CN117252063A - Rock high slope excavation anchoring deformation prediction method and system based on machine learning - Google Patents
Rock high slope excavation anchoring deformation prediction method and system based on machine learning Download PDFInfo
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Abstract
The invention discloses a machine learning-based rock high slope excavation anchoring deformation prediction method and system, wherein the method comprises the following steps: obtaining geological survey reports, slope excavation progress and monitoring information of a high arch dam area, and constructing a rock high slope multistage excavation anchoring model; based on a machine learning algorithm, importance ranking is carried out on the physical and mechanical parameters of the rock mass of the constructed model, and the key physical and mechanical parameters of the rock mass are identified as random variables to be updated; constructing a proxy model between random variables and slope response in each excavation anchoring stage based on a machine learning algorithm; constructing a Bayesian framework, and incorporating the monitoring information into posterior distribution of physical and mechanical parameters of the inverted rock mass; inputting posterior distribution of physical and mechanical parameters of the inverted rock mass into a proxy model of each excavation and anchoring stage to predict side slope deformation of the subsequent excavation and anchoring stage. The method and the device realize the prediction of rock mass high slope excavation anchoring deformation by utilizing the monitoring information to make up for the defect of rock mass physical and mechanical parameter test data.
Description
Technical Field
The invention belongs to the technical field of slope deformation prediction, and particularly relates to a rock high slope excavation anchoring deformation prediction method and system based on machine learning.
Background
In recent years, high arch dams with good economy and good safety are widely favored by engineers, and a large number of high arch dams in southwest regions are built and put into operation, such as a first-level hydropower station of a brocade, a river ferry hydropower station, a white crane beach hydropower station, a Wu Dongde hydropower station and the like. Because the excavation scale of the high arch dam construction process is huge, the problems of the excavation deformation and the stability of the rock mass high slope in the dam area are particularly outstanding, and the method is one of the main engineering technical problems in hydropower construction.
Generally, engineering predicts slope deformation based on finite element models. However, since the slope rock mass is a natural material, has the characteristics of concealment and space-time variability, and is influenced by limited test data, the rock mass physical mechanical parameters input into the finite element model for calculating the slope deformation cannot represent the actual rock mass physical mechanical properties, so that obvious errors can be caused by predicting the slope deformation only based on the finite element model. In recent years, along with the development of monitoring technology, a large number of monitoring instruments are usually installed in the construction process of a high arch dam to acquire monitoring data such as slope displacement, stress, osmotic pressure and the like in real time, and the data reflect the real state of the slope in real time, so that the method is more reliable compared with rock physical and mechanical parameters acquired based on survey data and experiments. How to invert the physical and mechanical parameters of the rock mass by using the monitoring information, and simultaneously, predicting the deformation of the side slope in real time by combining a finite element model and a machine learning algorithm to be further developed.
Disclosure of Invention
The invention aims to provide a machine learning-based rock high slope excavation anchoring deformation prediction method aiming at the defects of the prior art, and the method can utilize monitoring information to make up for the prediction of rock high slope excavation anchoring deformation under the condition of insufficient test data of physical and mechanical parameters of a rock mass.
In order to solve the technical problems, the invention adopts the following technical scheme:
the rock high slope excavation anchoring deformation prediction method based on machine learning is characterized by comprising the following steps of:
step 1, obtaining geological survey reports, slope excavation progress and monitoring information of a high arch dam area, and constructing a rock high slope multistage excavation anchoring model according to the geological survey reports, the slope excavation progress and the monitoring information;
step 2, sorting importance of physical and mechanical parameters of the rock mass of the constructed model based on a machine learning algorithm, and identifying key physical and mechanical parameters of the rock mass as random variables to be updated;
step 3, constructing a proxy model between random variables and slope response in each excavation anchoring stage based on a machine learning algorithm;
step 4, establishing a functional relation between the monitoring information and the proxy model, constructing a Bayesian framework, and incorporating the functional relation into posterior distribution of physical and mechanical parameters of the inverted rock mass;
and 5, inputting posterior distribution of the inverted rock physical and mechanical parameters into the proxy model of each excavation and anchoring stage to predict the slope deformation of the subsequent excavation and anchoring stage.
Further, the method for constructing the rock high slope multi-stage excavation anchoring model in the step 1 comprises the following steps: and generating grids of the finite element model in ANSYS according to the geological survey report of the dam area, the slope excavation progress and the monitoring information, and constructing a rock high slope multi-stage excavation anchoring model by leading the grids into FLAC3D through an insert.
Further, for a rock high slope multi-stage excavation anchoring model, a Moire-Coulomb constitutive model is adopted, normal constraint is applied to the periphery of the model, and the bottom side is fixed; and distinguishing various rock mass and structural surface materials in the model by adopting different groups, and simulating the excavation materials by adopting a null model and the prestressed anchor cable by adopting a cable model.
Further, the implementation method of the step 2 is as follows:
generating a rock physical and mechanical parameter data set based on Latin hypercube sampling, generating a corresponding command stream according to the rock physical and mechanical parameter data set, inputting the command stream into a FLAC3D model, and calculating a corresponding slope response data set;
the method comprises the steps of adopting a random forest algorithm to analyze, defining a rock physical and mechanical parameter data set as input, defining a slope response data set as output, sequencing importance of the rock physical and mechanical parameters based on an importance measurement method in the random forest algorithm, and identifying the rock physical and mechanical parameters which have key influence on the slope response as random variables to be updated.
Further, the physical and mechanical parameters of the rock mass include elastic modulus E, poisson's ratio mu, gravity gamma, cohesion c and internal friction angle。
Further, step 3 includes:
defining the physical and mechanical parameters of the key rock mass identified in the step 2 as a random variable x= [ x ] 1 ,x 2 ,…,x d ]The method comprises the steps of carrying out a first treatment on the surface of the And training a proxy model SVM (x) between random variables and slope responses in each excavation anchoring stage by adopting a support vector machine algorithm, and replacing a FLAC3D model by adopting the proxy model SVM (x).
Further, in step 4, the established monitoring information y= [ Y ] 1 ,y 2 ,…,y n ]The functional relation with the proxy model SVM (x) is as follows:
Y＝SVM(x)+ε
where ε represents the measurement error.
Further, based on Bayesian theory, the functional relation of the monitoring information is brought into the following formula, and the adaptive differential evolution Metropolis algorithm DREAM with multi-chain parallel calculation is adopted (ZS) To invert posterior distribution of physical and mechanical parameters of rock mass:
p(x|Y)＝cL(x|Y)p(x)
wherein p (x|Y) represents a parametric posterior probability density function; p (x) represents a parameter prior probability density function, and parameters obey logarithmic normal distribution and are independent of each other; c is a normalization constant; l (x|y) represents a likelihood function; subscript j represents a j-th rock physical-mechanical parameter; mu (mu) N Sum sigma N Mean and standard deviation of the logarithm of the parameters; subscript n represents the nth excavation anchoring stage; mu (mu) ε Sum sigma ε Mean and standard deviation of the measurement error epsilon are indicated.
Further, step 5 specifically includes:
and inputting posterior distribution of physical and mechanical parameters of the inverted rock mass into a proxy model SVM (x) of each excavation stage, so as to predict slope deformation of the subsequent excavation anchoring stage. And according to the calculation result, taking the average value as a predicted value of slope deformation in each subsequent excavation and anchoring stage, and comparing the predicted value with an actual slope monitoring value.
Another object of the present invention is to provide a system for predicting rock high slope excavation anchoring deformation based on machine learning, comprising:
the data acquisition module is used for acquiring geological survey reports, slope excavation progress and monitoring information of the high arch dam area;
the model construction module is used for constructing a rock high slope multi-stage excavation anchoring model according to the data acquired by the data acquisition module;
the random variable screening module is used for carrying out importance ranking on the physical and mechanical parameters of the rock mass of the constructed model based on a machine learning algorithm, and identifying the physical and mechanical parameters of the key rock mass as random variables to be updated;
the agent model training module is used for training an agent model between random variables and slope responses in each excavation anchoring stage based on a machine learning algorithm;
the posterior distribution acquisition module of the physical and mechanical parameters is used for establishing a functional relation between the monitoring information and the proxy model and constructing a Bayesian framework to incorporate the functional relation into posterior distribution of the physical and mechanical parameters of the inverted rock mass;
the slope deformation prediction module is used for inputting posterior distribution of the physical and mechanical parameters of the rock body inverted by the posterior distribution acquisition module of the physical and mechanical parameters into the proxy model of each excavation and anchoring stage so as to predict the slope deformation of the subsequent excavation and anchoring stage.
Compared with the prior art, the invention has the beneficial effects that: according to the rock high slope excavation anchoring deformation prediction method based on machine learning, provided by the invention, on the premise of considering the uncertainty of rock physical and mechanical parameters of the rock high slope, the posterior distribution of the rock physical and mechanical parameters is gradually inverted by using a Bayesian method in combination with actual engineering monitoring information, and the slope deformation in the subsequent excavation anchoring stage is predicted, so that the problem that the rock physical and mechanical parameters are difficult to reliably invert only based on limited survey data and test data is solved; according to the method, importance ranking is carried out on the physical and mechanical parameters of the rock mass input into the FLAC3D model based on a machine learning algorithm, the physical and mechanical parameters of the key rock mass are identified as random variables to be updated so as to reduce the number of inversion parameters, and meanwhile, the method trains the proxy model so as to reduce the calling times of the complex model, so that the calculation efficiency of Bayesian updating is greatly improved; the method provides a basis for realizing the rock high slope excavation anchoring deformation prediction method based on machine learning, and has good engineering application value.
Drawings
FIG. 1 is a flow chart of a machine learning-based rock high slope excavation anchoring deformation prediction method in an embodiment of the invention;
fig. 2 is a multistage excavation and anchoring model diagram of a rock high slope according to an embodiment of the invention.
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention will be further illustrated, but is not limited, by the following examples.
As shown in fig. 1, the embodiment of the invention provides a machine learning-based rock high slope excavation anchoring deformation prediction method, which comprises the following steps:
step 1, obtaining geological survey reports, slope excavation progress and monitoring information of a high arch dam area, and constructing a rock high slope multistage excavation anchoring model according to the geological survey reports, the slope excavation progress and the monitoring information;
and obtaining geological survey reports, slope excavation progress and monitoring information of the high arch dam area according to actual engineering conditions, generating grids of the finite element model in ANSYS, and constructing a rock high slope multistage excavation anchoring model by leading the grids into FLAC3D through an insert, wherein the rock high slope multistage excavation anchoring model is shown in figure 2. The rock high slope multistage excavation anchoring model adopts a Moire-coulomb constitutive model, normal constraint is applied to the periphery of the model, and the bottom side is fixed. The simulated rock mass and structural surface materials in the rock mass high slope multi-stage excavation anchoring model are distinguished by different groups, and a null model is adopted to simulate the excavation materials and a cable model to simulate the prestressed anchor cable.
Step 2, sorting importance of physical and mechanical parameters of the rock mass of the constructed model based on a machine learning algorithm, and identifying key physical and mechanical parameters of the rock mass as random variables to be updated;
determining physical and mechanical parameters of the rock mass according to the geological survey report, engineering experience and literature of the dam region, wherein the physical and mechanical parameters of the rock mass comprise elastic modulus E, poisson's ratio mu, gravity gamma, cohesive force c and internal friction angleGenerating a corresponding command stream based on the rock physical and mechanical parameter data set, and inputting the command stream into the FLAC3D model to calculate a corresponding slope response data set; adopting a random forest algorithm to analyze, defining a rock physical and mechanical parameter data set as input and a slope response data set as output; importance ranking is carried out on physical and mechanical parameters of rock mass based on importance measurement method in random forest algorithm, and the importance ranking is carried outThe physical and mechanical parameters of the rock mass which have a key influence on the slope response are identified as random variables to be updated.
In this embodiment, the obtained physical and mechanical parameters are specifically shown in table 1, where the elastic modulus E and the cohesive force c with higher variability are considered as uncertain parameters, and an input set of a random forest algorithm is constructed through latin hypercube sampling. And carrying out importance ranking on the physical and mechanical parameters of the rock mass based on an importance measurement method in a random forest algorithm. The physical and mechanical parameters of the rock mass, which have key influence on the displacement of the monitoring points of the slope, are identified as random variables to be updated, and the prior distribution of the selected random variables is shown in table 2.
Table 1 physical and mechanical parameter table for side slope rock mass
TABLE 2 random variable prior distribution Table to be updated
Step 3, constructing a proxy model between random variables and slope response in each excavation anchoring stage based on a machine learning algorithm;
according to the parameter importance ranking, the identified 5 random variables x= [ x ] to be updated 1 ,x 2 ,…,x d ]The method comprises the steps of constructing an input set and a corresponding FLAC3D model calculation result as an output set, constructing agent models between random variables and slope monitoring point displacement in each excavation anchoring stage by adopting a support vector machine algorithm, constructing the input set and the output set as data sets, dividing the data sets into a training set and a prediction set, training the agent models by adopting the training set and verifying by adopting the prediction set to obtain each agent model. Based on ground structure responseThe corresponding Bayesian updating method generally comprises two parts, namely posterior distribution of uncertain model parameters and structural response updating based on the posterior distribution, and a large number of numerical model simulations are required to be executed in the process, so that a proxy model is adopted to replace a FLAC3D model in the subsequent Bayesian updating, and high-efficiency calculation is realized on the premise of ensuring calculation accuracy.
Step 4, establishing a functional relation between the monitoring information and the proxy model, constructing a Bayesian framework, and incorporating the functional relation into posterior distribution of physical and mechanical parameters of the inverted rock mass;
established monitoring information y= [ Y ] 1 ,y 2 ,…,y n ]The functional relation with the proxy model SVM (x) is as follows:
Y＝SVM(x)+ε
wherein ε represents a measurement error;
wherein the measurement error epsilon obeys a standard normal distribution with a mean of 1mm and a variance of 0. Based on the bayesian theory p (x|y) =cl (x|y) p (x), combining prior knowledge and engineering actual monitoring information, constructing a parameter prior probability density function p (x) and a likelihood function L (x|y), and calculating a parameter posterior probability density function p (x|y). Because of the high-dimensional and nonlinear nature of the random variable x, the posterior distribution p (x|Y) is generally free of analytical solutions, and the embodiment adopts an adaptive differential evolution Metropolis algorithm DREAM with multi-chain parallel computing (ZS) Inverting the posterior distribution of the random variable x. Specifically, adaptive differential evolution Metropolis algorithm DREAM with multiple-chain parallel computing is adopted (ZS) The posterior distribution of inversion rock physical and mechanical parameters is as follows:
p(x|Y)＝cL(x|Y)p(x)
wherein p (x|Y) represents a parametric posterior probability density function; p (x) represents parameters firstThe parameters of the probability density function obey the lognormal distribution and are independent of each other; c is a normalization constant; l (x|y) represents a likelihood function; subscript j represents a j-th rock physical-mechanical parameter; mu (mu) N Sum sigma N Mean and standard deviation of the logarithm of the parameters; subscript n represents the nth excavation anchoring stage; mu (mu) ε Sum sigma ε Mean and standard deviation of the measurement error epsilon are indicated.
DREAM (ZS) The algorithm calculates a plurality of different Markov chains in parallel, if the parameter state of the ith chain is x i New proposed point x i,prop ＝x i +Δ i Delta in i For the incremental portion to be updated, it is recommended that the acceptance rate of the samples be determined by the Metropolis ratio α. In the embodiment, after the Markov chain converges, a later 25% sample is intercepted and taken as a posterior distribution sample of a random variable x, so that parameter posterior distribution inversion for making up insufficient rock physical mechanical parameter test data by using monitoring information is realized.
Step 5, inputting posterior distribution of inverted rock physical and mechanical parameters into a proxy model of each excavation and anchoring stage to predict slope deformation of the subsequent excavation and anchoring stage;
inputting posterior distribution of physical and mechanical parameters of the inverted rock mass into a proxy model SVM (x) of each excavation anchoring stage, so as to predict slope deformation of the subsequent excavation anchoring stage. And according to the calculation result, taking the average value as a predicted value of slope deformation in each subsequent excavation and anchoring stage and comparing the predicted value with an actual slope monitoring value, as shown in table 3.
TABLE 3 comparison table of slope deformation predicted value and monitored value
The above embodiments are merely illustrative of the technical solutions of the present invention. The machine learning-based rock high slope excavation anchoring deformation prediction method according to the present embodiment is not limited to the description of the above embodiments, but is subject to the scope defined by the claims. In the embodiment, a machine learning algorithm is adopted to identify the physical and mechanical parameters of the key rock mass, a proxy model is constructed, and the on-site monitoring information is incorporated into a Bayesian framework to realize rock mass high slope excavation anchoring deformation prediction, so that a basis is provided for dam area engineering safety supervision.
The invention also provides a system for predicting the rock high slope excavation anchoring deformation based on machine learning, which comprises:
the data acquisition module is used for acquiring geological survey reports, slope excavation progress and monitoring information of the high arch dam area;
the model construction module is used for constructing a rock high slope multi-stage excavation anchoring model according to the data acquired by the data acquisition module;
the random variable screening module is used for carrying out importance ranking on the physical and mechanical parameters of the rock mass of the constructed model based on a machine learning algorithm, and identifying the physical and mechanical parameters of the key rock mass as random variables to be updated;
the agent model training module is used for training an agent model between random variables and slope responses in each excavation anchoring stage based on a machine learning algorithm;
the posterior distribution acquisition module of the physical and mechanical parameters is used for establishing a functional relation between the monitoring information and the proxy model and constructing a Bayesian framework to incorporate the functional relation into posterior distribution of the physical and mechanical parameters of the inverted rock mass;
the slope deformation prediction module is used for inputting posterior distribution of the physical and mechanical parameters of the rock body inverted by the posterior distribution acquisition module of the physical and mechanical parameters into the proxy model of each excavation and anchoring stage so as to predict the slope deformation of the subsequent excavation and anchoring stage.
The foregoing is merely illustrative of the preferred embodiments of the present invention and is not intended to limit the embodiments and scope of the present invention, and it should be appreciated by those skilled in the art that equivalent substitutions and obvious variations may be made using the teachings of the present invention, which are intended to be included within the scope of the present invention.
Claims (10)
1. The rock high slope excavation anchoring deformation prediction method based on machine learning is characterized by comprising the following steps of:
step 1, obtaining geological survey reports, slope excavation progress and monitoring information of a high arch dam area, and constructing a rock high slope multistage excavation anchoring model according to the geological survey reports, the slope excavation progress and the monitoring information;
step 2, sorting importance of physical and mechanical parameters of the rock mass of the constructed model based on a machine learning algorithm, and identifying key physical and mechanical parameters of the rock mass as random variables to be updated;
step 3, constructing a proxy model between random variables and slope response in each excavation anchoring stage based on a machine learning algorithm;
step 4, establishing a functional relation between the monitoring information and the proxy model, constructing a Bayesian framework, and incorporating the functional relation into posterior distribution of physical and mechanical parameters of the inverted rock mass;
and 5, inputting posterior distribution of the inverted rock physical and mechanical parameters into the proxy model of each excavation and anchoring stage to predict the slope deformation of the subsequent excavation and anchoring stage.
2. The machine learning-based rock high slope excavation anchoring deformation prediction method of claim 1, wherein the method for constructing the rock high slope multistage excavation anchoring model in step 1 is as follows: and generating grids of the finite element model in ANSYS according to the geological survey report of the dam area, the slope excavation progress and the monitoring information, and constructing a rock high slope multi-stage excavation anchoring model by leading the grids into FLAC3D through an insert.
3. The machine learning-based rock high slope excavation anchoring deformation prediction method is characterized in that a Moire-Coulomb structure model is adopted for a rock high slope multistage excavation anchoring model, normal constraint is applied to the periphery of the model, and the bottom side is fixed; and distinguishing various rock mass and structural surface materials in the model by adopting different groups, and simulating the excavation materials by adopting a null model and the prestressed anchor cable by adopting a cable model.
4. The machine learning-based rock high slope excavation anchoring deformation prediction method of claim 1, wherein the implementation method of step 2 is as follows:
generating a rock physical and mechanical parameter data set based on Latin hypercube sampling, generating a corresponding command stream according to the rock physical and mechanical parameter data set, inputting the command stream into a FLAC3D model, and calculating a corresponding slope response data set;
the method comprises the steps of adopting a random forest algorithm to analyze, defining a rock physical and mechanical parameter data set as input, defining a slope response data set as output, sequencing importance of the rock physical and mechanical parameters based on an importance measurement method in the random forest algorithm, and identifying the rock physical and mechanical parameters which have key influence on the slope response as random variables to be updated.
5. The machine learning based rock mass high slope excavation anchoring deformation prediction method of claim 4, wherein the rock mass physical mechanical parameters comprise elastic modulus E, poisson's ratio μ, gravity γ, cohesion c and internal friction angle
6. The machine learning-based rock high slope excavation anchoring deformation prediction method of claim 1, wherein step 3 comprises:
defining the physical and mechanical parameters of the key rock mass identified in the step 2 as a random variable x= [ x ] 1 ,x 2 ,…,x d ]The method comprises the steps of carrying out a first treatment on the surface of the And training a proxy model SVM (x) between random variables and slope responses in each excavation anchoring stage by adopting a support vector machine algorithm, and replacing a FLAC3D model by adopting the proxy model SVM (x).
7. The machine learning-based rock high slope excavation anchoring deformation prediction method according to claim 1, wherein in step 4, the established monitoring information y= [ Y ] 1 ,y 2 ,…,y n ]And a proxy model SVM (x)The functional relationship of (2) is:
Y＝SVM(x)+ε
where ε represents the measurement error.
8. The machine learning-based rock high slope excavation anchoring deformation prediction method as claimed in claim 7, wherein the function relation of the monitoring information is incorporated into the following formula based on Bayesian theory, and the adaptive differential evolution Metropolis algorithm DREAM with multi-chain parallel calculation is adopted (ZS) To invert posterior distribution of physical and mechanical parameters of rock mass:
p(x|Y)＝cL(x|Y)p(x)
wherein p (x|Y) represents a parametric posterior probability density function; p (x) represents a parameter prior probability density function, and parameters obey logarithmic normal distribution and are independent of each other; c is a normalization constant; l (x|y) represents a likelihood function; subscript j represents a j-th rock physical-mechanical parameter; mu (mu) N Sum sigma N Mean and standard deviation of the logarithm of the parameters; subscript n represents the nth excavation anchoring stage; mu (mu) ε Sum sigma ε Mean and standard deviation of the measurement error epsilon are indicated.
9. The machine learning-based rock high slope excavation anchoring deformation prediction method of claim 1, wherein the step 5 specifically comprises:
and inputting posterior distribution of physical and mechanical parameters of the inverted rock mass into a proxy model SVM (x) of each excavation stage, so as to predict slope deformation of the subsequent excavation anchoring stage. And according to the calculation result, taking the average value as a predicted value of slope deformation in each subsequent excavation and anchoring stage, and comparing the predicted value with an actual slope monitoring value.
10. A system for machine learning based rock highslope excavation anchoring deformation prediction method according to any one of claims 1-9, comprising:
the data acquisition module is used for acquiring geological survey reports, slope excavation progress and monitoring information of the high arch dam area;
the model construction module is used for constructing a rock high slope multi-stage excavation anchoring model according to the data acquired by the data acquisition module;
the random variable screening module is used for carrying out importance ranking on the physical and mechanical parameters of the rock mass of the constructed model based on a machine learning algorithm, and identifying the physical and mechanical parameters of the key rock mass as random variables to be updated;
the agent model training module is used for training an agent model between random variables and slope responses in each excavation anchoring stage based on a machine learning algorithm;
the posterior distribution acquisition module of the physical and mechanical parameters is used for establishing a functional relation between the monitoring information and the proxy model and constructing a Bayesian framework to incorporate the functional relation into posterior distribution of the physical and mechanical parameters of the inverted rock mass;
the slope deformation prediction module is used for inputting posterior distribution of the physical and mechanical parameters of the rock body inverted by the posterior distribution acquisition module of the physical and mechanical parameters into the proxy model of each excavation and anchoring stage so as to predict the slope deformation of the subsequent excavation and anchoring stage.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115508206A (en) * | 2022-10-11 | 2022-12-23 | 昆明理工大学 | Method for inverting probability of rock strength parameter of jointed rock slope |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115508206A (en) * | 2022-10-11 | 2022-12-23 | 昆明理工大学 | Method for inverting probability of rock strength parameter of jointed rock slope |
| CN115508206B (en) * | 2022-10-11 | 2024-07-05 | 昆明理工大学 | Joint rock slope rock mass intensity parameter probability inversion method |
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