A method for determining the grouting layer location and timing of an artificial solidified body
By using a method to determine the grouting layer location and timing of artificial consolidation, the problems of rapid closure of mining space and poor rock strata stability in shallow-buried coal mines have been solved. This has enabled efficient solid waste disposal and resource utilization of mining space, thereby improving the production efficiency and safety of coal mines.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA UNIV OF MINING & TECH
- Filing Date
- 2025-03-21
- Publication Date
- 2026-05-26
Smart Images

Figure CN120277975B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of coal mining technology, and is particularly applicable to mining scenarios such as solid waste disposal in shallow and deep coal mines, underground space utilization, green mining, and backfilling mining. Specifically, it relates to a method for determining the grouting layer location and timing of artificial solidified bodies. Background Technology
[0002] Backfilling technology, as a reliable and low-cost green disposal method, is widely used by coal mining enterprises. This technology enables large-scale treatment of solid waste and reduces the accumulation and discharge of solid waste such as coal gangue. However, western coal seams are characterized by shallow burial, large coal seam thickness, and fast mining speed. As the working face advances, the deformation speed of the shallow mining space is fast, the degree of deformation is large, and the mining volume is quickly transmitted to the surface. This results in the rapid closure of the mining space in shallow fully mechanized longwall mining, with small backfill space and short backfilling opportunities, which restricts the efficient disposal of solid waste. Traditional gangue backfilling methods are difficult to meet the production and solid waste disposal needs of modern large mines, and the contradiction between high production and high efficiency of coal mines and solid waste disposal is significant. Summary of the Invention
[0003] To address the limitations of existing technologies in achieving high-volume, high-efficiency disposal of shallow-buried solid waste without impacting production, this invention provides a method for determining the grouting layer and timing of artificial solidification. This method can identify suitable grouting layers and timing for artificial solidification, ensuring sufficient existence of mining voids to slow their transmission to the surface. It solves the problems in western mining areas caused by shallow-buried rock strata and shallow fully mechanized longwall mining, which results in numerous mining voids and fissures, easy collapse, poor stability, difficulty in controlling rock strata, and lack of space and timing for solid waste backfilling and disposal.
[0004] To achieve the above objectives, the present invention provides the following solution:
[0005] A method for determining the grouting layer location and timing of an artificially consolidated body, the method comprising:
[0006] Obtain parameters for shallow-buried, deep fully mechanized longwall mining;
[0007] Based on the parameters of shallow-buried fully mechanized longwall mining, the grouting layer H of the artificially consolidated body was obtained according to theoretical calculations. g ;
[0008] Using measured data on overburden movement, the grouting layer H of the artificial consolidation body was obtained. s And the earliest grouting time T min ;
[0009] Using measured data of surface subsidence, the latest grouting timing T for the artificial consolidation body was determined. max ;
[0010] An evolution model of the mining space void controlled by artificially consolidated bodies was established using computer numerical simulation. The evolution law of mining space void under the grouting timing of different artificially consolidated bodies was analyzed, and the optimal theoretical grouting timing T for the artificially consolidated body with the largest mining space void was determined. r Theoretical grouting timing range T a ~T b ;
[0011] Finally, the grouting timing was adjusted based on the actual measurement and feedback. Combining the measured grouting volume of key rock strata, the grouting timing, and the porosity beneath the artificial solidified body, the final grouting timing range T for the artificial solidified body was obtained. am ~T bm .
[0012] Preferably, the parameters for shallow-buried deep fully mechanized longwall mining include the average daily advance distance D. e Coal seam thickness, mining-to-release ratio, burial depth, working face length, and physical and mechanical parameters of the coal seam and overlying rock mass.
[0013] Preferably, the grouting layer H of the artificial consolidation body is obtained based on the shallow-buried fully mechanized longwall mining parameters. g include:
[0014] Based on the parameters of shallow-buried fully mechanized longwall mining, the fracture distance of different overburden strata was obtained using the key rock layer theory.
[0015] The stratigraphic position of the key rock layer is obtained based on the fracture distance of different overburden strata.
[0016] Based on the stratigraphic position of the key rock strata, the grouting layer H of the artificial solidified body is obtained. g .
[0017] Preferably, the grouting layer H of the artificial solidified body s The judgment is based on the theoretical calculation of the grouting layer H of the artificial solidified body. g Based on the range, H was obtained through measured boreholes of overburden movement. g The actual grouting layer H of the artificially consolidated body was obtained by comparing and verifying the actual thickness, lithology, and fracture patterns of the rock strata within the preset range. s .
[0018] Preferred, earliest grouting time T min To design the grouting layer H of the artificial solidified body as the working face advances s The distance D at the start of fracture deformation min Divide by the average daily advance time D e The calculation formula is:
[0019] Preferably, the latest grouting time T for the artificial consolidation body maxAs the working face advances, the surface subsidence occurs, and the distance D in the mining space becomes so large that there are no gaps that can be filled. max Divide by the average daily advance time D e The calculation formula is:
[0020] Preferably, a computer numerical simulation is used to establish an evolution model of the mining space void controlled by the artificial solidified body. The evolution law of the mining space void under the grouting timing of different artificial solidified bodies is analyzed, and the optimal theoretical grouting timing T for the artificial solidified body with the largest mining space void is determined. r Theoretical grouting timing range T a ~T b include:
[0021] An evolution model of the void space controlled by the artificial solidified body was established using discrete element method software. The void evolution distribution pattern of the key rock strata at different advance distances was obtained by cloud map. The porosity of the key rock strata at different advance distances was obtained by binary method.
[0022] Based on the porosity of key rock strata at different advance distances, simulations of the evolution of mining-induced voids at different grouting timings for artificially consolidated bodies were conducted. Specifically: D min ~D max The distance D advancing per day e For intervals, simulate propulsion D min D1, D2, D3...D x ...and then grouting was performed on the voids in the key rock strata to form an artificial solidified body, after which excavation continued to D. max The evolution of voids beneath the artificially consolidated body after filling the voids in the key rock strata with grout at different advance distances following full excavation was determined; based on the average daily advance distance D... e The evolution law of mining voids during grouting at different artificial solidified bodies was obtained; among them, D min Design grouting layer H for advancing the artificial solidified body at the working face s The distance at which fracture deformation begins; D max D1 is the distance where there are no gaps to fill in the stable mining space caused by surface subsidence during the working face advancement; min Add 1 daily average advance distance D e ;D x D min Add x daily average advance distance D e ;
[0023] A comparative analysis of the mining void characteristics during grouting at different artificial solidified bodies was conducted, with the maximum porosity of the mining space being taken as the optimal theoretical grouting time T. r The theoretical grouting timing range T for artificial solidified bodies is defined as the time range within which the porosity of the mining space reaches a maximum of 80%. a ~T b .
[0024] Preferred, D x D min Add x Ds e The calculation formula is: D x =D min +xD e ;D min ≤D x <D max During the simulation, when advancing to D x After grouting to form an artificial key rock layer, further advancement continues until D is reached. max .
[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0026] This invention achieves precise control of the mining space in shallow-buried deep fully mechanized mining by accurately and reasonably determining the grouting layer and timing of artificial solidified bodies. It also enables the filling and disposal of solid waste to minimize the reduction of coal mining efficiency and maximize the utilization of coal gangue and underground space, thus contributing to the resource utilization of mining space, solid waste disposal, and green mining of coal mines.
[0027] This invention can determine the appropriate grouting layer and timing for artificial consolidation, ensuring sufficient existence of mining voids to slow their transmission to the surface. It solves the problems in western mining areas caused by shallow-buried rock strata and shallow fully mechanized longwall mining, which result in numerous mining voids and fissures, easy collapse, poor stability, difficulty in controlling rock strata, and lack of space and timing for solid waste backfilling and disposal.
[0028] This invention offers advantages such as improved surrounding rock mechanical properties, reduced grouting volume, optimized grouting parameters, and enhanced construction safety. It not only improves the safety and economy of the project but also enhances construction efficiency and quality. It has broad applicability within this technical field. Attached Figure Description
[0029] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0030] Figure 1 This is a flowchart of a method for determining the grouting layer location and timing of an artificial solidified body according to the present invention.
[0031] Figure 2 This is a diagram illustrating the measured movement of overburden rock in shallow-buried, deep-well fully mechanized mining according to the present invention.
[0032] Figure 3 This is a measured diagram of the surface subsidence pattern in shallow-buried fully mechanized longwall mining according to the present invention;
[0033] Figure 4 This is a key rock stratum void distribution diagram for shallow-buried fully mechanized longwall mining at different advance distances according to the present invention;
[0034] Figure 5 This is a schematic diagram of the grouting layer location and timing of the shallow-buried deep-laid artificial solidified body of the present invention;
[0035] In the figure: 1- Grouting layer of artificial solidified body, 2- Grouting timing of artificial solidified body, 3- Distribution of voids in the mining space below artificial solidified body. Detailed Implementation
[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0038] Example 1
[0039] This invention provides a method for determining the grouting layer location and timing of artificial solidified bodies, such as... Figure 1 The steps shown are as follows:
[0040] S1: On-site investigation to obtain parameters for shallow-buried deep fully mechanized longwall mining;
[0041] S2: Theoretical calculations are performed using the key stratum theory to determine the fracture distances of different overburden layers, thus identifying the key strata and the theoretically calculated grouting layer H of the artificial solidified body. g ;
[0042] S3: Analysis of measured parameters of overburden movement, the law of overburden subsidence and fracture under different advance distances, and the grouting layer H of the artificial consolidation body. s And the earliest grouting time T min ;
[0043] S4: Analysis of measured parameters of surface subsidence, the pattern of surface subsidence under different advance distances, and determination of the latest grouting timing T for artificial consolidation. max ;
[0044] S5: Numerical simulation of void evolution in key rock strata at different advance distances. Using discrete element method software, an evolution model of voids in the mining space controlled by artificial consolidation body is established. The void evolution distribution pattern of key rock strata at different advance distances is obtained. The void ratio of key rock strata at different advance distances is obtained by binary method.
[0045] The method of obtaining the porosity of key rock strata at different advance distances using the binary method includes: importing the simulated images into MATLAB software, setting different extreme values, converting the simulation results into black and white images, and then calling the calculation function in MATLAB to obtain the porosity.
[0046] S6: Numerical simulation of void evolution during grouting at different artificial consolidation times, D min ~D max The distance D advancing per day e For intervals, simulate propulsion D min D1, D2, D3...D x ...and then grouting was performed on the voids in the key rock strata to form an artificial solidified body, after which excavation continued to D. max The evolution of voids beneath the artificially consolidated body after filling the voids in the key rock strata with grout at different advance distances following full excavation was determined; based on the average daily advance distance D... e The evolution law of mining voids under different grouting timings in artificially consolidated bodies was obtained. Among them, D min Design grouting layer H for advancing the artificial solidified body at the working face s The distance at which fracture deformation begins (the distance from the borehole used for monitoring overburden movement to the grouting layer H) s (D is the distance from the working surface at the point where fracture deformation begins); max D1 is the distance from the working face to the surface subsidence stabilization mining area where there are no gaps that can be filled (the distance from the working face when the surface subsidence is stable); D1 is D min Add 1 daily average advance distance D e ;D x D min Add x daily average advance distance D e The evolutionary pattern was derived by simulation software, which simulated different excavation distances.
[0047] S7: The theoretical grouting timing range for artificially consolidated bodies is determined. A comparative analysis of the mining void ratio at different grouting timings for different artificially consolidated bodies is conducted, with the maximum porosity of the mining space being taken as the optimal theoretical grouting timing T. r The theoretical grouting timing range T for artificial solidified bodies is defined as the time range within which the porosity of the mining space reaches a maximum of 80%. a ~T b ;
[0048] S8: Actual measurement and verification feedback to adjust the grouting timing, actual measurement of the grouting volume of key rock strata, grouting timing and porosity below the artificial consolidation body, feedback to adjust the grouting timing of shallow buried deep fully mechanized artificial consolidation bodies.
[0049] In this embodiment, the shallow-buried fully mechanized longwall mining parameters in S1 include the average daily advance distance D. e Coal seam thickness, mining-to-release ratio, burial depth, working face length, and physical and mechanical parameters of the coal seam and overlying rock mass.
[0050] In this embodiment, the grouting layer H of the artificial solidified body in S2 s The judgment is based on the theoretical calculation of the grouting layer H of the artificial solidified body. g Based on the range, H was obtained through measured boreholes of overburden movement. g The actual thickness, lithology, and fracture patterns of the surrounding rock strata were compared and verified to determine the grouting layer H of the actual artificial solidified body. s .
[0051] In this embodiment, the earliest grouting timing T in S3 min To design the grouting layer H of the artificial solidified body as the working face advances s The distance D at the start of fracture deformation min Divide by the average daily advance time D e As shown in Equation 1:
[0052]
[0053] In this embodiment, the latest grouting timing T of the artificial solidified body in S4 is... max As the working face advances, the surface subsidence occurs, and the distance D in the mining space becomes so large that there are no gaps that can be filled. max Divide by the average daily advance time D e As shown in Equation 2:
[0054]
[0055] In this embodiment, D in S6 x D min Add x Ds e As shown in Equation 3:
[0056] D x =D min +xD e (3)
[0057] In this embodiment, D in S6 x D min ≤D x <D max During the simulation, when advancing to D xAfter grouting to form an artificial key rock layer, further advancement continues until D is reached. max .
[0058] In this embodiment, step S8 involves adjusting the grouting timing of the shallow-buried, fully mechanized artificial consolidation body. This is done by comparing the measured grouting volume and timing of the key rock strata, as well as the porosity below the artificial consolidation body, with the simulated porosity of the key rock strata and the porosity below the artificial consolidation body. If the deviation from the simulated value is greater than 30%, the simulation parameters in step S5 are updated with the actual porosity parameter as the target. Steps S5 to S8 are repeated until the deviation between the actual measured value and the simulated value is less than or equal to 30%. The theoretical grouting timing range T for the selected artificial consolidation body is then determined. a ~T b The optimal grouting timing range T for a rational and effective artificial consolidation body am ~T bm .
[0059] Specific Cases
[0060] Taking a fully mechanized longwall mining coal mine in western China as an example, the specific implementation steps are as follows:
[0061] S1: On-site investigation yielded parameters for shallow-buried fully mechanized longwall mining; based on the investigation of a fully mechanized longwall coal mine in western China, the coal seam depth is 259-284m, the coal seam thickness is 9m, the mining-to-loosening ratio is 1:0.621, and the average daily advance distance D... e The physical and mechanical parameters of the coal seam and overlying rock mass are shown in Table 1, with a working face length of 300m and a length of 10m.
[0062] Table 1. Physical and mechanical parameters of coal seams and overlying rock masses (comprehensive columnar section)
[0063]
[0064] S2: Theoretical calculations are performed using the key stratum theory to determine the fracture distances of different overburden layers, thus identifying the key strata and the theoretically calculated grouting layer H of the artificial solidified body. g ;
[0065] A key stratum is the overlying stratum in a mining area that controls the activity of local or even all strata up to the surface. If the first stratum is the first key stratum, and its control extends to the nth stratum, then the condition that the (n+1)th stratum must meet to become the second key stratum is:
[0066] (q n+1 )1<(q n )1 (4)
[0067]
[0068] In the formula: q n+1The load q represents the (n+1)th rock layer on the first hard rock layer. n The load exerted by the nth rock layer on the first hard rock layer; h i γ i E i Let be the thickness, volume force, and elastic modulus of the i-th rock layer, respectively (i = 1, 2, ..., n).
[0069] Substituting the above parameters into equations (4) and (5), we find that the hard rock layer that meets the criteria is layer 5, with a burial depth of 161m and a thickness of 35m, which is the key rock layer H. g It is 161m.
[0070] S3: Analysis of measured parameters of overburden movement. Measurement boreholes were drilled above the surface of the working face. Fiber optic cables were implanted in the boreholes to monitor the strain of the surrounding rock. During the drilling, the key siltstone stratum was measured at a depth of 135.5m and a thickness of 20.5m. The following parameters were obtained: H... s The depth is 135.5m; further analysis is needed to determine the subsidence and fracture patterns of the overlying strata at different advance distances, such as... Figure 2 As shown, when the working face advanced 11.7m past the monitoring hole, the lower part of the optical fiber showed slight strain changes, mainly tensile strain. At 19.0m past the hole, the optical fiber experienced its first breakage at a depth of approximately 162m. At 59.0m past the monitoring hole, the optical fiber broke again at a depth of 124m, within the key rock stratum. At this depth, the key rock stratum began to fracture, and the artificially consolidated body initially formed a mining space. Therefore, the designed grouting layer H of the artificially consolidated body was determined as the working face advanced. s The distance D at the start of fracture deformation min The length is 59.0m, combined with formula 1, to determine the earliest grouting time T. min It takes 5.9 days
[0071] S4: Analysis of measured parameters of surface subsidence, such as Figure 3 As shown, the surface subsidence monitoring points near the overlying rock movement measurement point exhibit a subsidence pattern. When the working face advances 700m, the surface subsidence rate approaches stability. The distance D at which the stable mining space has no gaps to fill is determined as the working face advances. max Given a depth of 700m, and combining Equation 2, the latest grouting time T for the artificial solidified body is obtained. max It lasts for 70 days.
[0072] S5: Numerical simulation of void evolution in key rock strata at different advance distances. An evolution model of voids in the mining space controlled by an artificially consolidated body was established using the discrete element method 3DEC. The simulation yielded a cloud map showing the void evolution distribution of key rock strata at different advance distances. The porosity of the key rock strata at different advance distances was obtained using the binary method. Figure 4 As shown.
[0073] S6: Numerical simulation of void evolution during grouting at different artificial consolidation times, D min ~D max That is, between 59m and 700m, the daily advance distance D e At 10m intervals, the excavation was simulated at depths of 59, 69, 79, 89...699m. During each stage, grouting was performed on the voids in key rock strata to create artificial consolidation bodies, after which excavation continued to D. max At 700m, the evolution law of voids under the artificial solidified body after filling the voids in the key rock strata with grout at different advance distances after full excavation was obtained. As the timing of grouting in the artificial solidified layer increased, the voids under the artificial solidified body first increased rapidly and then decreased slowly. Based on an average daily advance distance of 10m, the evolution law of mining voids at different grouting timings of the artificial solidified body was obtained.
[0074] S7: The theoretical grouting timing range for artificially consolidated bodies is determined. A comparative analysis of the porosity characteristics of different grouting timings for artificially consolidated bodies shows that the maximum porosity is reached when the grouting progresses 200m (i.e., 20 days behind the working face). Therefore, the optimal theoretical grouting timing T... r For 20 days, such as Figure 5 As shown in the figure (1 represents the grouting layer of the artificial consolidation body, 2 represents the grouting timing of the artificial consolidation body, and 3 represents the void distribution in the mining space below the artificial consolidation body), the theoretical grouting timing range T of the artificial consolidation body is defined as the time range within which the maximum void ratio of the mining space reaches 80%. a ~T b That is, 18 to 30 days;
[0075] S8: Actual measurement verification and feedback adjustment of grouting timing. Actual measurements were taken of the grouting volume, timing, and porosity beneath the artificial consolidation body in key rock strata. For shallow-buried fully mechanized longwall mining, the porosity beneath the artificial consolidation body was determined using 3D seismic exploration feedback. Monitoring results showed that grouting should be performed 18 days after the working face. The deviation between the measured and simulated values was 25%, which meets the requirements. The optimal grouting timing for shallow-buried fully mechanized longwall artificial consolidation bodies is determined by T. am ~T bm It takes 18 to 30 days.
[0076] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A method for determining the grouting layer location and timing of an artificially consolidated body, characterized in that, The method includes: Obtain parameters for shallow-buried, deep fully mechanized longwall mining; Based on the parameters of shallow-buried fully mechanized longwall mining, the grouting layer of the artificially consolidated body was obtained according to theoretical calculations. H g ; Using measured data on overburden movement, the grouting layers of the artificially consolidated body were determined. H s and the earliest grouting time T min Grouting layer of artificial solidified body H s The judgment is based on the theoretical calculation of the grouting layer position of the artificial solidified body. H g Based on the range, the results were obtained through measured boreholes of overburden movement. H g The actual grouting layer of the artificially consolidated body was obtained by comparing and verifying the actual thickness, lithology, and fracture patterns of the rock strata within the preset range. H s ; Using measured data on surface subsidence, determine the latest grouting timing for the artificial consolidation body. T max ; An evolution model of the mining space void controlled by artificially consolidated bodies was established using computer numerical simulation. The evolution law of mining space void under the grouting timing of different artificially consolidated bodies was analyzed, and the optimal theoretical grouting timing for the artificially consolidated body with the largest mining space void was determined. T r Theoretical grouting timing range T a ~T b ;include: An evolution model of the void space controlled by the artificial solidified body was established using discrete element method software. The void evolution distribution pattern of the key rock strata at different advance distances was obtained by cloud map. The porosity of the key rock strata at different advance distances was obtained by binary method. Based on the porosity of key rock strata at different advance distances, simulations of mining-induced porosity evolution were conducted for different grouting timings in artificially consolidated bodies. Specifically: D min ~ D max The distance between them is based on the average daily progress. D e For intervals, simulate propulsion D min D1, D2, D3...D x ...and then grouting was performed on the voids in the key rock strata to form an artificial solidified body, after which excavation continued until... D max The study yielded the evolution law of voids beneath the artificially consolidated body after filling the voids in the key rock strata with grout at different advance distances following full excavation; based on the average daily advance distance... D e The evolution law of mining voids under different grouting timings in artificially consolidated bodies was obtained; among them, D min Design grouting layers for advancing the artificial solidified body at the working face. H s The distance at which fracture and deformation begin; D max The distance that can be filled in the space where the ground subsidence is stabilized and the mining operation is progressing in the working face; for D min Add 1 daily average advance distance D e ; for D min Add x daily average advance distance D e ; A comparative analysis of the mining void characteristics during grouting at different artificial solidified bodies was conducted, with the maximum porosity of the mining space being considered the optimal theoretical grouting time. T r The theoretical grouting timing range for artificial solidified bodies is defined as the time range within which the porosity of the mining space reaches a maximum of 80%. T a ~T b ; Finally, the grouting timing was adjusted based on the measured grouting volume and timing of key rock strata, as well as the porosity beneath the artificial solidified body. The final range of grouting timing for the artificial solidified body was determined through verification and feedback. T am ~T bm ; D x for D min Plus x indivual D e The calculation formula is: ; D min ≤D x < D max During the simulation, when advancing to D x After grouting to form an artificial key rock layer, further advancement continues until... D max .
2. The method according to claim 1, characterized in that, Shallow-buried deep fully mechanized longwall mining parameters include average daily advance distance. D e Coal seam thickness, mining-to-release ratio, burial depth, working face length, and physical and mechanical parameters of the coal seam and overlying rock mass.
3. The method according to claim 1, characterized in that, Based on the parameters of shallow-buried deep fully mechanized longwall mining, the grouting layer of the artificial consolidation body was obtained. H g include: Based on the parameters of shallow-buried fully mechanized longwall mining, the fracture distance of different overburden strata was obtained using the key rock layer theory. The stratigraphic position of the key rock layer is obtained based on the fracture distance of different overburden strata. Based on the stratigraphic position of the key rock strata, the grouting positions of the artificial consolidation body are obtained. H g .
4. The method according to claim 1, characterized in that, Earliest grouting time T min To design grouting layers for the artificial solidified body as the working face advances H s Distance at the start of fracture and deformation D min Divide by the average daily advance distance D e The calculation formula is: .
5. The method according to claim 1, characterized in that, Latest grouting time for artificial solidified bodies T max As the working face advances, the surface subsidence occurs, creating a stable mining space with no gaps that can be filled. D max Divide by the average daily advance distance D e The calculation formula is: .