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Technical Manual for Design and Construction of Road Tunnels - Civil Elements
Chapter 6 - Rock Tunneling
Typical TBM's cut circular tunnels which are the most practical cross section but not always the cross section that provides the most useable volume as a proportion of the total volume excavated. The Japanese and others have developed specialized machines with multiple heads that cut "slots" or other shapes that can be more efficient in providing useable volume.
Another approach to cutting an opening closer to some actual required section is the roadheader. The basic cutting tool for a roadheader is a very large milling head mounted on a boom, which boom, in turn, is mounted on tracks or within a shield. Figure 6-16 shows a large size roadheader. Corners must be cut to the curvature of the milling head, but the rest of the walls, crown and invert can be cut to almost any desired shape. In addition and in contrast to a TBM, a single roadheader can cut variable or odd shapes that otherwise would require TBM excavation in combination with drill and blast or drill and blast itself. Because of their adaptability, availability (a few months rather than a year or longer), and lower cost, roadheaders also are the method of choice for relatively short tunnels, say less than one mile in length.
Figure 6-16 AM 105 Roadheader, Australia
On the negative side, roadheaders are far less efficient on longer drives and in hard rock. The picks on the roadheader are something like 10% as efficient as TBM disks at removing rock, must be replaced very frequently and simply may not be effective in rock with an unconfined compressive strength greater than 20,000 psi (140MPa). Changes and improvements in roadheader design are on-going, however, and it is expected that this will result in constant improvements in these limitations.
The following is a general list when roadheaders may be considered:
- Rock strength below about 20000 - preferably below 15000.
- Short runs, one of a kind openings
- Odd, non-circular shapes
- Connections, cross passages, etc
- Low to moderate abrasivity
- Preferably self supporting rock
- No or small inclusions - chert etc
- Nominal water pressure
6.4.4 Other Mechanized Excavation Methods
Other mechanized excavation methods are being developed by specialized equipment manufacturers to address specific issues in mining and civil applications. A good example of such developments is the "Mobile Miner" developed by Robbins as a "non-circular hard rock cutting system to be applied to underground mine development" (Robbins, 1990). The mobile miner is described as follows:
"A boom mounts a large cutter wheel with a transverse axis having rows of cutters arranged only on the periphery of the wheel. As the boom is swung from side to side an excavated shape is generated with a flat roof and floor and curved walls. Although the prototype machines have operated only with this side-swinging action, in order to cut openings which are better suited to vehicular tunnels the cutterhead boom must be elevated up and down and at the same time swung from side to side. In this way a horseshoe-shaped excavation can be generated.
To date such machines have had some success in excavating openings approaching a horseshoe or slot configuration, but they are not commonly used. However, they do illustrate the points that shapes other than circular can be cut and that inventive and special-purpose machines are constantly being developed.
6.4.5 Sequential Excavation Method (SEM)/ New Austrian Tunneling Method (NATM)
In actual practice, the Sequential Excavation Method (SEM)/New Austrian Tunneling Method (NATM) has been adapted from its original concept, which applied to rock tunnels only, to a more general concept that applies to tunnels in either soil or rock. Readers are referred to Chapter 9 "SEM Tunneling" for more detailed discussion.
Types of Rock Reinforcement and Excavation Support
6.5.1 Excavation Support Options
The purpose of an initial support (sometimes called temporary lining, or temporary support of excavation) in rock tunneling is to keep the opening open, stable and safe until the final lining is installed and construction is complete. As a consequence the initial support system in a rock tunnel can be one or a combination of a number of options:
- Rock reinforcement (i.e., rock dowels, rock bolts, rock anchors, etc.)
- Steel ribs
- Wood or other lagging
- Lattice girders
- Spiles or forepoling
- Re-steel mats
- Steel mats
- Precast concrete segments
The first five above are the most common on US projects, and of those, a combination of rock bolts or dowels and shotcrete is the single most common. Especially in good (or better) rock tunnels, modern rock bolting machines provide rapid and adjustable "support" close to the heading by knitting and holding the rock (ground) arch in place, thus taking maximum advantage of the rock's ability to support itself. Preferably, shotcrete is added (if needed) a diameter or so behind the face where its dust and grit and flying aggregate is not the problem for both workers and equipment that it is at the heading. Where there is a concern with smaller pieces of rock falling, the system can be easily modified by adding shotcrete closer to the face or more usually, by embedding any of a number of types of steel mats in the shotcrete.
Where the rock quality is lower there is currently a movement toward replacing steel ribs by lattice girders – perhaps somewhat more so in Europe than in the US. Like steel ribs, the lattice girders form a template of sorts for the shotcrete and for spiling. However, the lattice girders are lighter and can be erected faster. To provide the same support capacity, the lattice girder system may require nominally more shotcrete (e.g., an additional ½ to 1 inch) but that is more than compensated for by the easier and faster erection. A second new trend is the use of steel fiber reinforced shotcrete. The fiber doesn't change the compressive strength significantly but does produce a significant increase in the toughness or ductility of the shotcrete. Chapter 9 provides more detailed discussion about shotcrete and lattice girder.
6.5.2 Rock Reinforcement
Rock reinforcement including rock dowels and bolts are used to hold loose (key) blocks in place and/or to knit together the rock (ground) arch that actually provides the support for an opening in rock. Dowels and bolts are very similar but the differences in their behavior can be quite significant.
188.8.131.52 Rock Dowel
Rock dowels as shown in Figure 6-17a, are passive reinforcement elements that require some ground displacement to be activated. Similar to passive concrete reinforcement, the reinforcement effect of dowels is activated by the movement of the surrounding material. In particular, when displacements along discontinuities occur, dowels are subject to both shear and tensile stresses (Figure 6-17b). The level of shear and tensile stress and the ratio between them occurring during a displacement is dependent on the properties of the surrounding ground, the properties of the grout material filling the annular gap between the dowel and the ground and the strength and ductility parameters of the dowel itself. Also, the degree of dilation during shear displacement influences the level of stress acting within the dowel. Table 6-6 describes various types of rock dowels. In addition, Table 9-5 summarizes commonly used rock dowels and application considerations for the installation as part of initial support in SEM tunneling in rock.
For example a #9 dowel 10 ft. long will have to elongate almost 0.2 inch before it develops its full design capacity of 40,000 lb. This may not be a concern in most applications where there is some interlocking between rock blocks due to the natural asperities on discontinuity surface.
Figure 6-17 (a) Temporary Rock Dowel; (b) Schematic Function of a Rock Dowel under Shear
184.108.40.206 Rock Bolts
Rock bolts (Figure 6-18) have a friction or grout anchor in the rock and are tensioned as soon as that anchorage is attained to actively introduce a compressive force into the surrounding ground. This axial force acts upon the rock mass discontinuities thus increasing their shear capacity and is generated by pre-tensioning of the bolt. The system requires a "bond length" to enable the bolt to be tensioned. Rock bolts frequently are fully bonded to the surrounding ground after tensioning, for long-term load transfer considerations. They may or may not be grouted full length. In any case, bolts begin to support or knit the rock as soon as they are tensioned, that is, the rock does not have time to begin to move before the bolt becomes effective. Table 6-6 describes various types of rock bolts. In addition, Table 9-5 summarizes commonly used rock bolts and application considerations for the installation as part of initial support in SEM tunneling in rock.
Figure 6-18 Typical Section of Permanent Rock Bolt
|Resin Grouted Rock Bolt||
|Expansion shell rock bolt||
|Split set stabilizers||
|Self Drilling Anchor|
6.5.3 Ribs and Lagging
Ribs and lagging (Figure 6-19) are not used as much now as they were even a couple of decades ago. However, there are still applications where their use is appropriate, such as unusual shapes, intersections, short starter tunnels for TBM, and reaches of tunnel where squeezing or swelling ground may occur.
In 1946, Proctor and White (with major input from Dr. Karl Terzaghi) wrote the definitive volume "Rock Tunneling with Steel Supports". Their design approach assumes the ribs are acted upon by axial thrust and by bending moments, the latter a function of the spacing of the lagging or blocking behind the ribs. This approach is still valid when wood or other blocking is used with steel ribs and hence will not be repeated here. In today's applications, steel ribs are often installed with shotcrete being used instead of wood for the blocking (lagging) material. When shotcete is used, it often does not fill absolutely the entire void between steel and rock. Hence, with properly applied shotcrete it is recommended that the maximum blocking point spacing be taken as 20 in. and the design proceed according to the Proctor and White procedure.
Figure 6-19 Steel Rib Support
Shotcrete is simply concrete sprayed into place through a nozzle. It contains additives to gain strength quicker and to keep it workable until it is sprayed. Shotcrete can be made with or without the addition of reinforcing fibers and can be sprayed around and through reinforcing bars or lattice girders. Both the quality and properties of shotcrete can be equal to those of cast in place concrete but only if proper care and control of the total placement procedure is maintained throughout. The reader is referred to Section 9.5.1 for more details related to the design and use of shotcrete as a support and lining material.
6.5.5 Lattice Girder
Lattice girders are support members made up of steel reinforcement bars laced together (usually) in a triangular pattern (see Figure 6-20 ) and rolled to match the shape of the opening. Because their area is typically very small compared to the surrounding shotcrete, lattice girders do not, by themselves, add greatly to the total support of an opening. However, they do provide two significant benefits:
- They are typically spaced similarly to rock bolts, thus they quickly provide temporary support to blocks having an immediate tendency to loosen and fall
- They provide a ready template for assuring that a sufficient thickness of shotcrete is being applied
Figure 6-20 (a) Lattice Girder Configuration (Emilio-2-2901-1997); (b) Estimation of Cross Section for Shotcrete-encased Lattice Girders (Emilio-2-2901-1997)
Generally, lattice girders are used much more frequently in tunnels driven by the sequential excavation method. Therefore, the reader is directed to Chapters 9 for further discussion of these supports.
6.5.6 Spiles and Forepoles
Spiles and forepoles (Figure 6-21) are used interchangeably to describe support elements consisting of pipes or pointed boards or rods driven ahead of the steel sets or lattice girders. These elements (herein called spiles) provide temporary overhead protection while excavation for and installation of the next set or girder is accomplished. Typically, spiles are driven in an overlapping arrangement as shown in Figure 6-21 so that there is never a gap in coverage. Design of spiles is best described as "intuitive" as it must be kept flexible and constantly adjusted in the field as the ground behavior is observed during the construction. A working first approximation of design load might be a height of rock equal to 0.1B to 0.25B, where B is the width of the opening. Section 220.127.116.11 provides discussions for pre-support measures involving spiling or grouted pipe arch canopies that bridge over the unsupported excavation round.
Figure 6-21 Spiling (Forepoling) Method of Supporting Running Ground
6.5.7 Precast Segment Lining
Tunnel lining consisting of precast segments may be used in single-pass or double pass lining systems to support rock loadings and water pressures. Generally the concrete segments are reinforced either with reinforcement bar or fiber. The segment ring usually consists of five to seven segments with a key segment. The ring division and the segment dimension have to be optimized according to project specific requirements such as tunnel diameter, maximum size for transport and installation (erector), and number of thrust jacks and their distribution over the range of the ring. Figure 6-22 illustrates a typical seven ring plus one key segment concrete lining. A typical circumferential dowel (Figure 6-22a) and radial bolt (Figure 6-22b) are also presented.
The precast segment concrete lining is mostly used in TBM tunnel construction projects and, at this time, more frequently in soft ground tunnels. The segmental ring is erected in the TBM tail shield and during the advance, the rams act on the ring. The ring never can be independent from the TBM, hence the design of the TBM and the segmental ring must be harmonized. Rams must act on prepared sections of the ring, rolling of the tunnel shield and the ring must be taken into account. The ram axis should be identical with the ring axis. The ring taper should be designed according to the TBM curve drive capabilities and not only according to the designed tunnel axis. Details of design considerations for precast segment lining will be discussed in Chapter 10.
6.6 Design and Evaluation of Tunnel Supports
There exists a wide range of tunnel support systems as shown in previous sections. In recent years the tunneling community has moved away from support to reinforcement as the basic approach. That is, from providing heavy structures, primarily ribs and lagging, to using rock bolts and dowels, spiling, lattice girders and shotcrete. In all of these latter systems the goal is to keep the rock from moving and blocks from loosening thereby keeping a large dead load of rock from coming onto the support system; that is holding the rock together and causing the ground around the opening to form a natural and self supporting ground arch around the opening.
Figure 6-22 A Typical Seven Segment and a Key Segment Precast Segment Lining: (a) Circumferential Dowel; (b) Radial Bolt
This trend was started in the U.S. on the Washington D.C. subway system where on two successive sections the amount of structural steel support was reduced by three quarters. This was accomplished by holding the rock in place with rock bolts until the final lining of shotcrete with light ribs at four foot centers could be installed and become effective in causing the rock to help support itself. In contrast, the previous section relied upon steel ribs to carry the dead (rock) loads and thus required twice the weight of steel members at one-half the spacing.
Tunnel support design is an iterative process including assumptions on support type installed and evaluating the support pressure it provides. Table 6-7 lists typical tunnel support systems used in the current practice for various ground conditions. This table can be used for the initial selection of the support system to initiate the interaction and iteration.
|Ground||Rock bolts||Rock bolts with wire mesh||Rock bolts with shotcrete||Steel ribs and lattice girder with shotcrete||Cast-in-place concrete||Concrete segments|
In making the selection of support measures for a given project, however, the full range of possible support system should be considered simply because each project is unique. Factors to be considered include the following:
- Local custom: contractors like to use systems with which they are familiar.
- Relative costs: for example, is it cost effective to design bolts with suitable corrosion resistance to assure their permanence.
- Availability of materials
This Section introduces design practice and evaluation of initial tunnel supports, including empirical, analytical and numerical methods. Design of underground structures can be based largely on previous experience and construction observations to assess expected performances of specified ground support systems.
6.6.1 Empirical Method
Terzaghis's tunnelman's classification (Table 6-1) of rock condition and recommended rock loadings, expressed as a function of tunnel size are presented in Table 6-8. These recommendations sprang from Terzaghi's observations in the field and his trap door experiments in the laboratory.
|Rock condition||Rock Load, Hp (ft)||Remarks|
|Hard and intact||Zero||Light lining, required only if spalling or popping occurs|
|Hard stratified or schistose||0 to 0.5 B||Light support. Load may change erratically from point to point|
|Massive, moderately jointed||0 to 0.25 B|
|Moderately blocky and seamy||0.25B to 0.35|
(B + Ht)
|No side pressure|
|Very blocky and seamy||(0.35 to 1.10)|
(B + Ht)
|Little or no side pressure|
|Completely crushed but chemically intact||1.10 (B + Ht)||Considerable side pressure. Softening effect of seepage towards bottom of tunnel requires either continuous support for lower ends of ribs or circular ribs|
|Squeezing rock, moderate depth||(1.10 to 2.10)|
(B + Ht)
|Heavy side pressure, invert struts required. Circular ribs are recommended|
|Squeezing rock, great depth||(2.10 to 4.50)|
(B + Ht)
|Swelling rock||Up to 250ft. irrespective of value of (B + Ht)||Circular ribs required. In extreme cases use yielding support|
As a first approximation to rock bolt or dowel selection, Cording et al. (1971) provides a compilation of case histories for underground rock excavations based on excavation sizes (span width and height), as shown in Figure 6-23 and Figure 6-24, the following are recommended by Cording et al. (1971):
- A crown support pressure equal to a rock load having a height of 0.3B.
- A sidewall support pressure of 0.15H.
- A crown bolt length of 0.33B.
- A sidewall bolt length of 0.33H.
where B is the opening width. In rock with an RQD greater than 75%, it is expected that the sidewall pressure typically will be smaller (often zero) than estimated above and only spot bolts to hold obvious wedges will be required.
Two most widely used rock mass classifications, RMR and Q, incorporate geotechnical, geometrical, and engineering parameters. Using rock mass classifications and equivalent dimension of the tunnel, which is defined as ratio of dimension of tunnel and ESR (Excavation Support Ratio), Barton et al. (1974) proposed a number of support categories and the chart was updated by Grimstad and Barton (1993). The updated chart using the Q system is presented in Figure 6-25. Table 6-9 presents how the RMR is applied to support design of a tunnel with 10 m span.
Figure 6-23 Support Pressures (a) and Bolt Lengths (b) Used in Crown of Caverns (Cording, 1971)
Figure 6-24 Support Pressures (a) and Bolt Lengths (b) Used on Cavern Walls (Cording, 1971)
- Spot Bolting
- Systematic Bolting
- Systematic bolting with 40-100 mm unreinforced shotcrete
- Fiber reinforced shotcrete, 50 - 90 mm, and bolting
- Fiber reinforced shotcrete, 90 - 120 mm, and bolting
- Fiber reinforced shotcrete, 120 - 150 mm, and bolting
- Fiber reinforced shotcrete, > 150 mm with reinforced ribs of shotcrete and bolting
- Cast concrete lining
Figure 6-25 Rock Support Requirement using Rock Mass Quality Q System
It should be noted that "the Q-system has its best applications in jointed rock mass where instability is caused by rock falls. For most other types of ground behavior in tunnels the Q-system, like most other empirical (classification) methods has limitations. The Q support chart gives an indication of the support to be applied, and it should be tempered by sound and practical engineering judgment" (Palmstream and Broch, 2006).
Also note that the Q-system was developed from over 1000 tunnel projects, most of which are in Scandinavia and all of which were excavated by drill and blast methods. When excavation is by TBM there is considerably less disturbance to the rock than there is with drill and blast. Based upon study of a much smaller data base, Barton (1991) recommended that the Q for TBM excavation be increased by a factor of 2 for Qs between 4 and 30.
|Rock mass class||Excavation||Rock bolts (20 mm diameter, fully grouted)||Shotcrete||Steel sets|
|I - very good rock|
3 m advance
|Generally no support required except spot bolting|
|II - Good rock|
|Full face, 1-1.5 m advance. Complete support 20 m from face||Locally, bolts in crown 3 m long, spaced 2.5 m with occasional wire mesh||50 mm in crown where required||None|
|III - Fair rock|
|Top heading and bench 1.5-3 m advance in top heading. Commence support after each blast. Complete support 10 m from face||Systematic bolts 4 m long spaced 1.5-2 m in crown and walls with wire mesh in crown||50-100 mm in crown and 30 mm in sides||None|
|IV - Poor rock|
|Top heading and bench 1.0-1.5 m advance in top heading. Install support concurrently with excavation, 10 m from face||Systematic bolts 4-5 m long, spaced 1-1.5 m in crown and walls with wire mesh||100-150 mm in crown and 100 mm in sides||Light to medium ribs spaced 1.5 m where required|
|V - Very poor rock|
RMR: < 20
0.5-1.5 m advance in top heading. Install support concurrently with excavation. Shotcrete as soon as possible after blasting.
|Systematic bolts 5.6 m long, spaced 1-1.5 m in crown and walls with wire mesh. Bolt invert.||150-200 mm in crown, 150 mm in sides, and 50 mm on face||Medium to heavy ribs spaced steel lagging and forepoling if required. Close invert.|
Note: Table 6-9 above assumes excavation by drill and blast.
Barton et al. (1980) proposed rock bolt length, maximum unsupported spans and roof support pressures to supplement the support recommendations. The length of rock bolts, L can be estimated from the excavation width, B and the Excavation Support Ratio (ESR) as follow:
The maximum unsupported span can be estimated from:
|Maximum Unsupported Span = 2 ESR Q0.4, in meters||6-4|
Grimstad and Barton (1993) proposed a relationship between Q value and the permanent roof support pressure, Proof as follow:
The value of Excavation Support Ratio (ESR) is related to the degree of security which is demanded of the support system installed to maintain stability of the excavation. Barton et al. (1974) suggested ESR values for various types of underground structures as presented in Table 6-10. An ESR value of 1.0 is recommended for civil tunnel projects.
|Excavation Category||Suggested ESR Value|
|A||Temporary mine openings||3 - 5|
|B||Permanent mine openings, water tunnels for hydro power (excluding high pressure penstocks), pilot tunnels, drifts and headings for large excavations.||1.6|
|C||Storage rooms, water treatment plants, minor road and railway tunnels, surge chambers, access tunnels||1.3|
|D||Power stations, major road and railway tunnels, civil defense chambers, portal intersections||1.0|
|E||Underground nuclear power stations, railway stations, sports and public facilities, factories||0.8|
6.6.2 Analytical Methods
The state of stress due to tunnel excavation can be calculated from analytical elastic closed form solutions. Kirsch's elastic closed form solution is one of the commonly used analytical solutions and is presented in Appendix E. The closed form solution is restricted to simple geometries and material models, and therefore often of limited practical value. However, the solution is considered to be a good tool for a "sanity check" of the results obtained from numerical analyses.
The interaction between rock support and surrounding ground is well described by the ground reaction curve (Figure 6-26), which relates internal support pressure to tunnel wall convergence. General description of ground reaction curve is well described Hoek (1999).
Figure 6-26 Ground Reaction Curves between Support Pressure and Displacement (Hoek et al., 1995)
As shown in Figure 6-26a, zero displacement occurs when the support pressure equals in-situ stress, i.e., Pi = Po. When the support pressure is greater than critical support pressure and less than in-situ stress, i.e., Po >Pi >Pcr, elastic displacement occurs. When the support pressure is less than the critical support pressure, i.e., Pi < Pcr, plastic displacement occurs. Once the support has been installed and is in full and effective contact with the surrounding rock mass, the support starts to deform elastically. Maximum elastic displacement which can be accommodated by the support system is usm and the maximum support pressure, Psm is defined by the yield strength of the support system. As shown in Figure 6-26b, the tunnel wall displacement has occurred before the support is installed and stiffness and capacity of support system controls the wall displacement.
Hoek (1999) proposed a critical support pressure required to prevent failure of rock mass surrounding the tunnel as follow:
|Pcr||= Critical support pressure|
|Po||= Hydrostatic stresses|
|σcm||= Uniaxial compressive strength of rock mass|
|φ||= Aangle of friction of the rock mass|
If the internal support pressure, Pi is greater than the critical support pressure Pcr, no failure occurs and the rock mass surrounding the tunnel is elastic and the inward displacement of tunnel is controlled.
A more realistic design, especially for large tunnels and large underground excavations, is based on the true behavior of rock bolts: to act as reinforcement of the rock arch around the opening. This rock reinforcement increases the thrust capacity of the rock arch. The design objective is to make that increase in thrust capacity equivalent to the internal support that would be calculated to be necessary to stabilize the opening.
The increase in unit thrust capacity (ΔTA) of the reinforced zone (rock arch) shown in Figure 6-27 is given by the equation (see Figure 6-27) developed by Bischoff and Smart (1977):
Figure 6-27 A Reinforced Rock Arch (After Bischoff and Smart, 1977)
where ΔTA is increase in unit thrust capacity of the rock arch, φ is effective friction angle of the rock mass, Tb is stress at yield of the rock reinforcement steel (fully grouted rock bolts), Ab is cross-sectional area of the reinforcement steel, S is spacing of the reinforcement steel, in both directions, t is effective thickness of the rock arch (= L - S), and L is length of the reinforcement steel.
Analytical solutions to calculate support stiffness and maximum support pressure for concrete/shotcrete, steel sets, and ungrouted mechanically or chemically anchored rock bolts/cables are summarized in Table 6-11.
|Support System||Support stiffness (K) and maximum support pressure (Pmax)|
|Blocked steel sets|
|Ungrouted mechanically or chemically anchored rock bolts or cables|
NOTATION: K = support stiffness; Pmax = maximum support pressure; Ec = Young's modulus of concrete; tc = lining thickness (Figure 6-28a); ri = internal tunnel radius (Figure 6-28a); σcc = uniaxial compressive strength of concrete or shotcrete; W = flange width of steel set and side length of square block; X = depth of section of steel set; As = cross section area of steel set; Is = second moment of area of steel set; Es = Young's modulus of steel; σys = yield strength of steel; S = steel set spacing along the tunnel axis; θ= half angle between blocking points in radians (Figure 6-28b); tB = thickness of block; EB = Young's modulus of block material; l = free bolt or cable length; db = bolt diameter or equivalent cable diameter; Eb = Young's modulus of bolt or cable; Tbf = ultimate failure load in pull-out test; sc = circumferential bolt spacing; sl = longitudinal bolt spacing; Q = load-deformation constant for anchor and head.
Figure 6-28 Support Systems: (a) Concrete / Shotcrete Lining, (b) Blocked Steel Set
The size and shape of wedges formed in the rock mass surrounding a tunnel excavation depend upon geometry and orientation of the tunnel and also upon the orientation of the joint sets. The three dimensional geometry problems can be solved by computer programs such as UNWEDGE (Rocscience Inc.). UNWEDGE is a three dimensional stability analysis and visualization program for underground excavations in rock containing intersecting structural discontinuities. UNWEDGE provides enhanced support models for bolts, shotcrete and support pressures, the ability to optimize tunnel orientation and an option to look at different combinations of three joint sets based on a list of more than three joint sets. In UNWEDGE, safety factors are calculated for potentially unstable wedges and support requirements can be modeled using various types of pattern and spot bolting and shotcrete. Figure 6-28 presents a wedge formed by UNWEDGE on a horse-shoe shape tunnel
Figure 6-29 UNWEDGE Analysis: (a) Wedges Formed Surrounding a Tunnel; (b) Support Installation
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