Stability prediction method and system for rock slopes in seasonally frozen areas

Abstract

The present invention discloses a method and system for predicting the stability of rock slopes in seasonally frozen areas. The method includes: obtaining rock creep parameters and constructing a creep constitutive model; constructing a finite element model and obtaining sample pairs; forming multiple sample pairs and forming a sample library; obtaining the thickness of the second freeze-thaw zone at the sensor position, and obtaining a fitting displacement curve corresponding to the sensor from the sample library based on the thickness of the second freeze-thaw zone; obtaining the displacement monitoring data of the sensor along the time course to form a real-time displacement curve, and judging the stability of the corresponding position of the sensor based on the real-time displacement curve and the corresponding fitting displacement curve. Through the above technical solution, the present invention can more accurately calculate the damage of the freeze-thaw areas corresponding to different sensors, thereby facilitating further slope stability analysis. It has good applicability and can be applied to the monitoring and analysis of various high slopes, thereby buying valuable time for rescue and evacuation of geological disasters.

Description

Technical Field

[0001] The present invention relates to intelligent monitoring technology, and in particular to a method and system for predicting the stability of rock slopes in seasonally frozen areas. Background Art

[0002] Open-pit coal mine slopes have complex geological structures, and the mechanisms and controlling factors of slope deformation and landslides are complex and specific. Even for the same slope, deformation patterns and mechanisms vary significantly due to factors such as season, climate, and external disturbances. Precursor characteristics and patterns of safety hazards such as slope deformation and landslides are fundamental to mine slope safety risk perception and graded early warning. Once instability occurs, it can cause severe economic losses. Before a slope fails, it undergoes a progression from creep deformation to violent deformation and then to stability. Creep deformation lasts for a long time. Rocks in cold regions are subject to freeze-thaw cycles, and creep parameters change with the number of freeze-thaw cycles. Therefore, the stability calculation method for rock slopes in cold regions considers the effects of freeze-thaw cycles and time effects, making the calculation results more realistic.

[0003] However, when the existing technology is used to monitor the stability of rock slopes in seasonally frozen areas, the monitoring data has a lag, and the setting of the warning values corresponding to the monitoring data is not scientific enough, which makes the early warning of geological disasters insufficiently timely. Summary of the Invention

[0004] In order to at least overcome the above-mentioned deficiencies in the prior art, the purpose of the present application is to provide a method and system for predicting the stability of rock slopes in seasonally frozen areas.

[0005] In a first aspect, the present invention provides a method for predicting the stability of a rock slope in a seasonally frozen area, including:

[0006] A plurality of sensors are arranged on a target cold region rock slope, and temperature monitoring data and displacement monitoring data monitored by the sensors are received; the plurality of sensors are arranged linearly, and the linear direction is parallel to the landslide direction of the target cold region rock slope;

[0007] Obtaining distribution characteristics of rock layer temperature along with freeze-thaw weathering depth according to the temperature monitoring data, and dividing the target cold region rock slope into freeze-thaw zones and non-freeze-thaw zones according to the distribution characteristics;

[0008] Sampling rocks in the freeze-thaw zone and the non-freeze-thaw zone respectively, and performing rock creep tests on the sampled samples to obtain creep parameters before and after freeze-thaw as rock creep parameters;

[0009] Constructing a creep constitutive model of the target cold region rock slope according to the rock creep parameters;

[0010] Constructing a finite element model, and assigning the creep constitutive model to the freeze-thaw zone unit in the finite element model;

[0011] The finite element model is subjected to freeze-thaw cycle simulation until the freeze-thaw zone unit becomes unstable, and a surface displacement curve of the freeze-thaw zone unit and a first freeze-thaw zone thickness of the freeze-thaw zone unit are obtained during the simulation to form a sample pair; the surface displacement curve is a time-history curve of the surface displacement value of the freeze-thaw zone unit;

[0012] Adjusting the thickness of the first freeze-thaw zone in the finite element model and repeatedly calculating to form a plurality of sample pairs, and forming a sample library based on the plurality of sample pairs; the sample library is a correspondence between a plurality of different first freeze-thaw zone thicknesses and surface displacement curves;

[0013] Obtaining the thickness of the second freeze-thaw zone at the position of the sensor, and obtaining a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone;

[0014] The displacement monitoring data of the sensor along the time course is acquired to form a real-time displacement curve, and the stability of the corresponding position of the sensor is determined according to the real-time displacement curve and the corresponding fitting displacement curve.

[0015] When the embodiment of the present application is implemented, the sensor can be installed at different depths of the inclinometer tube to achieve displacement and temperature monitoring. The displacement and temperature of the rock slope in the seasonally frozen area are measured by temperature and displacement sensors. The rock temperature of 0°C is used as the dividing line. The rock above the 0°C dividing line is the freeze-thaw zone, and the rock below the 0°C dividing line is the non-freeze-thaw zone. The rock in the freeze-thaw zone of the slope is layered with the rock in the non-freeze-thaw zone, thereby obtaining the freeze-thaw depth of the rock slope in the cold region and layering the rock in the freeze-thaw zone of the slope with the rock in the non-freeze-thaw zone.

[0016] In the embodiment of the present application, in order to obtain rock sample data in the freeze-thaw zone and the non-freeze-thaw zone, it is necessary to sample the rocks in this area and conduct tests to obtain rock creep parameters. It should be understood that the test process belongs to the prior art and will not be repeated in the embodiment of the present application. Based on the rock creep parameters that have been obtained, a creep constitutive model of the target cold-region rock slope can be constructed to characterize the stability of the target cold-region rock slope. In scientific practice, the inventors found that although the analysis technology for freeze-thaw rocks is very rich in the prior art, for the rock slopes in the seasonally frozen zone, the freeze-thaw damage process that the rocks at the monitoring point have experienced cannot be tested, and for high slopes with a large number of monitoring points, the cost of sampling and experimental analysis for each monitoring point is too huge. Therefore, in the embodiment of the present application, the creep constitutive model constructed by experiment is used to assign simulation to the finite element model, so that a large amount of data can be obtained for subsequent analysis. A finite element model can be constructed first. This finite element model needs to have freeze-thaw zone elements for freeze-thaw damage simulation calculations. Then, a creep constitutive model is assigned as the constitutive model of the freeze-thaw zone elements for calculations. The surface displacement curve of the freeze-thaw zone elements from the beginning of the freeze-thaw cycle to the entire process of instability is calculated. This surface displacement curve is correlated with the overall thickness of the freeze-thaw zone elements. By adjusting the thickness of the first freeze-thaw zone and recalculating the process from freeze-thaw cycle to instability, corresponding sample pairs can be generated and ultimately a sample library can be formed.

[0017] In an embodiment of the present application, during the use of the sample library, different sensors may correspond to different freeze-thaw zone thicknesses. At this time, the corresponding fitted displacement curve can be calculated or extracted from the sample library based on the freeze-thaw zone thickness. After obtaining the real-time displacement curve in real time, the freeze-thaw damage of the freeze-thaw zone corresponding to the sensor can be found by comparing the real-time displacement curve and the fitted displacement curve, and then the stability of the point can be judged. Through the above-mentioned technical solution, the embodiment of the present application can more accurately calculate the damage of the freeze-thaw area corresponding to different sensors, thereby facilitating further slope stability analysis. It has good applicability and can be applied to the monitoring and analysis of various high slopes, thereby gaining valuable time for rescue and evacuation of geological disasters.

[0018] In a possible implementation, constructing the creep constitutive model of the target cold-region rock slope according to the rock creep parameters includes:

[0019] When the constant stress on the rock in the rock creep parameter is less than or equal to a preset value, a first creep model and a first constitutive model are constructed with the constraint that deformation does not occur before the yield limit is reached;

[0020] When the constant stress on the rock in the rock creep parameter is greater than a preset value, a second creep model and a second constitutive model are constructed by deducting friction resistance from the stress with deformation occurring at the yield limit as a constraint condition;

[0021] The first creep model, the first constitutive model, the second creep model, and the second constitutive model are introduced with damage variables to characterize the damage degradation of the viscosity coefficient caused by stress. Considering the influence of the number of freeze-thaw cycles and the action time, the damaged viscosity element under freeze-thaw conditions is constructed for analysis to form the creep constitutive model.

[0022] In a possible implementation, the first creep model adopts the following formula:

[0023]

[0024] The first constitutive model adopts the following formula:

[0025]

[0026] The second creep model adopts the following formula:

[0027] σ=σ1=σ2=σ3

[0028] ε=ε1+ε2+ε3

[0029]

[0030] The second constitutive model adopts the following formula:

[0031]

[0032] Where: ε is the total strain, σ0 is the load stress, E0(n) is the elastic modulus of the elastic body after freeze-thaw n times, E1(n) is the elastic modulus of the viscoelastic body after freeze-thaw n times, η1 is the elastic viscosity coefficient after freeze-thaw n times, η2 is the viscosity coefficient of the viscoplastic body after freeze-thaw n times, η3 is the viscosity coefficient of the viscous element damaged by freeze-thaw, σ s is the yield stress of rock, and t is the loading time.

[0033] In one possible implementation, a damage variable is introduced to characterize the damage degradation of the viscosity coefficient caused by stress, and the influence of the number of freeze-thaw cycles and the action time are considered. The damaged viscosity element under freeze-thaw conditions is constructed using the following formula:

[0034] D=1-eαt

[0035] η(t)=η(1-D)=ηe-αt

[0036] Where α is a coefficient related to the freeze-thaw number n, t is the creep time, and D is the rock freeze-thaw damage factor, D∈[0,1]. When D is 0, the rock is undamaged, and when D is 1, the rock is creep-damaged.

[0037] In a possible implementation, obtaining a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone includes:

[0038] Performing a traversal search in the sample library according to the thickness of the second freeze-thaw zone;

[0039] When a first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is retrieved from the sample library, the surface displacement curve corresponding to the first freeze-thaw zone thickness is used as the fitting displacement curve of the sensor;

[0040] When the first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is not retrieved in the sample library, a surface displacement curve corresponding to the lower limit freeze-thaw zone thickness is obtained as the lower limit curve, and a surface displacement curve corresponding to the upper limit freeze-thaw zone thickness is obtained as the upper limit curve; the lower limit freeze-thaw zone thickness is smaller than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; the upper limit freeze-thaw zone thickness is larger than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness;

[0041] The lower limit curve and the upper limit curve are interpolated according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness and the upper limit freeze-thaw zone thickness to form a fitting displacement curve of the sensor.

[0042] In a possible implementation, interpolating the lower limit curve and the upper limit curve according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness, and the upper limit freeze-thaw zone thickness to form the fitting displacement curve of the sensor includes:

[0043] Obtaining the displacement values of the lower limit curve at multiple moments as lower limit displacement values, and obtaining the displacement values of the upper limit curve at multiple moments as upper limit displacement values;

[0044] The lower limit displacement value and the upper limit displacement value at the same moment are linearly interpolated using the first difference and the second difference as weights to form a displacement value to be fitted corresponding to the moment; the first difference is the thickness of the second freeze-thaw zone minus the thickness of the lower limit freeze-thaw zone; the second difference is the thickness of the upper limit freeze-thaw zone minus the thickness of the second freeze-thaw zone;

[0045] A plurality of displacement values to be fitted are fitted along a time course to form a fitting displacement curve of the sensor.

[0046] In a possible implementation, judging the stability of the sensor at a corresponding position according to the real-time displacement curve and the corresponding fitted displacement curve includes:

[0047] Obtaining a displacement curve of a preset time length in the real-time displacement curve as a reference displacement curve;

[0048] Using the preset time length as the sliding window width, searching the fitted displacement curve to find the area closest to the reference displacement curve as the reference displacement area;

[0049] The stability of the corresponding position of the sensor is judged according to the distance between the reference displacement area and the unstable position in the fitting displacement curve; the closer the distance between the reference displacement area and the unstable position in the fitting displacement curve, the worse the stability.

[0050] In a second aspect, the present application also provides a system for predicting the stability of rock slopes in seasonally frozen areas, including:

[0051] The data acquisition unit is configured to set a plurality of sensors on the target cold region rock slope and receive temperature monitoring data and displacement monitoring data monitored by the sensors; the plurality of sensors are arranged linearly, and the linear direction is parallel to the landslide direction of the target cold region rock slope;

[0052] a dividing unit configured to obtain, based on the temperature monitoring data, a distribution characteristic of rock layer temperature as a function of freeze-thaw weathering depth, and to divide the target cold-region rock slope into a freeze-thaw zone and a non-freeze-thaw zone based on the distribution characteristic;

[0053] a sampling unit configured to sample the rocks in the freeze-thaw zone and the non-freeze-thaw zone respectively, and perform a rock creep test on the sampled samples to obtain creep parameters before and after freeze-thaw as rock creep parameters;

[0054] A constitutive unit is configured to construct a creep constitutive model of the target cold region rock slope according to the rock creep parameters;

[0055] A modeling unit is configured to construct a finite element model and assign the creep constitutive model to a freeze-thaw zone unit in the finite element model;

[0056] a simulation unit configured to perform freeze-thaw cycle simulation on the finite element model until the freeze-thaw zone unit becomes unstable, and obtain a surface displacement curve of the freeze-thaw zone unit and a first freeze-thaw zone thickness of the freeze-thaw zone unit during the simulation to form a sample pair; the surface displacement curve is a time-history curve of the surface displacement value of the freeze-thaw zone unit;

[0057] A sample unit is configured to adjust the thickness of the first freeze-thaw zone in the finite element model and repeatedly calculate to form a plurality of sample pairs, and form a sample library based on the plurality of sample pairs; the sample library is a correspondence between a plurality of different first freeze-thaw zone thicknesses and surface displacement curves;

[0058] an acquiring unit configured to acquire a thickness of a second freeze-thaw zone at the position of the sensor, and acquire a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone;

[0059] The analysis unit is configured to obtain the displacement monitoring data of the sensor along the time course to form a real-time displacement curve, and judge the stability of the corresponding position of the sensor according to the real-time displacement curve and the corresponding fitting displacement curve.

[0060] In a possible implementation, the constitutive unit is further configured as follows:

[0061] When the constant stress on the rock in the rock creep parameter is less than or equal to a preset value, a first creep model and a first constitutive model are constructed with the constraint that deformation does not occur before the yield limit is reached;

[0062] When the constant stress on the rock in the rock creep parameter is greater than a preset value, a second creep model and a second constitutive model are constructed by deducting friction resistance from the stress with deformation occurring at the yield limit as a constraint condition;

[0063] The first creep model, the first constitutive model, the second creep model, and the second constitutive model are introduced with damage variables to characterize the damage degradation of the viscosity coefficient caused by stress. Considering the influence of the number of freeze-thaw cycles and the action time, the damaged viscosity element under freeze-thaw conditions is constructed for analysis to form the creep constitutive model.

[0064] In a possible implementation, the acquiring unit is further configured to:

[0065] Performing a traversal search in the sample library according to the thickness of the second freeze-thaw zone;

[0066] When a first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is retrieved from the sample library, the surface displacement curve corresponding to the first freeze-thaw zone thickness is used as the fitting displacement curve of the sensor;

[0067] When the first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is not retrieved in the sample library, a surface displacement curve corresponding to the lower limit freeze-thaw zone thickness is obtained as the lower limit curve, and a surface displacement curve corresponding to the upper limit freeze-thaw zone thickness is obtained as the upper limit curve; the lower limit freeze-thaw zone thickness is smaller than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; the upper limit freeze-thaw zone thickness is larger than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness;

[0068] The lower limit curve and the upper limit curve are interpolated according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness and the upper limit freeze-thaw zone thickness to form a fitting displacement curve of the sensor.

[0069] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0070] Through the above technical solution, the present invention can more accurately calculate the damage conditions of the freeze-thaw areas corresponding to different sensors, thereby facilitating further slope stability analysis. It has good applicability and can be applied to the monitoring and analysis of various high slopes, thereby buying precious time for rescue and evacuation of geological disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0072] Figure 1 This is a schematic diagram of the method steps of an embodiment of the present application. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. It should be understood that the drawings in the present application only serve the purpose of illustration and description and are not used to limit the scope of protection of the present application. In addition, it should be understood that the schematic drawings are not drawn to scale. The flowcharts used in this application illustrate the operations implemented according to some embodiments of the embodiments of the present application. It should be understood that the operations of the flowcharts can be implemented out of sequence, and steps without logical context can be reversed or implemented simultaneously. In addition, those skilled in the art, under the guidance of the contents of this application, can add one or more other operations to the flowchart, or remove one or more operations from the flowchart.

[0074] In addition, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed application, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present application.

[0075] Please refer to Figure 1 , which is a flow chart of a method for predicting the stability of a rock slope in a seasonally frozen area provided by an embodiment of the present invention. The method for predicting the stability of a rock slope in a seasonally frozen area may specifically include the contents described in the following steps S1 to S9.

[0076] S1: multiple sensors are set on a target cold region rock slope, and temperature monitoring data and displacement monitoring data monitored by the sensors are received; the multiple sensors are arranged linearly, and the linear direction is parallel to the landslide direction of the target cold region rock slope;

[0077] S2: obtaining distribution characteristics of rock layer temperature along with freeze-thaw weathering depth according to the temperature monitoring data, and dividing the target cold region rock slope into freeze-thaw zones and non-freeze-thaw zones according to the distribution characteristics;

[0078] S3: sampling rocks in the freeze-thaw zone and the non-freeze-thaw zone respectively, and performing a rock creep test on the sampled samples to obtain creep parameters before and after freeze-thaw as rock creep parameters;

[0079] S4: constructing a creep constitutive model of the target cold region rock slope according to the rock creep parameters;

[0080] S5: constructing a finite element model, and assigning the creep constitutive model to the freeze-thaw zone unit in the finite element model;

[0081] S6: performing freeze-thaw cycle simulation on the finite element model until the freeze-thaw zone unit becomes unstable, and obtaining a surface displacement curve of the freeze-thaw zone unit and a first freeze-thaw zone thickness of the freeze-thaw zone unit during the simulation process to form a sample pair; the surface displacement curve is a time-history curve of the surface displacement value of the freeze-thaw zone unit;

[0082] S7: adjusting the thickness of the first freeze-thaw zone in the finite element model and repeatedly calculating to form a plurality of sample pairs, and forming a sample library based on the plurality of sample pairs; the sample library is a correspondence between a plurality of different first freeze-thaw zone thicknesses and surface displacement curves;

[0083] S8: obtaining a second freeze-thaw zone thickness at the sensor position, and obtaining a fitting displacement curve corresponding to the sensor from the sample library according to the second freeze-thaw zone thickness;

[0084] S9: Acquire the displacement monitoring data of the sensor along the time course to form a real-time displacement curve, and judge the stability of the corresponding position of the sensor according to the real-time displacement curve and the corresponding fitting displacement curve.

[0085] When the embodiment of the present application is implemented, the sensor can be installed at different depths of the inclinometer tube to achieve displacement and temperature monitoring. The displacement and temperature of the rock slope in the seasonally frozen area are measured by temperature and displacement sensors. The rock temperature of 0°C is used as the dividing line. The rock above the 0°C dividing line is the freeze-thaw zone, and the rock below the 0°C dividing line is the non-freeze-thaw zone. The rock in the freeze-thaw zone of the slope is layered with the rock in the non-freeze-thaw zone, thereby obtaining the freeze-thaw depth of the rock slope in the cold region and layering the rock in the freeze-thaw zone of the slope with the rock in the non-freeze-thaw zone.

[0086] In the embodiment of the present application, in order to obtain rock sample data in the freeze-thaw zone and the non-freeze-thaw zone, it is necessary to sample the rocks in this area and conduct tests to obtain rock creep parameters. It should be understood that the test process belongs to the prior art and will not be repeated in the embodiment of the present application. Based on the rock creep parameters that have been obtained, a creep constitutive model of the target cold-region rock slope can be constructed to characterize the stability of the target cold-region rock slope. In scientific practice, the inventors found that although the analysis technology for freeze-thaw rocks is very rich in the prior art, for the rock slopes in the seasonally frozen zone, the freeze-thaw damage process that the rocks at the monitoring point have experienced cannot be tested, and for high slopes with a large number of monitoring points, the cost of sampling and experimental analysis for each monitoring point is too huge. Therefore, in the embodiment of the present application, the creep constitutive model constructed by experiment is used to assign simulation to the finite element model, so that a large amount of data can be obtained for subsequent analysis. A finite element model can be constructed first. This finite element model needs to have freeze-thaw zone elements for freeze-thaw damage simulation calculations. Then, a creep constitutive model is assigned as the constitutive model of the freeze-thaw zone elements for calculations. The surface displacement curve of the freeze-thaw zone elements from the beginning of the freeze-thaw cycle to the entire process of instability is calculated. This surface displacement curve is correlated with the overall thickness of the freeze-thaw zone elements. By adjusting the thickness of the first freeze-thaw zone and recalculating the process from freeze-thaw cycle to instability, corresponding sample pairs can be generated and ultimately a sample library can be formed.

[0087] In an embodiment of the present application, during the use of the sample library, different sensors may correspond to different freeze-thaw zone thicknesses. At this time, the corresponding fitted displacement curve can be calculated or extracted from the sample library based on the freeze-thaw zone thickness. After obtaining the real-time displacement curve in real time, the freeze-thaw damage of the freeze-thaw zone corresponding to the sensor can be found by comparing the real-time displacement curve and the fitted displacement curve, and then the stability of the point can be judged. Through the above-mentioned technical solution, the embodiment of the present application can more accurately calculate the damage of the freeze-thaw area corresponding to different sensors, thereby facilitating further slope stability analysis. It has good applicability and can be applied to the monitoring and analysis of various high slopes, thereby gaining valuable time for rescue and evacuation of geological disasters.

[0088] In a possible implementation, constructing the creep constitutive model of the target cold-region rock slope according to the rock creep parameters includes:

[0089] When the constant stress on the rock in the rock creep parameter is less than or equal to a preset value, a first creep model and a first constitutive model are constructed with the constraint that deformation does not occur before the yield limit is reached;

[0090] When the constant stress on the rock in the rock creep parameter is greater than a preset value, a second creep model and a second constitutive model are constructed by deducting friction resistance from the stress with deformation occurring at the yield limit as a constraint condition;

[0091] The first creep model, the first constitutive model, the second creep model, and the second constitutive model are introduced with damage variables to characterize the damage degradation of the viscosity coefficient caused by stress. Considering the influence of the number of freeze-thaw cycles and the action time, the damaged viscosity element under freeze-thaw conditions is constructed for analysis to form the creep constitutive model.

[0092] When implementing the embodiments of the present application, the inventors discovered whether the displacement of multiple key points on the sliding belt can be stable over a long period of time. Since the rock mass under study has the characteristic of attenuated creep, for a stable slope, although the deformation develops over time, at a certain stage, its deformation will always tend to be stable. If the strength of the rock mass is reduced to the limit state of the slope, unlimited plastic shear deformation will occur along the sliding belt. Compared with the deformation caused by creep, this plastic deformation is much larger. At this time, the displacement of the rock mass on the slope, especially above the sliding belt, will not eventually stabilize after a period of time. In this way, some key points can be taken on the sliding belt, and the changes in the horizontal displacement of these points over time can be recorded. If the displacement of these points cannot be stabilized for a long enough time, it can be judged that the slope is unstable. When constructing a creep constitutive model based on this stability criterion, a rock freeze-thaw damage creep constitutive model that can reflect attenuated creep, constant-speed creep, and accelerated creep can be established based on the rock creep curves of different freeze-thaw times. According to the test results, the creep curve of freeze-thaw rock is related to the number of freeze-thaw cycles, stress state, and loading time. Therefore, a creep constitutive model based on the freeze-thaw damage factor of rock was proposed.

[0093] In the embodiments of the present application, to better describe accelerated rock creep, a nonlinear viscoplastic body is used to improve the classic Burgers model. When the constant stress on the rock is less than or equal to a preset value, the nonlinear viscoplastic model does not reach the yield limit and does not deform. The established rock viscoelastic creep model degenerates into the Burgers model. When the constant stress on the rock is greater than the preset value, the nonlinear viscoplastic model reaches the yield limit and deforms. At this time, the stress in the model needs to be deducted from the friction resistance. In this case, the Burgers model and the nonlinear viscoplastic model are connected in series. By introducing the damage variable D to represent the damage degradation of the viscosity coefficient of the specimen caused by stress, and considering the influence of the freeze-thaw number n and the action time t, the construction of a damaged viscosity element under freeze-thaw conditions can accurately assess slope stability.

[0094] In a possible implementation, the first creep model adopts the following formula:

[0095]

[0096] The first constitutive model adopts the following formula:

[0097]

[0098] The second creep model adopts the following formula:

[0099] σ=σ1=σ2=σ3

[0100] ε=ε1+ε2+ε3

[0101]

[0102]

[0103] The second constitutive model adopts the following formula:

[0104]

[0105] Where: ε is the total strain, σ0 is the load stress, E0(n) is the elastic modulus of the elastic body after freeze-thaw n times, E1(n) is the elastic modulus of the viscoelastic body after freeze-thaw n times, η1 is the elastic viscosity coefficient after freeze-thaw n times, η2 is the viscosity coefficient of the viscoplastic body after freeze-thaw n times, η3 is the viscosity coefficient of the viscous element damaged by freeze-thaw, σ s is the yield stress of rock, and t is the loading time.

[0106] In one possible implementation, a damage variable is introduced to characterize the damage degradation of the viscosity coefficient caused by stress, and the influence of the number of freeze-thaw cycles and the action time are considered. The damaged viscosity element under freeze-thaw conditions is constructed using the following formula:

[0107] D=1-eαt

[0108] η(t)=η(1-D)=ηe-αt

[0109] Where α is a coefficient related to the freeze-thaw number n, t is the creep time, and D is the rock freeze-thaw damage factor, D∈[0,1]. When D is 0, the rock is undamaged, and when D is 1, the rock is creep-damaged.

[0110] When the embodiment of the present application is implemented, the instability of the freeze-thaw unit area can be judged according to this criterion.

[0111] In a possible implementation, obtaining a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone includes:

[0112] Performing a traversal search in the sample library according to the thickness of the second freeze-thaw zone;

[0113] When a first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is retrieved from the sample library, the surface displacement curve corresponding to the first freeze-thaw zone thickness is used as the fitting displacement curve of the sensor;

[0114] When the first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is not retrieved in the sample library, a surface displacement curve corresponding to the lower limit freeze-thaw zone thickness is obtained as the lower limit curve, and a surface displacement curve corresponding to the upper limit freeze-thaw zone thickness is obtained as the upper limit curve; the lower limit freeze-thaw zone thickness is smaller than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; the upper limit freeze-thaw zone thickness is larger than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness;

[0115] The lower limit curve and the upper limit curve are interpolated according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness and the upper limit freeze-thaw zone thickness to form a fitting displacement curve of the sensor.

[0116] When the embodiment of the present application is implemented, in order to find the displacement curve that matches the sensor, it is necessary to traverse and retrieve the most suitable curve in the sample library. In the most ideal case, there is a first freeze-thaw zone thickness that is exactly the same as the second freeze-thaw zone thickness. At this time, it is only necessary to use the surface displacement curve corresponding to the first freeze-thaw zone thickness as the fitted displacement curve. When there is no first freeze-thaw zone thickness that is exactly the same as the second freeze-thaw zone thickness, it is necessary to see between which two adjacent first freeze-thaw zone thicknesses the second freeze-thaw zone thickness falls, and to achieve the generation of the fitted displacement curve by interpolation.

[0117] In a possible implementation, interpolating the lower limit curve and the upper limit curve according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness, and the upper limit freeze-thaw zone thickness to form the fitting displacement curve of the sensor includes:

[0118] Obtaining the displacement values of the lower limit curve at multiple moments as lower limit displacement values, and obtaining the displacement values of the upper limit curve at multiple moments as upper limit displacement values;

[0119] The lower limit displacement value and the upper limit displacement value at the same moment are linearly interpolated using the first difference and the second difference as weights to form a displacement value to be fitted corresponding to the moment; the first difference is the thickness of the second freeze-thaw zone minus the thickness of the lower limit freeze-thaw zone; the second difference is the thickness of the upper limit freeze-thaw zone minus the thickness of the second freeze-thaw zone;

[0120] A plurality of displacement values to be fitted are fitted along a time course to form a fitting displacement curve of the sensor.

[0121] When implementing the embodiments of the present application, a specific interpolation method is provided, in which the lower limit displacement value and the upper limit displacement value at the same time are required to be obtained as the basis for the interpolation data. The interpolation weight of the linear interpolation is the difference between the thickness of the lower freeze-thaw zone, the thickness of the second freeze-thaw zone, and the thickness of the upper freeze-thaw zone. This interpolation process belongs to the prior art and is not limited in the embodiments of the present application. After the interpolation is completed, the interpolation data corresponding to multiple time points can be obtained. By fitting these interpolation data in the time history direction, the required fitted displacement curve can be generated.

[0122] In a possible implementation, judging the stability of the sensor at a corresponding position according to the real-time displacement curve and the corresponding fitted displacement curve includes:

[0123] Obtaining a displacement curve of a preset time length in the real-time displacement curve as a reference displacement curve;

[0124] Using the preset time length as the sliding window width, searching the fitted displacement curve to find the area closest to the reference displacement curve as the reference displacement area;

[0125] The stability of the corresponding position of the sensor is judged according to the distance between the reference displacement area and the unstable position in the fitting displacement curve; the closer the distance between the reference displacement area and the unstable position in the fitting displacement curve, the worse the stability.

[0126] When the embodiment of the present application is implemented, in the actual monitoring process, in order to accurately judge the freeze-thaw damage of the rock at the current position, it is necessary to select a displacement curve of a preset time length from the monitored real-time displacement curve as a reference displacement curve. The characteristics of the reference displacement curve can represent the current rock damage state. By searching in the fitted displacement curve through a sliding window with the same length as the reference displacement curve, an area that meets the current damage state can be found, that is, the reference displacement area. Since the fitted displacement curve has an unstable position, that is, the end endpoint position of the curve, the current damage situation can be judged based on the distance between the reference displacement area and the end endpoint position.

[0127] Based on the same inventive concept, the present application also provides a system for predicting rock slope stability in seasonally frozen areas, including:

[0128] The data acquisition unit is configured to set a plurality of sensors on the target cold region rock slope and receive temperature monitoring data and displacement monitoring data monitored by the sensors; the plurality of sensors are arranged linearly, and the linear direction is parallel to the landslide direction of the target cold region rock slope;

[0129] a dividing unit configured to obtain, based on the temperature monitoring data, a distribution characteristic of rock layer temperature as a function of freeze-thaw weathering depth, and to divide the target cold-region rock slope into a freeze-thaw zone and a non-freeze-thaw zone based on the distribution characteristic;

[0130] a sampling unit configured to sample the rocks in the freeze-thaw zone and the non-freeze-thaw zone respectively, and perform a rock creep test on the sampled samples to obtain creep parameters before and after freeze-thaw as rock creep parameters;

[0131] A constitutive unit is configured to construct a creep constitutive model of the target cold region rock slope according to the rock creep parameters;

[0132] A modeling unit is configured to construct a finite element model and assign the creep constitutive model to a freeze-thaw zone unit in the finite element model;

[0133] a simulation unit configured to perform freeze-thaw cycle simulation on the finite element model until the freeze-thaw zone unit becomes unstable, and obtain a surface displacement curve of the freeze-thaw zone unit and a first freeze-thaw zone thickness of the freeze-thaw zone unit during the simulation to form a sample pair; the surface displacement curve is a time-history curve of the surface displacement value of the freeze-thaw zone unit;

[0134] A sample unit is configured to adjust the thickness of the first freeze-thaw zone in the finite element model and repeatedly calculate to form a plurality of sample pairs, and form a sample library based on the plurality of sample pairs; the sample library is a correspondence between a plurality of different first freeze-thaw zone thicknesses and surface displacement curves;

[0135] an acquiring unit configured to acquire a thickness of a second freeze-thaw zone at the position of the sensor, and acquire a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone;

[0136] The analysis unit is configured to obtain the displacement monitoring data of the sensor along the time course to form a real-time displacement curve, and judge the stability of the corresponding position of the sensor according to the real-time displacement curve and the corresponding fitting displacement curve.

[0137] In a possible implementation, the constitutive unit is further configured as follows:

[0138] When the constant stress on the rock in the rock creep parameter is less than or equal to a preset value, a first creep model and a first constitutive model are constructed with the constraint that deformation does not occur before the yield limit is reached;

[0139] When the constant stress on the rock in the rock creep parameter is greater than a preset value, a second creep model and a second constitutive model are constructed by deducting friction resistance from the stress with deformation occurring at the yield limit as a constraint condition;

[0140] The first creep model, the first constitutive model, the second creep model, and the second constitutive model are introduced with damage variables to characterize the damage degradation of the viscosity coefficient caused by stress. Considering the influence of the number of freeze-thaw cycles and the action time, the damaged viscosity element under freeze-thaw conditions is constructed for analysis to form the creep constitutive model.

[0141] In a possible implementation, the acquiring unit is further configured to:

[0142] Performing a traversal search in the sample library according to the thickness of the second freeze-thaw zone;

[0143] When a first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is retrieved from the sample library, the surface displacement curve corresponding to the first freeze-thaw zone thickness is used as the fitting displacement curve of the sensor;

[0144] When the first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is not retrieved in the sample library, a surface displacement curve corresponding to the lower limit freeze-thaw zone thickness is obtained as the lower limit curve, and a surface displacement curve corresponding to the upper limit freeze-thaw zone thickness is obtained as the upper limit curve; the lower limit freeze-thaw zone thickness is smaller than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; the upper limit freeze-thaw zone thickness is larger than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness;

[0145] The lower limit curve and the upper limit curve are interpolated according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness and the upper limit freeze-thaw zone thickness to form a fitting displacement curve of the sensor.

[0146] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the composition and steps of each example according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0147] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, or can be electrical, mechanical or other forms of connection.

[0148] The units described as separate components may or may not be physically separated. As units, it is obvious that a person of ordinary skill in the art can realize that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0149] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0150] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or grid device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0151] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting rock slope stability in seasonally frozen areas, characterized by: include: A plurality of sensors are arranged on the rock slope of the target cold region, and temperature monitoring data and displacement monitoring data monitored by the sensors are received; The plurality of sensors are arranged linearly, and the linear direction is parallel to the landslide direction of the target cold region rock slope; Obtaining distribution characteristics of rock layer temperature along with freeze-thaw weathering depth according to the temperature monitoring data, and dividing the target cold region rock slope into freeze-thaw zones and non-freeze-thaw zones according to the distribution characteristics; Sampling rocks in the freeze-thaw zone and the non-freeze-thaw zone respectively, and performing rock creep tests on the sampled samples to obtain creep parameters before and after freeze-thaw as rock creep parameters; Constructing a creep constitutive model of the target cold region rock slope according to the rock creep parameters; Constructing a finite element model, and assigning the creep constitutive model to the freeze-thaw zone unit in the finite element model; The finite element model is subjected to freeze-thaw cycle simulation until the freeze-thaw zone unit becomes unstable, and a surface displacement curve of the freeze-thaw zone unit and a first freeze-thaw zone thickness of the freeze-thaw zone unit are obtained during the simulation to form a sample pair; the surface displacement curve is a time-history curve of the surface displacement value of the freeze-thaw zone unit; Adjusting the thickness of the first freeze-thaw zone in the finite element model and repeatedly calculating to form a plurality of sample pairs, and forming a sample library based on the plurality of sample pairs; the sample library is a correspondence between a plurality of different first freeze-thaw zone thicknesses and surface displacement curves; Obtaining the thickness of the second freeze-thaw zone at the position of the sensor, and obtaining a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone; The displacement monitoring data of the sensor along the time course is acquired to form a real-time displacement curve, and the stability of the corresponding position of the sensor is determined according to the real-time displacement curve and the corresponding fitting displacement curve.

2. The method for predicting rock slope stability in seasonally frozen areas according to claim 1, characterized in that: Constructing the creep constitutive model of the target cold region rock slope according to the rock creep parameters includes: When the constant stress on the rock in the rock creep parameter is less than or equal to a preset value, a first creep model and a first constitutive model are constructed with the constraint that deformation does not occur before the yield limit is reached; When the constant stress on the rock in the rock creep parameter is greater than a preset value, a second creep model and a second constitutive model are constructed by deducting friction resistance from the stress with deformation occurring at the yield limit as a constraint condition; The first creep model, the first constitutive model, the second creep model, and the second constitutive model are introduced with damage variables to characterize the damage degradation of the viscosity coefficient caused by stress. Considering the influence of the number of freeze-thaw cycles and the action time, the damaged viscosity element under freeze-thaw conditions is constructed for analysis to form the creep constitutive model.

3. The method for predicting rock slope stability in seasonally frozen areas according to claim 2, characterized in that: The first creep model adopts the following formula: The first constitutive model adopts the following formula: The second creep model adopts the following formula: σ=σ1=σ2=σ3 ε=ε1+ε2+ε3 The second constitutive model adopts the following formula: Where: ε is the total strain, σ0 is the load stress, E0(n) is the elastic modulus of the elastic body after freeze-thaw n times, E1(n) is the elastic modulus of the viscoelastic body after freeze-thaw n times, η1 is the elastic viscosity coefficient after freeze-thaw n times, η2 is the viscosity coefficient of the viscoplastic body after freeze-thaw n times, η3 is the viscosity coefficient of the viscous element damaged by freeze-thaw, σ s is the yield stress of rock, and t is the loading time.

4. The method for predicting rock slope stability in seasonally frozen areas according to claim 3, characterized in that: The damage variable is introduced to characterize the damage degradation of the viscosity coefficient caused by stress, and the influence of the number of freeze-thaw cycles and the action time are considered. The damaged viscosity element under freeze-thaw conditions is constructed using the following formula: D=1-eαt η(t)=η(1-D)=ηe-αt Where α is a coefficient related to the freeze-thaw number n, t is the creep time, and D is the rock freeze-thaw damage factor, D∈[0,1]. When D is 0, the rock is undamaged, and when D is 1, the rock is creep-damaged.

5. The method for predicting rock slope stability in seasonally frozen areas according to claim 1, characterized in that: Obtaining a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone includes: Performing a traversal search in the sample library according to the thickness of the second freeze-thaw zone; When a first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is retrieved from the sample library, the surface displacement curve corresponding to the first freeze-thaw zone thickness is used as the fitting displacement curve of the sensor; When the first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is not retrieved in the sample library, a surface displacement curve corresponding to the lower limit freeze-thaw zone thickness is obtained as the lower limit curve, and a surface displacement curve corresponding to the upper limit freeze-thaw zone thickness is obtained as the upper limit curve; the lower limit freeze-thaw zone thickness is smaller than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; the upper limit freeze-thaw zone thickness is larger than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; The lower limit curve and the upper limit curve are interpolated according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness and the upper limit freeze-thaw zone thickness to form a fitting displacement curve of the sensor.

6. The method for predicting rock slope stability in seasonally frozen areas according to claim 5, characterized in that: Interpolating the lower limit curve and the upper limit curve according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness, and the upper limit freeze-thaw zone thickness to form the fitting displacement curve of the sensor includes: Obtaining the displacement values of the lower limit curve at multiple moments as lower limit displacement values, and obtaining the displacement values of the upper limit curve at multiple moments as upper limit displacement values; The lower limit displacement value and the upper limit displacement value at the same moment are linearly interpolated using the first difference and the second difference as weights to form a displacement value to be fitted corresponding to the moment; the first difference is the thickness of the second freeze-thaw zone minus the thickness of the lower limit freeze-thaw zone; the second difference is the thickness of the upper limit freeze-thaw zone minus the thickness of the second freeze-thaw zone; A plurality of displacement values to be fitted are fitted along a time course to form a fitting displacement curve of the sensor.

7. The method for predicting rock slope stability in seasonally frozen areas according to claim 1, characterized in that: Judging the stability of the corresponding position of the sensor according to the real-time displacement curve and the corresponding fitting displacement curve includes: Obtaining a displacement curve of a preset time length in the real-time displacement curve as a reference displacement curve; Using the preset time length as the sliding window width, searching the fitted displacement curve to find the area closest to the reference displacement curve as the reference displacement area; The stability of the corresponding position of the sensor is judged according to the distance between the reference displacement area and the unstable position in the fitting displacement curve; the closer the distance between the reference displacement area and the unstable position in the fitting displacement curve, the worse the stability.

8. The rock slope stability prediction system in seasonally frozen areas is characterized by: include: a data acquisition unit configured to set a plurality of sensors on the target cold region rock slope and receive temperature monitoring data and displacement monitoring data monitored by the sensors; The plurality of sensors are arranged linearly, and the linear direction is parallel to the landslide direction of the target cold region rock slope; a dividing unit configured to obtain, based on the temperature monitoring data, a distribution characteristic of rock layer temperature as a function of freeze-thaw weathering depth, and to divide the target cold-region rock slope into a freeze-thaw zone and a non-freeze-thaw zone based on the distribution characteristic; a sampling unit configured to sample the rocks in the freeze-thaw zone and the non-freeze-thaw zone respectively, and perform a rock creep test on the sampled samples to obtain creep parameters before and after freeze-thaw as rock creep parameters; A constitutive unit is configured to construct a creep constitutive model of the target cold region rock slope according to the rock creep parameters; A modeling unit is configured to construct a finite element model and assign the creep constitutive model to a freeze-thaw zone unit in the finite element model; a simulation unit configured to perform freeze-thaw cycle simulation on the finite element model until the freeze-thaw zone unit becomes unstable, and obtain a surface displacement curve of the freeze-thaw zone unit and a first freeze-thaw zone thickness of the freeze-thaw zone unit during the simulation to form a sample pair; the surface displacement curve is a time-history curve of the surface displacement value of the freeze-thaw zone unit; A sample unit is configured to adjust the thickness of the first freeze-thaw zone in the finite element model and repeatedly calculate to form a plurality of sample pairs, and form a sample library based on the plurality of sample pairs; the sample library is a correspondence between a plurality of different first freeze-thaw zone thicknesses and surface displacement curves; an acquiring unit configured to acquire a thickness of a second freeze-thaw zone at the position of the sensor, and acquire a fitting displacement curve corresponding to the sensor from the sample library according to the thickness of the second freeze-thaw zone; The analysis unit is configured to obtain the displacement monitoring data of the sensor along the time course to form a real-time displacement curve, and judge the stability of the corresponding position of the sensor according to the real-time displacement curve and the corresponding fitting displacement curve.

9. The seasonally frozen area rock slope stability prediction system according to claim 8, characterized in that: The constitutive element is also configured as: When the constant stress on the rock in the rock creep parameter is less than or equal to a preset value, a first creep model and a first constitutive model are constructed with the constraint that deformation does not occur before the yield limit is reached; When the constant stress on the rock in the rock creep parameter is greater than a preset value, a second creep model and a second constitutive model are constructed by deducting friction resistance from the stress with deformation occurring at the yield limit as a constraint condition; The first creep model, the first constitutive model, the second creep model, and the second constitutive model are introduced with damage variables to characterize the damage degradation of the viscosity coefficient caused by stress. Considering the influence of the number of freeze-thaw cycles and the action time, the damaged viscosity element under freeze-thaw conditions is constructed for analysis to form the creep constitutive model.

10. The seasonally frozen area rock slope stability prediction system according to claim 8, characterized in that: The acquisition unit is further configured to: Performing a traversal search in the sample library according to the thickness of the second freeze-thaw zone; When a first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is retrieved from the sample library, the surface displacement curve corresponding to the first freeze-thaw zone thickness is used as the fitting displacement curve of the sensor; When the first freeze-thaw zone thickness that is the same as the second freeze-thaw zone thickness is not retrieved in the sample library, a surface displacement curve corresponding to the lower limit freeze-thaw zone thickness is obtained as the lower limit curve, and a surface displacement curve corresponding to the upper limit freeze-thaw zone thickness is obtained as the upper limit curve; the lower limit freeze-thaw zone thickness is smaller than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; the upper limit freeze-thaw zone thickness is larger than the second freeze-thaw zone thickness and closest to the first freeze-thaw zone thickness; The lower limit curve and the upper limit curve are interpolated according to the lower limit freeze-thaw zone thickness, the second freeze-thaw zone thickness and the upper limit freeze-thaw zone thickness to form a fitting displacement curve of the sensor.

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