Safety-to-boundary mining control method for slope in landslide-containing risk area

Abstract

The invention provides a safe in-boundary mining control method for a slope in a landslide-containing risk area, and belongs to the technical field of open-pit mining. Firstly, local transverse mining replacement filling and local slope pressing treatment are conducted on the two sides of the landslide-containing risk area at the same time, and then longitudinal mining and transverse mining alternate mixed construction is conducted on the landslide-containing risk area and a non-landslide risk area; and according to the slope stability coefficient of each stage, construction parameters of each stage are determined, a finite element calculation model is established according to the parameters of each stage, and the transverse mining replacement filling tracking distance is determined. And finally, drawing a project position plan of each stage to guide open-pit coal mining. According to the method, how to treat the local landslide risk area of the side slope and how to reach the boundary after treatment are considered, the problem of treatment lag of the landslide risk area is avoided, and effective technical support is provided for follow-up treatment and follow-up mining of the landslide risk area of the open pit coal mine.

Description

Technical Field

[0001] This invention belongs to the field of open-pit mining technology, specifically relating to a method for controlling the safe mining of slopes in areas with landslide risk. Background Technology

[0002] The purpose of controlling mining at the boundary of landslide-prone slopes is as follows: first, to improve slope stability and avoid casualties and equipment damage caused by landslides; second, to leave sufficient depth space for subsequent mining, increase the amount of deep resources recovered in open-pit mines, and maximize resource recovery.

[0003] Patent CN116006181A provides a construction scheme for an internal spoil heap in an open-pit mine that facilitates safe end-side mining. It fully utilizes the pressure effect of the internal spoil heap to improve the stability of the open-pit coal mine slope under end-side mining conditions, effectively avoiding geological disasters. Patent CN118895974A discloses a method for strong-drainage steep-side mining in open-pit mines. This method involves zoned mining of composite coal seams, providing parameters for the working side, end side, and internal spoil heap steps, the safe distance between the working side and internal spoil heap in multi-coal-seam horizontal mining, and methods for determining the mining process. This guides strong-drainage steep-side mining operations in open-pit mines, improving mining efficiency and quality. Patent CN113742949B discloses a method for determining the mining width of high-level coal seams in open-pit mines with composite coal seams. This method adjusts the width of each horizontal plate between coal seams, calculates the difference before and after adjusting the plate width, finds the relationship between the plate width and the mining width, and utilizes the internal spoil heap support effect to extract the high-level coal seam.

[0004] These patents all focus on the overall stability design and mining methods for open-pit mine slopes, without considering how to manage local landslide risk zones and how to ensure safe access to landslide boundaries after management. This can easily lead to delayed landslide risk zone management, resulting in large-scale landslides that also encroach on significant resources. Therefore, there is an urgent need to find a method for controlling the safe access to landslide risk zone slopes during mining, providing technical support for subsequent landslide risk zone management and mining operations in open-pit coal mines. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method for controlling the safe mining of slopes in areas with landslide risk.

[0006] This invention provides a method for controlling safe mining operations at the boundary of slopes in landslide-prone areas, comprising:

[0007] Based on the actual geological conditions at the site, the three-dimensional geological model, the slope morphology, and the historical information of geological drilling, n engineering geological profiles of the slope are drawn, and the n engineering geological profiles of the slope and the slope area are numbered, and the slope is divided into landslide risk zone P1 and non-landslide risk zone P2.

[0008] According to the "Design Code for Open-Pit Coal Mines", the slope safety reserve coefficient is determined based on the slope service life during each stage of construction.

[0009] Using the step form and mining parameters of the end slope and the step form and mining parameters of the internal spoil heap, the slope morphology design of the landslide risk zone P1 under the dual support control of local cross mining and replacement and local lateral slope pressing was carried out simultaneously. By judging whether the slope stability coefficient under the dual support control meets the slope safety reserve coefficient, the slope morphology, lateral slope body and replacement body morphology parameters of the first stage were determined.

[0010] Using the bench form and mining parameters of the longitudinal mining working face, the slope morphology of landslide risk zone P1 after longitudinal mining is designed. By judging whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, the slope morphology of the second stage and the transverse mining elevation after the longitudinal mining are determined.

[0011] Using the bench form and mining parameters of the horizontal mining working face, the slope morphology of the weak layer in the landslide risk zone P1 is designed for horizontal mining and replacement. By judging whether the slope stability coefficient after horizontal mining and replacement meets the slope safety reserve coefficient, the slope morphology, weak layer replacement length and replacement body morphology parameters of the third stage are determined.

[0012] Using the bench form and mining parameters of the longitudinal mining working face, the coal resources covered by the non-landslide risk zone P2 are longitudinally mined. By judging whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, the slope morphology of the fourth stage is determined.

[0013] Using the bench form and mining parameters of the cross-mining working face, the cross-mining replacement slope design was carried out in the non-landslide risk zone P2. By judging whether the slope stability coefficient after cross-mining replacement meets the slope safety reserve coefficient, the slope morphology and replacement body morphology parameters of the fifth stage were determined.

[0014] Based on the slope morphology, backfill and replacement body morphology parameters of the first stage, the slope morphology and transverse mining elevation after the completion of longitudinal mining in the second stage, the slope morphology, weak layer replacement length and replacement body morphology parameters of the third stage, the slope morphology of the fourth stage and the slope morphology and replacement body morphology parameters of the fifth stage, a finite element calculation model is established, and a plan view of the engineering location of each stage is drawn to guide open-pit coal mining.

[0015] The division of the slope into landslide risk zone P1 and non-landslide risk zone P2 includes:

[0016] Using the location of the weak layer in the landslide risk zone as the dividing line, the slope area from the surface to the weak layer in the landslide risk zone is designated as the landslide risk zone, numbered P1, and the slope area below the weak layer in the landslide risk zone is designated as the non-landslide risk zone, numbered P2.

[0017] The slope safety reserve coefficient includes: slope safety reserve coefficient K1 for the first stage, slope safety reserve coefficient K2 for the second stage, slope safety reserve coefficient K3 for the third stage, slope safety reserve coefficient K4 for the fourth stage, and slope safety reserve coefficient K5 for the fifth stage. The first stage is the local transverse mining and replacement and local slope protection treatment stage of landslide risk zone P1; the second stage is the longitudinal mining stage of landslide risk zone P1 to the transverse-longitudinal mining boundary; the third stage is the transverse mining and replacement stage of landslide risk zone P1 to the weak layer stage of landslide risk zone; the fourth stage is the longitudinal mining stage of non-landslide risk zone P2; and the fifth stage is the transverse mining and replacement stage of non-landslide risk zone P2.

[0018] The process involves determining whether the slope stability coefficient under dual-support control meets the slope safety reserve coefficient, and then determining the slope morphology, backfill morphology parameters, and replacement morphology parameters for the first stage, including:

[0019] For the slope morphology design under the dual support control of local cross-mining and local lateral reinforcement on both sides of the landslide risk zone P1, the Morgenstern method was used to obtain the slope stability coefficient after local cross-mining and local lateral reinforcement.

[0020] When the slope stability coefficient after local cross-mining and replacement is greater than the slope safety reserve coefficient K1 of the first stage, and the slope stability coefficient after local rib stabilization is greater than the slope safety reserve coefficient K1 of the first stage, the slope morphology, rib stabilization body and replacement body morphology parameters of the first stage are determined.

[0021] The process of determining whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, and determining the slope morphology for the second stage and the transverse mining elevation after the completion of longitudinal mining, includes:

[0022] For the landslide risk zone P1, the longitudinal mining slope morphology was designed, and the Morgenstern method was used to obtain the slope stability coefficient after longitudinal mining depth of each slope engineering geological profile.

[0023] Calculate the difference m1 between the slope stability coefficient after longitudinal mining and drawdown of each slope engineering geological profile and the slope safety reserve coefficient K2 in the second stage;

[0024] If all differences m1 are less than or equal to a preset threshold, determine the slope morphology of the second stage and the transverse mining elevation after the longitudinal mining is completed.

[0025] The process of determining the slope morphology, weak layer replacement length, and replacement body morphology parameters in the third stage by judging whether the slope stability coefficient after transverse mining and replacement meets the slope safety reserve coefficient includes:

[0026] For the weak layer in the landslide risk zone P1, a transverse mining and replacement design was carried out, and the Morgenstern method was used to obtain the slope stability coefficient after transverse mining and replacement of each slope engineering geological profile.

[0027] Calculate the difference m2 between the slope stability coefficient after cross-mining and replacement in each slope engineering geological profile and the slope safety reserve coefficient K3 in the third stage.

[0028] When all differences m2 are less than or equal to the preset threshold, the slope morphology, weak layer replacement length, and replacement body morphology parameters of the third stage are determined.

[0029] The method utilizes the bench form and mining parameters of the longitudinal mining working face to conduct longitudinal mining of the coal resources overlying the non-landslide risk zone P2. By determining whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, the slope morphology of the fourth stage is determined, including:

[0030] For longitudinal mining of coal resources overlaid in P2 non-landslide risk zone, the Morgenstern method was used to obtain the slope stability coefficient of each slope engineering geological profile after longitudinal mining in P2 non-landslide risk zone.

[0031] Calculate the difference m3 between the slope stability coefficient after longitudinal mining of the non-landslide risk zone P2 and the slope safety reserve coefficient K4 in the fourth stage for each slope engineering geological profile.

[0032] The slope morphology of the fourth stage is determined when all differences m3 are less than or equal to a preset threshold.

[0033] The process of determining the slope morphology and replacement body morphology parameters in the fifth stage by judging whether the slope stability coefficient after transverse mining and replacement meets the slope safety reserve coefficient includes:

[0034] For the non-landslide risk zone P2, the slope design of cross-mining and replacement was carried out, and the Morgenstern method was used to obtain the slope stability coefficient of each slope after cross-mining and replacement in the non-landslide risk zone P2.

[0035] Calculate the difference m4 between the slope stability coefficient and the slope safety reserve coefficient K5 in the fifth stage for each slope engineering geological profile after cross-mining and replacement in the non-landslide risk zone P2.

[0036] When all differences m4 are less than or equal to the preset threshold, the slope morphology and replacement body morphology parameters for the fifth stage are determined.

[0037] Beneficial effects:

[0038] This invention proposes a method for controlling the safe mining of slopes with landslide risk zones. It considers how to manage local landslide risk zones and how to reach the boundary after management. It adopts a slope morphology design under dual support control of local transverse mining and replacement and local rib stabilization. It also combines transverse and longitudinal mining methods to avoid the problem of delayed landslide risk zone management and provides effective technical support for subsequent landslide risk zone management and mining in open-pit coal mines. Attached Figure Description

[0039] Figure 1 This application provides an embodiment of a method for controlling safe mining at the boundary of a slope in a landslide risk zone;

[0040] Figure 2 A plan view of the east side cross-section of this application embodiment;

[0041] Figure 3 DB1 engineering geological profile diagram of this application embodiment;

[0042] Figure 4 DB2 engineering geological profile diagram of this application embodiment;

[0043] Figure 5 DB3 engineering geological profile diagram of this application embodiment;

[0044] Figure 6 DB4 engineering geological profile diagram of this application embodiment;

[0045] Figure 7 The construction locations of the partial replacement fill and temporary lining in this application embodiment;

[0046] Figure 8 The partial replacement body morphology of this application embodiment;

[0047] Figure 9 The temporary pressing body form of this application embodiment;

[0048] Figure 10 The relationship curve between the length of the temporary slab support and the slope stability in this embodiment of the application;

[0049] Figure 11 The embodiment of this application describes the maximum longitudinal mining slope boundary shape of the DB1 landslide risk zone P1;

[0050] Figure 12 The embodiment of this application describes the maximum longitudinal mining slope boundary shape of the DB2 landslide risk zone P1;

[0051] Figure 13 The embodiment of this application describes the maximum longitudinal mining slope boundary shape of the DB3 landslide risk zone P1;

[0052] Figure 14 The embodiment of this application describes the maximum longitudinal mining slope boundary shape of the DB4 landslide risk zone P1;

[0053] Figure 15 The slope morphology of the DB1 landslide risk zone P1 after transverse mining and replacement in this application embodiment;

[0054] Figure 16 The slope morphology of the DB2 landslide risk zone P1 after transverse mining and replacement in this application embodiment;

[0055] Figure 17 The slope morphology of the DB3 landslide risk zone P1 after transverse mining and replacement in this application embodiment;

[0056] Figure 18 The slope morphology of the DB4 landslide risk zone P1 after transverse mining and replacement in this application embodiment;

[0057] Figure 19 The cross-sectional shape of the slope from the bottom of the coal seam to the longitudinal mining of the P2 non-landslide risk zone in this application embodiment;

[0058] Figure 20 The cross-sectional shape of the slope from the longitudinal mining of the P2 non-landslide risk zone DB2 to the coal seam floor in this embodiment of the application;

[0059] Figure 21 The cross-sectional shape of the slope from the bottom of the coal seam to the longitudinal mining of the P2 non-landslide risk zone in this application embodiment;

[0060] Figure 22 The cross-sectional shape of the slope from the bottom of the coal seam to the longitudinal mining of the P2 non-landslide risk zone in this application embodiment;

[0061] Figure 23 The spatial morphology of the slope after transverse mining and replacement in the DB1 non-landslide risk zone P2 of this application embodiment;

[0062] Figure 24 The spatial morphology of the slope after transverse mining and replacement in the DB2 non-landslide risk zone P2 of this application embodiment;

[0063] Figure 25 The spatial morphology of the slope after transverse mining and replacement in the DB3 non-landslide risk zone P2 of this application embodiment;

[0064] Figure 26 The spatial morphology of the slope after transverse mining and replacement in the DB4 non-landslide risk zone P2 of this application embodiment;

[0065] Figure 27 A schematic diagram of the finite element calculation model of this application embodiment;

[0066] Figure 28A schematic diagram of numerical simulation results under a 50m transverse mining and replacement step distance in this application embodiment;

[0067] Figure 29 A schematic diagram of numerical simulation results under a 100m transverse mining and replacement step distance in this application embodiment;

[0068] Figure 30 A schematic diagram of numerical simulation results under a 150m transverse mining and replacement step distance in this application embodiment;

[0069] Figure 31 A schematic diagram of numerical simulation results under a 200m transverse mining and replacement step distance in this application embodiment;

[0070] Figure 32 Plan view of the longitudinal mining depth location of landslide risk zone P1 in this application embodiment;

[0071] Figure 33 Plan view of the initial foundation pit location of the landslide risk zone P1 horizontal mining and replacement in this application embodiment;

[0072] Figure 34 Plan view of the mid-term engineering location of the landslide risk zone P1 horizontal mining and replacement project in this application embodiment;

[0073] Figure 35 Plan view of the final engineering location of the landslide risk zone P1 transverse mining and replacement in this application embodiment;

[0074] Figure 36 Plan view of the boundary location of longitudinal mining in non-landslide risk zone P2 in this application embodiment;

[0075] Figure 37 Plan view of the mid-term engineering location of cross-mining and replacement in the non-landslide risk zone P2 in this application embodiment;

[0076] Figure 38 Plan view of the final engineering location of the non-landslide risk zone P2 horizontal mining and replacement in this application embodiment. Detailed Implementation

[0077] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0078] Example:

[0079] This embodiment provides a method for controlling the safe mining of slopes in areas with landslide risk, such as... Figure 1 As shown, it includes:

[0080] Step S1:

[0081] Based on the actual geological conditions at the site, the three-dimensional geological model, the slope morphology, and the historical information of geological drilling, n engineering geological profiles of the slope are drawn, and the n engineering geological profiles of the slope and the slope area are numbered, and the slope is divided into landslide risk zone P1 and non-landslide risk zone P2.

[0082] In this embodiment, based on the on-site geological realism, three-dimensional geological model, slope morphology and geological drilling history information, n typical engineering geological profiles are drawn, namely the slope engineering geological profiles of n slopes, and the slope engineering geological profiles are numbered as DB1, DB2, ..., DBn.

[0083] The eastern side of an open-pit mine experienced two instances of localized deformation on March 22, 2024, and April 1, 2024, with a total deformation area of ​​627,000 m². 2 The slope is approximately 1270m long from north to south and 550m long from east to west, with deformation steps ranging from +860° to +980°, a difference in elevation of 120m. Therefore, considering the current state of the stripping project, the extent of the deformation zone, and the slope sections analyzed in the calculations, four typical engineering geological profiles were drawn perpendicular to the current east flank slope trend in November 2024, as shown below. Figure 2 As shown. They are respectively numbered DB1, DB2, DB3, and DB4, and their engineering geological profiles are as follows. Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown.

[0084] Using the location of the weak layer in the landslide risk zone as the dividing line, the slope area between the surface and the weak layer in the landslide risk zone is named the landslide risk zone and numbered P1, and the slope area below the weak layer in the landslide risk zone is named the non-landslide risk zone and numbered P2.

[0085] In this embodiment, based on the slope engineering geological profile, the location of the weak layer in the slope risk zone is used as the dividing line. The slope area between the surface and the weak layer in the landslide risk zone is named the landslide risk zone and numbered P1, and the slope area below the weak layer in the landslide risk zone is named the non-landslide risk zone and numbered P2.

[0086] The numbering is as follows: Figure 2 As shown, the numbering positions are detailed in Table 1;

[0087] Table 1. Summary Table of Slope Area Numbers;

[0088] ;

[0089] Step S2: According to the "Design Code for Open-Pit Coal Mines" (GB50197—2015), based on the slope service life, determine the slope safety reserve coefficient during each stage of construction, including:

[0090] Step S2.1: Based on the open-pit coal mine design, determine the bench form and mining parameters of the horizontal mining working side, the vertical mining working side, the end side, and the inner spoil heap slope;

[0091] In this embodiment, based on the open-pit coal mine mining design, the bench form and mining parameters of the transverse mining working side, longitudinal mining working side, end side and internal spoil heap of each slope area are detailed in Table 2.

[0092] Table 2 Summary of Mining Parameters and Bench Types;

[0093] ;

[0094] Step S2.2: According to the "Code for Design of Open-Pit Coal Mines" (GB50197-2015), determine the safety reserve factor K of the slope during each stage of construction based on the slope's service life. n ;

[0095] In this embodiment, the safety reserve coefficient of the slope during each stage of construction is determined according to the service life of the slope and the "Code for Design of Open-pit Coal Mines" (GB50197-2015), as detailed in Table 3.

[0096] Table 3 Summary of mining parameters and bench types;

[0097] ;

[0098] In this embodiment, the slope safety reserve coefficient includes: slope safety reserve coefficient K1 in the first stage, slope safety reserve coefficient K2 in the second stage, slope safety reserve coefficient K3 in the third stage, slope safety reserve coefficient K4 in the fourth stage, and slope safety reserve coefficient K5 in the fifth stage. The first stage is the local transverse mining and replacement and local slope protection treatment stage of landslide risk zone P1; the second stage is the stage of longitudinal mining in landslide risk zone P1 to the transverse-longitudinal mining boundary line (the transverse-longitudinal mining boundary line is the elevation of transverse mining and replacement after longitudinal mining of each section); the third stage is the stage of transverse mining and replacement in landslide risk zone P1 to the weak layer stage of landslide risk zone; the fourth stage is the longitudinal mining stage of non-landslide risk zone P2; and the fifth stage is the transverse mining and replacement stage of non-landslide risk zone P2.

[0099] Step S3: Using the bench form and mining parameters of the end slope and the bench form and mining parameters of the internal spoil heap, the slope morphology design is carried out simultaneously on both sides of the landslide risk zone P1 (in this embodiment, slope engineering geological profiles are designed on both sides of the landslide risk zone P1; specifically, slope engineering geological profile DB1 is designed on one side of the landslide risk zone P1, and slope engineering geological profile DB3 is designed on the other side of the landslide risk zone) under the dual support control of local cross-mining and local lateral slope pressing. By judging whether the slope stability coefficient under the dual support control meets the slope safety reserve coefficient, the slope morphology, lateral slope body, and replacement body morphology parameters of the first stage are determined. Using the slope stability coefficient and the slope safety reserve coefficient, local cross-mining and local lateral slope pressing are carried out simultaneously on the slope engineering geological profiles on both sides of the landslide risk zone to determine the construction parameters of the first stage, including:

[0100] Step S3.1: Design the slope morphology for both sides of the landslide risk zone P1 under the dual support control of local cross-mining and local lateral reinforcement. Use the Morgenstern method to obtain the slope stability coefficient after local cross-mining and local lateral reinforcement.

[0101] Step S3.2: When the slope stability coefficient after local cross-cutting and replacement is greater than the slope safety reserve coefficient K1 of the first stage, and the slope stability coefficient after local lateral slope treatment is greater than the slope safety reserve coefficient K1 of the first stage, determine the slope morphology, construction location, and morphological parameters of the lateral slope and replacement body for local cross-cutting and replacement and local lateral slope treatment, that is, the slope morphology, lateral slope and replacement body morphological parameters of the first stage.

[0102] In this embodiment, to prevent the landslide risk area from sliding again during the treatment process, the slope morphology design of the engineering geological profiles of the slopes on both sides of the landslide risk area P1 is required to be carried out under the dual support control of local cross-mining and replacement and temporary sloping (temporary sloping is local sloping treatment).

[0103] Temporary remediation in conventional landslide risk areas typically employs a single treatment scheme, such as localized lateral slope reinforcement or lateral excavation and replacement. However, for large-scale landslide risk areas, a single treatment scheme is not suitable. Therefore, it is necessary to design the construction locations of localized replacement bodies and temporary lateral slope reinforcement bodies in the slope remediation scheme based on the location of the landslide risk area, the occurrence conditions of weak layers, and the physical and mechanical parameters of the rock. In areas where the weak layers are exposed shallowly, lateral excavation and replacement are used (i.e., lateral excavation and replacement are applied to areas on one side of the landslide risk area where the exposed weak layers are less than or equal to a pre-set depth threshold). In areas where the weak layers are exposed deeply, localized lateral slope reinforcement is used (i.e., localized lateral slope reinforcement is applied to areas on the other side of the landslide risk area where the exposed weak layers are exposed greater than a pre-set depth threshold). The Morgenstern-Price method is used to obtain the slope stability coefficient Fs after localized lateral excavation and replacement. 11 And the slope stability coefficient Fs after temporary lining 12 When the constraint condition Fs is satisfied 11 K1 and Fs 12 When K1 is reached, the construction location and morphological parameters of the local replacement fill and temporary backfill body are determined.

[0104] In this embodiment, to prevent the landslide risk zone from sliding again during the treatment process, the slope morphology design of the engineering geological profiles DB1 and DB3 on both sides of the landslide risk zone P1 needs to be carried out under the dual support control of local cross-mining and temporary lining. Based on the location of the landslide risk zone, the weak layer occurrence conditions of the landslide risk zone, and the rock physical and mechanical parameters, the construction location and morphological parameters of the local replacement body and temporary lining body in the slope treatment scheme are designed. The Morgenstern-Price method is used to obtain the slope stability coefficient Fs after cross-mining and replacement of DB1. 11 =1.240>1.10, DB3 temporary slab backfill slope stability coefficient Fs 12 =1.117>1.10. The slope stability coefficients of DB1 and DB3 after emergency treatment both meet the constraint conditions. Therefore, the construction locations of the local replacement fill and temporary slab reinforcement can be determined as follows: Figure 7 As shown, the cross-sectional shape and parameters of the local replacement body are as follows: Figure 8 As shown, the cross-sectional shape and parameters of the temporary lining body are as follows: Figure 9 As shown, the temporary support structure has a length of 174m. Figure 10 As shown;

[0105] Step S4: Using the bench form and mining parameters of the longitudinal mining working face, design the slope morphology of landslide risk zone P1 after maximizing longitudinal mining. By judging whether the slope stability coefficient after maximizing longitudinal mining meets the slope safety reserve coefficient, determine the slope morphology of the second stage and the transverse mining elevation after the completion of longitudinal mining, including:

[0106] Step S4.1: Design the slope morphology for maximum longitudinal mining in landslide risk zone P1, and use the Morgenstern method to obtain the slope stability coefficient after maximum longitudinal mining depth of each slope engineering geological profile.

[0107] Step S4.2: Calculate the difference m1 between the slope stability coefficient after the maximum longitudinal mining depth of each slope engineering geological profile and the slope safety reserve coefficient K2 in the second stage;

[0108] Step S4.3: When all differences m1 are less than or equal to the preset threshold, determine the slope morphology and drawdown elevation of each slope engineering geological profile after maximum longitudinal mining in the landslide risk zone P1. The drawdown elevation is the elevation of the longitudinal and transverse mining boundary line, that is, the slope morphology of the second stage and the transverse mining elevation after the longitudinal mining is completed.

[0109] Conventional landslide risk zone management typically employs only a single mining method, either longitudinal or transverse. While longitudinal mining offers advantages such as convenient workline layout, small stripping volume, and simple production organization, it results in limited downslope space after longitudinal mining in landslide risk zones, impacting the recovery of deep coal resources. Transverse mining, on the other hand, features a short workline and rapid advance, but involves large stripping volumes, narrow pit bottoms, limited equipment operating space, and complex scheduling. Therefore, a coordinated approach combining longitudinal and transverse mining is needed for rapid landslide risk zone management. Based on the bench form of the longitudinal mining working face and end face, and mining parameters, the slope morphology of each profile is designed for maximum longitudinal mining in the landslide risk zone P1. The Morgenstern-Price method is used to obtain the slope stability coefficient Fs after longitudinal mining downslope for each profile. 21 、Fs 22 ..., Fs 2n When the constraint condition |Fs is satisfied 2n When -K2|≤m1 (i.e., when all first differences are less than or equal to the preset threshold), the slope boundary shape and the elevation of the transverse mining and replacement after the longitudinal mining are determined when each profile is subjected to maximum longitudinal mining in the landslide risk zone P1; where the preset threshold is 0.005.

[0110] In this embodiment, longitudinal mining is first selected for rapid treatment of the landslide risk area. Based on the bench form of the working face and end face during longitudinal mining and the mining parameters, the slope morphology of each profile is designed when longitudinal mining is maximized in the landslide risk area P1. The Morgenstern-Price method is applied to obtain the slope stability coefficient after longitudinal mining depth for each profile, where the slope stability coefficient Fs after longitudinal mining depth for DB1 is... 21=1.055, |1.055-1.05|≤0.005; Slope stability coefficient Fs after longitudinal mining depth reduction in DB2 22 =1.051, |1.051-1.05|≤0.005; Slope stability coefficient Fs after longitudinal mining depth reduction in DB3 23 =1.054, |1.054-1.05|≤0.005; Slope stability coefficient Fs after DB4 longitudinal mining depth reduction 24 =1.048, |1.048-1.05|≤0.005. After longitudinal mining depth is reached to a certain elevation in all four profiles, the slope stability coefficients all meet the constraints. Therefore, the slope boundary morphology of each profile at the maximum longitudinal mining depth in landslide risk zone P1 is determined as follows: Figure 11 , Figure 12 , Figure 13 , Figure 14 As shown, it should be noted that the elevation of the transverse backfill after the longitudinal mining of each section is not the standard transportation elevation. Therefore, in actual projects, the elevation of the transverse backfill after the longitudinal mining is completed needs to be adjusted according to the actual site conditions, as shown in Table 4.

[0111] Table 4 Summary of elevations of transverse backfilling after longitudinal mining of each profile;

[0112] ;

[0113] Step S5: Using the bench form and mining parameters of the cross-mining working face, design the slope morphology for cross-mining and replacement of the weak layer in the landslide risk zone P1. By determining whether the slope stability coefficient after cross-mining and replacement meets the slope safety reserve coefficient, determine the slope morphology, weak layer replacement length, and replacement body morphology parameters for the third stage, including:

[0114] Step S5.1: Design a transverse mining and replacement scheme for the weak layer in the landslide risk zone P1, and use the Morgenstern method to obtain the slope stability coefficient after transverse mining and replacement of each slope's engineering geological profile.

[0115] Step S5.2: Calculate the difference m2 between the slope stability coefficient after cross-mining and replacement in each slope engineering geological profile and the slope safety reserve coefficient K3 in the third stage;

[0116] Step S5.3: When all differences m2 are less than or equal to the preset threshold, determine the slope morphology, weak layer replacement length, and replacement body morphology parameters of each slope engineering geological profile to the boundary slope, that is, the slope morphology, weak layer replacement length, and replacement body morphology parameters of the third stage.

[0117] Because weak layers exist beneath the landslide risk zone, a horizontal mining and replacement method is required to break these weak layers. Conventionally, when using horizontal mining and replacement, the replacement length for weak layers is a fixed value. However, due to the complex and wide range of weak layer occurrence conditions in the landslide risk zone, a single replacement length cannot cover all areas of the risk zone. Therefore, based on the bench form and mining parameters of the horizontal mining working face and end face, the occurrence conditions of the main landslide-controlling weak layer R1, and the rock physical and mechanical parameters, the replacement lengths L1, L2, ..., L of the weak layers in each profile are adjusted. n Based on the morphological parameters of the replacement body, the slope morphology and cross-sectional morphology of the replacement body after transverse mining and replacement of the main controlling weak layer R1 in the landslide risk zone P1 of each profile were designed. The Morgenstern-Price method was applied to obtain the slope stability coefficient Fs after transverse mining and replacement of each profile. 31 、Fs 32 ..., Fs 3n When the constraint condition |Fs is satisfied 3n When -K3|≤m2 (i.e., when all second differences are less than or equal to the preset threshold), then determine the replacement lengths L1, L2, ..., L of the weak layer in each profile. n The morphological parameters of the replacement body and the slope boundary morphology after the weak layer is replaced by horizontal mining; the preset threshold is 0.005.

[0118] In this embodiment, since a large area of ​​weak layers still exists in the lower part of the landslide risk zone, a transverse mining and replacement method is required to destroy the weak layers. Based on the bench form and mining parameters of the transverse mining working face and end face, the occurrence conditions of the main controlling weak layer R1 of the landslide, and the rock physical and mechanical parameters, the transverse replacement length and replacement body morphology parameters of the weak layers in each profile are adjusted. The slope morphology and replacement body cross-sectional morphology after transverse mining and replacement of the main controlling weak layer R1 in the landslide risk zone P1 of each profile are designed. The Morgenstern-Price method is applied to obtain the slope stability coefficient after transverse mining and replacement of each profile. Specifically, the slope stability coefficient Fs is obtained when the transverse replacement weak layer transverse mining and replacement length L1 = 194m in DB1. 31 =1.102, |1.102-1.10|≤0.005; Slope stability coefficient Fs when the dip length of the weak layer in the DB2 transverse mining and replacement is 192m. 32 =1.103, |1.103-1.10|≤0.005; Slope stability coefficient Fs when the dip length of the weak layer in the DB3 transverse mining and replacement is 185m. 33 =1.098, |1.098-1.10|≤0.005; Slope stability coefficient Fs when the dip length of the weak layer in the DB4 transverse mining and replacement is L4=294m. 34=1.097, |1.097-1.10|≤0.005. The slope stability coefficients after transverse mining and replacement of the weak layer R1 in all four profiles meet the constraint conditions. The replacement length of the weak layer in each profile is determined as shown in Table 5. The cross-sectional morphological parameters of the replacement body and the slope boundary morphology after transverse mining and replacement of the weak layer are also shown in Table 5. Figure 15 , Figure 16 , Figure 17 , Figure 18 As shown;

[0119] Table 5 Summary of the length of cross-sectional weak layer dipping and replacement;

[0120] ;

[0121] Step S6: Using the bench form and mining parameters of the longitudinal mining working face, longitudinal mining is carried out on the coal resources covered by the non-landslide risk zone P2. By judging whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, the slope morphology of the fourth stage is determined, including:

[0122] Step S6.1: For the longitudinal mining of coal resources overlying the non-landslide risk zone P2, the Morgenstern method is used to obtain the slope stability coefficient of each slope engineering geological profile after longitudinal mining of the non-landslide risk zone P2.

[0123] Step S6.2: Calculate the difference m3 between the slope stability coefficient after longitudinal mining of the non-landslide risk zone P2 and the slope safety reserve coefficient K4 in the fourth stage for each slope engineering geological profile;

[0124] Step S6.3: When all differences m3 are less than or equal to the preset threshold, determine the slope morphology of each slope engineering geological profile after longitudinal mining of the non-landslide risk zone P2, i.e., the slope morphology of the fourth stage.

[0125] After the slope treatment in the landslide risk zone is completed, longitudinal mining can continue to reduce the depth of extraction to recover the P2 resources overlaid in the non-landslide risk zone. Based on the bench form of the working face and end face and the mining parameters, longitudinal mining design is carried out for the P2 non-landslide risk zone in each profile. The Morgenstern-Price method is used to obtain the slope stability coefficient Fs after longitudinal mining reduction in each profile. 41 、Fs 42 ..., Fs 4n When the constraint condition |Fs is satisfied 4n When -K4|≤m3 (i.e., when all third differences are less than or equal to the preset threshold), determine the slope cross-sectional morphology after longitudinal mining of the P2 slope in the non-landslide risk zone of each profile; where the preset threshold is 0.005.

[0126] In this embodiment, after the slope treatment of the landslide risk zone is completed, longitudinal mining can continue to reduce the depth of extraction to recover the resources covered by the landslide risk zone. Based on the bench form of the working face and end face and the mining parameters, longitudinal mining design is carried out for the lower slope area P2 of the landslide risk zone in each profile. The Morgenstern-Price method is used to obtain the slope stability coefficient after longitudinal mining reduction in each profile, where the slope stability coefficient Fs of the non-landslide risk zone P2 after longitudinal mining in DB1 is... 41 =1.046, |1.046-1.05|≤0.005; Slope stability coefficient Fs after longitudinal mining in the lower part of the DB2 landslide risk zone. 42 =1.050, |1.050-1.05|≤0.005; Slope stability coefficient Fs after longitudinal mining in the lower part of the DB3 landslide risk zone. 43 =1.055, |1.055-1.05|≤0.005; Slope stability coefficient Fs after longitudinal mining in the lower part of the DB4 landslide risk zone. 44 =1.047, |1.047-1.05|≤0.005. The slope stability coefficients after longitudinal mining in all four profiles meet the constraint conditions. Therefore, the cross-sectional morphology of the slope after longitudinal mining in the lower region P2 of the landslide risk zone in each profile is determined, see... Figure 19 , Figure 20 , Figure 21 , Figure 22 .

[0127] Step S7: Using the bench form and mining parameters of the cross-mining working face, design the cross-mining replacement slope for the non-landslide risk zone P2 to further recover coal resources. By judging whether the slope stability coefficient after cross-mining replacement meets the slope safety reserve coefficient, determine the slope morphology and replacement body morphology parameters for the fifth stage, including:

[0128] Step S7.1: Design the slope for cross-mining and replacement in non-landslide risk zone P2, and use the Morgenstern method to obtain the slope stability coefficient of each slope after cross-mining and replacement in non-landslide risk zone P2.

[0129] Step S7.2: Calculate the difference m4 between the slope stability coefficient after cross-mining and replacement in the non-landslide risk zone P2 and the slope safety reserve coefficient K5 in the fifth stage for each slope engineering geological profile;

[0130] Step S7.3: When all differences m4 are less than or equal to the preset threshold, determine the slope spatial morphology and replacement body morphology parameters of each slope engineering geological profile after transverse mining and replacement in the non-landslide risk zone P2, that is, the slope morphology and replacement body morphology parameters of the fifth stage.

[0131] Considering the mining parameters and slope cross-sectional morphology during longitudinal mining, the three-dimensional retaining effect of the replacement material on the slope during the tracking process is taken into account. Based on the slope cross-sectional morphology of each profile during longitudinal mining, the bench form of the working side, end side, and internal spoil heap during transverse mining, and the mining parameters, transverse mining replacement slope design is carried out in the lower area of ​​the landslide risk zone of each profile to further recover coal resources. The Morgenstern-Price method is applied to obtain the slope stability coefficient Fs of each profile after transverse mining and replacement in the non-landslide risk zone P2. 51 、Fs 52 ..., Fs 5n When the constraint condition |Fs is satisfied 5n When -K5|≤m4 (i.e., when all fourth differences are less than or equal to the preset threshold), the spatial morphology of the slope and the morphological parameters of the replacement body after transverse mining and replacement in the P2 non-landslide risk zone of each profile are determined; the preset threshold is 0.005. In this embodiment, the mining parameters during longitudinal mining and the slope cross-sectional morphology are considered, taking into account the three-dimensional retaining effect of the replacement body on the slope during the tracking process. Based on the slope cross-sectional morphology of each profile during longitudinal mining, the step form of the transverse mining working side, end side, and inner spoil heap, and the mining parameters, the transverse mining and replacement slope design is carried out in the lower area of ​​the landslide risk zone of each profile to further recover coal resources. The Morgenstern-Price method is applied to obtain the slope stability coefficient of each profile after transverse mining and replacement in the P2 non-landslide risk zone, where the slope stability coefficient Fs of the DB1 non-landslide risk zone P2 after transverse mining and replacement is... 51 =1.098, |1.098-1.10|≤0.005; Slope stability coefficient Fs after transverse mining and replacement in the lower part of the DB2 landslide risk zone. 52 =1.101, |1.101-1.10|≤0.005; Slope stability coefficient Fs after transverse mining and replacement in the lower part of the DB3 landslide risk zone. 53 =1.100, |1.100-1.10|≤0.005; Slope stability coefficient Fs after transverse mining and replacement in the lower part of the DB4 landslide risk zone. 54 =1.103, |1.103-1.10|≤0.005. The slope stability after transverse mining and replacement in all four profiles meets the constraint conditions. Therefore, determine the spatial morphology and replacement body morphology parameters of the slope after transverse mining and replacement in the lower region P2 of the landslide risk zone in each profile, such as... Figure 23 , Figure 24 , Figure 25 , Figure 26 As shown.

[0132] Step S8: Establish a finite element calculation model based on the construction parameters of the first stage, the second stage, the third stage, the fourth stage, and the fifth stage, and draw a plan view of the project location for each stage to guide open-pit coal mining.

[0133] Step S8.1: Establish a finite element calculation model based on the construction parameters of the first stage, the second stage, the third stage, the fourth stage, and the fifth stage (i.e., based on the slope spatial morphology and the replacement body morphology parameters), and use three-dimensional numerical simulation software to determine the coal seam transverse mining and replacement step distance.

[0134] In this embodiment, based on determining the optimal shape of the slope space and the replacement height, a finite element calculation model is established as follows: Figure 27 Using three-dimensional numerical simulation software, the numerical simulation results for 50m, 100m, 200m, and 300m transverse mining and replacement step distances were obtained, as shown below. Figure 28 , Figure 29 , Figure 30 , Figure 31 As shown. Taking into account the impact of engineering disturbances during coal mining in the lower part of the landslide risk zone on slope stability, and combining the landslide patterns in the simulation results, it is determined that the distance of the transverse mining and replacement step should be controlled within 50m;

[0135] Step S8.1: Based on the current status of the mining area and the morphological parameters of the end slopes at each stage, refine the mining stages. Based on the cross-mining and replacement step distance obtained from the numerical simulation results, draw the engineering location plan of each stage to guide subsequent open-pit coal mining.

[0136] In this embodiment, the mining stages are refined based on the current status of the mining area and the slope morphology parameters of each stage. First, the entire east side is longitudinally mined down to the elevation of the transverse mining and backfilling after the longitudinal mining is completed. The engineering location plan after the downsizing is shown in the figure. Figure 32 After the longitudinal mining depth in the potential danger zone of the eastern side reached the elevation of the horizontal mining and backfilling after the longitudinal mining was completed, the weak layer was further stripped to the boundary using the method of horizontal mining and backfilling. Since a relatively wide flat area was formed at the +875m, +905m, and +935m levels after the longitudinal mining, the initial excavation locations for the horizontal mining and backfilling were selected at the +875m, +905m, and +935m levels. Figure 33 As shown. The three working slopes advance simultaneously from north to south, leaving trenches for backfilling. The cross-mining and backfilling interval is maintained at 50m. During cross-mining, the weak strata floor are broken first, and then loose sandstone is used for backfilling. The intermediate and final engineering locations of the cross-mining and backfilling in the potential danger zone of the eastern slope are shown below. Figure 34 , Figure 35 As shown; after the landslide risk zone treatment is completed, the location of the lower part of the landslide risk zone from the longitudinal mining to the coal seam floor slope cross-section is drawn as follows: Figure 36 As shown; after the lower part of the landslide risk zone is longitudinally mined to the optimal shape, the mid-term and final engineering locations for controlling coal resource mining in the lower part of the landslide risk zone are determined based on the slope spatial morphology after transverse mining and replacement in the lower part of the landslide risk zone, such as... Figure 37 , Figure 38 As shown, this guides subsequent open-pit coal mining.

[0137] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0138] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of equivalent technology of this disclosure, then the intent of this disclosure also includes such modifications and variations.

Claims

1. A method for controlling safe mining operations at the boundary of a slope in a landslide risk zone, characterized in that, include: Based on the actual geological conditions at the site, the three-dimensional geological model, the slope morphology, and the historical information of geological drilling, n engineering geological profiles of the slope are drawn, and the n engineering geological profiles of the slope and the slope area are numbered, and the slope is divided into landslide risk zone P1 and non-landslide risk zone P2. According to the "Design Code for Open-Pit Coal Mines", the slope safety reserve coefficient is determined based on the slope service life during each stage of construction. Using the step form and mining parameters of the end slope and the step form and mining parameters of the internal spoil heap, the slope morphology design of the landslide risk zone P1 under the dual support control of local cross mining and replacement and local lateral slope pressing was carried out simultaneously. By judging whether the slope stability coefficient under the dual support control meets the slope safety reserve coefficient, the slope morphology, lateral slope body and replacement body morphology parameters of the first stage were determined. Using the bench form and mining parameters of the longitudinal mining working face, the slope morphology of landslide risk zone P1 after longitudinal mining is designed. By judging whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, the slope morphology of the second stage and the transverse mining elevation after the longitudinal mining are determined. Using the bench form and mining parameters of the horizontal mining working face, the slope morphology of the weak layer in the landslide risk zone P1 is designed for horizontal mining and replacement. By judging whether the slope stability coefficient after horizontal mining and replacement meets the slope safety reserve coefficient, the slope morphology, weak layer replacement length and replacement body morphology parameters of the third stage are determined. Using the bench form and mining parameters of the longitudinal mining working face, the coal resources covered by the non-landslide risk zone P2 are longitudinally mined. By judging whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, the slope morphology of the fourth stage is determined. Using the bench form and mining parameters of the cross-mining working face, the cross-mining replacement slope design was carried out in the non-landslide risk zone P2. By judging whether the slope stability coefficient after cross-mining replacement meets the slope safety reserve coefficient, the slope morphology and replacement body morphology parameters of the fifth stage were determined. Based on the slope morphology, backfill and replacement body morphology parameters of the first stage, the slope morphology and transverse mining elevation after the completion of longitudinal mining in the second stage, the slope morphology, weak layer replacement length and replacement body morphology parameters of the third stage, the slope morphology of the fourth stage and the slope morphology and replacement body morphology parameters of the fifth stage, a finite element calculation model is established, and a plan view of the engineering location of each stage is drawn to guide open-pit coal mining.

2. The method for controlling safe mining at the boundary of a slope in a landslide risk zone according to claim 1, characterized in that, The division of the slope into landslide risk zone P1 and non-landslide risk zone P2 includes: Using the location of the weak layer in the landslide risk zone as the dividing line, the slope area from the surface to the weak layer in the landslide risk zone is designated as the landslide risk zone, numbered P1, and the slope area below the weak layer in the landslide risk zone is designated as the non-landslide risk zone, numbered P2.

3. The method for controlling safe mining at the boundary of a slope in a landslide risk zone according to claim 1, characterized in that, The slope safety reserve coefficient includes: slope safety reserve coefficient K1 for the first stage, slope safety reserve coefficient K2 for the second stage, slope safety reserve coefficient K3 for the third stage, slope safety reserve coefficient K4 for the fourth stage, and slope safety reserve coefficient K5 for the fifth stage. The first stage is the local transverse mining and replacement and local slope protection treatment stage of landslide risk zone P1; the second stage is the longitudinal mining stage of landslide risk zone P1 to the transverse-longitudinal mining boundary; the third stage is the transverse mining and replacement stage of landslide risk zone P1 to the weak layer stage of landslide risk zone; the fourth stage is the longitudinal mining stage of non-landslide risk zone P2; and the fifth stage is the transverse mining and replacement stage of non-landslide risk zone P2.

4. The method for controlling safe mining at the boundary of a slope in a landslide risk zone according to claim 1, characterized in that, The process involves determining whether the slope stability coefficient under dual-support control meets the slope safety reserve coefficient, and then determining the slope morphology, backfill morphology parameters, and replacement morphology parameters for the first stage, including: For the slope morphology design under the dual support control of local cross-mining and local lateral reinforcement on both sides of the landslide risk zone P1, the Morgenstern method was used to obtain the slope stability coefficient after local cross-mining and local lateral reinforcement. When the slope stability coefficient after local cross-mining and replacement is greater than the slope safety reserve coefficient K1 of the first stage, and the slope stability coefficient after local rib stabilization is greater than the slope safety reserve coefficient K1 of the first stage, the slope morphology, rib stabilization body and replacement body morphology parameters of the first stage are determined.

5. The method for controlling safe mining at the boundary of a slope in a landslide risk zone according to claim 1, characterized in that, The process of determining whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, and determining the slope morphology for the second stage and the transverse mining elevation after the completion of longitudinal mining, includes: For the landslide risk zone P1, the longitudinal mining slope morphology was designed, and the Morgenstern method was used to obtain the slope stability coefficient after longitudinal mining depth of each slope engineering geological profile. Calculate the difference m1 between the slope stability coefficient after longitudinal mining and drawdown of each slope engineering geological profile and the slope safety reserve coefficient K2 in the second stage; If all differences m1 are less than or equal to a preset threshold, determine the slope morphology of the second stage and the transverse mining elevation after the longitudinal mining is completed.

6. The method for controlling safe mining at the boundary of a slope in a landslide risk zone according to claim 1, characterized in that, The process of determining the slope morphology, weak layer replacement length, and replacement body morphology parameters in the third stage by judging whether the slope stability coefficient after transverse mining and replacement meets the slope safety reserve coefficient includes: For the weak layer in the landslide risk zone P1, a transverse mining and replacement design was carried out, and the Morgenstern method was used to obtain the slope stability coefficient after transverse mining and replacement of each slope engineering geological profile. Calculate the difference m2 between the slope stability coefficient after cross-mining and replacement in each slope engineering geological profile and the slope safety reserve coefficient K3 in the third stage. When all differences m2 are less than or equal to the preset threshold, the slope morphology, weak layer replacement length, and replacement body morphology parameters of the third stage are determined.

7. The method for controlling safe mining at the boundary of a slope in a landslide risk zone according to claim 1, characterized in that, The method utilizes the bench form and mining parameters of the longitudinal mining working face to conduct longitudinal mining of the coal resources overlying the non-landslide risk zone P2. By determining whether the slope stability coefficient after longitudinal mining meets the slope safety reserve coefficient, the slope morphology of the fourth stage is determined, including: For longitudinal mining of coal resources overlaid in P2 non-landslide risk zone, the Morgenstern method was used to obtain the slope stability coefficient of each slope engineering geological profile after longitudinal mining in P2 non-landslide risk zone. Calculate the difference m3 between the slope stability coefficient after longitudinal mining of the non-landslide risk zone P2 and the slope safety reserve coefficient K4 in the fourth stage for each slope engineering geological profile. The slope morphology of the fourth stage is determined when all differences m3 are less than or equal to a preset threshold.

8. The method for controlling safe mining at the boundary of a slope in a landslide risk zone according to claim 1, characterized in that, The process of determining the slope morphology and replacement body morphology parameters in the fifth stage by judging whether the slope stability coefficient after transverse mining and replacement meets the slope safety reserve coefficient includes: For the non-landslide risk zone P2, the slope design of cross-mining and replacement was carried out, and the Morgenstern method was used to obtain the slope stability coefficient of each slope after cross-mining and replacement in the non-landslide risk zone P2. Calculate the difference m4 between the slope stability coefficient and the slope safety reserve coefficient K5 in the fifth stage for each slope engineering geological profile after cross-mining and replacement in the non-landslide risk zone P2. When all differences m4 are less than or equal to the preset threshold, the slope morphology and replacement body morphology parameters for the fifth stage are determined.

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