Method for measuring elastic modulus and poisson's ratio of irregular rock

Abstract

The application discloses a method for measuring the elastic modulus and Poisson's ratio of irregular rock, and belongs to the technical field of geotechnical engineering, and solves the problem that the existing rock mechanics characteristic evaluation technology needs to cut irregular rock samples, and destroys the structure and form of the rock samples. The application combines three-dimensional scanning technology, physical experiments and finite element numerical inversion, does not directly perform end face flattening treatment on original irregular rock samples which is difficult to realize, but uses a pouring material with known mechanical properties to encapsulate and pour the irregular rock samples, forms a composite sample which can be tested, measures the overall response of the composite sample under load, establishes a finite element numerical model which accurately corresponds to the composite sample, and finally inversely calculates the real elastic modulus and Poisson's ratio of the irregular rock through a multi-objective optimization algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geotechnical engineering, and in particular to a method for measuring the elastic modulus and Poisson's ratio of irregular rock. BACKGROUND

[0002] In major engineering construction such as water conservancy and hydropower, transportation tunnels, and mining, the mechanical parameters of rock mass are the core basis for engineering design, construction safety evaluation, and stability analysis, and directly determine the safety and economy of engineering construction. With the advancement of infrastructure construction to complex geological conditions, the engineering application of irregular rock blocks is increasingly widespread. Such rock mass is formed by geological structure movement, volcanic activity, and weathering erosion, and presents various characteristics such as columnar shape, scattered joint distribution, various cross-sectional shapes (quadrilateral to heptagonal), and irregular spatial posture. Typical examples include columnar joint basalt in the dam site area of Baihetan Hydropower Station and inclined joint rock mass in mountainous highway tunnels.

[0003] Accurate acquisition of the elastic modulus and Poisson's ratio of rock is the basis for evaluating the mechanical properties of rock and soil. However, existing methods for processing irregular rock samples usually involve forcibly pressing irregular rock samples using a pressing device or cutting and processing to obtain regular-shaped rock sample specimens. Such methods not only are difficult to process, but also destroy the original shape of the rock sample, causing the internal stress condition of the rock sample to change and not conforming to the true shape of the rock sample, thereby failing to obtain test data that conforms to the true environment. SUMMARY

[0004] In view of the above deficiencies of the prior art, the present application provides a method for measuring the elastic modulus and Poisson's ratio of irregular rock, which solves the problem of the need to cut irregular rock samples in existing rock and soil mechanics property evaluation techniques, which destroys the structure and shape of the rock sample.

[0005] To achieve the above-mentioned application purposes, the technical solution adopted by the present application is as follows:

[0006] A method for measuring the elastic modulus and Poisson's ratio of irregular rock is provided, comprising the following steps:

[0007] S1. Obtain the volume model of the original irregular rock test piece by three-dimensional scanning ; ;

[0008] S2. Pour two mutually parallel loading platforms at both ends of the irregular rock test piece using a pouring material with an elastic modulus and Poisson's ratio of and , respectively, to form a regularized composite test piece , and obtain the volume model of the composite test piece by three-dimensional scanning ; ​

[0009] S3, to Conduct uniaxial compression tests and obtain test data;

[0010] S4, Establish The finite element mesh model, based on Distinguish between the casting zone mesh and the rock zone mesh, and assign the casting zone mesh the mechanical parameters of the casting material. and Set the elastic modulus of the rock region mesh. Compared with Poisson The initial value;

[0011] S5. Perform finite element simulation of uniaxial compression test on the finite element mesh model to obtain simulation data;

[0012] S6. Using the difference between simulated and experimental data as the objective optimization function, the rock region mesh is optimized. and Iterative optimization;

[0013] S7. Repeat steps S5-S6 until the iteration termination condition is met, and then... and The final value as The elastic modulus and Poisson's ratio.

[0014] Furthermore, both the experimental and simulation data include axial displacement and lateral expansion displacement vectors, with the lateral expansion displacement vector including... or Lateral expansion displacement in four directions: front, back, left, and right of the middle section.

[0015] Furthermore, the expression for the objective optimization function is:

[0016] ; ;

[0017] ;

[0018] in, Optimize the function for the objective; for and A two-dimensional rock parameter vector; For transpose; The objective function is the axial displacement residual. The objective function is the lateral expansion displacement residual. and They are respectively and Weighting coefficients; is the total number of load steps or data points; and are the axial displacements at the i-th load step in the simulation data and the test data, respectively; is the maximum axial displacement in the test data; and are the j-th direction swelling displacements at the i-th load step in the simulation data and the test data, respectively, j = 1, 2, 3, 4, representing the front, back, left, and right directions, respectively; is the maximum swelling displacement in the j-th direction in the test data, is used for normalization to eliminate the dimensional influence and balance the contributions of displacements of different orders of magnitude.

[0019] Further, the rock regional grid is divided into a plurality of sub-regions, and the sub-regions are numbered as 1, 2, 3, …, n, where n is the total number of sub-regions. and The iterative optimization method is as follows:

[0020] S61, let the iteration number be k = 0, and set the convergence tolerance and ;

[0021] S62, construct the quadratic programming sub-problem of the objective optimization function in the k-th iteration process, and the expression is as follows:

[0022] ; ;

[0023] wherein, is the search direction; and are the parameter increments of and , respectively; and are the values of and in the k-th iteration, respectively; and are the lower limit and the upper limit of , respectively; and are the lower limit and the upper limit of , respectively; is the k-th iteration value of ; is the Hessian matrix of ; is the objective optimization function of ; is the objective optimization function of ; is the objective optimization function of​​ The gradient; hour, ; and They are respectively Compared to Poisson The initial value;

[0024] S63. Solve the quadratic programming subproblem to obtain the search direction. The optimal step size is determined by one-dimensional line search. and calculate No. Next iteration quantity ;

[0025] S64, Update Its expression is:

[0026]

[0027] ;

[0028] in, for The Hessian matrix; for The objective optimization function; for The gradient; for In the Number of iterations; for In the Increment in the next iteration; for of The gradient change in the next iteration;

[0029] S65, Calculation gradient norm ,as well as parameter variation norm ,like or If the iteration terminates, output the result. Otherwise Then return to step S62.

[0030] Furthermore, Boolean operations are used to distinguish between the casting region mesh and the rock region mesh. The Boolean difference operation expression for the casting region mesh is:

[0031]

[0032] in, A volume model of a pouring area grid is poured.

[0033] Further, And The acquisition method is:

[0034] The point cloud data of the three-dimensional laser scanner or photogrammetry is obtained, and the corresponding three-dimensional volume model is established based on the point cloud data. Or The point cloud data of the three-dimensional laser scanner or photogrammetry is obtained, and the corresponding three-dimensional volume model is established based on the point cloud data.

[0035] Further, the manufacturing method of the composite test piece The manufacturing method is:

[0036] S21, a rectangular cavity is made in a casting box by adopting a sand casting process;

[0037] S22, the original irregular rock test piece Is placed in the cavity, and the space between the cavity and the two end faces of the Is used as a pouring space;

[0038] S23, two parallel loading platforms are poured in the two pouring spaces by using a pouring material with an elastic modulus of And a Poisson's ratio of The composite test piece Is obtained.

[0039] Further, the pouring material includes epoxy resin, polyurethane or acrylic resin.

[0040] Compared with the prior art, the present application has the following advantages:

[0041] 1. The present application combines three-dimensional scanning technology, physical experiment and finite element numerical inversion, and does not directly perform end face flattening treatment on the original irregular rock test piece, which is difficult to realize, but uses a pouring material with known mechanical properties to encapsulate and pour it, forming a testable composite test piece. By measuring the overall response of the composite test piece under load, and establishing an accurate finite element numerical model corresponding thereto, the real elastic modulus and Poisson's ratio of the irregular rock are finally inverted through a multi-objective optimization algorithm, solving the problem of cutting and damaging the structure and shape of the rock sample in the prior art.

[0042] 2. The present application significantly improves the elastic modulus And Poisson's ratio The accuracy and reliability of the inversion result, and considering that the Poisson ratio depends on the lateral deformation, the deformation information of the original irregular rock sample in multiple directions is provided through the lateral expansion displacement vector, the calculation of the Poisson ratio is more reliable, deviation caused by relying on axial data alone is avoided, and at the same time, in the original irregular rock sample, the anisotropic deformation can be effectively quantified, the result reliability is improved, and a complete technical scheme for evaluating the mechanical properties of the irregular rock sample is provided.

[0043] 3、The target optimization function of the present application adjusts the contribution of the axial displacement and the lateral expansion displacement vector through the weight coefficient, avoids overfitting of a single target, makes the inversion parameters more balanced, adapts to changes of different rock properties, and both of them are normalized by using the maximum displacement, which eliminates the dimensional difference and ensures the fair comparison of displacements of different orders of magnitude, improves the universality and convergence efficiency of the algorithm. and the Poisson ratio The accuracy and reliability of the inversion result.

[0044] 4、The present application adopts the sequence quadratic programming (SQP) algorithm, solves the target optimization function by constructing quadratic programming subproblems, line search and parameter updating, updates the Hessian matrix combining the quasi-Newton method (BFGS), ensures fast convergence to the global optimal solution, reduces the calculation time and resource consumption.

[0045] 5、The present application ensures clear division of rock and pouring area in the finite element model through Boolean operation, avoids mesh confusion, makes the simulation more consistent with the actual composite specimen structure, and improves the geometric fidelity of numerical inversion.

[0046] 6、The present application avoids damage to the rock sample caused by physical contact through three-dimensional scanning or photogrammetry, maintains the integrity of the specimen, and quickly obtains high-precision geometric data, which is suitable for fragile or broken rock samples.

[0047] 7、The present application provides a uniform stress surface by setting a pouring loading platform, ensures the smooth progress of the uniaxial compression test, reduces the stress unevenness caused by irregular specimens, and improves the repeatability of experimental data. Attached Figure Description

[0048] Figure 1 A schematic diagram of a uniaxial compression test on a composite specimen.

[0049] Figure 2 This is a schematic diagram of the cavity structure in the casting box.

[0050] Figure 3 A schematic diagram of the structure in which the original irregular rock specimen is placed into the cavity.

[0051] Figure 4 This is a schematic diagram of the casting process for the loading platform.

[0052] Figure 5 This is a schematic diagram of the composite specimen. Detailed Implementation

[0053] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0054] This embodiment provides a method for measuring the elastic modulus and Poisson's ratio of irregular rocks. By combining three-dimensional scanning technology, physical experiments, and finite element numerical inversion, instead of directly performing difficult end-face flattening on the original irregular rock specimen, a casting material with known mechanical properties is used to encapsulate and cast the specimen, forming a testable composite specimen. By measuring the overall response of the composite specimen under load and establishing a corresponding finite element numerical model, the true elastic modulus and Poisson's ratio of the irregular rock are finally inverted using a multi-objective optimization algorithm. The specific steps include the following:

[0055] S1. Obtaining original irregular rock specimens through 3D scanning. Volume model .

[0056] S2, using elastic modulus and Poisson's ratio respectively and The casting material, in Two parallel loading platforms were poured at both ends to form a regular composite specimen. and obtain using 3D scanning Volume model .

[0057] refer to Figures 2-5 Composite specimen The manufacturing method is as follows:

[0058] S21. A rectangular cavity is made in the casting box using sand casting technology;

[0059] S22, the original irregular rock specimen Place it into the cavity, and connect the cavity with... The space between the two end faces serves as the pouring space;

[0060] S23, using an elastic modulus of... Poisson's ratio is The casting material was poured into two parallel loading platforms in two casting spaces to obtain composite specimens. .

[0061] S3, Reference Figure 1 ,right Conduct uniaxial compression tests and obtain test data.

[0062] S4, Establish The finite element mesh model, based on Distinguish between the casting zone mesh and the rock zone mesh, and assign the casting zone mesh the mechanical parameters of the casting material. and Set the elastic modulus of the rock region mesh. Compared with Poisson The initial value.

[0063] In this embodiment, Boolean operations are used to distinguish between the casting area mesh and the rock area mesh. The Boolean difference operation expression for the casting area mesh is as follows:

[0064]

[0065] in, A volume model of the mesh for the casting area.

[0066] and The method for obtaining it is as follows:

[0067] Obtained through 3D laser scanners or photogrammetry or The point cloud data is used to build a corresponding three-dimensional volume model.

[0068] S5. Perform finite element simulation of uniaxial compression test on the finite element mesh model to obtain simulation data. The finite element simulation conditions for the uniaxial compression test are as follows: The uniaxial compression test conditions are the same.

[0069] S6. Using the difference between simulated and experimental data as the objective optimization function, the rock region mesh is optimized. with iterative optimization.

[0070] S7, repeating steps S5-S6 until the iteration termination condition is met, and taking with the final value of as the elastic modulus and Poisson's ratio of

[0071] In this embodiment, both the test data and the simulation data include axial displacement and lateral expansion displacement vectors, and the lateral expansion displacement vector includes or lateral expansion displacement in the front, rear, left, and right directions of the middle part. The casting material is epoxy resin, polyurethane, or acrylic resin, preferably epoxy resin.

[0072] Specifically, the expression of the target optimization function is: ;

[0073] In the expression, ; ; ;

[0074] ;

[0075] wherein, is the target optimization function; is the two-dimensional rock parameter vector of and ; is the transpose; is the axial displacement residual objective function; is the lateral expansion displacement residual objective function; and are the weight coefficients of and , respectively; is the total number of load steps or data points; and are the axial displacements in the i-th load step in the simulation data and the test data, respectively; is the maximum axial displacement of the test data; and are the j-th direction expansion displacements in the i-th load step in the simulation data and the test data, respectively, j being 1, 2, 3, and 4, respectively, for the front, rear, left, and right directions; is the maximum expansion displacement in the j-th direction in the test data, is used for normalization to eliminate the dimensional influence and balance the contributions of displacements of different orders of magnitude.

[0076] In this embodiment, load level i reflects the vertical pressure. Therefore, both the simulation data and the experimental data include two types of data: ① vertical pressure. With axial displacement Relationship curve; ② Vertical pressure Lateral expansion displacement in four directions (front, back, left, and right) relative to the middle of the specimen The relationship curve. Among them, The values ​​of j correspond to the lateral expansion displacements in the four directions (front, back, left, and right) when j is 1, 2, 3, and 4, respectively. Therefore, the objective of the optimization function is to minimize the difference in the goodness of fit between the vertical pressure and the axial and lateral expansion displacement vectors in the simulated and experimental data, respectively, further improving the elastic modulus. Compared to Poisson The accuracy and reliability of the inversion results.

[0077] As a further embodiment, considering the elastic modulus... Compared to Poisson The inversion is essentially about finding a set of optimal rock parameters. This minimizes the difference between the numerical simulation results and experimental measurements. Since both axial displacement and lateral expansion displacement are utilized, this constitutes a multi-objective optimization problem. When constructing the optimization problem, parameter constraints based on the physical properties of the rock material must be introduced. Elastic modulus Compared to Poisson These are parameters with definite physical meaning, and their values ​​cannot be arbitrary. For example, the elastic modulus should be positive and has a typical range for common rocks; Poisson's ratio, on the other hand, is usually within a finite range. Therefore, the inversion process must be carried out under the following constraints:

[0078]

[0079] in, and They are respectively The lower and upper limits; and They are respectively The lower and upper bounds are given. Under this constraint, the Sequential Quadratic Programming (SQP) algorithm is used to solve the objective function. The SQP algorithm solves the objective function at the current iteration point. A quadratic programming (QP) subproblem is constructed to approximate the original problem, and the direction of the iterative search is obtained by solving this subproblem. .

[0080] Specifically, the grid of the rock region and The iterative optimization method is as follows:

[0081] S61, Let the number of iterations be... And set convergence tolerance and ;

[0082] S62, Construction of the The quadratic programming subproblem of the objective optimization function in the next iteration is expressed as follows:

[0083]

[0084] In the expression, ; ; ;

[0085] in, Indicating the search direction; and They are respectively and The parameter increment; and They are respectively and In the The value in the next iteration; for The Number of iterations; for The Hessian matrix; for The objective optimization function; for The gradient; hour, ; and They are respectively Compared to Poisson The initial value;

[0086] S63. Solve the quadratic programming subproblem to obtain the... Search direction in the next iteration The optimal step size is determined by one-dimensional line search. and calculate No. Next iteration quantity ;

[0087] S64, Update Its expression is:

[0088]

[0089] ;

[0090] wherein, is a Hessian matrix; is an objective optimization function; is a gradient; is an iteration amount at the first iteration; is an increment in the first iteration; is an increment in the first iteration; is a gradient change amount of the iteration; S65, a gradient norm of

[0091] is calculated , and a parameter change norm of is calculated , if or , the iteration is terminated, and is output, otherwise is set, and the step S62 is returned. Wherein, is the optimal rock parameter .

[0092] In the above manner, the scheme can ensure the accuracy of the geometric description through three-dimensional scanning, solve the loading problem of irregular specimens by using epoxy resin pouring with known material parameters, and combine physical experiments and finite element numerical simulation through a multi-objective optimization algorithm (SQP) to solve the elastic parameter testing problem of irregular rock specimens that are difficult to process into standard shapes. By simultaneously optimizing the fitting degrees of the axial and lateral expansion displacement amounts, the accuracy and reliability of the elastic modulus and Poisson's ratio inversion results are significantly improved, and a complete technical scheme is provided for evaluating the mechanical properties of irregular rock specimens.

Claims

1. A method for measuring the elastic modulus and Poisson's ratio of irregular rocks, characterized in that... The steps include: S1. Obtaining original irregular rock specimens through 3D scanning. Volume model ; S2, using elastic modulus and Poisson's ratio respectively and The casting material, in Two parallel loading platforms were poured at both ends to form a regular composite specimen. And obtain using 3D scanning Volume model ; S3, to Conduct uniaxial compression tests and obtain test data; S4, Establish The finite element mesh model, based on Distinguish between the casting zone mesh and the rock zone mesh, and assign the mechanical parameters of the casting material to the casting zone mesh. and Set the elastic modulus of the rock region mesh. Compared with Poisson The initial value; S5. Perform finite element simulation of uniaxial compression test on the finite element mesh model and obtain simulation data; S6. Using the difference between simulated and experimental data as the objective optimization function, the rock region mesh is optimized. and Iterative optimization; The expression for the objective optimization function is: ; ; ; in, Optimize the function for the objective; for and Two-dimensional rock parameter vector; For transpose; The objective function is the axial displacement residual. The objective function is the lateral expansion displacement residual. and They are respectively and Weighting coefficients; and In the simulated data and experimental data respectively, in the first i Axial displacement under level load; The maximum axial displacement from the test data; and In the simulated data and experimental data respectively, the first i Under level load, the first j Expansion displacement in each direction; for i The maximum series; For the first in the test data j The maximum expansion displacement in each direction; S7. Repeat steps S5-S6 until the iteration termination condition is met, and then... and The final value is as The elastic modulus and Poisson's ratio.

2. The method for measuring the elastic modulus and Poisson's ratio of irregular rocks according to claim 1, characterized in that... Both experimental and simulation data include axial displacement and lateral expansion displacement vectors. The lateral expansion displacement vector includes... or Lateral expansion displacement in four directions: front, back, left, and right of the middle section.

3. The method for measuring the elastic modulus and Poisson's ratio of irregular rocks according to claim 2, characterized in that... , rock region grid and The iterative optimization method is as follows: S61, Let the number of iterations be... And set convergence tolerance and ; S62, Construction of the The quadratic programming subproblem of the objective optimization function in the next iteration is expressed as follows: ; ; in, Indicating the search direction; and They are respectively and Parameter increment; and They are respectively and In the The value in the next iteration; and They are respectively The lower and upper limits; and They are respectively The lower and upper limits; for The Number of iterations; for The Hessian matrix; for Objective optimization function; for gradient; S63. Solve the quadratic programming subproblem to obtain the search direction. The optimal step size is determined by one-dimensional line search. and calculate No. Next iteration quantity ; S64, Update Its expression is: ; in, for The Hessian matrix; for Objective optimization function; for gradient; for In the Number of iterations; for In the Increment in the next iteration; for of The gradient change in the next iteration; S65, Calculation gradient norm ,as well as parameter variation norm ,like or Then the iteration terminates and the output is... Otherwise Then return to step S62.

4. The method for measuring the elastic modulus and Poisson's ratio of irregular rocks according to claim 1, characterized in that... Boolean operations are used to distinguish between the casting region mesh and the rock region mesh. The Boolean difference operation expression for the casting region mesh is as follows: in, A volume model of the mesh for the casting area.

5. The method for measuring the elastic modulus and Poisson's ratio of irregular rocks according to claim 1, characterized in that... , and The method for obtaining it is: Obtained through 3D laser scanners or photogrammetry or The point cloud data is used to build a corresponding three-dimensional volume model.

6. The method for measuring the elastic modulus and Poisson's ratio of irregular rocks according to claim 1, characterized in that... Composite specimen The manufacturing method is as follows: S21. A rectangular cavity is fabricated in the casting box using sand casting technology; S22, the original irregular rock specimen Place it into the cavity, and connect the cavity with... The space between the two end faces serves as the pouring space; S23, using an elastic modulus of... Poisson's ratio is The casting material was poured into two parallel loading platforms in two casting spaces to obtain composite specimens. .

7. The method for measuring the elastic modulus and Poisson's ratio of irregular rocks according to claim 1, characterized in that... The casting materials include epoxy resin, polyurethane, or acrylic resin.

Images