Method for rapidly evaluating stability of jointed rock slope block

Abstract

The invention discloses a jointed rock mass slope block stability rapid evaluation method, which combines a block theory and a discrete element method, and aims to solve the limitation of a traditional method in rock mass stability analysis. The method comprises the following steps: firstly, carrying out progressive failure search on jointed rock mass through kinematics analysis, identifying potential unstable blocks, and carrying out gradual analysis according to different modes such as free falling, single-sided sliding and double-sided sliding; thirdly, all the potential unstable blocks are divided into a plurality of key block groups which are independent of one another, and mechanical interaction exists between the blocks in each group; and finally, gradually adjusting material strength parameters by adopting a strength reduction technology of a discrete element method, and calculating a safety coefficient of each key block group so as to evaluate the stability of the rock mass. According to the method, the defect that interaction of multiple blocks cannot be considered in the block theory is effectively overcome, the efficiency of the discrete element method in large-scale model calculation is improved, and the stability of the jointed rock mass can be efficiently and accurately evaluated.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and in particular relates to a method for quickly evaluating the stability of a jointed rock mass slope block. Background Art

[0002] The stability of jointed rock mass is affected by the internal joints and fissures, which manifests as the instability of the blocks. Therefore, it is particularly important to identify the movable blocks that may be destroyed and analyze their stability. Block theory and discrete element method are commonly used rock mass stability analysis methods, which are suitable for the stability evaluation of rock mass with developed joints. Block theory can determine the potential unstable blocks only through the combination of factors such as the structural surface and the slope surface, and combine the limit equilibrium analysis to judge the stability of the blocks. Due to the advantages of block theory, which is simple to implement and has high computational efficiency, it is widely used in engineering. The discrete element method can comprehensively simulate all cracks and rock blocks, consider complex block failure modes and the interaction between unstable blocks, and calculate the safety factor through the strength reduction method.

[0003] Domestic and foreign studies have extensively applied block theory and discrete element method to analyze the stability of rock mass, but these two methods also have obvious limitations. Block theory can only calculate the stability of a single block, and cannot consider the mechanical effects and progressive failure between multiple blocks. It also has the defect of not being able to consider the failure modes of block rotation and torsion around the axis. The significant disadvantage of the discrete element method is that when the model contains a large number of blocks, the calculation efficiency is low and cannot meet the actual needs of engineering analysis.

[0004] This method aims to address the limitations of block theory, which cannot consider the interaction and rotational failure modes between multiple blocks, and the technical defects of discrete element method, which has low computational efficiency and is difficult to meet the needs of engineering applications. This method proposes a jointed rock mass stability evaluation method that combines block theory and discrete element method. This method overcomes the limitations of the two methods while retaining their respective advantages, and can efficiently realize the stability analysis of jointed rock masses. Summary of the invention

[0005] The present invention aims to solve the technical problems existing in the background technology and to provide a method for quickly evaluating the stability of jointed rock mass slope blocks.

[0006] In order to solve the technical problem, the technical solution of the present invention is:

[0007] A method for rapid assessment of block stability of a jointed rock mass slope, the method comprising:

[0008] S1: progressive failure search of jointed rock mass is carried out through kinematic analysis to identify potential unstable blocks and conduct step-by-step analysis according to different modes of free fall, single-sided sliding and double-sided sliding;

[0009] S2: All potentially unstable blocks are divided into multiple independent key block groups, and there is mechanical interaction between the blocks in each group;

[0010] S3: The strength reduction method of the discrete element method is used to gradually adjust the material strength parameters and calculate the safety factor of each key block group to evaluate the stability of the rock mass.

[0011] Further, the step S1 comprises:

[0012] S101: Free fall analysis, through a 1-row and m-column discriminant matrix T′ ff conduct:

[0013]

[0014] In the formula, is the unit normal vector pointing to the interior of the block, m is the number of structural faces of the block, sign(x) is the sign function, is the unit direction vector of the total external force acting on the block, when T′ ff When all elements in are 1, the block is movable and the motion mode is free fall; at this time, there is no need to perform single-sided or double-sided sliding analysis. ff When it contains -1 or 0, it is non-free fall motion and S102 analysis is required;

[0015] S102: Single-sided sliding analysis, through a p-row and m-column discriminant matrix T′ ss accomplish:

[0016]

[0017] In the formula, For the combined external force exist The projection vector in the direction, p is the or the number of structural faces of 0; when T′ ss When all elements in a row are 0 or 1, the block is movable and the motion mode is one-sided sliding; when T′ ss If all rows in the table contain -1, single-sided sliding is not possible and S103 analysis is required;

[0018] S103: Double-sided sliding analysis, through a q-row and m-column discriminant matrix T′ ds accomplish:

[0019]

[0020] In the formula, For the combined external force The projection vector on the intersection of face i and face j, q is satisfied and The number of intersections between two planes, when T′ ds When all the elements in a row are 0 or 1, the block can move and the motion mode is double-sided sliding; if all the elements in a row are 0 or -1, the block can move and is stable without friction; if T′ ds If all rows contain 1 and -1, the block cannot be moved;

[0021] S104: When all surface blocks have completed the above judgment process, remove the blocks whose motion mode is free fall, single-sided sliding or double-sided sliding, i.e., potentially unstable blocks; re-perform the motion mode judgment of steps S101 to S103 on the newly exposed surface blocks, and repeat the process until all potentially unstable blocks are found.

[0022] Further, in step S2:

[0023] After searching for all potential unstable blocks, multiple independent key block groups will appear within the model, each with different stability. All potential unstable blocks are divided into multiple key block groups according to the bottom-up search strategy. The division strategy follows the following principles:

[0024] S201: Start searching from the movable block at the lowest position;

[0025] S202: The movement of a block only causes the movement of the block above it, but has no effect on the block relatively below it;

[0026] S203: excluding the surface movable blocks that have already belonged to a certain key block group, and searching for the next block group;

[0027] S204: When all potential unstable blocks have their own key block groups, the division of key block groups is completed.

[0028] Further, after the division of the key block groups is completed, the safety factor of each key block group is calculated respectively by using the strength reduction method, and the step S3 includes:

[0029] S301: applying gravity acceleration to the model and calculating until the model reaches a stress equilibrium state;

[0030] S302: Set the material strength parameters to larger values, namely the cohesion, internal friction angle and tensile strength parameters of the structural surface, and then change the internal stress of the unit to twice the stress balance;

[0031] S303: Calculate until the model reaches a stress equilibrium state again, and record the characteristic time step Nr required for this process;

[0032] S304: Parameters after strength reduction Substitute into the equilibrium model and start calculation; if the unbalanced force of the model is less than 10 after Nr steps -5 , it is believed that the model has reached a state of equilibrium, making FoS up =FoS trail ; If equilibrium is not reached, continue to calculate Nr steps. If the unbalanced force is less than 10 -5 , then exit the loop and consider the model to be stable; if the unbalanced force at this time is greater than 90% of the previous unbalanced force, the model is considered to be unstable, FoS low =FoS trail If the unbalanced force is less than 90% of the previous unbalanced force, continue to calculate Nr steps and repeat the above judgment process; if the unbalanced force of the model is still greater than 10 after 5×Nr steps -5 , then the type is considered unstable;

[0033] S305: Calculate new FoS trail =(FoS low +FoS up ) / 2, repeat step S304;

[0034] S306: When FoS up -FoS low <0.005×(FoS low +FoS up ) / 2, the safety factor calculation is carried out, at this time FoS=(FoS low +FoS up ) / 2.

[0035] Compared with the prior art, the advantages of the present invention are:

[0036] A rapid assessment method for block stability of jointed rock slopes is used to calculate the safety factor of jointed rock mass. It can effectively identify all movable blocks in the rock mass and divide them into corresponding key block groups, while quickly calculating the safety factor of each key block group. This method takes into account the interaction and complex failure modes of multiple blocks, and improves the calculation efficiency by reducing the total number of blocks involved in the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 , a technical roadmap of a method for rapid assessment of block stability of a jointed rock mass slope according to the present invention;

[0038] Figure 2 , block progressive destruction search flow chart;

[0039] Figure 3 , Slope model geometric dimension drawing;

[0040] Figure 4 , two sets of disc-shaped structural surfaces;

[0041] Figure 5 , model after crack cutting;

[0042] Figure 6 , surface block motion pattern analysis results;

[0043] Figure 7 , progressive failure analysis result diagram;

[0044] Figure 8 , identification results of key block groups and unstable blocks obtained by strength reduction method;

[0045] Fig. 9 , comparison chart of safety factor between strength reduction method and analytical method;

[0046] Fig.10 , full-space stereographic projection of rock slope;

[0047] Fig.11 , the slope block model diagram after merging;

[0048] Fig.12 , key block group identification results (only display volume>3m 3 );

[0049] Fig.13 , Block displacement under critical stability state (only displayed for volume > 3m 3 );

[0050] Fig.14 , Typical failure mode of block (side view); DETAILED DESCRIPTION

[0051] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0052] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0053] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0054] Embodiment 1:

[0055] like Figure 1 and 2 As shown in the figure, a rapid assessment method for the stability of jointed rock mass slope blocks is presented. The following are the inputs and outputs of each step in the jointed rock mass stability assessment method:

[0056] 1. Progressive destruction search of movable blocks

[0057] Input: Jointed rock model (including block geometry, structural surface parameters, free surface / excavation surface orientation). External forces (such as gravity, geostress). Block kinematic parameters (such as structural surface normal vector, external force direction).

[0058] Output: Identification results of potentially unstable blocks (motion modes: free fall, single-sided sliding, double-sided sliding). Motion judgment matrix for each block. Updated surface blocks for the next iteration.

[0059] 2. Division of key block groups

[0060] Input: All potentially unstable blocks identified. Spatial position and motion characteristics of each block. Contact relationships and mechanical interactions between blocks.

[0061] Output: divided key block groups (multiple groups, each group contains several interacting blocks). Independence determination results of each key block group (whether they affect each other).

[0062] 3. Discrete Element Strength Reduction Method

[0063] Input: The geometry and mechanical parameters of each key block group (such as cohesion, internal friction angle, tensile strength). External forces (such as gravity) and initial stress field. Strength reduction parameters (initial value, reduction step).

[0064] Output: Safety factor of each key block group. Stability assessment results (stable / unstable). Block instability mode (sliding, overturning or rupture).

[0065] Overall summary: Each step uses the output results of the previous stage as input to form a cyclic analysis process. After the progressive failure search identifies the unstable block, its results are input into the key block group division step; the divided key block group is then used as the input of the strength reduction method for the final stability calculation.

[0066] Embodiment 2:

[0067] Take a jointed rock slope as an example. The model has a longitudinal width of 60m, a top length of 15m, a bottom length of 26.3m, a slope angle of 53°, and a south (S) orientation. The model dimensions are as follows: Figure 3As shown. The rock density is 2800kg / m 3 , the structural surface stiffness kn is 800GPa / m 2 , ks is 100 GPa / m 2 , structural surface strength c = 10kPa, There are two groups of structural surfaces in the model: J1 and J2. The two groups of structural surfaces are randomly generated, and their random parameters follow the following distribution model: the crack is assumed to be disk-shaped, with an area of ​​Area~U(100,400); the center coordinates of the disk are Xc~U(0,60), Yc=0, Zc=15. Crack J1, dip angle DIP~N(60,3), inclination DD~N(120,3), number n=15; crack J2, dip angle DIP~N(45,3), inclination DD~N(240,3), number n=15. The 30 randomly generated structural surfaces are shown in Figure 4 The surface blocks and boundary blocks formed after the cracks cut the model are shown in Figure 5 The following results were obtained by analyzing the three steps one by one:

[0068] (1) Progressive failure search for movable blocks: Analyze the motion pattern of surface blocks in the order of free fall analysis, single-side sliding analysis, double-side sliding analysis, and movable / immovable analysis. Figure 6 As shown in Figure 1, there are three analysis results for the surface blocks: double-sided sliding, movable and stable without friction, and immovable. After removing the movable blocks, new surface blocks will be exposed, and the block progressive failure analysis will continue until all movable blocks are identified (see Figure 1). Figure 7 ).

[0069] (2) Division of key block groups: Using the key block group division algorithm, eight key block groups were successfully identified, which are completely consistent with the results observed by naked eyes, such as Figure 8 In addition, it is not difficult to see that the number of blocks contained in each key block group is significantly lower than the total number of blocks in the discrete element model.

[0070] (3) Discrete element strength reduction method: The safety factors of the eight key block groups were calculated and compared with the safety factors calculated by the analytical method. Except for the safety factor of group (2), which has a large error (6.4%), the errors of the remaining groups are less than ±3%. The reason for the large error is that the shape of the unstable block identified by the strength reduction method is not a regular wedge, such as Fig. 9 shown.

[0071] Embodiment 3:

[0072] Taking the jointed rock slope as an example, the slope model considers four groups of V-level structural surfaces. The structural surfaces are modeled by discrete fracture networks (DFN). The size, occurrence, spacing and other parameters of the structural surfaces are shown in Table 1. Internal friction angle of all structural surfaces Both are 49.73°, and the cohesion is 0. Fig.10 The four groups of structural surfaces and slope excavation surfaces are shown in Figure 2. The slope block model after DFN cutting is shown in Figure 2. Fig.11 .

[0073] Through block progressive failure analysis and key block group division, a total of 18 key block groups were obtained, of which the largest block group is 224.5m 3 , the smallest is 0.12m 3 . Fig.12 Shows that the volume is greater than 3m 3 For each key block group, the block at the shear outlet takes the edge of the structural surface J3-J4 as the potential sliding direction, which is consistent with Fig.10 The full-space stereographic projection results are consistent.

[0074] The discrete element strength reduction method is used to calculate the safety factors of 18 key block groups. The safety factor results calculated by the volume and strength reduction method of each key block group are shown in Table 2. The safety factor ranges from 2.29 to 3.71, among which the safety factor of block group 12 is the smallest and the safety factor of block group 9 is the largest. The safety factor has a large range of variation, mainly due to the randomness and variability of the structural surface occurrence. Fig.13 Demonstrated volume greater than 3m 3 The displacement contours show that the failure modes of these block groups are highly similar. Fig.14 The side view shows their failure mode, which is a rotational sliding failure around point C (the rotation center is the intersection of the vertical line of the J3-J4 intersection S34 and the projection of S34 on J1). Fig.10 The two-sided sliding along the S34 direction predicted by the full-space stereographic projection is different, indicating that the block theory cannot consider the complex rotational motion, which further verifies the advantage of the proposed method in considering the rotational failure mode.

[0075] Table 1 - Input parameters of the structural surface of the discrete fracture network (DFN)

[0076]

[0077] Table 2- Volume and safety factor of key block groups

[0078]

[0079] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, 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 code.

[0080] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, 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 processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0081] 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 process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0082] 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 in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0083] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0084] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for rapid assessment of block stability of jointed rock mass slope, characterized in that: The method comprises: S1: progressive failure search of jointed rock mass is carried out through kinematic analysis to identify potential unstable blocks and conduct step-by-step analysis according to different modes of free fall, single-sided sliding and double-sided sliding; S2: All potentially unstable blocks are divided into multiple independent key block groups, and there is mechanical interaction between the blocks in each group; S3: The strength reduction method of the discrete element method is used to gradually adjust the material strength parameters and calculate the safety factor of each key block group to evaluate the stability of the rock mass.

2. A method for rapid assessment of block stability of jointed rock mass slope according to claim 1, characterized in that: The step S1 comprises: S101: Free fall analysis, through a 1-row and m-column discriminant matrix T f ' f conduct: In the formula, is the unit normal vector pointing to the interior of the block, m is the number of structural faces of the block, sign(x) is the sign function, is the unit direction vector of the total external force acting on the block, when T′ ff When all elements in are 1, the block is movable and the motion mode is free fall; there is no need to perform single-sided or double-sided sliding analysis. ff When it contains -1 or 0, it is non-free fall motion and S102 analysis is required; S102: Single-sided sliding analysis, through a p-row and m-column discriminant matrix T′ ss accomplish: In the formula, For the combined external force exist The projection vector in the direction, p is the or the number of structural faces of 0; when T′ ss When all elements in a row are 0 or 1, the block is movable and the motion mode is one-sided sliding; when T′ ss If all rows in the table contain -1, single-sided sliding is not possible and S103 analysis is required; S103: Double-sided sliding analysis, through a q-row and m-column discriminant matrix T′ ds accomplish: In the formula, For the combined external force The projection vector on the intersection of face i and face j, q is satisfied and The number of intersections between two planes, when T′ ds When all the elements in a row are 0 or 1, the block can move and the motion mode is double-sided sliding; if all the elements in a row are 0 or -1, the block can move and is stable without friction; if T′ ds If all rows contain 1 and -1, the block cannot be moved; S104: When all surface blocks have completed the above judgment process, remove the blocks whose motion mode is free fall, single-sided sliding or double-sided sliding, i.e., potentially unstable blocks; re-perform the motion mode judgment of steps S101 to S103 on the newly exposed surface blocks, and repeat the process until all potentially unstable blocks are found.

3. A method for rapid assessment of jointed rock mass slope stability according to claim 1, characterized in that: In step S2: After searching for all potential unstable blocks, multiple independent key block groups will appear within the model, each with different stability. All potential unstable blocks are divided into multiple key block groups according to the bottom-up search strategy. The partitioning strategy follows the following principles: S201: Start searching from the movable block at the lowest position; S202: The movement of a block only causes the movement of the block above it, but has no effect on the block relatively below it; S203: excluding the surface movable blocks that have already belonged to a certain key block group, and searching for the next block group; S204: When all the potentially unstable blocks have their own key block groups, the division of the key block groups is completed.

4. A method for rapid assessment of jointed rock mass slope stability according to claim 1, characterized in that: After the division of the key block groups is completed, the safety factor of each key block group is calculated using the strength reduction method. The step S3 includes: S301: applying gravity acceleration to the model and calculating until the model reaches a stress equilibrium state; S302: Set the material strength parameters to larger values, namely the cohesion, internal friction angle and tensile strength parameters of the structural surface, and then change the internal stress of the unit to twice the stress balance; S303: Calculate until the model reaches a stress equilibrium state again, and record the characteristic time step Nr required for this process; S304: Parameters after strength reduction Substitute into the equilibrium model and start calculation; if the unbalanced force of the model is less than 10 after Nr steps -5 , it is believed that the model has reached a state of equilibrium, making FoS up =FoS trail ; If equilibrium is not reached, continue to calculate Nr steps. If the unbalanced force is less than 10 -5 , then exit the loop and consider the model to be stable; if the unbalanced force at this time is greater than 90% of the previous unbalanced force, the model is considered to be unstable, FoS low =FoS trail If the unbalanced force is less than 90% of the previous unbalanced force, continue to calculate Nr steps and repeat the above judgment process; if the unbalanced force of the model is still greater than 10 after 5×Nr steps -5 , then the type is considered unstable; S305: Calculate new FoS trail =(FoS low +FoS up ) / 2, repeat step S304; S306: When FoS up -FoS low <0.005×(FoS low +FoS up ) / 2, the safety factor calculation is carried out, at this time FoS=(FoS low +FoS up ) / 2.

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