Comparison of the Generation of S-wave with different Simulation approaches

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1 Fragblast 11, 2015, Sydney, Australia Comparison of the Generation of S-wave with different Simulation approaches Gao Q D, Lu W B, Hu Y G, Chen M& Yan P Present by Wenbo Lu State Key Lab. of WRHES Wuhan University, China

2 Outline Introduction Mechanism of S-wave generated in blasting Comparison of different simulation approach Conclusion and discussion

1 Introduction T 水平径向速度 /( cm s -1 ) 3.0 2.0 1.0 0.0-1.0-2.0-3.

3 1 Introduction T 水平径向速度 /( cm s -1 ) IV-1 I-1 I-2 IV II-2 III-1 III-2 II-1 时间 /(ms) R V 水平切向速度 /( cm s -1 ) 竖直向速度 /( cm s -1 ) IV-1 I-1 I-2 IV III-1 III-2 II-1 II-2 时间 /(ms) I-1 I III-1 IV-1 III-2 IV-2 II-1 II-2 时间 /(ms) The evaluation and control of the impact of blasting vibration is an important issue during blasting operations

II-2 II-2 III-1 时间 /(ms) III-1 时间 /(ms) 0 200 400 600 800 III-1 III-2 IV-1

wave 竖直向速度 /( cm s -1 ) 水平切向速度 /( cm s -1 ) 水平径向速度 /( cm s -1 ) S wave

4 I-1 I I-1 I I-1 I-2 II-1 II-1 II-2 II-2 III-1 时间 /(ms) III-1 时间 /(ms) III-1 III-2 IV-1 IV-2 II-1 II-2 时间 /(ms) III-2 III-2 IV-1 IV-1 IV-2 IV-2 1 Introduction P wave 竖直向速度 /( cm s -1 ) 水平切向速度 /( cm s -1 ) 水平径向速度 /( cm s -1 ) S wave Blasting area Rayleigh wave Blasting vibrations = P wave + S wave + Rayleigh wave

5 1 Introduction T R V 水平径向速度 (cm/s) 水平切向速度 (cm/s) 竖直向速度 (cm/s) 29.2m 31.0m 8# 7# 6# Monitoring 探洞 points 时间 (ms) 时间 (ms) m II-2 I m 11.2m 19.0m 9.1m 11.2m 5# 4# 3# 2# 1# 0.8m II-3 I-2 监测点 Monitoring points 1.0m II-1 I-1 Blasting area P R T S R V S R P Distance =120m -2.0 时间 (ms) Waveforms induced by single blast hole

6 1 Introduction Most blasting seismic energy is carried by Rayleigh waves in the far field Rayleigh waves are generated by the interaction of P- and S- waves at the surface of the ground S-wave component plays an important role in damage to adjacent resident houses induced by blasting vibration Current situation S-wave component always be ignored during prediction of blasting vibration and its impact evaluation

7 1 Introduction Objectives of the current study Reviews on the mechanisms of the generation of S-wave during blasting Comparisons of several typical numerical models in regarding to the components of S-wave generated during simulation Give some advice to choose a suitable numerical model

8 Outline Introduction Mechanism of S-wave generated in blasting Comparison of different simulation approach Conclusion and discussion

9 2.1 S-wave induced by finite length of charge { { u u r φ 2 a dp CS 2 2 R = 0 [1 2( ) cos φ] g ( t ) 4µ CR C C P P P 2 a dp φ φ R g t 2µ CR S CS sin cos 0 = ( ) V V p s k1dp0 = ρcpr k2dp0 = ρc R S *Heelan, P. A. (1953). Geophysics, 18(3):

10 2.2 S-wave generated under finite VOD Numerical model Range of model Borehole diameter Charge diameter Charge length 30m*30m*10m 90mm 70mm 10m

11 2.2 S-wave generated under finite VOD Infinite rock mass: No Rayleigh wave is involved Constitutive model: Elastic model Calculating condition: instantaneous vs finite detonation Reference section : middle section of charge Reference points

12 2.2 S-wave generated under finite VOD condition 10 P R=10m P R=10m S v -5 ( cm/s) v ( cm/s) P t (ms) R=20m P t (ms) R=20m v 0 ( cm/s) v ( cm/s) S t (ms) Instantaneous detonation t (ms) Finite detonation

13 2.3 S-wave induced interaction of waves with interfaces Z SV(Α4,θ4) θ4 P(A3,θ3) θ3 ΙΙ X θ0 θ1 (A0,θ0) θ2 SV(A2,θ2) P(A1,θ1) sinθ0 sinθ1 sinθ3 sinθ2 sinθ4 = = = = v v v v v 1P 1P 2P 1S 2S = p

$Joints,fractures and bedding clearage in rook mass Interface between$ elastic-to-plastic rock face Interface between damaged-to-undamaged rock

elastic-to-plastic rock face Interface between damaged-to-undamaged rock

14 2.3 S-wave induced by waves conversion on interfaces Generalized interfaces Joints,fractures and bedding clearage in rook mass Interface between elastic-to-plastic rock face Interface between damaged-to-undamaged rock face Elastic-plastic face Fractures Joints and bedding clearages Damaged-to-undamaged face

15 2.4 S-wave induced by rock cracking and movement of fragments Cracking and sliding induced S-wave Casting of fragments induced S-wave

16 Outline Introduction Mechanism of S-wave generated in blasting Comparison of different simulation approach Conclusion and discussion

17 3 Comparison of different simulation approaches Continuous method: FEM Elastic model vs Damage model To study material damage induced S-wave Discontinuous continuous coupled method SPH-FEM coupled model To simulate the cracking of rock around blast hole To simulate the movement of fragments

18 3 Comparison of different simulation approaches Single hole blast in semi-finite rock mass is studied Explosive : JWL equation of state ω ω 1 ω 2 p = A 1 e + B 1 e + RV RV V RV R V E 1 2

19 3 Comparison of different simulation approaches FEM LS DYNA with self-defined modified damage model Tensile damage component C kk c D 2 m d = (5 / 2) ( IC / ρεmax) εv (1 ) D t = 2 16 (1 v ) C 9 (1 2 v) d Compressive damage component W = σ d ε p p ij ij D = c λw p 1 D t *Lu, WB; Hu, YG; Yang, JH, et al. Int. J. Rock Mech. Min. Sci. ;2013, 64:

3 Comparison of different simulation approaches Brief introduction of SPH (m j,ρ j ) j χ - i χ j Interpolation formula m f( x ) f( x ) W( x x, h) N j i = j i j j= 1 ρ j i 2h Governing equations The

20 3 Comparison of different simulation approaches Brief introduction of SPH (m j,ρ j ) j χ - i χ j Interpolation formula m f( x ) f( x ) W( x x, h) N j i = j i j j= 1 ρ j i 2h Governing equations The smooth particle hydrodynamics (SPH) is a mesh-free Lagrangian method Has advantage of dealing with larger local distortion than grid-based methods Widely used in simulation of metal forming, impact, crack growth, fracture, fragmentation, etc. N dρ ( x) = m [ vx ( ) vx ( )] A dt i j j i ij j= 1 α dv σ ( x ) σ ( ) ( x ) m A A dt N α, β α, β j xi i = j 2 ij 2 ji j= 1 ρi ρj de P ( x ) m [ vx ( ) vx ( )] A dt ρ = N i i = 2 j j i ij i j 1

21 3 Comparison of different simulation approaches Implementation of SPH-FEM coupled model SPH be employed in near field FEM be used in middle to far field

22 3 Comparison of different simulation approaches Damage distribution ( by FEM ) Deformation and damage distribution (by SPH-FEM)

23 Velocity (cm/s) 3 Comparison of different simulation approaches 径向速度 (cm/s) 80 Elastic Comparison of 15 different simulation approach 20 Velocity 径向速度 (cm/s) (cm/s) Damage Time (ms) -60 时间 (ms) S Time (ms) Time (ms) 时间 (ms) S 时间 (ms) R=5 m, Radial Waveforms on the middle section of charge Velocity 径向速度 (cm/s) (cm/s) 80 SPH-FEM From the radial waveforms of velocity, the arriving time of S-wave could be clearly discriminated The arriving time of S-wave is identical to time calculated with V P = E(1 ν ) E VS = ρ(1 + ν)(1 2 ν) 2 ρ(1 + ν) t = R/ V R/ V S P

24 3 Comparison of different simulation approaches Elastic Damage SPH-FEM Velocity (cm/s) 径向度 / 时间 (ms) Time (ms) Velocity (cm/s) 径向速度 (cm/s) S 时间 (ms) -3-4 Time (ms) R=25 m, Radial Velocity (cm/s) 径向速度 (cm/s) 时间 (ms) -4-6 Time (ms) -8 S Waveforms on the middle section of charge The arriving of S-wave can also be clearly discriminated Waveforms calculated with different models have obvious differences

25 3 Comparison of different simulation approaches Elastic Damage SPH-FEM Velocity Velocity (cm/s) (cm/s) Velocity (cm/s) (R=25 m,radial) Velocity (cm/s) Waveforms on the surface of the ground(r=25m) Elastic model induces the smallest S/R-wave Component SPH-FEM model has induces the biggest S/R-wave Component

3 Comparison of different simulation approaches Elastic 6 Damage 10 SPH-FEM Velocity Velocity (cm/s) (cm/s) Velocity (cm/s) 4 2 0-2 -4-6 0 5 10 15 20 25 30 35 40 45 R=25

26 3 Comparison of different simulation approaches Elastic 6 Damage 10 SPH-FEM Velocity Velocity (cm/s) (cm/s) Velocity (cm/s) R=25 m,vertical Velocity (cm/s) Waveforms on the surface of the ground(r=25m) From the vertical waveforms of velocity, obvious differences be found

27 3 Comparison of different simulation approaches Comparisons of calculated and measured waveforms on the surface(vertical) Velocity (cm/s) Elastic Velocity (cm/s) Damage Velocity (cm/s) SPH-FEM Calculated waveforms, R=45m, 1/3 Q R = QR 1/3 = 1/3 Site Site 2 Measured waveforms Q R = 0.060

surface (Radial) Velocity (cm/s) 径向度 / 6 4 2 0-2 -4

Velocity (cm/s) SPH-FEM -6-8 Calculated waveforms, R=45m,

28 3 Comparison of different simulation approaches Comparisons of calculated and measured waveforms on the surface (Radial) Velocity (cm/s) 径向度 / Elastic 时间 (ms) Velocity (cm/s) Damage Velocity (cm/s) SPH-FEM -6-8 Calculated waveforms, R=45m, 1/3 Q R = QR 1/3 = 1/3 Site Site 2 Measured waveforms Q R = 0.060

29 Outline Introduction Mechanism of S-wave generated in blasting Comparison of different simulation approach Conclusion and discussion

30 4 Conclusion and discussion Conclusion S-wave could be generated under conditions of finite length of charge, finite detonation velocity of explosive, the interaction of stress wave on medium interfaces, and the rock cracking and movement of fragments, etc. S-wave is an important component of total blasting vibration Different numerical model produce different results of s- wave components

31 4 Conclusion and discussion Suggestions on the numerical models choosing The chosen models be theoretically possible to describe the mechanism of s-wave induced in blasting Numerical methods that could describe rock cracking and movement of fragments during simulation, such as DDA, coupled SPH-FEM, etc, be as the first choice Further work required To calibrate numerical result with some controlled onsite or indoor experiments data Separation of S wave form the total vibration waveforms

32 The authors are very appreciated for the supports from: Chinese National Programs for Fundamental Research and Development (2011CB013501) Chinese National Science Fundation for Distinguished Young Scholars ( )

33 Thank you for your attention!

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