Rock Support Interaction

ce.umn.eduUniversity of Minnesota

Department of Civil Engineering

[Last revision – June 06]

These notes areavailable for downloading atwww.cctrockengineering.com

[UE-T9-1]

Class notes on Underground Excavations in Rock

Topic 9:

Tunnel support systems. Technologies and design.The Convergence-Confinement Method

written by

Dr. C. Carranza-Torres andProf. J. Labuz

These series of notes have been written for the course Rock Mechanics II,CE/GeoE 4311, co-taught by Prof. J. Labuz and Dr. C. Carranza-Torresin the Spring 2006 at the Department of Civil Engineering, Universityof Minnesota, USA.




[UE-T9-2]

Classification of tunnel supports in terms of time of installation (1)




[UE-T9-3]

Classification of tunnel support in terms of time of installation (2)




[UE-T9-4]

Common support systems used in tunnel construction

• Steel ribs (or steel sets) and lattice girders.

• Shotcrete or sprayed concrete.

• Cast-in-place concrete.

• Prefabricated segmental lining (used with mechanized excavation).

Note: Rockbolts do not fall into the category of support systems but intothe category of reinforcement systems —they will be treated separatelyin these series of notes.




[UE-T9-5]

Steel ribs and lattice girders. Technological aspects (1)

Bracing bars, wood or steel plates are normally installed between steelsets and lattice girders.

For squeezing ground, sliding joints and sliding arches are emplacedbetween segments conforming the steel section.




[UE-T9-6]


See explanation in the next slide.




[UE-T9-7]


Description photographs in previous slide

The previous slide shows photographs of tunnel sections supported with steel sets.Photograph (a) shows wood blocks used between the steel ribs and the rock (shotcreteis seen ahead of the steel sets). Photograph (b) shows steel sets failing under extremeground loading. Photograph (c) shows heavy steel sets used while traversing a faultzone (note the bracing bars between steel sets).

The photographs have been taken Dr. Evert Hoek, Rock Mechanics Consultant(www.rocscience.com/hoek/Hoek.asp) at various underground sites. (a) Drainagetunnel at Chuquicamata mine, Antofagasta, Chile. (b) Drifts at Sullivan mine, BritishColumbia, Canada. (c) Headrace tunnel for at Victoria Hydroelectric Scheme, SriLanka.




[UE-T9-8]Steel ribs and lattice girders. Technological aspects (4)





[UE-T9-9]



The photographs in the previous slide show the use of circular steel sets (with slidingjoints and shotcrete) as a mean of supporting a tunnel in highly squeezing ground atthe Yacambu-Quibor project, Lara State, Venezuela. The Yacambu-Quibor tunnel isa ∼24 km hydraulic tunnel of mean diameter ∼4 m with maximum overburden of1,200 m excavated in low strength phyllites and schists. The tunnel has been called‘the most difficult modern tunnel ever to excavate’ —excavation has been taking placesince the late 70s (by late 2004, ∼3.5 km of tunnel were still to be excavated).

The photographs in the previous slide have been taken by Drs. Mark Diederichs, BrentCorkum and Carlos Carranza-Torres, during a visit to the project in 2004, togetherwith Dr. Evert Hoek and Dr. Rafael Guevara (members of the panel of experts in theproject).









[UE-T9-11]



The photographs in the previous slide show the sequence of construction of steel setsand sliding joints used as primary support in the Yacambu-Quibor tunnel, Lara State,Venezuela. Photograph (a) shows the steel section before being bent into a curvedsegment (note the steel plates welded to the central flange of the section, to avoidbucking during the process of bending). Photograph (b) shows the steel section duringan early stage of bending in the press. Photograph (c) shows the curved segment afterfurther pressing (note that the oscillations of the upper and lower flanges in photograph(b) have been removed). Photograph (d) shows the different segments comprising thesteel section alienated for assembly. Photograph (e) shows the final assembly of thecircular steel set. Note the sliding joints installed between different segments.

These photographs have been taken by Drs. Mark Diederichs, Brent Corkum andCarlos Carranza-Torres, during a visit to the project in 2004, together with Dr. EvertHoek and Dr. Rafael Guevara (members of the panel of experts in the project).









[UE-T9-13]



The photographs in the previous slide show views steel sets used in the Driskos tunnelof Egnatia project, Greece (www.egnatia.gr), a tunnel excavated in weak rock. Photo-graph (a) shows shotcrete being applied in the vicinity of the (top heading) front. Notethe forepoling and fiberglass reinforcement used in the front, as a means of stabilizingthe front during excavation. Photograph (b) shows the complete section after the lowerbench has been excavated and supported.

The photographs described above have been taken by Prof. Paul Marinos (from theDepartment of Geotechnical Engineering, School of Civil Engineering, National Tech-nical University ofAthens, http://users.ntua.gr/marinos/) who is a member of the Panelof Experts in the Egnatia project.









[UE-T9-15]



The photographs in the previous slide show views of lattice girders used in tunnels of theEgnatia project, Greece (www.egnatia.gr). During excavation, lattice girder sectionsare delivered in ‘segments’ to the front of the tunnel, where they are assembled andinstalled.

The photographs have been taken by Prof. Evert Hoek (and independent rock mechan-ics consultant, www.rocscience.com/hoek/Hoek.asp) who is a member of the Panel ofExperts in the Egnatia project.









[UE-T9-17]



The photographs in the previous slide show the use of steel sets in tunnels. In pho-tograph (a) steel plates are emplaced between steel ribs. In photograph (b) bracingbars are emplaced between steel ribs (in this case, a wire mesh has also been installedbefore shotcreting the space between rock and steel sets).

The photographs were taken by Ing. Luca Perrone, Tunnel Design Engineer, GeodataSpa., Torino, Italy (www.geodata.it). Photograph (a) is at the portal for the St. Martinde la Porte tunnel (∼1,400 m), in France —this is an access tunnel for the futureTorino-Lyon railway system (to formally start construction this year). Photograph(b) is at the front of Traffic Release Tunnelling System (∼1,400 m), Western KualaLumpur, Malaysia.




[UE-T9-18]


To learn more about the system see:

Chapter 5, ‘Design of Steel Ribs and Lattice Girders’ in document‘Tunnels and shafts in rock’, U.S.Army Corps of Engineers, 1997 (avail-able for downloading at www.usace.army.mil).

‘Use of arches in the construction of underground works’, DocumentNo 27, 1978, Recommendations from AFTES (available for download-ing at www.aftes.asso.fr).

For use of sliding joints and sling arches, see Chapter 12, ‘Tunnelsin weak rock’, in document ‘Rock Engineering. Course Notes by EvertHoek’ (available for downloading at ‘Hoek’s Corner’,www.rocscience.com).

To find supliers of the system in the market see:

American Commercial Inc. (www.americancommercial.com) — seepages ‘Steel ribs’, ‘Liner Plates’ and ‘Lattice Girders’.

Tunnel Builder (www.tunnelbuilder.com). Go to ‘Suppliers’ andchoose ‘Support’.

InfoMine, Mining Intelligence andTechnology. (www.infomine.com).Go to ‘Suppliers’ and search for ‘Steel Ribs’, ‘Lattice Girders’, etc. (askeyword).




[UE-T9-19]

Shotcrete or sprayed concrete. Technological aspects (1)

Shotcrete is frequently applied on a wire mesh bolted to the rock face(wire mesh acts as reinforcement).

Steel fibers are sometimes added to the shotcrete mixture to increasethe strength of the shotcrete.




[UE-T9-20]Shotcrete or sprayed concrete. Technological aspects (2)





[UE-T9-21]



The photographs in the previous slide shows shotcrete used as support for an under-ground excavation. Photograph (a) shows a drift supported by steel sets near the front.A robotic sprayer is applying shotcrete on top of a wire mesh between steel sets. Pho-tograph (b) and (c) show shotcrete with fiber reinforcement (the fibers are the steelwires embeded in the mortar).

The photographs have been taken by Prof. Mark Diederichs, from the Geological En-gineering Group at Queen’s University (www.geol.ca), also an independent consultant,at Kidd Creek Mine, near Timmins, Ontario.




[UE-T9-22]



Document ‘Standard practice for shotcrete’, U.S. Army Corps ofEngineers, 1993 (available for downloading at www.usace.army.mil).

‘Sprayed Concrete — Technology and Practice’, Document No 1,1974, Recommendations from AFTES (available for downloading atwww.aftes.asso.fr).

‘Design of sprayed concrete for underground support’, Document No164, 2001, Recommendations from AFTES (available for downloadingat www.aftes.asso.fr).

Chapter 15, ‘Shotcrete support’, in document ‘Rock Engineering.Course Notes by Evert Hoek’ (available for downloading at ‘Hoek’sCorner’, www.rocscience.com).


American Commercial Inc. (www.americancommercial.com) — seepages ‘Hany’ and ‘Aliva’.


InfoMine, Mining Intelligence andTechnology. (www.infomine.com).Go to ‘Suppliers’ and search for ‘Shotcrete’.




[UE-T9-23]

Cast-in-place concrete. Technological aspects (1)

Traditionally, the use of cast in place concrete as a tunnel supportmethod has followed standard technological practices in general civilengineering works (e.g., standards regarding material component mix-tures, additives, curing, etc.).

For the case of final support, considering that the concrete structureworks mostly in compression, the use of plain concrete (i.e., massiveunreinforced concrete) is also a standard practice in tunnel construction—see ‘The use of plain concrete in tunnels’, recommendation byAFTES(full reference in the last slide on this topic).




[UE-T9-24]Cast-in-place concrete. Technological aspects (2)

The photographs above show views of cast-in-place concrete support used in TunnelTazon (6700 m), Central Railway System, Caracas, Venezuela. The photographs havetaken by Ing. Luca Perrone, Tunnel Design Design Engineer, Geodata Spa., Torino,Italy (www.geodata.it).




[UE-T9-25]

Cast-in-place concrete. Technological aspects (3)


Document ‘Standard practice for concrete for civil works structures’,U.S. Army Corps of Engineers, 1994 (available for downloading atwww.usace.army.mil).

‘The use of plain concrete in tunnels’, Document No 149, 1998,Recommendations from AFTES (available for downloading atwww.aftes.asso.fr).



InfoMine, Mining Intelligence andTechnology. (www.infomine.com).Go to ‘Suppliers’ and search for ‘concrete’.




[UE-T9-26]Pre-fabricated concrete blocks. Technological aspects (1)

The photographs above show views of pre-cast concrete blocks used as support intunnels of the Light Rail System at the Minneapolis-St.Paul International airport.The photographs have been reproduced from the article ‘Design and Constructionof Minneapolis-St.Paul International Airport Precast Concrete Tunnel System’, byJohnson R.M. et al., published in Precast-Prestressed Concrete Institute Journal, Vol.48, No 5, September/October 2003.




[UE-T9-27]

Pre-fabricated concrete blocks. Technological aspects (2)


Chapter 5, ‘Construction of Tunnels and Shafts’ in document ‘Tunnelsand shafts in rock’, U.S. Army Corps of Engineers, 1997 (available fordownloading at www.usace.army.mil).

‘The design, sizing and construction of precast concrete segmentsinstalled at the rear of a tunnel boring machine (TBM)’, Document No147, 1998, Recommendations from AFTES (available for downloadingat www.aftes.asso.fr).



American Commercial Inc. (www.americancommercial.com) — seepage ‘Charcon Segment’.




[UE-T9-28]

Types of analyses used in the design of tunnel support (1)

• Analyses that focus on structural behavior —e.g., structural frameswith ‘dead’ load, representing the action of the ground on the structure.

- From the models above, thrust, bending moments and shear forcesare computed, and based on their magnitudes, the structural sectionsdesigned (e.g., given appropriate dimensions).

- Main drawback of the approach: how to quantify realistically the val-ues of qx and qy? —and in the second case, how to quantify realisticallythe stiffness of springs representing the ground?




[UE-T9-29]


• Analyses that focus on rock-support interaction —e.g., pre-stressedelastic or elasto-plastic ground that ‘unloads’ onto the support.

- The main difference between approaches in this category lies on thetype of models considered for the ground and for the interface betweenground and support (e.g., elastic material, elastic-perfectly plastic ma-terial, frictional or frictionless interface between ground and support,etc.).




[UE-T9-30]


• Rock-support interaction analyses (continuation):

- Few (mechanically sound) closed-form solutions are possible in thiscategory. When the geometry of the tunnel and support are circular,and the materials are elastic, Einstein and Schawrtz (1979) present anelegant solution of the rock support interaction problem (see, list ofreferences).

- A semi-rigorous graphical-analytical approach is the Convergence-Confinement Method of support design. The method is based on strongrestrictive assumptions (see next slides), but it provides a basis for reduc-ing a complex 3D problem (increasing support loading with tunnel faceadvance) into simpler 2D (plane-strain) problem —see list of references.

- The most powerful approach in this category is the use of numeri-cal models (e.g., finite elements, finite difference methods). In thesenumerical models, the support can be represented by linear ‘structuralelements’ (a type of element supported by commonly used codes, thatdoes not require discretization of the structure along its thickness) or bynormal material elements (e.g., elastic-isotropic solid elements).




[UE-T9-31]

The Convergence-Confinement Method. Generalities

• The Convergence-Confinement Method is a 2D simplistic approachfor resolving the 3D rock-support interaction problem associated withinstallation of support near a tunnel front.

• The methodology allows estimation of the load that the rock masstransmits to the liner once the ‘supporting’ effect of the tunnel front onthe section analyzed has disappeared (the face has moved away fromthe section).




[UE-T9-32]

Basic assumptions of the Convergence-Confinement Method

Tunnel is circular.

Far-field stresses are uniform (or hydrostatic).

Material is isotropic and homogeneous —e.g., elastic or elasto-plastic.

Support is axi-symmetric —e.g., shotcrete layer forms a closed ring.

Effect of the tunnel front in the vicinity of the tunnel section regardedas a ‘fictitious’ support pressure.




[UE-T9-33]

Basic ‘ingredients’ of the Convergence-Confinement Method

• Ground Reaction Curve (GRC):

The Ground Reaction curve is the graphical representation of the rela-tionship between radial convergence and internal pressure for a circulartunnel excavated in a medium subject to uniform (hydrostatic) far-fieldstresses.

• Support Characteristic Curve (SCC):

The Support Characteristic curve is the graphical representation of therelationship between support radial displacement and uniform pressureapplied to the extrados of a circular (closed) support.

• Longitudinal Deformation Profile (LDP):

The Longitudinal Deformation Profile is the relationship between radialdisplacement and distance to the front for a circular tunnel excavated ina medium subject to uniform (hydrostatic) far-field stresses.




[UE-T9-34]

Ground reaction curve (GRC)

[Note: Positive radial displacement means inward radial displacement in theConvergence-Confinement Method.]




[UE-T9-35]

Construction of Ground reaction curves

- The elasto-plastic solutions described in the notes for Topic 6, ‘Elasto-plastic solution of a circular tunnel’, can be used to construct GroundReaction Curves.

- Construction of GRC requires computing the values of radial displace-ment for various values of internal pressure to outline the curve in theprevious slide.

- For an elasto-plastic material, the radial displacement for the criticalinternal pressure pcr

i (point C in the previous slide), and the radial dis-placement for various values of internal pressure in the interval [pcr

i , 0](between points C and M in the previous slide) must be computed —note that the upper most point of the GRC (point C in the previous slide)has the coordinates pi = σo and uw

r = 0.

- In the case of complex material behavior, numerical models can also beused. To construct the GRC with numerical models, radial convergenceof the tunnel wall is recorded for decreasing values of internal pressure,in the interval [σo, 0].




[UE-T9-36]Example of Ground Reaction Curve

The example above are discussed in Carranza-Torres and Fairhurst (2000).




[UE-T9-37]

Support characteristic curve (SCC)

[Note: Positive radial displacement means inward radial displacement in theConvergence-Confinement Method.]




[UE-T9-38]

Construction of SCC (1)

The elastic solution described in the notes for Topic 8, ‘Elastic solutionof a closed annular support’, for the particular case of uniform loading,can be used to construct a Support Characteristic Curve. From thosenotes we saw that the radial convergence of the closed annular ringexpressed as a function of the pressure applied on the extrados of thering was

usr = 1 − ν2

s

Es

12R ps

12(ts/R) + (ts/R)2(1)

where E is the Young’s modulus and ν is the Poisson’s ratio (for anexplanation of the other variables see previous slide).

Therefore, the stiffness Ks of the support, that represents the slope ofthe elastic part of the Support Characteristic curve (see previous slide)is

Ks = Es

1 − ν2s

12(ts/R) + (ts/R)2

12R(2)




[UE-T9-39]

Construction of SCC (2)

The relationship between the thrust Ts and the pressure ps applied onthe extrados of the support is (see notes for Topic 8, ‘Elastic solution ofa closed annular support’)

Ts = R ps (3)

If the ultimate compressive strength of the material is σ maxs , considering

that the normal stress on a radial section of the support is σs = Ts/t ,then the maximum value of support pressure pmax

s that makes the supportyield is (see figure in previous slide)

pmaxs = ts

Rσ max

s (4)




[UE-T9-40]

Support Characteristic Curves for various support systems (1)

The maximum support pressure is,

pmaxs = σcc

2

[1 − (R − tc)

2

R2

]

The elastic stiffness is,

Ks = Ec

(1 + νc)R

R2 − (R − tc)2

(1 − 2νc)R2 + (R − tc)2

where

σcc is the unconfined compressive strength of the shotcrete or concrete[MPa]

Ec is Young’s Modulus for the shotcrete or concrete [MPa]νc is Poisson’s ratio for the shotcrete or concrete [dimensionless]tc is the thickness of the ring [m]R is the external radius of the support [m] (taken to be the same as the

radius of the tunnel)

Note: The equations above are from Hoek and Brown (1980), ‘Underground Excava-tions in Rock’. The notation has been changed to make it consistent with the notationused in previous slides. For typical ranges of parameters to use in these equationssee the above mentioned reference. These equations and typical parameters are alsosummarized in Carranza-Torres and Fairhurst (2000) —see list of references.




[UE-T9-41]



pmaxs = 3

2

σys

SR θ

AsIs

3Is + DAs [R − (tB + 0.5D)] (1 − cos θ)(5)


1

Ks

= SR2

EsAs

+ SR4

EsIs

[θ(θ + sin θ cos θ)

2 sin2 θ− 1

]+ 2SθtBR

EBB2(6)

where

B is the flange width of the steel set and the side length of the squareblock [m]

D is the depth of the steel section [m]As is the cross-sectional area of the section [m2]Is is the moment of inertia of the section [m4]Es is Young’s modulus for the steel [MPa]




[UE-T9-42]


σys is the yield strength of the steel [MPa]S is the steel set spacing along the tunnel axis [m]θ is half the angle between blocking points [radians]tB is the thickness of the block [m]EB is Young’s modulus for the block material [MPa]R is the tunnel radius [m]





[UE-T9-43]



pmaxs = Tbf

sc sl


1

Ks

= sc sl

[4 l

πd2bEs

+ Q

]




[UE-T9-44]


The parameters in the equations in the previous slide are

db is the bolt or cable diameter [m]l is the free length of the bolt or cable [m]Tbf is the ultimate load obtained from a pull-out test [MN]Q is a deformation-load constant for the anchor and head [m/MN]Es is Young’s Modulus for the bolt or cable [MPa]sc is the circumferential bolt spacing [m]sl is the longitudinal bolt spacing [m]





[UE-T9-45]Example of Support Characteristic Curves





[UE-T9-46]

The advancing front

The objective of the Convergence-Confinement method is to determinefinal load in the support section A-A′, installed at time t0, once the effectof the tunnel face has disappeared, at time tD.

The figure above is from Carranza-Torres and Fairhurst (2000) —see list of references.




[UE-T9-47]

Longitudinal Deformation Profile (LDP)

The figure above is from Carranza-Torres and Fairhurst (2000) —see list of references.




[UE-T9-48]

Equations for the definition of LDP

With reference to the diagram in the previous slide, the equation pro-posed by Dr. M. Panet (see list of references) based on the analysis ofresults from finite element axi-symmetric elastic models is

ur

umaxr

= 0.25 + 0.75

[1 −

(0.75

0.75 + x/R

)2]

(7)

With reference to the diagram in the previous slide, the equation pro-posed by Dr. E. Hoek based on the analysis of actual data and resultsfrom numerical models is

ur

umaxr

=[

1 + exp

(−x/R

1.10

)]−1.7

(8)

The equations above are discussed in Carranza-Torres and Fairhurst (2000) —see listof references.




[UE-T9-49]

Use of numerical models to construct the LDP (1)

Numerical models of a longitudinal section of circular tunnel (includingthe front region) can be used to compute LDPs. The material constitutivemodels used in these numerical models should be the same used toconstruct the GRCs. The most efficient way of setting up and runningthese models is as 2D axi-symmetric numerical models (commercialcodes like Phase2 and FLAC do have an axi-symmetry option).

The figure in the next slide shows: (a) an axi-symmetric mesh in the finitedifference code FLAC (www.itascacg.com); (b) a 3D representation ofthe actual problem that the axi-symmetric mesh represents; (c)the LDPobtained from the model.




[UE-T9-50]

Use of numerical models to construct the LDP (2)




[UE-T9-51]

Ground-support interaction analysis. Final support pressure

The final support pressure pfinali is obtained from the superposition of

the GRC and the SCC (see point P in the diagram below). The LDPdefines the ‘starting point’ of the SCC (point S, of horizontal coordinateuA-A′

r ). This point is the horizontal projection of point A on the GRC.The vertical coordinate of point A is pA-A′

i and represents the fictitioussupport pressure provided by the tunnel front at the time of installationof the support at section A-A′.

A proper support design according to the Convergence-Confinementmethod is one for which the ratio of the maximum support pressurepmax

i and the final support pressure pfinali is larger than a factor of safety,

F.S., chosen for the design (normally F.S.∼ 1.5 ).




[UE-T9-52]Example of Ground-support interaction analysis





[UE-T9-53]

Illustration of Convergence-Confinement analysis (1)

The purpose of this exercise is to verify that the characteristics of the shotcrete liner(thickness, strength, distance to the front) for this tunnel are appropriate.




[UE-T9-54]


The Ground Reaction Curve (GRC) will be computed with Lamé’s solution (see equa-tion 16, in notes on Topic 3, ‘Elastic solution of a circular tunnel’), i.e.,

ur(pi) = 1

2G(σo − pi) R (9)

The Support Characteristic Curve (SCC) will be computed with equations for elasticloading of a closed annular ring (see equations 8 through 10 in notes on Topic 8,‘Elastic solution of a closed annular support’, and equations 1 through 4 in notes onTopic 9, ‘The Convergence Confinement Method’). Thus the relationship betweenradial displacement and support pressure is,

ur(pi) = uIr + 1 − ν2

c

Ec

12R pi

12(tc/R) + (tc/R)2(10)

and the maximum pressure that makes the ring of shotcrete (of compressive strengthσcc) yield plastically is

pmaxs = tc

Rσcc (11)

In equation (2), uIr is the horizontal coordinate of the intersection of the SCC with

the horizontal axis, that will be computed in this example using the expression forLongitudinal Deformation Profile (LDP) for elastic materials proposed by Dr. Hoek—see slides ‘Equations for definition of LDP’ in this note, i.e.,

uIr = umax

r

[1 + exp

(−x/R

1.10

)]−1.7

(12)

In the equation above, umaxr is the coordinate of the intersection of the GRC with the

horizontal axis, that for the case of elastic ground considered here is computed withequation (1) above, considering pi = 0, i.e.,

umaxr = σo

2GR (13)




[UE-T9-55]


The following slides shows the LDP, GRC and SCC for the properties considered inthis example, constructed with the equations described earlier. The following valuesare obtained from application of the mentioned equations and graphical constructionof LDP, GRC and SCC:

umaxr = 3.9 mm (from GRC)

uIr = 0.679 × umax

r = 2.65 mm (from LDP)

uFr = 0.308 × umax

r = 1.2 mm (from LDP)

pFs = 0.32 MPa (from GRC, see Note below the diagram)

pmaxs = 0.583 MPa (from SCC)

pfinals = 0.131 MPa (from intersection of GRC and SCC)

ufinalr = 3.39 mm (from intersection of GRC and SCC)

From the values above, the factor of safety FS for the shotcrete liner is found to be

FS = pmaxs

pfinals

= 0.583 MPa

0.131 MPa= 4.45

Since FS � 1.5, the proposed shotcrete liner is acceptable.

Note: The final thrust in the liner can be computed as T finals = Rpfinal

s and results tobe T final

s = 0.39 MN/m.




[UE-T9-56]





[UE-T9-57]





[UE-T9-58]The program Rocsupport (1)

Rocsupport implements the Convergence-Confinement Method (creation of GRC,SCC and LPD) through a user-friendly graphical interface. The code allows to per-form deterministic and probabilistic analyses of tunnel support design. Rocsupport isdeveloped and commercialized by Rocscience (www.rocscience.com).




[UE-T9-59]

The program Rocsupport (2)

Rocsupport implements the Convergence-Confinement Method (creation of GRC,SCC and LPD) through a user-friendly graphical interface. The code allows to per-form deterministic and probabilistic analyses of tunnel support design. Rocsupport isdeveloped and commercialized by Rocscience (www.rocscience.com).




[UE-T9-60]

Recommended references (1)

For technological aspects of tunnel support systems, see all references(including web sites) mentioned in the slides.

For a rigorous solution of the problem of rock-support intereaction inthe case of a circular tunnel lined by an elastic closed ring in an elasticground subject to non-hydrostatic far-field stresses, see:

• Einstein, H. H. and C. W. Schwartz (1979), ‘Simplified analysis fortunnel supports’. ASCE J. Geotech. Eng. Div., 105(4):449–518.

For tunnel support design and Convergence-Confinement method:

• Hoek, E. & Brown, E. T. (1980), ‘Underground Excavations in Rock’.London: The Institute of Mining and Metallurgy.

• Brady B.H.G. and E.T. Brown, 2004, ‘Rock Mechanics for Under-ground Mining’, 3rd Edition, Kluwer Academic Publishers.

• Hoek E., 2000, ‘Rock Engineering. Course Notes by Evert Hoek’.Available for downloading at ‘Hoek’s Corner’, www.rocscience.com.

• U.S. Army Corps of Engineers, 1997, ‘Tunnels and shafts in rock’.Available for downloading at www.usace.army.mil.




[UE-T9-61]

Recommended references (2)

• ‘The Convergence-Confinement Method’, Document No 170, 2002,Recommendations from AFTES (available for downloading atwww.aftes.asso.fr).

• Panet M. (1995), ‘Calcul des Tunnels par la Méthode de Convergence-Confinement’. Press de l’École Nationale des Ponts et Chaussées.

• Carranza-Torres, C. and C. Fairhurst (2000), ‘Application of the con-vergence confinement method of tunnel design to rock-masses that sat-isfy the Hoek-Brown failure criterion’. Underground Space, 15(2),2000.

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Rock Support Interaction

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