This document discusses methods for assessing the impact of blasting vibrations on slope stability. It describes analytical methods like pseudo-static and dynamic approaches for stability analysis. The pseudo-static approach uses a critical acceleration to model vibration effects, while the dynamic approach considers wave propagation principles. An energy approach is also presented for analyzing rock slope stability. The document provides case studies demonstrating the application of these methods. It concludes that pseudo-static and dynamic analyses provide conservative vibration limits, while the energy approach requires detailed rock characterization but may give more reasonable results.

1. Blasting Vibration Assessment of Slopes
Keith WK Kong
FICE FIMMM MHKIE RPE(GEL)

2. Rock Excavation
Excavation Methods (e.g.)
Underground:
• Drill and split
• Mechanical (e.g. hydraulic breaker/hammer)
• Tunnel Boring Machine
• Drill and Blast
Surface:
• Drill and break / Diamond-saw cuts
• Mechanical (e.g. hydraulic breaker/hammer; WBE)
• Drill and Blast

3. Blasting Mechanism

4. Blasting Mechanism

5. Blasting Video Clip

6. Body Waves
P-wave (Longitudinal)
S-wave (Transverse or shear)
R-wave (Rayleigh)
Love wave

7. Body Waves
P-wave (Longitudinal)
Resultant vibration
S-wave (Transverse)
Rayleigh wave

8. Wave Motion (Undamped Free Vibration)
ẋ
ẍ
Considered as a Simple Harmonic Motion (SHM)
A = Initial displacement from equilibrium 0 at time t = 0
x = Displacement from equilibrium 0 at time t
= A·Cos (ω·t) (ω = angular velocity or frequency)
ẋ = Velocity of body (or particle)
= -A·ω Sin (ω·t) = -A·ω Cos (ω·t + π/2)
ẍ = Acceleration of body (or particle)
= -A·ω² Cos (ω·t) = -A·ω² Cos (ω·t + π)
T = Period of Oscillation
= 2 π / ω
f = Frequency of Oscillation
= ω / 2 π (i.e. ω = 2 π f)

9. Risks of Ground Vibration
• Property loss
► Damage to buildings/structures
► Damage to underground services or utilities
• Failure occurred of geotechnical features
• Nuisance
• Complaints

10. Rock Slope Failure Due to Rock Blasting

11. Guidance Documents for
Blasting Assessment in Hong Kong
• GEO Circular No. 27 Geotechnical Control of Blasting
• Mines Division Practice Notes (Nos. 1 - 4 )
• Mines Division Guidance Note No. 1 on Vibration Monitoring
• Project Administration Handbook for Civil Engineering Works, 2014 Edition
• General Specification for Civil Engineering Works Vol. 1 (Section 6)
• Buildings Department Practice Note for Authorized Persons and Registered
Structural Engineers 178
• GEO Report No. 15 Assessment of Stability of Slopes Subjected to Blasting
Vibration
• GEO Report No. 45 Gravity Retaining Walls Subject to Seismic Loading
• GEO REPORT No. 102 A Study of the Effects of Blasting Vibration on
Green Concrete

12. Slope Stability of Vibration Analysis
Analytical Methods:
• Pseudo-static Approach
(GEO Report 15 suggested method)
(for soil slope)
• Dynamic Approach
• Energy Approach
(GEO Report 15 suggested method)
(for rock slope)

13. Slope Stability Analysis
Conventional limit equilibrium methods to be used [e.g. Bishop
(1955), Janbu (1972), Morgenstern & Price (1965), etc] :
 Limit equilibrium analyses assume the “Factor of Safety”
(FoS) is the same along the entire slip surface.
 If FoS is greater than unity (i.e. FoS > 1.0), the available
shear resistance will exceed the required for equilibrium;
and hence the slope will be stable with respect to sliding
along the specified slip surface as analysed.
 If FoS is less than 1.0, the slope will be unstable.
(Note: There are no “rules” for acceptable factors of safety under
seismic conditions)

14. Slope Stability Analysis
Standard slice in limit equilibrium methods (Fredlund and Krahn, 1977)

15. Pseudo-static Approach
Wong & Pang, 1992 (i.e. GEO Report 15) suggested:
PPVc = Kc·g / (ω·Ka)
where:
Kc = the critical acceleration (m/sec²) at which the slope has
a Factor of Safety of 1.0 against failure;
g = the acceleration due to gravity (m/sec²);
ω = the circular frequency of the ground motion (2·π·f).
f is the frequency of ground vibration during blasting;
Ka = the magnification factor
PPVc = Critical Peak particle velocity of ground mass

16. Pseudo-static Approach
• Kc - can be acquired from some of the geotechnical
computer programmes such as SLOPE/W and OASYS-
SLOPE
• ω - Ground vibration frequency of 30Hz is adopted as
recommended by Wong & Pang (1992).
National Institute of Rock Mechanics (NIRM, 2005) study,
the most common frequency of ground vibration (ω)
reported for construction blasts varies from 10 to 200 Hz,
typically greater than 20Hz.

17. Pseudo-static Approach
• Ka - A ratio of the “maximum of the net response
acceleration at the mass” to the “maximum of input
acceleration at bedrock”.
The response acceleration at the mass is subjected to
the geometry of the slope and the failure slip.

18. Determination of magnification factor (Ka)
Inclined Bedrock Formation
Soil mass shear wave velocity, S = 300 m/s (GEO Report 15)

19. Determination of Soil Shear Wave Velocity
SPT: 20 to 50 (typical CDG)
S = 240 m/s to 440 m/s
Average = 340 m/s

20. Determination of magnification factor (Ka)
Horizontal Bedrock Formation
Soil mass shear wave velocity, S = 300 m/s

21. Ground Vibration Prediction of Blasting
Hong Kong’s 84% Confidence Average-line (Li & Ng 1992)
Where:
PPV – peak particle velocity (mm/s)
R – distance between blast and measuring point (m)
W – maximum charge weight per delay interval (kg)
𝒑𝒑𝒗 = 𝟔𝟒𝟒 𝒙
𝑹
√𝑾
−𝟏.𝟐𝟐

22. Worked Example
25m
q = 39 degree
t = 9 + sn tan f’
SPT N-value = 40
blasting
site

23. Pseudo-static Approach
Determine the magnification factor, Ka
Shock wave Velocity of the soil, S = 300 m/sec
Total horizontal thickness of the deposit, D = 6m
S / D = 50
PPV = 644  W 0.61  R -1.22
(W)
Slope/w model

24. Dynamic Approach
By considering Hooke’s law in the uniaxial conditions, and
Newton’s second law, the compressive stress wave
equation can be written as:
σ = ρ·C·V
Where:
σ = compressive stress of wave
C = wave velocity of material
V = peak particle of material
Noted that “longitudinal (P-) wave velocity, Cp” in a material is always
greater than “transverse (S-) wave velocity, Ct (or Cs)”.

25. A list of typical Cp and Cs values (Press, 1966)
Material Cp (m/s) Cs (m/s) Density (kg/m³)
Sandstone 1400 – 4500 2450
Shale, Slate 2300 – 4700 2350
Limestone 2650
Soft 1700 – 4200
Hard 2800 – 6400
Crystalline 5700 – 6400
Dolomite 3500 – 6900 2840
Granite, Granodiorite 4600 - 6000 2800 – 3200 2670
Gabbro 6400 - 6700 3400 – 3600 2980
Basalt 5400 – 6400 2700 – 3200 3000
Schist 4200 - 4900 2500 – 3200 2800
Gneiss 3500 - 7500 3300 – 3700 2650
Water 1450 1000
Air 335 -

26. Dynamic Approach – Worked Exampple (1/2)
sn of Slip#2
at rest
Unstable Stable sn
sh
sv
t
q

27. Dynamic Approach – Worked Exampple (2/2)
PPV = 644  W 0.61  R -1.22
(W)
Unstable Stable
sn of Slip#2
at rest
Notes:
Young’s modulus of soil (E) = 1.1 x SPT-N (Davies,1987)
wave velocity of soil
 
   2ν1ν1ρ
ν1E
cp



σ = ρ·C·V

28. Case Study (1)
Source: GeoInfo Map, LandsD

29. Case Study (1)

30. Case Study – Slope Section
31 m
8m span tunnel

31. Case Study (1)
Slope
Portion
Potential
Failure
Calculated
allowable PPV
(mm/s)
Wt. of Explosive, W
(kg)
when PPV<25 mm/s
Soil Slip #1 51.91 5.49
Slip #2 15.28 2.14
Slip #3 15.41 2.25
Slip #4 95.33 5.30
Slip #5 12.59 1.52
Slip #6 6.01 0.46
Rock Rock wedge 17.3 2.56
Note: Governed eq. by PPV = 644  W 0.61  R -1.22

32. Vibration Monitoring Record by Vibrograph

33. Case Study – Trial Blast Results

34. Questions
• Liquefaction of soil ???
• Lateral spreading failure of slopes ???
Blasting vibration induce:
For controlled blasting:
• ppv ≤ 25 mm/sec
• Shock wave energy is low
(due to low dosage: range 0.2 to <50 kg per delay)
• peak vibration duration just about a second
• CDG/CDV SPT-N >30

35. Slope Stability of Vibration Analysis
Analytical Methods:
• Pseudo-static Approach
• Dynamic Approach
• Energy Approach (for rock slope)

36. Blasting Vibration Assessment of Rock Slope

37. Rock Slope Stability Analysis
V
Zw
Tension crack
yf
yp
W
U
yS
b
L
q
T
H
b
Z
Q
Resisting forces = c' L+ [ W (cos yp - a sin yp) - U - V sin yp + T cos q ] tan f
Disturbing forces = W (sin yp + a cos yp) + V cos yp – T sin q

38. Rock failure on slope: The blasting vibration energy
transmitted to the potential failure wedge (modelled as a rock
block) resting on the rock slope, as well as the energy
dissipation at the rock joint.
By principal (at rest):
Resisting Force of Rock Block > Distributing Force of Rock
Block
(i.e. FOS > 1.0, no sliding occurred)
As vibration force applied:
Resisting Force of Rock Block < Distributing Force of Rock
Block + Energy Loss at the Boundaries (i.e. change in Potential
Energy + Kinetic Energy to rock block), rock block sliding will be
occurred.
Rock Slope Stability Analysis

39. The critical particle velocity (PPVc) cab be
estimated as the rock block will be driven to a state
whereby peak shear is developed at the rock joint:
Where:
g = 9.81 m/s2
b = failure plane angle of rock block
dp and f’p which are empirical formulae given by Barton 1990
Energy Approach

40. Barton (1990) equations:
Where:
JCS = joint wall compression strength
JRC = joint wall roughness coefficient
L = length of joint (length of failure plane in 2D)
sn = normal stress of the block
f’r = residual angle of shear resistance of rock joint
i = roughness component of shear resistance of joint (in
degree)
∅′ 𝑝 = 𝐽𝑅𝐶 ∙ 𝑙𝑜𝑔
𝐽𝐶𝑆
𝜎 𝑛
+ ∅′ 𝑟 + 𝑖
𝛿 𝑝 =
𝐿
500
𝐽𝑅𝐶
𝐿
0.33
Energy Approach

41. Joint Wall Roughness, JRC
JRC joint wall roughness, estimation from joint surface profile matching
(Barton et. al., 1977)

42. Joint Wall Comp. Strength, JCS
Estimate of joint wall
compressive strength
(JCS) from Schmidt
hardness
(after Barton et. al., 1977
and 1985)
Or using point load
test result to
determine UCS of
rock
i.e. UCS = 24 · Is50

43. Ground Vibration Prediction of Blasting
Hong Kong’s 84% Confidence Average-line (Li & Ng 1992)
Where:
PPV – peak particle velocity (mm/s)
R – distance between blast and measuring point (m)
W – maximum charge weight per delay interval (kg)
𝒑𝒑𝒗 = 𝟔𝟒𝟒 𝒙
𝑹
√𝑾
−𝟏.𝟐𝟐

44. Case Study (2)

45. Case Study (2)

46. Case Study (2)
Calculation Summary:
 UCS of granite > 150 Mpa
 JCS = 75 Mpa
 JRC of 9 (i.e. Rough undulating surface)
 L = 3 m (as block height is 2 m and sliding
 Calculated PPVc = 9.9 mm/sec

47. Case Study (2)

48. Discussions and Conclusions
• Both Pseudo-static and Dynamic approaches governed by soil shear
strength envelop t = c' + σ'·tan f‘.
• Dynamic Analysis is more easy to use, especially for translation type
landslide; and can be done by hand calculation, but conservative
result (PPV) may be given.
• Pseudo-static Approach appears to give more reasonable result than
dynamic analysis but actual ground vibration frequency affects the
result of analysis.
• Energy approach is relatively simple but detailed rock mapping and
rock joint analysis are required (e.g. design friction angle, JCS and
JRC) .
• Case study demonstrated that the monitored PPVs of the blasting
works had only 28.5% to 60% of the estimated value, in an 84%
confidence level basis.

49. Photo Galleries

50. Detonator Caps

51. Explosives Charging

52. Underground Blasting Works
Source:
Olofsson 1988

53. Surface Blasting Works
Ammonium Nitrate

54. Blasting Control Measures
Blast Cages:
- Steel I-beam structure covered with heavy wire mesh
- Weigh 5 to 6 tonnes
- Cover all blastholes

55. Blasting Control Measures
Placement of Screens & Cages (Eagle’s Nest Tunnels)

56. Blasting Control Measures
Blast Door & Rubber Curtain

57. References
• GEO Report 15
• Kong, W.K. 2013. Blasting Vibration Assessment of Rock
Slopes and a Case Study. Slope Stability 2013.
Proceedings of the 2013 International Symposium on
Slope Stability in Open Pit Mining and Civil Engineering.
P.M. Dight (ed.), Australian Centre for Geomechanics,
Perth. pp. 1335-1344.
• Kong, W.K. 2012. Blasting Assessment of Slopes and
Risk Planning. Australian Journal of Civil Engineering.
Vol 10, No. 2, 2012, pp. 177-192

58. Thank You !