Design Guide for Rockfall Fences
Ghislain Brunet
1) Barrier destroyed by a boulder of
1.5 m
3
(estimated velocity 3 - 5
m/s – 55 kJ energy)
2) Barrier pierced by a boulder of
0.04 m
3
(estimated velocity 12-14
m/s, 18 kJ energy)
Why deformable rockfall barriers
F t = M v
The capacity of a “non deformable” barrier is related to the elastic
deformability of its components.
Since its components are stiff (cable, post), the “non deformable” barrier
must reduce the velocity (v) in a very short time (t = 0).
Then the force F of impact
F = M v
t
is huge.
So the stiff barrier is broken even if the energy level is low.
Why deformable rockfall barriers
ETAG 27 requires 2 tests
MEL = Maximum Energy Level
The barrier has to catch a boulder with the maximum energy level (100%). The
residual height of the panel after the impact indicates the quality level of the barrier.
SEL = Service Energy Level
The barrier has to catch two impacts of a boulder with 1/3 of the MEL energy without
damage. The residual height after the first impact must be greater than 70%. The
second impact needs only to catch the boulder.
ETAG 27 code
The field test is conducted on a barrier with 3 modules in a straight
line, that is why 3 modules are the suggested minimum length of a
barrier
Configuration of the Crash test barrier
p
ost interax =i
i/2
h
N
h
N
/2
Lateral post
Intermediate post
Lateral post
Intermediate post
Plan view
Front view
ETAG 27 code
2
2
1
impactc
VmE
Block size
Energy
FIELD TEST
Vertical field testInclined field test
Falling velocity >= 25 m/s
ETAG 27 code
ETAG 27 code
0°90°
-20° +20°
Nominal height of the barrier
Residual height (after
impact)
ETAG 27 code
Net before impact
unload position
Maximum elongation
during the impact
ETAG 27 code
Elongation after impact
Falling rock protection kit classes
A classification for residual height for MEL is as follows:
Category A : Residual Height ≥ 50 % nominal height
Category B: 30% nominal height < Residual Height < 50 % nominal height
Category C: Residual Height ≤ 30 % nominal height
ETAG 27 code
Design of barriers
The design of a barrier for Ultimate Limit State means to refer
the design to
MEL (Maximum Energy Level of crash test)
Maximum capacity of the barrier must be utilized.
Design based on a single hits
Frequent inspections and maintenance on site are possible and convenient.
Higher cost for the maintenance
The design of a barrier for Serviceability Limit State means to
refer the design to
SEL (Service Energy Level = 1/3 MEL)
No Damages on the barrier after impact
There are multiple hits on the barrier during test
Frequent inspections and maintenance works on site are more difficult to do.
Maintenance cost is minimum
Design approach for rockfall protections
Energy level of Barrier >= ½ m
d
v
d
2
+ ½ I
d
d
2
NEW Design approach for rockfall
Barrier
Reduce the “energy” of
the barrier with
coefficients in relation
with the index test
Add safety factor on the
components in relation with
the data precision
Height barrier >= Height of the trajectories
Reduce the height of the
barrier of the upper free
border
Increase the height with coefficient
Distance between infrastructure and barrier >= Elongation of barrier
Increase the elongation of the
barrier with coefficient
Barrier Design
DESIGN OF ROCKFALL
BARRIERS WITH NUMERICAL
SIMULATIONS
The main questions are:
Which is the best
position for the barrier?
What is the statistical
distribution of velocity
and height in that
position?
Software: RocFall – Rocscience Inc - Toronto
Topographic
section with
the rock
trajectories
Rockfall Simulation Software
PARAMETERS USED IN CODES
The main parameters are:
Topographic slope section;
Coefficients describing the energy
dissipation after the block impact;
Coefficients describing the rolling of
the block along the slope;
Boulder size.
N = axis perpendicular to the slope
T =axis tangent to the slope
N
T
VB
VA
VA > VB
Rockfall simulation software
Will the impact be on an hard
or soft soil ?
A
B
“Soft” and “hard” depend on
the size of the boulder.
Case A) the soil is hard
Case B) the soil is soft
Rockfall simulation software
The values of Rt and Rn suggested by the
bibliography can only be accepted as an
initial suggestion.
They must be verified with a back analysis.
Rockfall simulation software
HEIGHT OF IMPACT
Topographic
section with the
rock trajectories
STEP
STEP
BOUNCE
BOUNCE
The barriers must be higher than the path
of falling boulders.
We must take into account:
A) A statistical approach cannot forecast
100% of the events
B) Simulation gives the trajectory without
considering the actual boulder
dimensions.
C)
There is a relation between the
height of a rockfall barrier and its
capacity for energy dissipation.
Designing for rockfall protection - general remarks
Rock fall simulation is required to get velocity
and height of the trajectories
Design approach for rockfall protections
Position of the barrier
100%
velocity
95%
0%
v
95
CUMULATIVE PROBABILISTIC CURVE
Velocity of the design boulder
The velocity v
95 is taken at the 95% of the calculated
velocities and multiplied per the safety coefficient
F
:
v
d
= v
95
F
= V
95
(
Tr
Dp
)
Tr
= safety coefficient depending on the reliability of the simulation
= 1.02 for 2D and 3D simulation calibrated by back analysis;
= 1.07 for 2D simulations on the basis of bibliographic values;
Dp
= safety coefficient for precision of the slope:
= 1.01 for slope traced on the bases of topographic survey;
= 1.07 slope traced with low precision.
V
Design approach for rockfall protections
Height of the rock trajectory of design h
p
The height h
95
is taken at the 95% of the calculated trajectories and
multiplied per the safety coefficient
F:
h
d
= h
95
F
=(
Tr
Dp
)
h
95
= height of boulder trajectory over the slope
Tr
= safety coefficient depending on the reliability of the simulation
= 1.02 for 2D and 3D simulation calibrated by back analysis;
= 1.07 for 2D simulations on the basis of bibliographic values;
Dp
= safety coefficient for precision of the slope:
= 1.01 for slope traced on the bases of topographic survey;
= 1.07 slope traced with low precision.
ht
Design approach for rockfall protections
Size of the design boulder
It is useful to look at the rock mass
which the blocks originate.
But the best is to look at the
debris and choose the largest
diameter among the more
frequent blocks.
Evaluations of the height of the fence
(h
d
-h
f
) < 0 where
(h
d
–h
n
+ h
b
b
) < 0
h
n
nominal height according to ETAG 027
h
f
free border, that is the height of non impact zone on the border of the panel
h
b
average radius of the falling boulder
b
coefficient of safety for the radius of the boulder, generally 1.5
h
d
design height of the barrier
Design approach for rockfall protections
h
f
h
n
Evaluation of the position of the barrier on slope near infrastructure
(d
d
-d
A
) = (d
d
-d
maxMEL
D
) > 0
d
A
maximum deformation of the barrier MEL (d
maxMEL
D
)
D
safety coefficient
= 1.3 if there is the deformation of crash test MEL only.
= 1.20 if there is calculation to verify the impact on post and free zone
(lateral and upper)
d
d
minimum design distance between barrier and infrastructure
Design approach for rockfall protections
Evaluation of energy level of the barrier
(E
d
-E
BTE
,
barrier
/
E
) < 0
E
d
energy level calculated via simulation (0.5 v
d
2
m
d
)
v
p
, m
p
velocity, mass of design
E
BTE
,
barrier
energy level measured on crash test
E
safety coefficient
in case of MEL design :
= 1.2 if there is the energy level measure on crash test only;
in case of SEL design :
= 1.00
Design approach for rockfall protections
Design Example
Software Simulation
X= 132.989
Minimum distance between barrier and infrastructure
6.00 [m]
Slope - Clean Rock
Estimate Rock Size 0.85 [m3]
Density of the Rock
2500.00 [kg/m3]
Bounce Height Distribution at x=132.989
0
100
200
300
400
500
600
700
800
0.22 1.09 1.97 2.84 3.72 4.59 5.47 6.34 7.22 8.09
Height Above Slope [m]
Number of Rocks
Bouncing Height
Height Statistics of Raw Data at x = 132.989
***********************************************
Number of data points: 1000
Minimum: -0.0012
Maximum: 4.5714
Mean: 0.496102
Standard deviation: 0.755185
Range: 4.5726
Median: 0.1718
Variance: 0.570304
Height at 95% percentile 2.32
Bouncing Height
Translational Velocity Distribution at x=132.989
0
50
100
150
200
250
300
350
400
450
500
0.65 3.25 5.85 8.45 11 13.6 16.2 18.8 21.4 24
Translational Velocity [m/s]
Number of Rocks
Velocity
Velocity - Statistics of Raw Data at x =
132.989
Number of data points: 1000
Minimum: 16.6928
Maximum: 23.1255
Mean: 20.013
Standard deviation: 1.13327
Range: 6.4327
Median: 20.41
Variance: 1.2843
Velocity at 95% percentile 21.31
Velocity
Data analysis
Simulation developed with 1000 trajectories
Confidence limit: statistical approach on the 95%
of the
population
Average inclination of the trajectoies
[
]
30.00 [°]
Tollerance for the barrier inclination
[
]
20.00 [°]
Trajectory height on the vertical for the 95% of
the cases
[Hv]
2.32 [m]
Traj. height on the barrier plane [cos (a -b) * Hv]
[Ht]
2.28 [m]
Minimum distance between barrier and
infrastructure
[Di]
6.00 [m]
Velocity (translational) - confidence limit 95%
[Vt]
21.31 [m/s]
Size
[St]
0.85 [m3]
Density of the rock
[W]
2500.00 [kg/m3]
Simulation Result
Design trajectory
Design trajectory velocity [Vt *
tt *
tr]
[Vd]
21.31 [m/s]
Design trajectory mass [St *
tg * W *
tw]
[Md]
2146.2
5[kg]
Design trajectory height [Ht *
tt *
tr +
Boulder radius]
[Hd]
2.28 [m]
Design trajectory energy [0.5 * Md * Vd ^2]
[Ed]
517.20 [kJ]
Barrier Design - No Safety Factors
Design performance of the barrier
Design Energy [ E
BTE
/ (
EN
*i)]
[E]
521.00 [kJ]
Design elongation [ Db *
DB
]
[D]
2.95 [m]
Design height barrier [Hb - Fb]
[H]
2.5 [m]
Proof Barrier
Energy proof [(Ed - E) ≤ 0 ] -3.8 Fullfilled
Elongation proof [(D - Di) ≤ 0 ] -3.1 Fullfilled
Height barrier [(Hd - H) ≤ 0 ] -0.2 Fulfilled
Barrier Design - No Safety Factors
Data analysis
Simulation developed with 1000 trajectories
Confidence limit: statistical approach on the 95%
of the
population
Average inclination of the trajectoies
[
]
30.00 [°]
Tollerance for the barrier inclination
[
]
20.00 [°]
Trajectory height on the vertical for the 95% of
the cases
[Hv]
2.32 [m]
Traj. height on the barrier plane [cos (a -b) *
Hv]
[Ht]
2.28 [m]
Minimum distance between barrier and
infrastructure
[Di]
6.00 [m]
Velocity (translational) - confidence limit 95%
[Vt]
21.31 [m/s]
Size
[St]
0.85 [m3]
Density of the rock
[W]
2500.00 [kg/m3]
Barrier Design - With Safety Factors
Partial Safety coefficient
Quality of Topographic survey
[
tt]
1.07
Quality of Geomechanical survey - size
[
tg]
1.10
Quality of Geomechanical survey - density
[
tw]
1.05
Quality of rock fall simulation
[
tr]
1.07
Design trajectory
Design trajectory velocity [Vt *
tt *
tr]
[Vd]
24.40 [m/s]
Design trajectory mass [St *
tg * W *
tw]
[Md]
2454.38 [kg]
Design trajectory height [Ht *
tt *
tr +
Boulder radius]
[Hd]
2.97 [m]
Design trajectory energy [0.5 * Md * Vd ^2]
[Ed]
730.49 [kJ]
Barrier Design - With Safety Factors
MACCAFERRI barrier features
Maximum energy according to ETAG 27
[MEL]
1076.00 [kJ]
Service energy level according to ETAG 27
[SEL]
358.67 [kJ]
Maximum dynamic elongation MEL
[Db]
3.50 [m]
Standard Height of the barrier 3.5 m and 4 m
Nominal height of the barrier
[Hb]
4.0 [m]
Upper free border for the design boulder
[Fb]
0.7 [m]
Barrier Design - With Safety Factors
Design Method
Design procedure aimed to (MEL or SEL)
MEL
Maximum Energy Level - using energy
[E
BTE
]
1076.00
Amplification factor which considers the risk of
places having
(1)_low_economical_value,_and_can_be_easily_r
epaired
[i]
1.00
Safety coefficient for reduction of the barrier
energy
[
EN
]
1.2
Safety coefficient for the deformation
[
DB
]
1.3
Barrier Design - With Safety Factors
Design performance of the barrier
Design Energy [ E
BTE
/ (
EN
*i)]
[E]
896.67 [kJ]
Design elongation [ Db *
DB
]
[D]
4.55 [m]
Design height barrier [Hb - Fb]
[H]
3.3 [m]
Proof Barrier
Energy proof [(Ed - E) ≤ 0 ] -166.2 Fullfilled
Elongation proof [(D - Di) ≤ 0 ] -1.5 Fullfilled
Height barrier [(Hd - H) ≤ 0 ] -0.3 Fulfilled
Finalfactorofglobalsafetyofthebarrier 1.87
Barrier Design - With Safety Factors
500 kJ barrier with a high of 2.5 m
Design Example at MEL without safety factors
1000 kJ barrier with a high of 4 m
Design Example at MEL with safety factors 1.87
The impacted barrier, Aosta, Oct.. 2009
The area
The rockfall
Arnod – Aosta (Italy) - Barrier
OM CTR 30/04/A - 3.000 kJ
The rock block: 12 m3 The performance of the under – estimated
barrier
Multiple impact of dozens of blocks, the largest with an energy level of 4000 kJ
(33% more than the nominal capacity of the barrier!)
The impacted barrier, Aosta, Oct.. 2009 -Maccaferri-
