A tunnel surrounding rock chain collapse disaster prediction method and system
By constructing a model of the surrounding rock blocks in the tunnel and identifying their hazards, the problem of predicting the chain collapses within the surrounding rock during tunnel construction was solved. This enabled accurate identification and prediction of the chain collapse blocks, thereby improving construction safety.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2025-03-17
- Publication Date
- 2026-07-24
AI Technical Summary
Existing technologies are unable to accurately predict the chain collapses in the surrounding rock during tunnel construction, resulting in significant deviations between construction plan design and disaster control requirements, causing casualties and economic losses.
By collecting information on rock mass structure surfaces, a block model of the surrounding rock of the tunnel is constructed. The inner wall blocks are searched and identified to find the danger of the contact blocks. The danger identification method in block theory is used to identify possible chain collapse blocks inside the surrounding rock.
It enables accurate prediction of chain collapses in the internal area of the tunnel surrounding rock, improves the accuracy of identifying potentially unstable blocks at each stage of chain collapses, and ensures the safety of the construction process.
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Figure CN120234871B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of tunnel engineering disaster prediction technology, specifically to a method and system for predicting chain collapse disasters in tunnel surrounding rock. Background Technology
[0002] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art.
[0003] Tunnel construction involves extensive traversal of hard rock block strata, making collapse hazards a major challenge to the safe construction of tunnel projects. The essence of a collapse hazard is the catastrophic event of instability occurring in a complex structural system composed of different scales of structural planes and rock blocks within the rock mass under excavation disturbance. Current technologies struggle to accurately predict the interactions between these blocks and the construction evolution process, leading to significant discrepancies between construction plan design and actual disaster control needs. Block collapses cause substantial casualties and economic and resource losses. Existing collapse hazard prediction methods are limited to identifying dangerous collapse zones on the surface of the tunnel surrounding rock, failing to accurately predict potential cascading collapses within the surrounding rock. Summary of the Invention
[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and system for predicting chain collapse disasters in tunnel surrounding rock, and to identify chain collapse disasters during tunnel construction.
[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:
[0006] On the one hand, the technical solution of the present invention provides a method for predicting the cascading collapse disaster of tunnel surrounding rock, including:
[0007] Collect rock mass structural surface information, and construct a tunnel surrounding rock block model based on the rock mass structural surface information;
[0008] Based on the tunnel surrounding rock block model, all inner wall blocks are searched and the danger of the inner wall blocks is judged to find the dangerous blocks in the inner wall blocks;
[0009] Search for the contact blocks of the dangerous block, identify the block type of the contact blocks, and find the blocks among the contact blocks that have not been identified as dangerous;
[0010] The block that has not undergone hazard assessment is assessed for hazard. If it is not a dangerous block, it is ignored; if it is a dangerous block, the search for the contact blocks of the dangerous block is repeated, i.e., the hazard assessment, until none of the contact blocks of the dangerous block are dangerous blocks, thus obtaining information on all dangerous blocks in the tunnel surrounding rock.
[0011] In at least one embodiment, information on the rock mass structure surface within the tunnel is collected through manual geological logging or three-dimensional laser scanning.
[0012] In at least one embodiment, the search for all inner wall blocks based on the tunnel surrounding rock block model specifically involves: by traversing the vertex coordinates of each facet of the block and the coordinates of each point on the upper and lower edge surfaces, determining whether the angle between vectors m1 and m2 is an obtuse angle; if so:
[0013] m1·m2<0
[0014] If the patch is located on the inner wall of the tunnel, then the block containing the patch is the inner wall block; where m1 is the vector formed by connecting the vertex of the patch with the point on the upper edge surface, and m2 is the vector formed by connecting the vertex of the patch with the point on the lower edge surface.
[0015] In at least one embodiment, the hazard determination specifically involves: using the normal vector n from each structural surface of the block pointing to the interior of the block. i =(A i B i C i As A i x+B i y+C i The coefficients in z≥0 form a system of inequalities. Solve the system of inequalities. If there is one and only one solution (0, 0, 0), then the block is not a dangerous block; otherwise, the block is a dangerous block. The number of inequalities in the system of inequalities is the same as the number of structural surfaces of the block.
[0016] In at least one embodiment, after all contact blocks of the dangerous block are found, the block category of these contact blocks is determined. If the contact block is an inner wall block, it is ignored; otherwise, it is determined to be an internal block and its hazard needs to be assessed.
[0017] In at least one embodiment, a dangerous block vector array is formed using the contact vectors of the contact blocks, and the directions of the contact vectors in the vector array are determined sequentially.
[0018] If the contact vector is pointing downwards, ignore it and proceed to the next vector direction determination; if the contact vector is pointing upwards, remove it from the vector array and perform block hazard assessment.
[0019] If the judgment result is a dangerous block, the determination and hazard judgment of the contact block of the dangerous block are repeated; otherwise, the contact block is ignored and the judgment continues to the next block.
[0020] In at least one embodiment, the contact vectors in the vector array all point to the interior of the hazardous block.
[0021] On the other hand, the technical solution of the present invention also provides a tunnel surrounding rock cascading collapse disaster prediction system, comprising:
[0022] The model building module is configured to: collect rock mass structural surface information and build a tunnel surrounding rock block model based on the rock mass structural surface information;
[0023] The inner wall dangerous block identification module is configured to: search all inner wall blocks based on the tunnel surrounding rock block model and identify the dangerous blocks in the inner wall blocks;
[0024] The contact block search module is configured to: search for contact blocks of the hazardous block, determine the block type of the contact blocks, and find the contact blocks that have not been determined as hazardous.
[0025] The contact block identification module is configured to: perform hazard identification on the blocks that have not undergone hazard identification; if they are not dangerous blocks, they are ignored; if they are dangerous blocks, the search for contact blocks of the dangerous blocks, i.e., the hazard determination, is repeated until none of the contact blocks of the dangerous blocks are dangerous blocks, thus obtaining information on all dangerous blocks in the tunnel surrounding rock.
[0026] The beneficial effects of the above-described technical solution of the present invention are as follows:
[0027] 1) The method for predicting chain collapse disasters in tunnel surrounding rock according to the present invention can find all dangerous blocks on the inner wall of the tunnel surrounding rock and all internal dangerous blocks that are in contact with the dangerous blocks on the inner wall. It can obtain information such as the location and volume of the blocks that may cause chain collapses in the internal area of the surrounding rock, and thus can accurately predict the chain collapses that may occur in the internal area of the surrounding rock during tunnel construction.
[0028] 2) The tunnel surrounding rock chain collapse disaster prediction method of the present invention innovates the movable block identification method in block theory. Based on the contact vector, it judges whether the falling of a block will affect the block in contact with it, which improves the accuracy of identifying potentially unstable blocks at each stage of chain collapse and ensures the accuracy of tunnel surrounding rock chain collapse prediction. Attached Figure Description
[0029] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0030] Figure 1 This is a flowchart of a method for predicting interlocking collapse disasters in tunnel surrounding rock according to the present invention;
[0031] Figure 2This is a schematic diagram of the relationship between contact blocks in a method for predicting interlocking collapses of surrounding rock in tunnels according to the present invention.
[0032] Figure 3 This is a schematic diagram of the inner wall block and the internal block of the tunnel surrounding rock chain collapse disaster prediction method of the present invention;
[0033] Figure 4 This is an interface diagram of the tunnel surrounding rock block model constructed according to the method for predicting the chain collapse disaster of tunnel surrounding rock according to the present invention;
[0034] Figure 5 This is a schematic diagram of a tunnel surrounding rock block model constructed using a method for predicting cascading collapses in tunnel surrounding rock according to the present invention. Figure 5 (a) is an overall schematic diagram. Figure 5 (b) is a schematic diagram of the explosion;
[0035] Figure 6 This is a schematic diagram of the tunnel inner wall surface of the tunnel surrounding rock chain collapse disaster prediction method of the present invention;
[0036] Figure 7 is a schematic diagram of the same block from two observation angles in the tunnel surrounding rock chain collapse disaster prediction method of the present invention. Figure 7(a) is a schematic diagram of the block from the first observation angle, and Figure 7(b) is a schematic diagram of the block from the second observation angle. Detailed Implementation
[0037] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.
[0038] As described in the background section, the purpose of this invention is to overcome the shortcomings of the prior art and provide a method and system for predicting chain collapse disasters in tunnel surrounding rock, and to identify chain collapse disasters during tunnel construction.
[0039] Example 1
[0040] In a typical embodiment of the present invention, this embodiment discloses a method for predicting cascading collapse disasters in tunnel surrounding rock, comprising:
[0041] S1. Collect rock mass structural surface information, and construct a tunnel surrounding rock block model based on the rock mass structural surface information;
[0042] S2. Based on the tunnel surrounding rock block model, search all inner wall blocks and determine the hazard of the inner wall blocks to find the dangerous blocks in the inner wall blocks;
[0043] S3. Search for the contact blocks of the hazardous block; identify the block type of the contact blocks and find the blocks that have not been identified as hazardous;
[0044] S4. Perform hazard assessment on the blocks that have not undergone hazard assessment. If they are not dangerous blocks, ignore them; if they are dangerous blocks, repeat the search for the contact blocks of the dangerous blocks, i.e., hazard assessment, until none of the contact blocks of the dangerous blocks are dangerous blocks, and obtain information on all dangerous blocks in the tunnel surrounding rock.
[0045] The following is combined Figure 1 Figure 7 provides a detailed explanation.
[0046] In this embodiment, the block is an isolated structure formed by the surrounding rock being completely cut by structural planes and excavation faces, such as... Figure 2 Blocks 1, 2, 3, and 4 are shown; the dangerous block is one that would inevitably become unstable without engineering anchoring measures if only its own weight is considered; the inner wall block is an isolated block formed by the cutting of the structural surface and the free surface, i.e., the block in contact with the tunnel excavation face, such as... Figure 3 The inner wall blocks shown; isolated blocks formed by the cutting of structural surfaces, that is, blocks that do not contact the tunnel excavation face, are internal blocks, such as... Figure 3 The internal block shown; the contact block is all the blocks that share a common contact surface with this block, such as... Figure 2 As shown, the contact blocks of block 1 are block 2 and block 4.
[0047] S1. Collect rock mass structural surface information and construct a tunnel surrounding rock block model based on the rock mass structural surface information.
[0048] In this field, rock mass structural information refers to the two-dimensional planar geological interfaces with a certain direction, large extension, and small thickness, which are various structural traces (including faults, joints, bedding, and fracture zones) produced in the rock mass under tectonic stress. These structural surfaces cut the rock mass into fractured bodies that are both continuous and discontinuous, and have an important impact on the stability, strength, and deformation characteristics of the rock mass.
[0049] In this embodiment, information on the rock mass structure within the tunnel is collected through manual geological logging or 3D laser scanning. Based on the collected rock mass structure information, a model of the surrounding rock mass is constructed using rock mass modeling software such as UDEC and 3DEC. Figure 4 As shown, the constructed tunnel surrounding rock block model is as follows: Figure 5 (a) and Figure 5 As shown in (b).
[0050] S2. Based on the tunnel surrounding rock block model, search all inner wall blocks and determine the hazard of the inner wall blocks to find the dangerous blocks in the inner wall blocks.
[0051] In a chain reaction of tunnel collapses, the first batch of dangerous blocks must have a plane that serves as the outline of the tunnel's inner wall. Therefore, this embodiment assumes an upper and lower edge surface of the tunnel based on the actual inner wall, and determines whether a block has a surface located on the tunnel's inner wall. If so, the block is a block on the tunnel's inner wall; otherwise, it is not. Figure 6 As shown.
[0052] The specific method is to iterate through the vertex coordinates of each facet of the block and the coordinates of each point on the upper and lower edge faces, and determine whether the angle between vectors m1 and m2 is an obtuse angle. If it is:
[0053] m1·m2<0
[0054] This indicates that the patch is located on the inner wall of the tunnel, and therefore the block containing the patch is the inner wall block. Here, m1 is the vector connecting the vertex of the patch to a point on the upper edge, and m2 is the vector connecting the vertex of the patch to a point on the lower edge.
[0055] After searching for all inner wall blocks using the above method, a hazard assessment is performed on each inner wall block. In this embodiment, the hazard assessment method is implemented geometrically. After obtaining the vectors pointing from each plane of each block on the tunnel inner wall to the inside of the block, it is possible to determine whether a block is a hazard block based on these vectors. In this embodiment, a hazard block is a block that would inevitably become unstable without engineering anchoring measures if only its own weight is considered. The assessment method draws on the criteria for movable blocks in block theory and is improved upon. The specific method is as follows:
[0056] The normal vector n from each structural surface of the block to the interior of the block. i =(A i B i C i As A i x+B i y+C i The coefficients in z≥0 form a system of inequalities. Solving this system of inequalities, if there is one and only one solution (0, 0, 0), then the block is not a dangerous block; otherwise, the block is a dangerous block. The number of inequalities in the system of inequalities is the same as the number of structural surfaces that cut the block.
[0057] As shown in Figures 7(a) and 7(b), taking a block located on the inner wall of a tunnel as an example, this block contains a curved surface of the tunnel inner wall and three planes formed by structural surfaces. The normal vectors pointing towards the interior of the block from the three planes formed by the structural surfaces are denoted as n1, n2, and n3, respectively. Then:
[0058] n1 = (A1, B1, C1) (2)
[0059] n2=(A2,B2,C2) (3)
[0060] n3 = (A3, B3, C3) (4)
[0061] Determine whether the block is a dangerous block by judging the solution of the system of inequalities (5). If there is only one solution (0, 0, 0), it means that the block is not a dangerous block; otherwise, the block is a dangerous block.
[0062]
[0063] Using the above-mentioned hazard identification method, dangerous blocks in all inner wall blocks are screened out, and the information of these dangerous blocks is saved and marked as the first batch of dangerous blocks.
[0064] S3. Search for the contact blocks of the dangerous block; identify the block type of the contact blocks and find the blocks that have not been identified as dangerous.
[0065] In this embodiment, the search for blocks contacted by the hazardous block includes two aspects: searching for blocks contacted by hazardous blocks on the inner wall and searching for blocks contacted by hazardous blocks within the interior. The search for blocks contacted by hazardous blocks on the inner wall involves identifying all hazardous blocks within the inner wall and then searching each hazardous block individually to find all blocks in contact with it. The search for hazardous blocks within the interior occurs after the hazardous blocks within the interior have been identified; it involves searching for blocks in contact with all identified hazardous blocks within the interior.
[0066] The fall or sliding of a hazardous block can only affect the blocks it contacts. Therefore, correctly determining whether blocks are in contact is a prerequisite for locating hazardous blocks during a chain reaction of tunnel collapses. In this embodiment, contact means that the shortest distance between two blocks is infinitely close to the thickness of a given thin disk of structural surface, such as... Figure 2 As shown, block 1 is in contact with blocks 2 and 4, but not with block 3. That is, if block 1 is identified as a dangerous block, when it is removed (simulating the falling or sliding of dangerous block 1), the newly added free surface can only affect blocks 2 and 4. In other words, the contact blocks of dangerous block 1 are blocks 2 and 4, while block 3 is not a contact block of dangerous block 1. Using this method, the contact blocks of the first batch of dangerous blocks are identified.
[0067] After finding all contact blocks of the first batch of hazardous blocks, the block category of these contact blocks is determined. If the contact block is an inner wall block, it is ignored (because the inner wall block has already been identified as hazardous and does not need to be identified again). If it is not, it is identified as an internal block and needs to be identified as hazardous. In this way, all blocks in the contact blocks of the first batch of hazardous blocks that have not been identified as hazardous are found.
[0068] S4. Perform a hazard assessment on the blocks that have not undergone hazard assessment. If they are not dangerous blocks, ignore them; if they are dangerous blocks, repeat the search for the blocks that are in contact with the dangerous blocks, i.e., the hazard assessment, until none of the blocks that are in contact with the dangerous blocks are dangerous blocks.
[0069] like Figure 1 As shown, after identifying the contact blocks of the hazardous block, the contact vectors of these contact blocks are found to form a hazardous block vector array. All contact vectors in this array point inwards from the hazardous block. In this embodiment, a contact vector refers to two vectors with opposite directions on the common contact surface of two contacting blocks, and these two vectors point inwards from the two contacting blocks respectively. Therefore, in this vector array, one contact vector represents one common contact surface, and a block consists of multiple common contact surfaces, that is, a block consists of multiple contact vectors.
[0070] For a given block, all contact vectors point inward. Therefore, the directions of contact vectors in the dangerous block vector array are sequentially checked. If the contact vector points downward, it means that the surface from which the contact vector originates is a common contact surface above the block. Removing the surface above will not cause the block to fall, so the contact vector can be ignored, and the next vector direction is checked. If the contact vector points upward, it means that the surface from which the contact vector originates is a common contact surface below the block. Losing the common contact surface below the block (i.e., removing the block in contact with the block below) may cause the block to fall. Therefore, the contact vector is removed from the vector array, a new free surface is created, and the block's hazard is assessed. If the assessment result is a dangerous block, the determination and hazard assessment of the contact blocks of the dangerous block are repeated. Otherwise, the contact block is ignored, and the next block is checked.
[0071] Specifically, all found internal blocks are assessed for their hazard level. If an internal block is deemed hazardous, its relevant information is saved and it is marked as a second batch of hazardous blocks. If an internal block is not deemed hazardous, it is ignored.
[0072] Search for contact blocks again on all the hazardous blocks in the second batch to find all contact blocks of the hazardous blocks in the second batch. Judge these contact blocks: if they are blocks that have already undergone hazard assessment, ignore them; otherwise, assess the hazard of the contact blocks to find the hazardous blocks within them, and mark these blocks as the third batch of hazardous blocks.
[0073] Then, the search for contact blocks and the hazard assessment are repeated for the third batch of hazardous blocks until the contact blocks of all the last batch of hazardous blocks are no longer hazardous blocks, at which point the search stops.
[0074] By following the steps described above, all hazardous blocks in each batch can be located, and their location, shape, volume, and other information can be determined. By identifying the information on potentially unstable blocks at each stage of a chain collapse, the prediction of chain collapse disasters in tunnel surrounding rock can be achieved.
[0075] Example 2
[0076] In a typical embodiment of the present invention, this embodiment discloses a tunnel surrounding rock cascading collapse disaster prediction system, comprising:
[0077] The model building module is configured to: collect rock mass structural surface information and build a tunnel surrounding rock block model based on the rock mass structural surface information;
[0078] The inner wall dangerous block identification module is configured to: search all inner wall blocks based on the tunnel surrounding rock block model and identify the dangerous blocks in the inner wall blocks;
[0079] The contact block search module is configured to: search for contact blocks of the hazardous block; determine the block type of the contact blocks, and find the contact blocks that have not undergone the hazardous determination.
[0080] The contact block identification module is configured to: perform hazard identification on the blocks that have not undergone hazard identification; if they are not dangerous blocks, they are ignored; if they are dangerous blocks, the search for contact blocks of the dangerous blocks, i.e., the hazard determination, is repeated until none of the contact blocks of the dangerous blocks are dangerous blocks, thus obtaining information on all dangerous blocks in the tunnel surrounding rock.
[0081] Example 3
[0082] In a typical embodiment of the present invention, a computing device is disclosed, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the above-described method for predicting cascading collapses of surrounding rock in tunnels.
[0083] Example 4
[0084] In one typical embodiment of the present invention, a computer-readable storage medium is disclosed, on which a computer program is stored, which, when executed by a processor, performs the steps of the above-described method for predicting cascading collapses of surrounding rock in tunnels.
[0085] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for predicting chain collapse disasters in tunnel surrounding rock, characterized in that, include: Collect rock mass structural surface information, and construct a tunnel surrounding rock block model based on the rock mass structural surface information; Based on the tunnel surrounding rock block model, all inner wall blocks are searched and the danger of the inner wall blocks is judged to find the dangerous blocks in the inner wall blocks; Search for the contact blocks of the dangerous block, identify the block type of the contact blocks, and find the blocks among the contact blocks that have not been identified as dangerous; The blocks that have not undergone hazard assessment are assessed for hazard; if they are not considered hazardous blocks, they are ignored. If it is a dangerous block, the search for the contact blocks of the dangerous block, i.e., the hazard determination, is repeated until the contact blocks of the dangerous block are no longer dangerous blocks, thus obtaining information on all dangerous blocks in the tunnel surrounding rock. The specific steps of searching all inner wall blocks based on the tunnel surrounding rock block model are as follows: by traversing the vertex coordinates of each facet of the block and the coordinates of each point on the upper and lower edge surfaces, determine the vector... and Is the included angle an obtuse angle? If so: This indicates that the panel is located on the inner wall of the tunnel, therefore the block containing the panel is the inner wall block; among which, It is the vector formed by connecting the vertices of the patch with the points on the upper edge surface. It is the vector formed by connecting the vertices of the facet with the points on the lower edge facet.
2. The method for predicting chain collapse disasters in tunnel surrounding rock as described in claim 1, characterized in that, Information on the rock mass structure within the tunnel is collected through manual geological logging or three-dimensional laser scanning.
3. The method for predicting chain collapse disasters in tunnel surrounding rock as described in claim 1, characterized in that, The specific method for determining the hazard is as follows: using the normal vectors pointing from each structural surface of the block to the interior of the block. As Construct a system of inequalities using the coefficients in the equations. Solve the system of inequalities. If there is one and only one solution... If the condition is met, then the block is not a dangerous block; otherwise, the block is a dangerous block. The number of inequalities in the system of inequalities is the same as the number of structural surfaces that cut the block.
4. The method for predicting chain collapse disasters in tunnel surrounding rock as described in claim 1, characterized in that, After finding all contact blocks of the hazardous block, these contact blocks are classified. If the contact block is an inner wall block, it is ignored; otherwise, it is classified as an internal block and its hazard assessment is required.
5. The method for predicting chain collapse disasters in tunnel surrounding rock as described in claim 1, characterized in that, A dangerous block vector array is formed using the contact vectors of the contact blocks, and the directions of the contact vectors in the vector array are determined sequentially. If the contact vector is pointing downwards, ignore it and proceed to the next vector direction determination; if the contact vector is pointing upwards, remove it from the vector array and perform block hazard assessment. If the judgment result is a dangerous block, the determination and hazard judgment of the contact block of the dangerous block are repeated; otherwise, the contact block is ignored and the judgment continues to the next block.
6. The method for predicting chain collapse disasters in tunnel surrounding rock as described in claim 5, characterized in that, The contact vectors in this vector array all point to the interior of the hazardous block.
7. A tunnel surrounding rock cascading collapse disaster prediction system, characterized in that, A method for predicting cascading collapses of surrounding rock in tunnels as described in any one of claims 1-6 includes: The model building module is configured to: collect rock mass structural surface information and build a tunnel surrounding rock block model based on the rock mass structural surface information; The inner wall dangerous block identification module is configured to: search all inner wall blocks based on the tunnel surrounding rock block model and identify the dangerous blocks in the inner wall blocks; The contact block search module is configured to: search for contact blocks of the hazardous block, determine the block type of the contact blocks, and find the contact blocks that have not been determined as hazardous. The contact block identification module is configured to: perform hazard identification on the blocks that have not undergone hazard identification; if they are not dangerous blocks, they are ignored; if they are dangerous blocks, the search for contact blocks of the dangerous blocks, i.e., the hazard determination, is repeated until none of the contact blocks of the dangerous blocks are dangerous blocks, thus obtaining information on all dangerous blocks in the tunnel surrounding rock.
8. A computing device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method according to any one of claims 1-6.
9. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the method described in any one of claims 1-6.