CN116910889A - Combined inversion method and system for slope mechanical parameters and unloading loose zone - Google Patents

Combined inversion method and system for slope mechanical parameters and unloading loose zone Download PDF

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CN116910889A
CN116910889A CN202311175672.1A CN202311175672A CN116910889A CN 116910889 A CN116910889 A CN 116910889A CN 202311175672 A CN202311175672 A CN 202311175672A CN 116910889 A CN116910889 A CN 116910889A
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unloading
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CN116910889B (en
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狄圣杰
印昊程
张莹
黄鹏
苏超
吕庆超
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PowerChina Northwest Engineering Corp Ltd
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Abstract

The application belongs to the technical field of slope engineering, and particularly discloses a method and a system for joint inversion of mechanical parameters of a slope and an unloading loosening zone, wherein the method comprises the steps of obtaining an unloading loosening datum line of the slope and multiple groups of load loosening parameters in the unloading loosening zone, and the unloading loosening zone is a region between the unloading loosening datum line and a side line of a temporary face of the slope; calculating an initial side slope displacement calculation value at each elevation according to each group of unloading loosening parameters, and training an inversion model based on the initial side slope displacement calculation value and a plurality of groups of unloading loosening parameters; inputting the measured value of the slope displacement at each elevation into the trained inversion model to obtain inversion unloading loosening parameters; and determining an actual unloading loosening line according to the inversion unloading loosening parameter. The inversion method provided by the application has the advantages that the reliability of the mechanical parameters is higher, the result is more accurate, and the true condition of the slope can be reflected.

Description

Combined inversion method and system for slope mechanical parameters and unloading loose zone
Technical Field
The application discloses a joint inversion method and a system for slope mechanical parameters and unloading loose areas, and belongs to the technical field of slope engineering.
Background
In the slope safety evaluation, accurate slope rock mass partition and mechanical parameters are key points of reasonable analysis and evaluation of the slope. Along with the excavation unloading of the site construction of the side slope, the rock mass parameters are in the dynamic change process and are different from the rock stratum information provided by the initial investigation. On the other hand, in the slope excavation process, the internal stress of the original slope is readjusted to a new balance state, and the new deeper unloading area can be formed by expansion due to the influence of weathering erosion, precipitation infiltration and the like in the slope service engineering period. The determination of the unloading loosening area and the corresponding parameters has important significance for the safety and stability evaluation of the side slope.
The current slope mechanical parameters are mainly obtained through experiments, the excavation unloading range is usually manually deduced on the basis of investigation data, subjective factors are strong, and the artificial experience is relied on. Meanwhile, in the traditional method, the inversion method of slope stability only inverts parameters, the parameters are limited in the inherent engineering geological partition in the earlier stage, the core problem that the slope unloading loosening area also changes along with the engineering construction is ignored, and the actual situation is that the corresponding parameters are reduced along with the change of the loosening area and the two parameters are mutually linked. Meanwhile, joint inversion is carried out on the side slope parameters and the loosening area, so that the method is more in line with engineering practice and has practical guidance significance on engineering construction.
Disclosure of Invention
The application aims to provide a slope mechanical parameter and unloading loose region joint inversion method and system, which are used for solving the technical problems that in the prior art, the slope stability inversion method only inverts the mechanical parameter and ignores the unloading loose region change, and the accuracy of the obtained inverse analysis result is low.
The first aspect of the application provides a slope mechanical parameter and unloading loose zone joint inversion method, which comprises the following steps:
acquiring a plurality of groups of unloading loosening parameters in an unloading loosening datum line and an unloading loosening zone of a side slope, wherein the unloading loosening zone is a zone between the unloading loosening datum line and a side line of a side slope free surface;
calculating an initial slope displacement calculation value at each elevation according to each group of unloading loosening parameters, and training an inversion model based on the initial slope displacement calculation value and the multiple groups of unloading loosening parameters;
inputting the measured value of the slope displacement at each elevation into the trained inversion model to obtain inversion unloading loosening parameters;
and determining an actual unloading loosening line according to the inversion unloading loosening parameter.
Preferably, the unloading loosening parameters comprise slope mechanical parameters and unloading loosening depth from an unloading loosening datum line at each elevation to a side line of a slope free surface.
Preferably, the obtaining the unloading loosening datum line of the side slope specifically includes:
acquiring stable points of which the displacement change value of the slope at each elevation is smaller than a preset threshold value in a preset time period;
sequentially connecting a plurality of stabilization points at different heights to obtain a rock mass stabilization line;
and determining unloading loosening datum lines of the side slope according to the rock mass stabilizing lines and the side lines of the side slope free surface.
Preferably, the obtaining a plurality of groups of unloading loosening parameters in the unloading loosening zone specifically includes:
acquiring a value range of unloading loosening parameters in the unloading loosening region;
and determining a plurality of groups of unloading loosening parameters within the value range of the unloading loosening parameters by utilizing a uniform design test.
Preferably, the initial side slope displacement calculation value at each elevation is calculated according to each group of unloading loosening parameters, and specifically comprises the following steps:
inputting each group of unloading loosening parameters into a preset slope profile model to obtain an initial slope displacement calculation value at each elevation;
the calculation method used in the slope profile model is a finite element method.
Preferably, the determining an actual unloading loose line according to the inversion unloading loose parameter specifically includes:
acquiring unloading loosening depth in inversion unloading loosening parameters;
and sequentially connecting a plurality of edge points of the unloading loosening depth to obtain an actual unloading loosening line.
Preferably, after inputting the measured value of the slope displacement at each elevation into the trained inversion model, obtaining the inversion unloading loosening parameter, the method further comprises:
calculating an inversion side slope displacement calculation value at each elevation by using the inversion unloading loosening parameters;
according to the error of the inversion slope displacement calculated value at each elevation and the slope displacement measured value of the corresponding elevation, determining whether the inversion unloading loosening parameter can reflect the real situation of the slope;
if so, determining an actual unloading loose line according to the inverted unloading loose parameter, and if not, retraining the inversion model.
Preferably, the slope mechanical parameters include elastic modulus, cohesion and internal friction angle.
The second aspect of the application provides a slope mechanical parameter and unloading loose zone joint inversion system, which comprises a parameter acquisition module, a training module, an inversion parameter determination module and an unloading loose line determination module;
the parameter acquisition module is used for acquiring a plurality of groups of unloading loosening parameters in an unloading loosening datum line of the side slope and an unloading loosening zone, wherein the unloading loosening zone is a zone between the unloading loosening datum line and a boundary line of a side slope free surface;
the training module is used for calculating an initial slope displacement calculation value at each elevation according to each group of unloading loosening parameters and training an inversion model based on the initial slope displacement calculation value and the plurality of groups of unloading loosening parameters;
the inversion parameter determining module is used for inputting the measured value of the slope displacement at each elevation into the trained inversion model to obtain inversion unloading loosening parameters;
the unloading loose line determining module is used for determining an actual unloading loose line according to the inversion unloading loose parameter.
Compared with the prior art, the method and the system for joint inversion of the mechanical parameters of the bedding high steep slope and the unloading loose zone have the following beneficial effects:
according to the application, the comprehensive influence of natural actions such as excavation unloading, mechanical and artificial disturbance, weathering and degradation during service engineering period and precipitation infiltration is considered, and the reverse analysis is performed through the displacement variation value, so that compared with the defects of single consideration factor, strong subjective factor, low accuracy and the like in the traditional mechanical parameter test, the mechanical parameter obtained by the inversion method is higher in reliability and more accurate in result;
according to the application, the core problem that the slope unloading loose zone changes along with the adjustment of mechanical parameters in engineering construction is solved by carrying out joint inversion on the slope mechanical parameters and the unloading loose zone range, so that the inversion result can reflect the real condition of the slope;
the application considers the problem that the unloading loosening area range and the mechanical parameter obtained by initial investigation and parameter test are static, the actual measurement data of the displacement monitoring instrument are continuously updated in the slope service engineering period, inversion is carried out according to the monitoring updated value, the current mechanical parameter and unloading loosening range information are mastered in real time, and a reliable basis is provided for safe and stable evaluation.
Drawings
FIG. 1 is a schematic flow chart of a slope mechanical parameter and unloading loosening zone joint inversion method in an embodiment of the application;
FIG. 2 is a detailed flow chart of a slope mechanical parameter and unloading loosening zone joint inversion method according to an embodiment of the application;
FIG. 3 is a schematic cross-sectional view of a smooth high-steep slope in an embodiment of the application;
FIG. 4 is a horizontal displacement cloud graph calculated using inversion parameters according to an embodiment of the present application;
FIG. 5 is a schematic structural diagram of a slope mechanical parameter and unloading loosening zone joint inversion system according to an embodiment of the application.
In the figure: 1 is a smooth high steep slope; 2 is a rock mass stabilization line; 3 is an unloading loosening datum line; 4, actually unloading loose wires; 5 is a breeze area; 6 is a weak weathering zone; 7 is an unloading loosening area; 8 is an excavation area; 9 is a displacement monitoring instrument at the first stage platform; 10 is a displacement monitoring instrument at a secondary platform; 11 is a displacement monitoring instrument at a three-stage platform; 12 is the first high Cheng Xiehe loosening depth; 13 is the first high Cheng Xiehe loose depth; 14 is the third elevation unloading loosening depth; 15 is a reinforced anchor cable; 16 is a stabilizing segment; and 17 is a drainage section.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth such as the particular system architecture, techniques, etc., in order to provide a thorough understanding of the embodiments of the present application. It will be apparent, however, to one skilled in the art that the present application may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.
The first aspect of the application provides a joint inversion method for slope mechanical parameters and unloading loose regions, as shown in fig. 1 to 4, comprising the following steps:
step 1, acquiring a plurality of groups of unloading loosening parameters in an unloading loosening datum line 3 and an unloading loosening region 7 of a side slope, wherein the unloading loosening region 7 is a region between the unloading loosening datum line and a side line of a side slope free surface, and specifically comprises the following steps:
step 1.1, obtaining stable points of which the displacement change value of the slope at each elevation is smaller than a preset threshold value in a preset time period.
The side slope in the embodiment of the application is a bedding high steep side slope, and the method is suitable for large excavation and side slopes with obvious excavation unloading.
The displacement change value of the slope at each elevation in the preset time period in the step 1.1 is obtained by using a displacement monitoring instrument. Taking the smooth high steep side slope 1 shown in fig. 3 as an example, a reinforcing anchor cable 15 is arranged on the smooth high steep side slope. 3 sets of displacement monitoring instruments, in particular to a first-stage platform displacement monitoring instrument 9, a second-stage platform displacement monitoring instrument 10 and a third-stage platform displacement monitoring instrument 11 are buried in each level of excavation platforms of the bedding high-steep slope 1 shown in fig. 3, and each set of displacement monitoring instrument can obtain displacement variation values of different horizontal displacement depths on an elevation. For example, the displacement variation value measured by each set of displacement monitoring instrument in the embodiment of the application is a horizontal displacement monitoring value at the orifice, a 10m deep horizontal displacement monitoring value, a 20m deep horizontal displacement monitoring value and a 30m deep horizontal displacement monitoring value, and all monitoring points count 12 positions in total.
The displacement change value is reduced along with the increase of the embedded horizontal depth of the monitoring points of the displacement monitoring instrument, and the displacement change value of the monitoring points with larger embedded horizontal depth tends to be zero, so that the rock mass of the side slope tends to be stable.
In the embodiment of the application, the displacement change value of each monitoring point on each elevation is compared with a preset threshold, and the preset threshold can be 0.3-0.6, and if the displacement change value is smaller than the preset threshold, the monitoring point is marked as a stable point. If a plurality of monitoring points smaller than a preset threshold value exist on the same elevation, the monitoring point with the minimum displacement change value is selected as a stable point.
Step 1.2, sequentially connecting a plurality of stabilization points at different heights to obtain a rock mass stabilization line 2;
in the embodiment of the application, a plurality of stabilization points at different heights are sequentially connected, a formed line is used as a boundary between a rock mass stabilization area and a deformation area, the line is defined as a rock mass stabilization line 2, a slope top section in the rock mass stabilization area is a stabilization section 16, and a slope top section in the deformation area is a drainage section 17.
Step 1.3, determining an unloading loosening datum line 3 of the side slope according to the rock mass stabilizing line 2 and the side line of the side slope free surface, and taking the area between the unloading loosening datum line 3 and the side line of the side slope free surface as an unloading loosening area 7, wherein the inside of the smooth high and steep side slope 1 in fig. 3 can be divided into a breeze area 5, a weak breeze area 6 and the unloading loosening area 7.
In the embodiment of the application, fig. 3 shows that a region formed by a rock mass stabilizing line 2 and a side line of a side slope free surface after excavation in an excavation region 8 is a rock mass deformation region, and an unloading loosening range is adjusted and changed in the deformation region, so that an unloading loosening datum line 3 is positioned between the rock mass stabilizing line 2 and the side line of the side slope free surface, and can deviate to the rock mass stabilizing line 2 or the side slope free surface.
And 2, calculating an initial side slope displacement calculation value at each elevation according to each group of unloading loosening parameters in the unloading loosening zone 7, and training an inversion model based on the initial side slope displacement calculation value and a plurality of groups of unloading loosening parameters.
In the embodiment of the application, the unloading loosening parameters comprise slope mechanical parameters and unloading loosening depth from the unloading loosening datum line 3 at each elevation to the edge of the slope free surface.
Wherein the mechanical parameters of the side slope are determined by on-site investigation and test data, and comprise elastic modulusCohesive force->And internal friction angle->And the like. The mechanical parameters of the side slope of the embodiment of the application use elastic modulus +.>Cohesive force->And internal friction angle
The step 2 specifically includes:
step 2.1, obtaining a plurality of groups of unloading loosening parameters in an unloading loosening zone, which specifically comprises the following steps:
and 2.1.1, acquiring a value range of unloading loosening parameters in the unloading loosening region.
Illustratively, the value ranges of the mechanical parameters of the side slope are determined according to the on-site investigation and test data, the value ranges of the unloading loosening depths of the three elevations in the specific embodiment are determined according to the unloading loosening datum line 3 and the side line of the side slope free surface, and the obtained value ranges of the unloading loosening parameters are shown in table 1.
Table 1 values of unloading loosening parameters
In the table of the present application,a first high Cheng Xiehe loosening depth of 12 for the first stage platform>Unloading loosening depth 13 for the second elevation of the secondary platform>The loosening depth 14 is unloaded for the third elevation where the three-stage platform is located.
And 2.1.2, determining a plurality of groups of unloading loosening parameters within the range of values of the unloading loosening parameters by utilizing a uniform design test.
Because the unloading loosening parameters have more points in the value range, representative value points need to be selected as much as possible, and not only can all data in the range be contained, but also the workload is not too great.
In the embodiment of the application, because the inversion parameters are more in types, a uniform design table of parameters is shown in table 2, and the uniform design table is formed by adopting a uniform design test, wherein the number of levels of each factor is 20.
Table 2 design table for uniform test
Step 2.2, carrying each group of unloading loosening parameters into a preset slope profile model to obtain an initial slope displacement calculated value at each elevation;
based on actual excavation and construction supporting measures, a slope profile model is established by combining rock mass boundary and fault fracture geological structure, and initial slope displacement calculated values of monitoring points at the displacement monitoring instrument 12 corresponding to each group of unloading loosening parameters are calculated according to the uniform design table of table 2,/>,……,/>;/>,/>,……,/>;……;/>,/>,……,/>;/>,/>,……,/>
Wherein the displacement valueSubscripts 1,2, … …,12 indicate the sum of the number of monitoring points at each elevation, subscripts 1,2, … …And 20 represents the serial number of each group of unloading loosening parameters in the uniform design test table.
The calculation method adopted by the slope profile model in the embodiment of the application is a finite element method.
And 2.3, taking a plurality of groups of unloading loosening parameters as input values, taking an initial slope displacement calculated value at each elevation as an output value, and training an inversion model.
The inversion model in the embodiment of the application is a neural network model.
Exemplary, the input set of the neural network model is unloading loosening parameters of each group in the uniform test design table of the table 2, and the output set is the initial slope displacement calculated value of the monitoring points at 12 positions obtained in the step 2.2,/>,……,/>;/>,/>,……,;……;/>,/>,……,/>;/>,/>,……,/>. In order to eliminate the difference of each factor in the order of magnitude and dimension of the input set and the output set, normalization processing is carried out, normalized data are carried into a neural network model for training, and a trained inversion model is obtained.
And step 3, inputting the measured value of the slope displacement at each elevation into the trained inversion model to obtain inversion unloading loosening parameters.
Illustratively, the measured value of the monitoring point at the displacement monitoring instrument 12 is measured,/>,……,/>,/>And the inversion unloading loosening parameters are input into the trained inversion model as target values, and inversion results are shown in table 3 after errors meet the accuracy requirements of the neural network.
TABLE 3 determination of the results of parameter inversion at displacement
Step 4, determining an actual unloading loosening line according to the inversion unloading loosening parameter, which specifically comprises the following steps:
step 4.1, obtaining unloading loosening depth in inversion unloading loosening parameters;
and 4.2, sequentially connecting the edge points corresponding to the unloading loosening depths to obtain an actual unloading loosening line 4.
As shown in FIG. 3, the unloading loosening depth in the side slope、/>、/>The positions of the slope is marked, a line formed by connecting marking points in sequence is used as an actual unloading loose line 4, and the range formed by the actual unloading loose line 4 and the slope empty face after excavation is an unloading loose region 7.
In order to further ensure the accuracy of the actual unloading loosening line obtained by the method, the embodiment of the application further comprises the following steps after the actual slope displacement measured value at each elevation is input into the trained inversion model to obtain inversion unloading loosening parameters:
performing positive analysis calculation by using inversion unloading loosening parameters to obtain inversion slope displacement calculated value,/>,……,,/>As shown in fig. 4;
and determining whether the inversion unloading loosening parameters can reflect the real situation of the slope according to the errors of the inversion slope displacement calculated value and the slope displacement measured value, if so, determining an actual unloading loosening line according to the inversion unloading loosening parameters at each elevation, and if not, retraining the inversion model.
For example, table 4 is a comparison table of calculated displacement values and measured values, and as can be seen from fig. 4, the calculated error between the calculated displacement values and the measured values of the inversion slope calculated by using the inversion parameters is less than 10%, so as to satisfy engineering requirements, and the inversion parameters can reflect the actual condition of the slope.
Table 4 table for comparing calculated displacement values with measured values
The second aspect of the application provides a slope mechanical parameter and unloading loose zone joint inversion system, as shown in fig. 5, comprising a parameter acquisition module 101, a training module 102, an inversion parameter determination module 103 and an unloading loose line determination module 104;
the parameter acquisition module 101 is used for acquiring a plurality of groups of unloading loosening parameters in the unloading loosening datum line 3 and the unloading loosening zone 7 of the side slope, wherein the unloading loosening zone 7 is a region between the unloading loosening datum line 3 and a boundary line of a side slope free surface;
the training module 102 is used for calculating an initial side slope displacement calculation value at each elevation according to each group of unloading loosening parameters, and training an inversion model based on the initial side slope displacement calculation value and a plurality of groups of unloading loosening parameters;
the inversion parameter determining module 103 is used for inputting the measured value of the slope displacement at each elevation into the trained inversion model to obtain inversion unloading loosening parameters;
the unloading loose line determining module 104 is configured to determine an actual unloading loose line according to the inverted unloading loose parameter.
According to the application, the comprehensive influence of natural actions such as excavation unloading, mechanical and artificial disturbance, weathering and degradation during service engineering period and precipitation infiltration is considered, and the reverse analysis is performed through the displacement variation value, so that compared with the defects of single consideration factor, strong subjective factor, low accuracy and the like in the traditional mechanical parameter test, the mechanical parameter obtained by the inversion method is higher in reliability and more accurate in result;
according to the application, the core problem that the slope unloading loose zone changes along with the adjustment of mechanical parameters in engineering construction is solved by carrying out joint inversion on the slope mechanical parameters and the unloading loose zone range, so that the inversion result can reflect the real condition of the slope;
the application considers the problem that the unloading loosening area range and the mechanical parameter obtained by initial investigation and parameter test are static, the actual measurement data of the displacement monitoring instrument are continuously updated in the slope service engineering period, inversion is carried out according to the monitoring updated value, the current mechanical parameter and unloading loosening range information are mastered in real time, and a reliable basis is provided for safe and stable evaluation.
While the application has been described in terms of preferred embodiments, it will be understood by those skilled in the art that various changes and modifications can be made without departing from the scope of the application, and it is intended that the application is not limited to the specific embodiments disclosed.

Claims (9)

1. The joint inversion method for the mechanical parameters of the side slope and the unloading loosening zone is characterized by comprising the following steps of:
acquiring a plurality of groups of unloading loosening parameters in an unloading loosening datum line and an unloading loosening zone of a side slope, wherein the unloading loosening zone is a zone between the unloading loosening datum line and a side line of a side slope free surface;
calculating an initial slope displacement calculation value at each elevation according to each group of unloading loosening parameters, and training an inversion model based on the initial slope displacement calculation value and the multiple groups of unloading loosening parameters;
inputting the measured value of the slope displacement at each elevation into the trained inversion model to obtain inversion unloading loosening parameters;
and determining an actual unloading loosening line according to the inversion unloading loosening parameter.
2. The slope mechanics parameter and unload looseness region joint inversion method of claim 1, wherein the unload looseness parameter comprises a slope mechanics parameter and an unload looseness depth between an unload looseness datum line at each elevation to a side line of a slope empty face.
3. The method for performing joint inversion on mechanical parameters and unloading loosening areas of a side slope according to claim 1, wherein the step of obtaining the unloading loosening datum line of the side slope specifically comprises the following steps:
acquiring stable points of which the displacement change value of the slope at each elevation is smaller than a preset threshold value in a preset time period;
sequentially connecting a plurality of stabilization points at different heights to obtain a rock mass stabilization line;
and determining unloading loosening datum lines of the side slope according to the rock mass stabilizing lines and the side lines of the side slope free surface.
4. The slope mechanical parameter and unloading loosening zone joint inversion method according to claim 1, wherein obtaining multiple groups of unloading loosening parameters in the unloading loosening zone comprises the following steps:
acquiring a value range of unloading loosening parameters in the unloading loosening region;
and determining a plurality of groups of unloading loosening parameters within the value range of the unloading loosening parameters by utilizing a uniform design test.
5. The method of joint inversion of mechanical parameters of a slope and an unloading looseness region according to any of claims 1-4, wherein calculating an initial slope displacement calculation value at each elevation according to each set of unloading looseness parameters comprises:
inputting each group of unloading loosening parameters into a preset slope profile model to obtain an initial slope displacement calculation value at each elevation;
the calculation method used in the slope profile model is a finite element method.
6. The slope mechanical parameter and unloading loosening zone joint inversion method according to claim 1, wherein determining an actual unloading loosening line according to the inverted unloading loosening parameter specifically comprises:
acquiring unloading loosening depth in inversion unloading loosening parameters;
and sequentially connecting a plurality of edge points of the unloading loosening depth to obtain an actual unloading loosening line.
7. The method for joint inversion of mechanical parameters of a slope and unloading loosening zone according to claim 1, wherein after inputting the actual measurement value of the displacement of the slope at each elevation into the inversion model after training, the method further comprises:
calculating an inversion side slope displacement calculation value at each elevation by using the inversion unloading loosening parameters;
determining whether the inversion unloading loosening parameters can reflect the actual situation of the slope according to the calculated value of the inversion slope displacement at each elevation and the error of the actual measurement value of the slope displacement at the corresponding elevation;
if so, determining an actual unloading loose line according to the inverted unloading loose parameter, and if not, retraining the inversion model.
8. The slope mechanical parameter and unload loose zone joint inversion method according to claim 2, wherein the slope mechanical parameter comprises elastic modulus, cohesion and internal friction angle.
9. The slope mechanical parameter and unloading loose region joint inversion system is characterized by comprising a parameter acquisition module, a training module, an inversion parameter determination module and an unloading loose line determination module;
the parameter acquisition module is used for acquiring a plurality of groups of unloading loosening parameters in an unloading loosening datum line of the side slope and an unloading loosening zone, wherein the unloading loosening zone is a zone between the unloading loosening datum line and a boundary line of a side slope free surface;
the training module is used for calculating an initial slope displacement calculation value at each elevation according to each group of unloading loosening parameters and training an inversion model based on the initial slope displacement calculation value and the plurality of groups of unloading loosening parameters;
the inversion parameter determining module is used for inputting the measured value of the slope displacement at each elevation into the trained inversion model to obtain inversion unloading loosening parameters;
the unloading loose line determining module is used for determining an actual unloading loose line according to the inversion unloading loose parameter.
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