CN115046515A - Sliding surface position accurate determination method based on single-sliding-surface D-type deep hole inclination measuring curve - Google Patents
Sliding surface position accurate determination method based on single-sliding-surface D-type deep hole inclination measuring curve Download PDFInfo
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract
The invention discloses a sliding surface position accurate determination method based on a single-sliding-surface D-type deep hole inclination measuring curve, which comprises the steps of drawing a D-type deep accumulated displacement-time curve graph, calculating the relative displacement of soil bodies at different depths in a monitoring period, drawing a relative displacement-time curve graph of the soil bodies at different depths, drawing a relative displacement depth scatter diagram, drawing a relative displacement box diagram at different depths, extracting the relative displacement average value at different depths in the monitoring period, drawing an average relative displacement depth point diagram, intercepting monotonous interval data of a target inflection point, calculating interval scatter data by adopting a cubic spline interpolation method to obtain an equation set coefficient matrix, substituting the relative displacement as zero into an equation set, and obtaining the depth position of the inflection point, namely the position of the sliding surface. The invention adopts a simpler and more efficient data processing method based on the monitoring data, can accurately determine the position of the sliding surface, and effectively avoids the problem of large error caused by artificially and subjectively identifying the position of the sliding surface.
Description
Technical Field
The invention belongs to the technical field of landslide monitoring, and particularly relates to a sliding surface position accurate determination method based on a single-sliding-surface D-type deep hole inclination measuring curve.
Background
In landslide stability studies, landslide displacement monitoring is an important research direction. Through landslide displacement monitoring, data such as slope body deformation displacement rate and direction can be obtained, and through analyzing monitoring data, the knowledge of landslide deformation mechanism and deformation characteristics can be deepened, and an important basis is provided for unstability slope renovation. In landslide displacement monitoring, the accurate position of a landslide sliding surface is determined on the premise of evaluating the stability of a slope and effectively remedying the slope.
The slip plane identification method is classified into a non-deterministic method and a deterministic method. The nondeterministic method mainly comprises a simple mechanics identification method, a geophysical prospecting method, a numerical simulation method and the like; the sliding surface identified by the non-deterministic method is a speculative sliding surface and needs to be verified by the deterministic method; furthermore, non-deterministic methods are generally auxiliary means or means for conducting preliminary studies. And the landslide control engineering exploration, design and construction stages adopt a deterministic method to carry out sliding surface identification, and the deterministic method mainly comprises a field geological identification method, an exploration identification method and a deep layer displacement observation method.
At present, a deep level displacement observation method is a main sliding surface identification method, and the position of a sliding surface is visually judged according to the deformation characteristic of a deep accumulated displacement curve of a soil body in a monitoring period of a drill hole. Common landslide deep-hole inclination measurement curves (i.e., deep accumulated displacement-time curves) mainly include a "V" type, a "B" type, an "r" type, a "pendulum" type, a "compound" type and the like.
On the position recognition of the sliding surface of the D-shaped deep hole inclination measuring curve, the traditional visual judgment method has some obvious defects: 1. the method can only roughly judge the position of the sliding surface under the influence of the arrangement distance of the sensors and cannot accurately acquire the position information of the sliding surface; 2. the whole deep hole inclination measuring curve is approximately D-shaped in a bulge shape, the sliding range is large, the position of the sliding surface is the maximum bulge position of the bulge, but the depth corresponding to the maximum bulge position is usually difficult to directly and accurately obtain; 3. the horizontal and vertical coordinate observation scale of the deep accumulated displacement-time curve graph can also greatly influence the identification of the position of the sliding surface, and irrelevant deformation characteristics in the curve with too small observation scale are amplified, so that the capture of the characteristics of the sliding surface is not facilitated; 4. the observation scale is too large, the change characteristic of the accumulated displacement curve is not obvious, and the position of the sliding surface is difficult to determine.
Disclosure of Invention
The invention provides a method for accurately determining the position of a sliding surface based on a single-sliding-surface D-type deep hole inclination measuring curve according to the change characteristics of the D-type deep hole inclination measuring curve.
Therefore, the invention adopts the following technical scheme:
a sliding surface position accurate determination method based on a single-sliding-surface D-type deep hole inclination measuring curve is characterized by comprising the following specific steps:
1) and importing displacement monitoring data of the sensors of the deep hole inclinometer, drawing a drilling deep part accumulated displacement-time curve graph corresponding to each sensor according to the monitoring data, judging whether the deformation characteristic of the curve graph is D-shaped, and if the deformation characteristic is D-shaped, continuing to execute the following steps.
2) Taking the deep hole inclinometer at any position in the step 1), and calculating the data of each position sensor of the deep hole inclinometer by adopting a formula I to obtain the relative displacement of soil bodies at different depths in a monitoring period;
firstly, data of a topmost sensor and a secondary topmost sensor on the deep hole inclinometer are acquired;
Δs i =s i -s i+1 ①
in formula (I):
s i the displacement value of the soil body of the topmost sensor in a monitoring period is obtained;
s i+1 is a sub-top sensor ins i The displacement value of the soil body in the same monitoring period;
Δs i the soil body relative displacement value between the topmost sensor and the secondary topmost sensor in the monitoring period is obtained;
sequentially calculating soil body relative displacement values of the topmost sensor and the secondary topmost sensor in other monitoring periods by using a formula I;
and (3) sequentially calculating soil body relative displacement values of adjacent sensors at other depth positions on the deep hole inclinometer selected in the step 2) in different monitoring periods by using a formula (I).
3) Obtaining relative displacement values of the soil bodies at different depths in the monitoring period through the step 2), and drawing a 'relative displacement-time' curve graph of the soil bodies at different depths according to the relative displacement values;
according to the change characteristics of the D-type inclinometry curve, the characteristics of opposite positive and negative relative displacement can be generated in the upper and lower sections of the position of the sliding surface, so that a relative displacement-time curve graph is S-shaped, and the depth corresponding to the central inflection point (namely the position with the relative displacement value of 0) of the S-shaped curve is the position of the sliding surface.
4) Drawing a relative displacement-depth scatter diagram at different depths of the drilled hole according to the relative displacement numerical value obtained in the step 2), wherein the relative displacement-depth scatter diagram can more clearly master the deformation condition of the soil body at different depths of the drilled hole; then converting the relative displacement-depth scatter diagram at different depths into a relative displacement box type diagram;
the box chart is a statistical chart for displaying a group of data dispersion conditions, and can display an upper limit, a lower limit, a median, an upper quartile, a lower quartile, an abnormal value and the like of a group of data. The components and meanings of the box diagram are shown in figure 1.
Quartile: arranging a group of data according to a sequence from small to large, then dividing the data into four equal parts, wherein the numbers at the positions of three dividing points are quartiles;
a first quartile (q 1), also called "smaller quartile" or "lower quartile", equal to the 25 th percentile of all values in the sample, arranged from small to large, with the position of q1 = 1+ (n-1) 0.25;
a second quartile (q 2), also called "median", equal to the 50 th percentile of all values in the sample, arranged from small to large, the position of q2 = 1+ (n-1) × 0.5;
the third quartile (q 3), also known as the "larger quartile" or "upper quartile", is equal to the 75% of the numbers in the sample after all values are arranged from small to large. Position = 1+ (n-1) × 0.75 for q 3;
quartering spacing (IQR): the difference between the third quartile and the first quartile (q3 data-q 1 data);
whisser upper limit (an abnormal value if it is greater than this): q3 number + 1.5 IQR, (1.5 represents the excess ratio, is a coefficient, and can be adjusted according to actual conditions);
whisker lower limit (an abnormal value if less than this value): q1 number-1.5 IQR.
5) Calculating the average relative displacement value of data corresponding to each box-shaped graph according to the relative displacement box-shaped graphs, and drawing an average relative displacement-depth point line graph at different depths of the drill hole; and D-type curve monitoring data is converted into two-dimensional data between the average relative displacement and the depth through dimension reduction.
6) The "average relative displacement versus depth" point plot still retains the sigmoidal characteristic, and the determination of the sliding surface position is changed to determine the corresponding depth at which the average relative displacement is 0. The inflection point is positioned in the monotonous interval of the S-shaped curve; extracting scattered point data in a monotonous interval where an inflection point is located in an average relative displacement-depth point line graph as an analysis object;
calculating the extracted scatter data by a cubic spline interpolation method by taking the average relative displacement as an abscissa X and the depth as an ordinate Y to obtain a corresponding coefficient matrix; and (4) substituting the average relative displacement value at the inflection point into an X =0 to cubic spline interpolation method calculation formula to obtain a Y value, wherein the Y value is the position of the sliding surface.
Further, in the step 4): and the relative displacement-depth scatter diagram is converted into a relative displacement box type diagram by a quartile method, the median in the relative displacement box type diagram is the second quartile corresponding to each box type diagram, and the average relative displacement value of each single box type diagram data is calculated.
The calculation principle of cubic spline interpolation is as follows:
handle interval [ a, b]Divided into n intervals [ (x) 0 ,x 1 ),(x 1 ,x 2 ),...,(x n-1 ,x n )]A total of n +1 points, two of which are points x 0 =a,x n And (b). The curve of each small interval is a cubic equation, and the cubic spline equation meets the following conditions:
1) between each segmented cell [ x ] i ,x i+1 ]S (x) = S i (x) Are all a cubic equation
2) Satisfy the interpolation condition, i.e. S (x) i )=y i (i=0,1,..,n)
3) The curve is smooth, i.e. S (x), S ， (x),S ，， (x) Continuous
This cubic equation can be constructed as follows:
y=a i +b i +c i x 2 +d i x 3
this equation is called cubic spline S i (x) In that respect From S i (x) It can be seen that there are four unknowns (a) per cell i ,b i ,c i ,d i ) If there are n cells, there are 4n unknowns, and to solve these unknowns, we need 4n equations to solve.
First, S (x) since all points must satisfy the interpolation condition i )=y i (i =0, 1.. eta., n), except for two end points, each of all n-1 interior points satisfies S i (x i+1 )=y i+1 ,S i+1 (x i+1 )=y i+1 Two front and back piecewise cubic equations have 2(n-1) equations, and the two endpoints respectively satisfy the first and last cubic equations, so that there are 2n equations in total.
Secondly, the first derivatives of the n-1 interior points should be continuous, i.e. the same point at the end of the i-th interval and at the beginning of the i + 1-th interval, then their first derivatives are equal, i.e. S , i (x i+1 )=S ， i+1 (x i+1 ) There are n-1 equations.
Now there are 4n-2 equations in total, and we can solve all unknowns by subtracting the two equations, which we get from the boundary conditions. In practical calculations, a non-kinking boundary condition is generally used that forces the third derivative value of the first interpolated point to be equal to the third derivative value of the second point, and the third derivative value of the last first point to be equal to the third derivative value of the second to last point, i.e., S 0 ,,, (x 0 )=S 1 ,,, (x 1 ) And S n-2 ,,, (x n-1 )=S n-1 ,,, (x n )。
The specific derivation is as follows:
S i (x)=a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3
S i , =b i +2c i (x-x i )+3d i (x-x i ) 2
S i ,, (x)=2c i +6d i (x-x i )
is formed by S i (x)=a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 =y i Obtained a i =y i
② use of i =x i+1 -x i Denotes the step size, from S i (x i+1 )=y i+1 Push-out a i +h i b i +h i 2 c i +h i 3 d i =y i+1
③ from S i , (x i+1 )=S i+1 , (x i+1 ) Is pushed out
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
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
The following can be obtained:
b i +2h i c i +3h i 2 d i =b i+1
④S i ,, (x i+1 )=S i+1 ,, (x i+1 ) Push-out 2c i +6h i d i =2c i+1
Let m i =S i ,, (x i )=2c i Then 2c i +6h i d i =2c i+1 Rewritten as m i +6h i d i =m i+1 Can obtain the product
d i =(m i+1 -m i )/(6h i )
Fifthly, present at a i ,c i ,d i Can be expressed as a second derivative relation, substituted into
a i +h i b i +h i 2 c i +h i 3 d i =y i+1
Can obtain the product
b i =(y i+1 -y i )/h i -h i m i /2-h i (m i+1 -m i )/6
Sixthly, a i ,b i ,c i ,d i Substitution into b i +2h i c i +3h i 2 d i =b i+1 Can obtain
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 ]
In conclusion, a linear equation system with m as an unknown number is constructed.
Derived from the above formula, at non-kinking boundary conditions:
S 0 ,,, (x 0 )=S 1 ,,, (x 1 )
S n-2 ,,, (x n-2 )=S n-1 ,,, (x n-1 )
due to the fact that
S i ,,, (x)=6d i And d is i =(m i+1 -m i )/(6h i )
d 0 =d 1 d n-2 =d n-1
Namely, it is
h 1 (m 1 -m 0 )=h 0 (m 2 -m 1 )
h n-1 (m n-1 -m n-2 )=h n-2 (m n -m n-1 )
The new system of equations coefficient matrix can be written as follows:
the invention has the beneficial effects that:
1. the method analyzes and processes the D-type deep position displacement monitoring data of the drill hole, so that the utilization degree of the data is improved; on the other hand, the complete set of perfect calculation method provided by the invention can accurately determine the position of the sliding surface, has higher reliability and can provide basis and reference for identifying the position of the sliding surface;
2. compared with the traditional method, the method adopts a more efficient data processing method based on the actual monitoring data, can quickly and accurately determine the position of the sliding surface, greatly improves the working efficiency, and effectively avoids the situation of large error caused by artificially and subjectively judging and identifying the position of the sliding surface; and the situation that the calculation result is not ideal due to unreasonable parameter setting and large model assumed difference in theoretical derivation.
Drawings
FIG. 1 is a schematic diagram of box chart identifiers in step 5) of the present invention;
FIG. 2 is a graph of accumulated displacement versus time for the depth of a borehole in accordance with an embodiment of the present invention;
FIG. 3 is a graph of relative displacement versus depth for a borehole in accordance with an embodiment of the present invention;
FIG. 4 is a graph of relative displacement versus depth for a borehole in accordance with an embodiment of the present invention;
FIG. 5 is a box plot of relative displacement of the borehole according to an embodiment of the present invention;
FIG. 6 is a plot of the average relative displacement points of the boreholes for an embodiment of the present invention;
FIG. 7 is a monotonic interval depth-relative displacement scatter plot of an embodiment of the present invention;
FIG. 8 is a diagram illustrating the calculation results of cubic spline interpolation according to an embodiment of the present invention;
FIG. 9 is a schematic view of the position of the sliding surface according to an embodiment of the present invention;
FIG. 10 is a flow chart of the steps of the present invention.
Detailed Description
The invention is further explained with reference to the accompanying drawings and specific embodiments, which are deep hole displacement monitoring data of a certain landslide position in Yunnan:
1) the data is imported and a deep accumulated displacement-time curve (as shown in fig. 2) is drawn, and from fig. 2, it can be seen that the curve is in a "D" shape, the sliding surface of the slope body is already formed and the position is approximately 10m, and the following steps are continued in order to further determine the accurate position of the sliding surface.
2) The relative displacement of the soil bodies at different depths in the monitoring period can be calculated by a formula I, and a curve graph of the relative displacement-time of the soil bodies at different depths is drawn (as shown in figure 3);
3) the accumulated displacement at the position of the sliding surface is the maximum, when the relative displacement is calculated by adopting a formula (I), the characteristic that the positive and negative of the relative displacement are opposite appears in the upper and lower sections of the position, so that the whole curve graph of the relative displacement-depth is S-shaped, the depth corresponding to the central inflection point (namely the position with the relative displacement value of 0) of the S-shaped curve is the position of the sliding surface, and the square frame in the graph 3 is the area where the inflection point is located.
4) To determine the area of the inflection point in one step, the data of the relative displacement-time curve of the borehole in fig. 2 is plotted as a scatter diagram of the relative displacement-depth at different depths of the borehole, as shown in fig. 4: the discrete situation of the relative displacement of the soil bodies at different depths in the monitoring period can be clearly observed from the graph 4, and the interval where the inflection point is located can be more clearly displayed;
the relative displacement data of each day of any depth soil body in the monitoring process is represented by a box diagram, and then a relative displacement-depth scatter diagram of the soil body at different depths of the drilled hole in the figure 4 is converted into a relative displacement box diagram at different depths, as shown in the figure 5;
as can be found from the graph 5, the data characteristic change is clearer, the relative displacement average value in each box-type graph can clearly show the displacement change trend of soil bodies at different depths of the drill hole in the monitoring period, and the S-shaped characteristic is more obvious. Therefore, the relative displacement average value in each box type graph can be extracted for further data analysis.
5) From the relative displacement averages of the sets of data corresponding to each box plot, a plot of "average relative displacement versus depth" points at different depths in the borehole can be plotted, as shown in FIG. 6. And the monitoring data of the D-type deep hole inclination measuring curve is converted into two-dimensional data between the average relative displacement and the depth through dimension reduction. As can be seen from fig. 6, the curve has a distinct S-shape in the fluctuation section, and the inflection point falls in the monotonous section (as shown in the block region) in the middle of the S-shaped curve. Therefore, the inflection point position is locked in the monotonous interval in the curve of fig. 6, and the scatter data in the monotonous interval is extracted as a further study object.
6) And extracting scatter data in the monotonous interval, and drawing a depth-relative displacement scatter diagram by taking the average relative displacement as an abscissa X and the depth as an ordinate Y of the extracted scatter data.
From the foregoing analysis, it can be seen that the inflection point is a position where the relative displacement is 0, which is equivalent to finding the magnitude of the Y value when X =0, and the scatter data in the monotonic interval is discontinuous and is suitable for the interpolation method, and the ordinary linear interpolation has low accuracy and cannot consider the influence of the magnitude of the adjacent point data. And the influence of the adjacent points is required to be considered when the soil body sliding is involved and changes, so that all scattered points in the monotonous interval can be used as calculation data by adopting a cubic spline interpolation method, a coefficient matrix corresponding to the monotonous interval is further obtained, and the coefficient matrix is substituted into X =0, so that a Y value corresponding to the monotonous interval can be obtained.
In this case, the cubic spline interpolation calculation is completed by calling an interpolation function formula of the interplate library in python, wherein the formula adopts a non-kinking boundary condition. Let X =0, it is calculated that the corresponding Y value in the monotonic segment is 9.304, i.e., the sliding surface is located at a depth 9.304m (as shown in fig. 8).
As can be seen from fig. 9, for the relative displacement-depth plot, the horizontal line is located at the inflection point position of the sigmoid curve interval; for the cumulative displacement-depth plot, the slip plane position is close to the curve relief maximum. The sliding surface position 9.304m calculated by the method is scientific, reasonable and accurate.
Claims (2)
1. A sliding surface position accurate determination method based on a single-sliding-surface D-type deep hole inclination measuring curve is characterized by comprising the following specific steps:
1) leading in displacement monitoring data of sensors of the deep hole inclinometer, drawing a drilling deep accumulated displacement-time curve graph corresponding to each sensor according to the monitoring data, judging whether the deformation characteristic of the curve graph is D-shaped, and if the deformation characteristic is D-shaped, continuing to execute the following steps;
2) taking the deep hole inclinometer in the step 1), and calculating data of each position sensor of the deep hole inclinometer by adopting a formula I to obtain the relative displacement of soil bodies at different depths in a monitoring period;
firstly, data of a topmost sensor and a secondary topmost sensor on the deep hole inclinometer are acquired;
Δs i =s i -s i+1 ①
in formula (I):
s i the displacement value of the soil body of the topmost sensor in a monitoring period is obtained;
s i+1 is a sub-top sensor ins i The displacement value of the soil body in the same monitoring period;
Δs i the soil body relative displacement value between the topmost sensor and the secondary topmost sensor in the monitoring period is obtained;
sequentially calculating soil body relative displacement values of the topmost sensor and the secondary topmost sensor in other monitoring periods by using a formula I;
sequentially calculating soil body relative displacement values of adjacent sensors at other depth positions on the deep hole inclinometer selected in the step 2) in different monitoring periods through a formula I;
3) obtaining relative displacement values of the soil bodies at different depths in the monitoring period through the step 2), and drawing a relative displacement-time curve chart of the soil bodies at different depths according to the relative displacement values;
4) drawing a 'relative displacement-depth' scatter diagram at different depths of the drill hole according to the relative displacement numerical value obtained in the step 2), and converting the 'relative displacement-depth' scatter diagram at different depths into a 'relative displacement box type diagram';
5) calculating an average relative displacement value of data corresponding to each box-shaped graph according to the relative displacement box-shaped graphs, and drawing an average relative displacement-depth point line graph at different depths of the drill hole according to the average relative displacement value;
6) extracting scattered point data in a monotonous interval where an inflection point is located in an average relative displacement-depth point line graph as an analysis object;
calculating the extracted scatter data by a cubic spline interpolation method by taking the average relative displacement as an abscissa X and the depth as an ordinate Y to obtain a corresponding coefficient matrix; and (4) substituting the average relative displacement value at the inflection point into an X =0 to cubic spline interpolation method calculation formula to obtain a Y value, wherein the Y value is the position of the sliding surface.
2. The method for accurately determining the sliding surface position based on the single-sliding-surface D-type deep hole inclination measuring curve according to claim 1, wherein in the step 4): and the relative displacement-depth scatter diagram is converted into a relative displacement box type diagram by a quartile method, the median in the relative displacement box type diagram is the second quartile corresponding to each box type diagram, and the average relative displacement value of each single box type diagram data is calculated.
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| CN116026267A (en) * | 2022-12-12 | 2023-04-28 | 中铁西北科学研究院有限公司 | Sliding surface position accurate determination method based on multi-sliding-surface B-type deep hole inclinometry curve |
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| CN116026267A (en) * | 2022-12-12 | 2023-04-28 | 中铁西北科学研究院有限公司 | Sliding surface position accurate determination method based on multi-sliding-surface B-type deep hole inclinometry curve |
| CN116026267B (en) * | 2022-12-12 | 2023-09-08 | 中铁西北科学研究院有限公司 | Sliding surface position accurate determination method based on multi-sliding-surface B-type deep hole inclinometry curve |
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