

λ _i represents the i-th normal distribution probability density function weight, λ _i ≥ 0 and Σλ _i = 1;

μ _i represents the expected value in the i-th normal distribution probability density function;

σ _i represents the standard deviation in the i-th normal distribution probability density function;

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.

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.

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.

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.

The advantages of the present invention are:

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. 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. 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. 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.

Description of drawings

Fig. 1 is the statistical diagram of the rock mass wave velocity value measured in the embodiment of the present invention;

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;

Fig. 3 is a schematic diagram of normal distribution fitting rock mass quality classification in the embodiment of the present invention;

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.

detailed description

The technical solutions in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention.

The present invention provides a method for classifying rock mass quality by fitting rock mass wave velocity with normal distribution, comprising the following steps:

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.

Table 1 Statistical table of wave velocity values of rock mass

Wave speed (m/s) 2500 2530 2660 2730 2770 2810 2850 2890 2940 2980 3030 3070 amount) 1 1 1 1 4 5 6 7 3 13 11 27 Wave speed (m/s) 3120 3170 3220 3270 3330 3380 3440 3500 3570 3630 3700 3770 amount) twenty three 43 38 55 85 86 123 169 188 236 223 272 Wave speed (m/s) 3840 3920 4000 4080 4160 4250 4340 4440 4540 4650 4760 4870 amount) 257 251 195 264 270 269 275 299 330 404 379 429 Wave speed (m/s) 5000 5120 5260 5400 5550 5710 amount) 398 255 110 38 2 1

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).

In the above formula: n represents the number of different rock mass wave velocity values after sorting statistics;

Vpi represents the wave velocity value of the i-th rock mass;

N _i represents the number of wave velocity values of the i-th rock mass;

S represents the area between the wave velocity data curve and the horizontal axis of the coordinate;

D _i represents the probability density of wave velocity data after probability normalization;

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)

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 ):

In the above formula: n represents the number of normal distribution probability density functions;

λ _i represents the i-th normal distribution probability density function weight, λ _i ≥ 0 and Σλ _i = 1;

μ _i represents the expected value in the i-th normal distribution probability density function;

σ _i represents the standard deviation in the i-th normal distribution probability density function;

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.

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)

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.

See Figure 4 and Table 2 for the comparison between the grading of this method and the grading of the conventional method.

Table 2 Comparison table of rock mass classification standards

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.

Claims (4)

1. a method for normal distribution fitting rock mass wave velocity division rock mass quality classification is characterized in that comprising the steps: 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: $\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Vp</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Vp</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}$ ${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; S</span>}}$ In the above formula: n represents the number of different rock mass wave velocity values after sorting statistics; V _pi represents the wave velocity value of the i-th rock mass; N _i represents the number of wave velocity values of the i-th rock mass; S represents the area between the wave velocity data curve and the horizontal axis of the coordinate; D _i represents the probability density of wave velocity data after probability normalization; Step 2. Use the probability density function of the normal distribution under the least squares method $\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}$ Fit the wave velocity data after probability normalization to obtain the rock mass wave velocity data model function: $\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$ In the above formula: n represents the number of normal distribution probability density functions; λ _i represents the i-th normal distribution probability density function weight, λ _i ≥ 0 and Σλ _i = 1; μ _i represents the expected value in the i-th normal distribution probability density function; σ _i represents the standard deviation in the i-th normal distribution probability density function; 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). 2. the method for normal distribution fitting rock mass wave velocity division rock mass quality grading as claimed in claim 1, is characterized in that: in the step 3, classification basic principle is: when wave velocity fits single normal distribution probability density function curve fitting When the wave velocity is greater than the value of μ+σ, it is divided into the first level; if the wave speed is greater than μ-σ and less than the value of μ+σ, it is divided into the second level; if the wave speed is less than the value of μ-σ, it is divided into the third level. 3. the method for normal distribution fitting rock mass wave velocity division rock mass quality classification as claimed in claim 1, it is characterized in that: before step 2, also comprise that wave velocity data should carry out preprocessing step, after removing obvious isolated outliers , and then fit the normal distribution probability density function. 4. the method for normal distribution fitting rock mass wave velocity division rock mass quality classification as claimed in claim 1, is characterized in that: the normal distribution probability density function quantity that carries out fitting in step 2 depends on rock mass wave velocity statistical curve form The number of peaks in the middle is determined.