Rock slope seismic stability analysis method and equipment considering rock tension-shear damage

Abstract

The invention discloses a rock slope earthquake dynamic stability analysis method and equipment considering rock tension-shear damage, mainly aims at a rock slope with deep shear-trailing edge tension fracture as a main instability failure mode, such as a toppled and relaxed rock slope, and introduces a damage variable D to comprehensively consider potential shear and tension characteristics of a rock mass; in the earthquake action process, the rock damage condition is dynamically updated in real time according to the damage characteristics of the rock unit, the overall safety coefficient or the minimum point safety coefficient of the rock slope at any moment is calculated, and finally the dynamic safety coefficient change time history better conforming to reality is obtained. According to the method, the rock damage characteristics mainly including tension-shear damage can be accurately reflected, and meanwhile, the dynamic safety development process of the slope in the nonlinear earthquake action process can be more intuitively reflected.

Description

Technical Field

[0001] The invention relates to a slope seismic stability analysis method, in particular to a rock slope seismic stability analysis method taking rock tension and shear damage into consideration, and belongs to the field of geotechnical engineering. Background Art

[0002] Slope instability and sliding is one of the main types of earthquake geological disasters. This type of earthquake damage often occurs in mountainous and hilly areas, with the characteristics of wide distribution and great harm. Seismic slope stability analysis has become one of the important research topics in seismology and geotechnical engineering. In order to more intuitively show the weakening phenomenon of rock mass performance under earthquake action, scholars and engineering technicians often introduce the concept of damage to judge the process of rock mass yield evolution. However, in the mountainous areas of southwest my country, there are a large number of toppled loose rock slopes. The instability deformation characteristics of this type of slope are often more complex. The main existence of the rear edge of the upper rock mass is mainly tensile or tensile shear deformation and rupture, showing a composite deformation mode of front edge and deep shear controlled by bottom sliding deformation, and rear edge tensile cracking. For this composite deformation model, there is no unified damage representation method for the time being. The existing seismic slope stability analysis technology and methods mainly study the stability of the slope under the action of earthquake inertial force or after the earthquake, and cannot reflect the dynamic change process of slope stability during the earthquake.

[0003] Therefore, a rock slope seismic stability analysis method considering rock tension and shear damage is urgently needed. Summary of the invention

[0004] Purpose of the invention: In view of the defects of the prior art, the present invention provides a rock slope seismic stability analysis method and equipment taking into account rock tensile and shear damage, which can obtain the dynamic change process of slope stability during earthquake action and has the advantages of simplicity, high efficiency and accuracy.

[0005] Technical solution: According to a first aspect of the present invention, a rock slope seismic stability analysis method considering rock tensile shear damage comprises the following steps:

[0006] (1) Construct a slope numerical model, select a seismic input time history, where the total time of the time history is T and the time interval is dt, and set corresponding physical boundary conditions and seismic input boundary conditions on the model boundary;

[0007] (2) According to the strength parameters and deformation parameters of rock materials, the principal tensile strain damage threshold ε0 and the maximum shear strain damage threshold γ0 of rock are determined respectively;

[0008] (3) Dynamic time history analysis calculation begins. At any time t, the maximum shear strain value and principal stress value of each unit in the rock slope model are obtained, and the maximum shear strain γ is calculated. max and equivalent tensile strain

[0009] (4) According to the equivalent tensile strain of each rock unit at a specified time Comparison with the principal tensile strain damage threshold ε0 and the maximum shear strain γ max Compared with the maximum shear strain damage threshold γ0, the damage condition of each unit is judged and its damage variable value D is calculated. i (t);

[0010] (5) According to the damage variable value D of each rock unit i (t), calculate the current elastic modulus E of the corresponding unit considering the damage i (t);

[0011] (6) Based on the parameters of the damaged rock materials and the actual engineering needs, the strength reduction method is used to calculate the overall safety factor of the rock slope, or the minimum point safety factor of the rock slope is calculated, and the stability of the rock slope at the current moment is evaluated;

[0012] (7) As the duration of the earthquake action increases, steps (3) to (6) are repeated at each time step to obtain the stability of the rock slope considering the tensile and shear damage of the rock at any time, as well as the dynamic change process of the overall safety factor with the earthquake action.

[0013] In step (2), the deformation parameters include the initial elastic modulus E i (0) and Poisson's ratio μ; the principal tensile strain damage threshold ε0 is obtained according to the following formula: ε0 = σ t / E i (t), where σ t is the tensile strength of rock, E i (t) is the rock elastic modulus in the current state;

[0014] The maximum shear strain damage threshold γ0 is taken as the ultimate shear strain γ when the rock mass enters yield y ,Right now Among them G i (t) is the rock shear modulus in the current state.

[0015] In step (3), the maximum shear strain γ of the rock element max The calculation method is: γ max =0.5×(σ1-σ3) / G i (t), where σ1, σ2 and σ3 are the principal stresses of the rock unit in three directions in space, G i (t) is the shear modulus;

[0016] Equivalent tensile strain of rock element The calculation method is: where ε1, ε2 and ε3 are the principal strains of the rock unit in the three principal directions in space, and the angle brackets <x>The operation rule is

[0017] In step (4), the damage of the rock unit is judged as follows: when the maximum shear strain of the rock unit deformation does not reach the maximum shear strain damage threshold, or the equivalent tensile strain does not reach the principal tensile strain damage threshold, i.e., γ max <γ0 and When γ , the rock unit is judged to be undamaged; when the maximum shear strain reaches the maximum shear strain damage threshold, or the equivalent tensile strain reaches the principal tensile strain damage threshold, that is, γ max ≥γ0 or When the rock unit is damaged, it is judged that the rock unit is damaged.

[0018] In step (4), the damage variable D of each element of the rock mass is calculated i (t) Includes: For rock units that are judged to be undamaged, the damage variable D i (t) = 0; for rock units judged to be damaged, the rock damage variable is calculated according to the following formula: In the formula, the damage variable D i (t)∈[0,1], R1 and R2 are rock material related parameters.

[0019] In step (5), at any time t, the elastic modulus of each rock unit is E i (t) = E i (t)(1-D i (t)) calculation. Further, step (5) also includes: according to E i (t) Update the shear modulus G of each element i (t) and damage thresholds ε0 and γ0.

[0020] In step (6), since the seismic time interval is generally 0.005 seconds or 0.01 seconds, the amount of seismic time history data is large, and considering the accuracy requirements and computational efficiency requirements of actual engineering projects, it is generally possible to calculate and store the safety factor once every 1.0 second, that is, the safety factor calculation time interval is kdt, where k is a positive integer and can be selected according to the situation.

[0021] According to a second aspect of the present invention, there is provided a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the rock slope seismic stability analysis method considering rock tensile and shear damage as described in the first aspect of the present invention are implemented.

[0022] According to a third aspect of the present invention, there is also provided a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the rock slope seismic stability analysis method considering rock tensile and shear damage as described in the first aspect of the present invention.

[0023] Beneficial effects: Compared with the prior art, the present invention introduces the damage variable D to comprehensively consider the potential shear and tension characteristics of the rock mass for rock slopes with deep shear-rear edge tensile cracking as the main instability failure mode, such as the toppled relaxed rock slope; during the earthquake, the rock damage situation is dynamically updated in real time according to the damage characteristics of the rock unit, and the overall safety factor or the minimum point safety factor of the rock slope at any time is calculated, and finally a more realistic dynamic safety factor change time history is obtained. The present invention comprehensively considers the damage caused by the combined action of tension and shear on the rock, and carries out nonlinear dynamic time history analysis with measured or artificial earthquake motion time history as input, and can obtain the dynamic change process of slope stability during the earthquake. This method can more accurately describe the deformation characteristics of rock slopes with tensile shear deformation as the main failure mode, and realizes the real-time update of rock damage during the earthquake, which has important reference significance and application value for evaluating the safety of toppled relaxed rock slopes during earthquake motion. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a general flow chart of a rock slope seismic stability analysis method considering rock tension and shear damage according to an embodiment of the present invention;

[0025] Figure 2 It is the minimum point safety factor time history curve of the embodiment of the present invention. DETAILED DESCRIPTION

[0026] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0027] The present invention discloses a rock slope seismic stability analysis method considering rock tensile shear damage, which is specifically described below using a rock slope in southwest my country as an example:

[0028] (1) Based on the geological profile information and survey data of the collapsed and deformed rock slope, a numerical calculation model of the slope was established. The seismic input time history was selected with a total time length of T = 40 s and a time interval of dt = 0.01 s. Free field boundary conditions were set on the side boundaries of the model to eliminate wave reflection on the boundaries. The seismic acceleration time history was input from the bottom of the model.

[0029] (2) According to the strength parameters of rock materials (cohesion c and internal friction angle ) and deformation parameters (initial elastic modulus E (0) and Poisson's ratio μ), respectively determine the principal tensile strain damage threshold of rock ε0=σ t / E (0) , and the maximum shear strain damage threshold γ0, where σ t is the tensile strength of rock, The safety factor calculation time interval is every 1.0 second, that is, k=100.

[0030] (3) Carry out numerical simulation of finite element dynamic time-history response, and calculate the equivalent tensile strain of each unit based on the stress tensor and strain tensor of each rock unit at any time. and the maximum shear strain γ max Specifically, the programming language provided by the finite element calculation platform is used to extract the principal stresses σ1, σ2 and σ3 in the three principal directions of each rock unit, as well as the principal strains ε1, ε2 and ε3, where σ1>σ2>σ3, ε1>ε2>ε3; the maximum shear strain of each unit can be calculated as γ max =0.5×(σ1-σ3) / G, and the equivalent tensile strain of each unit:

[0031] (4) According to the equivalent tensile strain of each rock unit at this moment Comparison with the principal tensile strain damage threshold ε0 and the maximum shear strain γ max By comparing with the maximum shear strain damage threshold γ0, the damage of each unit is determined and its damage variable value is calculated. Specifically:

[0032] (4.1) When the maximum shear strain of rock mass deformation does not reach the initial maximum shear strain damage threshold, and the equivalent tensile strain does not reach the initial principal tensile strain calculation threshold, that is, γ max <γ0 and When the rock mass material is judged to be not damaged, its damage variable D i (t) = 0;

[0033] (4.2) When the maximum shear strain is greater than or equal to the initial maximum shear strain damage threshold, or the equivalent tensile strain is greater than or equal to the initial principal tensile strain damage threshold, that is, γ max ≥γ0 or When , it is judged that the rock mass material is damaged. At this moment, the damage variable of the i-th unit of the damage variable is

[0034] (5) According to the damage variable value of each rock unit, reset the elastic modulus E of each unit i (t) = E i (t)(1-D i (t)), and according to E i (t) Update the shear modulus G of each element i (t) and damage thresholds ε0 and γ0.

[0035] (6) Every 1.0 second, this embodiment selects to calculate the minimum safety factor of the rock slope to measure the stability of the rock slope, and specifically selects the strength reserve point safety factor F s (t), according to the formula Calculate the safety factor of each unit at the current time t, and take the minimum value of the safety factor of each unit as the minimum point safety factor of the rock slope at time t, that is, F s (t) = min(F si (t)).

[0036] (7) By repeating steps (3) to (6) over the time of ground shaking, the minimum safety factor time history of the rock slope can be obtained, as follows: Figure 2 shown.

[0037] The present invention proposes a rock slope seismic stability analysis method taking into account rock tension-shear damage, targeting a toppled loose rock slope, a rock slope with deep shear-rear edge tensile cracking as the main instability failure mode. The method comprehensively considers the rock damage under potential shear and tension conditions of the rock mass, and adjusts the rock material parameters according to the damage of the rock unit during the earthquake motion time-history response analysis. The method can more intuitively reflect the change process of the dynamic stability of the slope during the nonlinear earthquake action, and has important reference significance and application value for the safety evaluation analysis of the toppled loose rock slope with tension-shear failure as the main failure mode.

[0038] The present invention also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the rock slope seismic stability analysis method considering rock tensile and shear damage as described above are implemented.

[0039] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the rock slope seismic stability analysis method considering rock tensile and shear damage as described above are implemented.

[0040] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, devices (systems), computer equipment or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0041] The present invention is described with reference to a flowchart of a method according to an embodiment of the present invention. It should be understood that each process in the flowchart and a combination of processes in the flowchart can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the process in the flowchart. Figure 1 A device that specifies functions in a process or multiple processes.

[0042] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A function specified in a process or multiple processes.

[0043] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 The steps of a specified function in a process or multiple processes.< / x>

Claims

1. A method for analyzing the seismic dynamic stability of rock slopes considering rock tensile shear damage, characterized in that: The steps include: (1) Construct a slope numerical model, select a seismic input time history, where the total time of the time history is T and the time interval is dt, and set corresponding physical boundary conditions and seismic input boundary conditions on the model boundary; (2) According to the strength parameters and deformation parameters of rock materials, the principal tensile strain damage threshold ε0 and the maximum shear strain damage threshold γ0 of rock are determined respectively; (3) Dynamic time history analysis calculation begins. At any time t, the maximum shear strain value and principal stress value of each unit in the rock slope model are obtained, and the maximum shear strain γ is calculated. max and equivalent tensile strain ε; (4) According to the comparison between the equivalent tensile strain ε of each rock unit at a specified time and the principal tensile strain damage threshold ε0, as well as the maximum shear strain γ max Compared with the maximum shear strain damage threshold γ0, the damage condition of each unit is judged and its damage variable value D is calculated. i (t); (5) According to the damage variable value D of each rock unit i (t), calculate the current elastic modulus E of the corresponding unit considering the damage i (t); (6) Based on the parameters of the damaged rock materials and the actual engineering needs, the strength reduction method is used to calculate the overall safety factor of the rock slope, or the minimum point safety factor of the rock slope is calculated, and the stability of the rock slope at the current moment is evaluated; (7) As the duration of the earthquake action increases, steps (3) to (6) are repeated at each time step to obtain the stability of the rock slope considering the tensile and shear damage of the rock at any time, as well as the dynamic change process of the overall safety factor with the earthquake action.

2. The method according to claim 1, characterized in that In the step (2), the deformation parameters include the initial elastic modulus E i (0) and Poisson's ratio μ; The principal tensile strain damage threshold ε0 is obtained according to the following formula: ε0 = σ t / E i (t), where σ t is the tensile strength of rock, E i (t) is the rock elastic modulus in the current state; The maximum shear strain damage threshold γ0 is taken as the ultimate shear strain γ when the rock mass enters yield y ,Right now Among them G i (t) is the rock shear modulus in the current state.

3. The method according to claim 1, characterized in that In step (3), the maximum shear strain γ of the rock unit max The calculation method is: γ max =0.5×(σ1-σ3) / G i (t), where σ1, σ2 and σ3 are the principal stresses of the rock unit in three directions in space, G i (t) is the shear modulus; Equivalent tensile strain of rock element The calculation method is: where ε1, ε2 and ε3 are the principal strains of the rock unit in the three principal directions in space, and the angle brackets <x>The operation rule is < / x> 4. The method according to claim 1, characterized in that In the step (4), judging the damage of the rock unit includes: when the maximum shear strain of the rock unit deformation does not reach the maximum shear strain damage threshold, or the equivalent tensile strain does not reach the principal tensile strain damage threshold, i.e., γ max <γ0 and When γ , the rock unit is judged to be undamaged; when the maximum shear strain reaches the maximum shear strain damage threshold, or the equivalent tensile strain reaches the principal tensile strain damage threshold, that is, γ max ≥γ0 or When the rock unit is damaged, it is judged that the rock unit is damaged.

5. The method according to claim 1, characterized in that In step (4), the damage variable D of each unit of the rock mass is calculated i (t) include: For rock units that are judged to be undamaged, their damage variable D i (t) = 0; For rock units that are judged to be damaged, the rock damage variable is calculated according to the following formula: In the formula, the damage variable D i (t)∈[0,1], R1 and R2 are rock material related parameters.

6. The method according to claim 1, characterized in that In step (5), at any time t, the elastic modulus of each rock unit is calculated according to E i (t) = E i (t)(1-D i (t)) calculation.

7. The method according to claim 6, characterized in that The step (5) further comprises: i (t) Update the shear modulus G of each element i (t) and damage thresholds ε0 and γ0.

8. The method according to claim 6, characterized in that In the step (6), the safety factor calculation time interval is kdt, where k is a positive integer.

9. A computer device, characterized in that: include: one or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the method for analyzing the seismic dynamic stability of a rock slope considering rock tensile and shear damage as described in any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for analyzing the seismic dynamic stability of a rock slope considering rock tensile and shear damage according to any one of claims 1 to 8 are implemented.

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