macro 1 theory and background - rel 108 om format.pdf
TRANSCRIPT
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Rockfall protection system
MACRO 1
THEORY AND BACKGROUND MANUAL
Version 1.08 JANUARY 2014
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MACRO 1
THEORY AND BACKGROUND
INDEX
1 INDRODUCTION 6
2 BASIC DEFINITONS 7
3GENERAL CONCEPTS 8
3.1 COEXISTENCE OF ANCHOR AND MESH 8
3.2 CONCEPTUAL SOLUTION 9
3.3 DESIGN APPROACH 9
4 NAIL DIMENSIONING 11
4.1 FORCE INTO THE GEOMECHANICAL SYSTEM 11
4.2 STABILIZING CONTRIBUTION OF ANCHORS 16
4.3 EVALUATION OF NAIL LENGTH 17
5MESH DIMENSIONING 18
5.1 ULTIMATE LIMIT STATE 18
5.2 MAXIMUM ROCK VOLUME VSPUSHING ON THE MESH 21
5.3 MESH DEFORMATION UNDER PUNCH LOAD AND SCALE EFFECT 21
5.4 MESH DIMENSIONING:SERVICEABILITY LIMIT STATE 23
6GENERAL BIBLIOGRAPHY 24
7 END NOTES 26
LIST OF THE FIGURES
Figure 1 - Typical configuration of the secured drapery 6Figure 4 - Conceptual solution for the calculation of anchors and mesh 9Figure 5 - Thickness of the unstable slope "s" evaluated with geomechanical
survey (left), or with rough estimation of the detachment niches and
size boulders (right) 12Figure 6 Rock masses with different lithology; left: non homogeneous rock mass
(for example flysch); right: homogeneous rock mass (for example
mudstone) 13
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Figure 7 Left: the weathering quickly denudates the anchors. Right: despite of the
heavy jointed rock mass, the weathering is slow. If the weathering
velocity is negligible, the anchor length Le1 and Le2 into the sound
rock is enough to hold the unstable surficial portion for a long time. 13Figure 8 - Left: even slope morphology: the mesh lies in contact to the slope
surface. Right: uneven slope morphology: the mesh touches the slope
surface in few points 14Figure 9 - Left: even slope morphology: the mesh lies in contact to the slope
surface. Right: uneven slope morphology: the mesh touches the slope
surface in few points 14Figure 10 - Anchor bar in the rock mass. Li = length crossing the unstable mass; Lp
length in the plasticized rock mass; Ls length in stable rock mass 17Figure 12 - Scheme of the forces acting on the mesh 20Figure 13 Shapes of the rock volumes that can move among the anchors:
triangular (left) and trapezium (right) 20Figure 14 - Geometry of the volume between the anchors 20Figure 15 - Volumes B and C between the anchors 21Figure 16 - Sketch of the geometry of the mesh with punching load 22Figure 17 - Plan view of the punch test according to UNI 11437:2012. Legend: 1 =
tested mesh; 2 = punching device (1.0 m in diameter); 3 = perimeter
constraint between the mesh and the frame. 22Figure 18 - Example of a curve load-displacement used for the design of the mesh
at the Serviceability Limit State 23
LISTS OF THE TABLES
Table 1 - Recap of the safety coefficients for the reduction of the destabilizing
forces and of the resistances ............................................................................... 15
Table 2 - Global safety coefficients applied to the stabilizing end driving forces ................. 15
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LIST OF THE MAIN SYMBOLS
Factor of safety Factor applied to Symbol used
in the
formulas
showed
below
Partial factor
applied on the
nail
Yield stress of the steel ST
Adhesion grout-rock GT
Partial factor
applied on the
mesh
Longitudinal tensile strength of the mesh M
Maximum displacement admitted on the mesh M-BULG
Partial factorapplied on the
instability/rock
Thickness of the instability T
Unit weight of the rock W
Rock behavior (i.e. weathering of the rock) B
Load factor Slope morphology MO
External loads OL
Category of data Data and typical unit of measure Symbol used in
the formulas
shown below
Geotechnical andgeomechanical
data
Slope inclination [deg]
Thickness of instability [m] s
Unit weight of the rock [kN/m3]
Inclination of the most critical joint set [deg]
Roughness of the most critical joint set [-] JRC0
Compressive strength of the most critical joint set [MPa] JCS0
Nails Horizontal distance between nails [m] ix
Vertical distance between nails [m] iy
Nominal external diameter [mm] e
Nominal internal diameter [mm] (if the bar is hollow) i
Potential thickness of corrosion on the bar diameter [mm] tc
Yield stress of the steel [N/mm2] ST
Inclination from the perpendicular to the slope [deg] 0
Grout-rock adhesion (bond stress) [MPa] LIM
Mesh Type of mesh i.e. commercial
name
Ultimate longitudinal tensile strength [kN/m] Tm
Curve load displacement [kN / mm] P / PUNCH
Seismic action Horizontal seismic acceleration coefficient [-] c
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Parameter of the
joint
In-situ tool to define the parameter Typical values
JRC (roughness) Barton Comb Smooth joint: 0 to
2; Very rough joint:
18 to 20
JCS (jointcompressive
strength)
Schmidt Hammer From 3 to 200 MPadepending on the
strength of the rock
(JCS is approx. 1/3
of UCS*)
Inclination () Geological compass Can vary from 0
deg to 90 deg
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MACRO 1
THEORY AND BACKGROUND
1 INDRODUCTION
Macro 1 is the software of Officine Maccaferri aimed at calculating the pin drapery systems
for rockfall protection.
Pin drapery (called also secured drapery, or cortical strengthening, or superficial
stabilization) is composed of anchors and steel mesh (rockfall net). The goal of this system is
improving the surficial rock face stability and maintaining the debris/rock on place (Figure 1).
Figure 1 - Typical configuration of the secured drapery
The pin draperies could be included into the active protection measures, because they are
directly applied on the unstable zone in order to prevent the rockfall. In these terms they
absolutely differ from the rockfall barriers that are placed far from the detachment area and
can only mitigate the effect of the rockfall. But from the geomechanical point of view they
should be classified as passive interventions because they generate forces as the rockfall
displacement takes places1.
The design of secured drapery is not at all easy because of numerous variables, including
topography, rock mass properties, joint geometry and properties, mesh type and related
restraint conditions. Often the solution to the problem may require complex numerical
modelling which is not practical for every project, especially if the design is aimed at
interventions of modest size. Because of that, at the present, limit equilibrium models are
preferable. Taking this into consideration and incorporating field experience, Officine
Maccaferri has developed MacRo1, the limit equilibrium approach for the design of secured
drapery. The procedure is quite rough, but it is sufficient when considering the low accuracy
level of the input data, the reliability of the results and the speed of the calculations.
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2 BASIC DEFINITONS
The materials intended to the software are the following:
Mesh: steel meshes produced by Officine Maccaferri. The software contains a library with
the behaviour of the mesh under punch and tensile load. The knowledge of these behaviours
derives from a series of laboratory test carried out in accordance with standard UNI
11437:20122. The software does not allow inserting any other mesh type.
Anchors: in the description the terms anchors, and nail are interchangeable. The steel
bars used for pin drapery applications are preferably full threaded. They are installed in a
drilled hole, previously realized with specific drilling machines. They have to be centred into
the hole and then grouted along their entire length. Normally the grout has a compression
resistance of 20 to 50 MPa in order to guarantee an efficient bond stress between the steelbar and the rock3. The grout has also the function to protect the steel against corrosion. The
diameter of these bars is generally 20 to 50 mm. Frequently the drilling diameter is approx.
2.0-2.5 times the diameter of the bar. The length of the nails (L) in most of the cases is
between 2.5 to 4.0 m, and the spacing (ix and iy 4 see Figure 1) ranges between 2.0 and
4.0 m. On the rock slopes, nails mainly works in shear condition, because often they are
installed perpendicular to the sliding surface. Thus, the nail design requires the definition of
the type of steel and diameter. The software admits any steel anchor type.
Pin drapery: in these text pin drapery, secured drapery, cortical strengthening, areinterchangeable. In the pin drapery the anchor and the mesh should cooperate, and the
anchor should really stabilize the slope face. Very frequently the effective anchor spacing
ranges between 2 and 3 m: The designer should remember that the larger the spacing is, the
lower the interlocking between the instable block. Large anchor spacing means frequent
rockfall and heavy loads on the mesh facing. It is always possible choose spacing larger
than 3.0 m, but the intervention progressively loose effectiveness and smokes to something
else.
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3 GENERAL CONCEPTS
3.1 Coexistence of anchor and mesh
The calculation approach considers that on the slope there is a surficial weathered (or heavy
jointed, blasted, or disturbed) rock mass. The weathered mass is conveniently approximated
as pseudo continuous5; this continuous body most frequently generates shallow instabilities
and rockfalls. It has thickness s and inclination parallel to the slope. Several sets of
joints cross the surficial body; the most unfavourable has inclination (Figure 2).
The forces of mesh and nails are passively generated when one of these two conditions
happens:
- the whole weathered body slides down on the plane inclined . This is the problem of
the global stability of the weathered surface; it is solved by the raster of anchors
(Figure 3 on the left).
- one or more block move out from the weathered body. The dynamic of the instabilitycould be any one (planar or wedge sliding, toppling, bucking, fall). The software only
considers the planar sliding on the plane , which is the most unfavourable case.
Because this instability can happen only among the nails, it can be defined as local
instability of the weathered surface; the mesh fixed with the anchors answers to the
local instability (Figure 3 on the right).
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Figure 2 - Slope with the weathered unstable surface
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3.2 Conceptual solution
Both mesh and anchors can only develop reactions as the rock mass moves (passive
system). Macro 1 separately analyses the mechanisms anchors and mesh facing. But
because the spacing between the anchors dramatically changes the load on the mesh
facing, the user follows this iterative process (Figure 4):
Figure 4 - Conceptual solution for the calculation of anchors and mesh
3.3 Design approach
The adopted design approach only follows the general concepts of Eurocodes (UNI ENV
1997-1:2005). In these terms Macro 1 allows increasing the destabilizing forces and
reducing the resistances by mean of suitable safety coefficients, which should be calibrated
with probabilistic methodology. Unfortunately the Eurocodes cannot correctly be applied on
the geomechanical field6, and the secured draperies are quite far from the standard
problems. That is why the coefficients of Macro 1 have been based on specific parameterslike the slope morphology or the mesh behaviour. The user has to find out the suitable
Figure 3 - Elements of the pin drapery systems. Nails (left) stabilize the superficial portion. Mesh(right) keeps in place the unstable material between the nail.
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coefficients considering what he has directly seen on site. This approach is more realistic
and helps in designing the secured draperies.
Macro 1 calculates the raster of anchors in order to get a more favourable equilibrium
condition of the weathered rock mass.
According to the common design practice, Macro 1 purposes the calculation of the mesh
facing for the ultimate and the serviceability limit states. The ultimate limit state allows
understanding if the mesh can be broken because of the load, whereas the serviceability
allows foreseeing the facing deformation perpendicular to the mesh plane. The knowledge of
deformation is very useful because:
- when the deformation reaches the design limit, it means that the maintenance
(cleaning) of the secured drapery is needed before that further displacements
determine the mesh rupture. A simple visual monitoring let the owner programs the
interventions.
- Too much deformed mesh implicates easy stripping on the anchors and lower
durability of the intervention. The designer must be aware of this and foresee the
right mesh type accordingly.
- Since the meshes are largely deformable, the facing of the secured drapery could
interfere with close infrastructures or vehicles.
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4 NAIL DIMENSIONING
4.1 Force into the geomechanical system
Considering passive behaviour, the nail calculation must assume the unstable portion of the
slope lies in condition of limit equilibrium, where the safety factor is equal to 1.0. Therefore,
the resisting forces have the same value of the driving forces and the following equation is
true (Figure 4):
Resisting forces = W sin
= driving forces [1]where
W = weight of the unstable rock mass to be consolidated
= inclination of the slope surface, where the sliding of the unstable rock mass can
occur.
Using the resistance criteria of Barton-Bandis7for the joints, equation [1] can be rewritten to
describe the improved stability condition:
W (sin c sintan ) + R W (sin + c cos ) [2]
assuming
R = stabilizing contribution of the nails
c = seismic coefficients
= residual friction angle of the joint
The equation [2] is written in accordance with the concept of passive intervention 8.
Setting tan 1 (friction angle = 45)9, and posing the safety factors for reducing the
stabilizing forces (RW) and increasing the driving ones (DW), the stability condition simply
becomes:
Wsin (1- c) / RW + R W DW(sin + c cos ) [3]
or
FSslp> = FDslp [4]
assuming
FDslp= W (sin + c cos ) DW = Sum of the driving forces [5]
and
FSslp= W sin (1- c) / RW+ R = Sum of stabilizing forces [6]
Equation [3] allows determining the nail force that consolidates a rock mass in the limit
equilibrium state. It is a conservative equation and it is simple to be used since it basically
requires simple geometric variables.
The safety coefficients (RW, DW) depend on several factors. The rock mass features affect
the size of the stabilizing forces, so that their safety coefficient can be described as
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RW= THl WG BH [7]
where10
- THl describes the uncertainties in determining the surficial instability thickness s.
Its value ranges between 1.20, when the estimation is based on a geomechanicalsurvey, and 1.30, when it is based on rough estimation (Figure 5). It must be
considered that the thickness of the unstable layer is not homogeneous, locally its
thickness could be thicker.
- WG describes the uncertainties in the unitary weight determination of the rock
mass. Usually it is assumed to equal 1.00, but if there are severe uncertainties it
can be assumed to equal 1.05. For instance it can be noticed that for non
homogenous rocks (e.g. flysch rock masses where there are thin layered clay
stone alternated to hard mudstone), the mesh and the nails can locally be heavy
loaded, whereas in other places the load is lower being the same volume ofinstability (Figure 6).
- BHdescribes the uncertainties related to the rock mass behaviour. High erodibility
of the rock surface can cause stripping of the nails and weakness of the whole
system (Figure 7). One consequence is that the unstable portion held by the nails
(or by the mesh) could become quickly deeper. Usually the value is assumed
equal to 1.00, but if there are severe environmental conditions or the rock mass is
easily weathered (it is the case of several rock types containing clay), it can be
assumed to equal 1.05.
Figure 5 - Thickness of the unstable slope "s" evaluated with geomechanical survey (left), or with rough
estimation of the detachment niches and size boulders (right)
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Figure 6 Rock masses with different lithology; left: non homogeneous rock mass (for example flysch);
right: homogeneous rock mass (for example mudstone)
Figure 7 Left: the weathering quickly denudates the anchors. Right: despite of the heavy jointed rock
mass, the weathering is slow. If the weathering velocity is negligible, the anchor length Le1 and Le2
into the sound rock is enough to hold the unstable surficial portion for a long time.
External conditions, especially slope morphology, play an important role in the magnitude ofthe driving forces, whose safety coefficient is defined as
DW= MO OL [8]
where:
- MO describes the uncertainties related to slope morphology. If the slope is very
rough, then the mesh facing is not in continuous contact with the surface, and the
unstable blocks can freely move; in that case a safety coefficient of 1.30 should
be applied. If the slope surface is even, the mesh facing lies in better contact with
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the ground; in the case, the unstable block movement is limited, and a safety
coefficient of 1.10 is used (Figure 8 and Figure 9).
- OL describes the uncertainties related to additional loads applied on the facing
system. The additional loads could be related to the presence of ice or snow, or to
vegetation growing on the slope. Usually it is assumed to equal 1.00, but if severeconditions are foreseen, it can be assumed to equal 1.20.
Figure 8 - Left: even slope morphology: the mesh lies in contact to the slope surface. Right: uneven slope
morphology: the mesh touches the slope surface in few points
Figure 9 - Left: even slope morphology: the mesh lies in contact to the slope surface. Right: uneven slope
morphology: the mesh touches the slope surface in few points
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Table 1 - Recap of the safety coefficients for the reduction of the destabilizing forces and of the
resistances
The above safety coefficients (formula [7] and [8]) have been calibrated in order to get the
following range of values (Table 2):
Table 2 - Global safety coefficients applied to the stabilizing and driving forces
Safety coefficient Minimum value Maximum value
For stabilizing forces 1.20 1.43
For driving forces 1.10 1.56
With this procedure the global safety coefficient applied on the geomechanical system very
roughly ranges between 1.5 and 3.2 according to the most common experience and design
codes.
Partial/Load
factor
Description Value
T If the superficial instability thickness is defined by:- geomechanical survey:
- rough/visual estimation: 1.20
1.30
W If the rock unit weight is:
- homogeneous:
- not-homogeneous (i.e. flysh):
1.00
1.05
B If the rock:
- does not present any anomalous behavior (i.e. compact rock):
- is subjected to erosion and/or environmental condition that can create
weakness of the rock mass (i.e. weathering rock):
1.00
1.05
MO If the morphology of the rock is:
- regular (the mesh lies in better contact with the slope, thus the rock
movement are limited):
- rough (the mesh cannot be in adherence with the slope, thus the unstable
block can easily move):
1.10
1.30
OL If there are/are not external loads acting on the system:
- not significant loads are applied:
- additional external loads are applied (i.e. snow, ice, vegetation, etc.)
1.00
1.20
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4.2 Stabilizing contribution of anchors
The reinforcing nail bars work principally in proximity to the sliding joint, where it is
subjected to shear stresses together with tensile stresses. The resisting force R, due to the
bar along the sliding plane11, is derived utilising the maximum work principal12:
[9]
where:
m = cotg (+ ) [10]
= angle between the bar axis and the horizontal. It is equal to
= 90 - o , [11]
where ois the angle between the bar axis and the normal to the sliding plane.
= sliding surface dilatancy
Ne= bar strength (elasticity limit condition) = ESS adm= ESS ST /ST [12]
ST = coefficient of reduction for the steel resistance.
ESS = effective area of the steel bar = / 4 ((fe - 2 fc)2- fi2) [13]
fe = external diameter of the steel bar
fc = thickness of corrosion on the external crown
fi = minor diameter of the steel bar
In accordance with the Barton Bandis resistance criteria, the value is approximated as13
[14]
where 14:
[15]
= inclination of the most unfavourable sliding plane
plan= sliding plane normal stress
JRC = joint roughness coefficient15 = [15]
JCS = joint uni-axial compression resistance 16= [16]
JCS0 = joint compression strength referred to the scale joint sample
JRC0 = roughness referred to scale joint sampleL0= joint length (assumed to be 0.1 m for lack of available data)
Lg= sliding joint length (assumed to be equal to vertical nail spacing.
eNm
m
R
+
+
=
2
1
2
2
41
161
JRC log JCS
plan
#
$%&
'(
3
( )002.0
0
0
JRCg
L
L
JRC
( )003.0
0
0
RCJg
L
LJCS
plan =ixiy s cos
ixiy
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The equations from [14] to [16] are exclusively aimed at determining the dilatancy that
increases the stabilizing contribution R of the anchor especially when it is put perpendicular
to a very rough plane17. Macro 1 must adopt a conservative approach because on surficial
rock masses the joints are often opened, or with filling of clay, sometime with advanced
weathering process, the uniaxial compressive strength is very low; other times the rock mass
is disturbed by the excavation18. In these conditions the anchors mostly works with the shear
resistance of the anchor bar. In lack of input data, the user should remember the followings:
- the roughness JRC and the uniaxial compression resistance JCS should be estimated
on the most unfavourable joints inclined . Macro 1 assumes that the joint (parallel to
the slope face) has such most unfavourable resistance, and the anchors are calculated
accordingly.
- If JRC is unknown19it can be set at 0.
- If JCS is unknown20, it can be set at 5 MPa.
- If the joint inclination is unknown, it can be assumed between 40 and 50 in order to
get al large volume sliding on a very steep plane.
4.3 Evaluation of nail length
The evaluation of nail length should consider the following:
a) The nail plays the most important role in superficial consolidation of the slope. Its
length must be deeper than the instability thickness, and should allow the bar to
reach into the stable section.
b) The steel bar and the grout are exposed to weathering actions (ice, rain, salinity,
temperature variations, etc.).
c) The steel bar can develop the shear resistance because rock and grout develop the
same opposite strength. But because rock and grouting are weaker than the steel,
generally the rock plasticizes close the sliding plane21. The plasticized volume
depends on the rock type.
Figure 10 - Anchor bar in the rock mass. Li = length crossing the unstable mass; Lp length in the
plasticized rock mass; Ls length in stable rock mass
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The minimum theoretical length is derived by
Lt = Ls+ Li + Lp [17]
assuming:
Ls= length in the stable part of the mass = P / (drill lim/ gt) [18]Li= length in the weathered mass = s / cos dw [19]
LP = length of hole with plasticity phenomena in firm part of the rock mass. The values
ranges between 0.05 m for hard rock (e.g. granite or basalt) up to 0.30 m for weak rock (e.g.
marl), and exceptionally up to to 0.45 m for very weak rock (e.g. claystone or tuff).
With
drill = diameter of the hole for the bar
lim= bound stress (adherence tension) between grout rock22
gt= safety coefficient of the adhesion grout rock. According to the Eurocode EC7, it
should not be taken lower than 1.823.
P = pullout force; it is the greater of the following:
PMesh = ((WSbar- WDbar) cos (+ o)) ix = pull out due to the mesh [20]
PRock = (FSslp R FDslp) cos (+ o) = pull out due to the slope instability[21]
The length of the nail must be intended as a preliminary value. The final suitable length of
the bars has to be evaluated while drilling and confirmed with pull out tests.
5 MESH DIMENSIONING
5.1 Ultimate limit state
Some secondary blocks could slide among the nails on a plane with inclination , where is
smaller than the slope inclination , and push on the mesh facing. The maximum block size
pushing per horizontal linear meter of facing depends on the thickness s and the vertical
spacing iybetween two nails. Since the load pushing is asymmetric and the mesh deforms
unevenly, the forces acting on the facing are represented with the following simplified
scheme (Figure 11 and Figure 12):
Figure 11 - Deformed mesh with forces
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F - the force developed by the blocks sliding between the nails on a plane inclined at
.
T - the force acting on the facing plane, which rises when the sliding blocks push on
the facing. The force can develop because there is a large friction between mesh
and blocks, and a pocket is formed. The facing, which is considered to be nailedon the upper part only, reacts to T with the tensile resistance of the mesh.
M the punch force developed by the blocks perpendicular to the facing plane. The
force is developed since there are several lateral restraints, like the nailing (strong
restraint) and the next meshes (weak restraint). The magnitude of M largely
depends on the stiffness of the mesh: the higher the membrane stiffness of the
mesh is, the more effectiveness the facing is.
In the case of the mesh, the ultimate limit state is satisfied when
Tadm- T > = 0 [22]
where
Tadm= admissible tensile strength of the mesh
which is
Tadm = Tm/ MH [23]
where
Tm= Tensile resistance of the mesh
MH= safety coefficient for the reduction of the tensile resistance of the mesh. Taking into
account the inhomogeneous stress acting on the loaded mesh, the minimum safety
coefficient should be not lower than 2.50. This safety coefficient is based upon
empirical observations on the punch tests carried out in Pont Boset with Torino TechUniversity24 and Lab IUAV Venice University25, where it has been noticed that the
mesh between the anchors does not give a full contribution to hold the lower facing,
and the stress basically is absorbed by the nails. Those last hold a force Q ranging
between 30 and 55 kN per anchor26.
The real distribution of the stress has been seen with numerical analysis27. The stress acting
on the mesh depends on the membrane stiffness: the higher the stiffness is, the higher the
capacity of the mesh to be like a restrain between the anchors is. The stiffer mesh is more
effective, accordingly. From the theoretical point of view, the lower the stiffness is, the higher
the safety coefficient should be, since the stress in mainly concentrated on the anchors andnot homogenously distributed on the mesh.
The stress T on the mesh depends on the force pushing on the mesh (M Figure 12), which
can be calculated using the same principles as formula [3]:
M = F sin () ix= (Mbdrv Mbstb) sin () ix [24]
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Figure 12 - Scheme of the forces acting on the mesh
Where:
Mbdrv= Mb (sin + c cos ) DW = driving forces [25]
Mbstb= (Mb sin (1- c)) RW = resisting forces [26]
Mb = V = weight of the unstable rock mass [27]
V = maximum unstable volume between nails (Figure 13, Figure 14, Figure 15) which
is calculated in accordance with the next paragraph 5.2.
Figure 13 Shapes of the rock volumes that can move among the anchors: triangular (left) and
trapezium (right)
Figure 14 - Geometry of the volume between the anchors
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Figure 15 - Volumes B and C between the anchors
5.2 Maximum rock volume VS pushing on the mesh
Macro 1 assumes that the maximum volume pushing on the mesh has the following
boundaries (Figure 14):
- top: top and anchor (for simplicity the anchors are always considered perpendicular to
the sliding plane)
- bottom: sliding surface inclined . The plane intersects the surface at the head of the
lower anchor.
- Back: sliding surface inclined
There are several procedures for the calculation of the maximum rock volume that could
move among the anchors. Hereby is described the one followed by the analytical algorithm
of Macro 1.
If (arctan (s/iy)) and < [28]
Then the volumes simply becomes (triangular shape in Figure 13 left)
Volume A [29]
else, if < arctan (s/iy) [30]
can be distinguished the following volumes (Figure 15)
Volume B V = iys - s2/ tan () [31]
And volume C V = 0.5 s2 / tan () [32]
Macro 1 determines the maximum theoretical volume as the sum ofV = Volume A + Volume B + Volume C [33]
5.3 Mesh deformation under punch load and scale effect
Macro 1 assumes that in any case the punch load on the mesh can be greater than the
weight of the rock volume among the anchors. Then Macro 1 check if
M/ix/sin ( p) < Mb sen [34]
then
T = M / ix/ sin ( p)else
)tan(2
1 2 = yiV
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T = Mb sen [35]
With
Zbulg= displacement related to the punch load M.
p = angle of deformation of the mesh arctg (2 bulg / i) [36]
= average spacing between the anchors = (ix * iy)
0.5
[37]
Figure 16 - Sketch of the geometry of the mesh with punching load
Figure 17 - Plan view of the punch test according to UNI 11437:2012. Legend: 1 = tested mesh; 2 =
punching device (1.0 m in diameter); 3 = perimeter constraint between the mesh and the frame.
When the load induces the maximum displacement Zbulg, the process of the mesh rupture
stars. The maximum punch displacement Zbulg is related to the sample size: in accordance
with the results of the tests carried out28, it is possible to roughly say that the larger the
sample size is, the larger the displacement is (scale effect). The general law of the scale
effect is assumed in the simplified form
x = x0x [38]y = y0y [39]
where
(x, y) = generic coordinate of the scaled graphic
(x0, y0) = generic coordinate of the reference graphic
(x, y) = constants correlating the scaled to the reference graphic
As the curves have been determined following the standard UNI 11437 (a sample size 3.0 x
3.0 m), the reference size for the description of scale effect is 3.0 m (Figure 17).
Macro 1 automatically modifies the typical load vs displacement curves considering the
scale effect.
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Figure 18 - Example of a curve load-displacement used for the design of the mesh at
the Serviceability Limit State
5.4 Mesh dimensioning: serviceability limit stateThe serviceability limit state provides information concerning the following:
- required maintenance activity on the facing;
- risks of stripping because of anchor necking;
- interference between infrastructure and facing as consequence of excessive
displacements.
The serviceability limit state is satisfied if
Bulg- Zbulg >= 0
where
Bulg = Dmbulg/mbulg = admissible displacement
Dmbulg = maximum design displacement
mbulg = safety coefficient. Its value ranges between291.50 (facing installed properly on a
slope with an even surface) and 3.00 (facing installed improperly on a slope with
uneven morphology). The safety coefficient decreases the desired maximum
deformation and automatically gets the related admissible load.
bulg = deformation of the facing as derived from the results of Maccaferri tests on the
base due to punch force M (Figure 18).
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6 GENERAL BIBLIOGRAPHY
AICAP, (1993): Anchor in soil and rock: recommendations (in Italian).
Bertolo P. , Giacchetti G., 2008 - An approach to the design of nets and nails for surficial
rock slope revetment in Interdisciplinary Workshop on Rockfall Protection, June 23-25
2008, Morshach, Switzerland.
Bertolo P., Ferraiolo F., Giacchetti G., Oggeri C., Peila D., e Rossi B., (2007): Metodologia
per prove in vera grandezza su sistemi di protezione corticale dei versanti GEAM
Geoingegneria Ambientale e mineraria, Anno XLIV, N. 2, Maggio-Agosto 2007.
Besseghini F., Deana M., Di Prisco C., Guasti G., 2008 Modellazione meccanica di un
sistema corticale attivo per il consolidamento di versanti di terreno, Rivista GEAM
Geoingegneria ambientale e Mineraria, Anno XLV, N. III dicembre 2008 (125) pp. 25-30
(in Italian)
Bonati A., e Galimberti V., (2004): Valutazione sperimentale di sistemi di difesa attiva dalla
caduta massi in atti Bonifica dei versanti rocciosi per la difesa del territorio - Trento
2004, Peila D. Editor.
Brunet G., Giacchetti G., (2012) - Design Software for Secured Drapery- Proceedings of the
63rd Highway Geology Symposium, May 7-10, 2012, Redding, California.
Castro D., (2008) Proyetos de investigacin en la Universidad de Cantabria - II Curso
sobre proteccin contra caida de rocas Madrid, 26 27 de Febrero. Organiza STMR
Servicios tcnicos de mecnica de rocas.
Cravero M., Iabichino G., Oreste P.P., e Teodori S.P. 2004: Metodi di analisi e
dimensionamento di sostegni e rinforzi per pendii naturali o di scavo in roccia in atti
Bonifica dei versanti rocciosi per la difesa del territorio Trento 2004, Peila D. Editor.
Ferrero A.M., Giani G.P., Migliazza M., (1997): Interazione tra elementi di rinforzo di
discontinuit in roccia - atti Il modello geotecnico del sottosuolo nella progettazione
delle opere di sostegno e degli scavi IV Conv. Naz. Ricercatori universitari
Hevelius pp. 259 275.
Flumm D., Ruegger R. (2001): Slope stabilization with high performance steel wire meshes
with nails and anchors International Symposium Earth reinforcement, Fukuoka, Japan.
Goodman, R.E. and Shi, G. (1985), Block Theory and Its Application to Rock Engineering,
Prentice-Hall, London.
Jacob V., (2009): Engineering, unpublished thesis, Technical University Torino.
LCPC, (2001) : Parades contre les instabilits rocheuses - Guide technique - Paris.
Phear A., Dew C., Ozsoy B., Wharmby N.J., Judge J., e Barley A.D., (2005): Soil nailing
Best practice guidance - CIRIA C637, London, 2005.
Ribacchi R., Graziani A. e Lembo Fazio A. (1995). Analisi del comportamento dei sistemi di
rinforzo passivi in roccia, XIX Convegno Nazionale di Geotecnica: Il Miglioramento e il
Rinforzo dei Terreni e delle Rocce, Pavia, pp. 239-268
Ruegger R., e Flumm D., (2000): High performance steel wire mesh for surface protection in
combination with nails and anchors Contribution to the 2 ndcolloquium Contruction in
soil and rock Accademy of Esslingen (Germany).
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Saderis A., (2004): Reti in aderenza su versanti rocciosi per il controllo della caduta massi:
aspetti tecnologici e progettuali Tesi di Laurea in Ingegneria per lAmbiente e il
Territorio, unpublished thesis, Technical University Torino.
Torres Vila J.A., Torres Vila M.A., e Castro Fresno D., (2000): Validation de los modelos
fisicos de analisis y diseno para el empleo de membranas flexibile Tecco G65 como
elemento de soporte superficial en la estabilizacion de taludes.
Valfr A., (2007): Dimensionamento di reti metalliche in aderenza per scarpate rocciose
mediante modellazioni numeriche GEAM Geoingegneria Ambientale e mineraria,
Anno XLIII, N. 4, Dicembre 2006.
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7 END NOTES
1
See pag. 570 of Turner A.K, Schuster R.L. Editors (2012) Rockfall CharacterizationRockfall Characterization and control Transportation Research Board, Washington D.C.
2 UNI 11437 (2012). Rockfall protection measures : Tests on meshes for slope coverage -UNI Ente Nazionale Italiano di Unificazione. It is the first worldwide norm that describes theprocedures for the two basic resistances of a mesh (punch and tensile). It considers andextends the pre existing standards (ASTM 975-97 2003 and EN 15381:2008).
3The following graph shows the effect of water content on the compressive strength, bleedand flow resistance of grout mixes (Littlejohn and Bruce, 1975, from pag 322 of Wyllie D.C.(1999) Foundations on Rock Second edition E & FN SPON, London and New York).
4In Macro 1 the notation of the anchor spacing is referred to the horizontal inter-axis i xandthe vertical one iy(measured on the slope face). The Figure 1shows the configuration of theanchor pattern spaced ix and iy. In reality the anchor pattern could be also diamond, asrepresented in following figure. Macro 1 only accepts the input with the concept of squarepattern (left in the figure). If the user wants to change from square to diamond, he has toinput a fictitious square pattern that respects the anchor density (number of anchor per area
unit).Area per 1 anchor in the squared pattern Area = iy ixIf iy =ix, the squared area can be rewritten Area = ix
2Area per 1 anchor in the diamond pattern Area = dy dx / 2It must be that ix
2= dy dx / 2And then ix= (dy dx / 2)
0.5The last relationship allows adopting the diamond pattern in Macro 1 too.
Example: the diamond pattern to be calculated is dy = 5.5 m and dx = 2.9 m. The equivalentsquare pattern to be inserted in Macro 1 isix= iy= (dy dx / 2)
0.5= (5.5 2.9/ 2)0.5= 2.8 m
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The best position of the anchors happens when they can cooperate each other and interferewith the rock mass. Then the best theoretical pattern should be the diamond one, withanchor axis spaced in order to form an equilateral triangle. But more simply, it is importantthat the areal distribution of the anchor is as homogeneous as possible. In these terms it isstrongly recommended to avoid irregular pattern (examples: diamond 3.0 m x 8.0 m orrectangular 2.5 m x 4.8 m).For practical reasons many contractors prefer the squared pattern.
5 Ferraiolo F., Giacchetti G. (2004) Rivestimenti corticali: alcune considerazionisullapplicazione delle reti di protezione in parete rocciosa, in proceedings Bonifica diversanti rocciosi per la protezione del territorio Trento 2004 Peila D. editor. In Italian.
6At the present has been instituted a work group for the proposal of a new Eurocode for therock masses. For instance see: Alejano L.R., Bedi A., Bond A., Ferrero A.M., Harrison J.P.,Lamas L., Migliazza M.R., Olsson R., Perucho ., Sofianos A., Stille H., Virely D. (2013).Rock engineering design and the evolution of Eurocode 7. In Rock Mechanics for
Resources, Energy and Environment Kwasniewsky & Lydzba (eds.) 2013 Taylor & FrancisGroup, London, ISBN 978-1-138-00080-3, pag. 777-782
Anyway, with special reference to the DIN 1054:2010-12 (Subsoil Verification of the safetyof earthworks and foundations Supplementary rules to DIN EN 1997-1 - table A 2.1 for theapproach B-SP, GEO-2), and more generally to the EC7 concepts, the user can introducethe coefficients 1.35 for the estimation of the stabilizing forces, and 1.00 for the estimation ofthe driving ones (see Tabelle Teilsicherheitsbeiwerte F1 bzw. E2 fr Einwirkungen undBeanspruchungen, B-SP, STR und GEO-2: Grenzzustand des Versagens von Bauwerken,Bauteilen und Baugrund, pag 30 DIN EN 1997-1). This approach implicate that theefficiency for the system (Maccaferri internal report):
= FDslp / FSslp
is equals or greater than 0.77 (see equations [5] and [6]). In order to respect this efficiency,the safety coefficient DWand RW(see Table 2) have to respect at least the following value:
DW = (W sen / RW + Rd / W sen )
(for the meaning of W, and R, please see the symbol list table)
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The relation between DWand RW has been plot in the above graph for immediate use, as thefollowing examples shows:
Example 1: if DWis equals to 1.20, in order to get an efficiency not lower than 0.77,RW shall not be lower than 1.25.
Example 2: if RWis equals to 1.50, in order to get an efficiency not lower than 0.77,DWshall not be lower than 1.10.
The user can modulate the partial safety coefficients (see Error! Reference source notfound.) according to his knowledge of the slope until DWand RW (see the input data menu ofsafety coefficients in the software) do not satisfy the required efficiency of the system, as perthe graph above.
7The Barton-Bandis criteria does not consider the cohesion on the joints, but a peak frictionangle, which depends on a base friction angle (related to the rock type) and an incrementangle (related to JRC and JCS).Main references: Barton, N.R. and Choubey, V. (1977). The shear strength of rock joints in theory and
practice. Rock Mech. 10(1-2), 1-54. Barton, N.R. and Bandis, S.C. (1982). Effects of block size on the shear behaviour of
jointed rock. 23rd U.S. symp. on rock mechanics, Berkeley, 739-760
Practical synthesis can be found in- chapter 2 of Hoek E. (2000). Course Notes for Rock Engineering (CIV 529S) inwww.rocscience.com
8see pag. 352 354 of Hoek, E. and Bray, J.W. 1981. Rock Slope Engineering . 3rd edn.London: Institution of Mining and Metallurgy 402 pages.
9According to the Barton-Bandis failure criteria, the friction angle commonly ranges between28 and 70. Most frequently the value of 45 can be considered conservative.
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10Grimod A., Giacchetti G. and Peirone B., 2013. A new design approach for pin draperysystems. Proceedings of GeoMontreal 2013. 29thSpetember 3rd October 2013, Montreal(QC). Paper n. 491.
11The stabilizing contribution of a steel bar crossing a sliding plane can be described withthe following typical graphics:
The graph, developed for a specific type of steel bar, shows the effect of the dilatancy on the
stabilizing contribution R is higher when the bar perpendicular the sliding plane.See also pag. 337- 339 of Giani G. P. (1992), Rock slope stability analysis Balkema,Rotterdam
12pag. 95 96 of Pellet F., e Egger P., (1995): Analytical model for the behaviour of boldedrock joints and practical applications. In proceedings of international symposium Anchorstheory and practice. Widmann R. Editor, Balkema, Rotterdam.
13Giani G. P.see note 1114see the following references:
Singh B., Goel R.K. (1999) Rock mass Classification A practical approach in civil
engineering- Elsevier pag 69 of Bell F.G. (2007). Engineering Geology Elsevier BH
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15See pag 37 38 of Barton N. (1992): Scale effects or sampling bias?Proc. Int. WorkshopScale Effects in Rock Masses, Balkema Publ., Rotterdam
16
Barton N. - see note 1517 See pag. 169 171 of Goodman, R.(1989) - Rock Mechanics Second edition. JohnWiley.
18An idea of grade of disturbance can be found on the chapter describing the rock massproperties of Hoek E. (2000). Course Notes for Rock Engineering (CIV 529S) inwww.rocscience.com
19The value of JRC can be measured by the Barton comb and comparing the roughnessprofile to the typical of the table (from Barton, N.R. and Choubey, V. , 1977 see note 7).
20The value of JCS can be measured with the Schmidt hammer, or in lack o information,
deduced from the uniaxial compressive strength (UCS = c) of the rock. The following tablegives the compressive frame of the most common values (from Appendix 3 of Palmstrom A.,(1995) RMi - a system for characterization of rock masses for rock engineering purposes.Ph. Thesis, University of Oslo, Norway. In www.rockmass.net)
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21 See the references:
pag 139-141 of Wyllie D.C., e Mah C.W., (2004): Rock slope engineering civil andmining- 4th edition Spon Press London and New York.
ITASCA (2004). UDEC universal distinct element Code User manual: Specialfeatures Minneapolis, USA.
22 The following table the approximate relationship between rock type and working bond shearstrength for cement grout anchorages (from pag 331 of Wyllie D.C. (1999) Foundations on Rock
Second edition E & FN SPON, London and New York.)
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See also:
Littlejohn, G.S. and Bruce, D.A. (1975a) Rock anchors state of the art. Part 1: Design.Ground Eng., 8(4), 418.
Littlejohn, G.S. and Bruce, D.A. (1975b) Rock anchors - state of the art. Part 2: Construction.Ground Eng., 8(4), 3645.
Littlejohn, G.S. and Bruce, D.A. (1976) Rock anchors state of the art. Part 3: Stressing andtesting. Ground Eng., 9(5), 33141.
23UNI ENV 1997-1:200524 Bertolo P., Oggeri C., Peila D., 2009 Full scale testing of draped nets for rock fall
protection- Canadian Geotechnical Journal, No. 46 pp. 306-317.
25The typical load vs displacement curves of the mesh have been implemented in the libraryof Macro 1.
26The values have been seen with specific tests in Cottbus University test i.e. Test 2011-MPZ05SG/B-06 13/ May 2011
27See the following references:
Muhunthan B., Shu S., Sasiharan N., Hattamleh O.A., Badger T.C., Lowell S.M.,Duffy J.D., (2005): Analysis and design of wire mesh/cable net slope protection -
Final Research Report WA-RD 612.1 - Washington State Transportation CommissionDepartment of Transportation/U.S. Department of Transportation Federal HighwayAdministration.
Sasiharan N., Muhunthan B., Badger T.C., Shu S., Carradine D.M.(2006) Numerical analysis of the performance of wire mesh and cable net rockfall protectionsystems. Engineering Geology 88, 121-132. Elsevier
28See the following references: Majoral R., Giacchetti G., Bertolo P., 2008 Las mallas en la estabilizacin de
taludes II Curso sobre proteccin contra caida de rocas Madrid, 26 27 deFebrero. Organiza STMR Servicios tcnicos de mecnica de rocas.
Grimod A., Giacchetti G. , 2013, New design software for rockfall simple draperysystems. Proceedings 23nd World Mining Congress & Expo, Montreal. Paper No.
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255.
29The safety coefficients for the diplacement normal to the mesh plane should be alwaysquite large in order to compensate for all the uncertainties that affect the mesh. Theinstallation accuracy generates one of the largest uncertainties. The most relevant researchto analyze the performance of the mesh stressed by a punch test was done by thePolytechnic of Turin (see note 24 and the figures below with the cross section of the punchdevice acting on the tested meshes). The goal of the research was to study the real behaviorof different type of mesh installed on a rock slope. The meshes were anchored to the rock by4 nails distributed in a squared configuration. The distance between the nails was 3m x 3m.The falling block was simulated by a piston connected to a punch device (diameter = 1.5 m);the piston was installed in order to develop a 45 degree pressure against the mesh. Themaximum elongation of the piston was approx. 1.2 m ! The best way to reduce thedeformation is inserting cables into the mesh as suggested by Muhunthan ( see note 26).
.