(2006) 121–132www.elsevier.com/locate/enggeo

Engineering Geology 88

Numerical analysis of the performance of wire mesh and cable netrockfall protection systems

N. Sasiharan a, B. Muhunthan a,⁎, T.C. Badger b, S. Shu a, D.M. Carradine c

a Washington State University, Pullman, Washington, USAb Washington State Department of Transportation, Tumwater, Washington, USA

c Wood Materials Engineering Laboratory, Washington State University, Pullman, Washington, USA

Received 10 November 2005; received in revised form 2 August 2006; accepted 6 September 2006Available online 25 October 2006

Abstract

Wire mesh and cable net systems have long been used to control rockfall on actively eroding slopes. The design of thesesystems has been primarily based on empirical methods, engineering judgment, and experience; their performance has been mixed.There is a general consensus among specialists that in wire mesh systems that have functioned well some elements may be over-designed or even unnecessary. On the contrary, system failures under a variety of loading conditions have occurred within the lastfew decades, indicating that certain design elements may in fact be under-designed for their desired application.

This study presents the results of finite element analyses conducted to examine the performance of the individual elements aswell as the overall stability of the wire mesh systems. The load–displacement behaviors of widely used fabrics were determined inthe laboratory.

The friction between the mesh and rock can be a major contributor to the stability of the wire mesh and cable net systems. Theinterface friction is controlled by macro and micro roughness of the surface. Interface friction is a difficult parameter to quantify inpractice. Guidelines are provided to estimate this parameter from observed slope irregularity and surface roughness based on finiteelement analyses.

The top horizontal rope is an essential element in the design of wire mesh and cable mesh systems. The study also shows thatthe inclusion of interior horizontal support ropes does not reduce the stress within the mesh, and accordingly, provides nomechanical benefit. Results show that the use of vertical ropes eliminates stress concentration around the anchor support andreduces stresses on the top horizontal rope provided that they are clamped to the mesh at closed intervals.© 2006 Elsevier B.V. All rights reserved.

Keywords: Rockfall; Wire mesh; Cable net; Friction; Stability; Finite element analysis

⁎ Corresponding author. Department of Civil and EnvironmentalEngineering, Washington State University Pullman, WA 99164 USA.Tel.: +1 509 335 3921; fax: +1 509 335 7632.

E-mail address: muhuntha@wsu.edu (B. Muhunthan).

0013-7952/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.enggeo.2006.09.005

1. Introduction

Rockfall presents a common hazard to transportationroutes and structures in steep mountainous terrain.Geology and climate are the principal causal mechan-isms of rockfall factors that include intact conditionof the rock mass, discontinuities within the rock mass,

122 N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

weathering susceptibility, ground and surface water,freeze–thaw, root-wedging, and external stresses (Smithand Duffy, 1990; Hearn and Akkaraju, 1995; Hearn,1995). Rockfall initiation and trajectory is a function ofslope and rock geometry as well as the slope and rockmaterial properties (Ritchie, 1963; Pfeiffer and Higgins,1990). Since these are often extremely difficult to pre-dict and quantify, prevention of rockfall is often notviable or cost-effective. Therefore, it is a common practicealong highways to provide protection such as ditches,fences, barriers, and wire mesh and cable net protectionsystems.

Since the1950s, heavy gage wire mesh has beenplaced directly on the slope surface along NorthAmerican highways to control rockfall on activelyeroding slopes. Within the last fifteen years, smalldiameter wire rope (cable) nets have been employed as amore robust alternative to wire mesh. With the exceptionof the anchors and support ropes, the basic design ofunsecured systems is comparatively similar throughoutNorth America. It consists of a top horizontal ropesuspended by regularly spaced anchors, typically aperimeter or widely spaced grid of support ropes, anddouble-twisted, hexagonal wire mesh laced to thesupport ropes (Fig. 1).

The design of these elements has largely been basedon empirical guidelines. For example, the Washington

Fig.1. Schematic drawing shows basic e

State Department of Transportation used the followingguidelines until recently:

FabricDouble twist for block sizes b0.6 m (2 ft)Cable net for block sizes b9–1.5 m (3–5 ft)Minimal use of chainlink fabric on flatter slopes

Anchor15.24 m (50 ft) anchor spacing for slopes b22.86 m(75 ft) high7.62 m (25 ft) anchor spacing for slopes N22.86 m(75 ft) highLocate anchors 3–10m (10–30 ft) beyond active browNo mid slope anchors

Similar guidelines are followed by other states in theUnited States and Canada. There is, however, aconflicting opinion on the safety of such elements inpractice. While certain states have determined thecurrent empirical guidelines to be safe and conservative,other states such as Washington have experiencedfailure of individual, or a combination of all of thethree main elements. The failure has been in the form ofpullout of anchors (Fig. 2a), tear and rupture of thefabric due to large concentrated static load consistingof pockets of rock and/or snow (Fig. 2b and c, andpuncture of the fabric due to rock impact (Fig. 2d).

lements of a drape mesh system.

123N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

Snow loading has also contributed to an increase in theincidence of such failures in some states. It is understoodthat most of the failure due to the rupture of the fabrichas been towards the bottom of the mesh. This may bedue to the accumulation of debris at the foot of the slope,and the transmission of considerable impact energyfrom falling rocks, or a combination of both. There islittle information on what influence these concentratedor external loads have on these slope protection systems.To the authors' knowledge there is only one study by theMinistry of British Columbia that evaluated draperymesh system performance experimentally and numeri-cally (Sandwell Incorporated, 1995).

This paper presents the results of numerical analysesconducted to examine the performance of some of the keyelements of the wire mesh and cable net systems. Itfocuses on the effect of mesh weight, the interface frictionbetween mesh and rock surfaces, and the accumulation ofdebris on the overall stability of the systems.

Fig. 2. Illustrative examples of drapery mesh system failure: (a) anchor pulaccumulation; (c) rupture of vertical seam and fabric; the mid slope horizon

2. Fabric properties

Current practice for transportation applications inNorth America has generally utilized two types of fabricfor draped rockfall protection systems; hexagonal wiremesh and woven cable nets with pressed cross clips.Within the last several years, high tensile steel wiremesh (TECCO®) has been introduced in NorthAmerica. Each of these fabric types has distinctlydifferent weight, strength and elongation properties.Unfortunately, very little published data exist on theseproperties, and some of the published results variedsignificantly. Furthermore, while some manufacturershave independently tested their products, hexagonalmesh is the only fabric type that has a widely accepted,standardized test method (ASTM A 975) in NorthAmerica to evaluate these properties. Additionally, thereis no widely accepted test method to allow for thecomparison of engineering properties for a variety of

lout failure of drapery system; (b) mesh tear due to excessive debristal support cable (d) puncture of the fabric due to rock impact.

Fig. 4. Typical load–displacement curve for Maccaferri double-twisted, TECCO® wire meshes and Maccaferri cable net.

Fig. 3. Schematic diagram of mesh testing arrangement.

124 N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

fabric types. Therefore, independent tests were con-ducted at the Wood Materials and Engineering Labora-tory (WMEL) at Washington State University inPullman, Washington.

Fig. 3 shows the schematic of the test fixture that wasdesigned, fabricated and bolted to the reaction floorinside the WMEL's structural testing facility. The intentof the test fixture was to load the fabrics in tension alongthe longitudinal direction of fabrics while restraining theedges parallel to the direction of loading fromconstricting as loads were applied. Loads were appliedutilizing a 445 kN capacity hydraulic actuator with astroke of 25.4 cm that was controlled using an MTS 407Controller, which received actuator displacement feed-back using a string potentiometer. Load data wereobtained using a 445 kN capacity load cell placed in linewith the loading apparatus. Linear variable differentialtransformers (LVDTs) and string potentiometers wereused to monitor displacement of the loading head withrespect to the base of the test apparatus in order to get anaccurate record of the distance the meshes movedthrough the first 5 cm of displacement. Load data anddisplacement data from the string potentiometer and the2 LVDTs were recorded using LabVIEW version 6.1software. Differences in dimensions of the meshes madeit necessary to make a slight modification of the testapparatus. A detailed account of such modification andother relevant information are provided in a compre-hensive report (Muhunthan et al., 2005).

Attachment of the loading plates was done farenough from the ends of the meshes so that the wireswould not unwind or come undone prior to failure of thespecimens. All specimens were placed in the fixture insuch a way that as much slack could be taken out of thespecimens as possible. This was done to ensure thatthere would be enough deformation of the specimens tocause failure. In general there was very little loadapplied to the specimens as they were installed in the testfixture.

All specimens were secured in the test frame, andthen the LVDTs or string potentiometers were installedsuch that the maximum amount of displacement datacould be recorded before the instruments ran out ofstroke on the plunger or extension of the string.Following installation of the displacement measuringdevices, the data acquisition program was started andthe hydraulic actuator was put into action. Load wasinduced by the hydraulic actuator, which ran at 6.35 mmper minute under displacement control.

Fig. 4 shows the typical load–displacement behaviorof Maccaferri double-twisted hexagonal wire mesh,Geobrugg TECCO® wire mesh, and Maccaferri cablenet. It can be seen that the behavior of these fabrics canbe approximated to be linear elastic until a peak hasbeen reached. Accordingly, Table 1 summarizes thestrength and modulus parameters for the finite elementanalyses obtained from these tests. It is noted that insome cases the strength and modulus values that wereobtained from our testing varied from the valuesreported by the manufacturers. This may be due to

Table 1FE model parameters for different meshes

Type Young's modulus(MPa)

Yield or breakingstrength (MPa)

Maccaferri double-twisted mesh

850 15

TECCO® G65 mesh 170 30Maccaferri cable net 14000 175

125N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

differences in the type of tests, specimen size, and theboundary and loading conditions. It is emphasized herethat the testing performed for this research was notintended to compare the performance of fabric typesfrom different manufacturers. Rather, the testingenabled us to compare the performance of these systemsunder a range of modulus and strength values.

3. Finite element model

Finite element analyses were conducted using thecomputer code ABAQUS (2003). The finite elementdiscretization of the wire mesh system is as shown inFig. 5. Since the mesh carries the load with its endrestraint in a “membrane type” action, the mesh wasmodeled using a three-dimensional membrane elementfrom the ABAQUS library (ABAQUS, 2003). The tophorizontal rope and support ropes were modeled usingthree-dimensional hybrid beam elements. Hybrid beamelement is a special purpose element that is capable of

Fig. 5. Finite element model a

simulating a cable-type structural element. The externalsupport from the anchors is assumed to be pinned. Thetwo vertical edges and the bottom edge are left free asthese are not bolted or fixed to the ground in practice.The finite element model was first verified using somefield test results (Sasiharan et al., 2005).

4. Interface friction

In all but vertical to overhanging slopes, theinterface friction developed between the mesh and theground surface can be a major contributor to thestability of the wire mesh and cable net systems. Theinterface friction is controlled by macro and microroughness of the surface. Macro roughness is the degreeof large-scale irregularities of the slope, and microroughness is related to surface texture. In the case of asmooth planar slope, minimal interface friction may bepresent, and the mobilized force on the system is carriedlargely by the anchors. When a slope is highly irregularand the surface is rough or has abrupt protrusions, veryhigh interface friction may be present. In these cases,very little to no mobilized force may be imparted to theanchors. Interface friction is a difficult parameter toquantify in practice. In the absence of either back-calculated values or field measurements, the interfacefriction angle can be crudely estimated based onobserved slope irregularity and surface roughnessusing the guidelines below. Additional guidance on

nd boundary conditions.

Fig. 6. Von-Mises stress distribution on the mesh (load from meshweight only).

126 N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

the characterization and verification of the frictionangles recommended below are presented elsewhere(Muhunthan et al., 2005).

4.1. Rough slope

The slope surface is very irregular and undulatingand has many and/or prominent protrusions on thesurface. As a result, both micro and macro roughnesscontribute to a large effective increase in interfacefriction. For such cases, the interface friction angle isassumed to be above 60°. For moderate to high degreeof mesh contact with the slope, the possibility of globalinstability of a system on such a slope is very low undernormal conditions. Note, however, as slope irregularityand surface roughness increase, mesh contact areausually decreases.

4.2. Undulating slope

The slope is undulating but there are few and/or smallabrupt protrusions on the surface. As a result, both microand macro roughness contribute to an effective increasein the interface friction of the slope. Accordingly, theinterface friction angle is assumed to be between 36°and 59°.

4.3. Planar slope

The slope is planar, and the surface is fairly smooth andhas few small undulations. In this case, only microroughness is assumed to contribute to the frictional resis-tance. Accordingly, the interface friction angle is assumedto be between 25° and 35°.

The values of the interface friction angle proposedabove for the rough and undulating slopes were exam-ined and verified by finite element analyses and throughlimit equilibrium back analyses of existing stable andfailed installations. To examine the friction contribution,finite element analyses were carried out with selectedinternal supports within the mesh region for an assumed45° slope and the increases in “effective” friction anglewere determined. Several iterations were performed byvarying the location of the internal support to determinethe most critical configuration. For an undulating slope,the location of the internal support was varied whereasfor the rough slope two to three internal support pointswere varied inside the mesh. The reaction loads onanchors with the internal supports were obtained first.Subsequently, the interface friction angle on anequivalent slope with no internal support was varieduntil the results matched.

5. Element performance in wire mesh and cable netsystems

The current practice of wire mesh and cable netprotection systems often includes a widely spaced grid ofinterior horizontal and vertical support ropes throughoutthe field of the mesh (Fig. 1). However, it has been knownthrough field observations that this practice does notprovide significant mechanical benefit (Duffy et al.,2005). Optimizing the design of the system by eliminatingsome elements in the wire mesh/cable net protectionsystems could reduce construction costs. Therefore, finiteelement analyses were consecutively carried out toevaluate the mechanical contribution, if any, of eachsystem element.

First, the installation supported by anchors wasanalyzed without any horizontal and vertical supportropes (Fig. 5). The resulting von-Mises stress distribu-tion is shown in Fig. 6. Stresses are concentrated aroundthe anchor support and a significant segment of the meshexperiences much lower stress distribution.

Subsequently, the system was assumed to be installedwith a top horizontal support rope (Fig. 5). The resultingstress distribution is shown in Fig. 7. The use of a tophorizontal rope significantly reduces the maximum stresslevel around the anchor (5.5 MPa to 3 MPa) bydistributing it along the entire length of the support rope(Fig. 7).

Fig. 7. von-Mises stress distribution on the mesh with top horizontalrope.

127N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

The analysis was repeated with the addition of verticalsupport ropes on the anchor locations (Fig. 8). Theiraddition nearly eliminated the stress concentration on themesh around the anchors. The stresses on other segmentsalso dropped significantly. Further, the addition of thevertical rope reduced the stress level in the horizontal

Fig. 8. von-Mises stress distribution on the mesh with top horizontalrope and vertical support ropes.

rope. Therefore, it is evident that with the use of verticalsupport ropes the mesh system would remain stableimmediately after construction under its own weight.Note that the pattern of the stress distribution was foundto be dependent on the ratio of the modulus of the verticalrope and the mesh.When the modulus of the rope and themesh were nearly the same, the distribution patternfollowed that is shown in Fig. 7.

Analyses were also conducted to study the effective-ness of adding additional interior horizontal supportropes (Fig. 1). However, their addition did not makechanges to the stress levels or to the distribution. There-fore, their use in current practice does not have anymechanical benefit (see also Table 2).

The maximum value of the stress experienced by eachelement for the different cases is shown in Table 2. It canbe seen that the maximum stress on the vertical supportrope is much smaller than that on the top horizontalsupport rope. Consequently, the vertical ropes need not beas strong as the top horizontal rope in the design.

In the current practice, where vertical support ropesare included, the mesh is fastened to vertical ropes withlacing wire and does not grip the rope. Hence, there is novertical load transfer of the mesh weight to the verticalsupport ropes. Thus, there is no effective mechanicalbenefit. If the mesh were to be clamped at close spacingto the vertical ropes, the mechanical benefit wouldpotentially be realized up to the localized yield stress ofthe mesh connection detail.

Table 2Summary of von-Mises stresses for different support ropearrangements

Arrangement Description von-Mises stress (MPa)

Mesh Tophorizontalcable

Verticalsupportingcable

Arrangement1

Mesh only (no tophorizontal cable andsupport ropes)

5.60 – –

Arrangement2

Mesh with tophorizontal rope

3.20 65.0 –

Arrangement3

Mesh with tophorizontaland verticalsupporting ropes

.064 12.2 2.48

Arrangement4

Mesh with tophorizontal cableand horizontalsupporting ropes

3.20 71.0 –

Arrangement5

Mesh with tophorizontal, verticaland horizontalsupporting ropes

.064 11.8 2.03

128 N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

6. Anchor spacing and anchor load

FE analyses were also carried out to develop designcharts for a variety of combinations of slope lengths,fabrics, slope angles, and interface friction. The charts

Fig. 9. Variation of anchor load vs. spacing for (a) double-twisted hexagonal w

are developed for four slope lengths 15.2, 30.5, 61, and91.5 m, three types of fabrics, three types of slopesurfaces, and for slope angles of 45, 60, and 90°. Fig. 9shows the variation of anchor load with anchor spacingfor three different fabrics. Fig. 10 shows the variation

ire mesh, (b) TECCO®G65mesh and (c) cable nets for 60° planar slope.

129N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

of anchor load with spacing for different slope surfaceconditions. The results are for the mesh on a verticalslope without debris load, and the interface friction isabsent. Therefore, these values could be considered to

Fig. 10. Variation of anchor load vs. spacing for TECCO® G65 m

provide the most conservative anchor loads for a givenspacing. Similar analyses were conducted for a suite ofslope and interface friction angles and the results arereported in Muhunthan et al. (2005).

esh for 60° (a) planar, (b) undulating and (c) rough slopes.

Table 4Fabric yield states as a function of debris load

Fabric Maximum debris volumethat can accumulatebetween anchors of 15 mspacing

Maximum debrisvolume that canaccumulate betweenanchors of 6 mspacing

Double-twistedhexagonal mesh

1.9 m3 1.6 m3

TECCO®G65

3.7 m3 2.9 m3

Maccaferricable net

5 m3 [19 m3] 5.7 m3 [15 m3]

130 N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

7. Simple design example

Consider the case of a double-twisted wire meshplaced on a 60° planar slope with the height of 22.86 mand anchor spacing of 7.62 m. The anchor spacing waschosen to conform to the current empirical guidelinespresented earlier. The analysis of this system gives ananchor load of about 20 kN (Fig. 9(a)). Typical anchorsused in North America have the capacity that generallyexceeds 90 kN in both tension and shear. Thus, the use ofan anchor spacing of 7.62m results in a factor of safety of4.5. On the contrary, the use of Fig. 9(a) shows that thatthe anchor spacing as wide as 15 m could be used on thesame slope with the factor of safety of 2. Increasinganchor spacing will reduce the number of anchor, hencethe cost of construction. It is noted, however, if otherexternal loads such as snow are present then the designanchor spacingmust be reduced. Such considerations arepresented elsewhere (Shu et al., 2005; Muhunthan et al.,2005)

8. Limiting conditions on global stability

The FE analyses were also used to determine themaximum height of installation, the maximum debrisload for each fabric for different anchor spacing, and themaximum uninterrupted length of the top horizontalrope.

8.1. Maximum installation height

To determine the maximum height of installation fora specific fabric, the analyses used a 90° slope (nointerface friction) with a 6 m and 15 m anchor spacing.The three fabrics that were evaluated are as follows:

• a double-twisted hexagonal mesh of galvanized3 mm diameter wire, (supplied by Maccaferri),

Table 3Fabrics yield states as function of height

Fabric Maximum height ofinstallation for 15 mspacing (m)

Maximum height ofinstallation for 6 mspacing (m)

Double-twisted,hexagonalmesh

105–115 b170

TECCO® G65mesh

135–150 b215

Maccaferricable net

180–230 b250

• a high tensile steel, TECCO® G65 mesh of corrosionprotected 3 mm diameter wire (supplied by Geo-brugg), and

• a 300 mm square grid, cable net of 8 mm wire ropediameter (supplied by Geobrugg).

The result for each fabric is shown in Table 3. Notethat these yield states are considerably larger than thehighest installations of current practice, which approach125 m in North America.

8.2. Maximum debris load

FE analyses were carried out to determine themaximum debris load for a 45° slope, 30 m slopelength with a 6 m and 15 m anchor spacing. It isassumed that a debris load would be distributeduniformly over the entire width. The unit weight ofthe debris is assumed to be equal to 2100 kg/m3. Notethat the maximum debris load for double-twistedhexagonal mesh and TECCO® G65 mesh was deter-mined by limiting the yield strength of the meshes withan assumed anchor capacity of 90 kN. Since the yieldstrength of the cable net is much higher, the anchorcapacity (90 kN) will be the limiting factor indetermining the maximum debris load (Table 4). As-suming that the anchor capacity was not the limitingfactor but the cable net is the first to yield, then muchhigher debris loads can be carried by the cable nets asshown in the bracketed values in Table 4. Thecorresponding anchor loads for this yield state for a

Fig. 11. Load distribution in the top horizontal support rope.

Fig. 12. Schematic diagram of top horizontal cable under mesh load.

Table 5Maximum length for top horizontal support rope for Maccaferridouble-twisted mesh

Slopelength(m)

Maximum length for13 mm cable; fabric weightonly (m)

Maximum length for19 mm cable; fabric weightonly (m)

15 140 25030 75 13060 35 6590 25 45

Table 6Maximum length for top horizontal support rope for Maccaferridouble-twisted mesh with Maccaferri cable net backup

Slopelength(m)

Maximum length for13 mm cable; fabric weightonly (m)

Maximum length for19 mm cable; fabric weightonly (m)

15 50 9030 25 4560 15 2590 8 15

131N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

15 m and 6 m anchor spacing are 275 kN and 230 kN,respectively.

8.3. Horizontal rope

The top horizontal support rope is a critical structuralelement in any installation. Fig. 11 shows the typicalloading arrangement of a top horizontal support rope.Maximizing the uninterrupted length of the top horizontalrope and, thus, minimizing connections reduces theinstallation cost of a system. These lengths, however,are limited by their tensile capacity and sag of the rope,and can be calculated by using standard equations for alaterally loaded cable.

The schematic diagram of a circular membrane undera constant pressure p is shown in Fig. 12. For verticalequilibrium:

T ¼ pdr ð1Þ

where T is the tensile force and r is the radius of thecircle.

Let us assume that the length of the mesh segmentbefore deflection is Ls. If the strain εy at yielding withinthis segment is assumed to be uniform, the deformed arclength, A, can be given by:

A ¼ Lsð1þ eyÞ ð2Þ

The radius of the circle and the subtended angle α arerelated by:

r ¼ Lssin a

2

ð3Þ

Using the Taylor series expansion and approximating anexplicit expression, α can be obtained as:

a2¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi6 1−

LsA

� �sð4Þ

The maximum deflection at the mid section is,

DZ ¼ r l−cosa2

� �ð5Þ

From above equations, contact pressure p (in this case itwould be the uniformly distributed load along the rope)can be calculated as,

p ¼ 8TDZL2s

ð6Þ

Note an iterative procedure should be adopted, ascable weight is a function of the length of the horizontalrope. The calculations were carried out for wire ropesizes that are most typically used in North Americaninstallations. The tensile capacities of typical horizontalropes of 13 mm and 19 mm diameter are approximately110 kN and 220 kN, respectively. The maximum lengthof unsupported section of a rope with no interfacefriction was found for double-twisted hexagonal meshand TECCO® mesh (Table 5) and cable net backed withdouble-twisted hexagonal mesh (Table 6). Note thatthese values are calculated for mesh weight only. If otherexternal loads such as snow or debris contribute then therequired lengths will become shorter.

132 N. Sasiharan et al. / Engineering Geology 88 (2006) 121–132

9. Conclusions

This study presented the results of finite elementanalyses on the performance of wire mesh systems. It isfound that the load–displacement behavior of widelyused fabrics can be approximated to be linear elasticuntil a peak has been reached.

The friction between the mesh and rock is a majorcontributor to the stability of the wire mesh and cable netsystems. The interface friction is controlled by macroand micro roughness of the surface. Interface friction isa difficult parameter to quantify in practice. It is shownthat interface friction can be quantified into three majorcategories: rough, undulating, and planar, based onobserved slope irregularity and surface roughness.Based on finite element analyses and confirmed throughlimit equilibrium back analyses of existing stable andfailed installations, the friction angle of a rough slope isestimated to be above 60° and the corresponding rangesfor undulating and planar ranged from 36° to 59° andfrom 25° to 35°, respectively.

The study shows the top horizontal rope to be anessential element in the design. Under the self weight ofthe mesh as the only external load, the stress concentra-tions within the mesh and the stress on the top horizontalrope are relatively low. However, if external loads such assnow are present, the use of vertical ropes could reducestress concentrations around the anchor support bydistributing it over the mesh, provided only if the meshcan be securely clamped to the vertical support ropes atclose intervals. If such close securement can beaccomplished, the analyses show that vertical ropes donot need to be as strong as the top horizontal supportropes. In practice, however, closely spaced clamping ofthe mesh to vertical support ropes would be costly andtime consuming, likely proving to be too costly for thebenefit provided. The stiffness of vertical ropes must bemuch higher than the fabric for distributing the stress.More significantly in terms of reduced installation costand improved system performance, is the confirmation offield observations through finite element analyses thatinterior horizontal support ropes within the field of themesh provide no mechanical benefit for reducing stresseswithin the mesh.

Design charts for designing anchor spacing fordifferent fabrics are given. Limiting values for maxi-mum installation height, debris volume, and maximumuninterrupted top horizontal rope length were also

developed for typical fabrics and tabulated. A suite ofcomprehensive design charts and consideration of snowand impact loads are presented in Muhunthan et al.(2005).

Acknowledgements

The study was sponsored by the Washington StateDepartment of Transportation with financial contribu-tions from contributory state and provincial DOTs andtechnical input by the technical advisory committee forthis pooled-fund research program. The authors are alsograteful to Geobrugg of Sante Fe, New Mexico andMaccaferri of Virginia for providing materials fortesting and proprietary test data.

References

ABAQUS: Finite Element Software Package. Hibbitt, Karlsson andSorrenson, Inc. Version 6.3-1.

Duffy, J., Ingram, H., Badger, T.C., 2005. Personal Communications.Hearn, G., 1995. Testing and Modeling of Two Rockfall Barriers. .

Transportation Research Record. National Research Council,Washington, DC, pp. 1–11.

Hearn, G., Akkaraju, L., 1995. Analysis of cable nets for boulderimpacts. ASCE 10th EMD Boulder, CO, pp. 289–292.

Muhunthan, B., Shu, S., Sasiharan, N., Hattamleh, O.A., Badger, T.C.,Lowell, S.M., Duffy, J.D., 2005. Analysis and Design of WireMesh/Cable Net Slope Protection, Washington State Transporta-tion Center (TRAC) Report No. WA-RD 612.1, Seattle, Washing-ton. 267pp (http://www.wsdot.wa.gov/biz/mats/Geotech/WA-RD612.1WireMesh.pdf).

Pfeiffer, T.J., Higgins, J.D., 1990. Rockfall hazards analysis using theColorado Rockfall Simulation Program. Transportation ResearchRecord, vol. 1288. TRB, National Research Council, WashingtonD.C., pp. 117–126.

Ritchie, A.M., 1963. Evaluation of rockfall and its control. HighwayResearch Record, vol. 17. TRB, National Research Council,Washington D.C., pp. 18–23.

Sandwell Incorporated, 1995. Structural evaluation of slope meshsystem, prepared for British Columbia Ministry of Transportation.Sandwell Report, vol. 113576.

Sasiharan, N., Muhunthan, B., Shu, S., Badger, T.C., 2005. Analysis ofglobal stability, anchor spacing, and support cable loads in wiremesh and cable net slope protection systems. TransportationResearch Record: Journal of the Transportation Research Board1913, 205–213.

Shu, S., Muhunthan, B., Badger, T.C., 2005. Snow loads on wiremeshand cable net slope rockfall protection systems. EngineeringGeology 81, 15–31.

Smith, D.D., Duffy, J.D., 1990. Field tests and evaluation of rockfallrestraining nets. Report No. CA/TA-90/05, California Departmentof Transportation, Transportation Materials and Research.