the importance of geology and roof shape on the stability

THE IMPORTANCE OF GEOLOGY AND ROOF SHAPE ON THE
STABILITY OF SHALLOW CAVERNS
1
W.A. Peck1, D.P Sainsbury2 and M.F. Lee1
Principal Geotechnical Engineer, AMC Consultants Pty Ltd,
2
Principal Geotechnical Engineer Mining One Pty Ltd
ABSTRACT
Geology and ground conditions are critical to the design of underground openings, but shape is also a key design
parameter for assessing the long-term stability of shallow caverns and tunnels. The distinct element code UDEC has
been used to assess the performance of both flat and arched-roofed shallow tunnel and cavern designs for a variety of
geological settings. Three-dimensional modelling has shown that instability can develop at the intersection of flatroofed tunnels, with the greatest area of instability being associated with the flattest roof designs.
1
INTRODUCTION
The excavation of large tunnels and caverns is a key component of most underground infrastructure projects. Mined
caverns are used for a variety of purposes that include subway stations, car parks, tunnel intersections, power stations,
liquid and gas storage, crusher chambers, conveyor transfer stations, workshops and hoist rooms.
Urban underground infrastructure, such as road, rail and sewerage projects, often require shallow caverns with a cover
to span ratio as small as 0.25. A typical shallow cavern formed by the off-ramp of a dual lane road tunnel is illustrated
in Figure 1.
Figure 1: Schematic of a typical shallow cavern required for urban underground infrastructure
Rigorous site investigation, design and quality-controlled construction are critical to ensuring the long term (> 100 year)
stability of such shallow caverns. Whilst most underground caverns utilise arched profiles to eliminate large zones of
tensile stresses in the cavern roofs, there is significant precedent for the long-term stability of flat-roofed caverns in subhorizontal, massively bedded rock masses.
Based upon the success of flat-roofed caverns constructed in massive sandstone units around the Sydney region of
Australia, reported by Pells (2002), similar flat-roofed geometrical designs have been proposed for caverns in other
areas and different rock units. However, caution should be exercised when flat-roofed designs are used in other
geological settings without detailed consideration of site-specific ground conditions including geology, rock mass
bedding and joint fabric, intact rock strength and stresses.
As good site investigations can never guarantee full coverage of actual ground conditions, stability risks due to possible
latent geological conditions, must also be considered during design and construction.
There is limited discussion in the literature on the appropriateness of flat-roofed excavations based on idealised
voussoir, or linear arch theory. Diederichs and Kaiser (1999a) warn that flat-roofed, voussoir design methods are only
valid if low to mid-angle jointing is not present. These methods are not suitable for poor quality rock masses with a low
RQD rating and if more than three joint orientation sets are present.
This paper aims to address the major geological and geotechnical features that should be considered during the
geometrical design of shallow caverns. Of the rock mass models investigated by the authors, the greatest extent of roof
loosening was associated with flat-roofed underground openings.
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2
CONVENTIONAL ARCHED CAVERN DESIGN
Conventional arched cavern design is based on achieving uniform compressive tangential stresses around the perimeter
of the excavation. This is best achieved for harmonic holes, where the excavation shape (height : width) equals the farfield stress ratio (σh : σv); so long as the compressive strength of the rock mass is not exceeded, around the perimeter
and locally in the near-field of the excavation.
As discussed by Hoek and Brown (1980), there are significant limitations in applying such harmonic-hole excavations
in practice. However, the basic concept of limiting high compressive stresses (which can promote shear failure) and
zones of tensile stresses (which can significantly influence structure-controlled stability) still applies to the geometrical
design of caverns. The excavation shape that gives the most uniform compressive stress distribution is usually an
ovaloid or ellipse, which has the same axis ratio as the ratio of the far-field in situ principal stresses (Hoek and Brown,
1980).
For practical and geotechnical reasons, Hoek and Moy (1993) suggest that the conventional shape chosen for
underground powerhouse caverns, where rock mass failure is not a concern, is similar to that illustrated in Figure 2a.
The arched-roof provides stability in the rock above the cavern roof. In weaker rock where rock mass failure is a
concern, an alternate elliptical shape such as that illustrated in Figure 2b was proposed by Hoek and Moy. Although this
shape is a little more difficult to construct, the elliptical shape eliminates the potential for tensile failure in the sidewalls,
and the extent of potential shear failure has also been reduced.
Figure 2: a) Conventional arched roof cavern shape; b) Alternative elliptical cavern shape (after Hoek and Moy, 1993)
Hoek (2004) suggests that it is important to use three-dimensional numerical modelling to study complex geometrical
and geological aspects of cavern design. With the advent of multi-threaded computer hardware and software, together
with advancements in automated model generation techniques, three-dimensional numerical models of complex cavern
designs can be analysed with relative ease. But appropriate and representative geotechnical input data is required (ie
idealisation of the rock mass and geologic structures, rock properties, stresses and boundary constraints etc), the
collection of which can be the biggest challenge.
Figure 3: a) 3DEC model of cavern (after Chan et al., 2005); b) Cavern during construction (after Rozek, 2005)
Rozek (2005) and Chan et al. (2005) report on the use of two and three-dimensional numerical models for the design of
multiple large underground railway station caverns for the Epping to Chatswood Railway Project, Sydney; all within
Hawkesbury Sandstone (Figure 3).
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The design methodology for the station caverns included a study of cavern shapes to determine the stability and
feasibility of large span arched caverns, and their relative costs compared to precedent practice of flat-roof or
trapezoidal section caverns. Rozek (2005) reports that despite limited precedence for wide span arched construction in
the Hawkesbury sandstone, the architectural arch shape was technically and economically feasible.
3
FLAT-ROOFED CAVERN DESIGN IN HORIZONTALLY-BEDDED ROCK
MASSES
Due to the economics of mining stratabound coal, limestone and evaporate deposits, flat-roofed mining excavations are
required to maximize resource recovery whilst minimising the amount of waste mined to provide access to the resource.
Within the many underground limestone mines throughout eastern and mid-western USA, large (15 - 30 m spans) flatroofed rooms are routinely designed and implemented using voussoir arch or classic beam theory (Sterling, 1980;
Sofianos and Kapenis, 1998; Iannacchione et al., 1998). These limestone deposits typically comprise intact limestone
with UCS values greater than 150 MPa and horizontal layering that forms roof beams ranging from less than 0.15 to 0.6
m thick. Esterhuizen et al. (2007) report that 89% of these mines experience roof stability issues, while 55% have
experienced large-scale roof failures, some of which have caused fatal injuries and the abandonment of mining areas.
The main factors contributing to stability issues and large roof falls are listed below and illustrated in Figure 4:
•
•
•
•
•
Excessive roof beam deflection, caused by insufficient thickness of the immediate roof beam.
Locally poor quality roof conditions, caused by depositional processes such as cross-bedding or paleochannels
within the limestone (Kendorski, 2002).
Large-scale discontinuities that intersect the roof (see Figure 4b).
The presence of sub-vertical discontinuities, which form wedges within the roof (see Figure 4c).
High horizontal stresses, which initiate shear failure of the roof beams (see Figure 4d).
Figure 4: a) Stable self–supporting 13m roof span (after Esterhuizen et al., 2007); b) Stabilized roof fall caused by large
fault structure (after Esterhuizen et al., 2007); c) Roof fall caused by sub-vertical jointing (after Iannacchione and
Coyle, 2002); d) Failure of roof beams due to high horizontal stresses (after Esterhuizen et al., 2007)
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Flat-roofed cavern designs were successfully applied at the Bondi Pumping Chamber, Sydney Opera House Car Park
and for the Eastern Distributor Tunnel; all within competent massively-bedded Hawkesbury Sandstone of the Sydney
region. Cavern geometries were also in sympathy with the geological structure and the major horizontal principal stress.
The conceptual design and the exposed roof conditions for the flat-roofed Eastern Distributor Tunnel are shown in
Figure 5; within massive sandstone where the spacing between beds was typically 1.0 m to 2.5 m.
Figure 5: a) Eastern Distributor Tunnel design concept (after Pells, 2002); b) 24 m section of Eastern Distributor Tunnel
during construction (after PSM, 2003)
As discussed by Pells (1994), the original concept for a flat-roofed cavern, as opposed to the conventional arch design,
was designed and constructed at the 13.7 m wide Poatina Hydroelectric Cavern, Tasmania, during the 1960’s
(Endersbee and Hofto, 1963). Then in the 1970’s, the 16.5 m wide Drakensberg Pumped Storage Cavern, South Africa,
was also constructed with a flat-roof (see Figure 6). In both cases, the rock mass comprised weak horizontally-bedded
sedimentary rocks, which tended to fail to trapezoid cavity above the opening. Roof profiles were designed to be similar
to the stable configuration of failures. However, Hoek (2004) states that the geometrical design approach applied to
these caverns is not recommended today. The advances in numerical analysis methods since the 1960’s and 70’s
demonstrate that it is entirely feasible to construct a more conventional arched roofed design in weak, bedded rock
masses
.
Figure 6: Drakensberg Pumped Storage Project (Hoek, 2001)
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4
VOUSSOIR BEAM DESIGN METHODOLOGY FOR FLAT-ROOFED CAVERNS
The design concept for flat-roofed excavations (discussed above) are in part based upon linear arch theory (Evans,
1941) and analytical voussoir beam models. Rock bolts are used to provide surface support, and reinforcement of the
rock mass, to form an effective roof beam of sufficient thickness to limit roof deflections (Pells, 2002; Bertuzzi and
Pells, 2002a and Maconochie et al., 2005).
Evans used the term ‘voussoir beam’ to describe a jointed bed that formed the roof of an excavation; an analogy to the
voussoir arch in masonry structures whereby engineered wedge shaped blocks (termed voussoirs) are used to form
arches; as illustrated in Figure 7.
Figure 7: Failure mechanisms considered by Evans (1941); a) A typical voussoir arch with loose cover fill; b) The same
as (a) but with vertical joints; c) The same as (b) but with all equal voussoirs.
Under gravity loading, compressive forces form an arch within and across the beam, while the lateral thrust generated
by deflection of the beam against the abutments defines its stable span; as illustrated in Figure 8.
Figure 8: Voussoir beam problem geometry (Hutchinson and Diederichs, 1996).
Several researchers, notably Sterling (1977), Beer and Meek (1982), Sofianos (1996), Hutchinson and Diederichs
(1996) and Diederichs and Kaiser (1999a), have developed the linear arch theory further to produce simple analytical
solutions to determine the mid-span deflection, buckling potential and the crushing factor of safety; for a given roof
beam geometry and rock mass deformation modulus. The stability of the voussoir beam relies on the retention of the
compression arch within the beam. Stability is also very sensitive to abutment deformations, which can significantly
reduce forces acting within the compressive arch.
Diederichs and Kaiser (1999a) state that the voussoir beam approach to the design for flat-roofed excavations should
not be applied if any of the following conditions are present:
•
•
•
•
•
Poor quality rock masses (RQD < 50).
Rock masses where low to mid-angle jointing is present.
Joints that have low friction infill or coating (sliding along the joints in a voussoir beam is not considered during
design).
Rock masses where the lamination thickness is unknown.
The modulus of deformation in the horizontal plane cannot be reliably estimated.
Furthermore, due to the simplified geometries adopted in voussoir beam models, the effect of abutment relaxation is not
considered. The influence of adjacent excavations or abutment yielding can cause significant relaxation and reductions
in confinement. Diederichs and Kaiser (1999b) indicate that just a few millimetres of abutment relaxation can induce
failure in previously stable spans.
This mechanism was confirmed by Alejano et al. (2008) during the back-analysis of roof bed collapse in parallel roomand-pillar excavations; using both analytical voussoir beam and numerical models. They conclude that the analytical
voussoir beam models are largely reliable. However, from a practical engineering perspective and given the
heterogeneous nature of rock masses, joint roughness, joint strength and joint spacing, it is difficult to predict the
occurrence of instability, as small changes in material properties produce significant variations in stability.
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The two-dimensional distinct-element modelling code UDEC (Itasca, 2011) has previously been used by Sofianos and
Kapenis (1998) and Diederichs and Kaiser (1999a) to validate their respective analytical voussoir beam models. Results
from a series of simple UDEC analyses are illustrated Figure 9.
Figure 9: UDEC analyses of simulated voussoir beams
The analyses in Figure 9 demonstrate the acute sensitivity of the voussoir beam analogue to relatively minor variations
in joint orientation, joint shear strength and intact strength, which are inherent ‘features’ of all jointed rock mass:
•
•
•
•
•
The base-case voussoir beam (Figure 9a) has perfectly vertical joints; consistent with the voussoir model
presented by Diederichs and Kaiser (1999a). For the modelled parameters, the roof beam is predicted to be stable
with a maximum mid-point deflection of 13 mm. The Diederichs and Kaiser voussoir model, for the same beam
configuration, also predicts a stable beam (low buckling potential) with a maximum mid-point deflection of 13.5
mm and a high factor of safety (6.1) against crushing failure.
Figure 9b shows the behaviour of the base-case voussoir beam, when one of the vertical joints is re-oriented to
have a 70° dip. Slip along the sub-vertical joint prevents formation of a compressive arch forces and the roof
beam collapses.
Inclusion of a discontinuous sub-horizontal joint (Figure 9c), in one of the centre blocks, also initiates collapse
of the roof beam. Slip along the sub-horizontal joint allows excessive rotation at the point of maximum
deflection.
As discussed above, sliding failure along joints at the abutments or within the beam is not considered in the
analytical voussoir models. The behaviour of the roof beam that has a weak abutment contact (consistent with
minor joint infill) is illustrated in Figure 9d. Shear failure of the abutment contact initiates rotation of the entire
roof beam, which then collapses.
All analytical voussoir beam models assume uniform strength and modulus throughout the roof beam. The
behaviour of the roof beam, which has a small weak zone within the centre block, is illustrated in Figure 9e.
Crushing failure within the weak zone is predicted, which allows excessive rotation at the point of maximum
deflection, and the roof beam collapses.
5
TWO DIMENSIONAL ANALYSIS OF CAVERN SHAPE IN SHALLOW
HORIZONTALLY-BEDDED ROCK MASSES
Pells (1980, 1994, 2002, 2008a and 2008b) justified the design of flat-roofed caverns in horizontally-bedded sediments
based upon very simple two-dimensional, anisotropic-elastic finite element analyses. His results (see Figure 10) indicate
smaller compressive stress concentrations in horizontally-bedded strata with a (trapezoid) flat-roof shape, compared to
an arched profile.
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Figure 10: Contours of major principal stress as a function of the virgin horizontal stress field (after Pells, 1980, 1994,
2008a and 2008b)
Although the actual material properties used to generate the numerical results were not been reported, Pells (1980)
states that the model is analogous to a stack of playing cards with the cards being held together by extremely thin layers
having very low shear stiffness. This is achieved by arbitrarily setting the shear modulus in the vertical direction to 100
times the Young’s modulus of the material. Pells’ analyses also only considered the effects of horizontal stresses and
ignored the effects of rock density (gravity). They are therefore plane-strain analyses, in a series of horizontal planes,
and do not accurately model ground loosening behaviour, which mostly occurs in the vertical plane.
To provide a more realistic assessment of stress redistribution and displacements around different shallow cavern
shapes in horizontally-bedded strata, the two-dimensional distinct-element code UDEC (Itasca, 2011) has been used to
explicitly simulate the bedding and joint fabric, with representative geomechanical properties, and for four roof shapes
(see Figure 11). The properties used to simulate a typical horizontally-bedded sandstone are presented in Table 1.
Table 1: Rock and Joint mechanical properties
E (GPa)
13.7
Block Properties
c (MPa)
ν
φ (deg.)
0.25
3.2
59
σt (MPa)
1.3
kn / ks (GPa/m)
100
Joint Properties
c (MPa)
φ (deg.)
0.3
38
σt (MPa)
0.0
Figure 11: Schematic UDEC model of bedding and joint fabric, together with the four shallow cavern shapes (model
extents hidden)
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The synthetic sandstone rock mass has a P211 fracture density of 2.60. A horizontal to vertical stress ratio = 2.0 was used
for all of the analyses. Stress redistributions and displacements induced by excavating the various cavern shapes are
presented in Figure 12.
Figure 12: Stress redistributions and displacements induced by a cavern excavation in horizontally-bedded sandstone
with different roof profiles
The major principal stress induced in the cavern roofs, modelled by UDEC, contradict the results presented by Pells
(1980, 1994, 2008a and 2008b), which had suggested that the compressive stress concentrations, in horizontally-bedded
strata, are smaller for a (trapezoid) flat-roof shape, versus the traditional arched profile. The results presented in Figure
12 shows that the opposite is true (for the assumed 2:1 far-field stresses); the traditional arched-roof has lower major
1
8
P21 - Two-dimensional measure of fracture density; total fracture length / area (Dershowitz and Herda, 1992)
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principal stresses and roof displacements, plus more confining (i.e. more stable) minor principal stresses. The trapezoid
(Figure 12c) and the flat roof (Figure 12d) have large tensile zones with significant displacements above their roofs.
Whilst this might not be a problem in a massive, defect-free material, even Sydney’s Hawkesbury Sandstone contains
local defects, such as cross bedding and thin shale beds (in addition to its bedding), capable of creating rock wedges that
could fall from these large tensile zones.
As the maximum major principal stresses predicted, for all of the cavern shapes, are not sufficient to cause yielding of
the sandstone material, additional important parameters that should be used to assess cavern stability include the minor
principal stress, slip along pre-existing discontinuities and induced displacements. Although all of the cavern shapes are
predicted to be stable, significantly different volumes of rock are subjected to tensile stresses above the trapezoidal and
flat-roofed caverns, compared to arched-profile caverns. Greater displacements are also predicted in the immediate roof
of the flat-roofed caverns, and displacements extend through to the ground surface (18 m above for a 15 m span). Large
zones of shearing on bedding are also predicted, possibly resulting in some weakening of the rock mass in those areas.
The Figure 12 results are consistent with recommendations for tunnel shape provided by Martin et al. (1999), who
demonstrated that flat roofs cause a much larger region of unloading (low σ3). In order to minimise the potential for
structurally controlled failures in tunnels up to a depth of 250 m, Martin et al. state that an arched- roof is a better
choice.
6
THE INFLUENCE OF BEDDING AND JOINT FABRIC ON CAVERN STABILITY
The two dimensional UDEC analyses presented in Figure 12 are based on an ideal horizontally-bedded sandstone rock
mass with vertical joints. A series of analyses were also done to investigate the influence of variable bedding and joint
fabric on the stability, in terms of predicted displacement, for variously shaped caverns; Figures 13 through 16.
Figure 13 shows displacements induced around variously shaped caverns in an isotropic rock mass that has three joint
orientation sets. Very minor displacements (<2 mm) are predicted in the small radius of curvature arched design (Figure
13a). Higher displacements and associated rock mass damage are predicted as the cavern roof becomes flatter, leading
to fall-off in the flat roofed design (Figure 13d).
Figure 13: Displacements induced around variously shaped caverns in an isotropic rock mass that has three joint
orientation sets.
For the same cavern shapes, Figure 14 illustrates predicted displacements for a horizontally-bedded sandstone that has
sub-vertical jointing. Again, minor displacement and damage is predicted for the small radius of curvature arch design
(Figure 14a) and increasingly larger displacement and rock mass loosening for the flatter roofed cavern profiles. Failure
through to the surface is predicted for both the trapezoidal and flat-roofed caverns (Figures 14c and d).
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The arched-roofed designs maintain compressive forces around the cavern roof, which restricts loosening and
unravelling of the rock mass. Failure of the voussoir arch, in the immediate roof beams of the trapezoid and flat designs,
is caused by the presence of sub-vertical joints, which encourages fall-off and loosening.
Figure 14: Displacements induced around excavations in horizontally-bedded sandstone that has sub-vertical joints.
Predicted displacements, around variously shaped caverns mined within a shallow dipping bedded rock mass, are
illustrated in Figure 15. The results are very similar to the horizontally bedded case (Figure 14), excepting that failure
above the flat roofed caverns, is now skewed so as to be normal to bedding.
Figure 15: Displacements induced around excavations in a bedded shallow-dipping rock mass.
The destabilising influence of a thick steeply dipping fault is shown in Figure 16. Given the specific dip of the fault and
its intersection with the small radius of curvature arched design, the influence of the fault is limited to a small area of
fall-off in the haunch, plus more loosening above the roof (Figure 16a). Roof collapse is predicted for the all of the
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other flatter cavern roofs, the worst being the flat-roofed cavern. In general, the influence and significance of a fault will
depend on exactly where it intersects the cavern, its thickness and geomechanical properties.
Figure 16: Displacements induced around excavations intersected by a fault in horizontally bedded sandstone
For all of the models, an arched roof profile provides an inherently more stable design. The arched profile significantly
reduces the effect of natural rock mass variations and discontinuities on cavern stability.
7
THREE-DIMENSIONAL ANALYSIS OF SHALLOW CAVERN ROOF PROFILES
The two dimensional modeling results presented above, for of variously shaped caverns, give an initial understanding of
ground behaviour associated with shallow caverns in ideally bedded, jointed and faulted rock masses. Practical cavern
design, however, must account for the three-dimensional nature of the local rock mass conditions, complex cavern
geometries and the construction sequences.
Diederichs and Kaiser (1999b) state that the creation of intersections reduces the ability of jointed or fractured rock
masses to form a stable arch; by extending the zone of deformation, which is equivalent to relaxing the abutments of a
tunnel span. Barton et al, (1974) implies that the impact, on the effective rock mass quality, of creating an intersection is
equivalent to a minimum 50% reduction, a factor also confirmed by Hutchinson and Diederichs (1996).
Figure 17: Idealised geometry and geometry of a three-dimensional tunnel intersection
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The three-dimensional distinct-element code 3DEC (Itasca, 2007) was used to model a near-surface tunnel intersection
in a weak, horizontally-bedded and jointed shale, see Figure 17. While the gross plan geometry of the modelled
intersection is similar to the Lane Cove intersection, which collapsed in November 2005 (Brown, 2005; WorkCover
Authority of NSW, 2006), site-specific and potentially important discontinuities have not been included in the model.
The results should therefore not be considered as a definitive back-analysis of the collapse. For the purposes of this
paper, only the influence of roof shape is of interest.
Two roof profiles were modelled, arched and flat-roofed, with a mining sequence of blue, purple, green. The explicit
bedding and joint network presented in Figure 17a is consistent with a weak (Class III) Sydney shale material using the
classification system reported by Bertuzzi and Pells (2002b). The effect of ground support was included in these
analyses.
The analysis results further highlight the extra risks associated with flat-roofed cavern designs, compared to arched
caverns. Total displacements, after excavation, are shown in Figure 18.
Figure 18: Total displacements for arched and flat-roofed, near-surface, tunnel intersection.
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The arched-roof design for the intersection is predicted to be stable with a maximum displacement of 33 mm in the
centre of the intersection, and 12 mm on the ground surface. Some unstable blocks are predicted around the perimeter
of the tunnels away from the intersection, which would normally be retained by in-cycle fibrecrete and bolting.
In contrast, collapse of the flat-roofed intersection is predicted, with rapid propagation to the surface between subvertical sides, largely defined by the intersection walls.
The results highlight a dramatic change in ground behaviour based upon the roof profile of the intersection. Due to the
loss of lateral confinement, which can occur at intersections or around large caverns, geometrical design plays a much
greater role in the behaviour of three dimensional excavations, compared to tunnels, which are generally confined along
their long-axis.
8
CONCLUSIONS
Based on the success of flat-roofed caverns constructed within massive, horizontally-bedded sedimentary units, flatroofed geometrical designs are regularly proposed for caverns in poorer quality rock masses. Caution must, however, be
exercised for these designs. Very good and confident information is required regarding ground conditions, plus careful
consideration of roof span and shape and construction sequence.
Design concepts, for flat-roofed excavations, are often based on linear arch theory and analytical voussoir beam models.
However, from a practical engineering perspective and given the heterogeneous nature of rock masses, it is often
difficult to confidently predict the occurrence of instability using these models. Latent conditions and even small
variations in site geology can produce significant variations in the stability of flat-roofed openings.
A series of two-dimensional UDEC analyses demonstrate that an arched-roofed profile provides an inherently more
stable design than a flat roof for near-surface underground openings. Arched-roof profiles significantly reduce the
adverse effect of natural rock mass variations and discontinuities, on roof stability.
An example three-dimensional 3DEC analysis, of a shallow tunnel intersection in weak, horizontally-bedded and
jointed shale (Figure 18) further highlights the extra risks associated with flat-roofed cavern designs.
9
ACKNOWLEDGEMENTS
The authors would like to acknowledge the patience, understanding and support of their respective partners and
employees while this work was compiled. Special mention is required of AMC’s internal peer reviewers and valuable
comments and support by Charles Fairhurst.
10
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Beer G and Meek J L (1982) Design Curves for Roofs and Hangingwalls in Bedded Rock based on Voussoir Beam and
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Australian Geomechanics Vol 48 No 3 September 2013