software design theory and railroad application of simple drapery system
DESCRIPTION
Software Design Theory and Railroad Application of Simple Drapery SystemTRANSCRIPT
Software Design Theory and Railroad Application of Simple Drapery System
Giorgio Giacchetti
OFFICINE MACCAFERRI S.p.A.
Via Kennedy 10
40069 Zola Predosa
Ph: 01139051646000
Ghislain Brunet
Maccaferri, Inc.
10303 Governor Lane Blvd.,
Williamsport, MD 21795‐3116
Ph: 301‐223‐6910
gbrunet@maccaferri‐usa.com
Alberto Grimod
Maccaferri Canada Ltd.
400 Collier MacMillan Dr. Unit B
Cambridge, Ont, Canada, N1R7H7
Telephone: 519‐623‐9990
Prepared for the AREMA 2014 Annual Conference & Exposition
September 28th ‐ October 1st , Chicago, Il
ABSTRACT
Simple drapery systems are commonly used all around the world as a simple, fast and economical measure to mitigate rockfall hazards. It consists of installing steel mesh along a slope, as a curtain, which is suspended by longitudinal ropes and anchors at the crest and toe. The distance between the anchors depends on the design and the prevailing instability conditions at the site. They are commonly located in a line and are fitted with suitable terminations (often wire rope anchors or similar) to accept the crest rope. Once the crest anchors and the upper longitudinal cable are installed, the mesh can be fixed to them and left free all along the slope. The design of simple drapery depends on different variables related to the geometry of the slope, the type of the mesh and the hypothetical debris accumulation on the toe of the system. One of the most resent researches carried out to give a design guideline for these applications was done by Washington State Department of Transportation (Muhunthan et al. 2005). Using these studies, the catenary theory and the results obtained from several laboratories and field tests, Maccaferri has developed a new software (MacRo 2) to design the type of mesh, the diameter of the up-slope cable and the steel and geometric (diameter and length) characteristics of the up-slope anchors. This paper will cover the theory used in this new software and railroad application.
© AREMA 2014 1
INTRODUCTION
The natural processes of weathering, increased by climate change, generate geological instabilities, which frequently expose populated areas and infrastructures to a wide range of shallow instabilities varying from erosion to rockfall. Shallow instabilities should not be underestimated because they frequently cause rockfall events. Due to the fact that they happen with a high frequency over large areas, the probability of rock strikes and accidents is elevated. In this situation, the design must consider the efficiency of a remedial solution in terms of performance and low maintenance costs. The rockfall mitigation solution is divided into two different design approaches related to their means of stabilizing the slope area:
Active Protection Systems: are applied directly on an unstable zone in order to prevent or control the movement of the shallow instability. The most common solutions inside this category are the following:
o Soil Nailing: is to improve soil stability by inserting reinforcement bars in the soil in a regular pattern, the nails are then grouted and fixed soundly to the ground for their entire length (nailing). The frequency and the length of the nails can be calculated in accordance with FHWA, EN 1997 1 or BS 8006. The ground surface is reinforced with a structural facing which can be flexible (steel mesh) or rigid (shotcrete).
o Pre-stressed Soil Anchors (tie back anchors): pre-stressed anchors are installed in a shallow instability to modify the internal stability since an external force is applied to tie the instability into the slope area.
o Secured Drapery System: composed of an anchor system spaced at regular intervals where the rocks are held in place by a surficial structural, flexible (steel mesh), or rigid (shotcrete) facing interconnected to ground anchors.
Passive Protection Systems: are not implemented at the source area, but rather mitigate the hazard of instabilities by affecting the trajectories of falling rocks or arresting or reducing the falling rock velocities. They are generally applied far from rockfall source areas. This category includes the following solutions:
o Simple Drapery System: consisting of a steel mesh drape system, secured at the top of the slope with ground anchors and steel wire rope cables.
o Rockfall or Debris Flow protection Barriers: structures composed of posts, cables, energy dissipaters and interception structures (steel or wire mesh) capable of arresting and containing falling rocks. The barrier is also composed of elements to anchor support cables, post foundations, and ground anchors;
o Hybrid Barriers: structures composed of posts, cables, energy dissipaters, and a tail of mesh designed to reduce the energy and the velocity of falling rocks which are driven into the slope by a steel drape system reducing energy through ground collisions; and
o Rockfall or Debris Embankments: a gravity or mechanically stabilized earthfill structure forming a steep berm to contain falling rocks or debris, generally installed at the toe of a slope.
Simple Drapery System
A simple drapery system consists of a rockfall steel mesh installed along the face of the slope. As mentioned before, the drapery is hung as a curtain (figure 1), suspended by longitudinal ropes and anchors at the crest (Rc). Anchors are positioned along the crest (AC) and toe (AT) of the slope and their distance depends on the design and the prevailing rockfall conditions at the site. They are commonly located in a line and are fitted with suitable connections (often eye nuts, or plates, or similar) to accept the crest rope (RC). Once the crest anchors and the upper longitudinal cables are installed, the mesh can be fixed to them and left free-hanging all along the slope.
© AREMA 2014 2
Figure 1 – Sketch of a simple drapery system application (left) and disposition of the anchors (right)
Figure 2 (left) – Mesh installation at the crest (left) Figure 3 (center) – Debris accumulation at the toe of the simple drapery system Figure 4 (right) – West Virginia (USA) – more than 30,000 sqm of drapery system were installed in a rocky slope higher than 150 m
The steel mesh can be fixed as well at the bottom where space is limited, so that the falling debris can pile up into a pocket (figure 3). In order to reduce the stress on the mesh and reduce the costs as well, the mesh at the toe of the slope can be unsecured; in this case, a catchment trench or a fence is required to collect the fallen debris. This type of system is usually installed on a large rocky slope (figure 4), where the secured drapery systems are not cost-effective, or where the rockfall barriers and rockfall embankments cannot be installed because the slope morphology is either too uneven or too steep.
DESIGN: PRELIMINARY REMARKS
In order to design the most cost effective and suitable mesh system, the designers must first analyze the main factors affecting the effectiveness of the mesh.
First of all, the stress applied on the mesh and the performance of the simple drapery system largely
depends on the slope morphology. For example, for a very uneven slope, the drapery system may only be in contact with the slope on the crest area and convexities, whereas the debris can freely run down into the gullies and concavities. In this situation the drapery has a negligible capacity to control erosion, and the falling rocks can reach higher velocities. The installation of the drapery then requires particular care to maximize the contact between the ground and the steel mesh, or the slope must be preventively re-shaped and scaled.
© AREMA 2014 3
Another important factor affecting the selection of the mesh is the existing rock slope instability. If erosion is the main problem, typically on a gentle slope, the appropriate selection of drape system should have a small mesh opening and enough weight to maintain constant pressure on the ground surface. When there is contact between the mesh and the ground, the drapery is quite effective in erosion control and allows both the re-growth of the vegetation and the confinement of large boulders. If the slope is vertical, the drapery must be stronger to absorb impacts and funnel falling debris to the toe of the slope. In cases of large blocks (i.e. in the basalt cliffs), a “dynamic” drapery, like cable panels or ring nets, should be considered, whereas in cases of small blocks (i.e. thin layered limestone cliff) lighter draperies, like steel composite Rock Mesh or double twist wire mesh could be suitable.
Other important design factors are the expected life span of the drapery and its maintenance costs. Concerning the life span, designers should consider exposure to atmospheric conditions (i.e. salt spray or wind), and abrasion due to movement of falling debris. If the drapery is applied for temporary protection, as in the mining industry, a light corrosion protection could be enough. If the application must be permanent or it is close to aggressive environments (i.e. seaside), a stronger corrosion protection is required. In the last case, the designer has to plan for maintenance suggesting the maximum size of the debris pocket acceptable for the mesh. MACRO 2: CALULATION APPROACH
The design of simple drapery depends on different variables related to the geometry of the slope, the type
of the mesh, and the assumed debris accumulation at the base of the system. One of the available references to give as a design guideline for these applications was prepared by the Washington State Department of Transportation (Muhunthan et al. 2005).
Using this study and the results obtained from several laboratory and field tests, Maccaferri has developed
new software (MacRO 2) able to perform stability analysis for the selected mesh, the diameter of the crest wire rope cable and the steel and geometric (diameter and length) characteristics of the crest anchors. If time and money are not a problem, a complex numerical analysis with very precise data from the field could be completed, but this is not practical for every project, especially if the system has a modest size and has to be done in a short period of time (emergency protection). MacRO 2 allows designers to have a quick and reliable solution for design. The design procedure that is the basis of the software is simple, but it gives reliable results considering the low level of accuracy generally available from the input data. Mesh design
The simple drapery system is a passive system capable of controlling rockfalls and containing the debris at the bottom of the slope. It is designed considering all the different components able to transmit loads on the mesh per linear of slope section:
1) The proper weight of the selected mesh 2) The weight of the debris accumulated at the toe of the slope 3) External weight like the snow or ice accumulation on the drapery
These three loads may be described with the following formulas, based on the research from the U.S.
Department of Transportation FHWA (note: formulas 1, 2 and 4 are multiplied by unit length for simplification).Total load due to the mesh (Wm) has to be defined:
© AREMA 2014 4
Wm = m Hs / sin (sin – cos tan) g (1)
Where:
‐ m = steel mesh unit weight ‐ Hs =total height of the slope ‐ = inclination of the slope ‐ = friction angle between mesh and slope ‐ g = acceleration of gravity
It is possible to identify the load transmitted from the debris to the mesh (Wd) as follows:
Wd = ½ d Hd2 (1/tand – 1/tan) (sin – cos tand) g (2)
Where:
‐ d = debris unit weight ‐ Hd =debris accumulation height ‐ d = debris friction angle ‐ d = debris external inclination value (Muhunthan equation) :
d = arctan[Hd / (Td + Hd / tan)] (3)
‐ Td = debris accumulation width
Figure 5 – Geometrical input data to calculate the load on the mesh due to the debris accumulation
The last load acting on the mesh is due to the snow thickness above the mesh (Ws). It is considered that for a slope with an inclination () higher than 60 degrees this load is neglected since the snow cannot be accumulated.
© AREMA 2014 5
Ws = s ts Hs / sinsincos tans) g (4)
Where:
s = snow unit weight ts = snow thickness s = friction angle between soil and snow
To design the drapery system at a limit equilibrium state, three safety factors have to be introduced in the
calculation to increase the acting forces and decrease the resisting one:
Safety factor reducing resisting forces: mts = safety coefficient which reduces the tensile strength of the mesh (≥ 1.0; from the in-situ and
laboratory tests, this factor would not be lower than 2.0)
Safety factors increasing acting forces: vl = safety coefficient for the variable loads, like the snow thickness and the debris accumulation (≥
1.0; suggested value according to the Euro Code = 1.5) pl = safety coefficient for the permanent loads, like the drapery (≥ 1.0; suggested value according to
the Euro Code = 1.3)
The acting and resisting forces at the limit equilibrium state can be calculated introducing the partial safety factor coefficients listed above:
The total stress on the drape (S) will be:
Sw = (Wd + Ws) vl + Wm pl (5)
The serviceability tensile strength of the mesh (Rm) is calculated as:
Rm = Tm / mts (6) Where: Tm = ultimate longitudinal tensile strength of the mesh (defined by laboratory tests)
The design is satisfied if:
Rm - Sw ≥ 0 (7)
Thus, the safety coefficient of the mesh equals:
FSmesh = Rm / Sw ≥ 1 (7.a)
Cable design The mesh is secured on the crest with a wire rope cable connected to ground anchors. To design the wire rope cable, the maximum load acting on the drapery (defined above) and the spacing between the crest anchors is used to
© AREMA 2014 6
calculate the deformation and the stress distribution within the rope. This method uses the principle of the catenary loading to verify that the tensile strength of the cable is sufficient to support the total weight of the system: Wm + Wd + Ws.
The cable is verified if the following equation is satisfied:
Twlc – Fcbl ≥ 0 (8) Where: Twlc = cable working load limit [MLT-2]:
Twlc = Tcbl /cbl (9)
Tcbl = ultimate tensile strength of the designed rope (varies with steel grade, wire rope construction and
the diameter) cbl = safety coefficient decreasing Tcbl (≥ 1.0) Fcbl = max tensile strength acting on the cable (calculated with catenary theory)
Thus, the safety coefficient of the cable is:
FScable = Twlc / Fcbl ≥ 1 (8.a)
Moreover, using this theory it is possible to define the maximum length of the rope and its maximum sag
between two anchors.
Figure 6 – Example of the deformation of the crest wire rope cable between two anchors (A and B) calculated by the Catenary theory
Tm = ultimate longitudinal tensile strength of the mesh (defined by laboratory tests)
The design is satisfied if:
Rm - Sw ≥ 0 (7)
Thus, the safety coefficient of the mesh is equal to:
FSmesh = Rm / Sw ≥ 1 (7.a)
© AREMA 2014 7
Anchors design
Anchor’s design may be divided into 2 different steps: 1. The first step is for designing the anchor diameter taking into consideration the shared load transmitted
from the system, composed of the mesh + wire rope cable 2. The second is designing the minimum anchor length, which depends on soil or rock characteristics
Evaluation of the anchor diameter
Using catenary theory it is possible to determine the maximum force acting on the intermediate and lateral anchors. These two forces have to be related to the working capacity of the designed anchors:
Sbar(j) – N(j) ≥ 0 (10)
Where: Sbar(j) = working shear resistance of the anchor j :
Sbar(j) = (Ybar(j) / st) 3-1/2 (11)
Ybar(j) = yield load of the steel bar j :
Ybar(j) = ESS(j) adm(j) (12) ESS(j) = effective area of the steel bar j [L2]:
ESS(j) = / 4 {[fe(j) – 2 fc(j)]2 – fi(j)2} (13) adm(j) = yield stress of the steel of the bar j fe(j) = external diameter of the steel bar j fc(j) = thickness of corrosion on the external crown of the steel bar j fi(j) = internal diameter of the steel bar j st = safety coefficient for the steel strength of the bar (> 1.0) N(j) = force that the cable and the mesh develop on the anchor j (calculated with the catenary solution) j = position of the anchor: intermediate or lateral
Thus, the safety coefficient of the different cable may be calculated as follows:
FSanchor(j) = Sbar(j) / N(j) ≥ 1 (10.a)
Evaluation of anchor length The evaluation of the anchor length takes into account the following:
1. The anchor plays an important role because it has to support the entire system. Its length must be deep enough to reach the stable section
2. The steel bar and the grout are exposed to weathering influences (ice, rain, salinity, temperature variations, etc.)
The minimum theoretical length is derived by the equation:
Lt(j) = Ls(j) + Lp (14)
Assuming: Ls = minimum foundation length [L]:
Ls = P / (drill lim / gt) (15)
© AREMA 2014 8
Lp = length of hole with plasticity phenomena in firm part of the rock mass
With drilldiameter of the drill-hole lim = adherence tension between grout and rock gt = safety coefficient of the adhesion grout – rock P = maximum pullout forces depending on the cable load (Figure 7)
Figure 7 – Scheme of the load on up slope anchors
The minimum length of the anchor that was determined by the formulas will need to be verified onsite. The final suitable length of the bars has to be evaluated during drilling in order to verify the exact nature of the soil and be confirmed with pull out tests.
TYPE OF MESH
Today, the market offers a wide portfolio of rockfall draperies: single twisted or double twisted wire meshes, steel composites mesh with wire rope cables and wires, cable meshes, cable panels and ring panels. To define the drapery to be used, the designer should take into account different aspects of the material:
No unraveling phenomena if a part of the mesh is cut (i.e. a wire, a cable or a connection element): single twist
mesh should be rejected; Resistant to dynamic impact: ring nets or cable panels are the most suitable; High tensile resistance: it depends on the input parameters, but generally no lower than 50 kN/m; Capacity to transfer the load to the anchors: meshes with vertical support rope included are the most
appropriate; Easy installation.
The following table summarizes the main meshes available on the market giving also the principal characteristics.
© AREMA 2014 9
Table 1 – Rockfall mesh features – Note: (*) Value from literature; (**) Average value defined by Officine Maccaferri Full Scale Test carried out in Fonzaso (BL – Ita) on a sample 2.0x2.5m (6.6 ft x 8 ft), restrained on
4 sides; (***) supposed values
Type of Mesh Longitudinal Tensile
Resistance (*) Dynamic
Resistance (**)
Unraveling when one or more
wire/cable fail Photo
Double twist mesh
Up to 100 kN/m (6,854 lb/ft)
(usually 60 kN/m) (4,112 lb/ft)
Up to 15 kJ (3.69 ft-ton)
(usually < 10 kJ) No
Steel composite: cables woven in a double twist mesh
Up to 180 kN/m (12,337 lb/ft)
15 to 20 kJ (5.53 – 7.38 ft-
ton) No
Cable panel Up to 250 kN/m
(17,135 lb/ft) 20 kJ
(7.38 ft-ton) No
Ring net Up to 350 kN/m
(23,989 lb/ft) > 50 kJ (***)
(18.45 ft-ton) No
Figure 8 – comparison between the theoretical and the real case after the mesh installation
From figure 8, it is highlighted that the higher stress is on the mesh (black arrow), which deforms transversally (narrow neck) and stretches longitudinally (elongation). Using the Rock Mesh composite, the forces acting at the bottom of the system are directly transferred to the interwoven cables which reduce the load on the mesh increasing the reaction on the top anchors.
© AREMA 2014 10
Figure 9 – comparison between the theoretical and the real case after the installation of the Steelgrid HR”
The previous figure illustrates that Rock Mesh allows higher loads to be supported by the drapery system with less deformation on the mesh and lower loads on the crest line ropes due to the direct connection of the load supporting integrally woven steel ropes to the crest line anchorages. CASE HISTORY
Dunsmuir is a city in Siskiyou County, California, United States. The population was 1,650 at the 2010
census, down from 1,923 at the 2000 census. It is currently a hub of tourism in Northern California as visitors enjoy fishing, skiing, climbing, or sightseeing.
During steam engine days, it was notable for being the site of an important Central Pacific (and later Southern Pacific/Union Pacific) railroad yard, where extra steam locomotives were added to assist trains on the grade to the north. The area is still extremely important for rail traffic moving along the West Coast.
When UPRR started a modernization of track at Dunsmuir they had to resolve continuing safety issues caused by rockfall. The solution was designed to control rock falls with a system that would be easy to install, economic and low maintenance, and of course reliable.
Figure 10 – General overview of the protected slope
© AREMA 2014 11
The height of the slope was around 34 m (100 ft) and the falling block sizes were between 60 to 100 cm (24 to 36 inches). A hybrid barrier was the retained solution to catch the rocks coming from the upper area and safely control the falling rocks to the bottom of the slope.
A Rockfall Attenuator or Hybrid Rockfall Barrier combines features of a simple drapery and a Flexible Rockfall Barrier. The upslope portion of the drapery is raised off of the slope. Rock falling from above the drapery is caught by the lifted leading edge of the drape system and guided safely to the bottom of the slope by the mesh drapery system.
Figure 11 – None secured lower section of the drapery.
More than 1,850 m2 (19,800 ft2) of wire rope cable panels and double twisted mesh were installed to protect the railroad from debris. The dimension of the wire ropes cable net panels of 3.65 m x 7.3 m (12 x 24 ft) was selected to resist to the rock impact. In this case cable net is used not only for its high tensile strength but also to add weight to the system. The extra weight from the wire rope cable net is providing extra stability by maintaining the falling rocks in better contact with the soil and reducing the bouncing.
To prevent the small rocks from passing through the 30 cm x 30 cm (12 inches x 12 inches) mesh opening of the cable netting. The HEA panels were lined with double twisted wire mesh. To facilitate and accelerate the installation of the cable nets, the cable nets were pre-assembled in the factory in form of rolls of 12 ft by 96 ft long and lined with the double twisted mesh in the factory.
© AREMA 2014 12
Figure 12 – Detail of the cable of the Rock Mesh and the secured toe of the upper section.
The bottom of the drape system was not secured (Fig 11) at the toe allowing the rocks to fall between the grade rail and the rock face. But for the design, we have considered that a 1 meter cubic (1.3 yd3) could be trapped under the drape mesh system and increase the load on the rope cable and anchors. According to MacRO 2 calculation, the safety factor for the tensile strength of the wire rope cable net 8 with a design total stress 11.88 kN/m (815 lb/ft). If the system was a simple drapery and not a hybrid system, we could have selected a less robust material at a lower cost. But, the cable net was selected because of its capacity to reduce the bouncing of the rocks and its resistance to punch test. The selected head cable was 18 mm (3/4 inches) diameter steel core wire rope. The calculated maximum tensile force on the wire rope was 117.74 kN (26,000 lb) with a total safety factor of 1.74.
The minimum shear resistance of the treaded bar anchors should be 117.74 kN (26,000 lb) as per the
maximum forces in the top wire rope cable. But because the steel bar anchors are working more on shear stress than on tension, the minimum steel bar required is 30 mm diameter (1.25 inches) with a reduction factor of 1.73 for the shear only. Where cable anchors are flexing under lateral load, the minimum are working on tension required for cable anchors was 117.14 kN (26,000 lb).
CONCLUSION
Simple drapery is an effective rockfall protection system for rock slopes. This type of solution is economical, easy to install, and has a low level of maintenance. It is recommended in areas where other mitigation systems (i.e. pinned drapery or rockfall barriers) cannot be applied because their cost and/or the morphology of the site are not suitable.
Based on the researches done by Muhunthan et al. 2005 and the in-situ and laboratory tests, Maccaferri has developed a calculation approach (MacRO 2) able to design all the components of the drapery system, such as the mesh, crest cable and support anchors.
The latest advancements in mesh, marked “Steelgrid”, is a new concept of mesh to be used as a simple
drapery system in order to reduce the stress acting on the mesh, and consequently the maintenance costs, even if the amount of debris volume potentially accumulated at the base of the slope is larger.
© AREMA 2014 13
REFERENCES Bertolo P., Oggeri C. & Peila D. (2009). Full-scale testing of draped nets for rock fall protection. Canadian
Geotechnical Journal, 46, 306-317 Bustamante M., Doix B. (1985). Une méthode pour le calcul des tirants et des micropieux injectés, Bull. Liasion
Labo. Ponts et Chausséss, Paris, 149 Geldsetzer T. and B.Jamieson. 2000. Estimating dry snow density from grain form and hand hardness. Proceedings
ISSW 2000. Big Sky, Montana, USA, 121-127 Giacchetti G & Bertolo P. (2010). Approccio al calcolo dei sistemi di reti con chiodi per il consolidamento delle
pareti rocciose. Geoingegneria Ambientale e Mineraria, XLVII(1), 33-43 Peila D., Oggeri C. & Baratono P. (2006). Barriere paramassi a rete. Interventi e dimensionamento. GEAM ,
Quaderni di studio e di documentazione, 26 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. Washington State Transportation Commission - Department of Transportation, U.S. Department of Transportation - Federal Highway Administration.
© AREMA 2014 14