CN115830174A - Method for obtaining time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall - Google Patents
Method for obtaining time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall Download PDFInfo
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Abstract
The invention discloses a method for acquiring a time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall, belonging to the technical field of geological disaster management; the method is based on the SAR image with long time sequence, and the settlement information of the surrounding buildings of the subway line area in the construction period is obtained by utilizing a PS-InSAR method; verifying the PS-InSAR monitoring result by using the leveling monitoring result; determining the width of a time sequence settling tank by using a Mann-Kendall test method based on a long time sequence settlement monitoring result on a PS point; verifying the width of the settling tank by using engineering parameters and empirical parameters; and substituting the relevant parameters into a fitting formula to obtain a time sequence settling tank curve. According to the method, the advantages of the PS-InSAR and the Mann-Kendall are combined, the dynamic time sequence settling tank curve is finally obtained, the space-time evolution rule of ground settlement along the subway line can be accurately mastered, and a theoretical basis is provided for monitoring, preventing and controlling ground settlement disasters along the subway line.
Description
Technical Field
The invention relates to the technical field of geological disaster management, in particular to a method for acquiring a time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall.
Background
The large-scale construction of subway engineering easily causes ground settlement, and threatens the safety of surrounding buildings. In the excavation process of the subway tunnel, the excavation of the foundation pit and the underground structure can affect the rock stratum structure, disturb the soil body and cause the settlement and deformation of the earth surface. In addition, subway construction relates to foundation ditch engineering, and in the excavation of foundation ditch, construction precipitation causes groundwater level to reduce too big, causes excavation district and peripheral area to produce ground subsides, and then causes calamity such as wall body fracture, pipeline rupture, road collapse. When the settlement difference is large, the engineering phenomena of primary building deformation, ballast bed plate deformation, tunnel segment fracture, breakage, collapse and the like can be caused.
The monitoring method for ground settlement along the subway line generally comprises the traditional leveling monitoring and InSAR monitoring. The traditional level monitoring method has the defects of long operation period, poor real-time performance, high resource consumption, low efficiency and the like. In addition, due to the limitation of manpower and material resources, the number and range of the arrangement of the leveling points are limited, and large-range and long-time observation cannot be realized. The Peck formula is usually based on level monitoring results and subway engineering parameters to obtain a ground settlement curve within the influence range of subway construction. However, the Peck formula can only obtain the curve of the subsider after the subway construction, and is limited by the spatial position of the leveling point, so that the dynamic change condition of the ground subsidence along the subway line cannot be obtained in a large range. The PS-InSAR method has the advantages of long time sequence, large range, high precision and the like, and the monitoring precision can reach millimeter level. However, due to the limitation of the principle, the PS points are not uniformly distributed in space, and a spatially continuous ground settlement distribution cannot be obtained. In addition, the settlement information acquired by the PS-InSAR mainly comprises an average settlement rate and an accumulated settlement amount, so that the time point of sudden change caused by subway construction cannot be obtained, and the influence caused by subway construction is described.
Aiming at the problems, the invention provides a method for acquiring a time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall, which can dynamically describe the space-time evolution characteristics of ground settlement in the subway construction period. .
Disclosure of Invention
The invention aims to establish a regional ground subsidence numerical model containing spatial discontinuity phenomena such as cracks, collapse and the like under a unified framework, provides data support for urban ground subsidence simulation prediction and disaster prevention and control, and provides a method for acquiring a time sequence subsidence tank curve by fusing PS-InSAR and Mann-Kendall.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for obtaining a time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall comprises the following steps:
s1, acquiring an SAR image with a wide coverage range and a long time sequence, and acquiring ground settlement information of a building area in a subway line region based on a PS-InSAR technology;
s2, performing precision verification on the PS-InSAR result by using the level monitoring data, wherein the specific process is as follows: based on actually measured level monitoring data, selecting a PS point closest to each level point in space distance as a homonymous point by using a principle of a closest distance; then comparing the annual settlement amount and the time sequence settlement amount obtained based on the PS-InSAR technology with the annual settlement amount and the time sequence settlement amount obtained through actual measurement; will determine the coefficient R 2 And the root mean square error RMSE are used as a judgment standard for carrying out precision verification;
s3, determining the width of the time sequence settling tank by using a Mann-Kendall inspection method based on a long time sequence settling monitoring result on a PS point, wherein the specific process is as follows: carrying out mutation inspection on the time sequence settlement of the PS points by a Mann-Kendall inspection method, judging whether the development trend of the ground settlement has mutation during the construction period, if so, calculating the space distance between the PS points and the subway tunnel to be the width W of the time sequence settlement tank, and recording the maximum calculated width of the settlement tank as W 1 (ii) a According to the existing research, the settling tank is continuously enlarged towards two sides by taking the tunnel as the center in the horizontal direction, and the width of the settling tank is also continuously increased. When the construction is finished, the maximum sinking is achievedWidth W of the groove 1 The method is also the maximum influence range caused by subway construction;
s4, verifying and correcting the width of the settling tank by using engineering parameters and empirical parameters, wherein the specific process is as follows: collecting engineering geological parameters of subway construction and buried depth parameters of the subway, and calculating by a Peck formula to obtain the width W of the settling tank after the construction is finished 2 (ii) a Calculating the maximum width W of the settling tank obtained in the step S3 1 And the width W of the settling tank calculated by a Peck formula 2 Comparing the two to select a decision coefficient R 2 And the root mean square error RMSE is used as a judgment standard for carrying out precision verification;
s5, substituting the relevant parameters into a fitting formula to obtain a time sequence settling tank curve, wherein the specific process is as follows: and (4) constructing a fitting formula of the time sequence settling tank according to the Peck formula, and substituting the width W of the settling tank obtained by calculating through the PS points in the S3 into the fitting formula to obtain a time sequence settling tank curve.
Preferably, the sedimentation information includes an average sedimentation rate and a cumulative sedimentation amount based on the initial image;
the step of obtaining the ground settlement information of the building area along the subway based on the PS-InSAR technology in the step S1 specifically comprises the following steps:
s1.1, selecting a main image according to a space-time baseline and Doppler information, and registering and resampling other auxiliary images to the main image;
s1.2, conjugate multiplication is carried out on the main image and the auxiliary image, and an interference pattern is calculated;
s1.3, extracting a high-coherence point target by using a correlation index (such as a time coherence coefficient, an energy stability coefficient and the like), and performing time sequence analysis on the differential phase to finally obtain a millimeter-scale deformation rate result, deformation history information, DEM residual error and atmospheric delay error of discrete points.
Preferably, the software for processing the PS-InSAR of the radar image in S1 comprises commonly used software such as GAMMA, SNAP, PIE-SAR, ENVI/Sarscape, SARPROZ and the like.
Preferably, the method for determining whether the time-series sedimentation amount is mutated by using a Mann-Kendall test method in S3 includes:
assuming that the time-sequence settling volume at the point PS is sample X, the cumulative settling volume corresponding to the time t =1,2, ·, n of the sample X is X 1 ,x 2 ,···，x n Constructing a rank sequence S k The calculation formula is as follows:
wherein S is calculated separately k Mean value of E (S) k ) Sum variance var (S) k ) The calculation formula is as follows:
statistical quantity UF under the assumption that the time series is randomly independent k The calculation formula of (2) is as follows:
UF k is a standard positive Taiwan distribution, and is composed of time series (x) 1 ,x 2 ,···，x n ) Obtaining a statistic sequence; UB k Is UF k By the inverse order (x) of the time series n ,x n-1 ,···，x 1 ) Calculating to obtain;
the significance level was set at α =0.05 and the critical value was set at U 0.05 =. + -. 1.96, judge U 0.05 = 1.96 two straight lines and UF k 、UB k The curve position relationship of (1): if UF k Or UB k Greater than 0, indicating time-sequential settlingThe ascending trend is, conversely, the descending trend; the region of the curve exceeding the critical line is a time region in which the change occurs; if UF k And UB k The two curves have intersection points and the intersection points are positioned between critical lines, and the time corresponding to the intersection points is the mutation points, namely the time when the sedimentation is mutated.
Preferably, the width of the settling tank is calculated according to a Peck formula mentioned in S4, and the specific calculation formula is as follows:
W 2 ≈2.5i
wherein z is the tunnel axis burial depth m;
is the internal friction angle of the stratum around the tunnel; i is the distance m from the inflection point of the curve of the surface subsider to the central axis of the excavated body; w 2 The width of the ground settling tank is m, namely the influence range of ground settlement caused after tunnel construction.
Preferably, the fitting formula of the settling tank mentioned in S5 is:
wherein S is max The maximum settlement of the earth surface, m, is positioned at the central axis of the tunnel; x is the horizontal distance between the ground and the center of the tunnel, and m; s (x) is settlement amount at a position x away from the center of the tunnel; i is the distance m from the curve inflection point of the surface subsider to the central axis of the excavated body; v. of i Formation damage per unit lengthLoss rate, m 3 (ii)/m; w is the time sequence settler width m obtained by Mann-Kendall test.
Preferably, the Mann-Kendall test in S3, S4 and S5, the calculation of the Peck formula, the calculation of the time-series settler curve and the like are obtained by software calculation such as Matlab, python and the like.
Compared with the prior art, the invention provides a method for obtaining a time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall, which has the following beneficial effects:
(1) The method is based on SAR satellite remote sensing data, a PS-InSAR monitoring technology and a Mann-Kendall mutation detection method are fused, and a time sequence settlement curve of the subway with high spatial-temporal resolution in a construction period is obtained. By utilizing the design, the defects that the leveling monitoring is low in spatial-temporal resolution, the Peck formula is limited by the position of the leveling point and can only fit a settling tank curve after construction is completed, the PS point distribution density in the PS-InSAR method is low and the like can be effectively overcome. Compared with the traditional monitoring method, the method combines the advantages of monitoring the ground settlement by the PS-InSAR technology, obtains the influence range of subway construction on the ground settlement by using a Mann-Kendall mutation inspection method, obtains the time-sequence settling tank curve and realizes dynamic monitoring of the ground settlement in the subway line area.
(2) The method can obtain the ground settlement information with high precision and high space-time resolution in the area along the subway line, and provides a high-precision settlement data set for related departments. Based on the data set obtained by the invention, the mechanism research of ground settlement along the subway line is carried out, and the method has important significance for scientific development of cities and safe construction and operation of subway engineering.
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FIG. 1 is a schematic flow diagram of a method for obtaining a time-series settler curve by fusing PS-InSAR and Mann-Kendall according to the invention;
fig. 2 is a diagram illustrating accuracy verification of PS-InSAR monitoring results in embodiment 2 of the present invention;
FIG. 3 is a graph of a time-series settler obtained in example 2 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Example 1:
referring to fig. 1, a method for obtaining a time-series settler curve by fusing PS-InSAR and Mann-Kendall includes the following steps:
s1, obtaining an SAR image with wide coverage range and long time sequence, obtaining the average settlement rate of a building area along the subway line based on a PS-InSAR technology, obtaining the accumulated settlement based on an initial image and the like, and specifically comprising the following contents:
s1.1, selecting a main image according to a space-time baseline and Doppler information, and registering and resampling other auxiliary images to the main image;
s1.2, performing conjugate multiplication on the main image and the auxiliary image to calculate an interference pattern;
s1.3, extracting a high-coherence point target by using the correlation index, and performing time sequence analysis on the differential phase to finally obtain a millimeter-scale deformation rate result of the discrete point, deformation history information, a DEM residual error and an atmospheric delay error;
it should be noted that: the processing software of the PS-InSAR of the radar image in the S1 comprises GA MMA, SNAP, PIE-SAR, ENVI/Sarscape and SARPROZ software;
s2, performing precision verification on the PS-InSAR result by using the level monitoring data, wherein the specific process is as follows: based on actually measured level monitoring data, selecting a PS point closest to each level point in space distance as a homonymous point by using a principle of a closest distance; then comparing the annual settlement amount and the time sequence settlement amount obtained based on the PS-InSAR technology with the annual settlement amount and the time sequence settlement amount obtained through actual measurement; will determine the coefficient R 2 And the root mean square error RMSE is used as a judgment standard for carrying out precision verification;
s3, determining the width of the time sequence settling tank by using a Mann-Kendall inspection method based on a long time sequence settling monitoring result on a PS point, wherein the specific process is as follows: carrying out mutation inspection on the time sequence settlement of the PS points by a Mann-Kendall inspection method, and judging whether the development trend of the ground settlement has a mutation in the construction periodIf the sudden change exists, calculating the space distance between the PS point and the subway tunnel, and taking the space distance as the width W of the time sequence settling tank, and recording the maximum calculated settling tank width as W 1 ；
The method for judging whether the time sequence settlement amount is mutated or not by using the Mann-Kendall test method mentioned in the S3 comprises the following steps:
assuming that the time-sequence settling volume at the point PS is sample X, the cumulative settling volume corresponding to the time t =1,2, ·, n of the sample X is X 1 ,x 2 ,···，x n Constructing a rank sequence S k The calculation formula is as follows:
wherein S is calculated separately k Mean value of E (S) k ) Sum variance var (S) k ) The calculation formula is as follows:
statistical quantity UF under the assumption that the time series is randomly independent k The calculation formula of (2) is as follows:
UF k is a standard positive Taiwan distribution, and is composed of time series (x) 1 ,x 2 ,···，x n ) Obtaining a statistic sequence; UB k Is UF k By the inverse order (x) of the time series n ,x n-1 ,···，x 1 ) Calculating to obtain;
the significance level was set at α =0.05 and the critical value was set at U 0.05 =. + -. 1.96, judge U 0.05 = +/-1.96 two straight lines and UF k 、UB k The curve position relationship of (1): if UF k Or UB k If the time sequence sedimentation quantity is larger than 0, the time sequence sedimentation quantity shows an ascending trend, otherwise, the time sequence sedimentation quantity shows a descending trend; the region of the curve exceeding the critical line is a time region in which the change occurs; if UF k And UB k The two curves have intersection points and the intersection points are positioned between critical lines, and the time corresponding to the intersection points is a mutation point, namely the time when the sedimentation is mutated;
s4, verifying and correcting the width of the settling tank by using engineering parameters and empirical parameters, wherein the specific process is as follows: collecting engineering geological parameters of subway construction and burial depth parameters of the subway, and calculating by a Peck formula to obtain the width W of the settling tank after construction 2 The specific calculation formula is as follows:
W 2 ≈2.5i
wherein z is the tunnel axis burial depth m;
is the internal friction angle of the stratum around the tunnel; i is the distance m from the curve inflection point of the surface subsider to the central axis of the excavated body; w 2 The width m of the ground settling tank is the influence range of ground settlement caused after tunnel construction; calculating the maximum width W of the settling tank obtained in the step S3 1 And the width W of the settling tank calculated by a Peck formula 2 Comparing the two to select a decision coefficient R 2 And the root mean square error RMSE is used as a judgment standard for carrying out precision verification;
s5, substituting the relevant parameters into a fitting formula to obtain a time sequence settling tank curve, wherein the specific process is as follows: constructing a fitting formula of the time sequence settling tank according to a Peck formula:
wherein S is max The maximum settlement of the earth surface, m, is positioned at the central axis of the tunnel; x is the horizontal distance between the ground and the center of the tunnel, and m; s (x) is settlement amount at a position x away from the center of the tunnel; i is the distance m from the curve inflection point of the surface subsider to the central axis of the excavated body; v. of i Formation loss rate per unit length, m 3 (ii)/m; w is the width m of the time sequence settling tank obtained by Mann-Kendall inspection;
and substituting the width W of the settling tank obtained by the PS point calculation in the S3 into a fitting formula to obtain a settling tank curve of the time sequence.
The Mann-Kendall inspection in the S3, the S4 and the S5, the calculation of the Peck formula and the calculation of the time sequence settling tank curve are obtained through Matlab and Python software calculation.
In conclusion, the method is based on SAR satellite remote sensing data, a PS-InSAR monitoring technology and a Mann-Kendall mutation detection method are fused, and a time sequence settlement curve of the subway with high space-time resolution in a construction period is obtained. By utilizing the design, the defects that the leveling monitoring is low in space-time resolution, the Peck formula is limited by the position of the leveling point and can only fit a settling tank curve after construction is finished, the PS point distribution density in the PS-InSAR method is low and the like can be effectively overcome. Compared with the traditional monitoring method, the method combines the advantages of monitoring the ground settlement by the PS-InSAR technology, obtains the influence range of subway construction on the ground settlement by using a Mann-Kendall mutation inspection method, obtains the time-sequence settling tank curve and realizes the dynamic monitoring of the ground settlement of the subway line area. Meanwhile, the method can obtain the ground settlement information with high precision and high space-time resolution in the area along the subway line, and provide a high-precision settlement data set for related departments. Based on the data set obtained by the invention, the mechanism research of ground settlement along the subway line is carried out, and the method has important significance for scientific development of cities and safe construction and operation of subway engineering.
Example 2:
referring to fig. 2 to 3, based on embodiment 1 but with a difference,
beijing is the first city to open subways across the country. With the continuous development of economy, the Beijing area has entered the large-scale subway construction period. In the embodiment, a certain subway line interval of Beijing is selected as a research area. The feasibility of the invention is further proved by applying the method provided by the invention to practical cases.
Step one, respectively obtaining 55 scene Terrasar-X images (the spatial resolution is 3m, and the time coverage range is 2010.4.13-2016.05.14) covering Beijing subways. The Terrasar-X images are processed through a PS-InSAR method of GAMMA software, and finally ground settlement information (accumulated settlement amount and average settlement rate) of the time sequence of the year 2010-2016 of the research area is obtained.
And step two, selecting the PS point which is closest to each leveling point in space distance as a homonymy point based on the leveling monitoring data according to the principle of the closest distance, and comparing the annual settlement amount and the time settlement amount obtained by the two monitoring means. The results show a linear regression correlation coefficient R2 of 0.96 for both monitoring results. The root mean square error RMSE was 3.58mm/year. The PS-InSAR monitoring result is accurate, and the precision meets the requirement. The verification results are shown in fig. 2.
And step three, establishing a buffer area in a certain range by taking the subway construction line as a center, and cutting the result of the PS-InSAR. And carrying out mutation point detection on the PS points in the buffer area by using a Mann-Kendall detection method, judging whether the development trend of the ground settlement amount has mutation or not in the construction period, and if the development trend has mutation, calculating the space distance between the PS points and the subway tunnel by using Arcgis to be used as the width of the time sequence settling tank.
And step four, collecting engineering geological parameters of subway construction, burial depth of the subway and other parameters, and calculating by using a Peck formula to obtain the width of the settling tank after construction is finished. And comparing the maximum width of the settling tank obtained by mutation inspection with the width of the settling tank obtained by calculation of the Peck formula, and selecting a decision coefficient R2 and a root mean square error RMSE as judgment standards to carry out precision verification.
And step five, substituting the width of the settling tank obtained from the PS point in the step three into a fitting formula to obtain a time sequence settling tank curve, and finding that the settling tank presents a state of continuously expanding width and depth in a construction period and the settling is accelerated. The time sequence settler curve at a certain place of the subway is shown in figure 3.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be able to cover the technical scope of the present invention and the equivalent alternatives or modifications according to the technical solution and the inventive concept of the present invention within the technical scope of the present invention.
Claims (7)
1. A method for obtaining a time sequence settling tank curve by fusing PS-InSAR and Mann-Kendall is characterized by comprising the following steps:
s1, acquiring an SAR image with a wide coverage range and a long time sequence, and acquiring ground settlement information of a building area in a subway line region based on a PS-InSAR technology;
s2, performing precision verification on the PS-InSAR result by using the level monitoring data, wherein the specific process comprises the following steps: based on actually measured level monitoring data, selecting a PS point closest to each level point in space distance as a homonymous point by using a principle of a closest distance; then comparing the annual settlement amount and the time sequence settlement amount obtained based on the PS-InSAR technology with the annual settlement amount and the time sequence settlement amount obtained through actual measurement; will determine the coefficient R 2 And the root mean square error RMSE is used as a judgment standard for carrying out precision verification;
s3, determining the width of the time sequence settling tank by using a Mann-Kendall inspection method based on a long time sequence settling monitoring result on a PS point, wherein the specific process is as follows: carrying out mutation inspection on the time sequence sedimentation amount of the PS point by a Mann-Kendall inspection method, judging whether the development trend of the ground sedimentation amount has mutation in the construction period, and if so, calculatingThe space distance between the PS point and the subway tunnel is the width W of the time sequence settling tank, and the calculated maximum settling tank width is recorded as W 1 ；
S4, verifying and correcting the width of the settling tank by using engineering parameters and empirical parameters, wherein the specific process is as follows: collecting engineering geological parameters of subway construction and buried depth parameters of the subway, and calculating by a Peck formula to obtain the width W of the settling tank after the construction is finished 2 (ii) a The maximum width W of the settling tank calculated in the step S3 1 And the width W of the settling tank calculated by a Peck formula 2 Comparing the two to select a decision coefficient R 2 And the root mean square error RMSE are used as a judgment standard for carrying out precision verification;
s5, substituting the relevant parameters into a fitting formula to obtain a time sequence settling tank curve, wherein the specific process is as follows: and (4) constructing a fitting formula of the time sequence settling tank according to the Peck formula, and substituting the width W of the settling tank obtained by calculating through the PS points in the S3 into the fitting formula to obtain a time sequence settling tank curve.
2. The method for acquiring the time-series settler curve by fusing the PS-InSAR and the Mann-Kendall according to claim 1, wherein the settlement information comprises an average settlement rate and a cumulative settlement based on an initial image;
the step of obtaining the ground settlement information of the building area along the subway based on the PS-InSAR technology in the step S1 specifically comprises the following steps:
s1.1, selecting a main image according to a space-time baseline and Doppler information, and registering and resampling other auxiliary images to the main image;
s1.2, performing conjugate multiplication on the main image and the auxiliary image to calculate an interference pattern;
s1.3, extracting a high-coherence point target by using the correlation index, and performing time sequence analysis on the differential phase to finally obtain a millimeter-scale deformation rate result of the discrete point, deformation history information, a DEM residual error and an atmospheric delay error.
3. The method for acquiring the time-series settler curve by fusing the PS-InSAR and the Mann-Kendall as claimed in claim 1, wherein the PS-InSAR processing software of the radar image in the S1 comprises GAMMA, SNAP, PIE-SAR, ENVI/Sarscape and SARPROZ software.
4. The method for obtaining the time sequence settling tank curve by fusing the PS-InSAR and the Mann-Kendall according to claim 1, wherein the method for judging whether the time sequence settling volume is mutated by using the Mann-Kendall test method in the S3 comprises the following steps:
assuming that the time-sequence settling volume at the point PS is sample X, the cumulative settling volume corresponding to the time t =1,2, ·, n of the sample X is X 1 ,x 2 ,···，x n Constructing a rank sequence S k The calculation formula is as follows:
wherein S is calculated separately k Mean value of E (S) k ) Sum variance var (S) k ) The calculation formula is as follows:
statistical quantity UF under the assumption that the time series is randomly independent k The calculation formula of (2) is as follows:
UF k is standard positiveIs distributed by a time series (x) 1 ,x 2 ,···，x n ) Obtaining a statistic sequence; UB k Is UF k By the inverse order (x) of the time series n ,x n-1 ,···，x 1 ) Calculating to obtain;
the significance level was set at α =0.05 and the critical value was set at U 0.05 =. + -. 1.96, judge U 0.05 = +/-1.96 two straight lines and UF k 、UB k The curve position relationship of (1): if UF k Or UB k If the time sequence sedimentation quantity is larger than 0, the time sequence sedimentation quantity shows an ascending trend, otherwise, the time sequence sedimentation quantity shows a descending trend; the region where the curve exceeds the critical line is a time region where the change occurs; if UF k And UB k The two curves have intersection points and the intersection points are positioned between critical lines, and the time corresponding to the intersection points is the mutation points, namely the time when the sedimentation is mutated.
5. The method for obtaining the time-series settler curve by fusing the PS-InSAR and the Mann-Kendall as claimed in claim 1, wherein the width of the settler is calculated according to the Peck formula mentioned in the S4, and the specific calculation formula is as follows:
W 2 ≈2.5i
wherein z is the tunnel axis burial depth m;
is the internal friction angle of the stratum around the tunnel; i is the distance m from the curve inflection point of the surface subsider to the central axis of the excavated body; w 2 The width of the ground subsider, m, is the influence range of ground subsidence caused after tunnel construction.
6. The method for obtaining the time-series settler curve by fusing the PS-InSAR and the Mann-Kendall as claimed in claim 1, wherein the fitting formula of the settler mentioned in S5 is as follows:
wherein S is max The maximum settlement of the earth surface, m, is positioned at the central axis of the tunnel; x is the horizontal distance between the ground and the center of the tunnel, and m; s (x) is settlement amount at a position x away from the center of the tunnel; i is the distance m from the curve inflection point of the surface subsider to the central axis of the excavated body; v. of i Formation loss rate per unit length, m 3 (ii)/m; w is the time sequence settler width m obtained by Mann-Kendall test.
7. The method for obtaining the time-series settler curve by fusing the PS-InSAR and the Mann-Kendall as claimed in claim 1, wherein the Mann-Kendall test and the calculation of the Peck formula in the S3, S4 and S5 and the calculation of the time-series settler curve are obtained by Mat lab and Python software.
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