CN112182732A - Method and device for calculating breaking depth of toppled deformation body and storage medium - Google Patents
Method and device for calculating breaking depth of toppled deformation body and storage medium Download PDFInfo
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Abstract
The invention discloses a method and a device for calculating the breaking depth of a toppled deformation body and a storage medium, and aims to solve the technical problem that an accurate method for calculating the breaking depth of the toppled deformation body is lacked in the prior art. It includes: acquiring a rock stratum tensile stress balance equation based on a mechanical model of the single-layer beam slab, and calculating the critical fracture depth of the primary fracture of the single rock stratum; forming a critical fracture depth set by using the critical fracture depth of each stage of fracture of the single rock stratum, updating a rock stratum tensile stress balance equation according to the critical fracture depth set, and iteratively calculating the critical fracture depth of the next stage of fracture of the single rock stratum; and finishing iterative calculation according to the maximum rock layer bending depth criterion to obtain the final breaking depth of the toppled deformation body. The method can quickly and accurately calculate the breaking depth of the toppling deformation body, and provides a quantitative evaluation basis for the toppling deformation of the slope.
Description
Technical Field
The invention relates to a method and a device for calculating the breaking depth of an inclined deformation body and a storage medium, and belongs to the technical field of geological engineering, geotechnical engineering and hydraulic and hydroelectric engineering.
Background
In recent years, the rapid development of economic construction in China has increased along with the increase of the requirements on energy demand and the development of traffic and hydraulic and hydroelectric engineering, a large number of important infrastructures need to be constructed perfectly, and particularly the safety and stability of bank slopes of reservoir areas of hydropower stations corresponding to the important infrastructures in hydraulic and hydroelectric engineering are increasingly prominent. The breaking damage of the toppled deformation body is consistent at home and abroad, under the action of the self-weight stress of the rock mass, the toppling moment generated at the maximum bending moment point of the rock pillar is larger than the anti-toppling moment, the tensile stress of the maximum bending moment point is concentrated, when the tensile stress is generated to be larger than the tensile strength of a rock stratum material, a tensile crack is formed, and finally the breaking damage is carried out; therefore, the condition of reversely inclining the layered rock slope and having a good temporary condition is an important condition for the occurrence of the toppling deformation.
After the side slope is toppled and broken, the position pole of the sliding surface of the toppled deformation body can be searched and determined through the breaking depth of the rock stratum, the scale of the landslide can be estimated through the breaking depth, the significance of the research on the stability of the side slope is great, and however, no clear calculation method for the breaking depth of the toppled body exists at present.
Disclosure of Invention
Aiming at the problem that an accurate calculation method for the fracture depth of the toppled body is lacked in the prior art, the invention provides a calculation method, a calculation device and a storage medium for the fracture depth of the toppled deformation body.
In order to solve the technical problems, the invention adopts the following technical means:
in a first aspect, the invention provides a method for calculating the breaking depth of a pouring deformation body, which comprises the following steps:
acquiring a mechanical model of a single-layer plate beam for dumping a single rock stratum of a deformation body;
acquiring a rock stratum tensile stress balance equation based on a mechanical model of the single-layer beam plate, and calculating the critical fracture depth of the primary fracture of the single rock stratum by using the rock stratum tensile stress balance equation;
updating a rock stratum tensile stress balance equation according to the critical fracture depth of the primary fracture of the single rock stratum, and calculating the critical fracture depth of the secondary fracture of the single rock stratum by using the updated rock stratum tensile stress balance equation;
forming a critical fracture depth set by using the critical fracture depth of each stage of fracture of the single rock stratum, updating a rock stratum tensile stress balance equation according to the critical fracture depth set, and iteratively calculating the critical fracture depth of the next stage of fracture of the single rock stratum;
and finishing iterative calculation according to the maximum rock layer bending depth criterion to obtain the final breaking depth of the toppled deformation body.
With reference to the first aspect, further, the mechanical model of the single-layer plate girder is as follows:
setting the extending direction of the rock stratum surface of the toppled deformation body as an x axis, the normal direction of the rock stratum surface of the toppled deformation body as a y axis, and the dip angle of the rock stratum of the toppled deformation body as alpha and 0 degree<α<90 degrees, the thickness of the single-stratum plate beam of the single stratum of the toppled deformation body is b, and the fracture depth of the single-stratum plate beam is h; at the critical bending point (0, b/2) of the poured deformation body, the most satisfiedLarge tensile stress sigmaxGreater than tensile strength of rock formation value sigmat。
With reference to the first aspect, further, the expression of the formation tensile stress balance equation is as follows:
wherein the content of the first and second substances,
N1＝W1sinα，W1＝γbh1gamma is the severity of the rock formation, h1Critical fracture depth for primary fracture of a single formation;
according to σx＞σtThe rock stratum tensile stress balance equation is arranged to obtain the critical fracture depth h of the primary fracture of the single rock stratum1The calculation formula of (2):
with reference to the first aspect, further, the formation tensile stress balance equation is updated according to the critical fracture depth of the primary fracture of the single formation, and the expression of the updated formation tensile stress balance equation is as follows:
wherein the content of the first and second substances,
N2＝W1sinα+W2sinα，W2＝γbh2，h2critical fracture depth for a single formation secondary fracture;
critical fracture depth for single formation secondary fractureh2The calculation formula of (2) is as follows:
with reference to the first aspect, further, the method for calculating the critical fracture depth of the next-stage fracture of a single rock formation includes the following steps:
and (4) setting the current time, generating n-1 grade fracture damage in a single rock stratum, and acquiring a critical fracture depth set H ═ H1,h2,…,hn-1In which hn-1Critical fracture depth for single rock stratum n-1 grade fracture;
and updating a rock stratum tensile stress balance equation by using the critical fracture depth set H:
wherein the content of the first and second substances,
Nn＝W1sinα+W2sinα+…+Wn-1sinα+Wnsinα，Wn-1＝γbhn-1，Wn＝γbhn，hnthe critical fracture depth of single rock stratum n-level fracture is obtained, and n is a positive integer;
critical fracture depth of the next grade fracture of a single rock stratum, i.e. critical fracture depth h of n grade fracture of a single rock stratumnThe calculation formula of (2) is as follows:
with reference to the first aspect, further, the critical fracture depth of the poured deformation body satisfies: h is1＜h2＜...＜hn。
With reference to the first aspect, further, the criterion of the maximum rock formation bending depth is as follows: and after the rock stratum of the toppled deformation body is broken in one or more stages, forming intermittent breaking tension cracks in the toppled deformation body, and when the intermittent breaking surfaces in the toppled deformation body are communicated to form a continuous breaking zone and the shear strength on the continuous breaking zone is smaller than the downward sliding force applied by the breaking body, finishing the breaking damage of the toppled deformation body and generating the sliding damage.
And in combination with the first aspect, further, the iterative computation is ended according to a rock stratum maximum bending depth criterion, and the corresponding critical fracture depth of the single rock stratum at the end of the iterative computation is the final fracture depth of the toppled deformation body.
In a second aspect, the invention provides a device for calculating the breaking depth of a toppled deformable body, which comprises a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate in accordance with the instructions to perform the steps of the method of the first aspect.
In a third aspect, the invention proposes a computer-readable storage medium having stored thereon a computer program which, when being executed by a processor, carries out the steps of the method according to the first aspect.
The following advantages can be obtained by adopting the technical means:
the invention provides a method and a device for calculating the fracture depth of a toppled deformation body and a storage medium, which simplify the problem of rock slope toppling damage into the problem that a single rock layer plate beam is fractured under the action of self-weight stress, wherein the fracture depth of the single rock layer plate beam is the fracture depth of a rock layer, namely the fracture depth of the toppled deformation body. According to the method, a mechanical model is obtained through mechanical analysis of a single-layer plate beam, then a rock stratum tensile stress balance equation is obtained according to the toppling fracture failure principle, the critical fracture depth of single fracture of a single rock stratum is deduced, the limit fracture stage number of the rock stratum is determined according to the rock stratum maximum fracture depth criterion, and the final fracture depth of the toppling deformation body is obtained. The method simplifies the calculation problem of the rupture depth of the toppled deformation body, has concise rationality in approximate analysis, simple calculation process and high calculation speed, obtains the rupture depth of the toppled deformation body consistent with the actual toppled slope damage mode, has accurate calculation result, can meet the actual design calculation requirement, can provide quantitative evaluation basis for slope toppling deformation, and is favorable for the research of slope stability of the toppled deformation body.
Drawings
FIG. 1 is a flow chart of the steps of a method for calculating the fracture depth of a toppled deformable body according to the present invention.
FIG. 2 is a mechanical model diagram of a single-layer plate girder according to an embodiment of the present invention.
FIG. 3 is a schematic illustration of the fracture of a primary fracture of a single formation in an embodiment of the present invention.
FIG. 4 is a mechanical analysis of a second grade fracture of a formation in an embodiment of the invention.
FIG. 5 is a schematic illustration of the fracture of a single formation secondary fracture in an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the accompanying drawings as follows:
the invention provides a method for calculating the breaking depth of a toppled deformation body, which comprises the following steps of:
step 1, obtaining a mechanical model of a single-layer plate beam for dumping a single rock stratum of a deformation body;
step 2, acquiring a rock stratum tensile stress balance equation based on the mechanical model of the single-layer beam plate, and calculating the critical fracture depth of the primary fracture of the single rock stratum by using the rock stratum tensile stress balance equation;
step 3, updating a rock stratum tensile stress balance equation according to the critical fracture depth of the primary fracture of the single rock stratum, and calculating the critical fracture depth of the secondary fracture of the single rock stratum by using the updated rock stratum tensile stress balance equation;
step 4, forming a critical fracture depth set by using the critical fracture depth of each stage of fracture of the single rock stratum, updating a rock stratum tensile stress balance equation according to the critical fracture depth set, and iteratively calculating the critical fracture depth of the next stage of fracture of the single rock stratum;
and 5, finishing iterative calculation according to the maximum rock stratum bending depth criterion to obtain the final breaking depth of the toppled deformation body.
Generally, the slope body subjected to toppling deformation is sedimentary rock and distributed in a layered manner, the problem of fracture of the toppling deformation body is simplified into the problem of fracture of a single rock stratum single-layer plate beam on the slope body, and when the primary fracture depth of the toppling deformation body is calculated, a mechanical model of the single-layer plate beam needs to be applied, and as shown in fig. 2, the mechanical model of the single-layer plate beam is specifically as follows:
setting the extending direction of the rock stratum surface of the toppled deformation body as an x axis, the normal direction of the rock stratum surface of the toppled deformation body as a y axis, and the dip angle of the rock stratum of the toppled deformation body as alpha and 0 degree<α<90 degrees, the thickness of the single-layer plate beam of the single rock stratum for dumping the deformation body is b, the fracture depth of the single-layer plate beam of the single rock stratum is h, and the gravity of the single-layer plate beam of the single rock stratum is W1(ii) a At the critical bending point (0, b/2) of the toppled deformation body, the maximum tensile stress sigma is satisfiedxGreater than tensile strength of rock formation value sigmat，σtIs σxIs measured.
In the embodiment of the invention, the fracture position and the fracture form of the primary fracture of the single rock stratum in the layered reverse-inclined slope are shown in fig. 3, wherein the Aydan reference plane is parallel to the normal line of the layer surface, the included angle between the Adhikary reference plane and the normal line of the layer surface is theta, and the Adhikary is verified by experiments to be generally 12-20 degrees. The slope is in spatial distribution, and the toe of the slope is the district that slides, and the slope body middle part is for empting the deformation zone, and slope top table portion is for empting the deformation influence district, and the fracture face lies in and emptys the deformation zone and topples between the deformation influence district.
According to the mechanical model analysis, a rock layer tensile stress balance equation can be obtained, and the specific expression is as follows:
wherein the content of the first and second substances,
N1＝W1sinα，W1＝γbh1gamma is the severity of the rock formation, h1Is the critical fracture depth of the primary fracture of a single formation.
Simultaneous equations (7) and σx＞σtArranging the tensile stress equilibrium equation of the rock stratum, and utilizing sigma in the arranging processtInstead of sigmaxAnd obtaining a solving equation of the rock stratum critical fracture depth:
due to h1Is greater than 0, so the critical fracture depth h of the primary fracture of the single rock formation can be obtained according to the formula (8)1The calculation formula of (2):
the rock stratum will not stop deforming after breaking, the original fixed end after primary breaking of the rock stratum will become free end due to the broken surface, so the rock stratum will continue bending, breaking and deforming under the action of self-weight stress. When the derivation of the second fracture is carried out, the rock stratum is not deviated after the first fracture, no tensile fracture is formed, the fracture surface is flat and smooth, and the derivation process similar to the primary fracture is adopted to obtain the critical fracture depth of the secondary fracture of the single rock stratum.
In the actual dumping deformation process, the stratum is subjected to interlayer extrusion after being broken, the stratum is deviated, the deviation amount is very small, and the deviation error can be ignored through approximate calculation.
The specific operation of step 3 is as follows:
updating the formation tensile stress equilibrium equation based on the critical fracture depth for a primary fracture of a single formation, FIG. 4 is a mechanical analysis of a secondary fracture of a formation, in which two formation segments, F, appear due to a single fracture of the formation1Is the interaction force between two rock intervals, W2Is the gravity of the second interval. The expression for the updated formation tensile stress balance equation from fig. 4 is as follows:
wherein the content of the first and second substances,
N2＝W1sinα+W2sinα，W2＝γbh2，h2the critical fracture depth of the second grade fracture of the single rock stratum.
Deducing the critical fracture depth h of the secondary fracture of the single rock stratum according to the formula (10)2The calculation formula of (2) is as follows:
fig. 5 is a schematic diagram of the fracture position and the fracture form after the secondary fracture of the rock stratum in the embodiment of the invention, and it can be seen from the diagram that after the secondary fracture of the rock stratum, the fracture depth of the toppling deformation body is increased, the spatial partitions of the slope body are kept consistent, and the ranges of the slippage area, the toppling deformation area and the toppling influence area are enlarged.
As long as the condition that the rock stratum is continuously toppled and broken is met, namely as long as the toppling moment generated by the maximum bending moment point is greater than the anti-toppling moment, the maximum tensile stress is greater than the tensile strength value of the rock stratum, the rock stratum can be continuously toppled and deformed, the breaking depth of each toppling and deformation is not only related to rock stratum parameters, slope body forms and the like, but also related to the breaking depth of each previous stage, and the critical breaking depth of each stage of breaking can be iteratively calculated through deduction of the method.
The specific operation of step 4 is as follows:
step 401, setting the current time, generating n-1 grade fracture damage in a single rock stratum, and forming a critical fracture depth set H ═ H at the current time by using the critical fracture depths of the previous n-1 fractures1,h2,…,hn-1In which hn-1The critical fracture depth of a single rock stratum n-1 grade fracture.
Step 402, updating a rock layer tensile stress balance equation by using the critical fracture depth set H:
wherein the content of the first and second substances,
Nn＝W1sinα+W2sinα+…+Wn-1sinα+Wnsinα，Wn-1＝γbhn-1，Wn＝γbhn，hnthe critical fracture depth of n-grade fracture of a single rock stratum is shown, and n is a positive integer.
Step 403, calculating the critical fracture depth of the next grade fracture of the single rock layer, i.e. the critical fracture depth h of the n grade fracture of the single rock layer, by using the formula (12)nThe specific calculation formula is as follows:
according to the research of the invention, the stress form of the rock stratum in the process of toppling and breaking is basically consistent, for multi-stage breaking, due to the influence of the broken rock pillar at the upper part, toppling of the rock stratum at the lower part is blocked, so that the rock stratum is more difficult to topple and break and deform when the rock stratum develops downwards, and the required breaking depth is larger, namely the critical breaking depth of the toppled and deformed body is satisfied: h is1＜h2＜...＜hn。
And (3) as the rock stratum is continuously toppled and broken, the rock stratum has a maximum limit breaking grade which meets the criterion of the maximum bending depth of the rock stratum, and the rock stratum can not be broken after reaching the limit breaking grade, so that the iterative calculation in the step 4 can be finished, and the critical breaking depth corresponding to the limit breaking grade, namely the critical breaking depth of the single rock stratum corresponding to the end of the iterative calculation, is obtained and is used as the final breaking depth of the toppled deformation body.
The maximum bending depth criterion of the rock stratum is as follows: after the rock stratum of the toppling deformation body is broken in one or more stages, a large number of intermittent breaking tension cracks are formed in the slope body which is subjected to toppling deformation, and the deformation strength is gradually weakened from the surface of the slope body to the inside of the slope body, so that after the intermittent breaking surface in the slope body penetrates through to form a continuous breaking zone, if the shear strength on the continuous breaking zone is smaller than the downward sliding force applied by the breaking body, the toppling deformation body can be broken and damaged, and the whole sliding instability damage is generated.
According to the rock stratum maximum bending depth criterion, the fracture depth of the rock stratum is determined, the method is very important for searching and determining the position of the sliding surface of the toppled deformation body, the scale of the landslide can be estimated according to the fracture depth, and the stability of the landslide of the toppled deformation body is evaluated.
The critical snap depth expression in the present invention can be simplified as:
wherein h isiThe critical fracture depth of i-grade fracture of a single rock formation,
B＝-γsinα，Ci∈{C1,C2,…,Cj}，C1＝-σt，Ci＝-[σt+γsinα(h1+h2+...+hi-1)]and j is the ultimate fracture progression of the formation.
The invention also provides a device for calculating the breaking depth of the toppled deformation body, which comprises a processor and a storage medium; wherein the storage medium is configured to store instructions; the processor is used for operating according to the instructions to execute the steps of the calculation method for the breaking depth of the pouring deformation body.
The invention also proposes a computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method for calculating the breaking depth of a poured deformation according to the invention.
The method simplifies the rock stratum slope toppling failure problem into the problem that a single rock stratum single-layer plate beam is broken under the action of the dead weight stress, simplifies the calculation problem of the breaking depth of the toppling deformation body, and has concise rationality in approximate analysis. The method deduces the critical fracture depth of single fracture of a single rock stratum through mechanical analysis of the single-layer plate girder, determines the limit fracture stage number of the rock stratum according to the maximum rock stratum bending depth criterion, and further obtains the final fracture depth of the toppled deformation body.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (10)
1. A method for calculating the breaking depth of a pouring deformation body is characterized by comprising the following steps:
acquiring a mechanical model of a single-layer plate beam for dumping a single rock stratum of a deformation body;
acquiring a rock stratum tensile stress balance equation based on a mechanical model of the single-layer beam plate, and calculating the critical fracture depth of the primary fracture of the single rock stratum by using the rock stratum tensile stress balance equation;
updating a rock stratum tensile stress balance equation according to the critical fracture depth of the primary fracture of the single rock stratum, and calculating the critical fracture depth of the secondary fracture of the single rock stratum by using the updated rock stratum tensile stress balance equation;
forming a critical fracture depth set by using the critical fracture depth of each stage of fracture of the single rock stratum, updating a rock stratum tensile stress balance equation according to the critical fracture depth set, and iteratively calculating the critical fracture depth of the next stage of fracture of the single rock stratum;
and finishing iterative calculation according to the maximum rock layer bending depth criterion to obtain the final breaking depth of the toppled deformation body.
2. The method for calculating the breaking depth of the toppled deformation body according to claim 1, wherein the mechanical model of the single-layer plate beam is as follows:
setting the extending direction of the rock stratum surface of the toppled deformation body as an x axis, the normal direction of the rock stratum surface of the toppled deformation body as a y axis, and the dip angle of the rock stratum of the toppled deformation body as alpha and 0 degree<α<90 degrees, the thickness of the single-stratum plate beam of the single stratum of the toppled deformation body is b, and the fracture depth of the single-stratum plate beam is h; at the critical bending point (0, b/2) of the toppled deformation body, the maximum tensile stress sigma is satisfiedxGreater than tensile strength of rock formation value sigmat。
3. The method for calculating the fracture depth of a dump variant according to claim 2, wherein the expression of the rock formation tensile stress equilibrium equation is as follows:
wherein the content of the first and second substances,
N1＝W1sinα，W1＝γbh1gamma is the severity of the rock formation, h1Critical fracture depth for primary fracture of a single formation;
according to σx＞σtThe rock stratum tensile stress balance equation is arranged to obtain the critical fracture depth h of the primary fracture of the single rock stratum1The calculation formula of (2):
4. the method of claim 3, wherein the formation tensile stress balance equation is updated according to the critical fracture depth of primary fracture of a single formation, and the expression of the updated formation tensile stress balance equation is as follows:
wherein the content of the first and second substances,
N2＝W1sinα+W2sinα，W2＝γbh2，h2critical fracture depth for a single formation secondary fracture;
critical fracture depth h of single rock stratum secondary fracture2The calculation formula of (2) is as follows:
5. a method for calculating the fracture depth of a dump variant according to any of claims 1 or 4, wherein the method for calculating the critical fracture depth of the next stage fracture of a single rock formation comprises the following steps:
and (4) setting the current time, generating n-1 grade fracture damage in a single rock stratum, and acquiring a critical fracture depth set H ═ H1,h2,…,hn-1In which hn-1Critical fracture depth for single rock stratum n-1 grade fracture;
and updating a rock stratum tensile stress balance equation by using the critical fracture depth set H:
wherein the content of the first and second substances,
Nn＝W1sinα+W2sinα+…+Wn-1sinα+Wnsinα，Wn-1＝γbhn-1，Wn＝γbhn，hnthe critical fracture depth of single rock stratum n-level fracture is obtained, and n is a positive integer;
critical fracture depth of the next grade fracture of a single rock stratum, i.e. critical fracture depth h of n grade fracture of a single rock stratumnThe calculation formula of (2) is as follows:
6. the method of claim 5, wherein the critical breaking depth of the poured deformation body satisfies the following requirements: h is1＜h2＜...＜hn。
7. The method of claim 1, wherein the criterion of maximum formation fracture depth is as follows: and after the rock stratum of the toppled deformation body is broken in one or more stages, forming intermittent breaking tension cracks in the toppled deformation body, and when the intermittent breaking surfaces in the toppled deformation body are communicated to form a continuous breaking zone and the shear strength on the continuous breaking zone is smaller than the downward sliding force applied by the breaking body, finishing the breaking damage of the toppled deformation body and generating the sliding damage.
8. The method for calculating the fracture depth of the dumped deformation body according to claim 7, wherein the iterative computation is ended according to a rock stratum maximum fracture depth criterion, and the corresponding critical fracture depth of the single rock stratum at the end of the iterative computation is the final fracture depth of the dumped deformation body.
9. The device for calculating the breaking depth of the toppled deformation body is characterized by comprising a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate in accordance with the instructions to perform the steps of the method according to any one of claims 1 to 8.
10. Computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 8.
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