A method for accurately determining the sliding surface position based on the D-type deep hole inclinometer curve of a single sliding surface.

Abstract

The present invention discloses a method for accurately determining the position of a sliding surface based on a single sliding surface D-type deep hole inclinometer curve, drawing a "D" type deep cumulative displacement-time curve, calculating the relative displacement of soil at different depths during the monitoring period, drawing a "relative displacement-time" curve of soil at different depths, drawing a "relative displacement depth" scatter plot, drawing a relative displacement box plot at different depths, extracting the average relative displacement at different depths during the monitoring period, drawing a "average relative displacement depth" point-line plot, intercepting the monotonic interval data where the target inflection point is located, using the cubic spline interpolation method to calculate the interval scatter data, obtaining the coefficient matrix of the equation group, substituting the relative displacement into the equation group as zero, and obtaining the depth position of the inflection point, which is the position of the sliding surface. The present invention adopts a simpler and more efficient data processing method based on monitoring data, can accurately determine the position of the sliding surface, and effectively avoids the problem of large errors caused by human subjective judgment of the sliding surface position.

Description

Technical Field

[0001] The invention belongs to the technical field of landslide monitoring, and in particular relates to a method for accurately determining the position of a sliding surface based on a single sliding surface D-type deep hole inclinometer curve. Background Art

[0002] In the study of landslide stability, landslide displacement monitoring is an important research direction. Through landslide displacement monitoring, not only can we obtain data such as slope deformation displacement rate and direction, but also by analyzing the monitoring data, we can deepen our understanding of the landslide deformation mechanism and deformation characteristics, and provide an important basis for the treatment of unstable slopes. In landslide displacement monitoring, determining the accurate position of the landslide sliding surface is a prerequisite for evaluating the stability of the slope and effectively treating it.

[0003] Sliding surface identification methods are divided into non-deterministic methods and deterministic methods. Non-deterministic methods mainly include simple mechanical identification method, geophysical method, numerical simulation method, etc. The sliding surface identified by non-deterministic methods is a speculative sliding surface, which needs to be verified by deterministic methods. In addition, non-deterministic methods are generally auxiliary means or means of conducting preliminary research. Deterministic methods are used to identify sliding surfaces during the investigation, design and construction stages of landslide control projects. Deterministic methods mainly include field geological identification method, exploration identification method and deep displacement observation method.

[0004] At present, the deep displacement observation method is the main method for identifying the sliding surface. This method intuitively determines the location of the sliding surface based on the deformation characteristics of the deep cumulative displacement curve of the soil during the monitoring period. Common landslide deep hole inclinometer curves (i.e. deep cumulative displacement-time curves) mainly include "V" type, "B" type, "r" type, "pendulum" type and "composite" type.

[0005] In the identification of the sliding surface position of the "D"-type deep hole inclinometer curve, the traditional intuitive judgment method has some obvious defects: 1. Affected by the spacing of the sensor arrangement, this method can only roughly determine the position of the sliding surface, and cannot accurately obtain the sliding surface position information; 2. The deep hole inclinometer curve is generally bulging and approximates to the "D" shape, with a large sliding range. The position of the sliding surface is the maximum value of the bulge, but it is usually difficult to directly and accurately obtain the depth corresponding to the maximum bulge; 3. The horizontal and vertical coordinate observation scales of the deep cumulative displacement-time curve will also greatly affect the identification of the sliding surface position. If the observation scale is too small, the irrelevant deformation features in the curve will be magnified, which is not conducive to capturing the sliding surface features; 4. If the observation scale is too large, the change characteristics of the cumulative displacement curve are not obvious, and it is difficult to determine the position of the sliding surface. Summary of the invention

[0006] According to the changing characteristics of the D-type deep hole inclinometer curve, the present invention proposes a method for accurately determining the position of the sliding surface based on the single sliding surface D-type deep hole inclinometer curve. This method is based on relative displacement and gradually finds the inflection points of the curve characteristics through data dimensionality reduction to determine the interval where the sliding surface is located, and then uses the cubic spline interpolation method to accurately determine the position of the sliding surface.

[0007] To this end, the present invention adopts the following technical solutions:

[0008] A method for accurately determining the position of a sliding surface based on a single sliding surface D-type deep hole inclinometer curve, characterized in that the specific steps are as follows:

[0009] 1) Import the displacement monitoring data of the deep hole inclinometer sensor, draw the deep hole cumulative displacement-time curve corresponding to each sensor based on the monitoring data, and determine whether the deformation feature of the curve is type D. If it is type D, continue to perform the following steps.

[0010] 2) Take the deep hole inclinometer at any position in step 1), and use formula ① to calculate the sensor data at each position of the deep hole inclinometer to obtain the relative displacement of the soil at different depths during the monitoring period;

[0011] First, obtain the data of the top sensor and the second top sensor on the deep hole inclinometer;

[0012] Δs i =s i -s i+1 ①

[0013] In formula ①:

[0014] s i is the soil displacement value of the top sensor during a monitoring period;

[0015] s i+1 For the top sensor in the s i Soil displacement values ​​during the same monitoring period;

[0016] Δs i is the relative displacement value of the soil between the topmost sensor and the second topmost sensor during the monitoring period;

[0017] The soil relative displacement values ​​of the top sensor and the second top sensor in other monitoring periods are calculated in turn by formula ①;

[0018] The relative displacement values ​​of the soil at adjacent sensors at other depths on the deep hole inclinometer selected in step 2) during different monitoring periods are calculated in sequence by formula ①.

[0019] 3) The relative displacement values ​​of the soil at different depths during the monitoring period are obtained through step 2), and the "relative displacement-time" curves of the soil at different depths are drawn according to the relative displacement values;

[0020] From the changing characteristics of the D-type inclinometer curve, it can be seen that the upper and lower intervals of the sliding surface will have opposite positive and negative relative displacements, making the "relative displacement-time" curve S-shaped. The depth corresponding to the central inflection point of the S-shaped curve (that is, the relative displacement value is 0) is the location of the sliding surface.

[0021] 4) Draw a "relative displacement-depth" scatter plot at different depths of the borehole based on the relative displacement values ​​obtained in step 2). The "relative displacement-depth" scatter plot can more clearly grasp the deformation of the soil at different depths of the borehole; then convert the "relative displacement-depth" scatter plot at different depths into a "relative displacement box plot";

[0022] A box plot is a statistical chart used to show the dispersion of a set of data. It can show the upper and lower bounds, median, upper and lower quartiles, and outliers of a set of data. The components and meanings of a box plot are as follows: Figure 1 shown.

[0023] Quartile: Arrange a set of data in ascending order, and then divide it into four equal parts. The numbers at the three dividing points are the quartiles.

[0024] The first quartile (q1): also known as the "smaller quartile" or "lower quartile", is equal to the 25th percentile of all values ​​in the sample arranged from small to large. The position of q1 = 1+(n-1)*0.25;

[0025] The second quartile (q2): also known as the "median", is equal to the 50th number of all values ​​in the sample arranged from small to large. The position of q2 = 1+(n-1)*0.5;

[0026] The third quartile (q3), also known as the "larger quartile" or "upper quartile", is equal to the 75th percentile of all the values ​​in the sample arranged from small to large. The position of q3 = 1+(n-1)* 0.75;

[0027] Interquartile range (IQR): the difference between the third quartile and the first quartile (q3 data - q1 data);

[0028] Whisker upper limit (values ​​greater than this are considered outliers): q3 number + 1.5*IQR (1.5 represents the excess ratio, which is a coefficient and can be adjusted according to actual conditions);

[0029] Whisker lower limit (values ​​lower than this value are outliers): q1 number - 1.5*IQR.

[0030] 5) According to the “relative displacement box plot”, the average relative displacement value of the data corresponding to each box plot is calculated, and a point-line graph of “average relative displacement-depth” at different depths of the borehole is drawn; the monitoring data of the D-type curve is transformed into two-dimensional data between the average relative displacement and depth through dimensionality reduction.

[0031] 6) The “average relative displacement-depth” dot-line graph still retains the characteristics of the S-curve, and the determination of the sliding surface position becomes the determination of the depth corresponding to the average relative displacement of 0. Since the inflection point is located in the monotonic interval of the S-curve, the scattered data in the monotonic interval where the inflection point in the “average relative displacement-depth” dot-line graph is extracted as the analysis object;

[0032] The extracted scattered data are calculated using the average relative displacement as the horizontal coordinate X and the depth as the vertical coordinate Y using the cubic spline interpolation method to obtain the corresponding coefficient matrix; since the average relative displacement value at the inflection point is 0, substituting X=0 into the cubic spline interpolation method calculation formula will give the Y value, which is the location of the sliding surface.

[0033] Furthermore, in the step 4): the "relative displacement-depth" scatter plot is converted into a "relative displacement box plot" by the quartile method, the median in the relative displacement box plot is the second quartile corresponding to each box plot, and the average relative displacement value of each single box plot data is calculated.

[0034] The calculation principle of cubic spline interpolation is as follows:

[0035] Divide the interval [a,b] into n intervals [(x 0 ,x 1 ),(x 1 ,x 2 ),...,(x n-1 ,x n )], there are n+1 points in total, two of which are endpoints x 0 =a,x n =b. The curve between each cell is a cubic equation, and the cubic spline equation satisfies the following conditions:

[0036] 1) In each segmented interval [x i ,x i+1 ], S(x)=S i (x) is a cubic equation

[0037] 2) Satisfy the interpolation condition, that is, S(x i )=y i (i=0,1,..,n)

[0038] 3) The curve is smooth, that is, S(x), S ， (x),S ，， (x)Continuous

[0039] Then this cubic equation can be constructed as follows:

[0040] y=a i +b i +c i x 2 +d i x 3

[0041] This equation is called the cubic spline function S i (x). From S i (x) It can be seen that each small interval has four unknowns (a i ,b i ,c i ,d i ), there are n small intervals, then there are 4n unknowns. To solve these unknowns, we need 4n equations to solve.

[0042] First, since all points must satisfy the interpolation condition, S(x i )=y i (i=0,1,...,n), except for the two endpoints, each of the n-1 interior points satisfies S i (x i+1 )=y i+1 ,S i+1 (x i+1 )=y i+1 There are 2(n-1) equations for the two piecewise cubic equations before and after, plus the two endpoints satisfying the first and last cubic equations respectively, so there are a total of 2n equations.

[0043] Secondly, the first-order derivatives of the n-1 internal points should be continuous, that is, if the end point of the i-th interval and the starting point of the i+1-th interval are the same point, then their first-order derivatives are equal, that is, S , i (x i+1 )=S ， i+1 (x i+1 ) then there are n-1 equations.

[0044] Now there are 4n-2 equations in total. There are only two equations left to solve all the unknowns. We get these two equations through boundary conditions. In actual calculations, non-kink boundary conditions are generally used. This boundary condition forces the third-order derivative value of the first interpolation point to be equal to the third-order derivative value of the second point, and finally the third-order derivative value of the first point to be equal to the third-order derivative value of the second-to-last point, that is, S 0 ,,, (x 0 )=S 1 ,,, (x 1 ) and S n-2 ,,, (x n-1 )=S n-1 ,,, (x n ).

[0045] The specific derivation is as follows:

[0046] S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3

[0047] S i , =b i +2c i (xx i )+3d i (xx i ) 2

[0048] S i ,, (x)=2c i +6d i (xx i )

[0049] ① By S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 =y i , we can get a i =yi

[0050] ②Use h i =x i+1 -x i Represents the step length, represented by S i (x i+1 )=y i+1 Launch a i +h i b i +h i 2 c i +h i 3 d i =y i+1

[0051] ③ By S i , (x i+1 )=S i+1 , (x i+1 )roll out

[0052] S i , (x i+1 )=b i +2c i (x i+1 -x i )+3d i (x i+1 -x i ) 2 =b i +2c i h+3d i h 2

[0053] S i+1 , (x i+1 )=b i+1 +2c i (x i+1 -x i+1 )+3d i (x i+1 -x i+1 ) 2 =b i+1

[0054] We can get:

[0055] b i +2h i c i +3h i 2 d i =bi+1

[0056] ④S i ,, (x i+1 )=S i+1 ,, (x i+1 ) Launched 2c i +6h i d i =2c i+1

[0057] Assume m i =S i ,, (x i )=2c i , then 2c i +6h i d i =2c i+1 Rewrite as m i +6h i d i =m i+1 Available

[0058] d i =(m i+1 -m i ) / (6h i )

[0059] ⑤Now a i ,c i ,d i can be expressed as a second-order derivative relationship, substituting it into

[0060] a i +h i b i +h i 2 c i +h i 3 d i =y i+1

[0061] Available

[0062] b i =(y i+1 -y i ) / h i -h i m i / 2-h i (m i+1 -m i ) / 6

[0063] ⑥Will a i,b i ,c i ,d i Substitute b i +2h i c i +3h i 2 d i =b i+1 Available

[0064] h i m i +2(h i +h i+1 )m i+1 +h i+1 m i+2 =6[(y i+2 -y i+1 ) / h i+1 -(y i+1 -y i ) / h i ]

[0065] In summary, a system of linear equations with m as the unknown number is constructed.

[0066] According to the above formula, under non-kink boundary conditions:

[0067] S 0 ,,, (x 0 )=S 1 ,,, (x 1 )

[0068] S n-2 ,,, (x n-2 )=S n-1 ,,, (x n-1 )

[0069] because

[0070] S i ,,, (x)=6d i , and d i =(m i+1 -m i ) / (6h i )

[0071] d 0 =d 1 d n-2 =d n-1

[0072] Right now

[0073] h 1 (m 1 -m 0 )=h 0 (m 2 -m 1 )

[0074] h n-1 (m n-1 -m n-2 )=h n-2 (m n -m n-1 )

[0075] Then the coefficient matrix of the new system of equations can be written as follows:

[0076]

[0077] The beneficial effects of the present invention are:

[0078] 1. The present invention analyzes and processes the borehole D-type deep displacement monitoring data, thereby improving the utilization of the data; on the other hand, the present invention proposes a complete set of perfect calculation methods, which can accurately determine the position of the sliding surface, have higher reliability, and can provide a basis and reference for the identification of the sliding surface position;

[0079] 2. Compared with the traditional method, the present invention adopts a more efficient data processing method based on actual monitoring data, which can quickly and accurately determine the position of the sliding surface, greatly improving work efficiency, and effectively avoiding the situation where the error is large due to subjective judgment of the sliding surface position; and the situation where the calculation results are not ideal due to unreasonable parameter settings and large differences in model assumptions in theoretical derivation. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 This is a box plot identification schematic diagram of step 5) of the present invention;

[0081] Figure 2 is a graph of the cumulative displacement-time curve of the deep part of the borehole according to an embodiment of the present invention;

[0082] Figure 3 is a relative displacement-depth curve diagram of a borehole according to an embodiment of the present invention;

[0083] Figure 4 is a relative displacement-depth curve diagram of a borehole according to an embodiment of the present invention;

[0084] Figure 5 is a box diagram of relative displacement of drilling holes according to an embodiment of the present invention;

[0085] Figure 6 is a dot-line diagram of the average relative displacement of the borehole according to an embodiment of the present invention;

[0086] Figure 7 is a scatter plot of monotonic interval depth-relative displacement according to an embodiment of the present invention;

[0087] Figure 8 Schematic diagram of calculation results of cubic spline interpolation method according to an embodiment of the present invention;

[0088] Fig. 9 is a schematic diagram of the position of the sliding surface of an embodiment of the present invention;

[0089] Fig.10 It is a flow chart of the steps of the present invention. DETAILED DESCRIPTION

[0090] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, which are deep hole displacement monitoring data of a landslide location in Yunnan:

[0091] 1) Import data and draw the deep cumulative displacement-time curve (such as Figure 2 ),from Figure 2 It can be found that the curve is "D" shaped and the sliding surface of the slope has been formed, and its position is approximately 10m. In order to further determine the exact position of the sliding surface, continue to perform the following steps.

[0092] 2) Formula ① can be used to calculate the relative displacement of soil at different depths during the monitoring period, and the “relative displacement-time” curve of soil at different depths can be drawn (e.g. Figure 3 );

[0093] 3) The cumulative displacement at the location of the sliding surface is the largest. When the relative displacement is calculated using formula ①, the relative displacement will be opposite in positive and negative between the upper and lower intervals of this position, making the "relative displacement-depth" curve graph S-shaped as a whole. The depth corresponding to the central inflection point of the S-shaped curve (that is, the relative displacement value is 0) is the location of the sliding surface. Figure 3 The box in the middle is the area where the inflection point is located.

[0094] 4) In order to determine the region where the inflection point is located in one step, Figure 2 The borehole relative displacement-time curve data is plotted into a "relative displacement-depth" scatter plot at different depths of the borehole, such as Figure 4 Shown by: Figure 4 The discreteness of the relative displacement of the soil at different depths during the monitoring period can be clearly observed, and the interval where the inflection point is located can be more clearly displayed;

[0095] The daily relative displacement data of soil at any depth within the monitoring area are expressed by a box plot. Figure 4 The "relative displacement-depth" scatter plot of the soil at different depths of the borehole is transformed into a "relative displacement box plot" at different depths, such as Figure 5 As shown;

[0096] from Figure 5 It can be found that the data feature changes are clearer, and the average relative displacement in each box plot can clearly show the displacement change trend of the soil at different depths of the borehole during the monitoring period, and the S-shaped feature is more significant. Therefore, the average relative displacement in each box plot can be extracted for the next step of data analysis.

[0097] 5) Based on the average relative displacement of each group of data corresponding to each box plot, a point-line graph of "average relative displacement-depth" at different depths of the borehole can be drawn, such as Figure 6 As shown in the figure, the monitoring data of the D-type deep hole inclinometer curve is transformed into two-dimensional data between the average relative displacement and the depth after dimension reduction. Figure 6 It can be found that the curve is obviously S-shaped in the fluctuation section, and the inflection point falls on the monotonic interval in the middle of the S-shaped curve (as shown in the box area). Therefore, the inflection point position is locked at Figure 6 In the monotonic interval of the curve, the scattered data in the monotonic interval are extracted as the further research object.

[0098] 6) Extract the scattered data within the monotonic interval, and use the average relative displacement as the horizontal coordinate X and the depth as the vertical coordinate Y to draw a depth-relative displacement scatter plot.

[0099] From the previous analysis, we know that the inflection point is the position where the relative displacement is 0, which is equivalent to finding the size of the Y value when X=0. The scattered data in the monotonic interval is discontinuous and suitable for interpolation. Ordinary linear interpolation has low accuracy and cannot consider the influence of the size of adjacent point data. Soil sliding is a related change that requires consideration of the influence of nearby points. Therefore, the cubic spline interpolation method can be used to take all scattered points in the monotonic interval as calculation data, and then the corresponding coefficient matrix of the monotonic interval is obtained. Substituting X=0, the corresponding Y value under the monotonic interval can be obtained.

[0100] In this case, the cubic spline interpolation method is calculated by calling the interpolation function formula of the interpolate library in Python. The formula uses the non-kinked boundary condition. Let X = 0. After calculation, it can be obtained that the corresponding Y value in this monotonic interval is 9.304, that is, the sliding surface is located at a depth of 9.304m (such as Figure 8 as shown).

[0101] Depend on Fig. 9 It can be found that for the relative displacement-depth curve, the horizontal line is located at the inflection point of the S-curve interval; for the cumulative displacement-depth curve, the sliding surface position is close to the maximum value of the curve convexity. This shows that the sliding surface position of 9.304m calculated by this method is scientific, reasonable and accurate.

Claims

1. A method for accurately determining the position of a sliding surface based on a single sliding surface D-type deep hole inclinometer curve, characterized in that: The specific steps are as follows: 1) Import the displacement monitoring data of the deep hole inclinometer sensor, draw the deep hole cumulative displacement-time curve corresponding to each sensor based on the monitoring data, and determine whether the deformation feature of the curve is type D. If it is type D, continue to perform the following steps; 2) Take the deep hole inclinometer in step 1) and use formula ① to calculate the sensor data at each position of the deep hole inclinometer to obtain the relative displacement of the soil at different depths during the monitoring period; First, obtain the data of the top sensor and the second top sensor on the deep hole inclinometer; Δs i =s i -s i+1 ① In formula ①: s i is the soil displacement value of the top sensor during a monitoring period; s i+1 For the top sensor in the s i Soil displacement values ​​during the same monitoring period; Δs i is the relative displacement value of the soil between the topmost sensor and the second topmost sensor during the monitoring period; The soil relative displacement values ​​of the top sensor and the second top sensor in other monitoring periods are calculated in turn by formula ①; The relative displacement values ​​of the soil at adjacent sensors at other depths of the deep hole inclinometer selected in step 2) during different monitoring periods are calculated in sequence by formula ①; 3) The relative displacement values ​​of the soil at different depths during the monitoring period are obtained through step 2), and the "relative displacement-time" curves of the soil at different depths are drawn according to the relative displacement values; 4) Draw a "relative displacement-depth" scatter plot at different depths of the borehole based on the relative displacement values ​​obtained in step 2), and then convert the "relative displacement-depth" scatter plot at different depths into a "relative displacement box plot"; 5) According to the "Relative Displacement Box Plot", calculate the average relative displacement value of the data corresponding to each box plot, and draw a point-line graph of "Average Relative Displacement-Depth" at different depths of the borehole based on the average relative displacement value; 6) Extract the scattered data in the monotonic interval where the inflection point in the "average relative displacement-depth" point-line graph is located as the analysis object; The extracted scattered data are calculated using the average relative displacement as the horizontal coordinate X and the depth as the vertical coordinate Y using the cubic spline interpolation method to obtain the corresponding coefficient matrix; since the average relative displacement value at the inflection point is 0, substituting X=0 into the cubic spline interpolation method calculation formula will give the Y value, which is the location of the sliding surface.

2. The method for accurately determining the position of a sliding surface based on a single sliding surface D-type deep hole inclinometer curve according to claim 1 is characterized in that: In the step 4), the "relative displacement-depth" scatter plot is converted into a "relative displacement box plot" by the quartile method, the median in the relative displacement box plot is the second quartile corresponding to each box plot, and the average relative displacement value of each single box plot data is calculated.

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