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Citation: Guo, J.; Zhang, C.; Xie, S.;
Liu, Y. Research on the Prediction
Model of Blasting Vibration Velocity
in the Dahuangshan Mine. Appl. Sci.
2022, 12, 5849. https://doi.org/
10.3390/app12125849
Academic Editor: Ricardo Castedo
Received: 10 May 2022
Accepted: 6 June 2022
Published: 8 June 2022
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applied sciences
Article
Research on the Prediction Model of Blasting Vibration Velocityin the Dahuangshan MineJiang Guo 1 , Chen Zhang 1,*, Shoudong Xie 2 and Yi Liu 2
1 School of Resources and Safety Engineering, Central South University, Changsha 410083, China;[email protected]
2 Hongda Blasting Engineering Group Co., Ltd., Guangzhou 510623, China; [email protected] (S.X.);[email protected] (Y.L.)
* Correspondence: [email protected]
Abstract: In order to improve the prediction accuracy of blast vibration velocity, the model forpredicting the peak particle velocity of blast vibration using the XGBoost (Extreme Gradient Boosting)method is improved, and the EWT–XGBoost model is established to predict the peak particle velocityof blast vibration by combining it with the EWT (Empirical Wavelet Transform) method. Calculatethe relative error and root mean square error between the predicted value and measured value ofeach test sample, and compare the prediction performance of the EWT–XGBoost model with theoriginal model. There is a large elevation difference between each vibration measurement location ofhigh and steep slopes, but high and steep slopes are extremely dangerous, which is not conduciveto the layout of blasting vibration monitoring equipment. The vibration velocity prediction modeladopts the numerical simulation method, selects the center position of the small platform as themeasurement point of the peak particle velocity, and studies the variation law of the blasting vibrationvelocity of the high and steep slopes under the action of top blasting. The research results showthat the EWT–XGBoost model has a higher accuracy than the original model in the prediction ofblasting vibration velocity; the simultaneous detonation method on adjacent high and steep slopescannot meet the relevant requirements of safety regulations, and the delayed detonation method caneffectively reduce the blasting vibration of high and steep slopes. The shock absorption effect of theelevation difference within 45 m is obvious.
Keywords: elevation difference; blasting vibration velocity; EWT; XGBoost; prediction model
1. Introduction
Blasting plays a key role in open-pit mining [1], especially in construction stone mines,which account for a large share of open-pit mining. Although blasting is widely used forrock crushing in open pit mines, the impact of blasting vibration cannot be ignored [2].Sometimes, it is even necessary to use mechanical crushing to eliminate the negative impactof blasting vibration, so the prediction of blasting vibration velocity is particularly critical.The blasting vibration velocity prediction mainly refers to predicting the PPV (peak particlevelocity). Blasting workers in open-pit mines often use blasting vibration monitoring resultsto optimize blasting parameters. In this way, blasting workers can reduce the impact ofstructures below the steep slope by controlling the PPV.
In engineering blasting, people pay more and more attention to avoid serious acci-dents through conducting blasting vibration prediction in advance, which can help reducedamage to structures and improve personnel safety [3–5]. Many scholars have conductedextensive and in-depth research on blasting vibration prediction, and their research meth-ods include empirical formulas, machine learning, and numerical simulations.
The ground vibration level is described by empirical formulas mainly considering rockcharacteristics, distance, maximum single-shot charge, and other blasting conditions [6–8].
Appl. Sci. 2022, 12, 5849. https://doi.org/10.3390/app12125849 https://www.mdpi.com/journal/applsci
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The improved formula of the traditional Sadovskii formula is well applied. Lin et al. [9]used the dimensionless analysis method to improve the nonlinear regression predictionmodel of the blasting vibration propagation law. After the improvement, the model canreflect the elevation effect. According to the measured data, the prediction accuracy of theimproved model is improved by 13.55% compared with that of the original model.
Machine learning methods have been introduced into the field of blasting vibrationprediction, and many scholars have conducted in-depth research on it. Yue et al. [10]established a least squares support vector machine model to predict the blasting vibrationeffect of open pit mines and optimized the regularization parameters and kernel functionwidth coefficients through a particle swarm optimization algorithm, so that the model has ahigher generalization ability and prediction accuracy. Sun et al. [11] considered eight factors,including blast center distance, elevation difference, propagation medium conditions,maximum single-stage charge, total charge, differential time, detonation direction, andthe shock absorption effect of the excavated chamber, and established the PSO–LSSVMmodel to predict the blasting vibration of underground gas storage caverns. YAN et al. [12]used the GEO–ELM model to predict the PPV and frequency of the ground vibration when,caused by blasting demolition, the building collapses. The model has a higher predictionaccuracy after combining it with the gray wolf algorithm. The random forest algorithm iswidely used in the blasting vibration problem, and the improved method for its algorithmhas been proven to have a higher accuracy [13,14].
The low cost of the numerical simulation method can provide a certain referencefor blasting vibration safety evaluation and the optimization of blasting parameters. Laket al. [15] compared Green′s function solution, the experimental results, and the numericalsimulations for the PPV results of rock blasting, and the results show that the three arehighly consistent. Aiming at the problem of the demolition of adjacent buildings by benchblasting construction, Lei et al. [16] took a bench blasting project as the background andstudied the blasting vibration propagation law with a maximum single-shot charge of3.8 kg and a blast hole diameter of 38 mm under the combined action of horizontal distanceand elevation.
The blasting vibration velocity is affected by many aspects in the open-pit mine [17–19],which affects the accuracy of the blasting vibration velocity prediction. Compared with themachine learning method, the empirical formula has great disadvantages considering thenumber of factors and the consumption of resources and time. In this paper, the improvedmachine learning algorithm XGBoost and the finite element numerical simulation methodare used to establish the blasting vibration velocity prediction model of the Dahuangshantuff rock mine. This paper focuses on the prediction of blasting vibration velocity.
2. Materials and Methods2.1. Engineering Overview
The Dahuangshan Tuff Building Stone Mine is an open-pit mine. The mining area islocated in the hilly area in the north of Cezi Island and belongs to Taoyaomen Community,Cengang Street, Dinghai District, Zhoushan City, Zhejiang Province. The location of themine area is shown in Figure 1. The rock formations in the mining area are mainly tuffand hard rocks with a compact structure. The mining process includes DTH drilling,medium and deep hole blasting, mechanical secondary crushing, loader shovel loading,and truck transportation, and the mining process is discharged to the designated location.The minimum mining elevation is +6 m.
2.2. Blasting Vibration Monitoring
The blasting vibration monitoring uses the T-4850 sensor to collect blasting signals.The Figure 2 shows the layout of the monitoring points during blasting on the 141 platform.The blasting adopts a digital electronic detonator detonation network, a total of 77 holes, atotal of 195 detonators, and 18 m in the hole. The digital electronic detonator and the 10
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m digital electronic detonator are used to process the priming charge. The interval delaybetween the rows is set to 130 ms, and the interval delay between the holes is set to 50 ms.
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Figure 1. Geographical location of the mining area.
2.2. Blasting Vibration Monitoring
The blasting vibration monitoring uses the T-4850 sensor to collect blasting signals.
The Figure 2 shows the layout of the monitoring points during blasting on the 141 plat-
form. The blasting adopts a digital electronic detonator detonation network, a total of 77
holes, a total of 195 detonators, and 18 m in the hole. The digital electronic detonator and
the 10 m digital electronic detonator are used to process the priming charge. The interval
delay between the rows is set to 130 ms, and the interval delay between the holes is set to
50 ms.
(a)
Figure 1. Geographical location of the mining area.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 12
Figure 1. Geographical location of the mining area.
2.2. Blasting Vibration Monitoring
The blasting vibration monitoring uses the T-4850 sensor to collect blasting signals.
The Figure 2 shows the layout of the monitoring points during blasting on the 141 plat-
form. The blasting adopts a digital electronic detonator detonation network, a total of 77
holes, a total of 195 detonators, and 18 m in the hole. The digital electronic detonator and
the 10 m digital electronic detonator are used to process the priming charge. The interval
delay between the rows is set to 130 ms, and the interval delay between the holes is set to
50 ms.
(a)
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(b) (c)
Figure 2. Blasting Vibration Monitoring: (a) Measuring point layout (141 Blasting area); (b) Moni-
toring instrument at the measuring point; (c) The site of the blasthole layout.
2.3. Theory of the EWT Method
The empirical wavelet transform method was proposed by Gilles [20] in 2013. It in-
tegrates the EMD algorithm [21] and the wavelet transform method [22–24], so it has the
characteristics of both methods. The EMD algorithm has data-driven adaptivity, a high
signal-to-noise ratio, a good time-frequency focus, and advantages in terms of analyzing
nonlinear and non-stationary signal sequences, and the original signal can be decomposed
into each intrinsic mode function by the EMD algorithm. The equation is as follows:
𝑓(𝑡) =∑ 𝑓𝑘(𝑡)𝑁
𝑘=0 (1)
The algorithm process of the empirical wavelet transform method is as follows:
firstly, the Fourier transform is performed on the original input signal, the empirical scale
function and empirical wavelet are defined by the following formula, and, finally, the
wavelet filter is constructed to decompose the signal to obtain each mode function.
𝑛(𝜔) =
1 𝑖𝑓|𝜔| ≤ (1 − 𝛾)𝜔𝑛
cos [π
2β(
1
2γωn(|ω| − (1 − γ)ωn))]
𝑖𝑓(1 − 𝛾)𝜔𝑛 ≤ |𝜔| ≤ (1 + 𝛾)𝜔𝑛0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(2)
𝑛(𝜔) =
1 𝑖𝑓(1 + 𝛾)𝜔𝑛 ≤ |𝜔| ≤ (1 − 𝛾)𝜔𝑛+1
cos [π
2β(
1
2γωn+1(|ω| − (1 − γ)ωn+1))]
𝑖𝑓(1 − 𝛾)𝜔𝑛+1 ≤ |𝜔| ≤ (1 + 𝛾)𝜔𝑛+1
sin [π
2β (
1
2γωn(|ω| − (1 − γ)ωn))]
𝑖𝑓(1 − 𝛾)𝜔𝑛 ≤ |𝜔| ≤ (1 + 𝛾)𝜔𝑛0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(3)
2.4. Theory of the XGBoost Method
The XGBoost method is an ensemble learning method based on decision trees. It was
proposed by Chen Tianqi et al. [25] in 2016. Each decision tree learns the residual between
the target value and the sum of the predicted values of all previous trees. The XGBoost
model fuses multiple tree models and adds the prediction results of many trees to obtain
the final prediction result. The basic principles are as follows:
Figure 2. Blasting Vibration Monitoring: (a) Measuring point layout (141 Blasting area); (b) Monitor-ing instrument at the measuring point; (c) The site of the blasthole layout.
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2.3. Theory of the EWT Method
The empirical wavelet transform method was proposed by Gilles [20] in 2013. Itintegrates the EMD algorithm [21] and the wavelet transform method [22–24], so it has thecharacteristics of both methods. The EMD algorithm has data-driven adaptivity, a highsignal-to-noise ratio, a good time-frequency focus, and advantages in terms of analyzingnonlinear and non-stationary signal sequences, and the original signal can be decomposedinto each intrinsic mode function by the EMD algorithm. The equation is as follows:
f (t) = ∑Nk=0 fk(t) (1)
The algorithm process of the empirical wavelet transform method is as follows: firstly,the Fourier transform is performed on the original input signal, the empirical scale functionand empirical wavelet are defined by the following formula, and, finally, the wavelet filteris constructed to decompose the signal to obtain each mode function.
φn(ω) =
1 i f |ω| ≤ (1− γ)ωn
cos[
π2 β(
12γωn
(|ω| − (1− γ)ωn))]
i f (1− γ)ωn ≤ |ω| ≤ (1 + γ)ωn0 otherwise
(2)
ψn(ω) =
1 i f (1 + γ)ωn ≤ |ω| ≤ (1− γ)ωn+1
cos[
π2 β(
12γωn+1
(|ω| − (1− γ)ωn+1))]
i f (1− γ)ωn+1 ≤ |ω| ≤ (1 + γ)ωn+1
sin[
π2 β(
12γωn
(|ω| − (1− γ)ωn))]
i f (1− γ)ωn ≤ |ω| ≤ (1 + γ)ωn0 otherwise
(3)
2.4. Theory of the XGBoost Method
The XGBoost method is an ensemble learning method based on decision trees. It wasproposed by Chen Tianqi et al. [25] in 2016. Each decision tree learns the residual betweenthe target value and the sum of the predicted values of all previous trees. The XGBoostmodel fuses multiple tree models and adds the prediction results of many trees to obtainthe final prediction result. The basic principles are as follows:
yi = Φ(xi) = ∑Kk=1 fk(xi) ( fk ∈ F) (4)
F =
f (x) = ωq(x)
(q : Rm → T, ω ∈ RT
)(5)
In the formula, yi represents the predicted value of the XGBoost model, which issuperimposed by multiple decision trees fk(xi) in the series; K represents the number ofdecision trees; F represents the decision tree function space; q(X) represents that the sampleX is mapped to the leaf nodes of the tree; ωq(x) represents the weight of the leaf nodes;Rm represents the m-dimensional real vector; T represents the number of leaf nodes of thedecision tree; and RT represents the T-dimensional real vector.
The XGBoost method improves the calculation accuracy by adding a regular term tothe loss objective function and by performing a second-order Taylor expansion. The lossobjective function is composed of an error term l and a regular term Ω. The formula isas follows:
L(∅) = ∑i l(yi, yi) + ∑k Ω( fk) (6)
Ω( f ) = γT +12
λω2 (7)
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In the formula, l(yi, yi) represents the error between the predicted value and the actualvalue; Ω( fk) represents the regular term, which is used to constrain the number of leafnodes T and the leaf weight ω of the decision tree; γ represents the L2 square of the Tmodulus coefficient; and λ denotes the L2 squared modulus coefficient of ω.
For regression problems, the accuracy evaluation index of the model is often measuredby the RMSE (root-mean-square error). The formula is as follows:
RMSE =
√√√√Σni=1
(Xpred,i − Xmea,i
)2
n(8)
In the formula, Xpred,i represents the predicted value, Xmea,i represents the measuredvalue, and n represents the number of samples.
3. Model3.1. EWT–XGBoost Model
The process of using the EWT–XGBoost model to achieve PPV prediction is shown inFigure 3. The original data of the blasting vibration are denoised by EWT, and the obtaineddata are divided into the training set and the test set. The cross-validation method canobtain the parameters that optimize the generalization performance of the model. Thecommon hyperparameters of the XGBoost model are the learning rate, the minimum leafweight, the number and depth of the tree, etc. It divides the dataset into multiple subsets,among which a subset is used as the validation set, and the average error is calculatedfor multiple trainings to improve the generalization performance of the model. Becausethe amount of blasting vibration data collected this time is small, the leave-one-out cross-validation method is used to make the number of samples equal to the divided number oftraining subsets.
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Data Set
Train Set Validation Set
Test Set
Define inputs and outputs
LOO-CV
XGBoost Model
Forecast Result
Raw Data
EWT Noise reduction
Figure 3. EWT–XGBoost prediction model flowchart.
When predicting blasting vibration velocity, the amount of explosives (Q), blasting
center distance (R), and elevation difference (H) are input as features, and the output is
the blasting peak particle velocity (PPV). Both the training data samples and test data
samples are derived from the blasting vibration data of the Dahuangshan mine project
from July 8 to July 20; the original data samples are shown in Table 1:
Table 1. Raw sample data.
No. Q (Kg） R (m) H (m) PPV (cm/s)
1 9072 466 81 0.335
2 9518 389 81 0.343
3 9942 486 96 0.339
4 9975 38 30 8.390
5 9975 201 45 0.193
6 9975 70 75 3.710
7 9975 129 90 0.350
8 5745 671 121 0.043
9 5745 683 121 0.051
10 10,077 80 -15 6.730
11 10,077 152 30 0.210
12 10,077 522 45 0.783
13 10,077 678 90 0.192
14 7401 47 15 5.830
15 7401 140 15 1.774
16 7401 273 15 0.416
17 7401 432 30 0.143
Figure 3. EWT–XGBoost prediction model flowchart.
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When predicting blasting vibration velocity, the amount of explosives (Q), blastingcenter distance (R), and elevation difference (H) are input as features, and the output is theblasting peak particle velocity (PPV). Both the training data samples and test data samplesare derived from the blasting vibration data of the Dahuangshan mine project from July 8to July 20; the original data samples are shown in Table 1:
Table 1. Raw sample data.
No. Q (Kg) R (m) H (m) PPV (cm/s)
1 9072 466 81 0.3352 9518 389 81 0.3433 9942 486 96 0.3394 9975 38 30 8.3905 9975 201 45 0.1936 9975 70 75 3.7107 9975 129 90 0.3508 5745 671 121 0.0439 5745 683 121 0.05110 10,077 80 −15 6.73011 10,077 152 30 0.21012 10,077 522 45 0.78313 10,077 678 90 0.19214 7401 47 15 5.83015 7401 140 15 1.77416 7401 273 15 0.41617 7401 432 30 0.14318 7401 654 51 0.15219 9545 55 15 2.28320 9545 161 15 0.71721 9545 286 15 0.52422 9545 677 51 1.01223 8041 484 96 0.28724 9812 523 81 0.79825 8041 461 90 0.14926 9812 209 75 3.10827 8041 592 75 0.11628 9812 304 60 3.97929 8041 588 45 0.19830 9812 381 30 0.94831 8041 601 30 0.32332 9812 52 15 9.026
By performing empirical wavelet decomposition on the collected blasting vibrationsignals, each mra component can be obtained, as shown in Figure 4. The blasting signal canbe found by removing the noise, and the maximum value among them can be selected asthe new particle peak particle velocity data sample, as input to the EWT–XGBoost blastingvibration velocity prediction model.
3.2. High Steep Slopes Model
Simulation of the blasting on adjacent high and steep slopes is carried out, and theparameters of the model include the slope parameters and blasting parameters. The slopeparameters include the foot of the slope (+6 m), the step height (15 m), eight steps, the footof the step (75), the safety platform (5 m), the cleaning platform (8 m), and three safetyplatforms with one cleaning platform at the intervals (safety platform at the +111 m, +96 m,+81 m, +51 m, +36 m, +21 m mining levels; cleaning platform at the +66 m mining level).The blasting parameters include the borehole diameter (110 mm), the depth of the borehole(16.5 m), the length of the stemming (4 m), the length of the charge (12.5 m), the chargediameter (90 mm), the hole space (the column distance is 6.2 m; the row distance is 3.3 m),
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the minimum burden (3 m), and the subdrilling (1.5 m). The schematic diagram of the siteand the corresponding model are shown in Figure 5.
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18 7401 654 51 0.152
19 9545 55 15 2.283
20 9545 161 15 0.717
21 9545 286 15 0.524
22 9545 677 51 1.012
23 8041 484 96 0.287
24 9812 523 81 0.798
25 8041 461 90 0.149
26 9812 209 75 3.108
27 8041 592 75 0.116
28 9812 304 60 3.979
29 8041 588 45 0.198
30 9812 381 30 0.948
31 8041 601 30 0.323
32 9812 52 15 9.026
By performing empirical wavelet decomposition on the collected blasting vibration
signals, each mra component can be obtained, as shown in Figure 4. The blasting signal
can be found by removing the noise, and the maximum value among them can be selected
as the new particle peak particle velocity data sample, as input to the EWT–XGBoost blast-
ing vibration velocity prediction model.
Figure 4. Blasting vibration signal EWT and spectrogram.
3.2. High Steep Slopes Model
Simulation of the blasting on adjacent high and steep slopes is carried out, and the
parameters of the model include the slope parameters and blasting parameters. The slope
parameters include the foot of the slope (+6 m), the step height (15 m), eight steps, the foot
of the step (75°), the safety platform (5 m), the cleaning platform (8 m), and three safety
platforms with one cleaning platform at the intervals (safety platform at the +111 m, +96
m, +81 m, +51 m, +36 m, +21 m mining levels; cleaning platform at the +66 m mining level).
The blasting parameters include the borehole diameter (110 mm), the depth of the bore-
hole (16.5 m), the length of the stemming (4 m), the length of the charge (12.5 m), the
charge diameter (90 mm), the hole space (the column distance is 6.2 m; the row distance
is 3.3 m), the minimum burden (3 m), and the subdrilling (1.5 m). The schematic diagram
of the site and the corresponding model are shown in Figure 5.
Figure 4. Blasting vibration signal EWT and spectrogram.
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(a)
(b)
Figure 5. Schematic diagram of the scene and the corresponding model: (a) Site map of the slope;
(b) Schematic diagram of the model.
Among the various material ontological models provided by LS-DYNA, the ontolog-
ical models that are often used to describe the rock material are the RHT model, the HJC
model, etc. In this paper, the HJC ontological model is used to describe the tuff material,
and the relevant parameters of the tuff are derived from reference [26], as shown in Table
2.
Table 2. HJC model parameters of the tuff material.
ρ
/(g·cm-3)
G
/(MPa) A B C N
fc/
（MPa)
1.8 6543 0.55 1.77 0.0097 0.77 50
T/(MPa) ε0/(s−1) εf,min Smax Pc/(MPa) Uc PL/(MPa)
3.3 1 × 10−6 0.01 17 17 0.00253 2500
UL D1 D2 K1/(MPa) K2/(MPa) K3/(MPa) fs
0.38 0.04 1 3100 6000 8400 0.035
ρ: mass density, G: shear modulus, A: normalized cohesive strength, B: normalized pressure hard-
ening, C: strain rate coefficient, N: pressure hardening exponent, fc: quasi-static uniaxial compressive
strength, T: maximum tensile hydrostatic pressure, ε0: quasi-static threshold strain rate, εf,min:
amount of plastic strain before fracture, Smax: normalized maximum strength, Pc: crushing pressure,
Uc: crushing volumetric strain, PL: locking pressure, UL: locking volumetric strain, D1: damage con-
stant , D2: damage constant, K1: pressure constant, K2: pressure constant, K3: pressure constant, fs:
failure type.
The air domain is used for the contact between the solid and fluid media. The fluid-
solid coupling algorithm is used to couple the fluid parts, such as the air and explosives,
Figure 5. Schematic diagram of the scene and the corresponding model: (a) Site map of the slope;(b) Schematic diagram of the model.
Appl. Sci. 2022, 12, 5849 8 of 12
Among the various material ontological models provided by LS-DYNA, the ontologi-cal models that are often used to describe the rock material are the RHT model, the HJCmodel, etc. In this paper, the HJC ontological model is used to describe the tuff material,and the relevant parameters of the tuff are derived from reference [26], as shown in Table 2.
Table 2. HJC model parameters of the tuff material.
ρ/(g·cm−3) G/(MPa) A B C N f c/(MPa)
1.8 6543 0.55 1.77 0.0097 0.77 50
T/(MPa) ε0/(s−1) εf,min Smax Pc/(MPa) Uc PL/(MPa)
3.3 1 × 10−6 0.01 17 17 0.00253 2500
UL D1 D2 K1/(MPa) K2/(MPa) K3/(MPa) fs
0.38 0.04 1 3100 6000 8400 0.035ρ: mass density, G: shear modulus, A: normalized cohesive strength, B: normalized pressure hardening, C: strainrate coefficient, N: pressure hardening exponent, f c: quasi-static uniaxial compressive strength, T: maximumtensile hydrostatic pressure, ε0: quasi-static threshold strain rate, εf,min: amount of plastic strain before fracture,Smax: normalized maximum strength, Pc: crushing pressure, Uc: crushing volumetric strain, PL: locking pressure,UL: locking volumetric strain, D1: damage constant, D2: damage constant, K1: pressure constant, K2: pressureconstant, K3: pressure constant, fs: failure type.
The air domain is used for the contact between the solid and fluid media. The fluid-solid coupling algorithm is used to couple the fluid parts, such as the air and explosives,with the solid rock part. The keyword MAT_NULL is used to add air materials. The stateequation formula is:
P = C0 + C1µ + C2µ2 + C3µ3 +(
C4 + C5µ + C6µ2)
E (9)
In the formula, E is the specific energy, which refers to the energy per unit volume;C0~C6 are constants; and µ is the specific volume. The air-related parameters are shownin Table 3.
Table 3. Air parameters.
C0 C1 C2 C3 C4 C5 C6 E/(MPa)
0 0 0 0 0.4 0.4 0 0.25
The explosive material is defined by the keyword “MAT_HIGH_EXPLOSIVE_BURN”.The JWL equation of state is used to represent the pressure and volume changes duringthe explosion. The No. 2 rock emulsion explosive is used in the field. Its parameters arederived from reference [27], as shown in Table 4:
Table 4. Parameters of the No. 2 rock emulsion explosive.
ρ/(kg/m3) D/(m/s) G/(MPa) A/(GPa) B/(Gpa) R1 R2 ω E/(MPa)
1100 3600 3500 214.4 0.182 4.2 0.9 0.15 4 192
Set the top and slope faces as free boundaries and the rest as transmission boundarieswith fixed displacement directions.
4. Result and Discussion4.1. Analysis of the Learning Results
Import the test samples into the trained EWT–XGBoost blasting vibration velocityprediction model for prediction. The comparison of the test samples and prediction resultsis shown in Table 5:
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Table 5. Test sample data and comparison of forecast results.
No. Q(Kg) R(m) H(m)XGBoost Model EWT–XGBoost Model
MeasuredValue
PredictedValue
MeasuredValue
PredictedValue
1 9975 38 30 8.390 8.231 3.882 3.8772 5745 683 121 0.051 0.057 0.013 0.0123 7401 47 15 5.830 5.800 1.566 1.5634 9545 55 15 2.283 2.369 0.941 0.9465 9812 523 81 0.798 0.806 0.063 0.064
It can be seen from the Figure 6 that the maximum relative error of the prediction resultof the blasting vibration velocity of the EWT–XGBoost model is 7.69%, which is less thanthe maximum relative error of the XGBoost model (11.8%). The average relative error ofthe prediction results of the EWT–XGBoost model can be obtained by statistical calculationof the relative error, which yields 2.03%, which is less than the average relative error of theprediction results of the XGBoost model (4.49%). Formula 8 is used to calculate the rootmean square error of the two models. According to the calculation, it can be concluded thatthe root mean square error of the prediction result of the EWT–XGBoost model is 0.0035,which is smaller than the root mean square error of the prediction result of the XGBoostmodel, which is 0.0836. Therefore, in terms of predicting the blasting vibration velocity TheEWT–XGBoost model is better than the XGBoost model.
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Figure 6. Relative results histogram of the prediction results.
4.2. Predictive Analysis of Nodal Vibration Velocity
By building a numerical model of high and steep slopes and comparing and analyz-
ing the variation of blasting vibration velocity at the center positions of different plat-
forms, the following rules are found: the Figure 7 shows the blasting vibration velocity
changes at the center positions of the platforms 51, 66, 81, 96, and 111 within the initial 10
ms, when the blastholes are detonated at the same time. The vibration velocity of the 111
platform exceeds the safe vibration velocity specified in the blasting safety regulations
[28]. From the 96 platform to the 111 platform, the blasting vibration velocity decays rap-
idly. The vibration velocity of the 51, 66, and 81 platforms does not change significantly,
and the peak particle velocity is less than 1cm/s.
Figure 7. 10 ms blasting vibration velocity diagram of the 51–111 platform.
The 111 platform is close to the explosion source and is greatly affected by the shock
wave, so the response fluctuates violently in the vibration velocity. With the increase in
the explosion center distance, the vibration parameters change gradually. According to
this, the safety monitoring of the 111 platform should be strengthened, and active protec-
tion should be carried out.
The Figure 8 is a line chart of the peak blasting vibration velocity of each platform
height with different delay times. Compared with simultaneous blasting, delayed blasting
has a significant impact on the peak particle velocity of the 66–111 platform. The difference
in elevation is 45 m. The peak blasting vibration of the delay times of 130 ms and 80 ms is
Figure 6. Relative results histogram of the prediction results.
4.2. Predictive Analysis of Nodal Vibration Velocity
By building a numerical model of high and steep slopes and comparing and analyzingthe variation of blasting vibration velocity at the center positions of different platforms, thefollowing rules are found: the Figure 7 shows the blasting vibration velocity changes atthe center positions of the platforms 51, 66, 81, 96, and 111 within the initial 10 ms, whenthe blastholes are detonated at the same time. The vibration velocity of the 111 platformexceeds the safe vibration velocity specified in the blasting safety regulations [28]. Fromthe 96 platform to the 111 platform, the blasting vibration velocity decays rapidly. Thevibration velocity of the 51, 66, and 81 platforms does not change significantly, and thepeak particle velocity is less than 1 cm/s.
The 111 platform is close to the explosion source and is greatly affected by the shockwave, so the response fluctuates violently in the vibration velocity. With the increase in theexplosion center distance, the vibration parameters change gradually. According to this,the safety monitoring of the 111 platform should be strengthened, and active protectionshould be carried out.
Appl. Sci. 2022, 12, 5849 10 of 12
Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 12
Figure 6. Relative results histogram of the prediction results.
4.2. Predictive Analysis of Nodal Vibration Velocity
By building a numerical model of high and steep slopes and comparing and analyz-
ing the variation of blasting vibration velocity at the center positions of different plat-
forms, the following rules are found: the Figure 7 shows the blasting vibration velocity
changes at the center positions of the platforms 51, 66, 81, 96, and 111 within the initial 10
ms, when the blastholes are detonated at the same time. The vibration velocity of the 111
platform exceeds the safe vibration velocity specified in the blasting safety regulations
[28]. From the 96 platform to the 111 platform, the blasting vibration velocity decays rap-
idly. The vibration velocity of the 51, 66, and 81 platforms does not change significantly,
and the peak particle velocity is less than 1cm/s.
Figure 7. 10 ms blasting vibration velocity diagram of the 51–111 platform.
The 111 platform is close to the explosion source and is greatly affected by the shock
wave, so the response fluctuates violently in the vibration velocity. With the increase in
the explosion center distance, the vibration parameters change gradually. According to
this, the safety monitoring of the 111 platform should be strengthened, and active protec-
tion should be carried out.
The Figure 8 is a line chart of the peak blasting vibration velocity of each platform
height with different delay times. Compared with simultaneous blasting, delayed blasting
has a significant impact on the peak particle velocity of the 66–111 platform. The difference
in elevation is 45 m. The peak blasting vibration of the delay times of 130 ms and 80 ms is
Figure 7. 10 ms blasting vibration velocity diagram of the 51–111 platform.
The Figure 8 is a line chart of the peak blasting vibration velocity of each platformheight with different delay times. Compared with simultaneous blasting, delayed blastinghas a significant impact on the peak particle velocity of the 66–111 platform. The differencein elevation is 45 m. The peak blasting vibration of the delay times of 130 ms and 80 ms isnot significantly reduced, and, among them, the peak particle velocity of the 111 platformhas the largest decrease. The peak particle velocity of the 80 ms delayed detonation isreduced by 17% compared to the 130 ms delayed detonation on the 111 platform. The51 platform is located in the middle, and its peak particle velocity has been significantlystrengthened. The blasting vibration velocity below the 51 platform has an amplificationeffect, and the peak particle velocity has slightly rebounded.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 11 of 12
not significantly reduced, and, among them, the peak particle velocity of the 111 platform
has the largest decrease. The peak particle velocity of the 80 ms delayed detonation is
reduced by 17% compared to the 130 ms delayed detonation on the 111 platform. The 51
platform is located in the middle, and its peak particle velocity has been significantly
strengthened. The blasting vibration velocity below the 51 platform has an amplification
effect, and the peak particle velocity has slightly rebounded.
Figure 8. Line graph of the peak particle velocity of the 6–111 platform.
5. Conclusions
In this study, a machine learning model and a numerical simulation model were de-
veloped to predict blast vibration velocity at the Dahuangshan mine. A machine learning
model for blast vibration prediction considering elevation difference was established, and
the mean relative error and root mean square error were calculated by training the original
blast vibration monitoring data and predicting the test sample data. It was found that the
EWT–XGBoost model reduces the average relative error by 2.46% and the root mean
square error by 0.0801 compared with the XGBoost model, so the improved XGBoost
method can be applied to the analysis of blasting events in open-pit mines. In terms of
PPV prediction, the EWT–XGBoost model can achieve a higher prediction accuracy com-
pared with that of the original model. A numerical model for predicting the vibration
velocity of high and steep slope blasting is established, and the simulation results show
that the vibration velocity of platform 111 exceeds the safety regulations when the simul-
taneous detonation method is used compared with when the hole-by-hole method is used.
The peak particle velocity of blasting at the top of the mountain decreases sharply when
using the deferred detonation method, and the deferred blasting can have a good vibra-
tion damping effect on the high and steep slope. The vibration damping effect is especially
obvious within a 45 m difference in elevation. The high and steep slopes are dangerous,
so we did not place the sensors. This is an oversight in our work, and we will improve it
in future studies.
Author Contributions: J.G. and S.X. provided the experimental ideas and carried out the experi-
ment; Y.L. directed and assisted the experiment; C.Z. wrote the paper; J.G. reviewed the paper. All
authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the Central South University School-Enterprise Joint Project
“Research on rapid evaluation technology of open-pit blasting effect in plateau mines”
(2021xqlh065) and by the Central South University-Hongda Blasting Engineering Group Postgrad-
uate Joint Training Base (2020pyjd91).
Conflicts of Interest: The authors declare no conflict of interest.
Figure 8. Line graph of the peak particle velocity of the 6–111 platform.
5. Conclusions
In this study, a machine learning model and a numerical simulation model weredeveloped to predict blast vibration velocity at the Dahuangshan mine. A machine learningmodel for blast vibration prediction considering elevation difference was established, andthe mean relative error and root mean square error were calculated by training the originalblast vibration monitoring data and predicting the test sample data. It was found that theEWT–XGBoost model reduces the average relative error by 2.46% and the root mean squareerror by 0.0801 compared with the XGBoost model, so the improved XGBoost method canbe applied to the analysis of blasting events in open-pit mines. In terms of PPV prediction,the EWT–XGBoost model can achieve a higher prediction accuracy compared with thatof the original model. A numerical model for predicting the vibration velocity of highand steep slope blasting is established, and the simulation results show that the vibrationvelocity of platform 111 exceeds the safety regulations when the simultaneous detonation
Appl. Sci. 2022, 12, 5849 11 of 12
method is used compared with when the hole-by-hole method is used. The peak particlevelocity of blasting at the top of the mountain decreases sharply when using the deferreddetonation method, and the deferred blasting can have a good vibration damping effect onthe high and steep slope. The vibration damping effect is especially obvious within a 45 mdifference in elevation. The high and steep slopes are dangerous, so we did not place thesensors. This is an oversight in our work, and we will improve it in future studies.
Author Contributions: J.G. and S.X. provided the experimental ideas and carried out the experiment;Y.L. directed and assisted the experiment; C.Z. wrote the paper; J.G. reviewed the paper. All authorshave read and agreed to the published version of the manuscript.
Funding: This research was funded by the Central South University School-Enterprise Joint Project“Research on rapid evaluation technology of open-pit blasting effect in plateau mines” (2021xqlh065)and by the Central South University-Hongda Blasting Engineering Group Postgraduate Joint TrainingBase (2020pyjd91).
Conflicts of Interest: The authors declare no conflict of interest.
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