Rock slope stability method calculation method, device, medium and equipment based on non-continuous deformation analysis

Abstract

The application discloses a kind of based on non-continuous deformation analysis's rock slope stability strip method calculation method, device, medium and equipment, belong to geotechnical engineering slope stability evaluation technical field.The method includes: according to the development characteristics of discontinuous surface, potential sliding body strip is dispersed;Edge-edge contact system is established;Material parameters, initial conditions and boundary conditions are set;Overall stiffness matrix and load vector are assembled;Initial equilibrium equation is solved;Initial critical instability point is selected;Overall stiffness matrix and load vector are reassembled;Nonlinear equation set is established, Newton iteration and contact state iteration are solved;Determine whether critical instability point is the maximum relative tangent displacement point of sliding surface, if not, then re-solve;The strength of strip block is reduced, and repeat until stable;Output result, and draw corresponding physical quantity distribution diagram.The device, medium and equipment can be used to realize the above method.It provides reliable technical support for the stability evaluation of complex rock slope.

Description

Technical Field

[0001] This invention relates to the field of slope stability evaluation technology in geotechnical engineering, specifically to a method, apparatus, medium, and equipment for calculating the stability of rock slopes using the slice method based on discontinuous deformation analysis (DDA). This method is applicable to the stability calculation of rock slopes under complex conditions such as goafs and complex sliding surfaces, and can be widely used in slope safety evaluation and design in engineering fields such as mining, transportation, and water conservancy. Background Technology

[0002] The core of slope stability assessment lies in calculating the slope safety factor. After decades of development, various analytical methods have been developed, mainly including the limit equilibrium method, the finite element strength reduction method, the enhanced ultimate strength method, and the deformable body limit equilibrium method.

[0003] For rock slopes under complex working conditions, especially slopes with goaf, the existence of goaf can disturb the slope stress field, damage the rock mass strength, or directly remove the anti-sliding rock mass of the potential sliding surface, thus leading to a decrease in the overall stability of the slope. Summary of the Invention

[0004] In view of this, this invention proposes a method, apparatus, medium, and equipment for calculating the stability of rock slopes using the slice method based on Discrete Data Analysis (DDA). This method is applicable to rock slopes, especially those with complex morphologies. By discretizing the landslide body into slices and combining the DDA method with limit equilibrium conditions and critical instability conditions, it can accurately and efficiently calculate the slope safety factor under complex conditions without introducing physically meaningless inter-slice force assumptions as in conventional slice methods. This method expands the applicability of the widely used slice method in engineering and provides more reliable technical support for slope stability evaluation.

[0005] To achieve the above objectives, this invention provides a method for calculating the stability of rock slopes using the slice method based on DDA, the technical solution of which is as follows: The method includes the following steps: Based on the development of discontinuities in the rock slope, the sliding body is divided into several blocks or strips. If the influence of the sliding bed needs to be considered, the sliding bed is also discretized into blocks. Establish a contact system, set edge-to-edge contact between all adjacent blocks, and assign normal stiffness and tangential stiffness. If the influence of the slide is not considered, the sliding surface is regarded as the boundary contact, that is, the other side is a fixed rigid body. The block parameters include density, elastic modulus and Poisson's ratio. The parameters between blocks and potential sliding surfaces are shear strength parameters (or internal friction angle and cohesion if the Mohr-Coulomb criterion is used). Initial stress conditions and boundary conditions are also set. Assemble the overall stiffness matrix and overall load vector of the DDA to form the initial overall equilibrium equations; Solve the initial global equilibrium equations to obtain the displacement and stress fields under the initial self-weight and loads; The position with the highest slip surface safety is initially selected as the initial critical instability point. Here, the slip surface safety is defined as the ratio of the shear strength to the shear stress at that point on the potential slip surface under the initial stress field. Based on the limit equilibrium condition of the sliding surface, reassemble the overall stiffness matrix and load vector; The critical instability condition is coupled into the DDA equations to establish an unknown quantity containing the safety factor F. s The nonlinear equations are solved by combining Newton's iteration method with contact state iteration to directly solve for the safety factor and the displacement field under critical conditions; Determine whether the critical instability point is the point of maximum relative tangential displacement. If not, take the point of maximum relative tangential displacement on the sliding surface as the new critical instability point, reconstruct the critical instability conditions, and solve them iteratively. If it is necessary to consider that the shear strength between the blocks is reduced along with the potential sliding surface, then the obtained safety factor is used to reduce the strength between the blocks. Repeat the above steps until the change in the safety factor tends to stabilize, and then end the solution. Output the calculation results of safety factor, block degree of freedom, sliding surface and contact surface stress, etc., and draw the distribution diagram of the corresponding physical quantities.

[0006] The method provided by this invention can also be further implemented through the following technical measures: A two-dimensional model of the target slope is established, the sliding surface to be analyzed is determined, and the slope is divided into sliding bodies and sliding beds, which are then discretized into several blocks. The discretization of the sliding bodies should fully consider discontinuities such as faults and joints. The sliding bodies and sliding beds are in contact through potential sliding surfaces, and the blocks are in edge-to-edge contact. If the target slope contains a goaf, the supporting effect of the goaf roof can be simplified to the horizontal stress R after reduction by a safety factor. cm / F s , where R cm It represents the uniaxial compressive strength of the rock mass.

[0007] Given the limit equilibrium condition of the potential sliding surface: the shear stress q at any point on the sliding surface st It is equal to the reduced shear strength, i.e., q st = f s (q sn ) / F s ; where f s The shear strength criteria for the sliding surface (such as the Mohr-Coulomb criterion, Hoek-Brown criterion, or Barton-Bandis criterion, etc.); q sn Let q be the normal stress at that point on the sliding surface. The stress q on one side of the sliding surface of the sliding body.s It can be decomposed into normal stress q sn and shear stress q st , i.e. q s ≡ q sn n s +q st t s , where n s Let t be the normal to any point on the sliding surface (pointing towards the slide), s The direction is the tangent at any point on the sliding surface (corresponding to the clockwise direction of the sliding block). Therefore, sliding to the left points in the direction of sliding down, and vice versa, it points in the direction of resisting sliding.

[0008] Given the critical instability condition of the potential sliding surface, that is, when the sliding surface changes from its current state to a limit equilibrium state, a relative tangential displacement g must occur between the sliding body and the sliding bed. t Furthermore, there must exist a critical instability point on the sliding surface such that g at that point... t The value of g is 0, while the value of g at the other points is 0. t ≤ 0. The critical instability point was initially selected as the position with the highest safety margin on the sliding surface, and after trial calculations, it was adjusted to the relative tangential displacement g on the sliding surface. t The maximum point.

[0009] Based on the DDA principle, construct the overall equilibrium equation set K of the block system. D=F, where K is the overall stiffness matrix, D is the unknown vector of the block system, and F is the load vector. The assembly of these three components includes the following steps: Determine the block displacement function: Block displacement includes rigid body displacement and deformation; rigid body displacement is represented by the block's translation {u0, v0} and rotation r0, and deformation is represented by the block's normal strain ε. x ε y and shear strain γ xy It means, that is, D i = {u0, v0, r0,ε x , ε y , γ xy} T The displacement {u, v} of any point {x, y} on the block can be expressed as: {u, v} T =T i (x, y)·D i In the formula, the subscript i represents the i-th block, and T i Let be the displacement function matrix of the block; Construct the overall stiffness matrix K: It consists of the block elastic stiffness sub-matrix, the contact stiffness sub-matrix, and the displacement constraint stiffness sub-matrix; among them, the contact stiffness sub-matrix includes the normal and tangential contact stiffness sub-matrixes. The friction force will update the contact stiffness sub-matrix, and the updated stiffness sub-matrix is ​​an asymmetric matrix. Construct the load vector F: It consists of the initial stress load sub-vector, the concentrated force load sub-vector, the volume force load sub-vector, the contact load sub-vector, and the displacement constraint load sub-vector, where the volume force includes gravity, blasting vibration force, etc., and acts on the centroid of the block. Displacement constraint processing: A penalty spring with high stiffness is set at the location of the block to be constrained, so that the calculated displacement approximates the known constraint displacement, and the strain energy corresponding to the penalty spring is converted into an expression of the block displacement vector, thereby updating the overall stiffness matrix K and the load vector F.

[0010] Considering the tangential contact characteristics of the sliding surface, assemble the tangential stiffness matrix K of the sliding surface according to the limit equilibrium condition. st and the tangential load vector F of the sliding surface s Combining the overall equilibrium equations, a system with a safety factor F is constructed. s The nonlinear equation system: (F s ·K+K st )·D= F s ·F+F st .

[0011] The supplementary equation is K, where the relative tangential displacement at the critical instability point is zero. cup ·D = 0, combined with the nonlinear equations from the previous step, yields the solution vector for the unknown variable X = {D}. , F s} The corresponding nonlinear equation system H(X) = 0.

[0012] The nonlinear equation system H(X) = 0 is solved iteratively using Newton's method. The specific process is as follows: Set initial value: D 0 =0, Fs 0 = 1; Calculate the Jacobian matrix J(X) for the i-th iteration. i-1 ): ; Update the unknown vector: X i =X i-1 –J -1 (X i-1 )·H(X i-1 ); Iterative convergence criterion: Calculate the iterative error e = |H(X) i )| / |H(X 0 When e is less than the set threshold, the iteration converges and the results such as the safety factor Fs and block displacement are output; if it does not converge, the above steps are repeated until the maximum number of iterations is reached (solution failure) or convergence is achieved.

[0013] To address the reduction in shear strength between strips and the changes in contact states (including opening and closing, shear slip and their directions) between strips, a three-layer iterative strategy is adopted: the outermost layer is the iteration of shear strength reduction between strips, the middle layer is the iteration of contact states between strips, and the innermost layer is the solution of nonlinear equations using Newton's method.

[0014] Furthermore: If there is no stress disturbance at the slide section caused by excavation or loading, the slide can be ignored, and the sliding surface can be considered to be in contact with a rigid body. In this case, only strip separation of the slide body is required, which is consistent with the traditional limit equilibrium strip separation method.

[0015] The discretization of the sliding body can be carried out by vertical slicing using conventional slicing methods, or by oblique slicing formed by structural surfaces such as fault fracture zones, dominant joints, or bedding planes. The slicing method is not fixed.

[0016] Since the slope undergoes a small deformation process from its initial state to its critical instability state, the contact type between the blocks can be considered to remain constant; therefore, the DDA contact algorithm can be simplified by considering only edge-to-edge contact to improve computational efficiency.

[0017] Determine the relationship between contact shear stress and shear strength at the contact point. If shear failure occurs, cancel the shear penalty spring at that contact point, and obtain the corresponding stiffness submatrix and load subvector by differentiating the shear slip friction potential energy.

[0018] tangential stiffness matrix K of the sliding surface st and the tangential load vector F of the sliding surface st The assembly process is basically the same as the handling of friction in conventional contact, except that the direction of tangential stress needs to be directed in the anti-slip direction, and a safety factor F needs to be introduced. s Reduce the amount.

[0019] To achieve the second objective mentioned above, this invention provides a calculation device for rock slope slice method based on DDA, specifically including the following modules: Discretization and parameter initialization module: used to discretize and number the slope and potential sliding body, establish contact surfaces, and set various parameters of the blocks and contact surfaces; The standard DDA total stiffness matrix and total load vector assembly module is responsible for assembling the block elastic stiffness sub-matrix, contact stiffness sub-matrix, and displacement constraint stiffness sub-matrix into the overall stiffness matrix, and assembling the initial stress load sub-vector, concentrated force load sub-vector, volume force load sub-vector, contact load sub-vector, and displacement constraint load sub-vector into the total load vector. The standard DDA solver module is used to solve the overall DDA equilibrium equations, determine the contact state, and update the displacement and stress fields. The DDA slice method global stiffness matrix and global load vector assembly module is used to calculate the tangential stiffness matrix and load vector matrix of a new potential sliding surface based on the limit equilibrium condition, and update the global stiffness matrix and global load vector accordingly. The sliding body stability solution module is used to establish a set of nonlinear equations with the safety factor as an unknown by coupling critical instability conditions, solve the safety factor of the potential sliding body using a three-level iterative strategy, and determine the location of the critical instability point. The results output and plotting module is used to output the calculation results of safety factors, block degrees of freedom, sliding surface and contact surface stress, etc., and to plot the distribution of the corresponding physical quantities.

[0020] To achieve the third objective mentioned above, the present invention provides the following computer-readable storage medium technical solution: The present invention provides a computer-readable storage medium storing a program for calculating the stability of rock slopes using the slice method based on DDA. When the program is executed by a processor, it implements the steps of the method for calculating the stability of rock slopes using the slice method based on DDA provided by the present invention.

[0021] To achieve the fourth objective mentioned above, the present invention provides the following electronic device technical solution: The electronic device provided by the present invention includes a memory and a processor. The memory stores a program for calculating the stability of rock slopes based on the DDA slice method. When the program is executed by the processor, it implements the steps of the DDA-based rock slope stability slice method calculation method provided by the present invention.

[0022] This invention provides a method, apparatus, medium, and equipment for calculating the stability of rock slopes using the slice method based on Discontinuous Deformation Analysis (DDA). Its advantages lie in the following: This method achieves discretization of the slice method through discontinuous deformation analysis and introduces the slip surface limit equilibrium condition and critical instability condition, thereby ensuring the possibility and uniqueness of the safety factor solution. Compared to other slice methods, this method does not require the introduction of physically meaningless assumptions, has a clear calculation process, is easy to operate, can adapt to the complex geometry of slopes with goaf areas, and can consider the influence of strain field disturbances. Furthermore, this invention only requires simple slice discretization and can freely calculate the safety factor of any slip surface, overcoming the core limitations of existing methods and demonstrating its superiority in handling complex slope problems. Attached Figure Description

[0023] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1This is a flowchart of the rock slope stability calculation method based on DDA provided by the present invention; Figure 2 This is a signal flow diagram between the functional modules in the rock slope stability slice method calculation device based on DDA provided by the present invention.

[0024] Figure 3 This is a schematic diagram of the structure of the rock slope stability slice calculation device based on DDA provided by the present invention.

[0025] Figure 4 This is a schematic diagram of a planar sliding stability calculation example according to an embodiment of the present invention; Figure 5 This is an iterative convergence information diagram of the solution in case 4 of the planar sliding stability calculation example involved in the embodiment of the present invention; Figure 6 This refers to the force situation of the strip in case 4 of the planar sliding stability calculation example involved in the embodiment of the present invention; Figure 7 This is a schematic diagram of a calculation example of the broken-line sliding stability involved in an embodiment of the present invention; Figure 8 This refers to the distribution of normal stress on the sliding surface under different tangential contact states between blocks in the calculation example of the broken-line sliding stability involved in the embodiments of the present invention; Figure 9 This is a diagram showing the normal stress distribution on the sliding surface with different contact stiffnesses in the calculation example of the broken-line sliding stability involved in the embodiments of the present invention. Detailed Implementation

[0026] In view of this, this invention proposes a method, apparatus, medium, and equipment for calculating the stability of rock slopes using the slice method based on Discrete Data Analysis (DDA). This method is applicable to rock slopes, especially those with complex morphologies. By discretizing the landslide body into slices and combining the DDA method with limit equilibrium conditions and critical instability conditions, it can accurately and efficiently calculate the slope safety factor under complex conditions without introducing physically meaningless inter-slice force assumptions as in conventional slice methods. This method expands the applicability of the widely used slice method in engineering and provides more reliable technical support for slope stability evaluation.

[0027] Through arduous and persistent efforts, the inventors discovered that existing methods for calculating slope stability have many limitations and are difficult to adapt to the calculation needs of complex working conditions, such as those involving goaf areas. 1. Limit Equilibrium Method (Conventional Slice Method): This method divides the sliding body into several vertical slices, which makes it difficult to accurately characterize the complex geometry of slopes containing goaf areas; at the same time, it is based on rigid body force analysis and cannot consider the influence of strain field evolution on slope stability; in addition, the assumptions of this method regarding the forces between slices lack clear physical meaning.

[0028] 2. Strength Reduction Method: When reducing the overall strength of the slope, the critical state criterion may be triggered prematurely due to plastic flow in the surrounding rock or roof of the goaf; this method cannot freely calculate the safety factor of any potential slip surface as in the limit equilibrium method; when the critical slip surface size is relatively small compared to the slope, the calculation results are highly sensitive to the grid, and the calculation accuracy is difficult to guarantee; in addition, the selection of the instability criterion also has a significant impact on the solution results.

[0029] 3. Enhanced ultimate strength method: This method requires integrating the shear stress and shear strength along the sliding surface, but the integration process lacks a clear physical meaning; when calculating the ultimate state, the sliding body as a whole is not in equilibrium, which deviates from the actual engineering situation.

[0030] 4. Limit Equilibrium Method for Deformable Bodies: This method treats the sliding surface as a discontinuity and introduces the limit equilibrium condition and critical instability condition of the sliding surface into the equilibrium equations, constructing a set of nonlinear equations including a safety factor. However, this method is based on an elastic finite element framework and cannot consider the elastic-plastic deformation of the sliding body itself. When calculating polygonal sliding surfaces, significant stress concentrations occur at the turning points, leading to abnormal stress distribution on the sliding surface. In addition, finite element mesh reconstruction is required for each potential slip surface, which is not conducive to efficient searching for critical slip surfaces, resulting in low computational efficiency.

[0031] The slice method, with its simplicity and intuitiveness, has been widely used in engineering practice and adopted by various slope-related codes. However, existing methods still have shortcomings in handling complex geometries and stress disturbances. Therefore, there is an urgent need to develop a slope stability analysis method that can adapt to complex geometric conditions, consider stress disturbance effects, and balance computational efficiency and accuracy. This method should maintain the simple discrete form of the slice method, be easily accepted by the engineering community, and be able to seamlessly integrate with existing slope stability analysis software based on the slice method.

[0032] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following detailed description, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a DDA-based rock slope stability slice calculation method, apparatus, medium, and equipment proposed according to the present invention. In the following description, different "an embodiment" or "an embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0033] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0034] A method for calculating the stability of rock slopes based on the slice method of DDA. See appendix Figure 1 The DDA (Digital Drain Analysis) method for calculating rock slope stability using the slice method provided in this paper includes the following steps: Step S1: Based on the development of discontinuities in the rock slope, divide the sliding body into several blocks or strips. If the influence of the sliding bed needs to be considered, the sliding bed should be discretized into blocks at the same time. Step S2: Establish a contact system, set edge-to-edge contact between all adjacent blocks, and assign normal stiffness and tangential stiffness. If the influence of the slide is not considered, the sliding surface is regarded as the boundary contact, that is, the other side is a fixed rigid body. Step S3: Set the block parameters, including density, elastic modulus and Poisson's ratio. The parameters between blocks and the potential sliding surface are shear strength parameters (if the Mohr-Coulomb criterion is used, then the internal friction angle and cohesion are used). Also set the initial stress conditions and boundary conditions. Step S4: Assemble the overall stiffness matrix and overall load vector of the DDA to form the initial overall equilibrium equations; Step S5: Solve the initial overall equilibrium equations to obtain the displacement and stress fields under the initial self-weight and load. Step S6: Initially select the position with the highest slip surface safety as the initial critical instability point. Here, the slip surface safety is defined as the ratio of the shear strength to the shear stress at that point on the potential slip surface under the initial stress field. Step S7: Reassemble the overall stiffness matrix and load vector according to the limit equilibrium conditions of the sliding surface.

[0035] Step S8: Couple the critical instability condition to the DDA equations to establish unknowns including the safety factor F. s The nonlinear equations are solved by combining Newton's iteration method with contact state iteration to directly solve for the safety factor and the displacement field under critical conditions; Step S9: Determine whether the critical instability point is the point of maximum relative tangential displacement. If not, take the point of maximum relative tangential displacement on the sliding surface as the new critical instability point, reconstruct the critical instability conditions, and solve iteratively. Step S10: If it is necessary to consider the reduction of the inter-strip shear strength along with the potential sliding surface, the obtained safety factor is used to reduce the inter-strip strength. Repeat the above steps until the change in the safety factor tends to stabilize, and then end the solution. Step S11: Output the calculation results of safety factor, block degree of freedom, sliding surface and contact surface stress, etc., and draw the distribution diagram of the corresponding physical quantities.

[0036] This invention provides a slice method for calculating the stability of rock slopes based on Discontinuous Deformation Analysis (DDA). It achieves discretization of the slice method through discontinuous deformation analysis and introduces slip surface limit equilibrium conditions and critical instability conditions, thereby ensuring the possibility and uniqueness of the safety factor solution. Compared to other slice methods, this method does not require the introduction of physically meaningless assumptions, has a clear calculation process, is easy to operate, can adapt to the complex geometry of slopes with goaf areas, and can consider the influence of strain field disturbances. Furthermore, this method only requires simple slice discretization and can freely calculate the safety factor of any slip surface, overcoming the core limitations of existing methods and demonstrating its superiority in handling complex slope problems.

[0037] A DDA-based calculation device for rock slope stability using the slice method. See appendix Figure 2 The slope stability slice method calculation device based on DDA provided by the present invention includes: Discretization and parameter initialization module: used to discretize and number the slope and potential sliding body, establish contact surfaces, and set various parameters of the blocks and contact surfaces; The standard DDA total stiffness matrix and total load vector assembly module is responsible for assembling the block elastic stiffness sub-matrix, contact stiffness sub-matrix, and displacement constraint stiffness sub-matrix into the overall stiffness matrix, and assembling the initial stress load sub-vector, concentrated force load sub-vector, volume force load sub-vector, contact load sub-vector, and displacement constraint load sub-vector into the total load vector. The standard DDA solver module is used to solve the overall DDA equilibrium equations, determine the contact state, and update the displacement and stress fields. The DDA slice method global stiffness matrix and global load vector assembly module is used to calculate the tangential stiffness matrix and load vector matrix of a new potential sliding surface based on the limit equilibrium condition, and update the global stiffness matrix and global load vector accordingly. The sliding body stability solution module is used to establish a set of nonlinear equations with the safety factor as an unknown by coupling critical instability conditions, solve the safety factor of the potential sliding body using a three-level iterative strategy, and determine the location of the critical instability point. The results output and plotting module is used to output the calculation results of safety factors, block degrees of freedom, sliding surface and contact surface stress, etc., and to plot the distribution of the corresponding physical quantities.

[0038] The slope stability slice method calculation device based on DDA provided by this invention is applicable to rock slopes, especially complex rock slopes. By discretizing the landslide body into slices and combining the DDA method with limit equilibrium conditions and critical instability conditions, it can accurately and efficiently calculate the slope safety factor under complex conditions without introducing physically meaningless inter-slice force assumptions as in conventional slice methods. This method expands the applicability of the widely used slice method in engineering and provides more reliable technical support for slope stability evaluation.

[0039] Computer-readable storage media The present invention provides a computer-readable storage medium storing a program for calculating the stability of rock slopes using the slice method based on DDA. When the program is executed by a processor, it implements the steps of the method for calculating the stability of rock slopes using the slice method based on DDA provided by the present invention.

[0040] The computer-readable storage medium provided by this invention simplifies computer program implementation and is applicable to the stability calculation of rock slopes, especially those with complex shapes. By discretizing the landslide body into strips and combining the DDA method with limit equilibrium conditions and critical instability conditions, it can accurately and efficiently calculate the slope safety factor under complex conditions without introducing physically meaningless inter-strip force assumptions as in conventional slice methods. This method expands the applicability of the widely used slice method in engineering and provides more reliable technical support for slope stability evaluation.

[0041] electronic devices The electronic device provided by the present invention includes a memory and a processor. The memory stores a program for calculating the stability of rock slopes based on the DDA slice method. When the program is executed by the processor, it implements the steps of the rock slope stability calculation method based on the DDA slice method provided by the present invention.

[0042] The electronic device provided by this invention simplifies computer program implementation and is applicable to the stability calculation of rock slopes, especially those with complex shapes. By discretizing the landslide body into strips and combining the DDA method with limit equilibrium conditions and critical instability conditions, it can accurately and efficiently calculate the slope safety factor under complex conditions without introducing physically meaningless inter-strip force assumptions as in conventional slice methods. This method expands the applicability of the widely used slice method in engineering and provides more reliable technical support for slope stability evaluation.

[0043] Reference Figure 3 , Figure 3 This is a schematic diagram of the structure of a DDA-based rock slope stability slice calculation device for the hardware operating environment involved in the embodiments of the present invention.

[0044] like Figure 3 As shown, the DDA-based rock slope stability slice method calculation device may include: a processor 301, such as a central processing unit (CPU), a communication bus 302, a user interface 303, a network interface 304, and a memory 305. The communication bus 302 is used to enable communication between these components. The user interface 303 may include a display screen and an input unit such as a keyboard; optionally, the user interface 303 may also include a standard wired interface or a wireless interface. The network interface 304 may optionally include a standard wired interface or a wireless interface. The memory 305 may be a high-speed random access memory (RAM) or a stable non-volatile memory (NVM), such as a disk drive. Optionally, the memory 305 may also be a storage device independent of the aforementioned processor 301.

[0045] Those skilled in the art will understand that Figure 3 The structure shown does not constitute a limitation on the DDA-based rock slope stability slice calculation device and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0046] like Figure 3 As shown, the memory 1005, which serves as a storage medium, may include an operating system, a data storage module, a network communication module, a user interface module, and a DDA-based rock slope stability slice calculation program.

[0047] exist Figure 3 In the DDA-based rock slope stability slice method calculation device shown, the network interface 304 is mainly used for data communication with the network server; the user interface 303 is mainly used for data interaction with the user; the processor 301 and memory 305 in the DDA-based rock slope stability slice method calculation device of the present invention can be set in the DDA-based rock slope stability slice method calculation device. The DDA-based rock slope stability slice method calculation device calls the DDA-based rock slope stability slice method calculation program stored in the memory 1005 through the processor 1001 and executes the DDA-based rock slope stability slice method calculation method provided in the embodiment of the present invention.

[0048] Example 1: Stability Calculation of Planar Sliding Slope This embodiment uses a planar sliding body as an example to illustrate in detail the specific steps of the DDA-based rock slope stability slice calculation method described in this invention.

[0049] like Figure 4 As shown, the planar sliding body is a triangular sliding body 401 with a side length of 10m, located on an inclined plane 403 with an angle of 30°. The slide bed 402 is considered rigid and therefore not considered in this example. The sliding body is discretized into two blocks 404.

[0050] The blocks are connected by edge-to-edge contact 405, and the slider and the slide are connected by potential sliding surface contact 406.

[0051] Material parameters were set as follows: elastic modulus 28 GPa, Poisson's ratio 0.23, unit weight 27 kN / m³, and normal and tangential contact stiffness both 100 GPa. Four sets of inclined plane shear strength parameters were designed in this embodiment, listed in Table 1.

[0052] Assemble the overall stiffness matrix and load vector, solve the initial equilibrium equations, and select the midpoint of the sliding surface corresponding to block 2 as the initial critical instability point.

[0053] Define the limit equilibrium conditions and critical buckling conditions for the potential sliding surface: the limit equilibrium condition is that the shear stress at any point on the sliding surface equals the reduced shear strength; the critical buckling condition is that the relative tangential displacement at the critical buckling point is zero. Reassemble the overall stiffness matrix and load vector based on these conditions.

[0054] Based on the DDA principle, establish a system with a safety factor F. s The nonlinear equation system: (F s ·K+K st )·D= F s ·F+F st Meanwhile, the relative tangential displacement of the initial critical instability point is zero, which is used as the supplementary equation K. cup ·D=0, combining the equations, we get the information about vector X={D} , Fs} The nonlinear system of equations H(X) = 0.

[0055] Since the sliding body structure is simple, this example does not consider the contact state iteration and the strength reduction between the blocks, and directly uses Newton's method to iteratively solve the nonlinear equation system H(X) = 0.

[0056] It was confirmed that the sliding surface of the block where the initial critical instability point is located has the largest relative tangential displacement.

[0057] The calculation results of the safety factor for planar sliding under different parameter conditions are listed in Table 2. It can be seen that the results of the DDA slice method for planar sliding calculation are completely consistent with the analytical solution, indicating that the DDA-based slice method for rock slope stability provided by this invention has high accuracy. The Newton iteration process is as follows... Figure 5 As shown, the error has been reduced to 10 after two iterations. -10 The following explains why this method has high solution efficiency.

[0058] In scenario 4, this embodiment employs two discretization methods: two oblique blocks and ten vertical blocks. The force distribution and block stress tensor are as follows: Figure 6 As shown, the sum of the normal forces on the sliding surface calculated by the two discrete methods is 675kN, which is consistent with the component of the sliding surface's weight along the normal direction, further verifying the high accuracy of the method of the present invention.

[0059] Table 1. Shear strength parameters of the four groups of sliding surfaces in Example 1

[0060] Table 2 Results of safety factor calculation in Example 1

[0061] Example 2: Stability Calculation of a Broken Line Sliding Slope This embodiment takes a polygonal sliding body as the research object and analyzes the influence of different inter-segment states on the safety factor calculation results. It mainly considers factors such as whether shear slip is allowed at the contact surface, whether the strength between the segments is reduced, and the influence of contact stiffness. The specific steps are as follows: like Figure 7 As shown, the sliding body has a height of 400m and a weak anti-dip surface exists in the upper middle part. Based on the distribution of structural surfaces, the sliding body corresponding to the polygonal sliding surface is discretized into 8 blocks, numbered 1 to 8 from left to right. The slide bed is considered rigid and is not considered.

[0062] The blocks are in edge-to-edge contact with each other, and the slider and the slide are in contact through a potential sliding surface.

[0063] The material parameters are set as follows: elastic modulus 10 GPa, Poisson's ratio 0.2, specific weight 23 kN / m³, normal and tangential contact stiffness 100 GPa and 40 GPa respectively, cohesion and internal friction angle of the upper part of the weak surface 0 and 18° respectively, and cohesion and internal friction angle of the lower part of the weak surface 1 MPa and 30° respectively.

[0064] Assemble the overall stiffness matrix and load vector, solve the initial equilibrium equations, and select the midpoint of the sliding surface corresponding to block 1 as the initial critical instability point.

[0065] Set the limit equilibrium conditions and critical instability conditions for the potential sliding surface, and reassemble the overall stiffness matrix and load vector.

[0066] Based on the DDA principle, establish a system with a safety factor F. s The nonlinear equation system (F s ·K+K st )·D= F s ·F+F st Meanwhile, the relative tangential displacement of the initial critical instability point is zero, which is used as the supplementary equation K.cup ·D=0, combining the equations, we get the information about vector X={D} , Fs} The nonlinear system of equations H(X) = 0.

[0067] The nonlinear equation system H(X) = 0 was solved iteratively using the Newton method, and the safety factor, displacement field, stress field, and stress distribution on the contact surface and sliding surface were obtained by combining the contact state iteration.

[0068] To determine whether the relative tangential displacement of the sliding surface of the block where the initial critical instability point is located is at its maximum, in this embodiment, it is the initial critical instability point.

[0069] For cases where the inter-segment shear strength is reduced along with the potential sliding surface, the obtained safety factor is used to reduce the inter-segment shear strength. The aforementioned steps are repeated until the change in the safety factor is less than 0.001, at which point the solution is terminated.

[0070] Table 3 shows the calculated safety factor results for the polygonal sliding surface under different inter-strip conditions, and the corresponding normal stress distribution of the sliding surface is as follows: Figure 8 As shown. When inter-strip shear slip is not considered, blocks 6 and 8 exhibit significant tensile stress, resulting in higher normal forces at the bottom of blocks 4 and 5 compared to other cases. Since the sliding surface strength of the latter two is significantly higher than that of the former, the calculated safety factor reaches 5.121, significantly higher than other cases. When inter-strip shear slip is allowed, whether or not the sliding surface strength is reduced also affects the final result. For the upper blocks of the weak surface, due to their very low inter-strip strength and lack of cohesion, whether or not inter-strip strength reduction is considered has little impact on the bottom normal force, and the results are basically consistent with those calculated using the Sarma method. However, in the lower part of the anti-dip weak surface, the sliding surface normal stress varies under different working conditions, with safety factors of 2.173 and 1.998 respectively for those without and with reduction.

[0071] The example also analyzes the influence of contact stiffness on the calculation results. The normal stress distribution under different contact stiffnesses is as follows: Figure 9 As shown, the calculation results tend to stabilize when the normal and tangential stiffness are higher than the used values ​​of 100 GPa and 40 GPa, respectively. Therefore, in the calculation, the normal and tangential contact stiffness can be taken as 10 times and 4 times the material's elastic modulus, respectively.

[0072] Table 3 Calculation results of safety factors for different conditions in Example 2

[0073] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0074] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating the stability of rock slopes using a slice method based on discontinuous deformation analysis, characterized in that, Includes the following steps: Based on the development of discontinuities in the rock slope, the sliding body is divided into several blocks or strips. If the influence of the sliding bed needs to be considered, the sliding bed is also discretized into blocks. Establish a contact system, set edge-to-edge contact between all adjacent blocks, and assign normal stiffness and tangential stiffness. If the influence of the slide is not considered, the sliding surface is regarded as the boundary contact, that is, the other side is a fixed rigid body. The block parameters include density, elastic modulus and Poisson's ratio. The parameters between blocks and the potential sliding surface are shear strength parameters. Initial stress conditions and boundary conditions are also set. If the shear strength parameters adopt the Mohr-Coulomb criterion, they are the internal friction angle and cohesion. Assemble the overall stiffness matrix and overall load vector based on discontinuous deformation analysis to form the initial overall equilibrium equation; Solve the initial global equilibrium equations to obtain the displacement and stress fields under the initial self-weight and loads; The location with the highest safety margin on the slip surface was initially selected as the initial critical instability point. Based on the limit equilibrium condition of the sliding surface, reassemble the overall stiffness matrix and load vector; The critical instability condition is coupled to the analysis equation based on discontinuous deformation, and a set of nonlinear equations with an unknown quantity containing a safety factor Fs is established. The Newton iteration method combined with contact state iteration is used to directly solve the equations to obtain the safety factor and the displacement field under the critical state. Determine whether the critical instability point is the point of maximum relative tangential displacement. If not, update the critical instability point and iterate again to solve the problem. If the reduction of inter-strip shear strength needs to be considered, the obtained safety factor is used to reduce the inter-strip strength, and the iteration is repeated until the change in safety factor tends to stabilize. Output the calculation results of safety factor, block degree of freedom, sliding surface and contact surface stress, etc.

2. The method according to claim 1, characterized in that, The reassembly of the overall stiffness matrix and load vector based on the limit equilibrium condition specifically includes: Based on the tangential contact characteristics of the sliding surface, and according to the limit equilibrium condition, the tangential stiffness matrix K of the sliding surface is assembled. st and the tangential load vector F of the sliding surface s Combining the overall equilibrium equations, a system with a safety factor F is constructed. s The nonlinear equation system: (F s ·K + K st )·D= F s ·F + F st , where K is the overall stiffness matrix, D is the unknown vector of the block system, and F is the load vector.

3. The method according to claim 2, characterized in that, The coupling of the critical instability condition to the discontinuous deformation analysis equations specifically includes: The supplementary equation is K, where the relative tangential displacement at the critical instability point is zero. cup ·D = 0, this supplementary equation is combined with the aforementioned nonlinear equation system (F s ·K + K st )·D = F s ·F + F st By combining the two equations, we obtain the vector X = {D}, which represents the unknown variable. , F s } The nonlinear system of equations H(X) = 0.

4. The method according to claim 1, characterized in that, The solution is obtained by combining Newton's iteration method with contact state iteration. A three-layer iteration strategy is adopted, including: the outermost layer is the iteration of shear strength reduction between blocks, the middle layer is the iteration of contact state between blocks, and the innermost layer is the Newton's method iteration for solving the nonlinear equation system H(X) = 0.

5. The method according to claim 1, characterized in that, The discretization of the sliding body includes vertical striping or oblique striping formed by cutting through faults or joint structures.

6. The method according to claim 1, characterized in that, If the stress disturbance effect of the slide is not considered, the slide is regarded as a fixed rigid body, and only the slide body is separated by strip separation, and the sliding surface is regarded as the boundary contact.

7. The method according to claim 1, characterized in that, When the target slope is a slope containing a goaf, the supporting effect of the goaf roof is simplified to the condition described by the safety factor F. s Reduced horizontal stress R cm / F s , where R cm It represents the uniaxial compressive strength of the rock mass.

8. A calculation device for the stability of rock slopes based on discontinuous deformation analysis using a slice method, characterized in that, include: Discretization and parameter initialization module: used to discretize and number the slope and potential sliding body, establish contact surfaces, and set various parameters of the blocks and contact surfaces; The assembly module for the total stiffness matrix and total load vector in conventional discontinuous deformation analysis is responsible for assembling the block elastic stiffness sub-matrix, contact stiffness sub-matrix, and displacement constraint stiffness sub-matrix into the overall stiffness matrix, and assembling the initial stress load sub-vector, concentrated force load sub-vector, volume force load sub-vector, contact load sub-vector, and displacement constraint load sub-vector into the total load vector. The conventional discontinuous deformation analysis solution module is used to solve the overall equilibrium equations for discontinuous deformation analysis, determine the contact state, and update the displacement and stress fields. Assembly module based on discontinuous deformation analysis slice method for total stiffness matrix and total load vector: used to calculate the tangential stiffness matrix and load vector matrix of a new potential sliding surface based on limit equilibrium conditions, and update the total stiffness matrix and total load vector accordingly. The sliding body stability solution module is used to establish a set of nonlinear equations with the safety factor as an unknown by coupling critical instability conditions, and to solve the safety factor of the potential sliding body using a three-level iterative strategy, and to determine the location of the critical instability point. The results output and plotting module is used to output the calculation results of safety factors, block degrees of freedom, sliding surface and contact surface stress, etc., and to plot the distribution of the corresponding physical quantities.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program for calculating the stability of rock slopes using the slice method based on discontinuous deformation analysis. When the program is executed by a processor, it implements the steps of the method for calculating the stability of rock slopes using the slice method based on discontinuous deformation analysis as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, The system includes a memory and a processor. The memory stores a program for calculating the stability of rock slopes using the slice method based on discontinuous deformation analysis. When the program is executed by the processor, it implements the steps of the method for calculating the stability of rock slopes using the slice method based on discontinuous deformation analysis as described in any one of claims 1 to 7.

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