Rock mass deformation parameter calculation method based on elasticity modulus attenuation function

Abstract

The invention discloses a rock mass deformation parameter calculation method based on an elastic modulus attenuation function, and the method comprises the following steps: S1, collecting influence factor data of rock mass deformation parameters, and measuring the initial elastic modulus E0 of rock; s2, constructing an elastic modulus attenuation function according to the initial elastic modulus E0 of the rock, and calculating the elastic modulus En of the rock under the influence of the fracture density n; s3, according to the step S2, constructing a multi-factor rock mass deformation calculation model, and calculating a rock mass elastic modulus Rt under the influence of multi-factor coupling; s4, performing data fitting and optimization calculation according to the step S3, and calculating a fitting attenuation coefficient alpha * by adopting a gradient descent algorithm; and S5, according to S1 and S4, rock mass deformation prediction and result analysis are carried out, and the final rock mass elastic modulus Rfinal is calculated. According to the method, through nonlinear modeling, multi-factor coupling, dynamic updating capability and optimization algorithm application, rock mass deformation prediction is accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering and water conservancy and hydropower engineering, and particularly relates to a method for estimating rock mass deformation parameters based on an elastic modulus attenuation function. Background Art

[0002] In large-scale geotechnical engineering projects (such as tunnel excavation, hydropower dams and mining), deformation assessment of rock mass is a key link to ensure construction safety and stability. Unlike ordinary rocks, rock mass has a complex structure and is composed of multiple discontinuities such as cracks and faults, which makes its deformation characteristics highly nonlinear. In actual engineering, the construction environment often faces the challenges of changing geological conditions, such as the degree of weathering and the influence of faults, which directly affect the deformation characteristics of the rock mass. Traditional deformation prediction methods usually rely on a single parameter (such as the elastic modulus of undisturbed rock) for calculation, ignoring the dynamic influence of multiple factors coupling on rock mass deformation, which makes the prediction results prone to deviations.

[0003] The elastic modulus of rock will significantly decay when the complexity of the fracture system increases. However, the current rock deformation estimation methods are often based on linear assumptions, which makes it difficult to accurately describe the nonlinear changes of the elastic modulus under conditions of dense fractures. In addition, due to regional differences in rock mass parameters (such as fracture inclination, degree of weathering, etc.), deformation models under different geological environments are difficult to apply directly, resulting in a lack of universality in practical applications. Especially in areas with dense faults or strong weathering, conventional deformation assessments cannot fully quantify the combined effects of these factors, increasing construction risks.

[0004] The present invention proposes a method for estimating rock deformation parameters based on the elastic modulus attenuation function to solve the nonlinear complexity and dynamic update problems in the current rock deformation prediction. This method quantifies the nonlinear relationship between crack density and elastic modulus by constructing an elastic modulus attenuation function, and comprehensively considers the influence of various geological factors such as crack inclination and weathering degree on rock deformation. The model also uses integral terms and cumulative terms to simulate the coupling of multiple factors to ensure the accuracy of deformation prediction. In addition, the present invention introduces the construction disturbance coefficient and water erosion depth to achieve dynamic update of rock deformation, providing a scientific basis for engineering design and construction risk assessment. This method is suitable for rock deformation prediction in geotechnical engineering and water conservancy and hydropower engineering, and enhances the universality and stability through the model optimization algorithm, thereby improving the engineering safety level under complex construction environments. Summary of the invention

[0005] The purpose of the present invention is to provide a method for estimating rock mass deformation parameters based on elastic modulus attenuation function. The present invention makes accurate prediction of rock mass deformation through nonlinear modeling, multi-factor coupling, dynamic updating capability and optimization algorithm application.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0007] A method for estimating rock mass deformation parameters based on elastic modulus attenuation function comprises the following steps:

[0008] S1, collect the data of influencing factors of rock mass deformation parameters and determine the initial elastic modulus E of the rock 0 ;

[0009] S2, according to the initial elastic modulus E of the rock 0 , construct the elastic modulus attenuation function, and calculate the rock mass elastic modulus E under the influence of crack density n n ;

[0010] S3, based on S2, construct a multi-factor rock deformation estimation model and calculate the rock elastic modulus R under the influence of multi-factor coupling t ;

[0011] S4, according to S3, performs data fitting and optimization calculation, and uses the gradient descent algorithm to calculate the fitting attenuation coefficient α * ;

[0012] S5, based on S1 and S4, predict rock mass deformation and analyze the results, and calculate the final rock mass elastic modulus R final .

[0013] Preferably, in S2, the elastic modulus E of the rock mass affected by the crack density n is calculated. n , the specific formula is:

[0014]

[0015] Among them, E 0 is the initial elastic modulus of rock, α is the initial attenuation coefficient, β is the factor for adjusting density sensitivity, ln(β×n+1) is a logarithmic term used to avoid model instability caused by excessive changes in fracture density, and Γ(1+n) is a gamma function that quantifies the nonlinear effect of the complexity of the fracture system.

[0016] Preferably, in S3, the rock mass elastic modulus R under the influence of multiple coupling factors is calculated. t , the specific formula is:

[0017]

[0018] Among them, E n is the elastic modulus of the rock mass under the influence of the crack density n, f is the fault scale, is the polynomial form of f, ω is the weathering degree, θ is the crack inclination, is an integral term, which describes the nonlinear effect of weathering degree ω and crack inclination θ on rock deformation.

[0019] Preferably, in S4, a gradient descent algorithm is used to calculate the fitting attenuation coefficient α * , the specific formula is:

[0020]

[0021] Among them, α is the initial attenuation coefficient, m is the number of test samples, R t is the elastic modulus of rock mass under the influence of multiple factors, R obs is the test value of elastic modulus, λ is the regularization coefficient to prevent the model from overfitting, is the gamma integral, which is used to ensure the convergence of the model during the optimization process.

[0022] Preferably, in S5, the final rock mass elastic modulus R is calculated. final The specific steps are:

[0023] S501, according to the fitting attenuation coefficient α * Calculate the rock mass elastic modulus E′ after iterative fitting n ;

[0024] S502, according to the rock mass elastic modulus E′ after iterative fitting n The elastic modulus R′ of the rock mass after iterative fitting is calculated t ;

[0025] S503, calculate the final rock mass elastic modulus R final .

[0026] Preferably, the calculation formula of S501 is:

[0027]

[0028] Among them, E 0 is the initial elastic modulus of rock, α * is the fitting attenuation coefficient, β is the factor for adjusting density sensitivity, ln(β×n+1) is the logarithmic term used to avoid model instability caused by excessive changes in fracture density, and Γ(1+n) is the gamma function that quantifies the nonlinear effect of the complexity of the fracture system.

[0029] Preferably, the calculation formula of S502 is:

[0030]

[0031] Among them, E′ n is the elastic modulus of the rock mass after iterative fitting, f is the fault scale, is the polynomial form of f, ω is the weathering degree, θ is the crack inclination, is an integral term, which describes the nonlinear effect of weathering degree ω and crack inclination θ on rock deformation.

[0032] Preferably, the calculation formula of S503 is:

[0033] R final =R′ t ×e (-γ×d) ;

[0034] Among them, R′ t is the elastic modulus of the rock mass after iterative fitting, γ is the construction disturbance coefficient, and d is the water erosion depth.

[0035] The present invention has the following advantages:

[0036] (1) Nonlinear modeling: The present invention realizes nonlinear relationship modeling between crack density and rock elastic modulus through elastic modulus attenuation function, making deformation prediction more accurate.

[0037] (2) Multi-factor coupling: Comprehensive consideration of multiple geological factors such as fracture dip, fault scale, and weathering degree improves the model's adaptability to complex environments.

[0038] (3) Dynamic update capability: The construction disturbance coefficient and the depth of rock mass erosion caused by fissure water during construction are introduced to achieve dynamic update of rock mass deformation, ensuring that the prediction results are highly consistent with the actual construction conditions.

[0039] (4) Application of optimization algorithm: The gradient descent algorithm is used to optimize the model parameters, which improves the prediction accuracy and stability and makes the model more universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solution and advantages of the present invention clear, the technical solution of the present invention will be clearly described below in conjunction with the accompanying drawings of the present invention.

[0042] like Figure 1 As shown, a method for estimating rock mass deformation parameters based on elastic modulus attenuation function includes the following steps:

[0043] S1, collect the data of influencing factors of rock mass deformation parameters and determine the initial elastic modulus E of the rock 0 .

[0044] Collect the influencing factors such as crack density n, crack inclination θ, fault scale f, weathering degree ω, water erosion depth d, and measure the initial elastic modulus E of the rock 0 . These parameters are formed into a matrix M:

[0045] M=[n θ f ω d] Formula 1

[0046] S2, according to the initial elastic modulus E of the rock 0 , construct the elastic modulus attenuation function, and calculate the rock mass elastic modulus E under the influence of crack density n n .

[0047] Calculate the elastic modulus E of the rock mass affected by the crack density n n , the specific formula is:

[0048]

[0049] Among them, E 0 is the initial elastic modulus of rock (the test value when not affected by cracks), α is the initial attenuation coefficient, β is the factor for adjusting density sensitivity, which is used to smooth the influence of high-density cracks, ln(β×n+1) is a logarithmic term used to avoid model instability caused by excessive changes in crack density, and Γ(1+n) is a gamma function that quantifies the nonlinear influence of the complexity of the crack system.

[0050] S3, based on S2, construct a multi-factor rock deformation estimation model and calculate the rock elastic modulus R under the influence of multi-factor coupling t .

[0051] Combined with the rock mass elastic modulus E under the influence of crack density n in S2 n , construct a multi-factor rock mass deformation estimation model, and calculate the rock mass elastic modulus R under the influence of multi-factor coupling t , the specific formula is:

[0052]

[0053] Among them, E n is the elastic modulus of the rock mass under the influence of the crack density n, f is the fault scale, is the polynomial form of f, which improves the convergence and stability of the model and strengthens the interaction between f and other influencing factors. ω is the weathering degree, θ is the crack inclination, It is an integral term that describes the nonlinear effect of weathering degree ω and crack inclination θ on rock deformation. The k value depends on the comprehensive influence of the above-mentioned influencing factors and is generally taken as 3 to 5.

[0054] S4, according to S3, performs data fitting and optimization calculation, and uses the gradient descent algorithm to calculate the fitting attenuation coefficient α * .

[0055] The gradient descent algorithm is used to calculate the fitting attenuation coefficient α * , fitting attenuation coefficient α *Control the decay rate of the elastic modulus so that R t and R obs The error between them is minimized, and the specific formula is:

[0056]

[0057] Among them, α is the initial attenuation coefficient, m is the number of test samples, R t is the elastic modulus of rock mass under the influence of multiple factors, R obs is the test value of elastic modulus, λ is the regularization coefficient to prevent the model from overfitting, is the gamma integral, which is used to ensure the convergence of the model during the optimization process.

[0058] S5, based on S1 and S4, predict rock mass deformation and analyze the results, and calculate the final rock mass elastic modulus R final .

[0059] S501, according to the fitting attenuation coefficient α * Calculate the rock mass elastic modulus E′ after iterative fitting n .

[0060]

[0061] Among them, E 0 is the initial elastic modulus of rock (test value when not affected by cracks), α * is to fit the attenuation coefficient and control the attenuation rate of the elastic modulus. β is a factor that adjusts density sensitivity and is used to smooth the influence of high-density cracks. ln(β×n+1) is a logarithmic term used to avoid model instability caused by excessive changes in crack density. Γ(1+n) is a gamma function that quantifies the nonlinear influence of the complexity of the crack system.

[0062] S502, calculating the iteratively fitted rock mass elastic modulus R′ according to the iteratively fitted rock mass elastic modulus t .

[0063]

[0064] Among them, E′ n is the elastic modulus of the rock mass after iterative fitting, f is the fault scale, is the polynomial form of f, which improves the convergence and stability of the model and strengthens the interaction between f and other influencing factors. ω is the weathering degree, θ is the crack inclination, It is an integral term that describes the nonlinear effect of weathering degree ω and crack inclination θ on rock deformation. The k value depends on the comprehensive influence of the above-mentioned influencing factors and is generally taken as 3 to 5.

[0065] S503, calculate the final rock mass elastic modulus Rfinal .

[0066] According to the rock mass elastic modulus R′ after iterative fitting t , and finally calculate the final rock mass elastic modulus R final :

[0067] R final =R′ t ×e (-γ×d) Formula 7

[0068] Among them, R′ t is the elastic modulus of the rock mass after iterative fitting, γ is the construction disturbance coefficient, which is used to evaluate the impact of construction on rock deformation, and d is the water erosion depth, which describes the impact of the depth of fissure water erosion on the rock mass during the construction process.

[0069] By introducing the construction disturbance coefficient γ and dynamically calibrating the erosion depth d of the rock mass caused by fissure water during rock excavation, the prediction results can be updated in real time to ensure the accuracy and stability of the model, providing a reference for engineering scheme design and construction risk assessment.

[0070] The present invention is further verified and illustrated by the following examples and experiments.

[0071] S1, collect the data of influencing factors of rock mass deformation parameters and determine the initial elastic modulus E of the rock 0 .

[0072] The analysis is carried out in combination with field test data.

[0073] (1) Measurement environment and data collection: This embodiment simulates the real environment and uses the following parameters:

[0074] Fracture density n: the number of fractures recorded per cubic meter of rock mass.

[0075] Crack inclination angle θ: expressed in degrees.

[0076] Fault scale f: Fault width in meters.

[0077] Weathering degree ω: According to the weathering degree of the rock mass, a graded assessment method is adopted (grades 1-3, slightly weathered = 3, weakly weathered = 2, strongly weathered = 1).

[0078] Water erosion depth d: the depth of erosion of the rock surface by fissure water (in centimeters).

[0079] (2) Measured data table

[0080]

[0081] S2, according to the initial elastic modulus E of the rock 0, construct the elastic modulus attenuation function, and calculate the rock mass elastic modulus E under the influence of crack density n n .

[0082] According to the above test data, the rock elastic modulus E under the influence of crack density n of each sample is calculated using the following formula: n :

[0083]

[0084] Assuming the initial attenuation coefficient α = 0.8 and the factor adjusting density sensitivity β = 0.2, the elastic modulus E of the rock mass under the influence of the fracture density n is obtained by fitting the actual collected data. n The calculation results are as follows:

[0085]

[0086] S3, based on S2, construct a multi-factor rock deformation estimation model and calculate the rock elastic modulus R under the influence of multi-factor coupling t .

[0087] Based on the calculated rock mass elastic modulus E affected by the crack density n n And k is 3, and the calculation is done using the following formula:

[0088]

[0089] The calculation results are shown in the following table:

[0090]

[0091]

[0092] S4, according to S3, performs data fitting and optimization calculation, and uses the gradient descent algorithm to calculate the fitting attenuation coefficient α * .

[0093] Use the gradient descent algorithm to calculate the fitting attenuation coefficient α * , based on the value of α in S2, the fitting objective function is determined as:

[0094]

[0095] Rock mass elastic modulus R under the influence of multiple coupling factors t And the elastic modulus test value R obs As shown in the following table:

[0096]

[0097] The rock mass elastic modulus R under the influence of multiple factors coupling t And the elastic modulus test value Robs The fitting iteration is performed through formula 4. In the test, the regularization coefficient λ is assumed to be 0.01. After multiple iterations of optimization, the optimal fitting attenuation coefficient α is obtained. * =0.65.

[0098] S5, based on S1 and S4, predict rock mass deformation and analyze the results, and calculate the final rock mass elastic modulus R final .

[0099] Get α * After that, α * Substitute the parameters into Formula 5 and Formula 6 to calculate R′ t , and according to R′ t Substitute into formula 7 to calculate the final rock mass elastic modulus R final :

[0100] R final =R′ t ×e (-γ×d) Formula 7

[0101] At this time, it is assumed that the construction disturbance coefficient is γ = 0.05. According to this model, the final rock mass elastic modulus R is calculated. final The calculation results are as follows:

[0102]

[0103]

[0104] The present invention introduces multiple geological factors such as crack density, crack inclination, fault scale, weathering degree, etc., combines the construction disturbance coefficient and the depth of rock mass erosion by crack water during construction, and establishes a more comprehensive and complex rock mass deformation characteristic prediction model. 0 , R t , R′ t , R final The calculation results show that the elastic modulus attenuation function and the multi-factor rock deformation estimation model are reasonable. After the initial attenuation coefficient α is optimized through data fitting, the rock elastic modulus R′ after iterative fitting is t And elastic modulus test value R obs Especially close, the final rock mass elastic modulus R final Reflect the changes on site more realistically.

Claims

1. A method for estimating rock mass deformation parameters based on elastic modulus attenuation function, characterized in that: The following steps are involved: S1, collect the data of influencing factors of rock mass deformation parameters and determine the initial elastic modulus E0 of the rock; S2, based on the initial elastic modulus E0 of the rock, construct the elastic modulus attenuation function and calculate the rock mass elastic modulus E under the influence of the crack density n n ; S3, based on S2, construct a multi-factor rock deformation estimation model and calculate the rock elastic modulus R under the influence of multi-factor coupling t ; S4, according to S3, performs data fitting and optimization calculation, and uses the gradient descent algorithm to calculate the fitting attenuation coefficient α * ; S5, based on S1 and S4, predict rock mass deformation and analyze the results, and calculate the final rock mass elastic modulus R final .

2. The method for estimating rock mass deformation parameters based on elastic modulus attenuation function according to claim 1 is characterized in that: In S2, the elastic modulus E of the rock mass affected by the crack density n is calculated. n , the specific formula is: Among them, E0 is the initial elastic modulus of rock, α is the initial attenuation coefficient, β is the factor for adjusting density sensitivity, ln(β×n+1) is a logarithmic term used to avoid model instability caused by excessive changes in fracture density, and Γ(1+n) is a gamma function that quantifies the nonlinear influence of the complexity of the fracture system.

3. The method for estimating rock mass deformation parameters based on elastic modulus attenuation function according to claim 1 is characterized in that: In S3, the elastic modulus R of the rock mass under the influence of multiple coupling factors is calculated. t , the specific formula is: Among them, E n is the elastic modulus of the rock mass under the influence of the crack density n, f is the fault scale, is the polynomial form of f, ω is the weathering degree, θ is the crack inclination, is an integral term, which describes the nonlinear effect of weathering degree ω and crack inclination θ on rock deformation.

4. The method for estimating rock mass deformation parameters based on elastic modulus attenuation function according to claim 1 is characterized in that: In S4, the gradient descent algorithm is used to calculate the fitting attenuation coefficient α * , the specific formula is: Among them, α is the initial attenuation coefficient, m is the number of test samples, R t is the elastic modulus of rock mass under the influence of multiple factors, R obs is the test value of elastic modulus, λ is the regularization coefficient to prevent the model from overfitting, is the gamma integral, which is used to ensure the convergence of the model during the optimization process.

5. The method for estimating rock mass deformation parameters based on elastic modulus attenuation function according to claim 1 is characterized in that: In S5, the final rock mass elastic modulus R is calculated. final The specific steps are: S501, according to the fitting attenuation coefficient α * Calculate the rock mass elastic modulus E′ after iterative fitting n ; S502, according to the rock mass elastic modulus E′ after iterative fitting n The elastic modulus R′ of the rock mass after iterative fitting is calculated t ; S503, calculate the final rock mass elastic modulus R final .

6. The method for estimating rock mass deformation parameters based on elastic modulus attenuation function according to claim 5 is characterized in that: The calculation formula of S501 is: Among them, E0 is the initial elastic modulus of rock, α * is the fitting attenuation coefficient, β is the factor adjusting density sensitivity, ln(β×n+1) is the logarithmic term used to avoid model instability caused by excessive changes in fracture density, and Γ(1+n) is the gamma function to quantify the nonlinear effect of the complexity of the fracture system.

7. The method for estimating rock mass deformation parameters based on elastic modulus attenuation function according to claim 5 is characterized in that: The calculation formula of S502 is: Among them, E′ n is the elastic modulus of the rock mass after iterative fitting, f is the fault scale, is the polynomial form of f, ω is the weathering degree, θ is the crack inclination, is an integral term, which describes the nonlinear effect of weathering degree ω and crack inclination θ on rock deformation.

8. The method for estimating rock mass deformation parameters based on elastic modulus attenuation function according to claim 5 is characterized in that: The calculation formula of S503 is: R final =R′ t ×e (-γ×d) ; Among them, R′ t is the elastic modulus of the rock mass after iterative fitting, γ is the construction disturbance coefficient, and d is the water erosion depth.

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