Processing math: 89%
Haojun Wu, Min Gong, Renshu Yang, Xiaodong Wu, and Xiangyu Liu, Double-face intelligent hole position planning method for precision blasting in roadways using a computer-controlled drill jumbo, Int. J. Miner. Metall. Mater., 30(2023), No. 6, pp.1025-1037. https://dx.doi.org/10.1007/s12613-022-2575-4
Cite this article as: Haojun Wu, Min Gong, Renshu Yang, Xiaodong Wu, and Xiangyu Liu, Double-face intelligent hole position planning method for precision blasting in roadways using a computer-controlled drill jumbo, Int. J. Miner. Metall. Mater., 30(2023), No. 6, pp.1025-1037. https://dx.doi.org/10.1007/s12613-022-2575-4
Research Article

Double-face intelligent hole position planning method for precision blasting in roadways using a computer-controlled drill jumbo

Author Affilications
  • Corresponding author:

    Min Gong      E-mail: gongmustb@163.com

  • To solve the uneven burden of same-type holes reducing the blasting efficiency due to the limitation of drilling equipment, we need a double-face program-controlled planning method for hole position parameters used on a computer-controlled drilling jumbo. The cross-section splits into even and uneven areas. It also considers the uneven burden at the hole’s entrance and bottom. In the uneven area, various qualifying factors are made to optimize the hole spacing and maximize the burden uniformity, combined with the features of the area edges and grid-based segmentation methods. The hole position coordinates and angles in the even area are derived using recursion and iteration algorithms. As a case, this method presents all holes in a 4.8 m wide and 3.6 m high cross-section. Compared with the design produced by the drawing method, our planning in the uneven area improved the standard deviation of the hole burden by 40%. The improved hole layout facilitates the evolution of precise, efficient, and intelligent blasting in underground mines.
  • For a long time, drilling equipment and detonator materials have restricted the progress of tunnel blasting technology [12]. For example, after drilling with handheld rock drills or drilling jumbos, the actual angle and position of holes often have a deviation compared to the design values [34]. This method cannot clarify the relationship between design parameters and the blasting effect because the design values of the hole position do not match the actual ones. The concept and purpose of designers [56] are hard to achieve. These flaws were in mind when establishing the existing tunnel blasting system [7], which is characterized by a large redundancy tolerance in the blasting design. Hence, this traditional system cannot meet the need to develop an efficient and accurate tunnel blasting technology. Moreover, the waste of explosives is significant.

    Intelligent rock drilling and blasting [810] are promising directions for tunneling technology development. They are also crucial to solving the above-mentioned problems. They include at least two aspects. First, the automated process, based on computer-controlled drilling jumbos [1112], contains automatic planning of blasting parameters, automatic hole positioning for planned holes [1314], and automatic hole drilling [15]. Second, the high-precision delay blasting technique considers lithological changes based on machine learning methods [1618]. According to the latest regulations, China will stop the production and sales of industrial detonators other than industrial digital electronic detonators by the end of June and August 2022. The current application of computer-controlled drilling jumbos [1920] and digital electronic detonators [2123] in China has laid a good foundation for intelligent tunneling and blasting.

    However, considering the current application of computer-controlled drilling jumbos in tunnels, when using the program to plan holes, the hole layout still follows the traditional graphic design [2425]. It does not consider the problem that when laying holes along the curved area of the cross-section, the hole burden in the same row is hard to uniform. In addition, most of them only design the hole spacing at the entrance and seldom consider the change in burden at the hole bottom related to the cut hole angle. In the past, these problems were ignored and covered up for a long time. The reason is that increasing the charge amount of the hole compensated for the influence on the blast effect induced by the deviation from the hole formation when using an ordinary drilling machine.

    For efficient and precise intelligent blasting, addressing uneven burdens in automatic hole-layout design is essential. This study suggests a double-face program-controlled planning method to arrange holes for computer-controlled drilling jumbos. We planned hole positions on the two faces of the hole entrance and bottom. The cross-section splits into even and uneven areas through the hole position design. The coordinates and angles of the holes in the even area are derived by the recursion algorithm, and the errors of the hole layout are converged by the iteration algorithm. The hole layout in the uneven area is an optimization problem due to numerous limits. To optimize the hole spacing and enhance the burden uniformity, various qualifying factors must be considered, and the summation of relative differences must be used to create a comprehensive evaluation index combined with regional edge features and grid-based segmentation techniques. We wrote a program according to these methods and passed the on-site drilling and blasting test in the underground roadway as a part of the control system.

    Two principles guide laying holes in precision blasting. One is to equalize the burden of same-type holes, which are relief and contour holes with a similar blasting action and location. Another is to reduce the number of holes while ensuring blasting efficiency. In the past, technical limitations prevent realizing the first goal. Accordingly, a way to encrypt holes and increase the charge amount is applied to ensure the blasting effect. The widespread problem of uneven burdens in same-type holes has not yet been solved and set aside for a long time. Thus, we have not yet obtained the optimal results of the hole layout.

    (1) Problems with laying holes in the cross-section.

    Two classic patterns are usually used to lay holes in the cross-section. The first pattern is to initiate holes in the lower part of the cross-section first and then initiate the holes in the upper part row by row, as shown in Fig. 1(a). This pattern requires each row of holes in the upper part to be of equal spacing. The rock breaks to the red line after initiating the relief holes of each row in the upper part. There is a significant difference in the burden’s size (W) from each contour hole in the upper gray area to the red line. There are no holes in the gray area on both sides, and the burden direction of hole A points directly below when initiated. Because the spacing between holes A and B is too long, the rock between them may not destroy, resulting in an excessively long burden length of nearby contour holes and the possibility of under-excavation. The second pattern of the hole layout is shown in Fig. 1(b) [2628]. The cut holes, contour holes, and floor holes are the same as those of the first hole layout pattern, but the relief holes lay along curves parallel to the contour. This setting avoids defects in the first hole layout pattern near the contour holes in the upper part of the cross-section, but there are problems when laying holes near the cut area. The rock breaks to the red line after initiating these holes in this area. The burden is not equal for each hole, regardless of how to lay relief holes.

    Fig. 1.  Uneven burden problem: (a) pattern 1; (b) pattern 2.

    The area where the uneven burden problem exists has a uniform geometric feature; i.e., its edges have curves and straight lines. When the cutting area is square and the contour profile has curved segments, it must have an area of uneven burden in the cross-section regardless of which pattern the hole layout is adopted. There are no standard guides on how to place holes in this area now.

    (2) Differentiation of the hole layout in different faces.

    In the past, most hole position designs only considered the hole layout in the drilled face but rarely considered the reasonableness of the position at the hole bottom. When adopting inclined cuts, the uniformity of the burden at the hole bottom depends on the angle of relief holes in different rows. It is hard to control when without a computer-controlled drilling jumbo. In addition, the burden direction at the hole bottom differs from that at the hole entrance, as shown in Fig. 2. In the parallel hole cutting mode, the cut holes are perpendicular to the planned face. Thus, the burden direction at the bottom of all relief holes is within the planned face. The calculation cannot easily achieve a uniform distribution of the relief hole bottom when using inclined hole cutting. Conventional designs do not consider these primarily because distributing the burden equally does not make sense, given the significant angular deviation when using manual drilling.

    Fig. 2.  Variability when laying holes within different faces.

    As mentioned earlier, the problem of the uneven hole layout has not received much attention in traditional blasting. Handheld rock drills or regular drilling jumbos result in a considerable deviation between the planned and actual positions of holes. Computer-controlled drilling jumbos with precise positioning capabilities enable high blasting efficiency with few holes and uniform hole layout schemes. The hole layout still uses the traditional graphic design when promoting computer-controlled drilling jumbos. Some scholars have written automatic planning programs for hole position parameters based on blasting rules to establish a planning model. However, none of these methods solves the uneven burden of same-type holes in different locations in space.

    With the development of intelligent blasting, a set of intelligent planning methods with high universality must be designed. It can realize the standardization and unification of planning and solve the uneven hole layout burden. Intelligent planning transforms the hole layout problem into a mathematical problem, optimizes the hole position parameters through computational strategies, and achieves precise and efficient blasting. Intelligent planning of holes requires identifying the area that has the uneven burden problem and defining the metrics to measure uniformity. Then, we find an algorithm to achieve the best possible uniformity.

    We address the uneven burden of the same-type hole caused by changes in the shape of the cross-section in roadways and the angle of the inclined cut hole. The subject is mine roadways that contain straight walls and arches, using two hole layout patterns in Fig. 1. Given the difficulties and shortcomings of graphic design, we use the LabVIEW software to write the program to solve the problems. The general idea is to reduce the area of uneven burden as much as possible using a contour offset within the drilled and planned faces. Then, appropriate methods are used to lay holes in the uneven area after size reduction and in other areas.

    The solution has four steps: The first step is to create a coordinate system and contour profile equations using the cross-section information on the width, height, and arch height. It is the benchmark to derive the coordinates of various types of holes.

    The second step is to divide the cross section into even and uneven areas in Fig. 3 while considering the two different hole layout patterns in Fig. 1. The area that can realize the line segment offset is the even area. The offset distance is the burden’s size (W). Otherwise, it is the uneven area. We call the polyline segment formed by the line segment offset as the route. According to hole layout pattern 1, shown in Fig. 3(a), the uneven area is at the tunnel’s top. The triangular zone on either side and the interval directly above make up this area. According to hole layout pattern 2, shown in Fig. 3(b), the uneven area is above the cutting area. Of note, there are other uneven areas in Fig. 1(b) on both sides of the cutting area. However, this phenomenon can easily be seen in the partial excavation method of tunnels. For mine roadways with straight walls and arches in the contour profile of the cross-section, there is only one uneven area above the cutting area. It is the main difference to apply the method in roadways and tunnels.

    Fig. 3.  Line segment offset and area division: (a) pattern 1; (b) pattern 2.

    The third step uses different methods to derive the hole position parameters for the even and uneven areas. In the even area, the holes lay in each route according to the formulated hole spacing constraints. In the uneven area, the idea to solve the optimization problem in mathematics guides the hole layout so that the burdens of each hole are uniform enough.

    (1) Method to lay holes in the even area.

    As shown in Fig. 4, the holes lay on each route in the even area. The conventional practice (Fig. 4(a)) is to divide the total length (LR,T) by the number of holes (N) to obtain the hole spacing value (LR) and then calculate the parameters of each hole (B1, B2, …, BN). However, the hole spacing in the upper part of the cross-section can be large due to the effect of gravity on the actual blasting process. Conventional practice does not consider this case. Thus, we propose the concept of the hole spacing constraint function/series to precisely adjust the hole spacing value LD of holes within the same route. We use the recursion and iteration (Fig. 4(b)) to lay holes according to the hole spacing constraint function/series LD = F(x, y) or LD(n) = F(n). (x, y) refers to the position of hole, and n refers to the number of holes.

    Fig. 4.  Laying holes along the routes: (a) division algorithm; (b) recursion algorithm.

    (2) Method to lay holes in the uneven area.

    The burden uniformity varies depending on the hole layout schemes. We need an index to measure the different schemes’ burden uniformity. Laying holes to make the burden uniform enough is an optimization problem in mathematical planning. The idea is to solve for the optimal value of the objective function under relevant constraints. The specific steps are (I) to define the objective function, (II) to create constraint conditions, and (III) to calculate the optimal solution. Its basic form is shown in Eq. (1).

    {minf(X)s.t.{g1(X)g2(X),X=[x1,x2,] (1)

    where X is the set of independent variables x1, x2, …; g1(X), g2(X), etc. are the constraint functions; s.t. is the abbreviation of the subject to, indicating obedience to the constraint; f(X) is the objective function.

    Our method takes the hole spacing LD as the independent variable. The constraints are the equations that satisfy the coordinates and number of holes. Two metrics, σ2X and σ2W, evaluated the uniformity of holes distributed in the uneven area at different LD. σ2X is the sum of deviation squares about the hole layout along the route’s direction. σ2W is the variance of burden. Because we use two evaluation metrics, the objective function is established based on the summation of relative differences. The series of hole coordinates is solved so that the weighted sum of relative difference is as small as possible.

    The fourth step solves the uneven burden of the holes in three-dimensional (3D) space.

    The above three steps achieve the same-type hole uniformity in the drilled face. However, it has not realized the hole layout uniformity in space. Two factors need to be considered. One is the angle of relief holes per row changes according to the cut hole angle. Another is that the burden at the hole bottom differs from that at the entrance in direction and size. Thus, we repeat the three steps above in the planned face to calculate the hole bottom position of different holes. Then, the hole’s angle is calculated. The same-type hole uniformity in other cross-sections of the space is improved after achieving burden uniformity on both faces.

    After establishing the hole layout rules, computer programming realizes the intelligent design of double-face even hole layout in the drifting blasting of underground mines.

    Planning theories and solutions for the specific environment are needed to apply the above ideas in practice.

    We use the LabVIEW software to write the planning program to replace the drawing. The front panel and program block diagram are the two components of the software. They are used to create the human–machine interface (HMI) and develop the background program code. The technician enters the necessary information into the HMI. The algorithm in the background receives the input values and processes them to obtain the coordinates (x, y, z) and angle (α, β) of the holes. Then, the results are returned to the HMI for displaying the output. The technicians confirm the message and grant the drilling jumbo to position the holes according to the scheme.

    The process of information input–processing–output is described in detail below, taking a roadway with a complex line shape of the contour profile as an example.

    A roadway containing straight walls and a three-centered arch is shown in Fig. 5. The upper half of the contour profile is arch-shaped, and the lower half is rectangular. Three circular arcs splice the arch axis, so there are three circular centers. The round arch is a case of the three-centered one. The cross-section’s half-width is h1, the straight wall height is h2, and the arch height is f. In particular, f is equal to h1 in a cross-section with a round arch.

    Fig. 5.  Roadway, coordinate system, and hole position parameters.

    The hole’s entrance and bottom are on the drilled and planned faces. The angle between the hole and the heading direction is θ. The two faces are parallel, they are all perpendicular to the heading direction, and their distance is the vertical depth D of the hole. The arch consists of three circular arc segments joined in sequence. The three centers on the drilled face and planned face are OD1, OD2, OD3, OP1, OP2, and OP3.

    We create a coordinate system OG-XGYGZG to describe the roadway space. The origin OG is the intersection point between the midline of the roadway and the ground. The axis ZG points to the heading direction. The axis YG is vertically upward. The axis XG points to the left. ZG = 0 and ZG = D can express the drilled and planned face.

    The profile equation is established based on the above coordinate system. In the past, there was a strict plotting method when manually designing the contour profile. The programming language needs to describe the drawing process when using the program to plan. The cross-section’s contour profile has five segments containing straight walls and a three-centered arch. The articulation of each line, with the center, radius, and central angle of each circular arc, is shown in Fig. 6.

    Fig. 6.  Establishment of the contour profile equation.

    The profile’s center coordinates, radius, and central angle are derived in Eq. (2) using the cross-section’s half-width h1, straight wall height h2, and arch height f:

    {Radius:r1=h1fr2fh1;r2=h21+f2h1+fh21+f22(h21+f2h2)Center:OD1(fr2fh1,h2);OD2(0,h2+fr2);OD3(ffr2h1,h2)Centralangle:θD1=tan1(h1f);θD2=2tan1(fh1) (2)

    where r1 and r2 are the radii; OD1, OD2, and OD3 are the center; θD1 and θD2 are the central angles of the arcs in the profile; h1, h2, and f are the cross-section’s size.

    The profile’s equation of each segment is shown in Eq. (3).

    {Line1:x=h1Curve1:(xfr2fh1)2+(yh2)2=r21Curve2:x2+[y(h2+fr2)]2=r22Curve3:(xffr2h1)2+(yh2)2=r21Line2:x=h1 (3)

    Line segment offsets are the basis of partial hole position planning. Two patterns need to be discussed based on the line shape adopted for the relief hole route in which the upper half of the cross-section is straight or curved.

    As shown in Fig. 7, we obtain the contour hole route (No. q = 0) and relief hole routes (No. q = 1–K) parallel to the contour profile of the cross-section and the cut hole route (No. q = K + 1) and the floor hole route by the line segment offset in the curved pattern. They are all symmetrical along the midline of the cross-section. The cut holes have an over-depth DOD, which means they are deeper than other holes.

    Fig. 7.  Curved pattern of the route’s equidistant offset.

    The basic idea is to make a profile horizontal over the cutting area to derive the number K, location, and distance of the relief hole routes. Then, the calculation of the route’s offset amount in the profile is completed. As shown in Fig. 7, each contour-hole entrance is inside the profile, and the distance to the profile is l1; each contour-hole bottom is outside the profile, and the distance to the profile is l2. There is a trapezoidal area between the contour and the cut hole within this profile. The widths are h3 and h4 of the top line and baseline, respectively, of the trapezoid. K routes divide this trapezoid evenly to achieve equal burdens at the hole entrance and bottom. However, the burden’s direction at the hole bottom of some holes is not in the planned face. The recursion and iteration algorithms can solve this problem. The planning gets the burden as l3 and l4 at the hole entrance and bottom. Therefore, the blast-hole horizontal angle α (α0, …, αK+1) in each route can also be obtained. The upper half of the cross-section also plans K relief holes. Their burden at the hole entrance is l3, but that at the hole bottom is l4,U, which is different from l4.

    The straight pattern has a characteristic that the form of the relief hole route in the upper half of the cross-section is the straight line segment. However, we still arrange holes as the uniformity principle. Other parts of the route’s offset can refer to the curved pattern’s strategy.

    The main action in the even area is to lay holes along each route where the starting point, end point, and trajectory are known. Finding an appropriate hole spacing is crucial so that the holes can evenly divide the route. This section describes the algorithm to lay holes on a spliced route consisting of various line shapes by taking the contour hole route as an example.

    We only calculate the holes on the left side (x < 0) to save workload because they are symmetrical with that on the right side of the cross-section about the midline.

    The holes are on the route. The hole position parameters satisfy the constraints of the route equation and hole spacing. The hole spacing LD can be equal to some constants or vary with the hole position (x, y). A feasible constraint is to divide the route into upper and lower parts by the height h2 of the springing, as shown in Eq. (4).

    LD=f(x,y)={LD,1,y<h2LD,2,y>h2 (4)

    where LD,1 and LD,2 are the hole spacing of holes in the lower and upper parts of the route, respectively. LD,1 < LD,2, because gravity exists.

    The planning starts by calculating the coordinates of the hole entrance. The contour hole route is similar to the contour profile and has five segments. There are three segments from the bottom up on the left side, as shown in Fig. 8(a), line 1, curve 1, and curve 2. The detailed derivation is described in supplementary information (Part A).

    Fig. 8.  Calculation process of hole coordinates on the spliced route: (a) segments of the spliced route; (b) calculation on line 1; (c) calculation on curve 1; (d) calculation on curve 2.

    Each iteration of the hole position parameters on the planned face is similar to the drilled face. The method to calculate the hole’s spatial angle θ needs the coordinates (xD, yD, 0) and (xP, yP, D) obtained on both faces, as shown in Eq. (5). θ is the angle between the hole axis and heading direction. Then, the angle θ is decomposed into a horizontal angle α and a vertical angle β, as shown in Eq. (6).

    θ=cos1[D(xPxD)2+(yPyD)2+D2] (5)
    {α=cos1[D(xPxD)2+D2]β=tan1[yPyD(xPxD)2+D2] (6)

    After recursion, there is an error between the last hole and the route’s endpoint. We need to adjust the hole spacing and repeat the recursion until the error value is less than the tolerance one, which is an iterative process. It is hard to connect the error value and the change in the hole spacing for converging the error.

    At each iteration, the horizontal coordinate of the last hole BN3 is xN3. Three reference values Δ1, Δ2, and Δ3 are calculated as Eq. (7). They correspond to the cases where the gap between the last hole and the end of the route is close to 0, 1/2 hole spacing, and 1× hole spacing, obtained through a recursive calculation. They are all related to xN3. Because it is impossible to determine whether the number of holes on the route is odd or even until the completion of the calculation, it needs to instantly control the design accuracy according to the actual distribution of blast holes. The error ΔE is the minimum absolute value of the three.

    {ΔE=min{|Δ1|,|Δ2|,|Δ3|}Δ1=xN3Δ2=xN3LD,22Δ3=xN3L2D,2L4D,24r25,k (7)

    where xN3 is the horizontal coordinate of the last hole BN3, LD,2 is the spacing of holes higher up on the route, and r5,k is the radius of the large arc in the kth route.

    If ΔE is greater than the allowable error [ΔE], the error is still significant after the (j−1)th iteration. Eq. (8) derives the new hole spacing LD according to ΔE for the following jth iteration. LD is LD,1 and LD,2 for the holes above and below the arch springing, respectively. LD,2 divided by LD,1 equals η.

    {LD,1(j)=LD,1(j1)+λ×ΔE(N11)+η×(N3N1)LD,2(j)=η×LD,2(j1) (8)

    where λ is the learning rate, which is a discount factor to prevent the non-convergence of the error, and 0 < λ < 1; N1 and N3 refer to the total number of holes on the straight line and the total number of holes on the route.

    The planning is finished until ΔE < [ΔE] at the jth iteration. LD(j) is the final hole spacing.

    As shown in Fig. 9, the upper edge of the uneven area is a curve with the function expression y = F1(x), whereas the lower edge is a straight line with the function expression y = F2(x). The area’s height is HTR, which is equal to two times the distance of the relief hole routes in the even area. The area’s width is LTR. There may be an odd or even number of holes in this area.

    Fig. 9.  Laying of holes in the uneven area: (a) number of holes is even; (b) number of holes is odd.

    All holes’ coordinates satisfy Eq. (9) to ensure the even distribution of holes. There is also a value range (LD,H, LD,L) for the hole spacing LD. The hole coordinates and number will also change when the hole spacing varies. These conditions are constraints.

    y=12[F1(x)+F2(x)],12LTRx12LTR (9)

    One of the metrics to measure uniformity is the size variance σ2W of all blast hole burdens, as shown in Eq. (10).

    σ2W={2×N21(Wiμ)2N,N=2,4,6(W1μ)2+2×(N1)22(Wiμ)2N,N=1,3,5 (10)

    where N is the number of holes; Wi is the burden of each hole, i = 1, 2, …, N; μ is the burden’s mean value.

    σ2W can only describe the uniformity of the blast hole in the direction perpendicular to the route. Another metric to measure uniformity in the parallel direction is the sum of deviation squares σ2X. The uneven area is uniformly divided into N grids of width LTR/N, corresponding to N holes, as shown in Fig. 10. The dashed line represents the midline of each grid. The hole spacing affects how far each hole is from the matching grid’s dashed line.

    Fig. 10.  Deviation of the parallel distribution of holes: (a) number of holes is even; (b) number of holes is odd.

    σ2X is calculated in Eq. (11).

    σ2X={2×N21E2iN,N=2,4,62×(N1)22E2iN,N=1,3,5 (11)

    where Ei is the parallel deviation of each hole, i =1, 2, …, N.

    In general, any hole spacing LD cannot make the two independent metrics σ2W and σ2X optimal appear together. The summation of relative differences constructs a new index, the weighted sum of the relative difference S, to obtain the hole spacing that makes each evaluation metric better, as shown in Eq. (12).

    S(j)=WW|σ2W(j)σ2Wmin|2σ2Wmid+WX|σ2X(j)σ2Xmin|2σ2Xmid (12)

    where S(j) is the sum of differences corresponding to each hole spacing LD. WW and WX are the weight coefficients adopted for the burden and parallel distribution deviation. σ2W(j) and σ2X(j) are the burden variance and sum of squared deviations on the distribution in a parallel direction corresponding to each hole spacing LD. σ2Wmin, σ2Xmin, σ2Wmid, and σ2Xmid are the minimum and median values of σ2W(j) and σ2X(j).

    We compare all S(j) and take the hole spacing LD corresponding to its minimum value as the optimal solution. The optimal solution in the uneven area that makes holes relatively even in this area is finally used as the layout scheme.

    After completing all the above calculations, we will obtain the coordinates (xD, yD, 0) of each hole on the drilled face, vertical depth D, and decomposition values (α, β) of the angle θ in the horizontal and vertical directions. The drilling jumbo will position and drill the hole based on this information.

    The computer-controlled drilling jumbo realizes the automatic planning of holes through the program. The content should pass the industrial test in underground coal mines to verify its application effect. The test environment was a roadway containing straight walls and a three-centered arch. The half-width h1 of the cross-section is 2.4 m, the height h2 of the straight wall is 2 m, and the arch height f is 1.6 m. Given the cross-section shape and the mechanism size of the drilling jumbo, the blast hole vertical depth D per round was 1.9 m. Figs. 11 and 12 show the results of the hole planning in both faces for the two hole layout patterns.

    Fig. 11.  Curved pattern of laying holes in the section: (a) drilled face; (b) planned face (Unit: mm).
    Fig. 12.  Straight pattern of laying holes in the section: (a) drilled face; (b) planned face (Unit: mm).

    For the curved pattern, there are two relief hole routes. In the drilled face shown in Fig. 11(a), the route’s spacing is 457 mm. By adjusting the overall height of the cutting area and the number of cut holes, the uneven area’s height is regulated to be two times 457 mm. In the planned face, the burdens in the upper half of the cross-section and those in the lower half cannot be equal because the distance between the hole bottoms of the cut holes does not exceed 200 mm in general. The route’s spacings are 520 and 751 mm for the upper and lower halves through the calculation, respectively. Because most of the holes are not straight with angles, Fig. 11(b) cannot show the burden at the hole bottom of some of the holes, which is not parallel to the planned face.

    For the straight pattern, Fig. 12 arranges two relief hole routes in the upper half and the left and right sides of the lower half of the cross section. The equal values of the route’s spacing, as those in Fig. 11, can be obtained by adjusting the route’s position and standardizing the height of the uneven area.

    Four contents are analyzed: the hole-position parameters in the even area, the hole layout in the uneven area, the differences between our and traditional methods, and the results of the on-site application.

    We take the contour hole as an example to illustrate how to calculate the hole-position parameters. First, we specified the input parameters. The distance l1 between the hole entrance and contour profile is 200 mm. The distance l2 between the hole bottom and the contour profile is 50 mm. The hole spacing in the upper half of the cross-section is 1.1 times that in the lower half. In addition, the initial value of the hole spacing LD,1(0) is 400 mm for the holes below the springing on the drilled face.

    Then, we lay the holes along the route. When the error ΔE between the last hole and the route’s endpoint is too large, the algorithm adjusts the hole spacing and repeats the recursion. After several iterations, the error converges and is smaller than the predesign tolerance error [ΔE], and then the calculation is finished. As shown in Table 1, we realized the contour hole spacing within the drilled and planned faces after 4–7 iterations. The error is less than the tolerance value.

    Table  1.  Hole spacing of contour holes
    Position of holesLD,1 / mmLD,2 / mmΔE / mm[ΔE] (LD,1 × 10−2) / mmNumber of iteration
    In the drilled face3984382.44.04
    In the planned face4575032.64.67
     | Show Table
    DownLoad: CSV

    With the route equation and hole spacing values clarified, we can calculate the hole coordinates at its entrance and bottom and the hole angle, as shown in Table S1 in supplementary information (Part B). The computer-controlled drilling jumbo will drill holes according to the parameters xD, yD, α, β, and blast hole vertical depth D in Table S1.

    We define the area enclosed by two adjacent blast hole routes with different line shapes in the cross-section as an uneven area. An example of laying holes in the uneven area shown in Fig. 12(a) can illustrate this in detail. Based on the worker’s experience, the hole spacing of relief holes in the test tunnel is generally between 600 and 750 mm. In the actual computation, we set the range of the hole spacing LD to 550–800 mm to show the optimization process of the hole spacing values.

    As shown in Fig. 13(a), an even number of holes are laid in the uneven area. If LD ≤ 603 mm, six holes are required to cover the area. Conversely, only four holes are required. For a certain number of holes, the smaller the hole spacing is, the smaller the burden variance σ2W is. However, if the hole spacing takes a small value, the sum of deviation squares σ2X tends to be high. It is impossible to select a value of the hole spacing that makes both metrics optimal at the same time. Thus, the summation of relative differences derives the weighted sum of the relative difference S, where the weight coefficients WW and WX are both taken as 1. Fig. 13(b) shows the results. A value of 734 mm makes the hole spacing optimal. An odd number of holes is laid in the uneven area shown in Fig. 13(c). If LD ≤ 753 mm, five blast holes are required to cover the area. Conversely, only three holes are required. The relationship between the hole spacing and metrics σ2W and σ2X is shown in Fig. 13(c). After the calculation, as shown in Fig. 13(d), the optimal hole spacing is 585 mm, which is beyond the range of the empirical values of the hole spacing. The planned number of holes is five, which increases the drilling workload. In comparison, it is better to lay four holes with a hole spacing of 734 mm in the uneven area of the drilled face.

    Fig. 13.  Solution of laying holes in the uneven areas: (a) LD vs. {\boldsymbol \sigma }_{\boldsymbol W}^{2} and {\boldsymbol \sigma }_{\boldsymbol X}^{2} when the hole number is even; (b) LD vs. S when the hole number is even; (c) LD vs. {\boldsymbol \sigma }_{\boldsymbol W}^{2} and {\boldsymbol \sigma }_{\boldsymbol X}^{2} when the hole number is odd; (d) LD vs. S when the hole number is odd.

    Fig. 14 shows the design results obtained by drawing in computer-aided design (CAD) software. We arranged holes as evenly as possible in the drilled face. The design idea is as follows: First, we designed the cutting area based on experience. The cut hole spacing selected integer values to facilitate drilling. Second, the principle of the line segment offset and the equal division of the blast hole burden guided the location of the position of the contour holes, floor holes, and two rounds of relief holes. After several trial calculations, we designed the hole spacing of the contour and relief holes. In addition, we arranged independent relief holes along the horizontal line in the gray area enclosed by the inner round of relief holes and the upper edge of the cutting area so that the burden of each hole would meet the blasting experience.

    Fig. 14.  Comparison of the hole layouts in the drilled face: (a) drawing method; (b) our method (Unit: mm).

    As a comparison, Fig. 14(b) shows the hole planning results of our method within the same drilled face, as shown in Fig. 11(a). Compared with those in Fig. 14(a), four differences are noted: (I) Hole spacing is no longer rounded to the nearest multiple of 10 mm owing to the overall hole position design. (II) The algorithm derives the contour hole spacing and relief hole spacing accurately. The hole spacing of the upper contour holes is 1.1 times greater than that of the lower ones. For relief holes, the rate is 1.2 so that the blasting process can fully use gravity to improve efficiency. This design objective cannot be easily achieved through drawing. (III) We derived the location of the independent relief holes within the gray area precisely according to the concept and algorithm of the uneven area. (IV) Our results saved three holes. The technical advantages of the computer-controlled drilling jumbo positioning the holes ensured achieving the above differences in the field.

    We compared the standard deviation of the burdens of the holes in the uneven area of two design options. Nine holes are affected, as shown in Fig. 15(a) and (b). The figures indicate the burden’s direction and size of each hole. The burden’s standard deviations are 45.32 and 27.53 mm. The standard deviation obtained in this study was reduced by 40% as compared to that with the CAD scheme. Hence, our method improves the uniformity of the hole layout in uneven areas.

    Fig. 15.  Uniformity comparison of blast hole burdens in the uneven areas: (a) analysis for Fig. 14(a); (b) analysis for Fig. 14(b) (Unit: mm).

    The difference between the two design options is also reflected in the blast hole angle optimization and even hole layout in the planned face. As shown in Fig. 16(a), if we equally divide the planned face without considering other factors, such as the charge, the hole spacing of the hole’s bottoms is 783 mm. However, the flatly divided hole spacing between the hole bottoms is not the real burden because the burden direction at the hole bottom is not parallel to the connecting line of the hole bottoms. As a result, the contour hole tends to have less charge, but its burden size is large, whereas the opposite is true for the relief holes. Our algorithm accurately calculated the hole burden as 751 mm, as shown in Fig. 16(b).

    Fig. 16.  Burden evenness at the hole bottom and blast hole angle: (a) drawing method; (b) our method (Unit: mm).

    We also precisely derived the coordinates and angle values of the upper part holes except for holes related to the cutting area.

    This study established a hole layout procedure with standardized rules based on the operational advantages of the computer-controlled drilling jumbo. The hole layout relies on the judgment of strict guidelines and adopts a global perspective to deduce rather than improvised adjustments for individual problems or local contradictions.

    After device development and technical research, the computer-controlled drilling jumbo suitable for rock roadways with small-size cross-sections has completed industrial testing in an underground mine. The machine has a high accuracy of drilling positioning, fast moving velocity of the drilling arm, and control software in line with workers’ operating habits.

    According to our method, the obtained design scheme of the holes guided the drilling operation and achieved better effects after blasting. As shown in Fig. 17, the finished quality of the height and width of the roadway reached the quality standard of excellent or above, and there were no substandard products. The blast hole utilization factor is more than 90% (ratio of the actual advance to the vertical depth of the hole). The rate of the half-hole marks is 70%. The even block size of the blasting muck pile proves that the hole layout is reasonable and uses the blasting energy effectively.

    Fig. 17.  Operation in a roadway and quality after blasting.

    (1) This paper proposes a double-face intelligent hole position planning method based on a computer-controlled drilling jumbo. The method solves the current problem of still designing holes based on the traditional way to cause uneven burdens of same-type holes when using computer-controlled drilling jumbos. It creates conditions to improve the blasting efficiency and achieve precision blasting in the roadway.

    (2) We developed the hole design ideas by combining the graphic features of the cross-section profile for different hole layout patterns. The even and uneven areas divide the cross-section through the line segment offset. The summation of relative differences creates a comprehensive evaluation index in the uneven area. The calculation example proves that the standard deviation of the hole burden in the uneven area of the proposed scheme is reduced by 40% compared with the drawing designed by the drawing method.

    (3) Improving the evenness of the hole layout in the drilled face alone is not enough to ensure precise and efficient blasting results. In the case study, the recursion and iteration algorithms derived the relief hole burden at the hole’s entrance and bottom as 457 and 751 mm, respectively. All the holes lay in a cross-section of 4.8 m × 3.6 m. The hole layout met the burden and hole spacing planning requirements on both faces.

    (4) Various technical means were integrated to improve the intelligence of using the program to lay out holes and solve a series of problems of traditional graphic design. The first is to solve the problem of the uneven burden using a line segment offset and area division. The second is to fully use gravity to reduce the number of holes by changing the design mode of equal hole spacing in laying out holes according to the hole spacing constraint function/series. The third is to improve the evenness of the hole layout in the planned face of the hole bottoms using a precise design.

    In summary, the application of computer-controlled drilling jumbos and electronic detonators has created an opportunity for intelligent precision blasting in roadways. In this context, the double-face program-controlled planning method of the hole layout using a computer-controlled drill jumbo, together with other methods, can promote the development of the drill and blast method toward precision and efficiency. Further improving the safety, environmental protection, and technology level of shaft excavation is critical to developing green mines.

    This work was financially supported by the Fundamental Research Funds for the Central Universities (No. FRF-AT-19-005) and the National Natural Science Foundation of China (No. 51934001).

    The authors declare that they have no conflicts of interest in this work.

    The online version contains supplementary material available at https://doi.org/10.1007/s12613-022-2575-4.

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